mri of mass transport in porous media: drying and sorption processes

Progress in Nuclear Magnetic Resonance Spectroscopy 65 (2012) 1–65

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Progress in Nuclear Magnetic Resonance Spectroscopy

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MRI of mass transport in porous media: Drying and sorption processes

Igor V. Koptyug ⇑International Tomography Center, SB RAS, 3A Institutskaya Str., Novosibirsk 630090, Russian Federation

a r t i c l e i n f o

Article history:Received 21 September 2011Accepted 5 December 2011Available online 14 December 2011

Keywords:Magnetic resonance imagingPorous materialsDryingSorptionPolymer swelling

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Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1. The scope of this review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2. General considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3. MRI and porous media: problems and remedies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4. The MRI toolkit: what is measured, and how . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.5. Quantification of mass transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2. MRI techniques and instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1. Techniques used for porous media MRI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2. Specialized MRI equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.3. Toward an improved field homogeneity for single-sided and mobile instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.4. NMR spectroscopy in inhomogeneous fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3. MRI of sorption processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.1. General considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.2. Building materials and stones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.3. Building materials and stones with protective treatments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.4. Transport of solutes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.5. Sorption of gases and vapors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.6. Other studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4. MRI of polymer swelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.1. General considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.2. Polymer swelling in liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.3. Variation of temperature and pH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.4. Swelling in liquid mixtures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.5. Imaging of a swelling polymer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.6. Polymer swelling upon vapor uptake. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.7. Swelling and deswelling of coal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.8. Other studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
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5. MRI of model and commercial drug delivery systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
5.1. General considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315.2. Immediate release systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325.3. Cellulose and its derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335.4. Cellulose derivatives with model drugs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345.5. Other polysaccharides (starch, xanthan, alginate, chitosan) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365.6. Poly(vinyl alcohol) (PVA) and poly(vinyl pyrrolidone) (PVP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375.7. Acrylates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375.8. Poly(ethylene glycol) (PEG) and poly(ethylene oxide) (PEO) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375.9. Glycolide, lactide, poly(lactic-co-glycolic acid) (PLGA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385.10. Coated formulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385.11. Hydrodynamically balanced systems (HBS). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385.12. Osmotic systems and push–pull gastrointestinal therapeutic systems (GITS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395.13. Poly(N-isopropylacrylamide) (PNIPAM), stimulus response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.14. Other studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
6. MRI of drying processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
6.1. General considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436.2. Drying of rigid matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436.3. Drying-induced transport of salts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476.4. Drying accompanied by an extensive matrix change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506.5. Drying of thin films and coatings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536.6. Other materials and processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
7. Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

1. Introduction

1.1. The scope of this review

A title seldom gives exhaustive information about the content itprecedes. Consequently, we sometimes find ourselves disap-pointed when we realize that a paper is not about what we ex-pected it to be. Therefore, first of all, the scope of this review isoutlined. This is done through the introduction of the working def-initions of the terms used in the title. They are not intended to berigorous, but rather define the meaning of these terms within thecontext of this review, with the main goal of giving the reader abetter idea of what he/she can expect to find below and what isdefinitely not there.

i. Porous materials: A rather loose definition of a porous mate-rial is adopted below. Any material inside which transport ofa fluid is possible is considered to be ‘‘porous’’. Therefore,porous ceramics, cement-based materials, porous rocksand stones, coal, beds of porous and non-porous particles,elastomers, polymers and polymer gels, pharmaceutical dos-age forms, and thin films of adhesives, binders, coatings andpaints are included even though some of them may not beformally classified as porous. At the same time, the biomed-ical and/or in vivo studies and studies of plants are beyondthe scope of this review. In addition, not included (or men-tioned only briefly) are the studies of skin, food products,soil, textiles and wood.

ii. Drying and sorption: These are defined as processes in whichthe amount of a fluid (or a solute) in a solid material eitherdecreases or increases with time. This may be accompaniedby the changes in the molecular mobility of the fluid mole-cules and/or the porous material itself. Processes such ashardening of cementitious materials, solidification of poly-meric film coatings and paints are included even though insome cases (e.g., curing and hydration of cement) a fluidmay not actually leave the sample. At the same time, pro-cesses such as polymerization of monomers and curingand cross-linking of polymers are covered only briefly. Alsoexcluded are the studies of saturated or unsaturated single-or multi-phase flow and filtration of fluids in porous media.

iii. Mass transport: Only macroscopic mass transport is consid-ered below. Therefore, the studies of self-diffusion understeady-state conditions are not considered, whereas thestudies of transport diffusion carried out in the presence ofconcentration gradients are included only if transport isaccompanied by drying or sorption. Flow and filtration pro-cesses of fluids and transport of granular solids are notincluded.

iv. MRI: Surprisingly, this may be the most difficult term todefine. MRI is an extremely versatile toolkit, and many ofits tools are able to provide useful information about thevarious aspects of mass transport in porous materials.Besides, there is an almost unlimited potential for combin-ing various individual tools to meet the needs of a particularstudy. MRI here has its traditional meaning, i.e., the acquisi-tion of an image or a profile resolved in the space of actual(Cartesian) coordinates (‘‘k-space imaging’’), as opposed tothe average propagator studies sometimes referred to as‘‘q-space imaging’’ and performed in the space of displace-ments. Also not included are the studies where MRI isapplied to acquire images and parameter maps of an objectwhich is not changing over time, i.e., purely morphologicalstudies, the studies of relaxation and steady-state diffusionprocesses, etc. As already mentioned, MRI studies of flow, fil-tration and dispersion processes are not included either.

1.2. General considerations

Mass transport is ubiquitous in nature, in modern technologicalprocesses and in everyday life. Therefore, the first obvious reason tostudy mass transport processes is the need to better understandthem. And even if the original motivation of some studies is merecuriosity, once we understand these processes we inevitably cometo the point when we want to improve them, i.e., make them safer,more efficient, more environment-friendly, etc. In order to studymacroscopic mass transport in porous materials during the dryingand sorption processes, it is essential to perform dynamic measure-ments and to acquire spatially resolved information about the fluid(or solute, adsorbate, etc.) content in a porous sample as the objectunder study evolves in time. Of course, in certain cases such con-centration profiles or maps can be obtained in an old-fashioned

I.V. Koptyug / Progress in Nuclear Magnetic Resonance Spectroscopy 65 (2012) 1–65 3

way. For instance, in the gravimetric approach the process isstopped, the sample is cut and the pieces are weighed to determinethe liquid content. This approach is obviously destructive, time-consuming, and may appear to be inaccurate as it requires manyidentical samples to be sacrificed in order to investigate a dynamicprocess such as drying or sorption.

But here is a lesson that tells us not to disregard a study just be-cause it is performed using a rudimentary technique. The study per-formed by Kameı̈ using the gravimetric approach revealed a ratherstrange drying behavior of a clay plate (the figure showing watercontent profiles is reproduced by Collard et al. [1]). The distributionof water within the sample was initially uniform. As drying was ini-tiated, a pronounced water content gradient developed across thesample, with the water content gradually decreasing from the innerregions toward the drying surface of the sample, as expected. How-ever, at some later point in time during drying, the gradient sud-denly decreased and the distribution of water in the samplebecame essentially uniform. As drying continued further, the waterdistribution once again became significantly non-uniform. Such astrange sequence of transformations of water content profiles waslater dismissed as impossible [1]. Indeed, the destructive gravimet-ric study requires the sectioning of a large number of identicalsamples, which can lead to significant measurement errors. How-ever, MRI studies [2] discussed in Section 6.2 demonstrate thatthere is a good reason behind such an unusual behavior.

Yet, it is reasonable to expect the modern techniques to be fas-ter and more accurate than the old-fashioned approaches. A rangeof tomographic/imaging techniques [3–5] including MRI are avail-able at present that can be used for dynamic studies of mass trans-port processes. Most of these techniques are rather specializedtools. In contrast, MRI is best characterized as a versatile toolkitrather than a single tool. The reason behind this is the nature of im-age contrast in MRI, which is extremely diverse and furthermorecan be adjusted to the particular needs of a study. By using differ-ent tools from the MRI toolkit, one can obtain multiple images of asingle object each with a very different information content. In thecontext of porous media research, the NMR/MRI toolkit containsinstruments suitable for studying pore space morphology, connec-tivity and tortuosity of the porous space, and for evaluating poregeometry, pore sizes and their distributions, diffusive and convec-tive transport, etc. [6].

The studies that provide morphological information are quiteimportant because the structure of a porous object largely deter-mines its transport properties. In fact, in many cases the morphol-ogy of porous media is studied to assess and rationalize itsinfluence on some kind of mass transport. The morphological stud-ies are often combined with the studies of microscopic and macro-scopic mass transport. In particular, the question of how thestructure of the pore space influences the transport processes inporous media cannot be addressed without studying the samplemorphology. As mass transport can be strongly affected by thestructural inhomogeneities on very different length scales, themorphological and transport studies have to cover the entire range,from the size of an individual pore to the size of the entire object.The MRI toolkit possesses the tools necessary to address these is-sues. Application of MRI to the studies of the structure–transportinterrelation offers considerable prospects, since the technique al-lows the investigation of both structural and transport features forthe same sample under the same conditions. Furthermore, mor-phological NMR/MRI studies can be performed during a drying ora sorption process to see how the microstructure of a porous mate-rial evolves in time, for instance, during the drying and hydrationof cement-based materials. Finally, some studies of mass transportare performed with the objective of learning more about the struc-ture (morphology) of a porous material, whereas any imagingstudy of mass transport is bound to provide at least some

structural information. Therefore, the reason why numerousNMR/MRI approaches and studies that predominantly deal withporous media morphology and/or microscopic transport are notconsidered below is not because they are less important, but sim-ply because including everything would be impossible.

1.3. MRI and porous media: problems and remedies

The diverse nature of image contrast in MRI is both its blessingand its curse, as most studies cannot be classified as ‘‘routine’’applications. This may seem surprising, considering the widespreaduse of MRI in modern medical diagnostics and of high-resolutionNMR spectroscopy in many fields of science and technology. How-ever, compared to objects containing bulk liquids and to soft tissueof a living organism, MRI of fluids in porous materials encounters anumber of extra problems and difficulties. They are listed below.Some of them are closely interrelated, and depending on a particu-lar study they may not be equally important.

a. The pores are usually too small for MRI to provide directaccess to the processes on the length scale of individualpores. Therefore, each pixel (voxel) of an image normallycorresponds to a very large number of pores, with the mea-sured NMR signal essentially averaged over each voxel. Animportant exception is, e.g., a pack of mm-sized non-porousbeads often used as a model porous system.

b. For liquids and some gases, the interactions of the fluid mol-ecules with the pore walls can significantly reduce theirnuclear spin relaxation times, especially for samples with avery large specific surface area (i.e., very small pores) andfor materials containing paramagnetic impurities. Also, thestrong binding of molecules to a solid phase, such as waterbound in hydrates that form upon hydration of cement-based materials or water molecules interacting with poly-mer chains during polymer swelling, significantly affectsthe relaxation behavior as well. Shorter T1 times can beadvantageous since this reduces the required pulse sequencerepetition time (TR) and the overall time of image acquisi-tion. In contrast, shorter T2 times require a shorter echo time(TE) and often result in a drastically reduced sensitivity for agiven TE value. Besides, shorter T1 and T2 values also reducethe duration of the time intervals available for encoding spa-tial and other useful information. This limits both theachievable spatial resolution and the flexibility in accessingother characteristics of the spin system, for instance relaxa-tion and transport.

c. Porosity of a sample, defined as the ratio of the volume of thepores and the total sample volume, is less than unity. Thislimits the amount of liquid in the pores even in a fully satu-rated sample, and the reduced spin density decreases thesensitivity of an MRI experiment.

d. For T2 times comparable to or smaller than the minimum pos-sible TE, the T2-weighting of the signal cannot be avoided andthe quantification of liquid content becomes problematic. Inparticular, extrapolation of the signal intensity to TE = 0 canbe very difficult or impossible, especially if the signal decayis not single-exponential. In general, the T2 time is smallerfor a liquid in a smaller pore as the surface-to-volume (S/V)ratio of the pore becomes larger for smaller pores. Therefore,liquid in a smaller pore can give less signal per nuclear spinthan liquid in a larger pore. When liquid content in a poroussample changes, quite often larger pores tend to get emptiedfirst and filled last. Besides, for a given pore the relaxationtimes will change with the changing amount of liquid in thispore. Therefore, large variations of the liquid content in a por-ous sample often cause substantial changes in the relaxation


times, with lower liquid contents usually corresponding toshorter average relaxation times. As a result, the pixel inten-sity becomes a non-linear function of the degree of saturationof the porous sample with a liquid. Quantification of the fluidcontent can be also complicated by a number of other factors,including inhomogeneity of the sample or spatial variationsof the radiofrequency field B1 within it.

e. For a liquid with a large dielectric constant such as water,significant changes in the liquid content during drying andsorption processes lead to the changes in the optimal tun-ing/matching settings of the probe. As retuning of the probeduring the entire process is usually impossible, this can fur-ther degrade the signal-to-noise ratio (SNR) and complicateliquid content quantification. For electrically conducting flu-ids such as salt solutions, tuning/matching can be also prob-lematic and can cause reduced sensitivity and quantificationproblems.

f. Magnetic susceptibility mismatch at the interfaces betweendifferent phases (e.g., liquid/gas, liquid/solid, liquid/liquid)distorts the applied magnetic field B0 and can produce verylarge local gradients, especially for high-field studies andfor materials containing a significant amount of paramag-netic or ferromagnetic impurities. A substantial amount ofthe fluid in a porous object can experience these gradients,which lead to image distortion and shortening of the signal(e.g., free induction decay, FID) decay time T�2. In itself, ashort T�2 time is not a big problem. For instance, MRI of solidmaterials is also characterized by a rapid FID decay. In con-trast to solids, however, liquids and especially gases diffuserapidly in these large local gradients. This leads to a rapidand irreversible signal decay. Similar problems are encoun-tered when a technique or a device with a highly inhomoge-neous B0 field is used in the studies (see below).

g. Short FIDs mean broad spectral lines. Therefore, chemicalshift imaging (CSI, or detection of the spatially resolvedNMR spectra) and chemical shift selective imaging (CSSI, ordetection of images using a selected line in an NMR spec-trum) of fluids in porous materials can be problematic. Asmaller voxel is often better ‘‘shimmed’’, thus increasingspatial resolution can somewhat improve the situation forCSI, but even for a very small voxel the linewidth is still lar-ger than in a bulk liquid because of the reduced T2 valuesand the large short-range gradients caused by the suscepti-bility mismatch mentioned above.

h. Drying and sorption studies are often accompanied by cer-tain temperature variations. The temperature can be chan-ged intentionally, e.g., to accelerate the drying process. Inaddition, drying and sorption processes are inevitablyaccompanied by heat consumption or release. Pronouncedtemperature variations can measurably change the magni-tude of the equilibrium magnetization of the sample. Thecorresponding changes in signal intensity can be correctedfor if the temperature of the sample is known. However,the temperature can vary significantly across a sample. Fur-thermore, the temperature changes of the probe parts alsochange the measured signal by affecting the probe tuning/matching, which is difficult to compensate or correct for inthe duration of a continuous experiment. In addition, theprocesses involved are often temperature dependent as well.For instance, diffusivity is temperature dependent, and localadsorption–desorption equilibria are governed by adsorp-tion isotherms.

i. Not all processes can be studied in situ. Either the sampleitself or the apparatus required for carrying out the dryingor sorption process under the controlled conditions can beunsuitable for combining with a conventional MRI probe,

e.g., can be too bulky, contain metallic (electrically conduct-ing) or magnetic parts, requiring conditions unrealistic forconventional MRI, for instance extreme temperatures, pres-sures, and vibrations. Water cooling or heating of the samplecan introduce an overwhelming NMR signal and make thedetection of the actual process difficult.

j. Along with the fluid, the porous matrix itself can give a mea-surable NMR signal, which can vary as the sample evolves intime, for instance if the solid matrix is softened in the pres-ence of a liquid.

Given the number of problems, it may appear that one shouldnever attempt to use MRI in porous media research. However,many of these problems and difficulties can be dealt with. Further-more, some of them can be even used to an advantage to learnmore about porous media and the processes therein. Some of theknown tricks and trends are briefly listed below. Later in the re-view they will be illustrated with some practical examples.

a. It is highly unlikely that MRI in its conventional incarnationwill ever be able to provide a spatial resolution (much) bet-ter than 1 lm. Therefore, to address the individual pores inmicro- (<2 nm), meso- (2–50 nm), and even in many macro-porous samples (>50 nm) it may be necessary to resort toother techniques. In particular, magnetic resonance forcemicroscopy (MRFM) can resolve distances on the nanometerlength-scale [7,8] and even potentially detect individualspins [8,9]. At the same time, the MRI toolkit provides themeans of indirectly achieving the sub-voxel resolution bycombining the moderate spatial resolution with NMR spec-troscopy, diffusometry, relaxometry, etc., thus providingaccess to pore size distributions (PSD), chemical composi-tions, distribution of transport characteristics such as diffu-sion or dispersion coefficients (combination of k-space andq-space imaging) within individual image voxels. The stud-ies discussed below, however, deal with macroscopic trans-port processes in those situations where the spatialresolution provided by conventional MRI (from a few lmto a few mm) is sufficient for the purpose.

b. Many materials including modern building materials, soil,catalysts, etc., contain a substantial amount of paramagneticimpurities, which is often apparent from their color. It maythus be desirable to use model samples in which the amountof paramagnetic and ferromagnetic impurities is kept to aminimum. For instance, in the studies of building materials,white Portland cement (WPC) is preferred for sample prepa-ration as it contains a much smaller amount of Fe ions. Achoice of a liquid, if allowed by the experiment, is alsoimportant. For instance, in water–wet porous materials,non-wetting liquids such as hydrocarbons may have differ-ent relaxation times compared to water. For some gases atnormal pressures (e.g., SF6, H2, CH4), the relaxation timesare fairly short but, in contrast to liquids, tend to increaseonce the gas is admitted into the porous space. The relaxa-tion times of larger gas phase hydrocarbons and other gasessuch as 129Xe behave like those of liquids in this respect.

c. More often than not, the porous media MRI experiments arelimited by SNR. The latter is directly affected by the amountof the liquid in a porous sample, but in most cases the short-ening of the T2 ðT�2Þ time discussed above has an even moredramatic effect on sensitivity. At the same time, SNR is a keyfactor which in many cases determines the achievable spa-tial resolution and the image acquisition time. Long imageacquisition times lead to a low temporal resolution in thestudies of dynamic processes such as mass transport. Fullysaturated samples provide best SNR because of the


maximum spin density and longer relaxation times, but par-tial saturation cannot be avoided in drying and sorptionexperiments. One possibility to significantly improve SNRis by carefully choosing the experiment geometry. In partic-ular, the dimensionality of an image should be reduced, ifpossible. Indeed, 1D MRI (sometimes referred to as profilingrather than imaging) is fastest and gives the highest SNR.Therefore, cylindrical pellets or long cylinders are oftenused, with the mass transport made possible through oneor both flat ends. For cylindrical samples (either long or withthe flat ends covered), the radial transport is a 2D process,but can still be addressed as a 1D problem for samples/pro-cesses with cylindrical symmetry by detecting 1D projec-tions and using the inverse Abel transform to recoverradial profiles. In any case, a lower spatial resolution (largervoxel size or slice thickness) gives a higher SNR. The SNRissue is particularly severe for gases. Higher pressures canbe advantageous, but can damage certain materials. Thechoice of a gas can maximize spin density, for instance bychoosing molecules with many magnetic nuclei such asSF6. Hyperpolarization of nuclear spins leads to a substantialimprovement in the SNR, but accelerated spin relaxation of agas in contact with a high surface area material can signifi-cantly diminish the advantages of the use of hyperpolarizedgases.

d. The simplest way to deal with the quantification problem isto ignore it, as is done in some of the reported studies. Infact, this may be a reasonable approach as long as one doesnot attempt to interpret the data in a quantitative manner.However, drying and sorption curves (kinetics) are some-times calculated by integrating the corresponding images,which in most cases is not the right way to do it. For a reli-able quantitative interpretation of the results, it may be nec-essary to perform independent calibration measurements torelate the measured pixel intensity to the actual spin density(pore saturation). One way to experimentally determine thenecessary calibration curves is to detect an FID and to inte-grate the resulting NMR spectrum (or just take the first pointof the FID). This can be done by interleaving the FID and theimage detection or by performing separate experiments.Another option is to use a non-NMR technique to indepen-dently determine the amount of a liquid (solute) in the sam-ple and to relate it to a corresponding NMR signal intensityin an MRI experiment. Corrections for B1 and sample inho-mogeneities can be performed by normalizing the signal(pixel) intensity to the measurements performed on a fullysaturated sample.

e. If moisture content changes significantly during a measure-ment, it may be necessary to use modified or specialized rfprobes to avoid de-tuning and de-matching problems andthe associated problems with moisture quantification. Inparticular, a Faraday shield can be placed between the coiland the sample to suppress such effects [10,11]. Neverthe-less, an independent calibration experiment may still beneeded to make the measurements truly quantitative. Areduced quality factor of the probe can suppress rf-inducededdy current effects when salt solutions are used.

f. The distortions of the B0 field are lower for lower field values.It is not surprising, therefore, that many MRI studies of mate-rials and processes are carried out using low (<1–2 T) andeven ultra-low fields so that the applied gradients are largeenough to exceed the induced local gradients. To avoid rapidsignal decay, multiple refocusing of magnetization or a spin-lock pulse can be helpful, but more sophisticated pulsesequences may be required.

g. Several approaches can be used to map individual liquids ina mixture. A simple (and often expensive) approach is to useisotopically labeled compounds, e.g., deuterated liquids. Yet,care must be taken in certain cases. For instance, tracerexchange studies are often based on the use of D2O/H2Ocombinations. When D2O and H2O come into contact, theH/D exchange will produce HDO and will complicate inter-pretation of the transport behavior of individual species.The exchange of water protons with the exchangeablehydrogens of other molecules (e.g., a polymer) or hydrogenson a surface of a solid material is also possible. The choice ofthe nucleus being detected is important. For instance, 13CNMR spectra have a much broader range of chemical shiftsas compared to 1H NMR, but 13C MRI studies without usingthe isotope-enriched samples are difficult at best. NMR spec-troscopy in inhomogeneous B0 fields has attracted signifi-cant attention lately (Section 2.4), although mostly not inthe context of porous media research.

h. It may be important to monitor sample temperature and tocorrect for the temperature-induced signal variation. In par-ticular, for a quantitative interpretation or modeling of thedrying and adsorption data, an adsorption isotherm mea-sured independently may be needed. For very slow adsorp-tion and drying processes under conditions of efficient heattransport in the sample, it may be possible to neglect temper-ature variations during the process, but the actual sampletemperature may still be different from the ambient one.

i. In those cases where drying or adsorption cannot be per-formed inside an MRI instrument, it is still possible to per-form the study by temporarily interrupting the process,placing the sample in the MRI probe for the measurement,and then taking the sample back and resuming the process.The potential disadvantages of this approach are obvious.First, the repositioning of a sample in the MRI probe leadsto extra scatter in the measured data. Some kind of a refer-ence sample is often required for renormalization to correctfor tuning/matching and positioning inaccuracies. Rapidprocesses cannot be addressed in this way, and furthermoreeven if the sample is taken out of a drying or adsorptionchamber, this does not freeze the internal mass and heattransport processes within it. Yet, sometimes this is the onlyapproach possible. In some studies, an MRI-incompatibleapparatus is redesigned to make it MRI-compatible, whichis not always possible because of the limitations on sizeand construction materials. Alternatively, for samples andprocesses that cannot be studied in situ with conventionalMRI instruments, a whole range of devices for ex situ MRIis being developed (Section 2.2). To avoid confusion, itshould be stressed that the term ‘‘ex situ’’ refers here to anNMR/MRI technique itself, while the sample and the pro-cesses within it can be essentially studied ‘‘in situ’’, i.e., with-out the need to interrupt the process and reposition thesample. At the same time, an ‘‘ex situ study’’ means thatthe process has to be interrupted and/or the sample has tobe repositioned for an NMR/MRI measurement.

j. It is often possible to distinguish the contributions from amatrix and a fluid. This can be achieved by using and manip-ulating relaxation contrast, for instance by increasing theeffective TE to get rid of the matrix contribution if it has ashorter T2 time than the liquid phase. Isotope labeling is alsoan efficient approach. At the same time, the signal of amatrix can be a source of some useful information. Forinstance, mobilization of a polymer during swelling can bestudied as swelling increases the polymer mobility andmakes its signal observable.


1.4. The MRI toolkit: what is measured, and how

When discussing MRI studies, it is useful to distinguish(weighted) images from parameter maps. The contrast in a raw im-age is usually governed by one or several parameters such as spindensity (i.e., concentration), relaxation, diffusion, flow velocity, andtemperature. An image can be made sensitive to a certain param-eter intentionally, but for certain sample/method combinationssuch sensitivity can be intrinsic and impossible to completely elim-inate. In many drying and adsorption studies, the main goal is todetermine local concentrations, e.g., of water in a drying sampleor upon its accumulation in a sorbent. In such cases, spin densityimages are most suitable as they provide just that – the local con-centrations. As mentioned earlier, however, this is seldom the casein porous media research as some degree of relaxation weightingof the images cannot be avoided in most cases and has to be takeninto account (see above).

The raw images can be further processed to provide parameter(including spin density) maps. For instance, by acquiring a numberof images with a different degree of relaxation weighting, it is pos-sible to reconstruct the relaxation time maps (spatial maps of T1, T2,T1q, etc.). The relaxation times contain useful information on molec-ular mobility and the interaction of fluid molecules with the porewalls. The relaxometry technique relates nuclear spin relaxationtimes to pore sizes and pore size distributions [6,12–18]. Whencombined with MRI, relaxation porosimetry can thus yield theparameter maps reflecting the spatial distribution of mean poresizes or even maps of pore size distributions, the behavior of a liquidin partially filled pores, etc. Similarly, diffusion weighting can beused to characterize diffusive transport of fluids in porous mediaand to reconstruct the maps of diffusivity or even the diffusion ten-sor [12,19–25]. As diffusion also reflects the morphology of the por-ous space [6,13,22], spatial maps of pore sizes and tortuosity for theporous object can be produced. NMR cryoporometry [13,16,26,27]relates the freezing/melting temperature of a liquid to the size ofthe pore it occupies, and can also provide pore size or PSD mapswhen combined with MRI [28,29]. Relaxometry, diffusometry andcryoporometry can be applied in drying and sorption studies tomonitor the evolution of the microstructure of a porous material,the degree of pore saturation with the liquid, and to reveal otherprocesses that affect the solid matrix and/or fluid distribution with-in it. One of the examples is the hydration, gel formation, and mois-ture evaporation during drying and/or curing of cement-basedmaterials [30,31]. Spectroscopic modality is also quite important,and CSI or CSSI approaches can be used to produce chemical com-position maps, or maps of the spatial distribution of a certain chem-ical. NMR thermometry is based on the fact that certain parametersare temperature dependent, including equilibrium nuclear magne-tization, diffusivity, relaxation times and chemical shifts of certaincompounds. The corresponding weighted images can be processedto produce temperature maps of an object under study. These arejust a few of the existing possibilities, as their number is truly quitelarge and keeps growing. Among the recent additions are the mul-tidimensional experiments that allow one to correlate variousparameters such as T1–T2, T1–D, T2–D correlations, where D is diffu-sivity [12,32]. Besides, the dynamic exchange processes can bestudied in the space of relaxation, diffusion, velocity and otherparameters [22,32–38]. Interestingly, it appears that at least severalof the factors listed above as complications in NMR/MRI research ofporous materials can be utilized to provide useful informationabout the porous media. Another example of this is the use of diffu-sion in the local gradients of the magnetic field B0 induced by thesusceptibility mismatch at numerous solid/fluid interfaces to assessdiffusive transport [39] and evaluate pore shapes, pore sizes andPSD [40–42] through the exploration of the signal decay due to dif-fusion in the internal field (DDIF).

However, many of the studies mentioned in the preceding par-agraph are mostly performed without spatial resolution, and thusfall outside the scope of this review. In principle, they can be per-formed in the imaging mode, but before doing that one has to con-sider the necessity of this combination in a particular study andcompare the benefits with the inevitable degradation of SNR of aspatially resolved measurement and a much longer measurementtime. As a result, the number of such combined studies is limitedat present. At the same time, the acquisition of the relaxation timeand diffusivity maps is a fairly common approach used to charac-terize liquid-containing porous materials.

In principle, MRI is widely used to study mass transport understeady-state conditions, for instance, self-diffusion (see above)and flow [6,12,34,43–50] processes, and the corresponding imag-ing techniques with the appropriate image weighting are used insuch cases. In contrast, drying and sorption processes imply thepresence of a concentration gradient of a fluid or a solute. This isusually addressed by performing the repetitive imaging of thesample during a drying or a sorption process. In certain cases, con-centration gradients of isotopically labeled compounds are used,e.g. to distinguish between the native and the ingressing fluid orsolute. Some labels are intended to make the labeled fraction‘‘invisible’’ (e.g., deuteration of a liquid in combination with 1HNMR detection), while in other cases labeling introduces a nucleussuitable for image detection (19F, 31P, etc.). Transport of paramag-netic solutes can be imaged indirectly by detecting the relaxa-tion-weighted images. As already mentioned above, reducingdimensionality of the image to 2D or even 1D allows one to obtainhigher SNR and to improve temporal resolution.

While this review highlights the use of MRI techniques to studydrying and sorption processes, one should keep in mind that themost complete characterization of a sample or a process isachieved when MRI is applied in combination with other, non-MR, techniques, and the experimental results are complementedwith mathematical modeling of mass (and heat) transport. In fact,in many of the studies mentioned below a combination of variousexperimental techniques is used, and quite often the interpretationof the results is based on the models of transport processes of vary-ing degree of sophistication.

1.5. Quantification of mass transport

In this section, some simple formulas often used to interpretand quantify the results of the measurements will be briefly intro-duced. The transport mechanisms behind the sorption and dryingprocesses are not always diffusive in nature. Nevertheless, masstransport processes in many cases can still be described with thenon-linear diffusion equation, which in the case of a 1D problem is:

@S@t¼ @

@xD@S@x

� �; ð1Þ

where t is time, x is distance, and S is concentration of a liquid. Byformally integrating this equation, it is possible to evaluate D(S)from the known values of the spatial and temporal derivatives ofS(r, t) [51,52]:

DðSÞ ¼Z X0

L

dSdt

� �dx�

dSdx

� �X0: ð2Þ

If the effective diffusivity D is the function of the local liquidconcentration only (i.e., D = D(S)), the Boltzmann’s coordinatetransformation,

k ¼ x=t1=2; ð3Þ

can be used to collapse the 1D spatial profiles of liquid content, S(x),onto a single master curve. Indeed, the partial differential Eq. (1)can be converted into an ordinary differential equation:


� k2@S@k¼ @

@kD@S@k

� �: ð4Þ

Here, S depends only on k, and thus under the appropriate initialand boundary conditions the transformation can be used to collapsethe profiles onto a single master curve:

S ¼ Sðx; tÞ ! S ¼ SðkÞ: ð5Þ

The master curve can be used to evaluate numerically the desiredD(S) dependence:

DðSÞ ¼ �12

dSdk

� ��1 Z S

S0

kdS0: ð6Þ

The calculation of the derivatives in Eqs. (2) and (6) can be com-plicated in the presence of measurement noise because of the needto numerically evaluate the derivatives from the experimentaldatasets. Therefore, sometimes the experimental traces aresmoothed first. Another possibility is to fit the entire data set ac-quired in a dynamic MRI experiment using an appropriate mathe-matical model. This approach in most cases requires an a prioriknowledge of the functional form of D(S) or a discrete set of D(Si)values with interpolation. Eq. (2) or Eq. (6) can provide a usefulguidance for a starting point.

In sorption processes, in many cases the amount of adsorbed li-quid and the adsorption front position depend linearly on t1/2, asmay be expected for a diffusion process. At the same time, the sorp-tion front in certain cases can be quite sharp and lack the long tailsin concentration profiles often associated with diffusive transport.This is often the case when D(S) grows rapidly and progressivelywith S. For instance, in many studies a growing exponential depen-dence is a good approximation:

D ¼ DE expðbSÞ; b > 0; ð7Þ

or

D ¼ DC þ DE expðbSÞ; b > 0: ð8Þ

When both liquid and vapor phases are present, an effective diffu-sivity is often expressed as a function of the concentration of the ad-sorbed (liquid) phase SADS as:

Deff ¼ DC þ DE expðbSADSÞ; b > 0; ð9Þ

with the amounts of the adsorbed and the vapor (SVAPOR) phasesinterrelated through the adsorption isotherm, which in many casesis taken as the following exponential relation:

SVAPOR=S0VAPOR ¼ exp SADS=S0

ADS

� �; ð10Þ

where S0VAPOR and S0

ADS are constants. The D(S) dependences similar tothose given by Eqs. (8) and (9) are often used in studies of drying.

It is remarkable that mass transport during drying and sorptionprocesses can be successfully described with the diffusion equationeven though the underlying physics of transport mechanisms is of-ten different. Indeed, capillary action often governs the ingress ofwater into many hydrophobic materials. Capillary flow of a liquidis also an important mechanism of mass transport in the dryingprocesses, which can still be modeled by introducing the so-calledcapillary diffusivity. At the same time, it is obvious that anydescription based on the equations provided above is oversimpli-fied. In a number of studies, it is demonstrated that the actualtransport processes behind drying and sorption are quite compli-cated and their proper description may require the use of muchmore sophisticated models.

As mentioned above, the evaluation of D(S) relies on theassumption that diffusivity D depends only on the moisture con-tent S, implying that it has no explicit dependence on the spatialcoordinate or time. In general, this information cannot be obtained

in the kinetic studies that provide drying or sorption curves and re-quires the spatially and temporally resolved data on S(r, t). This isexactly the kind of information the MRI technique can provide.In addition, an MRI measurement can provide the boundary condi-tion essential for modeling – the value of S near the sample surface.

2. MRI techniques and instrumentation

2.1. Techniques used for porous media MRI

One has to admit that MRI of living organisms (lab animals andhumans) is a much more popular area of scientific research andpractical applications than MRI of non-living objects. It may seem,therefore, that the latter field can thrive on the progress and devel-opments in the biomedical MRI research. Unfortunately, many ofthe pulse sequences routinely used in biomedical MRI are oftennot applicable in porous media studies. In particular, rapid imagingschemes such as multiecho sequences may not work since in manycases even the first echo in the train may be hard to detect. For cer-tain porous materials, the short relaxation times of fluids in thepores and the associated problems of reduced SNR and spatial res-olution make the techniques from the arsenal of the narrow-lineMRI of liquids unsuitable. In fact, in this respect MRI of fluids incertain porous materials is closer to MRI of solids, and the dryingand sorption processes are often addressed by resorting to thearsenal of broad-line MRI approaches. Some of the techniques usedare briefly discussed below.

As mentioned above, short transverse T2; T�2� �

relaxation timesreduce SNR because of the rapid signal decay in the time domainand degrade spatial resolution because of the associated increaseof the linewidth in the spectral domain. Conventional gradientecho (GE) based pulse sequences are not generally applicable be-cause they lack any line-narrowing capabilities and utilize moder-ate gradients in combination with frequency encoding whichcannot provide high spatial resolution for broad-line applications.Nevertheless, examples of the application of GE sequences to studymass transport in porous materials do exist. Spin echo (SE) andsimilar echo-based sequences are used more often since they pro-vide some degree of line-narrowing owing to the fact that T2 (orT2eff) is often measurably longer than T�2. The use of the minimumpossible TE allows one to reduce the degree of T2-weighting of theimages and thus to minimize signal losses. Alternatively, a judi-cious choice of TE can be used to reduce or eliminate the contribu-tion of a rapidly relaxing component in a complex system, forinstance to suppress the signal of a semi-rigid matrix while pre-serving the signal of a fluid. Frequency encoding of the signal canbe disadvantageous as spatial resolution is limited by the largewidth of the spectral line. In contrast, phase encoding is muchmore immune to the influence of large linewidths as well as to sus-ceptibility and chemical shift artifacts. Therefore, detection of aspin echo in combination with pure phase encoding can be advan-tageous for many porous materials, and can be used to image evenrigid solid materials including ceramics and bones. Pure phaseencoding also means that the spectroscopic information is retainedand can be obtained by FT of the echo; however, because of the fastsignal decay the spectroscopic resolution for fluids in porous mate-rials is usually rather poor. In fact, for imaging applications it maybe advantageous to detect a single point of an echo, as done in thefamily of constant time imaging (CTI) or single point imaging (SPI)techniques [53–59]. At the same time, phase encoding requiresmultiple repetitions of a pulse sequence to properly sample thek-space, with sequential repetitions separated in time by TR = 3T1

or 5T1 to allow the spin system to return to thermal equilibrium.Thus, the minimum image acquisition time in many cases becomes(significantly) longer. Still, the minimum echo time TE cannot be


much shorter than a few hundred ls as the inter-pulse delayshould allow one to apply gradient pulses and to allow for the gra-dient stabilization and decay.

To further reduce the delay between excitation and detection,one has either to switch the gradients much faster, or not to switchthem at all during the signal excitation and detection interval. Fas-ter switching of ‘‘rectangular’’ pulsed gradients is generally not fea-sible because of the coil inductance and also because pulsinginevitably induces eddy currents in the electrically conductingstructural elements of the instrument that are present in the vicin-ity of the gradient coils. An alternative fast switching strategy is touse a sinusoidal gradient produced by a coil incorporated in a res-onant circuit [60–64]. In this case, there is essentially no ‘‘gradientswitching’’ delay, and the minimum TE is determined by the gradi-ent oscillation frequency and can be ca. 100 ls or even shorter witha typical gradient strength of 1–10 T/m. A frequency-encoded gra-dient echo or an echo train is acquired. The rf pulses are appliedwhen the gradient passes through the zero-crossing point[65,66]. The use of a doubly resonant coil can produce an inflectionpoint when the gradient amplitude crosses the zero value andmakes the gradient off time longer [62]. The schemes for 2D [67]and 3D [60] imaging based on the orthogonal oscillating gradientshave been reported. A disadvantage of the oscillating gradients forfrequency encoding is the permanent variation of the gradientamplitude in time. As a result, for a constant dwell time of a digi-tizer the sampling of k-space is no longer uniform. Therefore, re-gridding of the data points, an alternative non-FT image recon-struction or a non-linear sampling scheme is needed. Nevertheless,large oscillating field gradients can induce the undesired eddycurrents.

Alternatively, the gradient can be kept constant during the shortinterval between the excitation and signal detection, as done inone of the implementations of the SPI technique in which a singlepoint of an FID is detected a short time after the excitation pulse[54,68,69]. To perform phase encoding of the signal, the gradientsare turned on well before the excitation pulse and are switched offafter the detection event. In such an experiment, the encodingtimes tp can be as short as 10–100 ls. An undeniable advantageof SPI is the use of pure phase encoding which in many cases over-comes the problems associated with line broadening and suscepti-bility effects. A coupled disadvantage is a large duration of an SPIexperiment since only a single point in k-space is detected for eachpulse sequence repetition. To accelerate image acquisition and toavoid the necessity to repeatedly turn the gradients on and offfor each pulse sequence repetition, the SPRITE (Single-PointRamped Imaging with T1 Enhancement) technique was introduced[59,70–76]. In SPRITE, the gradients are rapidly ramped in a step-wise manner between the repetitions. SPRITE is much less noisythan SPI; however, care must be taken as the duty cycle of gradientamplifiers increases significantly compared to SPI and other imag-ing schemes (e.g., can exceed 50% [75]). Various types of relaxationcontrast can be incorporated in both SPI and SPRITE sequences[59,70,73,77,78].

Pure phase encoding used in SPI and SPRITE has an advantagethat the signal at the origin of k-space (k = 0) is detected in the ab-sence of an applied gradient, which prevents additional signallosses due to the diffusion of liquids and gases in the applied gra-dients. In both SPI and SPRITE, the rf pulses are applied in the pres-ence of the gradient, and thus should be very short in order toavoid the unnecessary spatial selection which in addition changesevery time the gradient is changed. The TR times are usually muchshorter than 3T1, leading to T1 contrast in the images even thoughthe flip angles are usually quite low. To facilitate spin densityimaging and to somewhat reduce the duty cycle of the gradientsystem in the SPRITE technique, centric sampling schemes havebeen introduced, in which the detection of the k-space points starts

at k = 0. These include the 1D double half-k-space (DHK) [79], 2Dspiral [75,78,80,81], 3D conical [75,81] and sectoral sampling[82] SPRITE schemes. Note, however, that in contrast to the con-ventional MRI sampling schemes where the spin system followscontinuously a certain trajectory in k-space, in SPRITE the trajec-tory is built point by point, with each rf pulse initiating a new tra-jectory that starts at k = 0. Therefore, it is usually not too difficult toensure that the data points detected in k-space fall on a regularrectangular grid suitable for a conventional Fourier transformation.A notable exception is the situation where bulk metal structuresare present near the field of view. An example is an object insidea thick-walled metallic cylinder imaged using centric scan SPRITEcombined with a careful evaluation of the actual gradients alteredby the strong eddy currents and with a re-gridding of the resultingk-space trajectory [83,84]. The rf coil was placed inside the metalcylinder in these experiments. SPRITE was also successfully usedto image water in aircraft-grade sandwich panels comprising analuminum honeycomb core and graphite–carbon fiber compositeface skins despite the significant distortions of the B0 and B1 fieldsproduced by the sample [85].

The smallest possible delay between the excitation and detectioncan be achieved by detecting an FID instead of an echo. The FID is de-tected in the presence of an applied gradient, and the experiment isrepeated for a number of different directions of the applied gradientin space. The multiple 1D projections of a sample obtained in thisway are then used to mathematically reconstruct the image by pro-jection–reconstruction [86]. This approach is known in MRI from itsearly days [87] and is used in other imaging techniques such as CT[88] and ESR imaging [89–91]. As frequency encoding is used, the ap-plied gradients have to compete with the spectroscopic linewidth.

The continuous wave (CW) magnetic resonance detectionscheme [92–95] has certain advantages compared to the conven-tional pulsed NMR. The use of CW rf irradiation and detection elim-inates the detector deadtime altogether and thus makes it possibleto address materials with sub-millisecond T2 times. The gradientsare also applied continuously and, in contrast to pulsed MRI, thehigh-SNR narrow-bandwidth detection is used irrespective of theamplitude of the read gradient. Besides, the required rf power is or-ders of magnitude lower as compared to the pulsed experiments.In the early days of NMR all experiments were done in a CW mode,but modern commercial NMR instruments no longer support thiscapability. In contrast, ESR imaging is often performed in this way.

A number of studies rely on the utilization of large constant gra-dients, i.e., gradients that cannot be switched on and off at all. Inparticular, some studies are performed by placing a sample inthe fringe field of a superconducting NMR magnet in the techniquethat was dubbed STRAFI (STRAy Field Imaging) [68,96–104]. For avertical bore superconducting magnet, the probe with the sampleis lowered to the point where the magnetic field is equal to ca.40–50% of that in the magnet center. This allows one to use thehigh static gradient which, depending on the particular magnet,is typically in the range 10–100 T/m, but can be even higher. Inthe presence of such gradients, even a short rf pulse becomes spa-tially selective and excites spins in a fairly narrow slice perpendic-ular to the vertical (z) axis unless the sample is very thin and theentire sample thickness is covered by the frequency bandwidthof the pulse. The (reduced) rf frequency defines the location ofthe so-called STRAFI plane, that is, the xy-plane in the stray fieldwhich is excited by the rf pulse. The STRAFI plane does not neces-sarily coincide with the position of the strongest GZ gradient, sincethe optimum location in the fringe field is determined not only bythe gradient amplitude but also by the field geometry (homogene-ity) which determines the spatial resolution. The achievable slicethickness can be 5–10 lm if the sample positioning is optimizedto achieve a reasonably flat excited slice, but in many cases the res-olution is on the order of 50–100 lm.


In a STRAFI experiment, the measured magnetization corre-sponds directly to the spin density in the STRAFI plane, and thusa Fourier transform is not required to recover it. The sensitive planecan be displaced within a finite range of distances either by chang-ing the rf frequency [98,99,102] or by adding an extra coil forsweeping the B0 field [98,99,105]. However, the simplest way ofperforming the 1D STRAFI profiling is by mechanically translatingthe sample through the STRAFI plane. A peculiarity of the sliceselection in such strong gradients is that nuclei such as 1H and19F can produce images that are very close to each other in the fre-quency domain [106,107]. Therefore, in those STRAFI experimentswhere the rf coil moves with the sample, the profiles for both nu-clei can be acquired during a single 1D scan. However, usually thecoil is kept stationary at the level of the sensitive plane and onlythe sample is moving during the experiment, in which case the19F responses will not be detected in a 1H NMR experiment. Forthin planar samples (films), when the thickness of the excited sliceexceeds the sample thickness, it is possible to acquire a frequency-encoded echo and to perform FT to obtain the 1D profile throughthe planar sample. This approach is known as FT-STRAFI[98,99,102]. To obtain 2D and 3D images, a stepwise rotation ofthe sample can be added. One of the recent developments is theuse of a MAS NMR probe in a STRAFI experiment [108–110]. How-ever, it may be undesirable to perturb a wet sample by moving orrotating it. In such cases, the strong static gradient in STRAFI can becombined with additional pulsed gradients applied in the orthogo-nal directions for 2D or 3D imaging of a sample [111]. This ap-proach allows one to achieve high spatial resolution through thedepth of the layer combined with the moderate resolution in thein-plane directions.

The advantage of large gradients in STRAFI is the possibility toimage a broad range of solid materials including paramagneticsubstances [106,112]. However, the use of very large gradients inSTRAFI and in some of the specialized deices described below canalso have certain complications and disadvantages (see Section2.3). In stray field techniques, it is not usually possible to recordan FID as the T�2 time is necessarily short in a strongly inhomoge-neous magnetic field. Therefore, the signal is observed in the formof an echo or a multi-echo train. Quite often, a ‘quadrature echo’sequence,

90�

x � s� 90�

y � s� echo� s��

nð11Þ

is used for signal detection [98,99,113]. All pulses in this sequencehave the same width and thus perform the same slice selection. Inthe presence of a large B0 gradient, however, a ‘‘90�-pulse’’ is a poorapproximation because of a wide distribution of resonance offsets.For a short inter-pulse delay, the signal in the time domain tendsto decay with a characteristic time T1q rather than T2 because ofthe spin-lock effects.

Of course, the arsenal of solid-state MR techniques is muchbroader [63,92,114–120] and includes a number of powerful line-narrowing techniques such as MAS and multiple-pulse line nar-rowing that are routinely applied in NMR to average out variousanisotropic interactions of nuclear spins in rigid solids. However,these techniques may be inefficient in porous media research sinceone often deals with liquids and not with true solids. Anotherinteresting approach is the rotating frame (or B1-) imaging thatuses gradients of the B1 rf field instead of, or along with, the gradi-ents of the static magnetic field B0 [114,121–126]. The advantageof this approach is its insensitivity to the inhomogeneity of theB0 field, which can be useful, for instance, in the studies of highlyinhomogeneous samples. B1-imaging may require the use of spe-cialized B1 coils/resonators. At the same time, for a surface coilthe B1 field naturally depends on the depth coordinate. In conduct-ing materials, a B1 gradient exists due to the skin-effect.

2.2. Specialized MRI equipment

The techniques mentioned above are mostly implementedusing conventional imaging systems, possibly with some modifica-tions. At the same time, a whole range of dedicated specialized de-vices has been designed and constructed. These devices aredeveloped with different objectives in mind, and differ in designdepending on the intended range of applications. Conventionalmagnetic resonance equipment is optimized for laboratory use,but may have very serious limitations if one attempts to considernon-traditional applications. For instance, modern NMR spectrom-eters can be essentially useless for on-stream or in-line character-ization in chemical engineering, in oilfield research and otherindustrial applications. At the same time, it is clear that such appli-cations are limited by the practical implementations of NMR andnot by the technique itself. Therefore, different NMR instrumenta-tion and methodology are needed to overcome the limitations onthe sample size and its properties, experimental environment,etc., inherent in modern lab NMR. One of the recent and very inter-esting trends is the development of the inside-out, unilateral and/or ex situ NMR techniques and the range of specialized unilateraland/or single-sided devices [127–130] applied in various studiesincluding porous media research [131]. The terms in the precedingsentence are not synonymous, and are often used to stress the spe-cific feature or aspect of a certain technique and/or device. At thesame time, some of these terms are often used interchangeably.What they all have in common is that the spatial distributions ofthe remotely generated inhomogeneous B0 and B1 fields define asensitive volume with either a roughly homogeneous B0 field or arelatively large B0 gradient. Not only the magnitudes but also theorientations of the two fields determine the sensitive volume, sinceB0 and B1 have to be orthogonal within it. This governs the selec-tion of the design of rf coils/probes for a chosen magnet geometry.

The original impetus for the development of the inside-out NMRcomes from the oil industry [127,132,133]. The understanding thatNMR can be performed in the fringe (stray) field of a magnet gaverise to a whole new area of research and development in magneticresonance. First of all, the use of a fringe field can eliminate the needto place the sample in a restricted space of a conventional NMRmagnet. This means, for instance, that the sample can be placed nextto the device. It may also happen that it is undesirable or impossibleto bring the sample to the lab. For instance, once the need to placethe sample inside the device is eliminated, the sample can now bemuch larger than the device itself. In an extreme case, the entire‘‘sample’’ can be even as large as planet Earth [134–136]. Of course,for large objects the measurement has to be performed locally, butcan be quite informative anyway. This initiated the development ofmobile or portable NMR and MRI systems – those that can be deliv-ered to the object under study. The commercial availability of newtypes of magnetic materials has led to the design of many devicesthat rely on permanent magnets. This eliminates a need to have amagnet power supply and reduces the weight and size of a mobilesystem. This also means that the magnetic field is not high in mostcases (<1 T), but for a range of applications this can even have cer-tain advantages (see below). This trend has also led to a renewedinterest in, and the rapid development of, magnetic resonance inlow and ultra-low magnetic fields [137], including ultralow-fieldNMR spectroscopy [138–141]. This diversification of the instrumen-tation and a (significantly) reduced cost of certain devices have ledto the development and production of tailor-made systems for par-ticular applications by matching the instrument to the sample, andnot the other way around.

As mentioned above, MRI of short-T2 materials may require alarge magnetic field gradient. Indeed, some of the specialized de-vices are characterized by having a large B0 gradient over the sen-sitive region. In particular, a bench-top permanent magnet called


GARField (Gradient At Right angles to the Field) was specificallydesigned for studying planar samples tens to hundreds of micronsthick (e.g., films, coatings, skin, etc.) with a high spatial resolutionin one dimension [129,142–147]. The shape of the pole pieces ofthe GARField magnet is such that it produces a large constant gra-dient in the direction orthogonal to the sample plane and a homo-geneous field within that plane. With such a magnet the 1Dprofiles of planar samples up to 500 lm thick can be obtained byexciting the nuclei across the entire sample thickness with a shortrf pulse and using FT to reconstruct the profile with the resolutionalong the depth coordinate as high as 5–20 lm. The characteristicB0 field in the sensitive plane is 0.7 T and the gradient strength is17 T/m. As gradient switching is not required, the echo times canbe as short as 100 ls. The price to pay is a degraded SNR and, inpractice, limitation to a single spatial dimension (i.e., profiling).The quadrature echo pulse sequence (Eq. (11)) with a typical rfpulse length of 1 ls is usually used for signal detection. In the earlydesign, the sample was placed between the magnet poles over therf coil. Later, the device was redesigned: with the surface GARFieldsystem the need to place the sample inside the magnet was elim-inated and the rf probe was also improved [129,148,149]. Thisone-sided version of GARField was developed to profile the near-surface regions of the arbitrarily large samples. The planar regionsof the B0 and B1 fields coincide over an area of approximately50 � 50 mm2. The thickness of the excitation slice is determinedby the B0 field gradient and the RF pulse length and is typicallyin the range 0.2–0.6 mm. The depth coordinate in the typical range0–40 mm from the sample surface is scanned by moving the mag-net relative to the surface, while the rf coil either moves with themagnet or remains fixed relative to the sample surface [148]. An-other single-sided NMR device was developed and used in 2Drelaxation correlation studies of hydrating cement pastes [150].

A unilateral device called NMR-MOUSE (MObile Universal Sur-face Explorer) was originally designed to conduct in situ investiga-tions of rubber products, and over the years was significantlyimproved [127–129,151–155]. The typical field strength is on theorder of 0.5 T and the gradient strength is around 10–20 T/m. Con-ventional NMR-MOUSE is based on a U-shaped magnet (a horse-shoe geometry) and is constructed from two permanent magnetspositioned on an iron yoke to have an anti-parallel polarization.The B0 field is predominantly oriented across the gap, and itsstrength decreases rapidly with increasing distance from the mag-net surface. A suitable rf coil (e.g., a solenoid or a surface coil) isplaced in the gap between the magnets. The unilateral magnetand the rf coil create the orthogonal B0 and B1 fields within an ob-ject near its surface. The small size and weight of the (palm-size)magnet/coil assembly make the device portable, and the unilateraldesign helps overcome the limitations on the size of the samplethat can be studied. Furthermore, the strong B0 gradient and a rel-atively low B0 field are essential for overcoming another complica-tion in the studies of objects like car tires, concrete structures, andconveyor belts, namely the presence of reinforcing steel parts.

The studies using NMR-MOUSE were originally performedwithout spatial resolution apart from the spatial localization pro-vided by the sensitive volume of the device and defined by the spa-tial distributions of the B0 and B1 fields. However, profiling andimaging applications were later developed as they are naturalextensions of the technique. Depth profiles can be obtained bychanging the sensitive slice position within the sample. Dependingon the design and intended applications of the sensor, this can bedone by varying the rf frequency, applying a bias field with an elec-tromagnet, or by displacing the sensor relative to the sample sur-face. The 1D Fourier imaging in the large static gradient is alsopossible for thin samples or sample slices. A coarse lateral resolu-tion of a few mm can be achieved by displacing the sensor over theobject surface. Additional gradient coils can be added to perform

1D or 2D phase encoding in the lateral directions [156–159]. TheMRI-MOUSE allows 1D spatial resolution of the sample structureof about 100 lm without sample repositioning. Rotating frame(B1-) imaging with a MOUSE sensor has been demonstrated as well[160].

One of the disadvantages of the original NMR-MOUSE designs isthat the large B0 gradient of the device (10–50 T/m) varies in thedirection normal to the magnet surface, i.e., the field variation withdistance is not linear. Furthermore, the B0 field is inhomogeneousin not just one but in all directions. This implies that the excitedslice is not flat and this curvature limits the spatial resolution thatcan be achieved. To improve the slice flatness, a number of im-proved geometries have been proposed. In particular, a modifiedversion known as Profile NMR-MOUSE was designed, in which aflat sensitive slice was achieved by placing two U-shaped magnetsnext to each other with a small gap between them. In this design,the curvature of the sensitive slice is a few micrometers over ca.1 cm2 [127,128,161]. A depth resolution of 5 lm was achieved bycombining the Fourier imaging and the stepwise sensor displace-ment. To increase the imaging depth, the dimensions of the magnetblocks and the gaps were increased, providing a flat slice at 18 mmfrom the magnet surface with B0 = 0.25 T and G = 11.1 T/m.

A different NMR-MOUSE design based on a single bar-shapedmagnet was also introduced, which has a constant B0 gradient inthe central part of the magnet directed from the pole face intothe sample [127,128,162]. In this design, the B0 field is orthogonalto the face of the magnet (along z), preventing the use of a simplesurface coil to generate B1. Different planar coil geometries such asspiral, figure-8, or butterfly must be used, which can decrease SNR.The principal magnetic field gradient component is also along the z(depth) direction defining rather flat slices of constant frequencyand a rather symmetric field of view in both perpendicular direc-tions (x and y). The additional x and y gradient coils were addedfor 2D SE imaging using phase encoding, which in combinationwith the natural slice selection along the depth coordinate canbe used to obtain 3D spatial resolution by tuning the probe to dif-ferent frequencies [158]. Alternatively, a bar magnet NMR-MOUSEequipped with a ‘‘crazy coil’’ with a sensitive region less than0.25 mm from the coil surface was designed for studying surfacelayers of materials [163].

A unilateral device with a moderate (0.3 T/m) but constant gra-dient for near-surface profiling was reported [164]. A lower gradi-ent allows the excitation of a thicker slice and facilitates 1D FT SEimaging with the resolution up to 150 lm, and reduces the diffu-sive attenuation of the signal. A portable unilateral NMR probebased on the barrel magnet design was developed for detecting1D profiles [165]. The region outside the barrel magnet is usedwhere the magnetic field has an approximately constant gradientof 5.7 T/m (B0 = 0.26 T) to obtain 1D profiles with a spatial resolu-tion of ca. 100 lm.

A simple and inexpensive unilateral device with a 10.2 T/m gra-dient was reported recently [166]. The utility of the ex situ NMR ap-proach using a unilateral probe with a large constant gradient hasbeen demonstrated also for the acquisition of velocity maps andvelocity distributions [167]. The mq-ProFiler is a Bruker compactNMR instrument with a one-sided sensor [168].

2.3. Toward an improved field homogeneity for single-sided andmobile instruments

A large static B0 gradient facilitates 1D profiling with a high spa-tial resolution in porous media research. Furthermore, low and/orhighly inhomogeneous B0 fields make the field distortions causedby susceptibility differences small in absolute value and/or in rela-tion to the B0 gradient. As a result, STRAFI, GARField, MOUSE andother high-gradient and/or low-field devices and techniques can


be used to study objects containing materials with magnetic prop-erties not suitable for conventional MRI measurements, such as ob-jects with strong variations in magnetic susceptibility or evencontaining ferromagnetic and conducting parts. Examples includecar tires, buildings, bridges, conveyor belts, polymer coatings onferromagnetic sheets, etc. At ultra-low fields, imaging of the ob-jects enclosed in a thin-walled metal container becomes possiblebecause the skin depth which determines the depth of rf penetra-tion increases with decreasing frequency. The mobile (portable)and unilateral design of the devices makes them suitable for thestudies of an ever growing range of object types (frescoes, mum-mies, paintings, etc.), including the studies of the local propertiesof very large objects.

However, the large static B0 gradient has certain disadvantagesas well. For one, it leads to a significant diffusive attenuation of thesignal of fluids and a rapid signal decay in the time domain. A verylarge B0 gradient implies a very broad spread in resonance frequen-cies and requires a large detection bandwidth, potentially reducingthe SNR by an order of magnitude or more. The wide distribution ofresonance offsets also leads to a spatially dependent flip angle andexcitation phase. The B1 field in unilateral devices is also inhomo-geneous and adds to the spatial dependence of the flip angle. In lowfields, the gradient field may be comparable to or even larger thanthe main B0 field, and in contrast to the high fields the concomitantgradients can no longer be ignored [169]. Furthermore, the B0 gra-dient can be spatially dependent. Even the effective relaxationtimes measured in the inhomogeneous B0 and B1 fields can be dif-ferent from those measured in homogeneous magnetic fields. Allthese factors lead to a very complex behavior of a spin system,for instance upon application of the echo-train sequences, whichoften has to be analyzed numerically [170]. In addition, the devel-opment and use of different spatial localization schemes may berequired. Finally, in an inhomogeneous B0 field the spectroscopicstudies can be difficult or impossible.

To overcome these limitations, another trend in modern NMR/MRI is the development of mobile magnets that have a region witha more or less homogeneous B0 field, which is sometimes called the‘‘sweet spot’’. Depending on the magnet design, the sensitive vol-ume can be located either inside or outside the magnet. It shouldbe mentioned, however, that many of the single-sided and mobilesystems with a ‘‘homogeneous’’ B0 field are not suitable for spec-troscopic applications since the inhomogeneities across the sensi-tive volume can be as large as 1000 ppm and more.

An example of a single-sided probe with the outside sensitivevolume is a GARField-like device, but designed with the objectiveof maximizing the magnetic field homogeneity within the saddlepoint in the spatial geometry of the field in order to maximizethe NMR signal in nondestructive testing applications [171]. Thedesign goals were a large sensitive volume to improve SNR, and alow rf frequency, which is important for electrically conductingsamples. Another reported device has an adjustable sensitive vol-ume and consists of an array of four cylindrical permanent magnetrods [172]. The location and size of the sensitive volume withB0 = 600–700 G can be changed by mechanically rotating the rods.Another possibility is to ‘‘shim’’ an inhomogeneous field of a mag-net. For instance, the U-shaped single-sided magnet was addition-ally equipped with a shim unit comprised of several additionalpairs of permanent magnets [173]. A volume with a fairly homoge-neous B0 field can be created by changing the positions of the shimmagnets, and a sub-ppm spectral resolution was achieved. Anotherdesign that provides a relatively homogeneous B0 field at a certaindistance from the sensor surface is based on the barrel magnet, ortwo concentric tube magnets with opposite polarization [174]. Aportable probe termed MObile Lateral (or Liquid) Explorer (NMR-MOLE) with B0 = 76.7 mT was designed to simplify imaging of liq-uids, e.g., in cement hydration studies [175]. It is essentially a

discrete version of a barrel magnet, with the inclined cylindricalrods arranged to form a truncated cone. The homogenous regionis a cylinder with a height of 10 mm and a diameter of 28 mm. Asingle-sided magnet array weighting 5 kg that consists of threemagnet blocks and generates a homogeneous B0 field parallel tothe magnet surface has also been reported [176]. Its applicationto monitor moisture in graphite/aluminum/epoxy composite sand-wich panels was demonstrated [177]. A unilateral device with ahomogeneous field intended for dental applications has been re-cently presented [178].

Among the portable systems with a sensitive volume inside themagnet/device, the Halbach-type magnets currently attract muchattention. The B0 field in the Halbach magnet is oriented perpen-dicular to the magnet bore, which makes it possible to use solenoi-dal rf coils oriented along the magnet bore. For Halbach magnets,the stray field is low, which is advantageous for applications out-side the controlled lab environment. Despite that, a single-sidedmobile NMR surface-type detector based on a small Halbach mag-net has been reported as well [179].

Various realizations of the Halbach-type magnets have been re-ported, with different geometries and the arrangement of the per-manent magnets that serve as building blocks. A simple designscheme named ‘‘NMR Mandhala’’ (Magnet Arrangements for NovelDiscrete Halbach Layout) was introduced to construct Halbachmagnet arrays from identical bar-shaped magnets with a squarecross-section [180]. The magnet representing a stack of eight sub-units containing 16 magnet blocks each was reported to haveB0 = 0.311 T and the homogeneity of ca. 300 ppm in a (5 mm)3 vol-ume, with the total weight of 11.4 kg. The concept was later gener-alized and the design improved [181]. A disadvantage of a magnetwith an inner sensitive volume is that not every sample can beplaced in it even if the sample dimensions allow this in principle,for instance tree branches, plant stems, etc. To partially overcomethis problem, an NMR-CUFF (Cut open, Uniform, Force Free) mag-net was designed that can be opened from the side without signif-icant force, and later closed around an object of interest [182]. TheNMR-CUFF magnet based on the NMR-Mandhala design was re-ported to have the homogeneity better than 50 ppm after mechan-ical shimming. A Halbach array with a shim unit comprising fourpairs of small movable permanent magnet blocks placed insidethe magnet bore was constructed [183]. A sub-ppm homogeneitywas achieved in a volume of ca. 1 cm3. The final system weighsca. 50 kg. The magnet bore is 200 mm and the average fieldstrength is 0.22 T. A recent paper reports a design of a smallHalbach magnet that can accommodate standard 5 mm NMR tubesand weighs only 0.5 kg [184]. Each of the individual magnets form-ing the Halbach rings can be displaced radially for mechanicalshimming, which allowed the authors to achieve the resolutionof 4.5 Hz (0.15 ppm). This magnet was later used to demonstratethat high-resolution 1H NMR spectroscopy can be performed usinga magnet residing in a fume hood [185], demonstrating the poten-tial of the approach for in situ NMR measurements and for theincorporation of NMR probes in chemical process lines.

Different magnet designs are also available. For instance, in a re-cent paper [186] a complete procedure for permanent magnet de-sign, fabrication, characterization and shimming was proposed andused to build a light-weight (1.8 kg) low-cost (100 Euro) magnetwith a 120 mT field (5.1 MHz 1H frequency) with a homogeneityof 12 ppm in a volume of 3 mm3.

2.4. NMR spectroscopy in inhomogeneous fields

As NMR is a spectroscopic technique, it is quite natural thatattention is now being paid to the development of the approachesfor performing spectroscopic studies with mobile and/or unilateraldevices. There are two main directions that are currently being


pursued in this area. One is to further improve the B0 homogeneityas much as possible, as illustrated in the preceding section. Andeven though the spectral resolution achieved with the permanentmagnet systems cannot at present compete with that routinelyavailable with the superconducting magnets, significant progresshas been achieved in this field. It is important to stress that the de-vices and approaches being developed are not intended to replacethe high-resolution laboratory instruments, but rather to expandthe range of samples and environments for which the spectro-scopic and imaging studies can be performed.

Another approach is based on the development of NMR tech-niques that are tolerant to magnetic field inhomogeneities, andmeasurement protocols that can provide fairly well resolved spec-tra even in inhomogeneous fields. One of the possibilities is tomatch the spatial inhomogeneity of the B0 field with that of theB1 field [187–192]. These experiments rely on the use of nutationechoes that refocus the effect of B0 inhomogeneity but retain thechemical shift information. A portable single-sided sensor withspatially matching B0 and B1 gradients was constructed and usedto achieve a spectral resolution of 65 Hz, corresponding to 8 ppmat the 0.2 T field [188,189]. Chemical shift imaging in inhomoge-neous fields was also demonstrated using the spatial B0–B1 match-ing [187,193]. The detection of resolved NMR spectra ininhomogeneous fields is also possible on the basis of the detectionof 2D correlation spectra for B0 and B1 fields with an arbitrary spa-tial correlation if there is a one-to-one correspondence betweenthe two fields [194].

Also being developed are the approaches based on the crea-tion and evolution of multiple quantum coherences including to-tal quantum coherence [195], inter-molecular DQC (iDQC)[196,197], iSQC [198], iZQC [197,199] and iNOE [200]. It is alsopossible to produce better resolved spectra by using coherencetransfer between different nuclei. For instance, a SECSY pulse se-quence yields pairwise chemical shift differences and thus can-cels the effect of an inhomogeneous B0 field [201]. A single-shot time-domain (no FT) spectroscopic experiment has beensuggested [202] which yields chemical shift differences of cou-pled hydrogens belonging to different chemical groups. A differ-ent approach based on the use of ‘‘shim pulses’’ comprising thecombination of modulated gradient pulses and adiabatic rfpulses was shown to ‘‘correct’’ the effective field [203]. Due tothe differences in the evolution times for the chemical shiftsand J couplings, the multiplets in such experiment appear ex-panded as compared to the conventional NMR spectra.

Fig. 1. 1D MR profiles of moisture distribution in a cylindrical sample of fired-claybrick during absorption of water. The experiment geometry is given in the inset.During the measurements, the sample was stepped through the coil, and for eachsample position a group of five points was obtained using frequency encoding andFT. The curves are a guide to the eye. Times after one end of the sample wasimmersed in water are shown near the profiles. The experiments were performed at0.78 T. Reprinted from Ref. [206], Copyright (1996), with permission from Elsevier.

3. MRI of sorption processes


Sorption is important in many technological processes andapplications of porous materials. Water and brine ingress intobuilding materials can accelerate their degradation caused byfreezing, their uptake of ions and corrosion, and affects the gas per-meability and thermal conductivity of materials. Permeability ofbuilding materials is particularly critical in the development anduse of protective engineering structures and containers for nuclearwaste. Transport of liquids and gases through porous materialsplays an important role in catalysis and separation of chemicalcompounds. Transport of moisture and other liquids and vaporsin sorbents is essential in drying processes and in the operationof adsorption pumps. This is only a short list of processes whereunderstanding of sorption is important. In some cases, sorptionof liquids is accompanied by the transport of various solutes, e.g.,the transport of dissolved salts in building materials, contaminantsin soil, etc.

Transport of liquids and gases or vapors is usually driven by therespective concentration or pressure gradients. At the same time,transport of a liquid can be induced by, e.g., a gradient in the con-centration of a solute (e.g., a water/salt system). Vapor pressuregradients can also cause liquid transport. For instance, if a water is-land is formed in a pore and if different vapor pressures exist oneach side of the island, vapor will condense on one side and evap-orate on the other, leading to an effective liquid transport. Othermechanisms of transport, which may act in parallel with othermechanisms, are surface diffusion and film flow.

Mass transport in porous media with a complex heterogeneousstructure of the pore space is a complex process that proceeds atdifferent length scales simultaneously. For instance, for beds ofzeolite crystallites it is common to distinguish diffusion in themacropores formed by the space between the crystallites (inter-crystallite diffusion) and diffusion in the micropores within thecrystallites (intra-crystallite diffusion).

3.2. Building materials and stones

Capillary absorption of water by the bars or rods made of plas-ter [204], mortar [204,205], fired-clay brick (Fig. 1) [10,205–207],sand–lime brick [205] and limestone [204,208] was studied bydetecting the 1D profiles of water content along the samples. Foreach material, the S = S(k) transformation (see Eq. (5)) collapsedthe profiles on a respective master curve (Fig. 2). The D(S) depen-dences demonstrate an approximately exponential growth in mostcases (Eq. (7)), which leads to a relatively sharp absorption front.Similar observations were reported for pre-dried mortar samples[209]. The transport of water in the sample with water/cement ra-tio w/c = 0.4 oven-dried at 105 �C was much faster than in the sam-ple first exchanged with isopropanol and then dried sequentially at

Fig. 2. Boltzmann transformation applied to the 1D moisture profiles measured forvarious types of building materials (symbols) and their simulations using anexponential D(S) dependence (lines). The experiments were performed at 0.78 T.Reprinted with permission from Ref. [205].


40 and 105 �C. Oven drying apparently led to the formation of acontinuous network of larger pores. The evolution of T2 with timewas analyzed and interpreted in terms of water redistribution be-tween the capillary and the gel pores. In another study, 1D profileswere detected for the samples prepared using eight different mor-tar mixtures and dried either in an oven or using isopropanol (as inthe preceding example) before placing one end in contact withwater [210]. For all samples, a sharp wetting front was observed.Both the composition and the drying treatment affected the imbi-bition process, with a slower ingress of water observed in the iso-propanol-dried samples. For each specimen, the profiles collapsedonto a single S(k) master curve. The D(S) dependences were calcu-lated numerically from the S(k) curves and were best described bya sum of two exponential terms, each responsible for a differentwater content range. The authors note that Eq. (7) commonly usedin the modeling of soils and many building materials is not appli-cable in this case. The studies of a brick–mortar interface [205]demonstrated that the picture of water sorption was found to bedifferent depending on whether water was absorbed through thebrick or the mortar end.

However, the results on water transport in the fired-clay brickand the limestone samples [205,208] were later reinterpreted[211] in terms of anomalous diffusion with a ta water front propa-gation and the x/ta coordinate transformation (a = 0.58 and 0.61 forbrick and mortar, respectively) to better collapse the water contentprofiles on a master curve.

GE and STRAFI techniques were used to observe capillary andtotal (including gel) water, respectively, during the water sorptionby cured cement samples [212]. STRAFI was used to observe bulkwater ingress into sealed cure 0.5 water/cement (w/c) ratio sam-ples that had been either air dried or exchange-dried with metha-nol before absorption experiments. A sharp water front wasobserved on the S(k) master curves. Based on the differences inthe T2 times of capillary water and of gel and bound water, the

authors were able to conclude that the advancing water front inthe air-dried sample corresponded to capillary water. Water wasobserved to ingress much more rapidly into the methanol ex-change-dried sample than into the air-dried sample (cf. [209,210]above). The air-dried samples with the 0.3 w/c ratio presumablyhad a closed capillary pore structure as water uptake was minimal,while the methanol exchange-dried sample exhibited an extremelyrapid uptake apparently associated with the drying-induced sam-ple microcracking. In the GE MRI studies of water uptake intocured cement samples, the lower end of the cylindrical sample dur-ing the absorption process was in contact with a wet spongewhereas the upper end was open to the atmosphere. The sealed,underwater or open cured 0.5 w/c ratio samples were studied.An overall drying of the samples was observed until a dynamicequilibrium between the evaporation at the top and the uptakeat the bottom was established. In the case of the open cured sam-ple, first a sharp water front was observed and the highest contentof mobile water was reached at the open end of the sample. Afterthat, a more uniform distribution of water was gradually attained.1D and 2D CW MRI was also used to study water ingress into ce-ment samples [92,94]. As an example, Fig. 3 shows the images de-tected for water penetrating into the rectangular cement sample.The results show that water has almost fully penetrated acrossthe sample after approximately 1 h of soaking, with a further in-crease in signal intensity after prolonged exposure to water. Theauthors note that signal in the right-hand side of the sample in im-age (a) belongs to the chemically combined water with T�2 ofapproximately 10 ls.

1D STRAFI was used to measure the profiles of water absorbedby the dried samples of ordinary Portland cement (OPC) [213]. Inthe S(k) coordinates, all the profiles collapsed on the same mastercurve with a sharp absorption front, indicating that D(S) was asharply rising function. The MRI experiments were combined withcryoporometry measurements and model calculations. The authorsnote that the experimental STRAFI profiles were T2-weighted andfailed to detect water in the partially filled pores at the advancingfront and in the gel pores.

2D SPI was used to observe the wetting profile shape for threedifferent concretes during the first and several subsequent rewett-ing experiments after the samples were dried [214]. To ensure alow content of paramagnetic species, the authors used low ironcontent cement, pure quartz aggregate and coarse sand and an al-most pure silica fine sand to prepare the samples. The water signalwas found to be a nonlinear function of saturation. A calibrationcurve was generated by drying a sample to a known mass (i.e., aknown saturation) and integrating the total signal from the sam-ple. The S(k) master curves exhibited steeper fronts for rewettingexperiments. Both Eq. (7) and a power law D(S) dependence(D = D0Sn) were found to adequately describe the results.

Water absorption by concrete was studied for samples pre-stored at various humidity levels [215]. The 1H SPI technique wasused to study samples with low initial water contents. Samplespre-stored at the high relative humidity levels (up to 90%) couldbe studied using D2O and 2H SE MRI in the absorption experiments.Sharp absorption fronts were observed. The 2H SE MRI and D2Owere also used in the earlier studies [216,217] where even forthe samples dried at 105 �C a significant residual 1H NMR signalwas observed in a SE experiment. A well defined front of ingressingD2O was observed in all experiments, and the front heights weresmaller for higher pre-storage humidity levels. In contrast, theheight calculated from mass gain was independent of the pre-stor-age humidity and was larger than those measured with MRI. Thiswas taken as the evidence that the incoming D2O displaced the‘‘resident’’ water in the sample. This may have significant conse-quences for the transport of solutes (e.g., ions) in porous buildingmaterials. The authors also note that water exchange through the

Fig. 3. 2D MR images of water penetration into a pre-dried sample of OPC detected using 2D MRI after 5 min (a), 10 min (b), 15 min (c), 30 min (d), 60 min (e) and 5 h (f) ofsoaking. The sample was completely sealed except for the left face which was exposed to liquid water. The water reservoir was removed for imaging which was performedusing the CW MRI technique. Lighter shades of gray correspond to higher signal intensities. The experiments were performed at 7 T. Reprinted from Ref. [94], Copyright(2003), with permission from Elsevier.


outer layers of concrete can differ significantly from water ex-change through cut surfaces.

For a hardened white Portland cement (WPC) paste, 1D SE wasused to monitor the replacement of H2O confined within the sam-ple with D2O surrounding it [218]. Formation of HDO and the var-iation of the concentrations of the three isotopic water speciesimply that effective diffusivity depends explicitly on both the timeafter immersion and the spatial coordinate. The effective long-range diffusivity values determined form the MRI profiles andmeasured using PFG NMR were found to be equivalent despitethe large differences in the time scales of the two experiments.The authors state that the diffusivity values are too high becauseca. 75% of the water protons were not detected due to a very shortT2 time.

1D SPI and 3D spiral SPRITE techniques were used to comparewater sorption by self-consolidating concrete containing variousamounts of fly ash [219]. For the sample with 50% fly ash, water in-gress was much faster in the 1 day cured samples than in thosecured for 7 days prior to drying and subsequent sorption. A sharpwetting front was observed to move around the void spaces asso-ciated with non-porous aggregates. Water penetration was incom-plete even after 2 months of exposure and was higher in thesample center than near the edges. In a very impermeable self-con-solidating concrete containing 30% fly ash, the front was parabolic,and changes in the microstructure caused a reduction in the per-meability by blocking the pores. For this sample, no significantchanges in the penetration depth were observed even after45 days. The authors stated that signal intensity in the MRI profilesdirectly correlates with the concentration of evaporable water,which is rather an exception than a rule in porous media MRI stud-ies (see above).

1D STRAFI was used to monitor the development of water con-centration profiles in dry industrial fibrous cement roofing tiles,with one side of the tile exposed to water and another to atmo-sphere [220]. After the initial equilibration period of ca. 30 h, a dy-namic equilibrium between the absorption on one side of the tileand evaporation on the other was achieved, and no further evolu-tion of profiles was observed. The water profiles reflected the lay-ered structure and the non-uniform porosity across the tile.Another type of tile studied had an extra protective layer com-posed mostly of cement and sand. The heterogeneity of the profiles

was much less evident for these samples, and the ingress of waterwas much slower through the protective outer layer than throughthe untreated inner layer of the tile. Water ingress into disks coredfrom various ceramic tiles was studied using 1D STRAFI profiling[221]. Water uptake was fast in unglazed tiles, and the propagationof the water front was Fickian, with the front position changing ast1/2. Glazed wall and floor tiles were resistant to water permeation,unless the glazed surface was damaged by abrasion, in which casethe gradient of water content and a dynamic equilibrium betweenwater entering one surface and evaporating from the other wereestablished. Similar behavior was observed for the lower-porosityvitreous and terracotta tiles. 2D spiral SPRITE, 1D SE, and fournon-MR techniques were used to monitor water uptake by acalcium silicate plate and a ceramic brick [222]. To compare the re-sults provided by the different techniques, Boltzmann transforma-tion (Eq. (3)) was applied. A systematic difference between theresults of different techniques could be observed, which was, how-ever, mostly attributed to the variability of the samples.

The behavior of 50 ll water drops on the surface of asphalts wasstudied at 25 �C [223]. Initially, the drop placed on the surface ofasphalt is expected to have a nearly hemispherical shape. It thenpenetrates into the asphalt surface by capillary rise of the asphaltonto the water drop forming a ‘dynamic lens’. Eventually, a nearlyspherically shaped drop submerged under the asphalt surface isformed (Fig. 4). NMR images were acquired for up to several weeksafter placing the drop on the surface, demonstrating the gradualsinking of the drops into the asphalt, with different rates for as-phalts with different physicochemical properties. At the same time,the drops did not diffuse into the asphalt in all directions but rathermaintained a sharp boundary. The drops were never completelyincorporated into the asphalt even after more than 3550 h of set-ting. The images were used to measure the contact angles aboveand below the asphalt surface at different times. This allows oneto directly calculate the asphalt–water interfacial tension. Wateringress in bitumen samples with embedded salt grains as a modelof bituminized waste products was studied by detecting 1D mois-ture profiles with SE [224]. For a sample containing a soluble salt(NaNO3; S-type), the water penetrated to the depth of only 2 mmeven after 8 months. The profiles increased in intensity with thewater uptake, whereas the penetration depth evolved very slowlyand showed a well-defined wetting front. For the sample with an

Fig. 4. 2D MR images of water drops falling into four different asphalts. Each row corresponds to one sample imaged at different times after the initial placement of the waterdrop on the asphalt surface (indicated in the respective images). The experiments were performed at 4.7 T. Reprinted from Ref. [223], Copyright (2005), with permission fromElsevier.


insoluble salt (BaSO4; I-type), near the surface the increasingamount of water was comparable to that observed for the S-typematrix. However, the moisture transport was much faster andthe front reached the far end of the sample in less than 8 months.For the sample containing both salts, the profiles changed fromthose of the S-type sample in the beginning to those of the I-typesample at long times. The results clearly demonstrated that BaSO4

facilitated the water transport through the hydrophobic materials.Differences were also found in the T1 times of water in thesesamples.

3D Conical-SPRITE was used to image water ingress into Bereasandstone [42]. When one end of the sandstone core was im-mersed in water, a plug-like water front movement was observed,with no further increase of water saturation behind it. When theentire sample was immersed in water, a front moving toward thecenter from all sides of the sample was observed, with a uniformwater saturation distribution behind it. After the penetrating waterfronts met in the sample center, further water saturation increasewas observed in the entire sample. The authors explained this by afilm-type water transport into the sample accompanied by thecounter-flow of air out of the sample in the middle of the poreswith a subsequent filling of larger pores. The interpretation ofthe observed behavior involved the results of DDIF experimentscombined with sample centrifugation. 1D profiling with CW MRIwas used to study water ingress into two cylindrical North Sea

oil reservoir sandstone samples cut in two different orientationswith respect to the sedimentary layers in the reservoir sea bed[94]. For the core with the axis parallel to the sedimentary layers,the ingress of water was much faster than for the sample with theaxis being perpendicular to these layers, as would be expected forthe water traveling along channels formed by the layers and thewater traversing the boundaries between the layers, respectively.The layering effect in the ‘perpendicular’ sample was apparent inthe detected profiles. Capillary water imbibition in the initiallydry samples was used to study the geometry and connectivity ofthe fractures in sandstone cores [225]. The open fractures were ob-served to act as channels for preferential water ingress, with theflood front becoming flatter at later times. The results were tenta-tively explained by a systematic difference in wettability of thenatural pore space and the fractures. The sealed fractures showedreduced water saturation.

3.3. Building materials and stones with protective treatments

To extend the lifetime and improve the properties of both mod-ern building materials and historic structures made of stone, a bet-ter control of water transport in these materials is required.Therefore, building materials are often treated with hydrophobic,consolidating or other surface coating materials in order to reducethe uptake of liquid water without restricting the evaporation of


water out of the porous material. In the case of cement-basedmaterials, the hydrophobic additives can be introduced while pre-paring the initial mixture. For instance, the permeability of hard-ened cement samples prepared with both clay and poly(vinylalcohol) (PVA) additives was shown to be much lower as comparedto the samples containing only one of the additives [226]. In thepresence of clay and hydrophilic PVA, cross-linking produced ahydrophobic structure that made the cement resistant to water.In addition to demonstrating the difference in water transport forthe treated and untreated samples, MRI can be used to visualizethe application of a treatment to a porous material since treat-ments are often applied in the form of a solution. The ingress ofalkyltrialkoxysilane solution in methanol into hardened mortarsamples was studied using 1D STRAFI [227,228]. To exclude thebackground signal, mortar was prepared using D2O. The treatmentsolution penetrated to a depth of 1.5 mm and then stopped. Afterthe sample was dried, it did not imbibe water added to its surface,whereas a rapid water penetration was observed for an untreatedsample. Application of two siloxane coats 24 h apart to the samesample revealed that the second coating penetrated to the samedepth as the first one.

Water uptake by the samples of a highly porous biocalcarenite(Lecce stone) was studied at 0.2 T using SE [229–232]. The stonesamples were treated with solutions of either an alkyl alkoxysilaneoligomer or an acrylic resin. Absorption of water by untreated sam-ples was rapid and uniform. The amount of water absorbed wasmuch lower for the siloxane than for the acrylic treatment. Therock sample treated with siloxane did not absorb any water what-soever through the treated face [231]. Absorption through the un-treated face exhibited a significantly decreased value of theequilibrium front height, indicating that the polymer was not uni-formly distributed in the sample. For the sample treated with ac-rylic polymer, the rate of water ingress decreased markedly ascompared to the untreated sample. The polymer solution, appliedfrom one side only, reached the far side of the sample as revealedby the absorption results. The quantity of water absorbed at thebeginning of the process was much higher for absorption throughthe untreated face than through the treated one. For sampleswhere the penetration depth of the treatment was intentionally re-duced, the polymer distribution was revealed when the water frontreached the polymeric material in the rock if absorption was per-formed through the untreated face (Fig. 5) [229]. Absorptionthrough the treated face depended on the treatment procedureand the amount of polymer introduced. No water absorptionthrough the treated face was observed at all in [230]. Displacementof the water front for the untreated sample and for the absorptionthrough the untreated face of the treated sample was proportionalto t1/2. Prolonged exposure to absorbed water and especially therepetitive absorption–desorption cycles led to the loss of hydro-phobic activity of the treatment [229]. The absorption processwas also compared for two different methods of application of

Fig. 5. 2D MR images detected during capillary water absorption by a sample of Lecce swas absorbed through the untreated face of the stone. The distribution profile of the poutlined in the images. The experiments were performed at 0.2 T. Reprinted from Ref. [

the hydrophobic treatments [232]. Application using a brush ledto essentially no absorption through the treated face, whereaswater penetration through the untreated face of the same sampleand for an untreated sample was similar. The sample treated bycapillarity displayed slower water absorption than the untreatedsample. Capillary treatment apparently leads to a good hydropho-bic behavior without blocking the pores, which is essential for effi-cient vapor transport.

A calcareous sedimentary stone called ‘‘Pale Finale’’ was treatedwith either 1,6-hexanediol diacrylate (HDDA) monomer or a mix-ture of butyl methacrylate (BMA)/ethyl acrylate (EA) applied as asolution in acetone containing polymerization initiator AIBN[233]. Polymerization was performed by either heating the entiresample to 50 �C for 24 h (in situ) or by briefly heating only one sideof the sample to 200 �C (frontal polymerization). A commercialpolymeric product Paraloid B72 was applied to control samples.A Bruker NMR ‘‘ProFiler’’ was used to measure T1 and T2 times atthree different depths at ca. 16–18 MHz, and 3D GEFI or MSMEand 2D SPI were used for imaging at 300 MHz. For the frontaland in situ polymerizations, the polymer was observed to give asubstantial signal, which was then subtracted. The treatment withParaloid B72 did not impair the water uptake. At the same time,water uptake was strongly reduced in the two other samples, espe-cially for the in situ polymerization of BMA/EA, as confirmed byboth the water signal intensity and relaxation times.

The ingress and spatial redistribution of a finite supply of alkylalkoxysilane solution in methanol applied to one face of a sand-stone specimen was studied at 30 MHz using oscillating gradients[234,235]. The 1D profiles demonstrated that the treatment pene-trated up to a depth of 6–10 mm in the first few minutes and didnot go much further after a period of 1 h (Fig. 6). Signal intensitywas observed to gradually decrease and approach the levels ob-served in the untreated specimen after 24 h. This loss of signalcan be attributed both to a reduction in the proton density (solventevaporation) and shortening of the spin–spin relaxation time of thetreatment. The ingress of water into the treated and the untreatedsamples was compared [234,236]. When a limited amount of waterwas applied to the untreated surface, during the first 24 h therewas relatively little redistribution of water within the treated sam-ple as compared to the untreated one, and in particular little waterpenetrated into the treated region. However, after 72 h liquidwater had moved from the untreated portion of the stone speci-men and entered the capillary pore structure of the treated stoneface. The experiments with an essentially infinite supply of water[234] confirmed that the treatment inhibited water movement atshort times, but after a prolonged continuous contact of the sam-ples with water the treated capillary structure was unable to pre-vent the ingress and redistribution of liquid water. The same MRIapproach was used to study the effect of the alkyl methoxysi-lane/methanol treatment cure time, cure temperature and hydra-tion of a sandstone sample on the subsequent water transport

tone. (a) Untreated sample; (b) sample treated with polymer solution. In (b), waterolymer becomes visible after 3 h of water absorption. The sample boundaries are

229], Copyright (2001), with permission from Elsevier.

Fig. 6. 1D MR profiles showing the ingress, cure and drying of alkoxysilanetreatment applied to the left side of a sandstone sample. The sample extends from 0to 20 mm. The profiles were recorded before treatment (dashed line) and (from top)12 min, 80 min and 18 days after treatment. The experiments were performed at0.7 T. Reprinted with kind permission from Springer Netherlands: Ref. [235], Fig. 2.

Fig. 7. 1D 23Na MR profiles detected during the ingress of brine into an OPC samplewith a water/cement (w/c) ratio of 0.4 as a function of soaking time. The profileswere detected using a CW MRI technique. The experiments were performed at 7 T.Reprinted from Ref. [95], Copyright (2005), with permission from Elsevier.

Fig. 8. 1D 7Li MR profiles of lithium absorption into a cement paste mortar. Areference sample is included as a check on the long term instrument stability. Theimages represent the lithium distribution after 3 (solid circles), 6 (open circles), 9(solid triangles) and 22 h (open triangles) of exposure. The DHK-SPRITE detectionscheme was used for profile detection. The experiments were performed at 2.4 T.Reprinted from Ref. [79], Copyright (2006), with permission from Elsevier.


[235]. When water was applied to the treated end of the samplecured at 50 �C, a substantial hydrophobic effect with very littlewater transport through the treated material in 2 days was ob-served. For the sample cured at ambient temperature, a pro-nounced hydrophobic effect was observed, too, but the profilesdetected provided the direct evidence of water pumping througha treated surface.

3.4. Transport of solutes

Transport of solutes such as salts is of paramount importance inbuilding materials. While the ingress of solutes accompanies thetransport of water, there can be some major differences betweenthe two processes. The absorption of 4 M NaCl aqueous solutioninto calcium silicate brick was studied by simultaneously detectingthe 1D profiles of water (1H MRI) and sodium (23Na MRI) distribu-tion [11]. The 23Na profiles reflected only the dissolved Na ions, butthe amount of adsorbed Na could be found using the experimen-tally measured adsorption isotherm. The adsorption front of so-dium lagged behind the water front, with hardly any Na presentnear the wetting front. In the S(k) coordinates, the water and the23Na profiles collapsed onto the respective master curves. Thewater results could be modeled assuming the D(S) dependence ofEq. (7). At the same time, the Na master curve did not exhibit asharp front of Na concentration and could not be modeled usinga diffusion equation even taking into account the adsorption ofNa ions. Pure water was shown to be absorbed somewhat fasterthan the NaCl solution. SPRITE was used to detect 1H, 23Na, and35Cl profiles during the capillary uptake of NaC1 aqueous solutionby WPC mortar with different water-to-cement ratios [219,237].Both sodium and chloride ions were observed to move with thewater being absorbed. For a higher w/c ratio, the penetration ofNaCl solution was more rapid, and after 3 h all three species werepresent along the entire sample and only an increase in concentra-tion with time was observed. After 72 h, however, the distributionsof the three species in the sample were quite different. The de-crease of the 35Cl signal with time was associated with the chem-ical and physical binding of chlorine ions to the cement paste. CWMRI with 23Na signal detection was also used to study the penetra-tion of brine into OPC samples prepared using various w/c ratiosand curing conditions (Fig. 7) [92,95].

Absorption of lithium into mortar was studied using 1D 7Li DHKSPRITE [79]. One end of a cylindrical sample was submerged

1–2 mm into a lithium nitrate solution and was periodically re-moved for imaging. Due to the short relaxation times of adsorbedand precipitated lithium, only Li ions in the solution gave an obser-vable NMR signal. As expected, the penetration depth of Li ions in-creased with contact time, and after 22 h the penetration depthwas approximately 35 mm (Fig. 8). In addition, the signal intensityat a given point within the penetration region, and therefore the lo-cal lithium concentration in solution, increased with time. Densityweighted profiles were constructed by extrapolating multipleT�2-weighted profiles to the zero encoding time tp. 1D centric scanDHK SPRITE was also used to acquire the distribution profiles offree Li (7Li MRI) and Na (23Na MRI) ions in cement paste, mortarscontaining inert sand, and mortars containing reactive silica[238]. The cylindrical surface was sealed with ceramic epoxy tomake the penetration of ions into the cylindrical sample possibleonly through the sample ends. The Na ions were shown to diffusefaster than Li ions, but soaking in a solution with a higher Li con-centration favored Li diffusion and hindered Na diffusion. Both Liand Na ions penetrated significantly slower in mortar as comparedto the cement paste. In mortars containing silica, reactive con-sumption of a substantial amount of Li and Na (at low Li contents)took place.


MRI was also used to monitor the dynamics of the preparationof supported catalysts by impregnation of a porous support bodywith a solution of an active component precursor and/or variousadditives [239]. Two general strategies were used in these studies.One is based on the detection of relaxation-weighted images of asolvent (e.g., 1H MRI of water) to indirectly map the distributionof a solute or an adsorbate within the support. Complexes of para-magnetic metal ions such as Co2+, Ni2+, Cu2+ or Fe3+ used in thepreparation of various supported catalysts measurably reduce theT1 and T2 times of the solvent. The dynamic redistribution of Co2+

(Fig. 9), Ni2+, and Cu2+ complexes within c-Al2O3 pellets in thepresence of various complexing agents and at various solutionpH values was imaged successfully during the impregnation stage[240–243]. These measurements can provide quantitative concen-tration maps of the paramagnetic ions within the porous supportsif combined with the appropriate calibration experiments that re-late signal intensity or relaxation times to the actual concentra-tions of paramagnetic ions.

During the subsequent drying stage, the active component pre-cursor can further redistribute within the support. To address this,one can saturate the dried sample with a different (e.g., a non-polar) liquid which will not re-dissolve the paramagnetic speciesadsorbed or precipitated on the pore walls and then use the samerelaxation weighting approach [240]. The relaxation contrast ap-proach also works for certain diamagnetic species. In particular,it was found that the relaxation times of water can increase whenaqueous solutions of H2PtCl6, H2PdCl4, and (NH4)6Mo7O24 are usedfor impregnation [240,244]. The origin of this effect is not known indetail, but it is assumed that diamagnetic species either stericallyhinder the access of water molecules to the paramagnetic impuri-ties normally present in the pore walls of the support, or block thesmallest pores of the support. Imaging of both the dynamicimpregnation processes and the final distributions achieved afterthe drying stage (after re-saturation with a non-polar liquid) weredemonstrated [240,244]. As diamagnetic and paramagnetic species

Fig. 9. (a) 2D 1H MR images of a cylindrical Al2O3 pellet at several times after its initial i(low concentration of Co2+), red: low 1H NMR signal (high concentration of Co2+). (b) Quanfrom the 2D images using a calibration curve determined experimentally. The experimeKGaA, Weinheim. Reproduced with permission. (For interpretation of the references to

have the opposite influence on the relaxation times of a solvent,their simultaneous transport can also be studied [245]. In the prep-aration of supported metal catalysts such as Pt/Al2O3, drying of theimpregnated support is usually followed by the reduction of plat-inum to its metallic state. It was reported that upon reduction ofadsorbed hexachloroplatinate, the T1 relaxation contrast becamemuch less pronounced or even unobservable [244]. However, in adifferent study [246] it was demonstrated that the spin–spin relax-ation time T2 of n-heptane was different in the catalyst (Pd/Al2O3)and support (Al2O3) particles. The same effect was observed in cat-alyst bodies with a non-uniform spatial distribution of the metal.The applicability of the relaxation weighting approach was alsodemonstrated for biocatalysts comprising bacterial cells of Arthro-bacter sp. immobilized by entrapment on silica xerogel poroussupport intended for a heterogeneously catalyzed glucose isomer-ization process [247]. The unmodified support and the biocatalystcould be distinguished on the basis of the T2 relaxation times ofglucose in an aqueous solution.

Another strategy is based on the direct imaging of the solute orthe adsorbate molecules containing suitable magnetic nuclei. Con-trary to the relaxation weighting approach, the direct imaging usu-ally reflects only the dissolved species and is insensitive to those inthe solid phase (e.g., adsorbed or precipitated) unless they are in arapid exchange with solution. For instance, 31P MRI was used tomonitor the transport of HxPOð3�xÞ�

4 ions into a c-Al2O3 pellet[240,248]. In addition, the distribution of the phosphates in the so-lid phase could be imaged directly using 31P MRI after the pelletswere dried at different stages of impregnation, demonstrating thatdirect MRI of the solid phase is sometimes possible without the re-course to solids imaging techniques (Fig. 10). These experimentswere also able to reveal a strong interaction of a solute with theporous support. When a dry c-Al2O3 pellet was immersed in anaqueous solution of H3PO4, the capillary imbibition of water wascomplete within a few minutes as confirmed by 1H MRI, while31P MRI revealed a much slower propagation of the phosphate

mpregnation with a 0.20 M aqueous solution of Co(NO3)2; blue: high 1H NMR signaltitative 1D profiles of the distribution of Co2+ ions along the pellet diameter derived

nts were performed at 7.05 T. Ref. [241]. Copyright Wiley-VCH Verlag GmbH & Co.color in this figure legend, the reader is referred to the web version of this article.)

Fig. 10. (a) Dynamics of the impregnation of a c-Al2O3 pellet with an aqueous solution of H3PO4. 2D 31P MR images of the liquid phase were detected with 8 min 38 s acquisitiontime per image. Only selected images are shown, with the time after pellet immersion indicated above each image. (b and c) 2D 31P MR images of the solid phase showingphosphate distribution in dried c-Al2O3 pellets. The pellets were dried after impregnation for 18.5 h (b) and 95 min (c). Images were acquired in 18 h (b) and 23 h (c) with114 lm � 247 lm spatial resolution. The experiments were performed at 7.05 T. Adapted with permission from Ref. [248].

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front in the pellet (Fig. 11). An example of the direct detection ofthe metal atom is the 195Pt MRI study of the impregnation of a c-Al2O3 pellet with an aqueous solution of H2PtCl6 [248].

1H MRI of the solvent (water) has been used to study transportof paramagnetic species and their sorption in other materials,including metal ion sorption in quartz sand columns [249] andNi2+ uptake by the roots of a hyperaccumulator plant [250]. Theuptake of paramagnetic Ni2+ ions from a liquid-saturated modelporous media (packs of glass beads or quartz sand, or loamy soil)into a layer of an ion-exchange resin separated from the solutionby an ion-permeable gel was studied using 2D TSE and spoiledGE [251]. A linear relation between the Ni2+ concentrations andthe signal intensity over a wide range of concentrations was ob-served. The gradient of Ni2+ ions near the gel surface was observedin real time using T1 mapping as Ni2+ ions were absorbed by the re-sin, with the depletion zone increasing over time in size and in the

Fig. 11. 2D 1H (a) and 31P (b) MR images detected 250 s after immersion of a dry Al2O3 psignal intensity. Bright outer ring in (a) corresponds to water outside the pellet. Th[248].

degree of Ni2+ depletion. A null-point imaging technique was ap-plied to monitor transport and accumulation of Cu2+ ions in algi-nate gel [252]. An important area of MRI application covers thestudies of immobilization of heavy metal ions by various matricesincluding alginate-based biosorbents [253,254], immobilized yeastcells and algal biomass [254], and various biofilms [255–257].

3.5. Sorption of gases and vapors

Many porous materials can adsorb various vapors and gases.Adsorption of water vapor by the sandstone rock cores of variouscompositions, porosities and permeabilities at saturation levels be-low the vapor percolation threshold has been studied using GEwith an oscillating gradient [228,258]. The results were modeledbased on parallel transport of water in the vapor phase and wateradsorbed on the pore walls, with a dynamic local equilibrium

ellet with an aqueous solution of H3PO4. Lighter shades of gray correspond to highere experiments were performed at 7.05 T. Reprinted with permission from Ref.

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Fig. 12. (a) Geometry of the sorption experiment. (b) 1D profiles showing sorptionof water vapor in a bed of zeolite 4A. Selected profiles detected using the SPRITEtechnique are presented. The time elapsed from the beginning of the process isshown for later profiles. The experiments were performed at 2.4 T. Adapted fromRef. [262], Copyright (1999), with permission from Elsevier.


between the two phases. Assuming the adsorption isotherm of theform of Eq. (10), the Deff(SADS) dependence was found to satisfy Eq.(9) below the vapor percolation threshold.

Mass transfer in zeolites is of interest because of their wide usein separation and drying processes and in industrial catalytic reac-tions. Zeolites are mostly available as small crystallites and are of-ten used as granular beds. MRI has been used to study adsorptionof various gases and vapors by zeolites. The movement of the ad-sorbed water front in the adsorbent bed comprised of zeolite 4Apowder has been studied in detail using oscillating gradients[259–261] or SPRITE [262]. The shape of the adsorption front andthe character of its propagation depended strongly on the relativeefficiency of the transport of water vapor in air in the inter-particlespace and the transport within the individual zeolite particles. Forthe relatively small particles (a few lm), it is expected that diffu-sion of water vapor in the inter-particle space is the rate-limitingprocess, while the equilibrium between the adsorbate concentra-tion in a particle and the vapor pressure above it is described byan adsorption isotherm. In such case, the adsorption process canbe described with one nonlinear diffusion equation, with the effec-tive diffusivity depending on the amount of the adsorbed water.For an exponential adsorption isotherm of Eq. (10), Deff(SADS) couldbe described with Eq. (9) [259,260]. Note that in these studies, thetransport of adsorbate was considered to proceed along the bed,i.e., in parallel to the vapor transport. Similar experiments wereperformed for two contacting layers comprised of 3 lm zeolite4A particles with different initial water contents [260,261]. The re-sults demonstrated that lower water contents and higher temper-atures made the intra-particle transport more important. Even fora sealed sample, about 10% of the integrated NMR signal was lostas a result of an increasing fraction of the short T2 component[261]. For relatively long zeolite beds, a sharp front advancing lin-early with time and with little concentration gradient behind thefront was observed at short times. At longer times, the front ad-vanced with time as t1/2. For two contacting layers saturated withH2O and D2O, respectively, the high vapor pressure led to a muchfaster equilibration than for a wet and a dry layers brought intocontact [260].

When a loosely packed dry zeolite bed was brought in contactwith humid air, in the beginning of the adsorption process theamount of adsorbate in the surface layer rapidly reached a maxi-mum value, followed by the propagation of a sharp adsorptionfront into the adsorbent bed which apparently was according tot1/2 (Fig. 12) [262,263]. At the later stages of the adsorption process,the front became less sharp and a low adsorbate concentrationwing developed. The T1 times of water at the adsorption frontand behind it were different, possibly indicating that the localiza-tion of the molecules in the zeolite cages and the accompanyingchanges in molecular mobility were not instantaneous [262]. Fora compacted zeolite sample, absorption of atmospheric moisturewas observed to lead first to the full hydration of the exposed sur-face in about 6 h, and then the front of full hydration started topropagate into the sample approximately linearly with time (CaseII transport – see Section 4.1) [264].

Adsorption of vapors and gases by zeolites was studied in theabsence of air by MRI [265] or combination of MRI with PFGNMR [266,267]. Gradual propagation of a sharp adsorption frontwas observed in a bed of NaX zeolite particles a few lm in sizeupon adsorption of water vapor or butane [265] or n-hexane vapor[266,267]. Initially, the adsorption took place in the entrance re-gion of the bed [265,266]. This region attained the maximum ad-sorbed amount before the front started to move into the bed,indicating that intra-particle transport was fast. Propagation ofthe front into the bed was accompanied by a reduction of theamount of adsorbate in the entrance region as the overall amountof adsorbate in the system was limited. The reduction of the vapor

supply rate to the bed by placing glass wool on top of the zeolitebed led to a more gradual concentration change in the sample[266]. For 40 lm particles, the inter-particle transport was no long-er the limiting process and the adsorbate (butane) remained uni-formly distributed within the bed, whereas the overall amount ofthe adsorbed butane gradually increased with time [265]. Adsorp-tion and desorption behavior of propane (mixture with He) andwater vapor in a single NaX extrudate was monitored and analyzedin terms of the diffusive transport of adsorbate in the macroporesof the extrudate and the accumulation in zeolite crystals governedby the adsorption isotherm [263]. The forms of the concentrationprofiles during adsorption and desorption were found to be mark-edly different and provided direct evidence of the onset of capillarycondensation at high loadings.

The study of adsorption of hydrocarbons in a fixed bed ofHZSM-5 zeolite was performed [268,269] by bringing the degassedsample of the zeolite into contact with the supply of liquid hydro-carbon in equilibrium with the vapor phase. For benzene adsorp-tion, 1D profiles showed a strong concentration gradient at shorttimes (<0.1 h), with benzene concentration decreasing from thetop of the bed where vapor adsorption took place toward the bot-tom of the sample. At times longer than 0.2 h, the profiles becameuniform, and thus further adsorption was controlled by the intra-crystallite transport. For n-hexane, the profiles were uniform al-ready after 0.03 h. When both hydrocarbons were present, benzenewas first adsorbed preferentially in the bottom layers and thenstarted to displace n-hexane adsorbed in the top layers until equi-librium was reached over the entire sample. To distinguish the twohydrocarbons during the competitive adsorption, one of the twowas used in a perdeuterated form.

A setup was designed to perform chemical shift imaging with-out the use of magnetic field gradients. It is based on the use of a

Fig. 13. Chromatographic response for a pulse of a mixture of ethane and propaneinjected into a He carrier stream flowing through a column packed with pellets ofzeolite 5A. The 1D MR profiles were detected in 30 s each for 3.5 h. Theexperiments were performed at 2.35 T. Adapted with permission from Ref.[263].

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small-height rf coil for detecting NMR spectra and a vertical repo-sitioning of the sample with a stepper motor in 50 lm incrementsto add spatial resolution in one dimension [270]. In addition, aniterative algorithm was implemented to reconstruct the spectracorresponding to each elementary slice from the spectra measuredfor all sample positions to improve spatial resolution. This setupwas employed to study benzene vapor penetration into a ZSM-5zeolite bed [270,271]. The adsorption was initiated by breakingthe glass wall between the volume containing liquid benzeneand a small hammer and the evacuated volume containing the zeo-lite bed. The concentration of adsorbed benzene was monitored asa function of the coordinate along the bed. The results were mod-eled under an assumption that transport of the vapor took placealong the bed axis while transport of the adsorbed phase occurredin a perpendicular direction in a large number of very thin layers ofa porous solid material. As a result, the diffusivity values Dinter andDintra as functions of a spatial coordinate and time were extracted.In this study only one chemical was present, but the approachshould be applicable for studies of multicomponent transport aswell since chemical shift information is available in suchmeasurements.

Diffusion of benzene in HZSM-5 zeolite in powder or pellet form[272] and of 2,3-dimethylpentane (DMP) in HY zeolite pellets withdifferent coke amounts formed during n-heptane cracking[272,273] was studied. For adsorption of benzene vapor inHZSM-5, the 1D profiles remained rectangular at all times. Theamount of adsorbed benzene as a function of time was differentfor the zeolite powder and a palletized sample. Modeling was usedto evaluate the intra-crystallite diffusivity of adsorbed benzene.For DMP in coked HY pellets, the profiles exhibited a maximumwhich was moving along the sample during adsorption. This wasinterpreted as the superposition of two competing processes: theinter-crystallite diffusion and the intra-crystallite diffusion ofDMP from uncoked to highly coked zones of the crystallites. The1H MRI studies were performed in combination with 129Xe NMRspectroscopy. Adsorption of benzene (n-hexane) in a zeolite bedwith or without preadsorbed n-hexane (benzene), and simulta-neous adsorption of the two chemicals was studied for 40 lmHZSM-5 zeolite crystallites forming a loose bed or packed withor without binder [274]. In the co-adsorption experiments, one ofthe two chemicals was perdeuterated. Modeling of the experimen-tal results was used to evaluate intra-crystallite diffusivity values.Differences in the transport behavior were clearly observed for thethree bed types. Competitive adsorption showed a transient behav-ior with a non-uniform adsorption of both chemicals, initiallyreflecting the kinetics of adsorption and later leading to a uniformdistribution with relative amounts governed by thermodynamics.Hexane was shown to diffuse faster but to adsorb more weaklyas compared to benzene. Propagation of an adsorbate (methane,ethane, or propane) introduced as a pulse into a He carrier streamwas studied in 5A zeolite bed or bed of 13X zeolite extrudatesusing 1D SE or SPRITE [263]. The results were modeled takingthe corresponding adsorption isotherms into account. For a mixedpulse of ethane and propane, two peaks propagating at differentvelocities along the bed were observed, with the weaker adsorbingethane propagating faster (Fig. 13).

3D GE was employed to study the single-sided ingress of liquidwater into cylinders prepared by compacting moist zeolite NaYpowder at ca. 15 MPa and its subsequent drying [275]. A calibra-tion curve was measured to obtain quantitative local water satura-tion values. Moisture profiles were plotted as a function of k0 =x/tc/2. The profiles appeared to collapse on a single master curvefor c = 0.36 ± 0.04 and not for c = 1 as in the case of normal diffu-sion (see Eq. (3)). The anomalous subdiffusive behavior could bethe result of the irreversible changes in the pore structure duringthe ingress of water into a fine particle zeolite powder compacted

by high pressure. The measured value of c was not a universalproperty of zeolite systems and depended upon their previous his-tory. For instance, for two other samples subjected to differentthermal treatment, the values c = 0.64 and 0.84 were found. TheDc(S) dependences were determined for different values of c, andthe behavior of Dc(S) for c = 0.36 was reasonably close to that ofEq. (7). Interestingly, only relatively small changes in the Dc(S)dependences were found in all three cases in spite of the largechanges in the water transport dynamics. Further studies [276] re-vealed an even more complex behavior. In particular, it was foundthat the Dc(S) dependence found at the early stage of water ingressmay be inapplicable over the entire duration of the process. Theobserved loss of signal at longer times suggested that some kindof a material relaxation process might be involved. It was possibleto separate the process into two regimes: a short time regimewhere the relaxation had not yet affected appreciably the diffusionprocess, and a long time regime where the relaxation process hasbeen completed and further transport was governed by diffusiononly. For the sample with c ca. 0.4 at the early stages of water in-gress, the long time regime scaled with the same value of c but theshort and long time concentration profiles collapsed onto two dif-ferent master curves. A relaxation of the short time regime towarda long time regime was deduced, with the Dc(S) dependence dis-playing a more rapid growth at long times. The water ingress pro-cess in a more porous sample prepared using lower pressure wasmuch faster and led to a much larger water uptake.

SE SPI with 13C NMR signal detection was employed to detect1D profiles of 13CO2 (99% 13C-enriched) density with 1 mm spatialresolution inside a bed of dehydrated zeolite 5A during adsorptionand desorption processes [277]. The acquisition bandwidth couldbe significantly reduced using this technique, which led to a factor4.3 improvement in SNR. During CO2 adsorption, propagation of anadsorption front along the bed was observed (Fig. 14). Desorptionof CO2 was achieved by passing a stream of He through the bed ini-tially saturated with CO2. In contrast to adsorption, desorption wascharacterized by a gradual and almost uniform decrease of theamount of adsorbed CO2 along the bed. The differences in behaviorwere discussed in terms of the concentration-dependent diffusivitymechanism and heat release/consumption effects. A linear rela-tionship between the desorption rate and the square root of timewas observed.

The so-called selective water sorbents (SWS) are based on por-ous materials impregnated with hygroscopic salts. SWS are able toefficiently absorb water (or alcohols) vapor and release significantquantities of heat, and therefore can be used in the drying of gasesand for the development of heat pumps and chemical heat accu-mulators. To study adsorption of water vapor by silica gel or alu-mina pellets containing CaCl2, an individual cylindrical pellet was

Fig. 14. Adsorption of 13CO2 in a bed of zeolite 5A. The intensities were obtained byextrapolating the T2-weighted profiles to TE = 0. The 1D 13C MR profiles showncorrespond to 10 min (solid circles), 40 min (open circles), 80 min (solid triangles),and 120 min (open triangles) of 13CO2 adsorption which was flowing from left toright. The bed is located between 5 and 30 mm positions. The experiments wereperformed at 2.35 T. Reprinted with permission from Ref. [277].

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Fig. 15. Dynamics of water vapor sorption by a cylindrical silica gel pelletcontaining CaCl2. Air was supplied at 390 l/h flow rate and 55% relative humidity.(a) 2D MR images accumulated in 13 min 39 s each using SPI technique. The overalltime span of the experiment was 218 min. (b) 1D MR profiles of water content alongthe diameter of the pellet accumulated in 34 s each using SE technique; every 8thprofile is shown. The overall time span of the experiment was 290 min. Theexperiments were performed at 7.05 T. Reprinted with permission from Ref.[278].

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placed in the MRI probe with its flat surfaces covered to ensure ra-dial transport only [278,279]. A constant stream of humidified airwas supplied to the pellet. Both the 1D profiles of the radial distri-bution of water and 2D transverse images (Fig. 15) have revealedthe formation of a sharp adsorption front, indicating that the pres-ence of a hygroscopic salt within the pores of a mm-sized pelletmade capillary transport inefficient. The limiting stage of theadsorption process was the transport of adsorbed water from thesurface into the interior regions of the pellet. Numerical simulationof the diffusive water transport reproduced the experimental pro-files quite well (Fig. 16) for a D(S) dependence of Eq. (7) [278,280].For the pellets containing CuCl2 with an initially non-uniform dis-tribution of the salt, the contrast introduced by the paramagneticCu2+ ions made it possible to qualitatively monitor the redistribu-tion of the salt upon the repetitive adsorption/drying cycles[278,279]. For the pellets with a substantial initial water content,a sharp adsorption front was not observed [278]. Water vaporadsorption studies were also performed with granular beds ofSWS pellets [279,281]. A stream of humidified air was passedthrough a cylindrical bed, and 1D profiles were detected alongthe bed axis. For an adequate description of the propagation ofthe adsorption front along the bed, the effects of the intra-pelletmass transport, the flow dispersion within the bed and the charac-ter of the water vapor adsorption isotherm had to be taken into ac-count in the numerical model.

The studies were also extended to water vapor adsorption in theabsence of air [245,279]. In the beginning of such an experiment,an evacuated cell containing an SWS pellet (Fig. 17) or bed wasconnected to a flask with water or an aqueous solution of a salt.The important observation was a faster penetration of adsorbedwater front into the pellet as compared with the adsorption atatmospheric air pressure. The rate of adsorption front propagation

Fig. 16. Experimental (a) and simulated (b) 1D water content profiles for a silica gelpellet containing CaCl2 showing distribution of water along pellet diameter. In themathematical modeling, an exponential D(S) dependence was assumed. Theexperiments were performed at 7.05 T. Reprinted with permission from Ref.[278].

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and thus the optimum performance of an SWS material wereshown to depend critically on the pellet composition and

Fig. 17. 1D MR profiles of water content along the axis of a cylindrical silica gel pelletdetection of each profile took 130 s, every fourth profile is shown. The entire sorption expboth (b) flat surfaces. The experiments were performed at 7.05 T. Reprinted from Ref. [2

Fig. 18. Adsorption of water vapor by SWS layers CaCl2/(Al2O3 + binder) in the absenceright: 2.5 mass% of binder). (b) Variation of the size of primary alumina particles (lef24 mass% of CaCl2; right: 5 mass% of CaCl2). The profiles showing the distribution of adexperiments were performed at 7.05 T. Adapted from Ref. [284], Copyright (2010), with

properties such as density, porosity, and permeability. In particu-lar, consolidated layers were prepared from silica gel [282,283]

impregnated with CaCl2 detected during water vapor sorption under vacuum. Theeriment lasted ca. 14.5 h. The pellets were allowed to sorb water through one (a) or45], Copyright (2001), with permission from Elsevier.

of air. (a) Variation of binder (pseudoboehmite) content (left: 20 mass% of binder;t: fraction 0.25/0.5 mm; right: 0.04/0.056 mm). (c) Variation of salt content (left:sorbed water were detected along the axis of a cylindrical layer every 86 min. Thepermission from Elsevier.

Fig. 19. (a) Schematic drawing of the sample used in the adsorption experiment.Five porous materials used in the model sample were a nanoparticulate Al2O3

powder, a nanoparticulate ZnO powder, partially sintered ceramics made from thepowders, and Vycor glass. A sealed vial of C4F8 gas was included as a fixed reference.(b–d) 2D 19F MR images of the C4F8 gas density in several porous materials. Theimages were acquired at equilibrium gas pressures of 80 (b), 238 (c), and 253 kPa(d) with in-plane spatial resolution of 750 lm � 750 lm and 6 mm slice thickness.Differences in local (sample-to-sample) gas density reflect differences in local gasadsorption due to variations in the porosity, pore microstructure, and surfacechemistry. At low pressures, the stronger signal in the Vycor glass is a reflection ofits higher surface area, while at high pressures the stronger signal in the ceramics isa reflection of the greater porosity. (e) Local adsorption (solid symbols) anddesorption (open symbols) isotherms extracted from NMR images of Al2O3 ceramicsat C4F8 gas pressures ranging from 28 to 253 kPa. The data are plotted as theamount of gas adsorbed per unit mass of solid adsorbate vs. the absoluteequilibrium gas pressure. The experiments were performed at 1.9 T. Reprintedwith permission from Ref. [287].

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Fig. 20. 1D 129Xe MR profiles of hyperpolarized Xe adsorbing into a 7.35 mm o.d.cylinder of porous Vycor glass at 293 K. A lower SNR at longer delays is the result ofthe loss of hyperpolarization. The experiments were performed at 9.4 T. Reprintedwith permission from Ref. [294].

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Fig. 21. Chemical shift imaging of hyperpolarized 129Xe for a glass tube filled withpellets of CaA and NaY zeolites, as shown in the top diagram (a). A 3D image withtwo spatial and one spectroscopic dimensions is shown (b) together with thesections taken at the indicated chemical shifts (c). A 1D 129Xe NMR spectrum isshown at the bottom (d). The 93 ppm chemical shift region corresponds to xenonadsorbed in CaA zeolite, the region at 58 ppm to NaY, and that near 0.5 ppm toxenon in the inter-particle space. The experiments were performed at 9.4 T.Reprinted from Ref. [297], Copyright (2000), with permission from Elsevier.


or alumina [283,284] particles and a binder and were impregnatedwith CaCl2. A systematic variation of the size of the primary silicagel or alumina particles, the size of their mesopores, and theamounts of binder and CaCl2 was used to influence the relativerates (diffusional resistances) of the vapor transport in the inter-particle macropores and of the water transport in the intra-particlemesopores. When the former process was the rate-limiting one, arelatively sharp adsorption front was observed to propagate along


the layer as t1/2. In contrast, for a non-consolidated bed of silica gelparticles [282,283] or for a layer of alumina particles prepared withlow binder content [283,284], the amount of adsorbed water in-creased uniformly along the entire bed. The results demonstratethat by varying the composition and structure of the sorbent layer,it is possible to intentionally switch between the two limiting masstransport regimes within the layer (Fig. 18). Even for the SPI detec-tion with tp = 111 ls, the observed signal intensity was not propor-tional to the amount of adsorbed water at lower water contents, asrevealed by the calibration curve measured experimentally [284].

19F MRI of fluorinated gases (SF6, C2F6, CF4, C4F8) was used tocharacterize ceramic materials [285,286]. 19F MRI of gases in alu-mina and ZnO powders, ceramics and porous Vycor glass at varyingpressures was demonstrated in an MRI-based technique to recover

Fig. 22. (a) 2D MR images of moisture ingress into a paper sample through one surface. Thpaper sample was initially dry. The area below the sample was maintained near 100% relaplacing a granular desiccant directly on the paper sample. (b) Moisture ingress into a papthrough both surfaces of the paper (left) and through one surface of the paper (rightexperiments were performed at 9.4 T. Adapted with permission from Ref. [312].

spatially resolved BET-like adsorption isotherms [287,288], analo-gous to the conventional BET curves but obtained for each imagevoxel (Fig. 19). The capabilities of the technique were demon-strated for Y-TZP ceramic samples with spatially heterogeneousporous structure [288,289].

The sensitivity in gas phase NMR and MRI can be enhanced byseveral orders of magnitude using the so-called hyperpolarizationtechniques. In particular, optical pumping can be used to hyperpo-larize noble gases such as 3He, 129Xe and 83Kr [48,290–298]. For in-stance, 1D MR profiles were detected as a function of time forhyperpolarized xenon diffusing into a cylinder made of Vycor glass[294] (Fig. 20). Fitting the experimental results with the diffusionmodel, the authors determined the diffusivity value D = 2.2 �10�8 m2/s, which is in good agreement with the values obtained

e physical dimensions of the paper sample are outlined with dashed rectangles. Thetive humidity (RH), while the area above the sample was maintained near 0% RH byer sample through both surfaces. (c) Through-plane 1D moisture profiles for ingress). The profiles were extracted from the center of the images shown in (a,b). The

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from the uptake and PFG experiments. Continuously flowinghyperpolarized xenon was used to demonstrate the possibility toacquire separate images of hyperpolarized 129Xe (129Xe⁄) in thegas phase and in different porous materials based on the differencein the respective chemical shifts [297] (Fig. 21). Hyperpolarizedgaseous hydrocarbons can be produced by hydrogenation of theirunsaturated precursors with parahydrogen over heterogeneouscatalysts [239,299–303]. In combination with cross-polarizationor SPINOE (spin polarization induced nuclear Overhauser effect),this can be used to enhance NMR studies of surface species[304–306]. However, the relaxation is often accelerated by theinteraction of gas molecules with the pore walls, which may resultin certain limitations on the use of hyperpolarized gases in porousmedia research.

3.6. Other studies

MRI has been employed to investigate the sorption of liquids bya broad range of other materials as well. The NMR MOUSE wasused to study the ingress of oil under different load conditions intoa sample constructed from three 80 lm thick layers of non-woventextile material composed of meltblown polypropylene fibers, withthe two outer layers pretreated with a fluorocarbon to make themliquid-repellent [307]. The 1D profiles of oil content along thedepth coordinate were extracted. The gradual increase in the oilcontent in the middle layer was observed with essentially no oildetected in the repellent layers, presumably because the overallvolume of transport channels in the repellent layers was small. Dif-fusion of silicone oil from an oil wet sodium carbonate powder tosodium perborate powder packed vertically in a tube was studiedby detecting 1D profiles [308]. The oil concentration remainedessentially uniform across the sodium carbonate powder in thecourse of the redistribution process.

The ability of polyurethane foams to resist water penetrationwas studied [309]. For polyurethane cubes immersed in water,after a 67-day exposure time only small soaked regions close tothe surface were visible, whereas for a sample with manifoldimperfections a network of water-filled channels and cavitiescould be observed. One sample studied exhibited a very high rateof water ingress and a complete saturation with water after 3 days.To test the sealing properties of polyurethane foams, the sampleswith centrally embedded PVC rods were subjected to a water pres-sure of 0.1 bar for 21 days. The elevated signal intensity inside thefoams indicated various degrees of water penetration. The samplewith morphology characterized by only a small number of visibleimperfections nevertheless demonstrated a high isotropic waterpenetration rate after 8 h and completion of water absorption after3 days. The sample with most imperfections showed a dense net-work of water-filled caverns and channels after an exposure timeof 67 days.

Capillary imbibition of liquids into a porous bundle of alignedglass fibers was studied using 2D SE [310]. The samples weresealed at the ends so that 2D radial transport took place. Aqueoussolution of CuSO4 or its mixture with corn syrup were used. Tomonitor the process from the very beginning, a release mechanismwas devised to drop the sample into the liquid inside the MRIinstrument. The deviation of the results from an analytical solutionwas explained as a result of the air being trapped in the inner partof the sample by the incoming liquid. Indeed, for samples with anaxially inserted perforated tube the impregnation was faster andthe liquid front reached the perforated tube, indicating that air inthat sample could leave without creating significant back pressurethat could retard the liquid front propagation. Also, for sampleswith a higher solid volume fraction the water uptake was slower,and the density of packing became a governing factor toward the

end of the impregnation process when the presence of the perfo-rated tube was much less important.

Water penetration into the 0.5 mm thick pine layers glued to-gether with polyvinyl acetate (PVAc), urea formaldehyde (UF) orphenolic resorcinol formaldehyde (PRF) resins was studied withthe use of GARField 1D profiling [143]. The UF glue clearly formeda barrier to water transport for times up to 1 day. In contrast, thePVAc glue redissolved in water and thus did not present a barrierto water transport. The PRF glue exhibited an intermediate behav-ior and allowed water transport but at a reduced rate. Polyester–styrene was polymerized in situ on a block of spruce and imagedusing 2D SPRITE in combination with sample heating by a streamof hot air [311]. The polymer was observed at the penetrationdepths from 0.2 to 0.7 mm across the sample as a result of the pen-etration of the polymer precursors before the polymerization pro-cess was complete.

Sorption of water vapor by 1.2 mm thick samples of two-ply pa-per, both from one and both sides, was studied using 2D SE MRI formoisture contents in the range from 0% to 20% with ca. 50 lm spa-tial resolution along the sample thickness (Fig. 22) [312]. Success-ful modeling of the results was achieved with the D(S) dependenceof Eq. (7). A calibration curve was used to compare calculatedmoisture content profiles with the experimental results.

Other studies that may be mentioned cover the transport ofwater in soil (humus) [313,314], clays [92,315,316] and chalk plugscontaining oil [317], soaking of wood [318], in vivo and in vitrostudies of moisturization and drying of skin and the effects of otherliquids and moisturizing products [147,319–321], and formationand dynamic behavior of solid gas hydrates in porous materials[322,323].

4. MRI of polymer swelling


The interactions between polymers and liquids or gases accom-panied by swelling, gelation and dissolution of the polymers are ofpractical importance for fabrication, processing and use of manypolymeric materials. The polymer–solvent systems can exhibit var-ious types of mass transport. Case I transport of a solvent obeysFick’s law, with the solvent concentration front propagating insuch a way that the distance traveled (L) changes with time as

L � tn ð12Þ

with n = 1/2. In addition, the solvent front is usually characterizedby a gradual change of the concentration between the dry and thefully hydrated (swollen) regions. Irrespective of the polymer sampleshape, the solvent front contour acquires a circular shape soon afterthe transport begins. Fickian (Case I) transport is observed either inamorphous polymers with the glass transition temperature (Tg) be-low the temperature of the experiments, or in glassy polymers ifdiffusive transport of the solvent is much slower than the segmentalrelaxation of the polymer network. A very different behavior calledCase II transport is observed when the solvent diffusion rate is high-er than the segmental relaxation rate of the (initially) glassy poly-mer. Swelling of a polymer is usually accompanied by a decreasein Tg and can lead to transition of the polymer from the glassy tothe rubbery state. For Case II transport, a sharp solvent front is ob-served to propagate into the polymer linearly with time (n = 1 in Eq.(12)). The solvent concentration behind the front remains constant.The contour of the solvent front in 2D images matches that of thesample perimeter through which the solvent ingress occurs. Inaddition to these two limiting cases, an intermediate type of trans-port (anomalous, or Case III transport) is sometimes observed. Morecomplex behavior is also encountered. For instance, the character of

Fig. 23. 2D MR images of solvent swelling: isobutyl rubber swelling in toluene (leftcolumn); high-volatile A rank bituminous vitrain swelling in pyridine (rightcolumn); poly(ethy1 methacrylate) swelling in methanol (middle column). In eachcase, time evolves from top to bottom. The light regions correspond to high spinconcentrations. The experiments were performed at 2.35 T. Reprinted withpermission from Ref. [328].

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transport can change with time during the solvent ingress into apolymer. Solvent transport into the interior of a polymer is oftenaccompanied by the disruption of hydrogen bonds, weakening ofother inter-molecular interactions and by disentanglement and sep-aration of the polymer chains. An infinite swelling of a polymerleads to its dissolution. Swelling is also important in the physicalchemistry of coal.

To establish the character of transport, the characteristic fea-tures of the solvent uptake listed above (front sharpness and itspropagation with time, front contour shape, etc.) can be monitoredusing MRI. In addition, the T2 time of the solvent is the source ofvaluable information as it is a direct reflection of the mobility ofthe solvent molecules and also indirectly reflects the mobilityand the structural relaxation of the polymer network. A nearly con-stant T2 time of the solvent in the swollen polymer behind the frontis observed in the case of Fickian transport, whereas for Case IItransport the T2 time of the solvent decreases from the polymersurface contacting the solvent toward the solvent concentrationfront.

In certain cases, Fickian transport with the t1/2 front propaga-tion can be characterized by a sharp solvent front, for instance inthe case of an exponentially growing D(S) dependence (e.g., Eq.(7)). To establish the D(S) behavior, the availability of the spatiallyresolved information is essential. Also, the Fickian t1/2 front propa-gation behavior is valid only for infinite or semi-infinite mediawith uniform initial concentrations. To correctly track the frontpropagation, one may need to make corrections for the changesin sample size caused by polymer swelling, but these changescan be directly deduced from the images.

The MRI measurements can be done either by periodicallyinterrupting the process to acquire the images or by monitoringthe dynamics in situ. The conventional liquid-phase MRI tech-niques allow one to selectively visualize the solvent, whereas thesignal of the solid matrix is often not observed due to the shortT2 times. However, the mobility of the macromolecules tends to in-crease in the presence of a solvent, and the direct imaging of thepolymer may become possible without the need to use broad-lineMRI techniques. This further complicates the quantification of thesolvent content as compared to other porous media. Indeed, whenthe short TE or broad-line MRI techniques are used, care must betaken since the swelling polymer can contribute to the observedsignal, whereas measurements with a longer TE may not captureall the solvent molecules. However, this can be also used to obtainseparate images of the solvent and the polymer. In the in situ stud-ies, longer relaxation times (e.g., T1) of the bulk liquid surroundingthe polymer can be used to suppress it in the images. When solventmixtures are used, the images of individual liquids can be obtained.Swelling of polymers and coal can be fairly slow, and the experi-ments may last from tens of minutes to tens of days.

4.2. Polymer swelling in liquids

Periodic detection of 1D profiles revealed the Fickian transport(i.e., the t1/2 front propagation) for acetone in a vulcanized rubbersheet at room temperature (T > Tg) [324]. The propagating acetonefront was found to be relatively sharp, owing to the exponentiallygrowing D(S) dependence (Eq. (7)) for acetone in the polymer. 2Dimages of 1,4-dioxane in a PVC rod revealed the Case II radial trans-port with n = 0.91 in Eq. (12) [325]. The solvent content behind thefront was uniform, while the T2 time decreased with increasingdepth.

Water transport in 2-hydroxyethyl methacrylate (HEMA) at37 �C was found to be Fickian with constant D, whereas sharp sol-vent fronts were observed for copolymers of HEMA and ethyleneglycol methacrylate phosphate (MOEP) and the extracted D(S)dependence could be described with Eq. (7) [326]. Above

20 mol% MOEP, the copolymers exhibited extensive fracturing dur-ing swelling. An abrupt change of the sample dimensions was ob-served once the glassy core disappeared.

Fickian transport was also observed for toluene in butadienerubber [327] and in isobutyl rubber [328] and for hexafluoroben-zene (19F MRI) in methylsiloxane rubber [327]. Case II transportwith a constant velocity front propagation (n = 1 in Eq. (12)) wasobserved for methanol in poly(methyl methacrylate) (PMMA)[329] and poly(ethyl methacrylate) [327,328] (Fig. 23). The authorspoint out that spatial variation of T2 in Case II transport can makethe front appear sharper than it actually is [327]. Residual watercontent and the cyclic absorption/desorption of water in PMMAcan cause the transition from Case II to Fickian transport, with ananomalous induction period observed in all cases [330]. For tolu-ene in poly(vinyl chloride) (PVC), the propagating front was foundto reflect the shape of the object under study or geometry of theexperiment [331,332]. In contrast, for Fickian transport of n-pen-tane in high-density polyethylene (HDPE), a diffuse front rapidlybecame circular irrespective of the sample shape [331]. Permeationof several organic solvents (hexane, cyclohexane, octane, decane,and dodecane) into semicrystalline polyethylene (PE) sampleswas studied at 40 �C [333]. Higher liquid contents and faster per-meation were observed in linear low-density polyethylene (LLDPE)as compared to HDPE. Swelling can be used to reveal the aniso-tropic nature of a sample which is hard to detect with other tech-niques. For instance, a fragment of an initially stretched PVC pipeexhibited anisotropic solvent transport and expansion/contractionupon swelling in toluene or trichloroethylene [331].

The character of solvent transport strongly depends on the de-gree of polymer cross-linking. By increasing the fraction of divinyl-benzene (DVB), a higher degree of cross-linking of styrene-DVBcopolymers is achieved. This was observed to switch the transportof paramagnetically doped dioxane at 50 �C from Case II for 1% DVBto Fickian for 5% DVB, and to slow down the front propagation[334]. Swelling of commercial polyacrylate-based superabsorbing(SAP) polymer particles additionally cross-linked in outer partswas observed upon water ingress [335]. Lower T2 and D valueswere observed in the outer shell, corresponding to reduced water


mobility throughout the swelling process. To study water redistri-bution under a mechanical load, a pack of particles was imaged in aspinning MAS rotor. This produced a hole at the sample axis and aradial variation of spin density in the ring around the hole.

A complex behavior was observed for swelling of a bisphenol Apolycarbonate rod in acetone. While the 2D images and T2 mapsexhibited all the characteristics of Fickian transport, they also re-vealed a narrow contracting high intensity ring around the core.The concentration and the mobility of the solvent inside this ringwere higher than behind it. These observations were associatedwith the solvent-induced crystallization of the polymer which ex-pelled the solvent toward the core and also led to the cracking ofmaterial [325]. Fickian transport with a narrow high intensity ringaround the core was also observed for water in 2-hydroxyethylmethacrylate polymer (PHEMA) and its copolymers with tetra-hydrofurfuryl methacrylate (THFMA) and other methacrylates forcompositions rich in HEMA [336–339]. The increased water con-tent around the core was explained as the result of the formationof small cracks at the interface of the glassy and rubbery regionsof the sample caused by the swelling-induced stress at the inter-face. High intensity feature observed near the diffusion front canappear enhanced relative to the Fickian feature owing to the longerT2 time [338]. A similar high-intensity ring on top of the Fickianprofile was observed for water ingress at 310 K into P(HEMA-mEG-DMA) copolymer with 0.3 wt.% monoethyleneglycol dimethacry-late (mEGDMA) prepared by radiation-initiated polymerizationinstead of a commonly employed chemical initiation [340]. The in-crease in the diameter of the cylinder as it absorbed water couldalso be seen.

Permeation of D2O into cured epoxy samples at 70 �C was stud-ied using 1D SE-SPI profiling with 2H NMR signal detection [341].The samples were periodically removed from D2O for imaging.The results demonstrated that the content of unbound D2O in-creased continuously with time throughout the entire sample.Even after 2.5 months of immersion in D2O at 70 �C, the surfacewater concentration of the epoxy was still increasing. The experi-mental results were compared to four different models of moistureabsorption. Water uptake by polyamide 4,6 plates was studiedwith SE using inversion-recovery suppression of the surroundingbulk water [342]. Both the water content and the T2 time decreasedfrom the sample surface toward the core, which was related to thesample inhomogeneity created at the stage of material crystalliza-tion. Annealing of the sample led to a lower water uptake and re-duced molecular mobility of the absorbed water molecules.

Water transport in dental materials has significant practicalimportance. Transport of water in cylindrically shaped samples ofdental cement was observed to exhibit the t1/2 front propagationbehavior [343]. Glass ionomer cements (GICs) are widely used asdental restoration materials. To reduce their sensitivity to waterduring the early stages of the setting reaction, the resin-modified(RM) GICs containing HEMA are employed, for which the photoini-tiation of the setting reaction reduces the curing time. Cylindersprepared from RM GIC Fuji II were either exposed to a light sourceor allowed to set chemically in the dark [344]. One hour after thestart of mixing, they were immersed in water and stored at 37 �Cfor varying periods of time before they were removed for SE imag-ing. Water penetration was significantly faster in the chemicallycured material. When the water front reached the center for allsamples (after 192 h), the light-cured samples demonstrated a uni-form water distribution throughout the cross-section, whereas inthe chemically cured samples a few large areas of high signalintensity appeared, implying the existence of large pores filledwith water. Water penetration into cavities restored using RMGIC Fuji II, with and without surface protection, was studied in[345]. After 24 h of immersion, water diffused into both fillingsfrom pulpal and axial dentinal walls. In the unprotected sample,

water also diffused into the material from the surface of the resto-ration facing bulk water (‘‘oral cavity’’), whereas in the restorationprotected with the surface coating there was no signal correspond-ing to the water diffusing through the coated surface of the ce-ment. Complete penetration of water after 72 was observed forthe unprotected restoration but not for the protected one. The re-sults demonstrate that fast initial photopolymerization settingdoes not prevent water uptake during the initial stage of the set-ting process and the perturbation of water balance can impairthe acid–base setting reaction which is slower in RM GICs thanin conventional GICs since PHEMA matrix formed immediatelyafter photopolymerization reduces the setting rate. In addition,HEMA enhances water sorption. Thus, the application of surfacecoating over the RM GIC restorations is desirable since it protectsthe restoration during the early setting of cement.

Studies of a solvent desorption from a swollen polymer havebeen reported as well. Desorption of water from the nylon 6,6 rodsat 30 and 100 �C was studied [346]. The water content profiles re-vealed Fickian transport, with the highest water contents at thesample axis and the lowest contents at the surface. Evaporationwas much faster at the higher temperature. The exchange pro-cesses of D2O-saturated nylon rods with either the atmosphericwater vapor or liquid water were also studied. The authors men-tioned that H/D exchange process could be involved. A poly(methylmethacrylate) rod, after swelling in CH3OD at 30 �C, was placed incyclohexane-d12 at 30 �C [347]. At the polymer surface, a relativelyrapid loss of methanol led to the rubber-to-glass transition. Thisglassy shell reduced the polymer mobility and the rate of furthermethanol desorption.

GARField was used to study the effect of a mechanical stress onthe water uptake by a two-layer polymeric film consisting of ahydrophilic water-borne base layer and a hydrophobic solvent-borne top coat [348]. A glass tube was glued on top of the coatingand served as water reservoir. When an epoxy–amine glue wasused for this purpose, the interaction of the glue with water causeda mechanical response of the glass slide, which was absent whensilicon glue was used instead. Different combinations of base coatand top coat thicknesses were examined. The observed signal in-crease in the base coat was shown to be associated only with theincrease in the amount of water in the layer and not with theswelling polymer. The redistribution of water inside the base coatwas shown to be fast and the water uptake was limited only by thepenetration through the top coat layer. Water penetration causedswelling which appeared to be linear with the total amount of ab-sorbed water. It was also observed that the applied external stressincreases both the uptake rate and the total amount of absorbedwater. A significant difference between the rates of water uptakeand the D2O/H2O exchange was observed, caused by the differ-ences in the transport mechanisms in the two experiments.

4.3. Variation of temperature and pH

Temperature can significantly affect not only the rate of liquidingress but also the character of transport. As demonstrated formethanol in PMMA [349,350], including atactic PMMA [351],increasing the temperature from ca. 26 to 60 �C can switch thetransport from Case II to Fickian, with a gradual change from onemechanism to the other at temperatures in between these two lim-iting cases. Water ingress into nylon 6,6 at temperatures up to100 �C was studied ex situ, by periodically removing the samplefrom water and imaging with 1D SSFP [352,353] or GE [353]. Ficki-an transport with an increasing D(S) dependence was observed.The effect of applied external pressure (up to ca. 170 atm) wasstudied at 65 �C [353]. Fickian diffusion of water in nylon 6,6 at100 �C was also observed with 2D FLASH [346]. Both T2 and T�2times of water were found to decrease toward the center of the


sample while a concentration gradient of water was present in thepolymer, reflecting differences in water mobility at different watercontent levels.

Transport of decalin into crosslinked ultra-high molecularweight polyethylene (UHMWPE) at 130 �C was studied ex situusing 2D SE with T1 or T2 preconditioning [354]. The correlationsbetween T1 (T2) and signal intensity were employed to extract spindensity images. The experiments were performed for polymerswith different degrees of cross-linking under an assumption thatfor a given cross-linking degree the relaxation times of the liquiddepend only on its concentration in the polymer. Higher cross-link-ing degree was observed to reduce swelling and solvent uptake andT1, while T2 was affected less. The Fickian transport was observed.The decalin/UHMWPE system was also studied at 150 �C (see[355]).

The ingress of boiling water into injection-molded bisphenol Apolycarbonate was studied ex situ using 2D SE or FLASH [356].The amount of absorbed water was <0.5% w/w after 24 h. Thetwo-stage ingress was observed, with a uniform distribution ofwater and a small number of additional ‘‘free’’ water pools ca.200–300 lm in size observed at early times, and an increase inthe relative amount of water in these pools and their size as wateringress continued. Boiling of the sample in D2O produced no obser-vable signal, indicating that polymer does not contribute to theimages.

A polymer gel based on poly(N-isopropylacrylamide) (PNIPAAm)is known to have the lower critical solution temperature in waterand its mixtures with organic solvents [357]. As the temperatureexceeds the critical value or as the concentration of the organiccomponent of the solvent increases, the gel undergoes a transitionfrom a swollen to a collapsed state. MRI of a cylindrical sample inH2O revealed a decrease in the diameter of the sample with an in-crease in the temperature of water. The process was accompaniedby the change in the T2 contrast due to the variation of the mobilityof the polymer and water molecules. Experiments with a D2O/CH3OD mixture showed that the initial stage of CH3OD diffusionin the polymer gel was Fickian, but the swelling-induced changesin the polymer gel structure led to the non-Fickian behavior at latertimes. Sometimes the formation of a surface layer was observed,which slowed down or precluded further ingress of the solvent intothe polymer gel. Swelling of copolymers of N-isopropylacrylamide(NIPAM) and N,N-dimethylacrylamide (DMA) in the course ofwater uptake for various sample compositions was also studiedwith MRI [358]. It was concluded that concentration profiles wereclose to Case II transport behavior.

Variation of the pH value may be extremely important whenaqueous solutions are used, especially for drug delivery relatedapplications (see Section 5) where pH values can vary dramati-cally. Hydrogels based on copolymers of methacrylic acid andpoly(ethylene glycol) monomethyl ether monomethacrylate,P(MAA-co-PEGMEMA), belong to the group of pH sensitive materi-als. MRI of the swelling of the disk-shaped samples in water at pH7 revealed the presence of a swollen external region and a rigidcore where swelling was delayed depending on the PEGMEMAcontent [359,360]. As compared to P(MAA-co-PEGMEMA), thehydrogels synthesized by copolymerization of the hydrophobicpoly(propylene glycol) monobutyl ether methacrylate (PPGMEMA)with MAA (P(MAA-co-PPGMEMA)) exhibited lower swelling atequilibrium and a lower swelling rate as a consequence of thehigher hydrophobicity of the PPG side chains [360]. The develop-ment of the swelling front was clearly observed. The rigid coreof the sample did not change much during the initial stage andstarted to swell only after an induction period of ca. 1800 min.Hydrogels of P(MAA-co-PEGMEMA-co-PPGMEMA) terpolymersdemonstrated a behavior intermediate between those observedfor the equimolecular copolymers. Copolymeric hydrogels with

high MAA content followed the Fickian diffusion model reasonablywell. For other compositions characterized by the sigmoidal up-take kinetics and swelling fronts, a combination of the Fickianand Case II mechanisms was assumed. Similar behavior was ob-served for P(NIPAAm-co-MAA) hydrogels [361]. Copolymers pre-soaked in acidic solution at pH 2 exhibited sigmoidal swellingkinetics when swelling took place at basic and neutral pH. Theexternal swollen region was observed along with the rigid corewhich started to swell with a delay, but after that swelled uni-formly. In contrast, non-presoaked copolymers and homopolymersexhibited progressive and uniform swelling from the onset of theprocess. A similar pH-dependent behavior with a delayed coreswelling followed by its rapid acceleration was reported forthe hydrogels of P(NIPAAm-co-MAA-co-PEGMEMA) terpolymers[362]. The swelling behavior is composition-dependent and fasterin the radial than in the thickness direction. The observed behaviorwas linked to the disruption of the hydrogen bond network by thepenetrating water molecules.

4.4. Swelling in liquid mixtures

Swelling of a polymer can proceed very differently when a mix-ture of two or more liquids is used instead of the individual liquids.The ingress of ethanol/water mixtures into dental light cureddiacrylate resin sheets 500 lm thick was studied using fre-quency-swept STRAFI [363]. A 3 mm rf coil was located belowthe stationary sample. Fickian transport (n = 1/2 in Eq. (12)) wasobserved. The diffusivity value was found to increase with increas-ing methanol fraction. For pure water, penetration was not ob-served even after 9 months. Swelling of epoxy resin rods inwater–acetic acid mixtures was studied for pure and 85% aceticacid [364]. Fickian transport with the D(S) dependence of Eq. (7)and a sharp liquid ingress front were observed in both cases, butless swelling was observed for diluted acetic acid. At the sametime, the ingress of pure water was negligible. NMR spectra ofthe entire sample were used to distinguish acetic acid and water,whereas the overall NMR signal was used for imaging. Swellingof a bisphenol A polycarbonate rod in a mixture of acetone andmethanol was studied using either CSSI [325] or acetone-d6/CH3OD and acetone/CD3OD mixtures [365]. It was shown thatthe rates of transport of individual components can be markedlydifferent as compared to individual liquids. CSSI was used to study,both in situ and ex situ, the swelling of a vulcanized rubber (VR) cyl-inder in acetone/benzene mixture [355,366]. Both liquids in themixture diffused with the same rate equal to 80% and 250% ofthe single-component diffusion rates of benzene and acetone,respectively. Diffusion of acetone into a sample of VR presaturatedwith benzene proceeded at a rate greater than that of either of theindividual liquids [355]. Isotopic substitution was used to followthe ingress of cyclohexane into VR previously saturated with ace-tone-d6 [355]. In this case, the concentration profiles were muchsteeper than those derived either for the diffusion of acetone intoa benzene-saturated VR or isooctane into a cyclohexane-saturatedsample. Transport of isooctane could be studied in the presence ofcyclohexane using DQC even though the resonances of the two liq-uids overlapped [355,366]. 19F MRI was used to demonstrate thedifferences in the character of transport of C6F6 in cross-linkedpolystyrene in the presence and in the absence of C6H6 [367].The ingress of a mixture of methyl ethyl ketone (MEK) and ethanolinto polystyrene was visualized using 1H and 2H MRI of selectivelydeuterated solvents [368]. Also, chemically selective 13C–1H cycliccross-polarization (CYCLCROP) was applied to map the two sol-vents in a single experiment despite a relatively low SNR for theexperiments with a natural abundance of the 13C isotope. Thetwo solvents were found to ingress together but exhibited quitedifferent concentration profiles. CSI was used to visualize


individual components absorbed by polymers from mixtures ofmiscible liquids [369]. Studies were performed for PMMA in ace-tone/water and polyester resins in a quaternary model petrol.

4.5. Imaging of a swelling polymer

MRI can be used to study not only the solvent behavior, but alsothe changes in the properties of a polymer itself. For instance, largedifferences in the relaxation times of the solvent and the swellingpolymer were used to study the transport of decane in the peroxidevulcanizate of natural rubber using GE with oscillating gradientsafter immersing the sample in the solvent for 15 min [66,259].Longer TE values (later echoes) were used to monitor the solvent,while shorter TR values were used to suppress the signal of decaneand to extract spatial variations in the polymer T2 which increasedwith increasing decane concentration. The diffusivity of decane in-creased with its content according to Eq. (7) or Eq. (8). Separate sol-vent and polymer images were obtained for H2O in poly(ethyleneoxide) (PEO) based on the two-component T1 analysis of 1D profileswith a variable T1-weighting [370] or by subtracting the profiles ob-tained with H2O and D2O (Fig. 24). During the simultaneous ingressof H2O and D2O into the sample from the opposite ends, the redis-tribution of the liquid phase could be monitored even after the twosolvent fronts have met. STRAFI was used to detect the signals ofboth water and the polymer upon swelling of sodium polyacrylate[371], demonstrating that swelling and gelation of the polymerwere twice as fast as the water transport measured with conven-tional low field MRI. Swelling of poly(methyl methacrylate)(PMMA) was studied in CHCl3 or CDCl3 to image the ingressing li-quid and the swelling polymer, respectively [372]. CD2Cl2 was usedto observe the signal of the nematic-like polymer network preparedby cross-linking the prepolymer chains consisting of statisticallydistributed segments of methylhydroquinone, sebacic acid, 4-hydroxybenzoic acid and itaconic acid [357]. The anisotropy ofthe material was induced by applying a mechanical load duringcross-linking. The 1H NMR signal of the polymer was shown to in-crease with the degree of swelling of the sample. Solvent diffusionwas anisotropic and was much faster along the polymer chains thanin the transverse direction, the latter being stepwise. STRAFI wasused to monitor the ingress of hexafluorobenzene into PMMA/poly(n-butyl methacrylate), with 1H detection of the polymer and19F detection of the ingressing liquid [107]. The T2-weighted

Fig. 24. (a) 1D 1H MR profiles of the polymer distribution in the swelling polymer detecfronts that move toward each other are clearly visible. (b) Profiles of the water and polymbottom. The profiles at the sample top were obtained by analyzing the bi-exponential spiat 4.7 T. Adapted from Ref. [370], Copyright (1998), with permission from Elsevier.

profiles show that the mobility of the liquid within the polymer isinitially quite low but later increases as the polymer softens.

Ageing of polymers also strongly affects the transport processes.This was shown, in particular, in the study of natural rubber ex-posed to high-temperature ageing at 170 �C by detecting the signalof the polymer that was swelling in C6D6 [357]. The behavior ofcross-linked poly(dimethylsiloxane) (PDMS) and semicrystallineLLDPE was studied in situ in supercritical CO2 (scCO2) at pressuresup to 300 bar and 45 �C in a PEEK cell using 3D 1H MRI [373]. ForPDMS, a high degree of swelling was observed for all cross-linkdensities. Rapid swelling was found, and the extent of swelling in-creased with increasing fluid density and decreasing cross-linkdensity. In contrast, no measurable increase in dimensions was ob-served for LLDPE at any pressure because of a relatively low sorp-tion of scCO2.

The image of the PNIPAAm matrix swelling in D2O demon-strated that temperature-induced shrinking was a two-step pro-cess [357]. Above LCST, the T2-weighted signals of the matrixvanished rapidly due to the change of the network to a more rigidlattice.

4.6. Polymer swelling upon vapor uptake

Swelling of polymers brought in contact with vapors ratherthan liquids has been studied as well. Ionic conductivity of polymerelectrolytes can be enhanced by several orders of magnitude uponabsorption of water vapor. For instance, swelling of (Pb,Zn)(CF3SO3)2(PEO)n films in contract with H2O or D2O vapor was stud-ied in [374]. The spatial variations in the proton spin densityimages and the T2 maps were shown to be quite different for waterand the polymer. The apparent velocity of the swelling front wasmuch higher for experiments with H2O as compared to D2O. Waterwas absorbed mainly by the amorphous regions of the sample, andwater transport in the film was accompanied by a rapid destruc-tion of the crystalline regions [374]. 1D STRAFI was used to studythe ingress of methanol and methanol–acetone vapor mixturesinto poly(methyl methacrylate) (PMMA) cylinders [228,375]. Deu-terated fluids were used to observe the polymer images only, whilenon-deuterated fluids were employed to observe both the polymerand the solvent that could be distinguished based on the differ-ences in their T2 values. Case II transport with constant velocityfront propagation was observed at least for the samples with lowacetone fractions. STRAFI was also used to study swelling of poly

ted during diffusion of D2O from both ends of the sample. The two sharp penetranter in a swelling polymer sample. H2O was diffusing from the top and D2O from the

n–lattice relaxation decays of the observed signal. The experiments were performed

Fig. 25. 1D 1H MR profiles of diffusion of H2O from agarose gel to reservoir withD2O. The agarose gel is on the right-hand side of the image. Profiles obtained at 0, 6,32, 87, 156, 336, and 500 min after the D2O reservoir was placed adjacent to theagarose gel are shown. The profiles were detected using 1D DHK-SPRITE. Theexperiments were performed at 0.2 T. Reprinted with permission from Ref. [386].


(vinyl chloride) after its contact with acetone vapor [376]. Thepolymer and acetone contributions were separated using eitherdifferent TE values or the deuterated acetone. The results suggestthat softening of the swollen polymer continues long after the pen-etration of acetone into the sample. Swelling of poly(methyl meth-acrylate) or polystyrene bars in contact with CDCl3 or CCl4 vaporwas studied using a variant of the SPI technique to observe thepolymer as its mobility changed [335]. The profiles seemingly indi-cated Fickian ingress, but the mobility of the polymer exhibitedspatial variations even in a completely swollen sample.

Conventional MRI and STRAFI were used to compare the ingressof toluene liquid and vapor into polystyrene [377]. A biexponentialrelaxation analysis of the STRAFI data in the swollen region wasused to separate the polymer and the liquid contributions. For li-quid toluene, Fickian transport (n = 1/2 in Eq. (12)) accompaniedby rapid polymer swelling and dissolution was observed. In thecase of vapor ingress, after an initial period during which the sur-face concentration apparently increased, a sharp solvent front wasobserved to ingress linearly with time into the sample (n = 1 in Eq.(12)), which the authors explained as a surface-flux-limited Case IItransport. A good correlation between the estimated vapor fluxarriving at the sample surface and the front velocity was observedby varying the distance between the liquid reservoir and the poly-mer. At higher temperatures, a transition from n = 1 to n = 1/2 in-gress (Eq. (12)) was observed.

4.7. Swelling and deswelling of coal

Imaging of coal swelling and deswelling has been reported. CaseII transport with constant velocity front propagation (n = 1 in Eq.(12)) was observed for pyridine in bituminous coal [327,328](see Fig. 23). MRI of coal swelling in pyridine-d5 or acetone-d6has been reported [378]. The observable 1H NMR signal in the coalwas detected only after 48 h of swelling, demonstrating the in-creased mobility of some proton-containing constituents.

Pyridine transport in Illinois No. 6 coal was observed to proceedvia Case II transport for swelling of the sample in contact with pyr-idine vapor [379]. At the same time, deswelling was initially Fickianbut became non-Fickian at the later stages [379,380]. Swelling wasanisotropic, being 13% greater in a plane perpendicular to the coalbedding plane than parallel to it; however, the deswelling was al-most isotropic. A solvent-induced glass-to-rubber phase transitionoccurred at the relative solvent concentration of 0.65 during swell-ing and at 0.5 during deswelling. The shape of the coal specimenwas distorted irreversibly after the first swelling and deswelling cy-cle because of the dimensional changes related to the ‘‘locked-in’’strain in the coal bedding plane. The softening and melting of coalat high temperatures was investigated using SPRITE [381].

Gas phase 1D GE 19F MRI was used to characterize the transportof heptafluoropropane (CF3CHFCF3) in coal [382]. The cylindricalsamples were cored with their bedding planes parallel to the axisof the cylinder and embedded in epoxy resin. The gas was allowedto enter and leave the sample through the two 1 mm apertures atthe two ends of the sample. When the outlet aperture was sealed,the ingress of the fluorinated gas into the coal sample accompaniedby the increase in the gas content was attributed to both the gasadsorption by the coal and the structural rearrangements thatled to the sample ‘‘inflation’’.

4.8. Other studies

Water diffusion is of great importance for food polymers sincethe presence of water affects the quality and the shelf life of foodproducts. Examples of MRI studies are quite diverse and includestarch [383], starch amylose [384] and other substances. Water dif-fusion into high amylose starch blend studied ex situ at 25–45 �C

has revealed Fickian transport with the D(S) dependence of Eq.(7) [385]. 1D DHK-SPRITE experiments were performed at8.3 MHz proton frequency to monitor the replacement of H2O withD2O in a sample of agarose gel to evaluate water diffusivity(Fig. 25) [386].

A variety of NMR tools were used to study the developing inter-facial region of soap bars in water [387]. Swelling of natural andstyrene–butadiene tire rubbers in the presence of asphalt at170 �C was imaged using 3D SE [388].

5. MRI of model and commercial drug delivery systems


Liquid uptake by polymers and their swelling are important forthe design of controlled drug delivery systems with a well-definedrate of drug release independent of the environmental conditionsand a prolonged action as compared to the immediate release sys-tems. Various polymeric matrices are often used as excipients, i.e.,carriers of active ingredients of a pharmaceutical dosage form.Upon hydration and swelling of a polymer, a gel layer is formedin the outer part of a tablet. It can significantly reduce the ratesof further hydration and of dissolution and outward diffusion ofan active substance. Formation of a gel layer is one of the mecha-nisms for controlled (or sustained, regulated, modulated, extended,timed, modified) drug release, but more sophisticated formulationshave been developed as well. Depending on the type of the poly-mer, other processes such as polymer erosion and dissolutionmay take place, which can affect differently the release of solubleand insoluble drugs.

In the MR images, usually the swelling and erosion fronts can beeasily identified. The swelling front is an interface between theglassy and the rubbery regions of a swelling polymer. Its propaga-tion with time leads to a decrease of the dry tablet core size. Anerosion front separates the hydrogel layer from the bulk solventor solution. In addition, in some studies the solvent penetrationfront is observed which separates the dry core and the hydratedglassy polymer with the degree of hydration insufficient to causethe glass-to-rubber transition. Depending on the polymer and theimaging technique, complications may arise due to the contribu-tion of the swelling polymer to the observed signal. The NMR sig-nal of water may be affected by exchange between the waterprotons and the protons of polymer macromolecules. The water


uptake and swelling behavior depends on the experimental condi-tions such as the composition of the dissolution medium and itstemperature and pH values, the use of static or circulating liquid,etc. Needless to say, it is important to correlate the MRI data withthe results of drug release studies. Several reviews describing theapplications of the MRI technique to study the behavior of drugdelivery systems have been published [389–395].

5.2. Immediate release systems

The disintegration of immediate release systems can be fairlyrapid and may require the use of fast imaging techniques. TheFLASH sequence was used to image the liquid phase during the dis-integration of paracetamol tablets that lasts a few minutes (Fig. 26)[396,397]. The experiments were performed at pH 2 and either37 �C or 19 �C. Penetration of the dissolution fluid was homoge-neous, with tablet size decreasing with time. The results were com-pared for tablets from different manufacturers. In addition, 1D SPIwith tp = 105 ls was used to image dry tablets before dissolution,demonstrating that all tablets had a spatially uniform distributionof paracetamol. The release of N-(4-hydroxyphenyl) acetamidefrom four different types of commercially available paracetamoltablets under continuous stirring in aqueous 0.1 N HCl dissolutionmedium at 37 �C was studied in situ using localized volume-selec-tive NMR spectroscopy with water signal suppression at 500 MHz[398].

The study of a food-induced delay in disintegration of HPMC-coated fosamprenavir immediate release tablets was performedusing both the gastrointestinal model (a computer-controlled mul-ticompartmental dynamic in vitro system modeling the human

Fig. 27. 2D MR images of a HPMC tablet undergoing hydration in water at 37 �C. (a) Imadetected in the axial plane after 10, 30, 60 and 120 min of swelling. The experiments wefrom Elsevier.

Fig. 26. 2D MR images of a 2 mm slice at the center of a paracetamol tablet as a functionsignal from the protons of the solvent surrounding the tablet in the glass whereas theperformed at 7 T. Reprinted from Ref. [397], Copyright (2011), with permission from Els

stomach and the small and large intestines) and MRI [399]. Inthe MRI experiments, the 2D TSE (RARE) sequence was used to im-age the tablet immersed in either simulated gastric fluid (SGF)without pepsin or in a nutritional drink at 22 �C under static con-ditions. Compared to SGF, disintegration in the nutritional drinksimulating a high-fat meal was clearly delayed. Even after 3 daysunder static conditions, the tablet was swollen but not disinte-grated, whereas in SGF both swelling and disintegration were ob-served. For the nutritional drink, the impaired water ingress andtablet disintegration could be associated with a reduced transla-tional and rotational diffusion of water molecules and the forma-tion of a precipitate layer on the tablet surface.

Current density imaging (CDI) is based on the measurements ofthe magnetic fields induced by electric currents in a sample understudy. Techniques for three different frequency ranges are avail-able: zero frequency (direct current density imaging, DC-CDI),the kHz frequency range (alternating current density imaging,AC-CDI), and the Larmor frequency (rf current density imagingtechnique, RF-CDI). The DC-CDI technique was employed to followdissolution of several tablets immersed in agar–agar gel by detect-ing the conductivity changes in the sample that are closely relatedto the ion concentration [400,401]. Electric conductivity images ac-quired with the DC-CDI method were used for tracing the dissolu-tion of tablets and ion migration processes. Dissolution and ionmigration of tablets made of various carboxylic acids (citric, oxalic,maleic, tartaric) and of sodium chloride were investigated. Carbox-ylic acids ionize on dissolution in the surrounding aqueous gel(RCOOH ? RCOO�(aq) + H+(aq)), while a tablet made of NaCldissolved with the release of hydrated ions to solution (Na+Cl�(s)? Na+(aq) + Cl�(aq)). Immediately after the tablet was inserted

ges detected in the radial plane after 10, 30, 60 and 180 min of swelling. (b) Imagesre performed at 11.7 T. Adapted from Ref. [403], Copyright (1994), with permission

of immersion time in the acidic (pH = 2) solvent at 37 �C. White pixels represent theblack pixels in the center of images represent the tablet. The experiments were

evier.

Fig. 28. Swelling of hydroxypropyl methyl cellulose (HPMC) in water. Quantitativemaps of water concentration (a), transverse relaxation time T2 (b) and self-diffusioncoefficient D (c) at different hydration times: (1) 0.5 h; (2) 2 h; (3) 8 h; (4) 10.25 h;(5) 29.75 h; (6) 40.25 h. The experiments were performed at 9.4 T. Ref. [408].Copyright Wiley-Liss, Inc. Reproduced with permission.


into the gel, it started to dissolve and released mobile positive andnegative ions that began to migrate away from the tablet into thegel. The modeling of results was used to extract the correspondingdiffusivity values.

5.3. Cellulose and its derivatives

1D water absorption by cylindrical cellulose fiber plugs was stud-ied by 2D spiral scan imaging [402]. A reasonably sharp advancingliquid front was observed despite the complicated microscopic porestructure of the sample. From the complex evolution of the watercontent profiles, two different water penetration processes were de-duced. The front region with unchanged sample boundaries exhib-ited a lower and inhomogeneous water concentration distributionand was attributed to water penetration in the inter-fiber capillarypores with no fiber swelling. A slower propagating front region withdistorted sample boundaries was associated with the intra-fiber dif-fusion and fiber swelling, which was significant in the directiontransverse to the capillary water transport.

Various cellulose ethers have been examined using MRI, includ-ing hydroxypropyl methyl cellulose (HPMC), hydroxypropyl cellu-lose (HPC), and hydroxyethyl cellulose (HEC). The behavior islargely affected by the sample composition, including molecularweight (MW) of the polymer, the degree of substitution, etc. Thetablets are usually produced by compressing the powders with orwithout additives.

Swelling of the tablets in water at 37 �C was studied for differ-ent types of HPMC [403,404]. Formation and growth of the externalgel layer was clearly observed. The overall size of the swelling tab-let increased by a factor of 3 in the axial direction and 1.5 in theradial direction (Fig. 27) [403]. Significant changes in the core sizewere also observed: it shrank in the radial dimension and ex-panded in the axial plane. The D and T2 maps of water in the gelboth showed that the mobility of water molecules was differentat different (flat, cylindrical) surfaces of the tablet and decreasedtoward the tablet core [404]. In a similar study, lower D values inthe axial direction compared to the radial direction in the first hourand more erosion of the polymer in the radial direction after 8 hwere observed [405]. Swelling of HPMC at 22 �C showed that waterfront demonstrated Fickian transport (n = 1/2 in Eq. (12) [406]. TheT2 times of water were converted into the 1D polymer concentra-tion profiles along the direction of swelling using the results ofNMR calibration experiments for samples with the known HPMCcontent. Comparison of the experiments in which HPMC tabletswere saturated with water in air or under vacuum demonstratedthat trapped air bubbles can lead to image distortions because ofthe susceptibility differences and can degrade the accuracy ofquantitative evaluation of polymer concentration [407].

The swelling and dissolution of HPMC tablets in water wasstudied quantitatively (Fig. 28) using T2- and diffusion-precondi-tioned ultra-fast 2D RARE MRI techniques [408]. The rapid in situquantification of both the concentration and self-diffusion coeffi-cient of water in HPMC was achieved in less than 3 min withoutthe need for an external reference correction. The contribution ofHPMC to the image intensity was shown to be negligible. The for-mation and evolution of the gel layer exhibited significant differ-ences between the uncorrected images and the corrected waterconcentration maps. In particular, the gel layer in the correctedimages showed a much more uniform water concentration acrossthe gel layer than the original images. The tablet changed its sizeand shape as hydration proceeded. From the analysis of the T2

maps, the authors were able to identify the location of the swollen(hydrated) glassy layer. The diffusivity maps appear to show an en-larged dry core region compared with the corresponding concen-tration images, an apparent effect caused by an extra degree ofT2-weighting of diffusion-preconditioned images. The gel thickness

increased as t1/2, with the axial growth being faster than the radialone.


2D MRI with inversion-nulling for bulk water suppression wasused in combination with X-ray microtomography (XlT) for track-ing the movement of the embedded glass microsphere markers tostudy the swelling behavior of the tablets [409]. The advantage ofXlT is that it can visualize the regions that are insufficiently hy-drated to give an observable NMR signal. HPMC, microcrystallinecellulose and lactose were mixed and compacted into tablets,and glass microspheres were added if needed. The swelling exper-iments were performed in a phosphate-buffered saline (PBS) solu-tion at pH 7.4. A thin surface gel layer was observed to formrelatively quickly. The water content appeared to rise rapidly be-hind the hydration front, then more slowly toward the gel–liquidinterface. The results were highly suggestive of Case II transport.Indeed, the hydration fronts moved at constant speed toward thecenter of the tablet and met there in ca. 3 h. The gel swelled out-ward, causing movement of the glass microsphere tracers. A signif-icant expansion of the tablet core (30% over 1 h) occurred ahead ofany observable water ingress, which can be attributed to the relax-ation of residual compaction stress. Core expansion may be animportant mechanism affecting the disintegration and releasecharacteristics of tablets.

Swelling of HPMC, HEC [410] and HPC [410,411] in water atroom temperature was studied for tablets covered with an imper-meable hydrophobic polymer, so that only one circular surface wasopen for water penetration. Signal intensity or relaxation times ofwater in the gel layer were used to calculate polymer concentra-tion profiles in swelling tablets using reference samples withknown polymer contents. Gel layer growth and tablet erosion werefastest in HEC tablets and slowest in HPC [410]. The polymer con-centration was found to increase very steeply toward the tabletcore, and the profile was observed to change continuously duringswelling. Swelling of HPC and HPMC tablets in water at room tem-perature was compared to that of micronized low-substituted HPC(L-HPC) by detecting images and T2 and ADC maps [412]. Tabletswere removed from solution for imaging. Swelling, deformationand cracking of L-HPC tablet was observed. In L-HPC, the growinggel layer and the dry core were clearly seen, whereas in HPC andHPLC the interface layer between the gel layer and the dry corewas additionally seen. The uptake of water by L-HPC was muchlower as compared to the other two samples. Larger gel layergrowth in transverse direction than in the axial one was observedfor HPC and HPMC, but not for the L-HPC tablet.

Swelling of a number of HPMC samples with different polymerMW was studied at 37 �C and pH 12 [413]. Images and parametermaps obtained indicated that the degree of swelling increased withmolecular weight while water transport became slower. The diffu-sivity of water molecules in the forming gel decreased from the out-er surface toward the dry core and was larger at the cylindricalsurface and smaller at the top and bottom surfaces of the tablet[413]. Faster gel layer growth was observed for tablets with a higherpolymer MW at pH values of 2, 7, and 12 [414]. The influence of thepH value of the dissolution fluid on the swelling of HPMC tablets wasstudied [397,414–416]. From the spatial behavior of spin densityand T2 and from the character of front propagation, for all polymerMW values the Case II transport was deduced at pH 2, Fickian trans-port at pH 12 [397,414,416], while at intermediate pH values (pH 6–7) it was reported as Fickian [415] or anomalous [397,414,416]. T2

was observed to be pH-dependent, but at all pH values a single-exponential T2 relaxation was observed, indicating that protonsare involved in a fast exchange process. For HPMC, fast exchangeof bound and free water in the hydrogel and a single-exponentialrelaxation of the solvent were observed in many other studies aswell. It was pointed out [416] that chemical exchange of water pro-tons with the exchangeable hydrogens of the polymer should alsoaffect the measured T2 values. In all studies, the solvent was re-moved from the NMR tube before imaging and reintroduced later.

A 20 MHz benchtop MRI system dedicated to the characteriza-tion of monolithic oral dosage forms has been described [417].Its use was demonstrated in the study of hydration and swellingof single- and double-layer HPMC tablets (Fig. 29).

5.4. Cellulose derivatives with model drugs

Swelling of low-substituted HPC (LH41) tablets prepared withtheophylline or procaine amide hydrochloride or without drugswas found to be much lower than for HPMC and HPC tablets[418]. A correlation between the T2 in the gel layer of the tabletsand the drug release rate from the tablets was observed. Case IItransport was observed for HPMC with different amounts of loadedtetracycline hydrochloride at pH 2 [397,419,420]. The diffusion andrelaxation measurements revealed that higher drug loadings led toan increase in the degree of swelling, larger T2 and D values in thegel layer and higher rates of water penetration. For HPMC tabletsprepared without or with diclofenac or insoluble calcium phos-phate particles, the growth of the gel layer with time was observedwhile the dry core was reducing in size in one direction andexpanding in the other as a result of stress relaxation in the com-pressed tablet [421]. The presence of diclofenac led to the disrup-tion of the gel layer. Dissolution of HPC capsules loaded withpseudoephedrine hydrochloride using the US Pharmacopeia (USP)method 2 was studied by periodically removing the capsules fromthe dissolution apparatus for imaging [422]. The rate of the hydra-tion front penetration was observed to decrease exponentially withtime, presumably because of the gel formation. The results indi-cated that water penetration was not a rate controlling factor indrug release for these formulations.

19F MRI of model drugs was used to monitor the drug distribu-tions within swelling HPMC tablets [423]. The concentration of thepolymer was mapped based on the measured dependence of therelaxation times of drugs (19F) or water (1H) on HPMC concentra-tion. By comparing the distributions of the drug and the polymerit was shown that triflupromazine hydrochloride remained withinthe swollen tablet even at long swelling times and was releasedwhen erosion of the tablet took place. In contrast, 5-fluorouracilcould diffuse within the tablet from the beginning of the swellingprocess and was thus released more easily. It was possible to relatethe efficiency of drug release with the diffusivity value of the drugmolecule.

Solid dispersions containing HPMC and the water soluble modeldrug antipyrine were prepared by either rotoevaporation/millingor spray-drying [424,425]. The two procedures produced solid dis-persions with different particle sizes. The use of D2O in the swell-ing experiments allowed the authors to detect both thedistribution of ingressing water (2H SE) and the mobilization ofthe HPMC polymer (1H CTI) during the swelling process. After pro-longed swelling, the volume of HPMC was several times the origi-nal tablet volume. Larger grain sizes resulted in a faster spread ofthe hydrated and mobilized polymer front. Additionally, the hydra-tion of the tablets with larger grain sizes was more heterogeneous.Air evacuation increased the amount of mobilized polymer slightly,but left the kinetics of the polymer mobilization front unchanged.The authors conclude that tablets that were prepared by rotoeva-poration/milling and, therefore, contain larger particles, evolveinto a more inhomogeneous gel than the gels that are formed inspray-dried tablets with a smaller dry grain size because largergrains hydrate less evenly. The inhomogeneous gels with widechannels that form provide a faster drug diffusion and release thanthe homogeneous gels. In samples prepared by rotoevaporation,some water penetrated very quickly into the depth of the tablet,possibly through some large pores [424]. The authors note thatin the swelling experiments, exchangeable protons could be re-leased into the aqueous phase and give the background NMR signal

Fig. 29. (a) Hydration and swelling of a HPMC tablet monitored with the benchtop MRI instrument. The bottom of the vial was filled with glass spheres. (b) Photograph(double-layer tablet and 1 eurocent) and images of HPMC-based double-layer tablets after different exposure times to buffer. The images show clearly the water penetrationbetween the lower and the upper layers. The experiments were performed at 0.5 T. Adapted from Ref. [417], Copyright (2008), with permission from Elsevier.


[425]. The same imaging approach was used to study water uptakeand swelling of HPMC tablets loaded with various model drugs[425,426].

To compare the MRI data with the conventional protocols ofdrug release measurements, the experiments have to be performedwhile dissolution medium is in motion. A conventional flow-through dissolution system (USP apparatus 4) was redesigned tobe compatible with an MRI instrument [427]. Swelling of HPMCtablets was compared in static and continuously circulating simu-lated gastric fluids. Released bubbles were observed in the imagesat later times. Smaller gel volume was observed for flowing condi-tions, presumably the result of enhanced destruction of the outerhydrated layer. The swelling/dissolution study under dynamic flowconditions using a probe-head that incorporated a flow-throughcell (US Pharmacopoeia 4) was performed also in [428]. Commer-cially available controlled release quetiapine fumarate tablets wereused, with the formulation containing HPMC and microcrystallinecellulose. The experiments used 1 l of distilled water at 37 �Ccirculating at 10 ml/min. The histogram-based thresholding wasused for the segmentation of the images into the dry glassy, swol-

len glassy and gel regions. Proper segmentation required that thebulk liquid contribution be removed from the images. The evolu-tion profiles of the regions were then extracted. The influence ofthe solubility of additives on swelling and erosion of HPMC tabletsin a circulating solution was studied in situ at pH 6.8 and 37 �C[429]. Tablets were attached to a rotating disk which was stoppedfor imaging. Some HPMC tablets contained a soluble or an insolu-ble drug. Positions of the swelling and erosion fronts were deter-mined from the imaging data. The presence of drugs acceleratedmatrix erosion. HPMC loaded with insoluble dicalcium phosphate(DCP) had the lowest swelling degree, while faster hydration wasobserved for HPMC loaded with highly soluble mannitol. Erosionwas somewhat accelerated for both loaded tablets.

To image and quantify the hydrodynamics inside a USP 4 celland around a tablet, MRI was used to obtain quantitative flowvelocity maps inside the cell under the conditions of pulsatile flowproduced by a piston pump [430]. The original USP 4 dissolutioncells (i.d. 12 or 22.6 mm) were adapted by replacing allferromagnetic parts with Perspex or PEEK. The cells containeda bed of 1 mm glass beads to distribute flow and a larger ruby bead


to act as a valve, and also a model PEEK tablet. 2D velocity mapswere detected for water at 37 �C with flow-sensitized SE sequencetriggered from the pump to acquire images that were 27.8 msapart in the pump cycle. The experiments demonstrated that thetablet was contacted by a distribution of velocities around itsperimeter and throughout the pump stroke. In both cells, the bot-tom surface and edges of the tablet were contacted by the hetero-geneous undeveloped flow field emerging from the bed of glassbeads. The top surface of the tablet experienced lower velocities.Both the flow and the expanding bed of glass beads can changethe position (and possibly orientation) of a tablet if it is not fixedin the apparatus.

5.5. Other polysaccharides (starch, xanthan, alginate, chitosan)

Swelling of the crosslinked high amylose starch (CHAS) excipi-ents in water was studied under various conditions [395,431–434]. Unlike many other excipients, CHAS tablets do not dissolveor disintegrate upon hydration and exhibit a higher swelling fora higher degree of crosslinking. Despite the uniform penetrationof water into the tablets, their swelling was anisotropic and lim-ited, leading to the shape retention of the tablet without its disso-lution or erosion, caused by the reorganization of the hydratedstarch chains. Formation of a highly hydrated gel membrane atthe water/tablet interface was observed in the images [433]. At25 �C, this low porosity membrane did not progress toward thecenter of the tablet. Water kept penetrating slowly into the coreof the tablet until a constant water concentration was reached.Only after a uniform water concentration was reached, the gelationof the interior of the tablet occurred. An identical behavior was ob-served at 37 and 45 �C. However, at 60 �C, the gel membrane stea-dily progressed toward the center of the tablet. Swelling was thesame between 25 and 45 �C, and twice as large at the onset of gela-tinization at 60 �C [395]. The diffusion process was Fickian be-tween 25 and 45 �C and Case II at 60 �C [395,433]. The effects of10 wt.% drug loading were analyzed in water at 37 �C [395,434].The presence of the drug did not influence the swelling of the tab-lets, while the average water diffusivity in the tablet (the rate ofwater uptake) increased. This was ascribed to a higher gradientof chemical potential at the water/tablet interface for drug-con-taining tablets. Diffusion-weighted images were reported to givea better contrast between the different regions of the hydrated tab-lets including the better delineation of the membrane boundaries[434]. In contrast to the unloaded tablets, for the drug-loaded tab-lets the membrane thickness was increasing at all times. Compar-ison of the diffusion-weighted and the spin density imagesrevealed the existence of a correlation between the mobility ofwater molecules and the local water content throughout the entirepellet.

Swelling of CHAS tablets with different loadings of acetamino-phen (APAP) was studied at 37 �C [435]. A uniform water distribu-tion was observed at 20 h for 40% APAP loading and only after 50 hfor 10% loading, which indicates that hydrophilic APAP accelerateswater imbibition. The swelling rate for 10% APAP loading was thelowest, while the tablets with 20% and 40% APAP swelled at a sim-ilar rate and had a similar size in the end. Diffusivity measure-ments have shown that in the outer gel the D values changedlittle with time and were similar for different tablets, whereas inthe inner regions the D values varied with time significantly andwere dependent on the drug loading. At the same time, the per-centage of the released drug was the same for all loadings, indicat-ing that the gel layer formation controls the drug release process.

1D STRAFI was used to study water ingress in loosely packedxanthan powder beds with different levels of compaction [436].Boltzmann transformation (Eq. (3)) was used to collapse the dataon a master curve. A model based on coupled liquid water and va-

por diffusion in combination with the measured adsorption iso-therm was used to extract the D(S) dependence, which exhibiteda maximum at a water volume fraction of 0.05 associated withthe diffusive transport of water vapor at low saturations. Theauthors note that even for a STRAFI experiment, the use of a cali-bration curve obtained from the measurements of a number of uni-formly equilibrated samples at various hydrations is essential for aproper quantitation of water content corrected for the relaxationand diffusion effects.

A combination of three MRI techniques was used to accuratelyidentify the positions of the penetration, swelling and erosionfronts upon one-sided swelling of xanthan tablets in six differentmedia: water, HCl at pH 3.0 and HCl at pH 1.2, and the same liquidswith added NaCl [437]. The penetration front separating the dryand the hydrated glassy polymer was visualized using 1D SPI pro-files detected with tp = 0.17 ms as the position where signal inten-sity increased above that of a dry tablet that was used as areference. The erosion front was located using 2D multiechoimages. The swelling front separating the glassy and rubbery(gel) polymer state was determined from T2 maps. The resultsdemonstrate that the penetration front is not the same as theswelling front since xanthan is not in the rubbery state in the re-gion between these two fronts. The positions of the swelling andpenetration fronts were found to be quite similar for all solutions.At the same time, the position of the erosion front and thus thethickness of the gel layer were strongly dependent on solutionpH and ionic strength. This affected the release rate of pentoxifyl-line which was the smallest in water (the thickest gel layer)whereas the fastest release was observed in HCl at pH 1.2 (thethinnest gel layer). In HCl at pH 1.2, a high-intensity region was ob-served next to the dry tablet core. It was identified as the regionwhere polymer is in a maximally hydrated glassy state and thusshows a local maximum in water T2 and signal intensity. Upon fur-ther hydration, formation of the gel reduced T2 and the measuredsignal since xanthnan in the glassy and the rubbery states influ-enced the T2 time of water differently. Further hydration of therubbery polymer increased the T2 once again. The experimentssimulating physiological conditions showed that changes in pHand ionic strength influence the xanthan gel structure relativelyquickly. The authors conclude that combination of SPI, multi-echoMRI and T2 mapping eliminates the limitations of standard ap-proaches for locating the moving fronts in swelling polymers.

MRI and TEM were used to study the effects of preparation con-ditions on the homogeneity of calcium alginate beads during theirswelling under simulated gastric and intestinal conditions in termsof spin density and T2 maps [438]. The results demonstrated thatpolymer concentration was higher at the edge of the bead thanin its center, and this difference persisted throughout the experi-ment. The observed changes in porosity could be useful for thedevelopment of controlled delivery systems.

A null-point imaging technique was employed to monitor thetransport of Cu2+ ions into a calcium alginate plug for various tem-peratures and various concentrations of the gel and Cu2+ ions[252]. The aim was to gain understanding of the cation diffusionin charged biopolymer systems, which can be quite different fromthe transport of neutral species. A t1/2 behavior of the concentra-tion front propagation was observed. The reaction–diffusion equa-tion was used in data modeling, which revealed a Fickian transportof a minimally reacting system.

MRI combined with a flow-through cell apparatus was used tostudy the relationship between swelling and drug release kineticsfrom chitosan acetate (CSA) matrix tablets containing diclofenacsodium (DS) and theophylline (TH) as an acidic and a basic modeldrug, respectively, at 37 �C and various pH values [439]. The effectof molecular weight of chitosan on swelling and drug release in pH6.8 Tris–HCl buffer was also examined. The most rapid swelling


was observed in 0.1 N HCl, and all regions turned into a gel after420 min. The swelling of CSA at pH 6.8 and pH 5.0 was slowerand the tablets tended to split at 430 and 560 min, respectively.The rate of water ingress into the core at pH 5.0 was slower thanat pH 6.8. The tablet splitting and rupture occurred because ofswelling of the partially hydrated core. The tablets made of thepolymer with a higher MW were observed to disintegrate earlierin the process.

5.6. Poly(vinyl alcohol) (PVA) and poly(vinyl pyrrolidone) (PVP)

Water penetration and polymer swelling were observed for un-loaded poly(vintyl alcohol) (PVA) tablets for different MW poly-mers [405,440,441]. Hydration of PVA causes a transition of thepolymer to the rubbery state under normal conditions [441]. The1D water content profiles exhibited a steep liquid front indicativeof Case II transport. For the rubbery domain, the water distributionprofiles had a plateau suggesting a low resistance to diffusion.

Cross-linked hydrogels were prepared by radiolysis of the solu-tions of PVA, poly(vinyl pyrrolidone) (PVP) and their mixtures[442]. Water sorption experiments for the cross-linked hydrogelswere performed at 298 K. Despite a high initial water content of87.2 wt.%, the samples were able to absorb more water. The uptakecurve shows an overshoot phenomenon before reaching the equi-librium value, reflecting the balance between the rate of rearrange-ment of the macromolecular chains and the rate of water diffusioninto the gel. The images have revealed Fickian transport up toabout 50–60% of the equilibrium water uptake. Water diffusivitywas found to increase with increase in PVP content in the gelsand with the increase in temperature.

Poly(vinyl pyrrolidone) (PVP) matrices, unmodified or loadedwith model drugs, were imaged using a 1D CTI approach whileswelling in D2O [426]. This way the propagation of polymer mobi-lization front could be studied.

5.7. Acrylates

Water transport in PHEMA cylinders loaded with either vitaminB12 or aspirin has been studied at 37 �C [443]. The samples wereperiodically removed from the liquid and imaged. Fickian diffusionwas observed in the presence of either drug. Similar to the obser-vations for unloaded polymers, in the presence of B12 a bright ringassociated with water in the cracks formed upon water ingress fol-lowed by their ‘‘healing’’ behind the diffusion front, making thebright ring feature travel with the diffusion front. For the aspirin-loaded samples, crack formation was much less significant thanfor the unloaded polymer, and no high-intensity ring was ob-served. Cracking was also observed for P(THFMA-co-HEMA)copolymers loaded with vitamin B12, while the copolymers withlow HEMA contents and those containing aspirin exhibited no evi-dence for crack formation [444]. No bright-ring feature at the inter-face between the rubbery region and the glassy core was observedfor a PEMA/PHEMA semi-interpenetrating network (semi-IPN)upon water ingress at 37 �C, even though the shape of the profilesstill suggested some cracking [445]. The presence of PEMA reducedthe rate of water transport. For the PEMA/PTHFMA and some of thePEMA/P(HEMA-co-THFMA) semi-IPNs, a two-stage water penetra-tion was observed, with no evidence of crack formation. Transportof water was Fickian for all samples and was slower for the sam-ples loaded with the chlorhexidine diacetate (CDA) drug.

A nominally non-swelling Eudragit matrix (a copolymer ofacrylic and methacrylic acid ester) loaded with a highly water-soluble particulate drug diltiazem hydrochloride was studied[446,447]. The absorption of a small amount of water throughoutthe pellet was observed within a few minutes, followed by a slowerFickian propagation of a sharp front of the freshly incoming water.

Similar behavior was observed for all drug loadings and drug par-ticle sizes. The ingress rate was spatially inhomogeneous, whichwas attributed to the tablet heterogeneity. A dissolution–diffusionmodel was employed to describe the drug release mechanism. Thefate of the potential air voids in the swelling compressed tabletsupon liquid ingress has been addressed [447]. In the drug-loadedEudragit tablets, air voids visualized as dark spots were seen toform and grow with time [447].

5.8. Poly(ethylene glycol) (PEG) and poly(ethylene oxide) (PEO)

The FLASH sequence was used to study the dissolution at 37 �Cof the tablets prepared from a mixture of poly(ethylene glycol)(PEG), lactose, potato starch and magnesium stearate and contain-ing bromhexin hydrochloride as the active substance [448]. The re-sults demonstrated that the preparation procedure based on themixing of solid ingredients before compressing into tablets pro-duced tablets characterized by a high rate of disintegration,whereas the tablets prepared by solid dispersion, especially witha slow solvent evaporation, exhibited a lower dissolution rate.The use of PEG with a higher molecular weight and of higherPEG contents also reduced the tablet dissolution rate.

A flow-through cell was used in combination with MRI tosimultaneously evaluate the cumulative drug release profiles byUV–vis spectroscopy and the internal states of tablets preparedfrom PEO and PEG by MRI [449]. In addition, the amount of thepolymers eroded from the tablets was quantified by size-exclusionchromatography using a HPLC system. The flow-through cell wasfilled with 1 mm glass beads to create laminar flow, and a plasticholder with a rubber retaining band was used to hold the tabletin the original position. The closed loop circuit contained 900 mlof water at 37 �C that was circulated at 4 ml/min. The MRI experi-ments were performed at 0.5 T under continuous flow conditions.Several tablets were prepared from materials with three differentmolecular weights, 7 � 106 and 2 � 106 g/mol (PEO-7M andPEO-2M, respectively) and 8.3 � 103 g/mol (PEG), and were loadedwith acetaminophen (AAP) as a water-soluble drug. For all tablets,the hydration was observed to be complete within 3 h. For bothPEO-2M and PEO-7M mixed with PEG, higher contents of PEG haveled to a faster penetration of the dissolution medium. The hydrogellayer thickness was observed to increase with time, except in thetablets with the highest PEG content. The PEO-7M tablets exhibiteda much thicker hydrogel layer than the PEO-2M tablets. No corre-lation between fluid ingress behavior and the cumulative drug re-lease profiles could be established. For the lower molecular weightcompositions, tablet erosion may control the release rate, whereasfor the higher molecular weight compositions the diffusion of thedrug through the hydrogel layer governs the release process.

For performing qualitative and quantitative imaging of theswelling, erosion and dissolution processes under controlled stir-ring conditions, a small release cell in the form of a rotating diskwas constructed to fit into the MRI equipment [450]. It was usedto determine the tablet size, the core size and the gel layer thicknessof extended release (ER) matrix formulations based on poly(ethyl-ene oxide). The tablets were glued to the rotating disk, vacuumedand then brought in contact with the dissolution medium at25 �C. The sample rotation and the pumping of dissolution mediumwere paused for image acquisition. Diffusion-weighted SE was em-ployed to suppress the signal from the liquid and to image the poly-mer only, and calibration experiments were performed withsamples of known polymer content to extract semi-quantitativepolymer concentrations during swelling. The interfaces betweenthe dry core and the swollen tablet and between the swollen tabletand dissolution medium could be easily distinguished, and arelatively steep polymer concentration profile within the gel layerwas observed. Sample rotation led to the increase in the rate of ero-


sion after the dry core disappeared. Both the erosion and the swell-ing were found to proceed faster in the radial than in the axial direc-tion of the tablet. The front synchronization (constant gel layerthickness) observed for the sample with a lower MW was associ-ated with the formation of an almost invariable polymer concentra-tion profile through the gel layer. For a high MW polymer, theswelling and erosion fronts were never fully synchronized duringthe time course of the dissolution process and a constant gel layerthickness was therefore not obtained. For the same reason, theslope of the polymer concentration profile changed during dissolu-tion. The shape of the tablets was observed to change at later times,and the tablet size increased faster in the axial than in the radialdirection.

5.9. Glycolide, lactide, poly(lactic-co-glycolic acid) (PLGA)

MRI was used to observe liquid ingress in cylindrical polyglyco-lide tablets loaded with theophylline as a model drug and com-pared to unloaded tablets [451]. The tablet degradation wasperformed at 37 �C and pH 7.4, with the tablet periodically re-moved for imaging. The polymer did not contribute to the imageas confirmed with the buffer prepared using D2O. The liquid inthe tablets could be visualized with MRI only 13 days after theimmersion (stage III of swelling). The reaction–erosion front ap-peared at the surface. A 100% drug release was achieved in the hy-drated porous region, and the front propagated linearly in time. Ahomogeneous distribution of water was achieved after 75 days.The ingress of the buffer was faster from one side because of a tab-let fabrication inhomogeneity. The same liquid ingress rate was ob-served for the blank and the drug-loaded samples. The T2

decreased from the tablet surface toward the reaction–erosionfront. The authors concluded that the transport was neither Fickiannor Case II, but rather the process was controlled by the autocata-lytic hydrolysis of the matrix by the forming acidic oligomers.

The effect of the incorporation of a high molecular weight drug(peptide) on the behavior of poly(lactic-co-glycolic acid) (PLGA)was addressed [452]. Both drug-loaded and blank polymers werestudied in a phosphate buffer at pH 7.4. The solid phase was notobserved, and the dissolved drug contributed less than 5% to theobserved signal. Signal intensities were corrected for relaxation ef-fects and converted into quantitative water concentration profilesusing a reference sample. In the placebo sample, buffer ingress wasuniform and exhibited a well-defined front. The uptake results(integrated profiles and gravimetric data) indicated super-Case IIbuffer ingress corresponding to n > 1 in Eq. (12), while the frontpropagation with a constant velocity was in agreement with CaseII transport. The drug could be distinguished from the buffer basedon the relaxation time differences. A non-uniform drug distribu-tion was deduced based on the T2-weighted images and T2 mapsof the swollen samples, and drug-rich regions were identified asan outer ring and the inner region of the tablet. The drug-loadedsamples exhibited a remarkably different buffer uptake kineticsdemonstrating a much slower buffer uptake and the approximateFickian and Case II kinetics in the inner and outer regions of thesample, respectively. The MRI study of the hydration and degrada-tion of PGLA also included the diffusivity mapping [453].

It is generally assumed that isotope substitution does not affectthe processes under study, but in certain situations this may not bethe case. For instance, degradation of polyglycolide in water at37 �C and pH 7.4 was studied ex situ with the use of a H2O/D2Omixture so that the MRI results could be compared with nuclearreaction analysis data since the latter technique is sensitive toD2O [454]. The degradation of polyglycolide proceeded over afew weeks. It was caused by ester hydrolysis, an autocatalyticprocess accelerated by its acidic by-products. Degradation wasfound to be slower in D2O as compared to H2O because of the ki-

netic isotope effect in the hydrolysis. The autoaccelerating degra-dation caused the front to propagate with a constant velocity(n = 1 in Eq. (12)).

5.10. Coated formulations

Two types of the regulated drug release systems comprised of adrug-loaded tablet core and a coating have been studied in [455].Only part of the core surface was not coated and was directly ex-posed to the simulated gastric fluid. The tablets were residing inthe static USP dissolution medium while the images were detected.The results showed that the tablet with a faster than predicteddrug release had a porous coating. Its core was hydrating not onlyat the open cylindrical surface but at the entire core-coating inter-face much earlier than intended, with the fluid penetratingthrough the porous coating. This effect was much less pronouncedfor a modified coating formulation, for which after the dissolutionof the core the degradation of the coating was clearly observed(Fig. 30). In both cases, erosion of the core was uniform, with thedissolving core face remaining sharp. No significant swelling ofthe eroding polymer was observed.

Time-delayed capsules consisting of an insoluble shell contain-ing an HPC excipient as the expulsion system and sealed with aplug were studied [456]. The plugs used were erodible lactose/dibasic calcium phosphate tablets. To prevent water ingress, cap-sule bodies were film coated with ethylcellulose by an organic oran aqueous process. The capsules were immersed in water at 18or 37 �C and imaged in situ with SE or RARE. The organic-coatedcapsules produced the expected delayed pulse release behavior.Gradual hydration of the top of the plug was observed, with no evi-dence of hydration underneath, until the plug was eroded at thetop and water started to penetrate between the plug and the shellleading to the hydration of the capsule content. At 37 �C, the plugthickness was reducing linearly with time. For the aqueous-coatedcapsules, the hydration was much faster and less regular. Earlypenetration of water between the plug and the capsule walls andan early hydration of the capsule content and little plug erosionwere observed, and the plug could not be ejected. The resulting sig-nificant pressure build-up caused premature release by distortionand disruption of the capsule shell. Blurring of the images at latertimes indicated rapid swelling of the excipient.

5.11. Hydrodynamically balanced systems (HBS)

Hydrodynamically balanced systems (HBS) are intended to re-lease an active substance in the stomach while floating on the sur-face of the gastric content. The reduced density of the tablet and itsflotation can be achieved by means of trapped air or evolution ofCO2. To simulate in vivo conditions as close as possible, an MR-com-patible flow-through cell was designed and used to study HPMCloaded with L-dopa as a model drug and enclosed in gelatin cap-sules in simulated gastric fluids at 37 �C using flow-compensatedSE [457–459]. The dry core area of these HBS systems containednon-compressed powder, and the air trapped among the powdergrains was responsible for their floating properties. The evolutionin time of the total area of the HBS cross-section, the areas of thehydrogel and the dry core regions were obtained by constructingthe histogram of pixel intensities, separating it into groups, andusing intensity thresholding for the subsequent image segmenta-tion into the corresponding regions of the swelling tablet. The areasof the regions were determined and the tablet dimensions changeswere measured throughout swelling. The behavior was also com-pared for the tablets containing HPMC with different viscositiesand substitution types [459,460]. The results demonstrate thatthe dosage forms with similar dissolution profiles may have differ-

Fig. 30. (a) Schematic cross-sectional view of the controlled-release tablet designedto release drug at a constant rate: (1) coating; (2) active soluble core; (3) cylindricalface which controls dissolution rate of core; (4) central pillar attached to the upperand lower faces of the coat; (5) core/coat interface. (b) MR images of the tablet atvarious stages of dissolution: (A) 15 min, (B) 1 h, (C) 2 h, (D) 3 h, (E) 5 h, (F) 6 h, (G)7 h, (H) 14 h. The experiments were performed at 9.4 T. Adapted from Ref. [455],Copyright (1998), with permission from Elsevier.


ent temporal changes of physical and geometrical properties duringswelling.

The same approach was used to study the behavior of L-dopaloaded HPMC mixtures with carrageenans, the high molecularweight sulfated polysaccharides [461]. The swelling, formation ofthe gel, flotation behavior and changes in shape depended on thetype of carrageenan used in the formulation. In particular, thehighest swelling capacity was observed for the formulations withcarrageenan iota. The differences in the matrix behavior were par-alleled by the differences in the drug dissolution. It was shown thatcarrageenans promote water uptake by polymeric matrices and

thus their mixtures with HPMC can be used to produce tailor-madematerials for drug delivery systems.

A benchtop MRI system operating at 20 MHz was used to studythe dissolution of the tablets made of 80% water-insoluble poly(vi-nyl acetate) (PVAc) and 19% water soluble poly(vinyl pyrrolidone)with additives and loaded with different amounts of the highlywater soluble drug propranolol hydrochloride [462]. The tabletswere removed from the dissolution medium (0.1 N HCl) and placedin a cell with 2 ml of the same solution for imaging. All tablets werefloating owing to their low density. A high-intensity edge repre-senting the hydrated polymer layer surrounding the dry tablet coreappeared 10 min after the tablet immersion and was observed togrow with time (Fig. 31). Isotropic water diffusion and similarhydration rates were observed for the tablets with different drugloadings. The high initial porosity (the lowest density) of the tabletwith the lowest drug loading led to the visualization of air bubblestrapped inside the matrix. The same instrument and similar proce-dures were used to study the influence of the coating formulationson drug release and floating characteristics of the tablets [463]. Thetablets in that study were additionally coated with a polymericfilm and contained sodium bicarbonate in the tablet core. Uponcontact of the tablet with an acidic medium, HCl was expected todiffuse through the polymer coat and initialize CO2 evolution in-side the tablet, leading to the tablet flotation. All tablets initiallysank in the HCl solution, and only after a certain time lag movedup to the surface and stayed there (Fig. 32). The swollen polymerfilm was visible as a bright edge surrounding the core due to therapid water penetration into the film. Swelling processes startedwith an initially hydrated polymer film and a dry unswollen tabletcore, whereas in this phase the device was not yet afloat. The accu-mulation of CO2 started at the top side of the tablet directly abovethe surface of the tablet core, leading to an expansion of the filmcoat and observation of a dome-shaped floating tablet. Addition-ally, the swelling of the outer parts of the tablet core occurred,whereas the inner part remained dry. The continuing diffusion ofHCl inside the tablet led to a biconvex and swollen tablet withgas accumulation above and below the tablet core. Accumulationof CO2 inside the floating device expanded the tablet coat, leadingto the formation of a balloon shaped floating tablet. In the finalphase, the tablet was often slightly reduced in size and exhibiteda disintegrated core entrapping several smaller gas bubbles.

5.12. Osmotic systems and push–pull gastrointestinal therapeuticsystems (GITS)

Osmosis-based drug release mechanisms can be quite efficient.Swelling of a silicone matrix containing NH4F in water was studiedin [464]. In the presence of the salt, the T1 and T2 times of waterwere shortened and the ability of the cylindrical polymer sampleto absorb water was significantly enhanced. Water diffusion inthe matrix was accompanied by the formation of concentratedbrine droplets that grew under the action of osmotic pressure.The process was monitored over a period of 3 months. The spatialdistribution of water in a cylindrical sample containing 1% NH4Fwas more or less homogeneous during the observation time. At5% NH4F, after swelling for 7 days the content of water in the innerregion of the sample was lower than in the outer region, and after35 days of swelling the content of water in the outer region of thesample decreased. This was due to the development of stresscracking in the matrix and the release of the content of brine‘pools’. Cracking of the sample was initiated at the surface andgradually moved into the inner regions.

It is possible to design osmotic systems with controlled waterdiffusion into a semi-permeable external membrane which in-duces drug release through an orifice. Single core systems are oftenused for highly soluble drugs. For instance, commercial osmotic

Fig. 31. 2D MR images showing water penetration into the floating tablet loaded with 10% Propranolol HCl in 0.1 N HCl as a function of time. Lighter shades of graycorrespond to higher signal intensities. The experiments were performed at 0.5 T. Reprinted from Ref. [462], Copyright (2008), with permission from Elsevier.

Fig. 32. 2D MR images of a coated HBS tablet containing HaHCO3 and swelling in HCl solution. Lighter shades of gray correspond to higher signal intensities. The experimentswere performed at 0.5 T. Reprinted from Ref. [463], Copyright (2008), with permission from Elsevier.


tablets containing salbutamol (albuterol) sulfate and possessing acore covered with a punctured semipermeable membrane demon-strated [427] a relatively fast increase in tablet volume in the firsthour, but in the images the signal intensity in the core region re-mained low, presumably because it contained water in a boundstate. Further hydration was observed at later times.

For poorly soluble drugs, a push–pull system can be used. Apush–pull osmotic pump, commonly called a gastrointestinal ther-apeutic system (GITS), is designed to provide a well-defined pro-longed drug release. It consists of two layers, a drug layer and anosmotic layer, enclosed in a semi-permeable membrane. Both lay-ers get water across the membrane at a constant rate by osmosis.The expanding osmotic push layer squeezes the drug-containingsuspension through an existing puncture in the membrane, usuallyat a constant rate. Comparison of the images for a slow and a fastdrug releasing tablet [465,466] swelling in deionized water at anambient temperature demonstrated that the image of the slow re-lease tablet was virtually black (no signal), with some bright spotsindicating local water penetration, while in the case of the fast

release tablet, water has penetrated the membrane over the entireface. For both tablets, water penetration appeared to be greaterthrough the sides of the tablet than through the face. This observa-tion allowed the authors to conclude that the membrane could bethinner in the fast tablet compared to the slow tablet and was thin-ner on the sides of the tablet.

The behavior of a commercial formulation (Isradipine, DynacircCR) was compared to modified formulations using a 20 MHzbenchtop MRI system [467]. Tablets were periodically withdrawnfrom the dissolution buffer at defined time points and T1-weighted2D images were detected, with each measurement using a differ-ent tablet. A well-behaved gradual hydration of both layers wasobserved, with higher water contents in the drug layer which con-tained NaCl (Fig. 33a). The swelling and the increase in the pushlayer thickness and the corresponding decrease in the drug layerthickness observed in the images led to a constant rate of drug re-lease from 4 h to 12 h. A delicate balance between the swelling ofthe two layers defines this behavior, therefore the formulationused (e.g., drug load and composition of the layers) can have a

Fig. 33. (a) T1-weighted MR images and signal intensity profiles of a commercially available push–pull osmotic controlled release tablet (DynaCirc CR) after exposure to thedissolution buffer for 2 h (A), 4 h (B), 8 h (C), 12 h (D) and 16 h (E). (b) Images and signal intensity profiles of a laboratory formulation after 1, 2 and 4 h of exposure. Theexperiments were performed at 0.5 T. Adapted from Ref. [467], Copyright (2009), with permission from Elsevier.



dramatic influence on the drug release. Heterogeneities in thehydration of the drug and the push layers were clearly observedwith modified formulations. The most dramatic changes were seenfor a formulation which contained NaCl in the push layer only(Fig. 33b). Images indicated that pieces of the drug layer have beenpushed through the orifice before they could be fully hydrated. Atthe same time, the highly hydrated push layer was observed to by-pass the drug layer. This undesirable behavior is caused by the veryhigh osmotic pressures developing in the hydrating push layer,which lead to significant deformations of the tablet shape and in-crease of the overall dimensions.

Similar studies were performed for a commercially availablegastrointestinal therapeutic system tablet Cardura XL (Pfizer™)[468]. The essential difference was that 2D imaging was performedon a single pellet residing inside the rf probe for the entire exper-iment. A 500 ml volume cell was constructed in order to approxi-mate the in vivo release environment, but deionized water wasused in the experiments. Signal intensity variations in time indi-cated that transport of water was diffusional in the drug layer atall times, while for the push layer the diffusive transport at earlytimes switched to osmotic transport after 600 min of swelling. Dif-fusivities and osmotic transport rates were estimated from 1Dmodeling. The T2 distributions were obtained for the entire tabletat different stages of hydration. The peaks assigned to the drug(longer T2) and the push layers (shorter T2) could be identifiedand their evolution in time monitored. T2 times were found to in-crease, while T1 times became shorter with hydration time.

5.13. Poly(N-isopropylacrylamide) (PNIPAM), stimulus response

Certain hydrogels can respond to various stimuli. For instance,thermoresponsive hydrogels such as poly(N-isopropylacrylamide)(PNIPAAm) are known to have a lower critical solution temperature(LCST) in water and its mixtures with organic solvents. As the tem-perature exceeds the critical value or as the concentration of the or-ganic component of the solvent increases, the gel undergoes atransition from a swollen to a collapsed state. Such hydrogels canthus reversibly deswell above the LCST and lose significant amountsof water, which can be used to modulate drug release. MRI of acylindrical sample of PNIPAAm in H2O revealed a decrease in thediameter of the sample with an increase in the temperature of water[357]. The process was accompanied by a change in the T2 contrastdue to the variation of the mobility of the polymer and water mol-ecules. Experiments with a D2O/CH3OD mixture showed that theinitial stage of CH3OD diffusion in the polymer gel was Fickian,but the swelling-induced changes in the polymer gel structure ledto the non-Fickian behavior at later times. Sometimes the formationof a surface layer was observed, which slowed down or precludedfurther ingress of the solvent into the polymer gel. Volume phasetransition in PNIPAAm induced by the temperature change [469]and shrinkage of a cross-linked poly(methacrylic acid) gel uponapplication of an electric field [470–472] were reported. Swellingof copolymers of N-isopropylacrylamide (NIPAM) and N,N-dimeth-ylacrylamide (DMA) in the course of water uptake for various sam-ple compositions was also studied with MRI [358]. It was concludedthat concentration profiles were close to Case II transport behavior.19F MRI was used to study transport of 2,2,2-trfuoroacetamide(TFAm) along the copoly(NIPAAm/AAm) cylinders [473]. At thebeginning of the MRI experiment, a TFAm loaded sample wasbrought in contact with an unloaded hydrogel sample, and redistri-bution of TFAm was monitored by detecting 1D profiles along thesample axis. The extracted diffusivity values decreased significantlyabove LCST, reflecting the reduced water content in the hydrogel.

The release of a model drug tetramethyl ammonium bromide(TMABr) from the so-called ‘‘plum-pudding’’ gel, a composite gelstructure formed by a cross-linked hydrogel (DMA) containing

responsive microgel particles (acrylic acid–N-tert-butylacryla-mide–N-isopropylacrylamide microgels), was investigated by 1DCSI [474]. The microgel particles act as a reservoir of TMA+ ions.The release of TMA+ was triggered by the dications of methyl green(MG2+) diffusing into the gel from the surrounding solution, releas-ing two TMA+ ions per each MG2+ ion bound to the microgel. A sub-stantial release of TMA+ was observed in the first 10 h, whereas forthe control sample with no MG in the solution the TMA+ concen-tration did not change significantly in 40 h. 1D CSI was also usedto monitor the simultaneous release of two species with differentmolecular weights, imidazole and PEG, from DMA into an externalaqueous environment [474].

The behavior of P(MAA–co-PEGMEMA) hydrogel containingmodel drug diltiazem hydrochloride was examined in [475]. Thepolymer was synthesized directly inside a soft gelatin capsule fromwater/ethanol solutions containing methacrylic acid (MAA) andpoly(ethylene glycol) monomethyl ether monomethacrylate(PEGMEMA), the drug, the UV-light sensitive photoinitiator 1-hydroxycyclohexyl phenyl ketone and the cross-linker tetraethyl-ene glycol dimethacrylate. Four different initial molar percentagesof MAA were used (25, 50, 70 and 85 mol.%), and swelling in a PBSdissolution medium and drug release were studied at pH 1.2 and 7.The NMR images were acquired at room temperature, and the 2DSE images were converted into proton density maps. For the co-polymers with 70 and 50 mol.% MAA, after swelling of the gelatinecapsule the swelling was not homogenous. The inner part of thecapsule started to swell and at the same time the formation of askin was apparent. After ca. 1 day of swelling, the skin had clearlydeveloped while the mobility of water in the deeper regions wassimilar to that of the dissolution medium outside the capsule. Incontrast, the hydrogels with 25 and 85 mol.% of MAA exhibited aslight but isotropic swelling. Comparison of the MRI results withthe drug release data allowed the authors to conclude that forma-tion of the skin, which is caused by the efficient hydrogen bond for-mation between co-monomer units at low pH for samples with anequimolecular composition, provides an impermeable barrier pre-venting total release of the drug but allows water penetration. Incontrast, hydrogels with 25 and 85 mol.% MAA that did not showthe formation of such skin, released the total amount of the drug.Hydrogels with medium compositions are thus expected to beeffective in protecting the drug against the acidic medium of thestomach but allow its release at the higher pH of the intestine. Atneutral pH, the constant advance of a swelling front, observed byMRI, can provide drug release at a constant rate over a long periodof time.

5.14. Other studies

A drug-loaded matrix consisting of an amphiphilic lipid andparaffin in varying proportions and containing dicalcium phos-phate particles was studied ex situ with a 22 lm in-plane spatialresolution at 600 MHz [476]. A well-defined moving penetrantfront was observed. Significant heterogeneities in the distributionof buffer solution within the beads were observed even after thecompletion of the process. The authors note that such heterogene-ity can affect drug release.

The ingress of saline solution at pH 7.4 into calcium polyphos-phate tablets demonstrated that relaxation time maps can be usedto follow the evolution (degradation) of the matrix even when li-quid concentration profiles no longer change with time [477].Enzymatic degradation of thin films of poly(hydroxyalkanoates)has been studied by 1H MRI as an example of a biodegradable sys-tem [478].

The NMR based porosimetry techniques represent valuabletools for studying the evolution of the pore space of placebo anddrug-loaded tablets during their swelling [479]. Modeling of the


MRI data on polymer tablet swelling and dissolution was reported[480].

A recent trend concerns the development of the approaches forstudying the behavior of pharmaceutical dosage forms and of otherbiocompatible and biodegradable polymers in vivo. Such studiesare much more demanding and are often characterized by a muchlower spatial resolution and sensitivity. Nevertheless, examples ofsuch applications have been published [389,390,481–484]. Abenchtop MRI imager suitable for in vivo studies was used to exam-ine polymer precipitation in vivo [485].

6. MRI of drying processes


Drying is widely employed in various technological processesand involves a broad variety of porous and non-porous materials.For instance, the performance and durability of concrete and othercement-based materials depend greatly on the completion of theirhydration and the amount of residual moisture content. Drying isused in various film-based technologies (adhesives, binders, coat-ings, paints, etc.) and in the preparation of supported catalysts.Many foods and natural products undergo moisture removal pro-cessing. Some materials, such as calcined ceramics, pre-dried con-crete, porous rocks, etc., represent rigid matrices with an intrinsicporous space structure which undergoes little modification uponthe removal of a liquid phase. For some other materials, the pro-cesses that take place during drying are much more complex. Forinstance, hydration of cement-based materials and drying and cur-ing of polymeric film coatings and paints can lead to a dramaticchange in mobility of the liquid phase which can be accompaniedby little or no liquid loss. In what follows, these processes are nev-ertheless classified as drying as the mobile liquid is removed and/or becomes significantly less mobile.

The quality and durability of the final product can depend cru-cially on the drying technology employed. For most materials, theresidual liquid content, its distribution and state determine theproperties of the final product. The removal of a liquid from solidmaterials can be rather slow. Accelerated drying and/or reducedenergy consumption can make technological processes more effi-cient. However, even a slight violation of the drying regime canlead to unacceptable consequences such as shrinkage, deformationor cracking of materials and coatings. Therefore, optimization of adrying process requires an ability to monitor the changes in theamount, the distribution and the state of liquid in the materialand the accompanying changes in the properties of the material it-self directly in the course of the drying process. This can help re-veal and quantitatively characterize the mass transport processesinvolved. MRI technique can provide this kind of information.

Many mass transport mechanisms can be operative during dry-ing of porous materials. These include capillary and film flow of theliquid phase, diffusion and pressure-driven flow of the vapor andpossibly other transport mechanisms. These mechanisms, in com-bination with the drying conditions, determine the character of thedrying process. At high liquid contents when most of the pores arestill filled, the liquid phase is continuous (the so-called funicularstate) and transport is mostly caused by capillary action. Dryingat this stage often proceeds at a constant drying rate, and liquidcontent gradually decreases in the entire sample. This is referredto as the ‘‘slow drying regime’’, because redistribution of the liquidphase in the pores is able to proceed much faster than the removalof the liquid phase from the sample surface. However, liquid phaseremoval inevitably comes to a point when the system of liquid ele-ments is disrupted and can no longer sustain the effective trans-port of the liquid phase and replenish the liquid pool near the

surface (pendular state). At this stage, vapor transport and possiblyfilm flow become the main transport mechanisms. At this stage,mass transport becomes slower, the drying rate starts to fall, andoften a receding drying front which moves into the sample awayfrom its surface is observed. This is called the ‘‘fast drying regime’’as redistribution of the liquid phase can no longer compete with itsremoval from the sample.

Capillary flow is an interesting transport mechanism. It is in-duced by the pressure difference which arises whenever a contin-uous element of a liquid in a system of pores has menisci withdifferent diameters. It leads to a number of remarkable features,some of which are discussed later. The important consequencefor, e.g., water transport in a drying hydrophilic porous materialis that smaller pores tend to stay filled until all of the larger poresin the vicinity are emptied. This means that in the funicular state,larger pores are drained first. This process of refilling smaller poresat the expense of the larger ones can be extremely efficient sincecapillary pressures in drying materials can be so high that theycan damage the solid matrix. Obviously, one would like to avoidsuch damage in practical applications. For hydrophobic materials,capillary transport of water can be much less efficient, and thereceding front is usually observed early in the drying process.

There are various ways to induce or intensify drying. One possi-bility is the forced convection of air (gas) supplied at an ambienttemperature, which is sometimes called ‘‘isothermal drying’’,which is an approximation. Strictly speaking, drying cannot be iso-thermal since it is inevitably accompanied by a phase transition(evaporation, sublimation) which usually leads to a decrease inthe material temperature. If drying is fairly slow, however, thiscan still be a reasonable approximation. Drying can be also per-formed at elevated temperatures. In any case, heat transport isan important process during drying. It is difficult but possible toperform temperature measurements in combination with MRimaging, using, e.g., IR thermometry or implanted thermocouples.It appears that NMR thermometry has never been attempted incombination with drying experiments. We also note that dryingdoes not imply boiling and can be very efficient not only belowthe boiling point of a liquid but also below its melting point (sub-limation). Other drying methods include contact drying, spray dry-ing, etc. The transport of the liquid phase during drying can alsosignificantly affect the transport of solutes (e.g., dissolved salts).

All the liquid content quantification problems discussed in Sec-tion 1.3 are also applicable to most porous materials that undergodrying, and in particular for cement-based materials where the T�2time of water molecules in hydrates can be shorter than 20 ls.Even the solid-state imaging techniques such as STRAFI and SPIcan fail to detect some of the water in the hydrates. The randomdistribution of non-porous aggregates used in the preparation ofmortar and concrete can lead to significant image heterogeneities.Both cement and aggregates are often chosen to have a low contentof paramagnetic and ferromagnetic substances to avoid additionalrelaxation-induced signal losses. GARField is a suitable instrumentand technique for studying the drying of thin films and coatingswith the thickness of tens to hundreds of microns.

6.2. Drying of rigid matrices

Mass transport in porous oxides (Al2O3, SiO2, TiO2, etc.) isimportant in many areas including catalysis. Drying of liquid-satu-rated mm-sized oxide pellets in a stream of dry air has been stud-ied to reveal their morphological and transport properties[279,486,487]. Drying of alumina cylinders and silica beads wasstudied by detecting 2D images and converting them into 1D radialprofiles of water content [486]. For an alumina pellet with a mono-modal pore size distribution (PSD), the radial profiles were foundto be almost rectangular, while for a bimodal PSD, high gradients


of water content were observed. The D(S) dependence was mea-sured by performing PGSTE experiments at different stages of dry-ing and was compared with the numerical simulation of a diffusionprocess. The drying time of mm-sized pellets is short (less than anhour), therefore 2D imaging is generally too slow for a quantitativeanalysis of the drying process. The detection of 1D profiles alongthe diameter of a cylindrical pellet made it possible to reduce theimaging time down to 0.5–1 min per profile [2,279,487]. Signifi-cant shortening of T2 in the course of drying caused the NMR signalto diminish with time faster than the actual water content of thepellets (Fig. 34a), and calibration experiments were required tocorrect for this effect (Fig. 34b). The original and the corrected pro-files are shown in Fig. 35. The results and their mathematical mod-eling demonstrate that the early stages of drying correspond to theconstant drying rate (slow drying) regime because of an efficientredistribution of the liquid phase in the material. As a result, an al-most uniform reduction of water content throughout the pellet isobserved. The drying rate starts to fall (fast drying regime) onlyafter a substantial fraction of water is removed from the pellet.At this stage, significant moisture content gradients develop. Math-ematical modeling of the evolution of radial profiles with time wasused to extract the D(S) dependence [2,488]. At high S values, the‘‘capillary diffusivity’’ D by far exceeds the self-diffusivity of water.It was demonstrated that D(S) reflects the PSD of the pellet, andwhile generally D decreases with decreasing S, in the case of a

Fig. 35. (a) Temporal evolution of the apparent water distribution along the diameterprofile started simultaneously with turning on the nitrogen gas flow. The profiles are noevery 60 s. The arrow points to the curved profile which then suddenly becomes flat asalumina II sample obtained by correcting the profiles shown in (a) for the T2-weighting ethe alumina II sample. Horizontal lines show saturation levels corresponding to the avera(a and b) Reprinted from Ref. [2], Copyright (2000), with permission from Elsevier. (c) Ad

Fig. 34. (a) The dependence of water T�2 time on the degree of pore filling for two aluminis assumed to be proportional to the total amount of water in the sample; 100% value corelation between the 1D water content profile height and the actual water content iinterpolation. The value of 100% on both horizontal and vertical axes corresponds to a samwith permission from Ref. [487].

complex (e.g., bimodal) PSD the D(S) dependence can have localmaxima. Experimentally this was observed as a sudden accelera-tion of the capillary flow resulting in a peculiar flattening of theconcentration profile in the middle of the drying process, as al-ready mentioned in Section 1.2. In fact, the explanation of suchbehavior is rather straightforward.

The morphology of alumina pellets used in these drying studiescan be described as an agglomerate of clusters of primary particleswith mesopores inside the clusters and macropores between them,as confirmed by the cumulative PSD measurements [487]. In thebeginning of the drying process, the macropores close to the exter-nal surface of the sample start to drain which leads to the develop-ment of a moisture content gradient within the pellet. Thisgradient leads to the transport of water from the inner regions ofthe pellet toward the surface where water evaporates, and is re-flected as the pronounced curvature of the water distribution pro-file (see Fig. 35). At the same time, mesopores tend to stay filleduntil all macropores are drained. When the residual water contentnear the pellet surface reaches the level when all surface macrop-ores are empty, some of the macropores in the inner pellet partsare still filled as the water content is larger in the inner regions.If the bimodality in the PSD is quite pronounced (see Fig. 35c), cap-illary action will make sure that the mesopores near the surfacewill stay filled until all macropores in the inner parts of the pelletare drained. This leads to the diminishing of the moisture content

of cylindrical alumina II sample during its drying. Acquisition of the first (highest)t corrected for the T2-weighting effects. Alumina II sample; profiles were detecteddrying continues. (b) The profiles of the actual water content during drying of the

ffects using the calibration curve of Fig. 34b. (c) Cumulative pore size distribution ofge height of the corresponding profiles. The experiments were performed at 7.05 T.apted with permission from Ref. [487].

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a samples with different pore size distributions. The integral of water 1H NMR signalrresponds to the sample fully saturated with water. (b) Experimentally determinedn the alumina II sample. Solid line shows a double-exponential fit used for data

ple fully saturated with water. The experiments were performed at 7.05 T. Adapted

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Fig. 36. Temporal evolution of water content in straight glass capillaries in thecourse of drying. The sample was sealed at one end and was initially fully saturatedwith water. The 1D MR profiles of water content along the capillaries in the entiresample (no slice selection) were detected. The successive averaged profiles weredetected every 180 s; every eighth profile is shown (60 profiles in total are shown).The experiments were performed at 7.05 T. Reprinted with kind permission fromSpringer: Ref. [279], Fig. 1.


gradients within the pellet and the gradual flattening of the ob-served concentration profile until an almost uniform water distri-bution is established at this stage of the drying process. Thiscorresponds to a faster apparent diffusion of water in the pelletand leads to the appearance of a maximum in the D(S) dependence.Once all macropores in the sample are drained, mesopores start tolose water and the water content gradient that drives water trans-port appears again. As demonstrated in [2], the observed peculiarbehavior arises because the relation between the concentrationand pressure gradients depends crucially on the local slope of thecumulative PSD of the porous material, and because the local con-centration gradient (i.e., the profile shape) tends to readjust itselfpermanently in order to maintain a certain capillary flow of liquidtoward the sample surface.

In fact, the profiles can reveal the degree of the pellet’s non-uni-formity [279]. If a pellet is not uniform and has smaller pores nearthe edges, in the course of drying the value of S can become smallerin the inner parts of the pellet as compared to its edges. This dem-onstrates that capillary flow can transport a liquid in the directionof the saturation gradient thus increasing this gradient in time, incontrast to conventional diffusion that can only reduce the existinggradients. For acetone, cyclohexane and benzene the capillary flowwas much less efficient and the concentration profiles along thepellet diameter exhibited much larger concentration gradients[2,279,487].

Catalysts and catalyst supports made of porous oxide materialsoften have a more sophisticated shape than simple rods or beads.For instance, catalytic purifiers of automotive exhaust gases utilizemonoliths, which are structures with multiple parallel channelsand porous oxide walls with deposited catalytic species. A frag-ment of an alumina monolith ca. 21 mm in diameter with a4 � 4 mm2 cross-section and 1 mm thick channel walls presaturat-ed with water was dried with a stream of air flowing through itstransport channels. The 1D profiles of the water content were de-tected along the sample (i.e., along the channels) [279]. Despite alarge sample length (25 mm), the drying was uniform along themonolith. For comparison, the drying of a modified sample wasinvestigated. It had the same overall shape but the redistributionof water along the sample was made impossible by cutting themonolith into 10 sections perpendicular to the channels and thenre-assembling it with epoxy. In this case, the drying rate was ob-served to decrease with increasing distance from the inflow edge,as expected [245]. These comparative studies clearly demonstratethe efficient capillary redistribution of water in the porous matrixduring its drying. 2D MRI of monolith drying was also reported[489]. Also investigated were the room-temperature dry-curingof monoliths [490] and their adsorption-contact drying with fine-grained alumina or zeolites [491].

Capillary flow should be inefficient during the drying of a longcapillary of a constant diameter. This was confirmed for a samplecomprising a large number of identical parallel capillaries filledwith water and sealed at one end [279,492]. Drying was inducedby a stream of dry air flowing over the open end of the sample.The 1D profiles detected along the direction of the capillaries re-vealed the propagation of a sharp drying front toward the sealedend from the very beginning of the drying process (Fig. 36). Thefront position changed with time as t1/2, and the evaluation ofeffective diffusivity yielded the value D = 0.24 cm2/s which is closeto water vapor diffusivity in air.

Evaporation of liquid droplets from porous surfaces is impor-tant in, e.g., environmental and technological applications. Evapo-ration of droplets impinged onto a bed of glass beads (50, 120 and400 lm) or sand particles (180 lm) in a stream of air flowing par-allel to the surface has been addressed by detecting the 1D depthprofiles and 2D images for water [493,494] or a water/butanol mix-ture [493]. The 2D images (Fig. 37) have shown that the water

droplet with a relatively sharp interface resided as a semi-spheroidbeneath the bed surface, with different depths of penetration andspread ratios for different beds. 1D profiles were used to extractdrying curves (S(t)) and drying rates as the droplet was evaporatingfrom beneath the bed surface. A distinct constant drying rate per-iod was observed for 400 lm glass beads but not for 50 lm beads.Pronounced differences in the droplet shapes and drying behaviorwere observed between the glass beads and sand. As compared towater, for water/butanol mixture the increased droplet spread,smaller penetration depth and much faster drying with no con-stant rate period were observed. While evaporation of water pro-ceeded more or less uniformly along the depth coordinate[493,494], evaporation of a droplet of diethyl malonate [495]started from the upper surface and led to the formation of a reced-ing drying front. Only after the front receded to ca. half of the drop-let depth, did the evaporation of the droplet become uniform. Thedifferences in behavior were attributed to the increased viscosityand the reduced surface tension of diethyl malonate as comparedto water.

A number of studies have investigated the drying of variouswater-saturated beds comprised of porous or non-porous particles.Beds of glass beads (0.3–0.8 mm diameter), sand (50–100 lm), po-tato starch granules (20–50 lm) and silica (40–60 lm) were driedwith an air flow over the bed surface and imaged ex situ by detect-ing 1D profiles along the bed [496]. The results demonstrated thespatially non-uniform drying of the beds. Both constant rate andfalling rate drying periods were observed. The effect of surface ten-sion was considered by comparing the results for water and anaqueous solution of SDS detergent. The experimental results werediscussed with the use of a model which included the diffusivetransport of liquid and the capillary and gravitational forces. Thelatter become important for larger particle sizes. The 3D imagingof a bed of 1 mm glass beads [497] also demonstrated non-uniformbed drying (Fig. 38). Beds of liquid-saturated porous alumina pel-lets and of mixed non-porous and liquid-saturated porous pelletswere examined [279] as a model to reveal the differences in masstransport processes for pellets located at different distances fromthe walls of a cylindrical packed bed.

Issues relating to the drying of porous rocks and building mate-rials have been addressed in a large number of papers. Isothermalor heat-induced drying of a fired-clay brick was studied by

Fig. 37. Time evolution of the water concentration profiles along with the images of the shape of the droplet in the bed of 400 lm glass beads during drying. Both time (T⁄)and concentration (c⁄) are given as normalized quantities. The experiments were performed at 7.05 T. Reprinted from Ref. [494], Copyright (2003), with permission fromElsevier.


detecting 1D profiles along the axis of a cylindrical sample [498].Signal intensity for this sample was linearly related to moisturecontent [207], which is rather unusual. The two drying stages wereclearly distinguishable from the temporal evolution of the profiles.During the first stage, some concentration gradients developed, butthe water content decreased along the entire sample. Capillaryflow at this stage was efficient enough to deliver the liquid phaseto the external surface of the sample where it evaporated. Duringthe second stage, a receding drying front with large differencesin moisture contents behind and ahead of it was observed. Duringthis stage, transport to the external surface and out of the sampleproceeds through vapor diffusion, which is fairly slow. As a result,the drying front moves further away from the open end into thesample, the vapor has to travel a longer path, and the drying ratedecreases further. The profiles were integrated to yield the dryingkinetics (S(t)) which also clearly showed the two stages of the pro-cess. Similar results were obtained for the isothermal drying offired-clay brick, sand–lime brick, [51,205], gypsum [51] and mortar[205]. The D(S) extracted using Eq. (2) was found to decrease withdecreasing S in the range S = 20–5 vol.%, have a minimum at S = 2–5 vol.%, and grow as S decreased further. To better determine D atlow S values where vapor transport dominates, the velocity of thereceding drying front measured experimentally was compared tothe results of simulations.

The same approach was used to study drying of water-saturatedfired-clay brick, calcium-silicate brick and concrete under intenseheating conditions [499]. Under such conditions (e.g., for buildingmaterials in a fire), the boiling of water in the pores can result inthe heat-induced spalling of the material which can be explosive.Due to the boiling-induced pressure build-up in the pores, the li-quid water temperature can significantly exceed 100 �C. The trans-port of evaporated water out of the sample is driven not bydiffusion but rather by pressure gradient-induced vapor flow. Thereceding front during the second drying stage was less pronouncedfor concrete as compared to the two brick samples. Due to the low-er porosity and permeability, the speed of the receding front wasmuch lower in concrete, leading to much higher temperatures(measured) and pressures (evaluated) at the front as comparedto the brick samples. Experimental results for brick and concretewere compared to model calculations [499,500]. In a later study,an array of halogen lamps was used to heat the sample surfaceto 400–500 �C [501]. The concrete sample was equilibrated at97% relative humidity (RH) before drying. The quadrature echo se-quence was used in combination with frequency switching to gen-erate a 1D water distribution profile upon one-sided heating of acylindrical sample sealed on all other sides. In addition, a numberof thermocouples were implanted along the sample to obtain tem-perature profiles. The signal profiles have shown that immediately

Fig. 38. A series of slices through three-dimensional 1H MR images obtained during drying of a packed bed of 0.5-mm glass beads inside a 10-mm-diameter glass tubeinitially filled with deionized water. The images are detected 0 h (a), 1.5 h (b), 3 h (c), 4.25 h (d), 5.25 h (e), and 7 h (f) after starting the drying process. The experiments wereperformed at 4.7 T. Reprinted from Ref. [497], Copyright (1999), with permission from Elsevier.


after the heating was started, a boiling front was observed to enterthe sample. Some residual signal observed behind the drying frontwas attributed to water chemically bound in the cement paste.Ahead of the front, the signal increased by ca. 10% above the initiallevel. This peak reached the saturated moisture content of the con-crete and widened until it reached the far end of the 100 mm longsample. A high vapor pressure which builds up at the boiling fronttransports water vapor both toward the dry surface and in thedirection of the far end of the sample. In the latter case, as vaporenters the regions with a lower temperature, it condenses (at ca.140 �C) thus leading to an increase in liquid water content aheadof the front. The authors note that given the large changes and gra-dients of the temperature of the liquid phase, the correct interpre-tation of the observations requires that the signal intensity becorrected for the temperature dependence of the relaxation timesand nuclear magnetization.

In [502], a cubic sample of limestone was dried at 105 �C in anoven and was periodically taken out and imaged at 0.1 T after an

equilibration period of 90 min. Both 1D profiles and 3D imageswere acquired. A substantial signal was observed behind the dry-ing front at the second drying stage (and in the dry sample), withT2 and T1 times ca. 3–10 times larger than ahead of the dryingfront. Two stages for the drying limestone sample were also ob-served in [503]. 2D projection–reconstruction MRI was used tomonitor drying of water-saturated limestone samples [504]. Thedrying surface of one of the two samples was painted with an ac-rylic emulsion paint. The unpainted specimen was observed to dryfaster, especially during the first drying stage. As a consequence,the drying front receded earlier into the unpainted specimenwhich can potentially affect the salt deposition in a dryingmaterial.

6.3. Drying-induced transport of salts

Transport of liquids during drying can be accompanied by thetransport of various solutes. In particular, the presence of salt in


the pores of buildings and monuments belonging to cultural heri-tage can cause their accelerated degradation. The effect of salt onthe drying of masonry specimens was studied using 2D projec-tion–reconstruction MRI [505]. The samples saturated with eitherpure water or a 3 M NaCl aqueous solution were subjected to astream of dry air. The presence of NaCl made drying slower. Be-sides, contrary to pure water, no receding drying front stage wasobserved with NaCl solution. The possible reasons are the lowerequilibrium relative humidity values for the salt solution and thecrystallization of salt in the pores as water is removed. A directstudy of salt transport upon drying was also reported [506,507].Fired-clay brick cylinders were saturated with a 3 M NaCl aqueoussolution and dried from one open end with a stream of air. The 1Dprofiles were acquired for both 1H and 23Na nuclei. The 1H profilesshowed that the moisture distribution within the sample remainedhomogeneous for up to 14 days, with no receding drying front ob-served. By calculating the ratio of the 23Na and 1H profiles, localconcentrations of the dissolved NaCl in the pores were obtainedsince only Na+ ions in the liquid phase were detected in the 23NaMRI experiments (Fig. 39). The results demonstrated that whileboth the 1H and the 23Na profiles decreased in intensity with time,during the initial drying the NaCl concentration in solution slowlyincreased near the drying surface to the saturation value of 6 M be-cause of the advection-induced transport of Na ions toward thesurface. At this point, salt crystallization at the drying surfacewas observed and the NaCl concentration profile in the samplestarted to level off until the total sample was at 6 M. Experimentswere repeated [507] for different salt concentrations and drying(air flow) rates, and the results were presented as an efflorescencepathway diagram, the total amount of NaCl in solution (the quan-tity measured directly by NMR) plotted against the average satura-tion of the sample with the liquid phase. This diagram allows oneto distinguish the two limiting cases: for slow drying, the ion

Fig. 39. NaCl concentration profiles obtained using 23Na MRI during drying of afired-clay brick sample of 45 mm length after 0, 1, 3, 6, 9, 12, and 15 days. Theexperiments were performed at 0.8 T. Reprinted from Ref. [506], Copyright (2003),with permission from Elsevier.

concentration increases gradually and uniformly throughout thesample up to the 6 M value, whereas for fast drying the ions are ad-vected to the sample surface and the concentration throughout thesample (excluding an infinitely narrow area near the surface) re-mains unchanged. Some of the drying experiments demonstratedthe behavior that was close to the fast drying limit. The experi-ments were performed [506,507] at 0.8 T, and a Faraday shieldwas used in the rf probe to suppress the effects caused by thechanging conductivity and dielectric properties of the sample dur-ing drying. To profile the entire sample length, the cylindrical sam-ple was repositioned vertically by a stepper motor. The typicalsample drying time was several days.

The influence of a difference in PSD between the plaster andsubstrate layer on the water and salt transport and the salt accu-mulation during drying of the two-layer plaster–substrate systemswas studied using 1H and 23Na 1D SE [508]. Bentheimer sandstoneand calcium-silicate brick were used as substrates, in combinationwith lime–cement plaster. The pores of the plaster were an order ofmagnitude smaller than those of Bentheimer sandstone and an or-der of magnitude larger than the nanometer pores in the bimodalPSD of the calcium-silicate brick. Water was allowed to evaporatethrough the air/plaster interface only. For pure water, its profiles inthe plaster/Bentheimer sandstone system have revealed the exis-tence of two drying stages. During the first stage (t < 2 h), the Bent-heimer sandstone dried, whereas the plaster remained saturated.After that, the plaster started to dry, and after ca. 6 h a recedingdrying front was observed to enter the plaster. When salt solutionwas used (Fig. 40), the same two drying stages were observed, butthe drying was much slower and no receding drying front could beobserved. In the 23Na experiments, at t < 25 h the distribution of Nain the Bentheimer sandstone remained uniform at the initial con-centration of 4 M, while the total amount of dissolved Na in thesystem decreased due to precipitation. At the same time, theamount of dissolved Na in the plaster increased, and a Na peakdeveloped at the drying surface. At the top of the plaster after25 h of drying, the concentration reached the solubility limit of6 M. For pure water in the plaster/calcium-silicate brick system,three drying stages were observed. During the first drying stage(t < 4 h), both the calcium-silicate brick and the plaster dried rap-idly. During the second drying stage (4–40 h) the plaster continuedto dry rapidly, whereas the drying of the calcium-silicate brick slo-wed down significantly. During the third drying stage (t > 40 h) theplaster was almost dry, and the calcium-silicate brick still con-tained a significant amount of water. For the salt solution, onceagain the drying was much slower and no receding drying frontwas present. The 23Na experiments demonstrated that fort < 12 h, the amount of dissolved Na in the plaster stayed constantand decreased in the calcium-silicate brick. As a result, salt wastransported from the calcium-silicate brick to plaster where itaccumulated near the drying surface. During the second dryingstage (12–100 h), the amount of dissolved Na in the plaster de-creased due to crystallization. At the same time, the amount of dis-solved Na in the calcium-silicate brick increased. At t > 100 h, theplaster was essentially dry, and the quantity of dissolved Na in cal-cium-silicate brick decreased due to crystallization. In addition, thetransport in a plaster/Bentheimer sandstone sample was studiedwhen the plaster layer was saturated with pure water and theBentheimer sandstone was saturated with a NaCl solution. Thedrying was much faster than that of the sample with a uniform ini-tial salt distribution. The salt was observed to be transported to thedrying surface, and the total amount of salt in the plaster in-creased. The drying experiments demonstrated that the same plas-ter applied on different substrates may exhibit different dryingbehavior. When the plaster has small pores compared to the sub-strate, as in the plaster/Bentheimer sandstone system, the saltaccumulates in the plaster for all drying rates. On the other hand,

Fig. 40. Evolution of moisture profiles (a) and the profiles of dissolved Na (b) in the plaster/Bentheimer sandstone system during drying detected using 1H and 23Na 1D SEmeasurements, respectively. Dry air is blown over the top of the sample (x = 4 mm). The sample was initially saturated with an aqueous NaCl solution. Total amount of water(c) or dissolved Na ions (d) in the plaster and Bentheimer sandstone as a function of drying time. The experiments were performed at 0.7 T. Adapted with kind permissionfrom Springer: Ref. [508], Figs. 5 and 6.


when the plaster has larger pores than the substrate, as in the plas-ter/calcium-silicate brick system, a significant amount of salt crys-tallizes within the substrate itself. When the drying rate is low,little salt crystallization takes place in the plaster, whereas at highdrying rates advection dominates the ion transport and salt crys-tallizes in both the plaster and the substrate.

Transport of moisture and salt has also been studied [509] intwo three-layer samples: a fired-clay brick substrate with two dif-ferent lime–cement plaster layers and a Bentheimer sandstonesubstrate with a lime–cement plaster on which a gypsum layerwas applied as a finishing. The original idea was to prepare thethree-layer samples in such a way that the base (inner) plasterlayer would have the smallest pores and the outer (gypsum orplaster) layer would have the largest pores. That way the base plas-ter layer could stay liquid-filled longest and thus could accumulatesalt in its pores. In practice, the two plaster layers of the first sam-ple had bimodal PSD but similar pore sizes, while for the secondsample the pore sizes of the outer gypsum layer were intermediatebetween the pore sizes of the base plaster layer and the substrate.1H and 23Na 1D MRI were used in an interleaved manner to detectwater and Na profiles along the sample. During the drying experi-ments, dry air was blown over the open end corresponding to theouter plaster layer. Initially, either the samples were uniformly sat-urated with the aqueous NaCl solution, or only the substrate partcontained the salt solution while the two plaster layers contained

pure water. For comparison, drying of the samples fully saturatedwith pure water was also performed. For salt-loaded systems, thedrying is slower than for pure water because of the lower vaporpressure above the salt solution, and also possibly because the saltprecipitation during drying blocks part of the porous network. Atthe same time, the initial drying is fast enough to induce significantadvective transport of dissolved salt at the early stages of drying. Inthe first system, after the initial emptying of the largest pores thesubstrate continued to dry while the two plaster layers tended toremain wet, as expected from the relative pore sizes of the threelayers. Similar drying behavior was observed for the salt-loadedsample, therefore drying-induced transport of salt from the sub-strate toward the plaster layers caused significant accumulationof salt in the external plaster layer and at the drying surface. Inthe second system saturated with water, the substrate and theexternal gypsum layer were observed to dry first, whereas the baselayer remained wet, again in agreement with what could be ex-pected based on the relative pore sizes. Significant transport of saltfrom the substrate to the base plaster layer and the gypsum layerwas observed, and accumulation of the salt occurred in both gyp-sum and plaster layers, with some precipitation of the salt at theouter surface. If only the substrate were initially loaded with salt,the very fast drying of the gypsum layer led to the predominantaccumulation of salt in the base plaster layer. The authors note thatnot all the dissolved Na ions are detected in the plaster layers


because of the faster relaxation in the smaller pores, and the pre-cipitated (solid) NaCl is not detectable in the MRI experiments.Therefore, the final distributions of the Na and Cl ions were deter-mined using ion chromatography in the cut samples. This study re-veals that the simple pore size arguments are not sufficient andseveral other factors can affect behavior significantly, such as theinitial distributions of water and salt in the sample, and changesof the wetting properties in the presence of salt.

6.4. Drying accompanied by an extensive matrix change

Some materials can shrink during drying, which along with thevarying capillary pressure can lead to the development of mechan-ical stresses and the risk of cracking. Kaolin clay drying at roomtemperature was studied with 2D MRI [510]. Obtaining 2D imageswas essential since the peculiarities of the evolution of moisturedistribution for a right-angled triangle (brick corner) were ad-dressed (Fig. 41a). The images were used to extract the moisturecontent gradients for the evaluation of D(S) (Fig. 41b). The D(S)dependence was also determined from the 1D profiles of Kaolinclay drying for a broader range of S values (Fig. 41c). D was con-stant at high S, decreased as S decreased, and then increased againowing to the increasing role of vapor transport. Mathematicalmodeling using a modified diffusion equation to calculate themoisture content evolution and shrinkage-induced displacementsof the solid phase was performed to evaluate mechanical stressesand the risk of cracking during drying.

Setting of fresh concrete, mortar or cement paste is much morecomplex than just drying, and water is an ingredient which is ofparamount importance in these materials. In many cases, theamount of moisture that leaves the sample is smaller than theamount of water which becomes a part of the final material as a re-sult of the formation of hydrates and the gel phase. Water in ce-ment-based materials is often classified as non-evaporable andevaporable water. Non-evaporable water is chemically bound inthe hydrates and can be removed only by thermally destroyingthe material microstructure. Evaporable water can be removedduring drying and is usually further subdivided into capillary waterresiding in macropores and gel (inter-layer) water in the micro-and mesopores of the solid gel formed upon cement hydration.For the initial water-to-cement mass ratios of 0.3–0.4, almost allwater molecules are retained in the newly formed phases that oc-cupy the porous space. Cement-based materials are often

Fig. 41. (a) 2D MR imaging of drying of a clay brick corner in a stream of air at 0% relativeto right): 0 h, 1.5 h, 3 h, 5 h, 10 h. D(S) dependence determined from 2D images (b) and 1DCopyright (2002), with permission from Elsevier.

moist-cured under high humidity conditions prior to the dryingstage. The distribution of water in the final product is importantas it determines its durability and resistance to corrosion, freeze–thaw and fire-induced spalling. During the drying of cement-basedmaterials, higher initial water contents usually lead to higher sam-ple porosity and thus more efficient capillary removal of moistureduring the initial stages of drying. Extended moist curing of thesamples tends to lead to a lower porosity and permeability of thematerials and thus to a reduced efficiency of capillary flow. As withother drying materials, during the later stages moisture is removedby diffusion and a receding drying front is formed.

Hardening of cement-based materials leads to dramaticchanges in mobility of water molecules and thus significantlyshortens their relaxation times. Significant relaxation time changescan take place even in sealed samples which undergo curing.Therefore, any quantitative interpretation of the MRI data requiresa detailed analysis of the relaxation behavior in order to establishthe relation between the signal intensity and the water content inthe samples. With most MRI techniques, the signal intensity islikely to reflect only the evaporable water [511–513]. For instance,in an SPI study with tp = 55 ls, only evaporable water was ob-served [512], whereas STRAFI was reported to detect all water inthe sample [514]. To ensure that only removable water is visual-ized, the tp or TE values can be increased intentionally [515]. Ithas been reported that for concrete samples moist-cured for a longtime (28 and 90 days), the signal intensity was proportional to themoisture content, whereas for the samples cured for less than aday, this proportionality was observed only after 1 week of drying[511]. This is presumably caused by the presence of at least threetypes of water with different relaxation times, and the changesin their relative contributions and the relaxation time values. Atthe same time, in certain cases T�2 can be independent of moisturecontent, which can make the amplitude of a moisture content pro-file proportional to the actual moisture content [516].

Many studies examine the drying processes of cement, mortarand concrete samples for various compositions, initial water/ce-ment (w/c) ratios and moist curing times. As an example, Fig. 42shows 1D profiles of drying cement detected using the SPI tech-nique. The 1D profiles were also detected using SPI with tp = 290 lsto monitor drying of moist cured white Portland cement (WPC)containing 50 mass% of water [516]. Surprisingly, T�2 ¼ 170 lsand T1 = 1.2 ms did not change as drying proceeded for 1 month.Rapid loss of water near the drying surface was apparent, but the

humidity (RH) and 19 �C. The images are shown for the following drying times (leftprofiles (c). 1D MR experiments were performed at 25 �C. Adapted from Ref. [510],

Fig. 44. 1D MR profiles detected using SPI to study concrete reparation. A newcement paste was laid on the old sample. The profiles were acquired at 10 min to15 h with 10-min intervals, and the last profile was acquired after 6 days. Theexperiments were performed at 0.5 T. Reprinted from Ref. [517], Copyright (2005),with permission from Elsevier.

Fig. 43. Drying and hydration of concrete. 1D MR profiles were detected using theSPI technique with a spatial resolution of 0.55 mm. (a) Isolated sample. In this case,water intensity decrease is only due to cement hydration. (b) Unidirectional dryingof the sample at 53.5% relative humidity and 20 �C. In this case, both drying andhydration lead to water signal intensity decrease. The process was monitored for2 months. The experiments were performed at 0.5 T. Reprinted from Ref. [517],Copyright (2005), with permission from Elsevier.

Fig. 42. 1D MR profiles of drying cement samples with w/c = 0.6 (a) and w/c = 0.4(b) following a moist curing period of 90 days: profiles are shown for 0, 1, 3, 7, 28,and 90 days of drying. Drying occurs from the open face at 0 cm. The profiles wereobtained using SPI with tp = 130 ls. The experiments were performed at 2.4 T.Reprinted from Ref. [515], Copyright (1998), with permission from Elsevier.


decrease in water content was observed along the entire sample.Similar observations were made during the drying of concretestudied using 1D SPI with tp = 133 ls [511]. The results also dem-onstrated that lower w/c ratios (0.3–0.4) and longer moist-curingtimes led to less efficient capillary flow and diffusive transport dur-ing the drying stage. 1D SPI was used to study drying-hydration ofconcrete (Fig. 43) [517], demonstrating that free and bound watercan be distinguished. Evolution of a T1 distribution with time wasalso observed. For repaired concrete (an old sample with a freshsample on top), water migrated from the new to the old concrete,and the transition zone evolution was observed (Fig. 44). 1D and2D SPI images of ordinary Portland cement (OPC) during hydrationwere reported in [518]. Drying of mortar in a stream of dry airstudied for ca. 3 days demonstrated that moisture profiles re-mained rather flat [519]. The bimodal T2 distributions were recov-ered for each spatial position, and the results indicated that thepores with longer T2 times (capillary pores) were preferentiallyemptied (Fig. 45). The distribution of capillary water was also stud-ied using GE for the PC samples with different w/c ratio and curedunder different conditions (sealed, open and underwater) [212]. 1DCW MRI was used to study curing and subsequent drying of cylin-drical OPC samples [92]. During curing, only one flat surface of thesample was exposed to air to introduce some inhomogeneity intothe cured sample. A gradual decrease of the signal intensity alongthe profile was consistent with a loss of water through the exposedface. The authors state that CW MRI detects not only capillary andgel water but also the chemically combined water, and thereforethe decrease in the measured intensity indicates water loss andnot the increased proportion of the chemically combined wateras the hydration proceeds. The largest non-uniformity in the sam-ple was observed after 14 days of curing, after which the profile be-gan to level off as the sample was drying. The drying was over after24 days and the sample was characterized by a residual slope ofthe 1D profile, indicating an inhomogeneous cure along the sampleaxis. At this point, the sample exhibited a T�2 value of ca. 10 ls.NMR-MOLE was used for the spatially localized measurements of

PC drying [175]. From the changes in signal intensity and T2, fourstages of hydration were identified.

The release and transport of water in a model of the internalpost-curing of hardening cement pastes was studied in [31]. Thepaste sample was prepared from white cement with the w/c ratioof 0.3 and incorporated one bead of alginate gel. The 1D SE profilesdetected periodically demonstrated the release of water by the

Fig. 46. A set of 1D MR profiles of unfrozen water in a concrete cylinder at varioustemperatures. The magnetization variation due to Curie’s law was removed. Atemperature equilibration time of 1 h was allowed following each temperaturechange. The experiments were performed at 2.4 T. Reprinted from Ref. [522],Copyright (1998), with permission from Elsevier.

Fig. 45. Pore water distributions in drying mortar sample for 10 h steps asdetermined from 1H NMR relaxation measurements. In the inset, the total amountof water, the water in the capillary pores and the water in the gel pores is given as afunction of time. The lines are only guides to the eye. The experiments wereperformed at 0.8 T. Reprinted with kind permission from Springer Netherlands: Ref.[519], Fig. 6.


alginate into the surrounding hydrating cement. The alginate beadwas clearly discernible in the profiles. It was initially water-satu-rated, and started to lose water once the accelerated hydration ofthe cement paste started. The MRI experiments were comple-mented with relaxation porosimetry and self-diffusion measure-ments. While hydration led to a decrease in D, the diffusivetransport was still fast enough to ensure the efficient and uniforminternal post-curing of cement.

The 1D STRAFI profiles of drying cement [514] revealed thepresence of bulk water displaced to the top of the sample andthe sample shrinkage during drying. Even with TE = 30 ls, the de-crease in T2 caused by the hydration process made the signal de-crease faster than the actual water content. Samples with addedgypsum and lime exhibited reduced shrinkage and a faster hydra-tion-induced signal decrease. The influence of an organic additive(methanol) and a model organic contaminant (2-chloroaniline)on cement hardening has been studied [520]. The results demon-strated that the presence of organic liquids significantly delayedthe hydration process and led to the formation of macroscopic li-quid pockets, which was consistent with the T2 relaxation dataanalysis.

Concrete was shown to lose water faster at the early stages andslower at the late stages of drying as compared to cement, whilethe presence of large aggregates in concrete prevented its crackingunder the influence of the tensile stresses induced by dryingshrinkage [515]. Rapid loss of water near the drying surface andthe decrease in water content along the entire sample were appar-ent. Water distribution was studied in drying concrete samples ofvarious compositions subjected to different curing conditions[512]. The T�2 maps and the true local content of evaporable waterwere extracted using the 1D SPI technique with tp = 55–300 ls. Itwas demonstrated that profiles not corrected for the effects causedby the variation of T�2 during drying can give an incorrect picture ofwater distribution in the drying samples. To determine the D(S)dependence, the Boltzmann transformation (Eq. (3)) was used tocollapse several water content profiles onto a master curve. At highmoisture contents, D was decreasing rapidly with decreasing S,whereas at lower S values D remained almost constant. The mois-ture diffusivity was observed to significantly decrease with in-creased moist curing period.

Drying of concrete and mortar specimens made from WPC andquartz fine and coarse (14 mm) aggregates was studied at 23 �Cand 40% RH using SPRITE [219]. 1D profiles of evaporable moisturecontent at various drying periods were detected for concrete cylin-ders. The authors showed that signal intensity in the MRI profilesdirectly correlated with the concentration of evaporable water.The profiles demonstrate an increase in water-tightness with in-creased curing. Indeed, concrete cured for only 1 day at 100%humidity exhibited a faster depletion of water than the samplecured for 90 days. In addition, freezing experiments were per-formed on 1-day and 7-day moist cured specimens, both for fullywet samples and for samples dried for 1 month from a single ex-posed face. The cryoporometry approach was used to obtain the lo-cal pore size distributions at the specific locations of interest. Inaddition, freezing front propagation in a mortar cylinder with asingle face maintained at ca. �20 �C using cold nitrogen vaporwas investigated. The time-resolved observation of the freezingfront was only possible using 2D spiral SPRITE. The images clearlyshowed the presence of a propagating freezing front. Freezing andthawing of water in cement-based materials was examined in anumber of studies [77,521–524]. Such studies can provide, for in-stance, the PSD for water-filled pores. The presence of superplast-icizer in cement paste was shown to lower porosity and to preventformation of macropores [521].

Spatially resolved NMR cryoporometry was applied to charac-terize the drying of the moist-cured concrete sample using 1DSPRITE with tp = 80 ls [513]. After curing, water was uniformly dis-tributed along the cylindrical sample, whereas after 30 days of dry-ing, a gradient in water content developed, with lower watercontents near the open ends of the sample. The sample was imagedas its temperature was lowered gradually down to �55 �C (Fig. 46).Below �9 �C, the freezing started in the center of the sample andthen spread toward the ends. This is a clear indication that largerpores (ca. 5 nm) remained filled in the center but were empty nearthe ends of the sample. At the lowest temperatures, the freezingproceeded uniformly, indicating that all smaller pores (below3 nm) stayed filled with water in the entire sample. Pore size dis-tributions were obtained from the experimental data. The resultsclearly demonstrate the tendency for smaller pores to stay filleduntil the larger pores are emptied, which is the result of the actionof capillary forces.

For large samples, localized measurements can be performedusing a range of approaches. For instance, small (30 mm in diame-ter and 12 mm in height) NMR sensors comprising an rf coil and apermanent magnet were embedded in a drying mortar sample andused to monitor changes in the local amounts of evaporable waterand the evolution of relaxation times [525]. Embedded rf coilswere also used for localized STRAFI measurements of water

Fig. 47. (a) Spin–spin relaxation time (T2) profiles of sodium silicate films dried at48 �C for 15 h (open circles), 23 h (squares), 45 h (triangles), and 63 h (solid circles).(b) Hydration levels for the same films as in (a). The experiments were performed at2 T in the fringe field of a 7.05 T magnet. Reprinted from Ref. [532], Copyright(1996), with permission from Elsevier.


content in a sample comprising a layer of mortar and a layer ofcementitious topping (cement with an organic binder) during sam-ple wetting and drying [526]. In the same paper, the measurementsof water content and the distribution of T2 times in the drying plas-ter, cement and concrete samples with the use of the NMR MOUSEwere reported. This technique has a clear potential for performingmeasurements at a construction site.

Drying of refractory mortar used in a steel making process wasstudied at 50 �C using 1D STRAFI profiles with a 60 lm spatial res-olution [527]. Addition of surfactants during sample preparationmade the drying much slower. Drying of the samples was observedto proceed from the surface, with a roughly Fickian displacementof the drying front. Echo decays were biexponential, which wasinterpreted as arising from the contributions of the capillary andchemically bound water fractions, and separate diffusivities ofthese fractions were estimated.

Hydration of commercial a and b gypsum plasters was studiedusing 1D SE so that only the mobile water was detected [528]. Asmore water became bound in the hydrates, the profile intensity de-creased. Integration of the profiles was used to obtain hydrationkinetics. Both the profiles and the kinetics revealed the presenceof three hydration stages, namely the initiation, the acceleration,and the completion period. The b plaster exhibited a substantiallylonger initiation period (constant signal intensity) and a fasterhydration rate during the acceleration period (decreasing signalintensity) as compared to the a plaster, so that both plasters re-quired the same time to hydrate completely. Relaxation porosime-try (T1 and T2 distributions) was used to make conclusions aboutthe evolution of pore sizes. In addition, SEM and XlT were appliedto reveal the morphology of the material.

The study of water extraction from a fresh mortar layer with abrick sample placed in contact with mortar compared the behaviorof fired-clay and sand–lime bricks [529]. For the initially dry bricks,the mortar lost most of the water within 90 s, which was compara-ble to the temporal resolution of the experiments. The effect ofprewetting of the bricks was investigated. The moisture profilesin the mortar remained rather flat during the water extraction pro-cess, indicating that the moisture diffusivity for liquid water in themortar was greater than that in the bricks. The final moisture con-tent of the mortar was significantly higher for initial moisture con-tent in the bricks of 0.22 m3/m3, and water extraction from themortar almost completely stopped for bricks initially saturatedwith water. The suction (capillary pressure) curve of the mortarthat cannot be measured directly was extracted from the measure-ments of the water distribution profiles for the mortar that was in ahydraulic contact with the brick. In another set of experiments,methyl tylose was added to the mortar as a water retention agent.The water extraction process slowed down, but the final moisturecontent in the mortar was not affected. Similar studies were per-formed for the fired-clay brick in contact with a cement–lime mor-tar or a cement mortar with or without an air entraining agent[530]. The MRI experiments were combined with polarizing andfluorescent microscopy (PFM) and X-ray diffraction (XRD) to studythe composition and porosity of mortars after curing. The resultsshowed that the morphology of mortar (the contents of sand, curedbinder and voids) and chemical composition of the cured binderchanged with distance to the brick–mortar interface.

Mapping relaxation times of water during drying and hydrationof cement-based materials [70,531] can provide information on theevolution of pore sizes with time.

6.5. Drying of thin films and coatings

Drying of thin films has many practical uses including adhesives,coatings, paints, etc. Drying of sodium silicate films in an oven at22–62 �C was studied using STRAFI (TE = 100 ls) by detecting the

depth profiles of the 1–2 mm thick films with the spatial resolutionof 50–100 lm [532]. Moisture was preferentially lost from the filmsurface and significant water content gradients developed along thedepth coordinate (Fig. 47). The drying was more uniform at lowertemperatures. The T2 values spatially resolved along the depth coor-dinate decreased significantly with decreasing moisture content,but for a given moisture content were independent of the dryingconditions. The quantitative moisture content profiles were recov-ered using a calibration experiment. GARField was used to obtain1D profiles for pine glued to glass with urea formaldehyde (UF) re-sin [143]. The glue signal was seen to decrease with time, providingan estimate of the cure time. The wood and glue layers were ob-served to first shrink as water was diffusing from the glue layer intowood. After 100 min, the signal intensity in the wood began to fall,possibly indicating a change in the water mobility due to wood fi-bers swelling. Pre-heating of the sample to 70 �C immediately be-fore the measurement gave a much quicker cure. A longer curetime was observed for spruce as compared to pine.

Drying of aqueous poly(vinyl alcohol) (PVA) layers was studiedusing both 1D GARField profiling with the spatial resolution of17 lm and 2D FLASH MRI [533]. The samples were characterizedby the initial thickness of 300–1300 lm and different PVA concen-trations and were dried at different evaporation rates. The overall


thickness of the layers was observed to decrease with drying time.For slow drying regimes (low evaporation rate, thin films, largemutual diffusivity), the water distribution remained uniform with-in the remaining layer thickness. In the opposite limit of fast dry-ing, the profiles were not rectangular, with the reduced waterconcentration near the drying surface. For drying times that werelong compared to the characteristic time of amorphous–crystallinetransition, the top surface of the drying layers turned into a crystal-line skin which was not observable in the profiles, whereas the skindid not develop in the opposite limit. Formation of the skin layerwas observed to measurably inhibit the rate of water evaporation.The existence of the skin layer was demonstrated by depositing afresh wet layer on top of a dry layer. The fresh solution dried with-out penetrating a more crystalline underlying layer, but permeatedthe full thickness of a less crystalline one.

Fig. 48. (a) Experimental set-up for the NMR imaging studies of the macroscopic film-fotube with a diameter of 5 mm and 3.5 cm length. A constant air stream with a temperatrecord the proceeding film-formation process. (b) Drying of a latex dispersion with 0.5 (to5, 9, 13, and 18 h were mapped. (c) 1H spin–spin relaxation rate (1/T2) maps for the samVCH Verlag GmbH & Co. KGaA, Weinheim. Reproduced with permission.

Drying of water-based (water-borne) colloid dispersions at-tracts significant attention because of its environmental safety.Aqueous latex dispersions consist of polymer particles stabilizedand dispersed in water by surfactants. In such systems, water actsboth as a solvent and a plasticizer and has an important influenceon the film formation process. Drying of latex dispersions can pro-duce polymer films that can be used as paints, glues, coatings, etc.It proceeds in three stages. During the first stage, evaporation ofwater leads to the close contact between the latex particles. Fur-ther evaporation leads to an even closer packing of particles dueto their deformation. Finally, diffusion of the polymer across theparticle boundaries leads to the formation of the final structure,with individual particles no longer distinguishable. In such pro-cesses, water is present outside the latex particles, in the interfacialsurfactant layer and inside the particles.

rmation process. Latex dispersions were added to a height of 5 mm in an NMR glassure of 333 K was applied to the samples. Twenty-five images were taken in 24 h top row) and 5 wt.% (bottom row) ionic PEO surfactant. Different drying states after 1,e samples. The experiments were performed at 7.05 T. Ref. [534]. Copyright Wiley-


Two aqueous polymer latex dispersions containing poly(vinylacetate) (PVAc) and various amounts of a PEO-based surfactantwere studied using 2D SE [534]. Small glass containers were filledwith the mixtures to a height of 5 mm and kept in a slight airstream at 333 K (Fig. 48). The T2 and spin density maps were recov-ered and demonstrated the loss of molecular mobility and waterloss in the course of drying which proceeded from the open toppart of the samples because of the large sample thickness andthe high surfactant content. The formation of a rigid skin at the dis-persion/air interface was particularly pronounced for the samplewith lower surfactant content, while the increase in the surfactantconcentration led to a more homogeneous drying of the dispersion.The 1H NMR spectra spatially resolved along the sample depthwere in agreement with the decreasing mobility and progressivewater loss during drying even though the individual contributionsof water and PEO could not be resolved in the spectra.

In contrast, the drying of planar colloidal films proceeds in thelateral direction from the film edges. The redistribution of wateris important because its lateral transport leads to the redistributionof solutes and other ingredients. The lateral drying of acrylic latexand polystyrene latex dispersions were studied under a systematicvariation of the particle size, film thickness and the drying rate[535]. A long value of TE (14.5 ms) in a 2D SE experiment ensuredthat polymers did not contribute to the observed signal. For thelarge values of reduced capillary pressure pc (i.e., larger particles,slower evaporation and a lower film thickness), the edges of thefilm stayed partially wet for the extended periods of time(Fig. 49a). The drying front was observed to eventually recedeaway from the film edges, with a particle-packing front movingwell ahead of it. In the opposite limit of low pc, the drying andthe particle-packing fronts coincided and started their inward mo-tion already at the onset of the drying process (Fig. 49b). Duringthe drying of an acrylic latex dispersion [536], drying profiles wereobserved to move in from the thinner sample edges when dryingwas performed in static air, whereas in flowing air the sampledried near its surface first, forming a ‘‘crust’’. Film formation uponthe simultaneous drying and photoinduced cross-linking of water-borne poly(vinyl acetate-co-ethylene) latex dispersion has demon-strated a complex picture of the changes in the concentrations andmolecular mobility of the components as a function of depth. Thisreflects the coupling of various processes such as diffusion of watermolecules, oxygen and cross-linker, light transmission and thefree-radical polymerization [537].

GARField was used to obtain 1D water distribution profiles dur-ing film formation of the water-borne acrylic latex pressure-sensi-tive adhesives (PSA) [538]. The latexes studied were randomcopolymers of primarily 2-ethylhexyl acrylate (2-EHA) and methylmethacrylate (MMA) and also contained vinyl acetate and acrylicacid, prepared with the use of nonionic and anionic surfactants.The results were compared to those from a BA-MMA-MAA latex

Fig. 49. 2D MR images obtained during drying of thick films of waterborne colloidal particpolystyrene latex particles is 4.4 lm, cross-sectional area is 1.2 mm by 22 mm. (b) Low rparticles is 25 nm, cross-sectional area is 2.4 mm by 22 mm. The experiments were perfor

used as a reference sample. Initially the thickness of the wet regionof all films decreased approximately linearly with time and thewater concentration steadily decreased as well. When the closepacking of latex was reached, the rate of thickness decrease sloweddown. For the reference sample, the decrease in water concentra-tion accelerated at this stage. In contrast, for PSA latexes the rateof water loss decreased once close packing was reached. The watercontent was very low near the film/air interface and increased lin-early with the depth into the film. As drying proceeded further, thewater content decreased, and the slope of the linear profile gradu-ally decreased toward zero. The authors concluded that deforma-tion of particles was not accompanied by coalescence but ratherwater-filled spaces existed at the particle boundaries. It was sug-gested that transport of solutes including the anionic surfactantto the surface was driven by the capillary pressure.

GARField was also used to study the latex that was based on acopolymer of vinyl acetate and ethylene with the reactive mono-mer and a photo-initiator added for cross-linking [539]. The filmswith an initial thickness of 200–400 lm were prepared for imagingon a glass substrate. During drying, the decrease in film thicknesswas clearly observed (Fig. 50a). The signal decreased faster at thefilm/air interface than at the film/substrate interface. The softenedlatex may contribute to the detected profile. Indeed, the dried mix-ture of latex and cross-linker did give a substantial signal whichmay originate from the cross-linker itself and/or the plasticized la-tex. Upon light-induced cross-linking of the dry latex/cross-linker/photo-initiator system, the signal was observed to decrease as a re-sult of the cross-linking process which started at the film/substrateinterface, presumably because of an inhibitory effect of air oxygenon the radical reaction near the film/air interface (Fig. 50b). As thesignal was still observed after 2 days of light exposure, the authorsconcluded that cross-linking did not make the film harder than theoriginal latex, In another set of experiments, the wet film was im-aged while exposed to light immediately after its casting on theglass substrate. In this case, signal intensity was decreasing in timebecause of both water evaporation and latex cross-linking, and theprofiles demonstrated the minimum signal intensity at the filmcenter. This was explained as being the result of the interplay ofseveral processes including oxygen transport and inhibition ofcross-linking, water evaporation and light scattering. For compari-son, the cross-linker/photo-initiator mix (with no water and latex)was imaged while exposed to light. The signal was quite strong asthe cross-linker had a low MW. An induction period with constantsignal intensity was followed by the signal decrease at the sub-strate/film interface and later the gradual displacement of thecross-linking front toward the film/air interface.

Some papers are devoted to studies of the drying of aqueousemulsions of alkyd resins. The use of alkyd polymers as paints isgaining popularity because they are made from natural productssuch as fatty acids and oils. In contrast to the solid particles of

les. (a) High reduced capillary pressure, initial film thickness is 0.32 mm, the radius ofeduced capillary pressure, initial film thickness is 1.2 mm, the radius of acrylic latexmed at 9.4 T. Reprinted with permission from Ref. [535].

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Fig. 51. 1D MR profiles of the drying alkyd emulsion cast on a glass slide. Thecrosses show the profile of an alkyd emulsion film 4 min after evaporation isstopped during the second stage of drying. The subsequent profiles recorded after afurther 1 h and 15 h show how the water fraction re-equilibrates. The experimentswere performed at 0.7 T. Reprinted from Ref. [143], Copyright (2003), withpermission from Elsevier.

Fig. 50. (a) MRI profiles at different times (as indicated) of water evaporation in a film of latex only. The dashed line shows a latex/crosslinker mixture imaged 24 h after filmformation, for comparison. (b) Profiles obtained at various times during the crosslinking of a film being exposed to light after previously being dried in the dark for 48 h. Theexperiments were performed at 0.7 T. Reprinted from Ref. [539], Copyright (2001), with permission from Elsevier.


colloid dispersions, alkyd droplets in the emulsions are easilydeformable which can affect the drying process. The alkyd fractionis mobile enough to contribute to the detected NMR signal even ifTE is fairly long. The chemical difference between oil and water canlead to the chemical shift artifacts, but it is sufficient in principle toallow acquisition of the separate images of the two phases. In anMRI study, an alkyd emulsion droplet was spread on a flat glasssurface and dried in either static or flowing air [536]. In both cases,the diameter and the height of the droplet were observed to de-crease with time. The loss of water was lowest at the dropletperiphery and was highest in the droplet center as a result of thelateral transport of water from the center toward the edges whichnevertheless did not increase the alkyd concentration at the drop-let periphery. Throughout most of the drying process, the watercontent decreased almost linearly with time.

Drying of alkyd emulsions was studied with a spatial resolutionof 8.7 lm using GARField [143,540,541]. Drying was performedunder three different experimental conditions: sealed sample, flowof dry air, or natural convection. The contribution of water to thesignal was somewhat larger than that of the alkyd phase. Underslow drying conditions, the thickness of the film and the profileintensity were diminishing but the profiles remained essentiallyrectangular, implying that redistribution of droplets was fasterthan the rate of surface recession. Under fast drying conditions, agradient in water concentration was observed in the upper layerca. 10 lm thick. It was larger in samples that contained a thickener.At later stages of drying when water volume fraction dropped toca. 0.15, the profiles became rectangular again regardless of evap-oration rate. Further drying led to the formation and expansion of askin layer and a pronounced water content gradient with depthcoordinate. In one of the experiments, the film was covered at thisstage to stop the drying process, and eventually the profiles be-came rectangular again (Fig. 51). In another experiment, the filmwas re-wetted by spreading a dilute emulsion on it and was ob-served to swell again [143]. These two experiments provided evi-dence that the droplets have not coalesced at the end of thesecond stage of drying.

In the drying of alkyd coatings, the physical removal of the sol-vent is followed by the curing stage – a lipid autoxidation process(catalytic oxidation with atmospheric oxygen). The resulting de-crease in polymer mobility allows one to image the curing process.GARField was used for depth profiling of films 100–200 lm thickwith 3–7 lm spatial resolution to compare water-borne and or-ganic solvent-borne alkyd emulsions. The front position variedwith time as t1/2 in both systems [144,146]. An additional experi-ment was performed in which the oxygen supply was limited bycreating an argon atmosphere above the coating film. When oxy-gen was removed, the front was observed to stop. When the air

atmosphere was restored, the front resumed its motion with theoriginal speed, demonstrating that oxygen supply was the limitingfactor for the reaction. A higher curing rate observed for the sol-vent-borne sample was the result of a higher polymer mobilityin the polymer matrix and thus faster O2 transport compared tothe water-borne system (Fig. 52). Indeed, in the solvent-borne sys-tem the signal has not vanished completely after the cross-linkingfront has passed, demonstrating that the network is not as rigid asin the water-borne sample. The MRI profiles for both organic sol-vent-borne and water-borne paints were compared to the profilesobtained with confocal Raman microscopy (CRM) which character-izes the spatial degree of cross-linking by monitoring the disap-pearance of the double bonds [146,542]. The positions of thefronts in the MRI and CRM profiles were found to coincide.

The cross-linking front was observed for a cobalt catalyst con-centration of 0.007% and higher [146]. The front speed was foundto increase with decreasing catalyst concentration. Below this cat-alyst content, no front was observed and a more homogeneous cur-ing occurred, meaning that oxygen diffusion was no longer thelimiting factor. GARField was used to demonstrate that, comparedto the alkyd film without drier, cross-linking was much faster inthe presence of a Co based catalyst [539]. The cross-linking startedat the surface of the film and continued toward the film/substrateinterface. The cobalt drier facilitated the surface auto-oxidativecross-linking drying more than the through-drying of the film.The final film hardness after the cross-linking reaction was similarto that of the original latex.

The influence of the type of catalyst on the curing (chemicaldrying) process was also investigated [543,544]. Two different

Fig. 52. 1H NMR profiles of a water-borne (a) and a solvent-borne (b) alkyd samples during drying. The left side is the top of the coating, at the right the cover glass is located.The vertical dashed line shows the top of the film after evaporation. (a) The profiles are plotted for 0, 1.25, 2.5, 5, 8, 10.5, 26, 53, 79, 105, 132, and 158 h. (b) The first 7 profilesare plotted for 10, 20, 30, 50, 70, 90, and 120 min. After the seventh the profiles are plotted for every 3 h 20 min. The experiments were performed at 1.4 T. Reprinted withpermission from Ref. [144].

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manganese (Mn) and one cobalt (Co) based catalysts were com-pared. First, the drying stage with the reduction of the film thick-ness was observed. After about 5 h of drying, a front wasobserved to develop and move toward the bottom of the coating.Behind this front a glassy skin layer was formed, and ahead of itthe resin remained un-cross-linked. The front was visible becauseof the mobility change upon cross-linking. The front was sharperfor the Co-based catalyst as compared to the two Mn-based cata-lysts. In the latter case, the samples cured more homogeneously,indicating that oxygen penetrated the coating much further thanfor the cobalt catalyst. The final curing stage was reached in ca.1 week for the Mn based catalyst, while in case of Co the observedsharp front took several months to reach the bottom of the coating.For both Mn catalysts, the relative signal decrease during curingwas much smaller than for the Co catalyst, reflecting the lowercross-link density for the Mn catalysts. When Co based catalystwas diluted 100-fold, no sharp curing front was observed and theresults were closer to those obtained with the Mn based catalysts.A clear correlation between Tg and T2 was found: the value of T2 de-creased with increasing Tg. The effect of added promoters was alsostudied [543]. Addition of Ca and Zr as secondary driers to theemulsion containing Co as the primary drier (catalyst) resulted ina faster propagation of the curing front but did not affect the ob-served �t1/2 signal decrease ahead of it. The authors concluded thatcontrary to the findings reported in the literature, no accelerationof the through-drying took place in the presence of Ca and Zr, onlya faster growth of the skin layer was observed. The simple modeldeveloped to describe the temporal dependence of signal intensitycorrectly predicted the t1/2 dependence. For the non-aqueousemulsions, the signal was observed to depend linearly on the in-verse film thickness. Another study concentrated on the effect ofpigment concentration on the curing stage of the drying process[545]. The results demonstrated that below the critical concentra-tion (ca. 50% by volume), an observable reaction front has devel-oped at the coating/air interface and moved into the coating,whereas above this concentration a homogeneous curing was ob-served. This behavior was explained by the differences in the trans-port of O2 induced by the different properties of the porousnetwork.

Alkyd paints are often applied on porous surfaces. Thedifferences in the drying behavior of the solvent-borne and thewater-borne alkyds on the porous and non-porous substrates werestudied using GARField [546]. The films were applied on thin

(0.3–0.5 mm) layers of porous substrates. For a water-borne alkydapplied on glass, the t1/2 front propagation behavior was observed,and the front speed vs. catalyst concentration dependence exhib-ited a minimum. For the water-borne alkyd applied on gypsum,the penetration of the water phase into the gypsum layer was al-most instantaneous and wetted the gypsum layer, while the resindid not penetrate the substrate within the experimental resolution.After the evaporation stage, the curing front was visible not only atthe surface of the coating but also at the coating/gypsum interface,presumably because oxygen transport was taking place through theporous gypsum layer. Again, the t1/2 front propagation was ob-served. However, the front speeds for the coating on the gypsumlayer were always higher than for the same coating applied on glass,possibly associated with the presence of Ca2+ ions in gypsum. Thesolvent-borne alkyd applied on gypsum completely penetratedthe gypsum layer. In this particular case it was difficult to distin-guish the evaporation of the solvent and the curing process. Forthe same alkyd applied on a thin layer of pine wood, the solventand resin were both observed to penetrate the wood almost instan-taneously. After the detection of the first profile, no changes wereobserved in the deeper region of the wood. Again, a curing frontdeveloped and slowly moved down into the wood.

6.6. Other materials and processes

Textiles are anisotropic porous materials, therefore the studiesof their drying pose additional problems for data quantification.The principles, obstacles and solutions for quantitative MRI of li-quid transport in textile materials are nicely summarized in[547]. Through-air drying of tufted textile materials (unbackedcut-pile nylon carpet) at elevated temperatures was studied using1D SPI [548,549]. The 2D images of moisture distribution in a sliceof a single carpet yarn were obtained with FLASH as a function ofdrying time [548]. The drying by free convection of loop-pile (ny-lon fiber) carpet pieces with primary and secondary backingswas studied using 1D and 2D SE with TE as short as 30–50 ls[550]. Drying of woven fabrics made of glass fibers was addressedin [551].

Moisture transport in food products during drying and otherprocesses has been addressed by MRI in multiple studies [552–554]. One of the important model systems is gelatine gel. Singleface drying of a gelatin gel sample was reported [555]. The gelatinfilm formation during the drying of an initially homogeneous gel


layer ca. 1 mm thick was studied by imaging the gel with a spatialresolution of 50 lm using NMR MOUSE [556,557]. Water transportin the drying of gel cylinders prepared from agar, cellulose andwater was studied using Overhauser (or proton–electron doubleresonance, PEDRI) imaging in a 16 mT field [558]. Local moisturecontents were evaluated using an independently measured calibra-tion curve. Changes of only a small fraction of 1% in the moisturecould be detected, but the accessible range of local moisture con-tents is limited in a PEDRI experiment. The authors note that inaddition to T2 contrast of conventional MRI, PEDRI introduces othersources of contrast. Drying of agar gel mixed with microcrystallinecellulose was also studied using conventional 2D imaging [559].

The nature and the distribution of moisture are important in themultiple industrial uses of wood, and MRI has been applied tostudy wood and pulp drying [560–564]. It was demonstrated, inparticular, that drying rate depends measurably on the orientationof the rays and growth rings with respect to the external surface.Drainage of wood samples under applied gas pressure was success-fully visualized [565]. Drying of various paper and cardboard prod-ucts has been addressed as well. For instance, moisture transportduring drying was studied in laboratory-made handsheets, heavypaperboard, polyethylene-coated paperboard [566] and compositemulti-layer liquid packaging cardboard [567]. MRI studies of dry-ing of wood, paper, food products and related materials are consid-ered in [568].

Transport of moisture in soil is an important process and hasalso been investigated by MRI. For instance, the soil samplesundergoing controlled single-sided drying from one end werestudied using 1D SPRITE with tp = 40 or 60–300 ls [569]. Drainageof soil was studied by using a mobile NMR sensor [570].

The effect of added silica on the desiccation of the poly-dimethylsiloxane/polydiphenylsiloxane (PDMS/PDPS) copolymerwas studied with 1D SPI [571]. An increase in cross-linking and/or the degree of chain entanglement that reduce chain mobilitywas observed in the unfilled material but not in the SiO2-filledcopolymer. MRI was also used to study the mechanism behindthe helical gel formation when a colloidal solution was dried in asmall capillary [572]. Tetramethylammonium permanganate saltsin 2-butanol/H2O were heated in open 5 mm NMR tubes in an ovenand imaged ex situ at 85 �C. After ca. 15 min of evaporation, MRIwas able to discern the formation of an internal column of gel richin colloid surrounded by a thin annular film of the clear solventforming a loose spiral. With further heating led to the increase inthe number of pitches per unit length. The important role of grav-ity in helix formation was demonstrated by drying the tubes posi-tioned at different inclination angles with respect to the horizontal.

To better understand spray drying processes, a suspended 10 ll(ca. 1.6 mm) drop of an industrial detergent paste was imagedusing SE and SPI with the spatial resolution of 73 lm [573]. SEwas shown to underestimate the water content while SPI overesti-mated it because of the contribution of other constituents (surfac-tant and polymer) and bound water to the observed signal.

Spatially resolved studies of the polymerization of acrylamides[574,575], methacrylates [576,577], methacrylic acid [578], epoxyresin [579] and other monomers were reported. Recently, the cureof an epoxy resin was studied using a purpose-built portable sin-gle-sided device [580]. Traveling waves were observed duringmethacrylic acid polymerization, with a well defined polymer–monomer interface propagating at a constant velocity [581]. A sub-stantial amount of work was done on the studies of curing of mod-el and commercial dental adhesives [582–586], and dental resincomposites [587–591] under a variety of experimental conditionsusing STRAFI in most cases, including dual-cured resin cementsthat combine photoinitiated and chemical curing processes [592].Hardening of dental glass-ionomer cements was also reported

[593,594]. Vulcanization [595,596] and ageing [597] of elastomerswas addressed as well.

MRI of polymer gels can be used to map and quantify the 3Ddose distributions of absorbed ionizing radiation [598–609]. Poly-mer gel dosimetry is a promising technique used to verify spatialdose distributions delivered by cancer radiotherapy equipment.The approach is based on the variation of T2 of water with the irra-diation dose that induces free radical polymerization of the mono-mers dispersed in a hydrogel.

Polymer electrolyte (or proton exchange) membranes (PEM) areimportant in a range of practical applications including PEM fuelcells (PEMFC). Under operating conditions, management of waterproduction, transport and removal is of utmost importance for anefficient and reliable PEMFC operation. In particular, dehydrationof the PEM decreases its ion conductivity, whereas flooding atthe cathode side can block pores in the gas diffusion and catalystlayers and narrow gas flow channels, inhibiting the transport ofthe oxidant gas. MRI was applied to study operation of the poly-mer-electrolyte membrane fuel cells for both perfluorinated andhydrocarbon membranes. The cells are usually purpose-con-structed from MRI-compatible materials and comprise relativelythick membranes (>50–100 lm). A 7 T magnetic field apparentlydoes not affect the fuel cell operation [610]. The MRI studies wereperformed on operating cells under a variety of experimental con-ditions, but mostly at room temperature [610–621]. Distribution ofwater and its relaxation times and diffusivity are mapped to eval-uate homogeneity, swelling, deformation and hydration/dehydra-tion of the membranes, flooding of gas diffusion and catalystlayers and gas flow channels. DHK SE-SPI was used to producewater profiles in a Nafion membrane of an operating cell in6 min with a 6 lm spatial resolution, with electrodes of the cellused as part of the rf circuit for signal excitation and detection[622]. D2 fuel and D2O for inlet humidification can be used toinvestigate water distribution and transport processes in detail[623]. Experiments were also performed with model systems suchas membranes with or without the catalyst layers and model cells[624–628]. Comparison of a perfluorinated membrane with ahydrocarbon membrane [629] revealed that the latter had a higherdegree of hydration. Release of water and methanol through PVA–PSSA (poly(vinyl alcohol)–polystyrene sulfonic acid) membraneswith incorporated mordenite utilized in a direct methanol fuel cellwas studied using MRI and volume-localized NMR spectroscopy[630].

7. Conclusions

This review, while possibly exhausting, is definitely not exhaus-tive. An attempt has been made to introduce the relevant MRI tech-niques and to give examples of their applications to the studies ofdrying and sorption processes that involve porous materials. It wasnot possible to include all relevant publications in this review, andmany of those not included are no less important than those cited.In addition, several books should be mentioned [631–634]. Theyrepresent the contemporary collections of contributions from theresearchers actively and productively involved in the NMR andMRI studies of mass transport and related processes and also coverthe essential techniques and hardware. This field of research, how-ever, continues to grow rapidly, and novel applications will defi-nitely continue to emerge in the foreseeable future.

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Glossary

AC-CDI: alternating current density imagingADC: apparent diffusion coefficientAIBN: azobisisobutyronitrileAPAP: acetaminophen

B0: permanent magnetic fieldB1: radiofrequency magnetic fieldBA–MMA–MAA: butyl acrylate–methyl methacrylate–methacrylic acid (latex)BAM: N-tert-butylacrylamideBMA: butyl methacrylate

CDA: chlorhexidine diacetateCDI: current density imagingCHAS: crosslinked high amylose starchCRM: confocal Raman microscopyCSI: chemical shift imagingCSSI: chemical shift selective imagingCTI: constant time imagingCUFF (NMR-CUFF): Cut open, Uniform, Force Free (magnet)CW: continuous waveCYCLCROP: cyclic cross-polarization

Deff: effective diffusivityD(S): liquid content dependent diffusivityDC-CDI: direct current density imagingDCP: dicalcium phosphateDDIF: decay (of magnetization) due to diffusion in the internal fieldDHK: double half-k-spaceDMA: N,N-dimethylacrylamideDQC: double-quantum coherenceDVB: divinylbenzene

EA: ethyl acrylate2-EHA: 2-ethylhexyl acrylateER: extended release


FID: free induction decayFLASH: fast low-angle shot (pulse sequence)FT: Fourier transform

GARField: Gradient At Right angles to the Field (device)GE: gradient echoGEFI: gradient-echo fast-imaging (pulse sequence)GIC: glass ionomer cementGITS: gastrointestinal therapeutic system

HBS: hydrodynamically balanced systemHDDA: 1,6-hexanediol diacrylateHDPE: high-density polyethyleneHEC: hydroxyethyl celluloseHEMA: 2-hydroxyethyl methacrylateHPC: hydroxypropyl celluloseHPMC: hydroxypropyl methyl cellulose

iDQC: intermolecular double-quantum coherenceiNOE: intermolecular nuclear Overhauser effectIPN: interpenetrating networkiSQC: intermolecular single-quantum coherenceiZQC: intermolecular zero-quantum coherence

LCST: lower critical solution temperatureL-dopa: L-3,4-dihydroxyphenylalanineL-HPC: low-substituted hydroxypropyl celluloseLLDPE: linear low-density polyethylene

MAA: methacrylic acidMandhala (NMR Mandhala): Magnet Arrangements for Novel Discrete Halbach

LayoutmEGDMA: monoethyleneglycol dimethacrylateMEK: methyl ethyl ketoneMOEP: ethylene glycol methacrylate phosphateMMA: methyl methacrylateMOLE: MObile Lateral (or Liquid) ExplorerMOUSE: MObile Universal Surface ExplorerMSME: multi-slice multi-echo (pulse sequence)MW: molecular weightNIPAM: N-isopropylacrylamide

OPC: ordinary Portland cement

PBS: phosphate-buffered salinePC: Portland cementPDMS: polydimethylsiloxanePDPS: polydiphenylsiloxanePE: polyethylenePEDRI: proton–electron double resonance imagingPEEK: polyether ether ketonePEG: poly(ethylene glycol)PEMA: poly(ethyl methacrylate)PEM: polymer electrolyte (or proton exchange) membranesPEMFC: PEM fuel cellsPEO: poly(ethylene oxide)PFG: pulsed field gradientPFM: polarizing and fluorescent microscopyPGSTE: pulsed gradient stimulated echoPHEMA: poly(2-hydroxyethyl methacrylate)P(HEMA-mEGDMA): copolymer of 2-hydroxyethyl methacrylate and monoethyl-

eneglycol dimethacrylateP(HEMA-co-THFMA): copolymer of 2-hydroxyethyl methacrylate and tetra-

hydrofurfuryl methacrylatePLGA: poly(lactic-co-glycolic acid)P(MAA-co-PEGMEMA): copolymers of methacrylic acid and poly(ethylene glycol)

monomethyl ether monomethacrylateP(MAA-co-PEGMEMA-co-PPGMEMA): terpolymers of methacrylic acid, poly(ethyl-

ene glycol) monomethyl ether monomethacrylate and poly(propylene glycol)monobutyl ether methacrylate

P(MAA-co-PPGMEMA): copolymers of methacrylic acid and poly(propylene glycol)monobutyl ether methacrylate

PMMA: poly(methyl methacrylate)P(NIPAAm-co-MAA): poly[(N-isopropylacrylamide)-co-(methacrylic acid)]PNIPAAm, PNIPAM: poly(N-isopropylacrylamide)PPG: poly(propylene glycol)PPGMEMA: poly(propylene glycol) monobutyl ether methacrylatePRF: phenolic resorcinol formaldehydePSA: pressure-sensitive adhesivesPSD: pore size distributionPSSA: polystyrene sulfonic acidP(THFMA-co-HEMA): copolymer of tetrahydrofurfuryl methacrylate and 2-

hydroxyethyl methacrylatePTHFMA: poly(tetrahydrofurfuryl methacrylate)PVA: poly(vinyl alcohol)PVAc: poly(vinyl acetate)PVA–PSSA: poly(vinyl alcohol)–polystyrene sulfonic acidPVC: poly(vinyl chloride)PVP: poly(vinyl pyrrolidone)

RARE: rapid acquisition with relaxation enhancement (pulse sequence)Rf: radiofrequencyRF-CDI: rf current density imaging techniqueRH: relative humidityRM: resin-modified

SADS: concentration of the adsorbed (liquid) phaseS(r, t): spatially and time dependent concentration of a fluidSVAPOR: concentration of the vapor phaseSAP: superabsorbing polymer particlesscCO2: supercritical CO2

SDS: sodium dodecyl sulfateSE: spin echoSECSY: spin-echo correlation spectroscopySEM: scanning electron microscopySGF: simulated gastric fluidSNR: signal-to-noise ratioSPI: single point imagingSPINOE: spin polarization induced nuclear Overhauser effectSPRITE: Single-Point Ramped Imaging with T1 EnhancementSSFP: steady-state free precession (pulse sequence)STRAFI: STRAy Field ImagingS/V: surface-to-volume ratio

T1: nuclear spin–lattice (longitudinal) relaxation timeT1q: nuclear spin–lattice relaxation time in the rotating frameT2: nuclear spin–spin (transverse) relaxation timeT�2: nuclear effective (apparent) spin–spin relaxation timetp: (phase) encoding timeTE: echo timeTEM: transmission electron microscopyTFAm: 2,2,2-trifluoroacetamideTHFMA: tetrahydrofurfuryl methacrylateTR: repetition time (of a pulse sequence)TSE: turbo spin echo (pulse sequence)

UF: urea formaldehydeUHMWPE: ultra-high molecular weight polyethyleneUSP: US Pharmacopeia

VR: vulcanized rubberWPC: white Portland cementXlT: X-ray microtomographyXRD: X-ray diffraction

k = x/t1/2: Boltzmann transformation of coordinates, x – spatial coordinate, t – time

mri of mass transport in porous media: drying and sorption processes

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