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Molecular-level controls on water and organics
intercalation in layered minerals
Jerry Lindholm
Department of Chemistry Umeå 2020
This work is protected by the Swedish Copyright Legislation (Act 1960:729) Dissertation for PhD ISBN: 978-91-7855-341-9 Electronic version available at: http://umu.diva-portal.org/ Printed by KBC Service Center, Umeå University Umeå, Sweden 2020
To my friends and my family,
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Table of Contents Abstract ........................................................................................... ii Abbreviations .................................................................................. iii Enkel sammanfattning på svenska .................................................. iv List of Papers ................................................................................... v Author Contribution ....................................................................... vi Introduction ..................................................................................... 1 Objectives of this thesis .................................................................... 3 Materials and Methods ..................................................................... 4
Montmorillonite ............................................................................................................. 4 Birnessite ........................................................................................................................ 4 Intercalation of alcohol in Montmorillonite .................................................................. 4 Intercalation of CTAB in montmorillonite ..................................................................... 5 Dynamic Vapour Sorption .............................................................................................. 6 Brunauer-Emmett-Teller (BET) ..................................................................................... 6 Attenuated Total Reflectance Fourier Transform Infrared spectroscopy (ATR-FTIR) 7 Powder X-ray Diffraction (XRD) .................................................................................... 8 Modelling of alcohols intercalated into montmorillonite .............................................. 9
Theory ............................................................................................. 13 Isotherm modelling ....................................................................................................... 13
Langmuir isotherm ................................................................................................. 13 Freundlich isotherm ................................................................................................ 13 Do & Do isotherm .................................................................................................... 14 Dubinin & Astakhov isotherm ................................................................................. 15
Molecular Dynamics simulations .................................................................................. 16 Short-range interactions ......................................................................................... 17 Long-range interactions ......................................................................................... 19 What is a force field? .............................................................................................. 20
1-Dimensional XRD Modelling ..................................................................................... 21 Multivariate Curve Resolution (MCR) ......................................................................... 24
Results and Discussion ................................................................... 26 Modelling intercalation of water in the interlayer ....................................................... 26 Intercalation of water as predicted from MCR decomposition of spectral series ........ 31 Intercalation in multi-component systems .................................................................. 34 Intercalation of CTAB in Montmorillonite ................................................................... 37
Conclusion and Future research .................................................... 40 Acknowledgement .......................................................................... 42 References ..................................................................................... 43
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Abstract
Layered minerals are naturally abundant and often display a large surface area in relation to their weight. For swelling layered minerals, most of this area is contained between the layers in the interlayer space. Their large surface area makes them interesting in many different fields and applications, such as adsorbents, catalysts or as carriers for other particles that can be intercalated and exchanged. In order for the materials to be used effectively, it is hence necessary to have a fundamental understanding of how these processes occur, and ways to predict them.
To address adsorption of water, an isotherm model was created to describe the hydration process on layered materials. The model decomposed the process of adsorptions into internal and external, adsorption and condensation, and could specifically handle hydration in the expanding interlayer nanopores. Adsorption and desorption isotherms of two different materials, Montmorillonite and Birnessite was successfully modelled, where the former was ion-exchanged with the counter-cations Li+, Na+, K+, Cs+, Mg2+, Ca2+, Sr2+, Cu2+, whereas the latter contained K+. This indicated that this isotherm model is applicable to also other layered materials. The adsorption process was also characterized experimentally with vibrational spectroscopy (FTIR) and multivariate statistical techniques (MCR), in order to generate spectral- and concentration profiles of the involved components.
In order to also investigate adsorption of different organic molecules, the intercalation of alcohols and a cationic surfactant was investigated in separate studies. Clay-water-alcohol systems of eight alcohols were characterized experimentally by XRD as well as by molecular dynamics simulations, using different combinations of classical force fields for the clay (ClayFF, ClayFFMod, INTERFACE) and for the alcohols (CGenFF, GAFF, OPLS). It was found that the optimal force field combination varied with the fitting approach. A brute force sensitivity analysis indicated that the comparison with the experimental XRD data was more dependent on the relative interlayer loading than the positions of the atoms, an important result for future similar benchmarking studies.
By intercalating and adsorbing a cationic surfactant (CTAB) to Montmorillonite at increasing concentrations, the effects of solvent polarity and the CTAB interlayer content on the Montmorillonite interlayer swelling was investigated. It was found that moderately polar solvents such as DMSO, in combination with CTAB in a planar bilayer configuration resulted in the greatest adsorption of the lipophilic solute alizarin.
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Abbreviations BET – Surface area measurement technique CEC – Cation Exchange Capacity CGenFF – CHARMM general force field for organic molecules ClayFF – Force field for clays, basically ionic/unconstrained ClayFFMod – Force field for clays, modified from ClayFF CMC – Critical Micelle Concentration CMMT – CTAB modified MMT CSD – Coherent Scattering Domain CTAB – Cetyltrimethylammonium bromide DA – Dubinin-Astakhov DFT – Density Functional Theory DI – Deionized (water) DoDo – Adsorption mechanism by Do and Do DR – Dubinin-Radushkevitch DTG – Derivative Thermogravimetry DVS – Dynamic Vapor Sorption FFT – Fast Fourier Transform FTIR ATR – Fourier Transformed Infrared Attenuated Total Reflectance GAFF – Amber general force field for organic molecules INTERFACE – Force field for clays, highly constrained LJ – Lennard-Jones (potential) MHG – Modular Humid Generator MD – Molecular Dynamics MM – Molecular Mechanics MMT – Montmorillonite OPLS – Force field for all-atom organic molecules, also called OPLS/aa PBC – Periodic Boundary Conditions PME – Particle Mesh Ewald (method) QM – Quantum Mechanics RH (%) – Relative Humidity in percent SKB – Svensk Kärnbränslehantering AB SSA – Specific Surface Area SWy-2 – Smectite clay mineral from Wyoming, a form of MMT TGA – Thermogravimetric Analysis VdW – Van der Waals (interactions) Wx – X monolayers of water in the interlayer space X–MMT – Homoionic MMT having the counter-ions X XPS – X-ray Photoelectron Spectroscopy XRD – X-ray Diffraction XRF – X-ray Fluorescence
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Enkel sammanfattning på svenska
Skiktmineraler kännetecknas av en väldigt stor ytarea för sin vikt och förekommer naturligt i vår miljö samt används i många industriella sammanhang. För så kallade svällande skiktmineral är ytarean extra stor, där största delen förekommer i det så kallade mellanskiktet mellan skiktmineralens flak. Den höga ytarean leder till att svällande skiktmineraler agerar som bra adsorptionsmedel. Då mellanskiktets egenskaper och förehavanden är väldigt beroende på mineralets egenskaper är det dessutom möjligt att modifiera och kontrollera vilka typer samt hur mycket av olika ämnen som kan adsorberas.
För att bidra till ökad kunskap om just hydratisering av skiktmineraler, d.v.s. upptag och adsorption av vatten, presenteras i detta arbete en matematisk modell för så kallade adsorptionsisotermer. Modellen delar upp adsorptionen av vatten i mindre delar där varje del går att beräknas individuellt, och där en metod särskilt fokuserar på hydratisering i mellanskikten. Modellen prövades på två olika skiktmineral, dels den svällande smektitleran montmorillonit samt mineralet birnessit (en manganoxid). Mellanskikten på de svällande montmorillonitproverna innehöll åtta olika typer av motjoner (Li+, Na+, K+, Cs+, Mg2+, Ca2+, Sr2+, Cu2+), emedans birnessit innehöll främst K+. Modellen var framgångsrik i att beskriva adsorptionen på både de externa ytorna samt i det interna mellanskikten för bägge mineral, vilket tyder på att modellen kan användas på flera olika typer av skiktmineraler.
Utöver adsorption av vatten adsorberades även organiska ämnen i två olika studier. I den första studien adsorberades åtta alkoholer i montmorillonit och analyserades med XRD. Motsvarande system återskapades sedan med molekyldynamik genom olika kraftfältskombinationer. Resultaten jämfördes sedan genom en-dimensionell XRD modelleringen, med avseende på avstånd mellan basalplanen (d001) samt strukturen av vatten och alkohol i montmorillonits mellanskikt. Ett entydigt resultat gällande en optimal kraftfältskombination erhölls ej. Dock visade en känslighetsanalys att atomernas kvantitet snarare än position i mellanskikten var avgörande för anpassningen till de experimentella XRD resultaten.
I den sista studien interkalerades en katjonisk surfaktant (CTAB) i montmorillonit främst via katjonsutbyte med olika CTAB koncentrationer. Olika lösningsmedel adsorberades sedan i olika försök, som visade att lösningsmedel måttlig polaritet så som DMSO hade störst affinitet till montmorillonit proverna, samt även var bäst på att lösa andra fettlösliga ämnen i mellanskikten fyllda med CTAB.
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List of Papers
I. Deconvolution of Smectite Hydration Isotherms
ACS Earth Space Chem. 2019, 3, 2490-2498.
II. Nanoscale hydration of layered manganese oxide
Manuscript to be submitted.
III. Alcohol intercalation into montmorillonite: A combined 1D-XRD and molecular dynamics benchmarking study
Manuscript to be submitted.
IV. Solvent and lipophilic solute effects on the swelling behavior of an organoclay
Manuscript to be submitted.
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Author Contribution
I. The author performed the whole body of experimental work, analysed and created the model and contributed heavily to the writing of the article.
II. The author aided with experiments and sample analysis. Furthermore aided with parts of the writing.
III. The author performed all experiments and simulations. The author performed primary sample analysis and writing.
IV. The author aided in planning and performing of experiments and sample analysis.
Introduction Clay minerals are interesting materials that demonstrate many different properties and uses depending on the surface chemical properties of the mineral and how it has been treated.1–9 Montmorillonite is an example of a clay mineral in the smectite group, because it is a so-called 2:1 clay mineral that has a negative charge due to isomorphic substitutions. This charge is countered by cations associated with the external and internal surfaces of the clay particles. Simply by changing the cation types to ones with different hydration energy or another valency, will significantly alter how the material interacts with, and adsorbs, other substances.
The adsorption for layered materials is particularly interesting in the case where the material undergoes swelling. This results in the separation of the layers and exposure of the typically very large internal surface area.10–12 The large surface area means that large amounts of material can be adsorbed, and with the right choice of counter-ion this volume can be controlled in discrete steps. But it is also possible to affect what is adsorbed. This is what gives layered materials so many potential uses, but also what makes it hard to model. The adsorption is a complex mechanism with water adsorbing externally and internally simultaneously. And in the case of swelling minerals the adsorption also radically alters the adsorbing surface area, rendering traditional adsorption mechanisms like Langmuir and Freundlich unable to give any insight of the adsorption. This is further complicated by the often-random placements and positioning of the substitutions and counter-ion effects. A highly adsorbing cation may cause the adsorption of multiple hydration layers and combined with the random charge distribution results in interstratified layers of varying surface area and adsorbed content.13,14 Due to all these factors the adsorption, and how water uptake evolves in the smectite clay minerals is still poorly understood. This is challenged in Paper I and Paper II where the adsorption of water is modelled, and the interstratification is estimated.
The counter-ions are not chemically bonded to the mineral and in addition to coordination to- and hydration by adsorbate they can undergo cationic exchange reactions. If, for example, montmorillonite is exposed to positively charged surfactants the adsorption and intercalation of the surfactant alter the interlayer space to become hydrophobic. This new hydrophobic interlayer changes the behaviour of the clay mineral and can be relevant for pharmaceutical purposes, where the modification can lead to selective adsorption of otherwise non-interacting compounds and the clay mineral can be used as a drug compound carrier15. But other modifications may allow for the production of catalysts9,16–18, interacting with and protecting DNA,19–21 or composite materials22. What can be
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done depends largely on the understanding of the processes involved and the capability to modify the materials in the correct manner, which is why in Paper III and Paper IV the interactions of clay mineral with organic compounds are investigated
In this work the aim was to improve our fundamental level understanding of intercalation processes into the interlayers of layered minerals. How these processes proceed for different types of molecules and how different factors control the intercalation and how it can be described and modelled.
Objectives of this thesis In this project the main objectives were to further our understanding of the interactions between layered minerals, water as well as organics by:
• Developing an adsorption isotherm that can be used describe the intercalation of water into the interlayer of layered minerals as a function of the relative humidity, type of counter-ion, and surface area.
• Investigate the suitability of combinations of classical force fields
for molecular dynamics simulations of organic and inorganic systems of biogeochemical relevance.
• Investigate the swelling and adsorption behaviour of
hydrophobic surfaces and interlayers present in organoclays, with respect to different solvents and additional organic solutes.
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Materials and Methods
Montmorillonite Montmorillonite is a naturally abundant layered mineral belonging to the group of smectite clay minerals. Each layer consists of an Al2O3 octahedral (O) sheet sandwiched in between two SiO4 tetrahedral (T) phyllosilicate sheets. The clay mineral is thus referred to as TOT clay indicating the sheet structure.23,24 The Al and Si are to a certain degree isomorphically substituted with other elements of a lower charge, which results in a net build-up of negative charge distributed over the clay sheet. This is counteracted by cations intercalating and adsorbing on the external surfaces. The hydration, coordination to, or cationic exchange of these cations is the main cause of the intercalation and swelling of the material, with the exception of large cations.10,25–30 The extent of these occurring processes can vary significantly, as it depends both on the cations and the Al/Si substitution and substitution ratio, as a higher degree of tetrahedral Si substitutions puts the negative charge closer to the surface of the sheet, creating a much more localized charged site compared to the octahedral Mg/Al sites. 31–33
Birnessite Birnessite is a naturally abundant layered manganese oxide mineral. It consists of layers of edge-sharing MnO6 octahedral sheets that via structural vacancies and mixed oxidation states of Mn build up a net negative charge that is counteracted by the intercalation of cations.34 Similar to Montmorillonite the hydration, coordination and exchange of the counter-ions as a driving force cause the swelling of the material. Natural variations in particle size, counter-ion and oxidation states alter the behaviour of the material, hence just as for Montmorillonite, it is thus necessary for Birnessite to note either the geographic procurement site or exact synthesis method of the material.31,35
Intercalation of alcohol in Montmorillonite Montmorillonite samples intercalated with alcohol was measured in both reflection mode and in transmission mode, using sealed sample cups for the latter to avoid evaporation of the smaller alcohols. Hence it was necessary to obtain reference XRD profiles free from alcohols in both measurement geometries, in order to estimate background effects of the chamber housing and the hk0 reflections seen in transmission mode. This was done by preparing native montmorillonite samples for XRD experiments in both reflection and transmission modes.
In the reflection mode experiments the samples were first deposited on glass slides by coating the slide with a dispersion of Ca-MMT. After drying over night the coating and drying process was repeated until the deposition had a sufficient thickness. The slides were then gently soaked with alcohol and sealed in a plastic bag with excess alcohol.
The transmission mode experiments were performed by depositing Ca-MMT in powder form in a Kapton transmission cup, which were gently soaked with alcohol, followed by a plastic film cover to prevent evaporation and ensure full saturation.
Eight alcohols of reagent grade or purer were intercalated into montmorillonite, namely: methanol, ethanol, propanol, butanol, hexanol, octanol, ethylene glycol and phenol. All were primary alcohols. Due to the high melting point phenol, heating was necessary to allow the phenol be intercalated in liquid form.
Intercalation of CTAB in montmorillonite In order to examine how montmorillonite interact with larger organic molecules Cetyltrimethylammonium bromide (C16H33N(CH3)3·Br), henceforth referred to as CTAB was intercalated in the interlayer space of purified Na-MMT. This was done by adding CTAB which is a cationic surfactant (due to an amine headgroup) to a dispersed MMT suspension. As CTAB initially intercalates by cationic exchange the amount added to the solution was calculated based on the cation exchange capacity (CEC) of the clay mineral, ranging from 0.6 to 5.2 times the CEC. Due to CTABs relatively low critical micelle concentration (CMC), CTAB dissolved in deionized water (DI) was added drop wise to promote the presence of monomers.
Experiments were performed on the CTAB treated MMT (CMMT) to determine different stages of CTAB uptake, and how the CTAB concentration affected the loading of an organic dye, alizarin. Contrary to the study with different alcohols using Ca-MMT as an adsorbent, Na-MMT was chosen in this study due to the ability of Na-MMT to better delaminate in water suspensions, maximizing the intercalation into the interlayers. In addition to the dye intercalation the effect of polar/non-polar solvents on the CMMT was investigated with water, ethanol, DMSO and hexanol as solvents. The CMMT’s interaction with solvents and dye was measured with DVS, FTIR and XRD with the devices previously mentioned. These experiments were also measured with XPS and TGA.
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Dynamic Vapour Sorption Dynamic Vapour Sorption (DVS) is often referred to a gravimetric technique where a sample (adsorbent) is exposed to a gaseous substance (adsorbate), such as vapour from water or an organic solvent.
As the vapour pressure of the adsorbate substance is varied, the gas will either adsorb onto or desorb from the sample surface. By measuring the change in the sample weight by for instance microgravimetry it is possible to determine the amount of substance adsorbed onto the sample as a function of the vapour pressure, and relate it to the several physical properties of the adsorbate- adsorbent ability to interact.
DVS can also be used in several other techniques apart from gravimetry. By using flow cells in for example FTIR or XRD experiments it is possible to resolve where and how much of a substance is adsorbed relative to the vapour pressure. For swelling materials in particular, the adsorption and desorption of a compatible substance result in structural changes in the sample that can be observed by XRD. 36–40
In this thesis work, water was adsorbed and desorbed on samples in a range from 0% up to 98% relative humidity (%RH), typically in a full adsorption-desorption cycle. Samples were initially either dried under a flow of dry N2(g) or via heating. Sequentially the samples were measured with the relevant method (gravimetry, FTIR, XRD) at specific %RH. To ensure proper equilibrium throughout the adsorption-desorption cycle, for each specific %RH the sample was measured repeatedly over time until the relative changes in the measured properties of the sample was below a set value, or simply by allowing for a pre-determined equilibrium time to be reached between for each %RH step. A full adsorption-desorption cycle typically took 3 days to 1.5 weeks based on equilibrium settings and measuring methods.
Brunauer-Emmett-Teller (BET) BET measurements are a common analysis method where a gas is adsorbed onto a sample to determine the specific surface area (SSA). The name heralds from S. Brunauer, PH. Emmet and E. Teller who published the first article about the method in 1938.41 BET has since been a part of untold amounts of analysis studies.
The theory applies to the multilayer adsorption of a gas that does not react with the sample, commonly using N2 at 77K (boiling point of N2). BET measurements are commonly used on powdered samples and adsorbents, as the obtained SSA is a common method of determining particle size.
In the case of layered materials however the probing gas can only measure pores/interlayer areas where the pore size or layer spacing is sufficiently large to allow for intercalation of the probing gas.12,25 This can be due to particles or adsorbed layers separating the sheets. Separation by intercalated particles may permit the measurement of the interlayer, but in the case where there is adsorbed layers they may be frozen due to the low temperature and normally occupy the entire interlayer volume, thus blocking the probing gas molecules. In addition to blocking the pores intercalated liquids can lead to further problems such as vaporisation and modification to the layered material. The intercalation of a material typically causes an increase in height of the layered stacks and possible changes in the average amount of stacked layers in a tactoid, and from this affect the SSA. Thus, due to the nature of the experiment it is commonly necessary to remove water and similar liquids adsorbed onto the samples, especially in the case of layered materials. It is however not always possible to remove all water as the temperatures necessary to fully remove strongly adsorbed may cause thermal decomposition of the material.42,43
Attenuated Total Reflectance Fourier Transform Infrared spectroscopy (ATR-FTIR) The use of infrared (IR) light and its properties has had a long history in science. From the discovery of IR in the beginning of the 19th century44 to the first implementation of IR spectroscopy in the end of it. The first commercial IR spectrometer appeared on the market in the mid-20th century whereas the Michelson interferometer and the use of Fourier transformation technique in the latter half of the century fully enabled the potential of IR light to allow an ever-increasing understanding of the world around us, often by providing insights from the molecular scale.
IR spectroscopy operates by using light in the infrared region (often reported to be between 10-15000 cm-1, or approx. 0.8-1000 μm), which by specific frequencies interact on the molecular level transferring its energy into vibrational or rotational energy in the molecules. This process causes the light intensity to decay in a manner described by Beer-Lambert’s law. Measuring the remaining light intensity and the corresponding frequency yields the transmittance in the frequency range measured. This does however apply two limitations on IR spectroscopy. First the molecule/sample must follow certain rules as to how the atoms and bonds are arranged, that is it must belong to a space group that is IR active or it will not absorb any light and can thus not be measured. The second limitation is the opposite. IR spectroscopy measures the loss of intensity, thus it is necessary for there to be remaining light intensity, in order to determine how much was absorbed. If no light remains it only indicates that the specific
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frequency range is completely absorbed and many details of the measurement are lost.
The second limitation especially can prove a problem with solid samples as many are not transparent to infrared light. This can be solved with the use of attenuated total reflectance, ATR. In this case the sample is placed upon a crystal such as a monolithic diamond, which creates a total reflection of the IR light within the crystal, only allowing evanescent waves of the IR light to probe any material sample deposited onto the ‘outside’ diamond surface. The evanescent wave probe depth is frequency-dependent but this is not an issue with the samples of this thesis work, where there is relative homogeneity in the layered materials investigated.
In this study, FTIR experiments were performed using a Bruker Vertex 70v and a Vertex 80v in the mid-infrared 600-4000 cm-1 range. The solid samples were deposited onto the ATR diamond stage and dried under a dry N2 gas flow, after which it was connected to a DVS set up to expose the samples under a flow cell to gradually increase and decrease the water content. This permitted for near real-time measurement of the water uptake of the samples and the resulting change in the IR spectra, as water adsorbed onto surfaces and hydrated the interlayer material, causing the samples to swell. In addition, the near real-time observation allowed for the observation of equilibria with the corresponding humidities.
Powder X-ray Diffraction (XRD) XRD is a method that provides insight into the atomic structure of solid crystalline or semi-crystalline samples. The method operates by exposing a sample to an incoming beam of X-rays while monitoring how much of the X-rays are emitted by the process of diffraction, and proceeds as a function of the angle between the incident and diffracted X-rays. The X-rays themselves interact with the individual atoms in a sample by elastic scattering with electrons. As a result the measured X-ray reflections not only depend on the (semi-)crystal structure, but also on the element (e.g. H, O, Fe), as well as the chemical state of the atoms (e.g. O/O-/O2-, Fe/Fe2+/Fe3+) to a lesser extent. As the X-rays are scattered by individual atoms they will undergo either destructive or constructive interference. Randomly scattered X-rays yield very low intensities due to the high degree of destructive interference, whereas repetitive structural patterns in the sample result in constructive interference at a specific angle and thus yield high intensities, or so-called X-ray reflections. Since X-rays have a wave-like properties, higher order X-ray reflections are also possible.
In samples of crystalline nature, these repetitive patterns are the constitute the smallest volume-filling building blocks of the material, i.e. the unit cells. In the
case of swelling clays minerals the swelling occurs in the normal direction to the clay mineral layers, since the intercalated material is also part of the unit cells. By measuring the angle between the incident and diffracted beam of X-rays it is possible to calculate the size of the repeating unit cells and attain the so-called basal spacings (d00l), meaning the separation distance between any parallel 00l crystallographic plane in the crystal. The l in this case refers to the order of X-ray reflection, which also correspond to the reciprocal length of the unit cells, that is d001 represents the full unit cell height in the z direction for an orthogonal system (or along the c axis for triclinic unit cells), and d002 represents half the height of the unit cell, where as d003 represents one third of the unit cell height, and so on. Since this thesis is focused on intercalation in layered materials, all attention has been placed on the l-reflections, hence all theoretical XRD models are thus 1-dimensional (1D).45
The XRD experiments presented in this thesis work were made with a PANalytical X’Pert3 Powder working in 2θ with CuK𝛼!" X-rays radiation operating at 45 kV and 40mA. The experiments were performed either in reflection mode with oriented mounts in transmission mode for controlled relative humidity conditions. For these experiments an Anton Paar MHC-trans Transmission humidity chamber was used along a 24-point adsorption/desorption cycle ranging from 3-98 %RH. All diffractograms were collected in the 2-50° (2θ) range with a resolution of 0.0334° unless otherwise stated.
Modelling of alcohols intercalated into montmorillonite Classical Molecular Dynamics (MD) simulations with Gromacs46 were performed using combinations of force fields and different alcohol and water contents, in order to simulate the corresponding experimental samples of alcohol being intercalated into MMT. Different force fields can have significant differences in e.g. partial charges or Lennard-Jones potentials, as displayed for example in Figure 1, which details the non-bonded force field parameters used to model MMT in this thesis work. Different force field parameters would be expected to lead to different intermolecular interactions and behaviours, and hence potentially also the overall performance with respect to the agreement with experimental observables.
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Figure 1. Differences between the INTERFACE force field (blue bars), ClayFF (red bars) and the modified ClayFFMod (red/green bars) with respect to similar atomtypes (a) the partial charges, and the Lennard-Jones potential parameters related to the atomtypes (b) size (σ in Å) and (c) strength (𝜖 in kJ/mol). Note that custom atomtype names are used here for convenience, and hence differ compared to the respective original ClayFF and INTERFACE publications. 47–49
With the eight different alcohols, a total of 72 clay-alcohol systems were simulated by combining either ClayFF47, the modified ClayFF (ClayFFMod)50 and the INTERFACE force field48 for the clay minerals, and the Charmm general force field (CGenFF)51, the General Amber force field (GAFF)52 and the all atom OPLS(/aa)53 force field to simulate MMT intercalated alcohols. In combination with these force field combinations, the water model chosen depended on the force field used to simulate the alcohols, where Tip3p54 was used with CGenFF and SPC/E55 was used with GAFF and OPLS.
To find what amount of intercalated alcohol and water resulted in stable solvation states that would supposedly match the experimental d001 values, the immersion energy (Q) was computed from the potential energy (U) in simulations with different water and alcohol content. In general for montmorillonite, birnessite and other layered minerals, an immersion energy curve typically show several local minima with respect to interlayer loading of a solvent. This energy minima in principle indicate the stable solvation (hydration in case of water) states, with the caveat that entropic effects are neglected. This is because the immersion energies are computed from the system potential energy and not the free energy. The equation used to compute the immersion energy is expressed as follows:56
𝑄(𝑁) = ⟨𝑈(𝑁)⟩ − ⟨𝑈(𝑁°)⟩ − (𝑁 − 𝑁°)𝑈$%&'
Eq 1
Where 𝑁 is the number of solvent molecules used in the individual simulations (alcohol or water) and 𝑁° is the solvent molecules in the reference simulation, commonly the global minima (the most thermodynamically stable solvation state, neglecting the entropy) in the immersion curve. 𝑈$%&' is the mean interaction energy of a solvent molecule under bulk solvent conditions.
All MD systems were built using the functions in the atom MATLAB library.57 A MMT lattice consisting of one unit cell was replicated into a three-layered structure of 6x4x3 unit cells with a x/y/z box size of 31.188×36.060×Z. The Z dimension (three times the d001) varied with the alcohol type and the alcohol/water content. To represent the Ca2+ exchanged Swy-2 MMT, random isomorphic substitution were performed on 2/3’s of the Al sites while obeying Löwenstein’s rule.58 The resulting charge was counterbalanced by Ca2+ ions. The systems were solvated by inserting preequilibrated solvent boxes of water and alcohol. The assembled systems were prepared for the production run by running a set of three equilibration simulations. First, an energy minimization simulation, followed by a thermal equilibration at 298K in the NVT ensemble and finally volume equilibration in the NPT ensemble simulation. In order to generate a data point in the evaporation series used to compute the immersion energies, production runs were also simulated in the NPT ensemble for 5 ns.
Following every production run, a small fraction (1/60) of the solvent molecules (alcohol or water) was randomly removed from each interlayer to emulate evaporation. A full evaporation series hence consisted of 61 evaporation steps, which comprised of (in an iterative manner): short volume equilibration runs, production runs, and solvent evaporation, until the solvent (water or alcohol) was completely removed. This overall simulation approach was performed in three stages for all 72 force field combinations, where first the alcohol was evaporated and an immersion energy curve was generated. The preliminary alcohol loading to be chosen for the second stage was obtained by identifying the stable solvation state having a simulated d001 being in close proximity the experimental d001. In the second stage, excess water was instead added and in a similar fashion evaporated from the system, leaving only the alcohol content determined from the first stage of simulations. The water loading then suggested in stage 2 was then used in stage three, where the alcohol loading once more was optimized in order to find the optimal water-alcohol composition.
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From the final stage 3 simulations, three simulated systems were selected based on being in the two nearest stable states to the experimental d001 and the simulation with the closest d001 value. These simulations were then used to extract structural data for 1D-XRD modelling, which is described in greater depth in the Theory section of this thesis. The 1D-XRD modelling was performed using an in-house MATLAB code called OneDXRD2C (1-dimensional XRD code handling phases containing two interstratified sub-phases) which is based on the recursive algorithm in Newmod.59 It has however been given additional features such as the ability to refine 1D-UC structural data and perform a brute force sensitivity analysis with respect to the modelled parameters. In addition it can operate in a batch mode which increases fitting speed for large datasets, but also minimizes the user bias in the fitting procedure.
The three selected simulations for each force field combinations were used to generate the one-dimensional unit cells needed to calculate the theoretical XRD profiles, via so-called layer structure 𝐺( factors (Eq 27) which were used by OneDXRD2C to fit to the corresponding experimental XRD profiles. OneDXRD2C uses a non-linear optimization algorithm to minimize the difference (residual) between the experimental and simulated XRD profiles, which is evaluated as a goodness-of-fit parameter Rwp (in %):
𝑅)* = 2∑4𝐼+,*(2𝜃) − 𝐼-./(2𝜃)8
(
∑𝐼+,*(2𝜃)(× 100 Eq 2
In total three fitting approaches was performed on each of the 72 force field combinations. First a predictive 1D-XRD modelling approach using unmodified MD density profiles and the respective 𝐺( factors and d001 values. In the second fitting exercise the 𝐺( factors and the d001 values were also optimized, in a similar manner to XRD Rietveld refinement.60 This was accomplished by modifying the loading and position of the interlayer material, corresponding to the density profiles obtained from the MD simulations. Lastly, a trial-and-error sensitivity analysis was made by performing 500 random changes to the position and loading of the interlayer material while monitoring the effect on the goodness-of-fit parameter 𝑅)*.
Theory
Isotherm modelling
Langmuir isotherm The Langmuir adsorption isotherm model is an old, but still heavily utilized model (1918) based on the kinetic adsorption concept.61 That is, particles adhere and particles desorb in a monolayer, and when the rates are equal the system is in equilibrium. The model relates the adsorbed substance (Cµ) to the material maximum adsorption (Cµs), vapour pressure of the substance (P) and a material and temperature dependent constant (b) that can be seen in equation 1.
𝐶0 = 𝐶0-
𝑏𝑃1 + 𝑏𝑃 Eq 3
The Langmuir adsorption isotherm model is based on flat homogeneous surfaces but there is leeway to be found for heterogeneous materials. With sufficient insight into the material it can be considering the surface a sum of homogeneous sections.
𝐶0 =?𝐶0-𝑏1𝑃
1 + 𝑏1𝑃
2
134
Eq 4
Freundlich isotherm Contrary to the Langmuir model, the Freundlich equation is an adsorption model that can be used to describe heterogeneous systems. The equation describes the adsorbed substance (Cµ) by multiplying the pressure (P) with two typically material and temperature dependent constants (K and n).62
𝐶0 = 𝐾𝑃4/6
Eq 5
As the equation has an empirical origin there is no description of adsorption model, however it can be theoretically justified with the Langmuir model as a multiple of homogeneous patches. There are still however limitations to the model in that it does not follow Henry’s law for low pressures and there is no
14
upper adsorption limit, thus the Freundlich equation is only applicable in constrained pressure ranges.
Do & Do isotherm Limitations imposed upon the earlier mentioned adsorption models makes them less appropriate for layered swelling minerals. A theoretical model developed by Do and Do (DoDo) primarily for adsorption and desorption of water on carbon, has instead been used to describe the process on the minerals.63,64 The DoDo model can be split in two separate parts.
The first part describes the binding of water to suitable sites on the surface of an adsorbent. The adsorbed water molecule then also become a site for further adsorption. The result is an equation that bears resemblance to the expressions in both the Langmuir and Freundlich isotherm models.
𝐶04 = 𝑆7𝐾8 ∑ 𝑛𝑝/𝑝76
639:44
1 + 𝐾8 ∑ 𝑝/𝑝76639:4
4
Eq 6
Here Cµ1 is the adsorbed amount of water, S0 is the concentration of surface sites, p/p0 is the relative water vapour pressure, Kf is a binding constant and β is the amount of water that can coordinate to a binding site.
The second part of the equation arises from the formation of water clusters. As the clusters grow to a sufficient size, they can initiate condensation in the micropores. Here we will note a difference between adsorption and desorption. As the pore has been filled the smaller water cluster will coalesce and form interlinking hydrogen bonds thus lowering the energy. Upon desorption these larger clusters must be broken apart into the smaller clusters while introducing hysteresis.
𝐶0( = 𝐶0-𝐾0(1 + 𝐾;)∑ 𝑝/𝑝7663!:4
4
𝐾0(1 + 𝐾;)∑ 𝑝/𝑝76 + ∑ 𝑝/𝑝7
6<!63!:44
63!:44
Eq 7
Here Cµ2 is the adsorbed water, is the maximum adsorption, Kµ is the condensation sites, Kr is the relaxation constant and α is the size of the water clusters.
By combining the two parts of the DoDo equation one can describe how water first adsorbs onto the surface and secondly condensates in the micropores.
𝐶0 = 𝐶04 + 𝐶0( = 𝑆7
𝐾8 ∑ 𝑛𝑝/𝑝76639:44
1 + 𝐾8 ∑ 𝑝/𝑝76639:4
4
+ 𝐶0-𝐾0(1 + 𝐾;)∑ 𝑝/𝑝7663!:4
4
𝐾0(1 + 𝐾;)∑ 𝑝/𝑝76 +∑ 𝑝/𝑝7
6<!63!:44
63!:44
Eq 8
This does however not describe the adsorption of water in swelling layered minerals as there is no description of the adsorption causing the swelling process.
Dubinin & Astakhov isotherm
The Dubinin & Asthakov (DA) equation was originally developed from the form of the Weibull distribution. By expressing it as a cumulative probability distribution the probability can be used to describe the probability that a pore is filled.
𝑓F𝐴 𝐸I , 𝑛K = exp O−F𝐴 𝐸I K6P
Eq 9
It was Dubinin and Radushkevich whom originally suggested the adsorption model and designated it with the parameter n=2. This was later expanded upon by Dubinin and Astakhov as the pore size parameter n=2 restricted systems with greater distribution.
𝑤 = 𝑊exp S−T𝐴𝐸U
6
V Eq 10
Here w is the adsorbed volume whereas W is the pore volume, E is the interaction energy between the pore and the adsorbent and adsorbate, Rg is the universal gas constant, P0/P is the inverse partial pressure and A is the adsorption potential as a function of pressure and temperature (T).
𝐴 = 𝑅=𝑇𝑙𝑛 T𝑃7𝑃 U Eq 11
From adsorption potential it can be seen that the DA equation (Eq 11) does not display Henry’s Law behaviour as the pressure approaches zero.
16
Molecular Dynamics simulations Classical Molecular dynamics (MD) simulations is a means to model thermodynamic and/or time dependent processes in organic and inorganic systems on the molecular scale, often with the goal of understanding macroscopic phenomena based on the microscopic (or actually the molecular-scale) properties in a system. Although there are no limits to the maximum size of such modelled systems apart from the limitations in available computational resources, there is a lower size limit. If the scale of the system becomes too small, the corresponding laws of physics needed to describe molecules change from the classical physics and Newtonian and molecular mechanics (MM), to quantum mechanics (QM). There are in fact schemes to model molecules using hybrid classical and quantum mechanics, i.e. QM/MM but that is outside the scope of this work. Here we will discuss MD that utilize classical mechanics based on Newton’s second law (vectors in bold):
𝒂.(𝑡) =𝑭𝒊(𝑡)𝑚.
= −1𝑚.∇.𝑈(𝒓.) Eq 12
where ai, Fi, mi, ∇iU, and ri are acceleration, force, atomic mass, gradient of the potential energy and atomic position respectively.
We are however interested in dynamics and thus the evolution over time of the system. Thus, to advance the evolution of time in a molecular system, algorithms are used that iterate Newton’s second law for the individual particles over discrete time steps. The forces applied are calculated from the potential energy which in turn comes from the force fields that will be discussed below. This yields accelerations and positions of the particles for the next time-step and the process is repeated.
That said, in order to evolve a molecular system over time, certain thermodynamic and mechanical constraints must be placed in order to allow the system to behave in a physically realistic way. This is accomplished by regulating both thermodynamic system variables such as the temperature (T) or the total energy (ETot), as well as certain mechanical system variables; such as the number of particles (N), and either the pressure (P) or the volume (V) of the system. Given the specific combination of thermodynamic and mechanical constraints placed on a system, one attains different so called statistical equilibrium ensembles, for example the isothermal–isobaric ensemble abbreviated NPT, where the number of particles (N) is kept constant and the pressure (P) and temperature (T) is maintained through the use of isobaric controls and thermostats respectively. The NPT ensemble type is in fact predominately used in this thesis work, since it allows for the volume and potential energy to depend on the system and how it
evolves over time, however other ensembles also exists such as the NVE, NVT, and µVT ensembles. In the latter ensemble called the grand-canonical ensemble (often used in Monte-Carlo simulations) the chemical potential µ is fixed, whereas the number of particles N is not.
In order to calculate the potential energy of a system, it needs to be mentioned that these types of systems generally utilize a so called periodic boundary condition (PBC) where the system simulated “contained” within a cell of a specified geometric shape and is duplicated infinitely in all directions, see Figure 2. As a particle moves beyond the boundary of the cell, represented by a blue square, an identical particle enters on the corresponding site in the cell as it would gain in the cell the particle moved into. With this it is possible to take into account for the fact that particle-to-particle interaction decays to zero over infinity. In order to calculate the energy the interactions are divided into short- and long-range interactions. They are separated by so called cut-off schemes here represented by a circle surrounding a particle.
Figure 2. Simulated cell (blue) with surrounding periodic boundary conditions. Circle marks cut-off range between long- and short-range interactions.
Short-range interactions The short-range interactions consist of intra-molecular bonded interactions as well as intra-molecular and inter-molecular non-bonded interactions. The bonded and non-bonded interactions can in turn be split into several potential energy (Epot) contributions, which typically are the (bonded) bond stretch, angle bend and optionally different types of dihedral terms, as well as the (non-bonded) Van der Waal (VdW) interaction terms, represented by a so-called Lennard-Jones (LJ) potential described below, and finally the electrostatic (Coulombic) term.
18
𝐸*?@ =𝐸$?6A- + 𝐸B6=&+- +𝐸A.C+A;B&- + 𝐸DA) + 𝐸+&+E@;? Eq 13
The intramolecular pair potential energies between bonded atoms are typically calculated by parabolic equations:
𝐸$?6A- =12?𝑘$(𝑟.1 − 𝑟7)(.F1
Eq 14
𝐸B6=&+- =12?𝑘G(𝜃.1 − 𝜃7)(.F1
Eq 15
where kθ and kb are force constants and θ0 and r0 are the equilibrium bond length and angle, respectively. The optional factor 4
( is simply used to turn the
corresponding force (F) equation into Hooke’s law (since F = -dE/dr). The corresponding energy expressions for different types of dihedral terms depends on the force field and simulation package used and will not be covered here. Coulombic attraction is a force with both long and short distance effects, however due to the cut-off condition it is split in two parts (long range discussed later). The electrostatic energy contribution is thus expressed by a slightly modified Coulomb’s law as follows:
𝐸+&+E@;? =?1
4𝜋𝜀7𝑞.𝑞1𝜀;𝑟.1.F1
Eq 16
where ε0 and εr are the vacuum and a relative dielectric constant, respectively.
The Van der Waals energy contribution is typically described with the so-called Lennard-Jones potential, although other more realistic potential types such as the Buckingham potential also exists, however it is more computationally expensive.
The often used ‘12-6’ Lennard-Jones potential describe both the attractive dispersion energy by the negative -1/r6 term, as well as the repulsive short-range energy component with its positive +1/r12 term, representing the effect of overlapping electron orbitals and the so-called Pauli exclusion principle. The Lennard-Jones potential can be expressed in several ways, for example:
𝐸!"# =#
𝐶$%('()
𝑟$%'(−𝐶$%(*)
𝑟$%*$+%
Eq 17
𝐸!"# =#4𝜖$% )*
𝜎$%𝑟$%,'(
− *𝜎$%𝑟$%,*
-$+%
Eq 18
where C(12), C(6), σ and𝜖 are atomtype specific parameters, and are related as C(12) = 4𝜖𝜎4( and C(6) = 4𝜖𝜎H. Out of these parameters, σ and𝜖 has a direct physical meaning since they represent the separation distance r where the Lennard-Jones potential is zero, and the magnitude of the potential well depth, respectively. In order to use these atom type specific parameters to describe the Lennard-Jones potential between pairs of atoms (between any atom i and j, where i ¹ j), they need to be mixed and averaged which is done by so-called certain combination rules, expressed either as the geometric (Eq 19-Eq 21) or arithmetic (Eq 22) mean values.
𝐶.1(H) = F𝐶..
(H)𝐶11(H)K
4/( Eq 19
𝐶.1
(4() = F𝐶..(4()𝐶11
(4()K4/(
Eq 20
𝜖.1 = (𝜖..𝜖11)4/( Eq 21
𝜎.1 =
12 (𝜎.. + 𝜎11) Eq 22
Long-range interactions The computationally most expensive part of the direct pair-wise short-range interactions mentioned above are the electrostatic interactions, which scales rapidly (i.e. inefficiently) with the number of atoms as O (N2). Hence, for pair-wise interactions beyond a certain cut-off distance rcut (typically 0.8-1.4 nm, Figure 2), the long-range tail of the electrostatic interaction is instead calculated using a more computationally efficient method. The technique often used is based on Ewald summation, which uses a special form of the Poisson equation for periodic systems and calculates the electrostatic interaction potentials for the long-range tail in (reciprocal) Fourier space. The specific Ewald method used in this thesis work was the efficient Particle Mesh Ewald (PME) method, which is the default method used in the MD package Gromacs. In PME the interacting
20
charges belonging to the long-tail interactions are distributed by interpolation onto a 3D grid (mesh size usually 0.12-0.16 nm), which allows fast Fourier transformation (FFT) to be used in order to evaluate the charge density field in Fourier space. This significantly reduces computational cost, especially for medium to large scale systems, for which PME scales as O (N logN) (ideally).
Since the electrostatic energy between pair-wise particles decays slowly (1/r) with the separation distance rij, PME calculations are normally only applied to the electrostatic interactions, although recently LJ-PME has also been implemented in for instance Gromacs. Nevertheless, since the attractive component of the LJ potential decays much faster (1/r6), long-range VdW interactions are so far seldom used in MD simulations, especially for highly charged and predominantly ionic systems. Hence, with the long-range electrostatic PME contribution, the total energy of a MD system can thus be generically summarized as show below, where the electrostatic term is divided into a short-range term and one long-range term:
𝐸𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 = 𝐸𝑏𝑜𝑛𝑑𝑠 + 𝐸𝑎𝑛𝑔𝑙𝑒𝑠 +𝐸𝑑𝑖ℎ𝑒𝑑𝑟𝑎𝑙𝑠 + 𝐸𝑣𝑑𝑤 + 𝐸𝑒𝑙𝑒𝑐𝑡𝑟𝑜,𝑆𝑅 + 𝐸𝑒𝑙𝑒𝑐𝑡𝑟𝑜,𝐿𝑅 Eq 23
What is a force field? As perhaps evident at this point, in order to perform a MD simulation of a particular atomistic system, much information about the atoms to be modelled is needed. Apart from the chemical element of each atom, which determines the atomic mass, one needs to know the atomic partial charges (𝑞.), effective radii (𝜖. , 𝜎.), bond stretch (𝑘$ , 𝑟.), angle bend (𝑘G , 𝜃.) and any existing dihedral bonding information. One note about the atom specific parameters – the different parameters are not assigned to different elements, but rather to so-called atom types, i.e. atoms of the same element having different partial charges, radii, bonding characteristics etc. For instance, the oxygens: O-Si, O-Al, O-CR3. O=CR2 could be expected to have significantly different atom type parameters, simply by being bonded to different atoms.
In addition to this, the particular choice of cut-off settings, combination rule/s to be used, as well as the exact short-range and long-range expressions used for calculating the total potential energy must be decided (and preferably be consistent with the way the atom specific parameters were derived). It is this information, together with the atom type parameters mentioned above, that comprises what is normally called a force field.
In order for the simulations to perform realistically with respect to the relevant properties sought for, atom type parameters used in force field are typically
(semi-)empirically derived from either experimental data or calculations with more accurate QM methods (e.g. DFT).
Force fields are typically composed of a collection of atom types relevant to specific fields or circumstances. An example of this would be INTERFACE, ClayFF and a modified ClayFF (ClayFFmod) proposed by Ferrage et al.50 that are used to simulate the minerals as the atom types included optimized to fit this purpose. The force fields just mentioned would however be unable to model organic molecules in the interlayer and a second force field must be implemented and combined with the mineral force field. Examples of force fields fit for that purpose would be GAFF, OPLS and CGenFF. These force fields are optimized to be used on organic systems but are not intended to simulate water and this needs a force field of its own.
Water is of course a very common component in chemistry, and this transfers of course also to MD simulations, so special effort has been made to properly convey all properties of water. Most force fields for organic and inorganic molecules are often intended to be modelled with water (and solute ions), however no model of water can cheaply and accurately describe all properties which has led to multiple models having different atom type properties and combination rules. Examples of popular 3-site water models are SPC, SPC/E, TIP3P, and the recent OPC3, whereas popular 4-site water models (carrying a mass-less charge site below the oxygen site), are TIP4P, TIP4P-Ew, TIP4P/2005, TIP4P/Ice, and the recent OPC water model.54,55,65–71
1-Dimensional XRD Modelling In an XRD experiment, as the diffractometer scans the2𝜃 range of interest X-rays penetrate the sample. This produces angle dependent constructive- or destructive interference of the X-rays resulting in increased or decreased intensity to be detected, respectively. The position of the peaks, or the so-called Bragg reflections, in the diffractogram can then be related to the size of the unit cell/s in the material using Bragg’s law.45
𝑛𝜆 = 2𝑑C'& sin 𝜃 Eq 24
Here n is an integer, λ is the X-ray wavelength (in this work Cu𝐾!" , 1.54187 Å), dhkl is the size of the repeating pattern between any hkl plane (where hkl indicates the so-called Miller index in a crystal lattice) and θ is half the angle between the experimental incident and diffracted X-rays directions.
In the case of a 1-dimensional XRD modelling, dhkl will effectively be reduced to d00l, since this type of modelling do not consider all hkl reflections, i.e. it is 1-
22
dimensional in that sense. 1-dimensional XRD modelling is often applied to layered materials such as clay minerals, since the 00l reflections stems from the basal spacing of these materials, and will in effect measure the thickness of any layered lattice including any intercalated material.
The intensity of the diffractograms for these materials can be theoretically derived using four terms: the measurement geometry based Lorentz and the polarization factors, often combined and denoted LP, the squared structure factor (𝐺(), and finally the interference function (Φ). (The following segment is based on formalism described by Moore and Reynolds45 Moore Reynolds 1989 + reynolds 1989)
𝐼(𝜃) = 𝐿𝑃𝐺(𝜙 Eq 25
The L factor depends on the orientation of the crystallite particles and the incident angle of the X-rays, which to a lesser extent also affects the polarization (P) of the X-rays. The layered minerals investigated in this work differs significantly from many other minerals due to the chemical heterogeneity and defects. This causes small particle sizes, interstratification, potential particle reorientation and as a result broadening and reduced intensity of the peak reflections.
Although particle size and interstratification will be discussed later, the particle orientation primarily governs the mean degree of particle orientation, σ*, which determines the powder ring distribution factor (ψ), which represents the fraction of particles that are oriented in a fashion such that they diffract the X-rays into the detector. For randomly orientated particles ψ is proportional to 1 sin 𝜃⁄ ; and for perfectly orientated particles ψ is independent of 𝜃. For this reason, well-orientated clay mineral aggregates produce much stronger diffraction intensities than do poorly or randomly oriented particles, especially at high angles where the higher order Bragg reflections are found. The powder ring distribution factor is the last parameter necessary to determine the LP factor:
𝐿𝑃 = (1 + 𝑐𝑜𝑠(2𝜃)𝜓/𝑠𝑖𝑛𝜃 Eq 26
While the LP factor describes the intensity variations that originate from particle orientation, the squared structure factor 𝐺( (also called layer factor or transform) describes the intensity of X-rays scattered from the individual unit cells. This 𝐺 function, being continuous with respect to 𝜃, corresponds to the discrete 𝐹(ℎ𝑘𝑙) structure factor used in normal (3D) crystallography. However, since the Bragg reflections of clays and other layered materials are usually very broad, it is better to use a continuous form of the structure factor. Furthermore, as we are only
considering the l reflections the one-dimensional G can be described without the consideration of any h or k information as:
𝐺(𝜃) =# 𝑝%𝑓(𝜃)% cos(4𝜋𝑧% sin 𝜃 𝜆)⁄ + 𝑖# 𝑝%𝑓(𝜃)%sin(4𝜋𝑧% sin 𝜃 𝜆⁄%%
) Eq 27
As a general note, for centro-symmetric systems such as the layered materials investigated in this thesis work, the imaginary part cancels due to the sine term. This is obvious by realizing that for any number 𝛼; sin(𝛼) + sin(−𝛼) = 0.
p and z describe the occurrences and position along the z axis respectively, where the z-axis is normal to the 001 basal plane. f(θ) is the angle dependent and temperature corrected atomic scattering factor, which primarily depends on i) the number of electrons in each atom, as well as the ii) Debye-Waller temperature factor. f(θ) is by definition normalized by the single electron scattering factor, and explains why an O atom scatters X-rays 8 times more efficiently than a H atom (at 2𝜃 = 0°), and why the Fe content in clays are is crucial information in structural investigations of geologic materials.
Lastly the third term, the interference function. It is a periodic function that describes the 00l Bragg reflections of periodic structures with the peak width and integrated intensity proportional to the number of layers. Thus, being affected by the particle size as ‘seen’ b the X-rays, i.e. the coherent scattering domain (CSD). It is comparable to the 𝐺( factor in the sense that it represents the scattering of the layers as if they were single electrons rather than the individual atoms of the unit cell. In the case of an ideal crystal it can be described as follows:
𝜙(𝜃) =
𝑠𝑖𝑛((2𝜋𝑁𝑑𝑠𝑖𝑛𝜃 𝜆)⁄𝑠𝑖𝑛((2𝜋𝑑𝑠𝑖𝑛𝜃 𝜆⁄ ) Eq 28
where d is the periodic separation distance, or in the case of this work the basal spacing, N is the number of periods or layers in a stacked particle. The materials used however are not ideal crystals as is mentioned earlier and is better described as a Fourier series:
𝜙(𝜃) =
1⟨𝑁⟩ x
⟨𝑁⟩ + 2 ? y? 𝑝(𝑁)(𝑁 − 𝑛)232!
232"
z632<4
634
×𝑒<KL!6!!-.6!G M!⁄ cos(4𝜋𝑛𝑑 sin 𝜃 𝜆)⁄ ~
Eq 29
24
In this equation, p(N) represents the layer size distribution of the coherent scattering domain (CSD), and <N> is the average number of layers per particle and α is a size strain parameter which models deviation form fully discrete basal spacing, d001, similar to the Debye-Waller temperature factor for atoms.
One remaining factor that is unaccounted for this far, is that of interstratification, meaning mixing of different types of unit cells within the same CSD. This is because in natural layered materials such as clays, the structural heterogeneity often cause the particles to have multiple coexisting yet stable states (sets of layers), i.e. to have unit cells with different d values within the same CSD (hence also in the above equation). In order to deal with this mathematically, i.e. more than one layer or interlayer type, every possible sequence of interstratified and scattering layer with different 𝑑774 values and layer structure factors G must be accounted for.
In 1-dimensional XRD modelling, this is accomplished by creating multiple subphases, one for each relevant state and combining the individual subphases to a final composite phase, by considering the probability and sequence (taken as random in this work) of the subphases in the total composite phase. Mathematically, this can be done via the so-called matrix formalism or as in this thesis a recursive algorithm, implemented in the in-house code OneDXRD2C. The supporting information (Figure S1-S4) to Paper III demonstrate the 𝐿𝑃 factors as a function of mean degree of particle orientation, σ*, the interference functions 𝜙 dependence of the CSD, typical 𝐺(factors for hydrate MMT and theoretical XRD profiles, generated by OneDXRD2C.
Multivariate Curve Resolution (MCR) FTIR data can collected as single measurements for a sample but can also be used to analyse a series of samples or a sample being altered. Repeated sampling can be used to measure changes over time or to measure as a sample enters a series of equilibria, due to changing the conditions of the sample. The result of this is a dataset where that can be used to gain additional information that a single spectra cannot provide.
A method known as Multivariate Curve Resolution (MCR) can process a data set to describe changes by creating representative spectra and a concentration profile. The method is similar to Beer-Lambert’s law:
where A is the adsorption, C is the concentration, l is the path length and ε is the absorptivity. This is an equation that commonly describes absorption for a single
wavelength, but MCR is a method that measures over multiple wavelengths simultaneously. It uses a matrix version of the same law in order to do so.
𝐴 = 𝐶𝑆O + 𝐸
Eq 31
A is now a matrix with the adsorption for the individual wavenumbers for all selected measurements in the data set. C is a matrix describing the concentration profile of the pure spectra S, T is an indicator that the matrix is transposed. E is the deviation from Beer-Lambert’s Law as it is the residuals not explained by the model. MCR can normally not describe a dataset perfectly, it instead attempts to describe the variation between measurements with a number of spectral components. The appropriate amount can be estimated either by having insight into the samples or estimations such as inspecting the eigenvector of the matrixes given by the single value decomposition.72,73
The method calculates initial values for C and ST using methods such as evolving factor analysis74 or SIMPLISMA75 and then refines the values by minimizing the lack of fit:
𝑙𝑜𝑓(%) = 1002
∑ 𝑒.1(.,1
∑ 𝑎.1(.,1
Eq 32
Here eij and aij are the elements of the E and A matrixes respectively.
𝐴 = 𝜀 × 𝐶 × 𝑙 Eq 30
26
Results and Discussion In this thesis the focus lies on the adsorption and intercalation of materials into the interlayer of layered materials. The intercalated material can be divided into three groups and the discussion as well. The intercalation and behaviour of water, of alcohol and finally of CTAB.
Modelling intercalation of water in the interlayer In Paper I and Paper II the intercalation of water into the interlayer of Montmorillonite and Birnessite respectively was analysed and modelled. This was done via fitting of experimental DVS data to a composite adsorption isotherm model that accounts for the different sources of adsorption. In Figure 3 the adsorption of water in Cu-MMT is fitted to the model to depict the progressive intercalation and the adsorption on external surfaces.
Figure 3. The adsorption of water in Cu-MMT (a) and the DoDo component split into its constituents (b).
In Paper I the model is first proposed where the adsorption of water of Montmorillonite is described as a multicomponent process resulting from three co-existing processes, the surface adsorption, the pore condensation and the intercalation. The first two processes can be modelled using the equations proposed by Do & Do (Eq 8), leaving the intercalation process to be modelled.
The intercalation in Montmorillonite is difficult to model as the natural defects in the layered materials result in interstratification of layers. Furthermore, characteristics of the material, such as average layer charge and counter ion affects the extent of intercalation, i.e. how many monolayers of water can be intercalated between two layers. The isomorphic nature of the material further
introduces the potential that not only does the intercalation occur simultaneously in all interlayers but also it cannot be guaranteed that all layers are capable of intercalating water to the same extent.
To create a model for the intercalation given these behaviours of the material, five restrictions are placed on the procedure to create a predictive model.
1. The system is assumed to exist in stable hydration layers, that is the number of intercalated monolayers between any two sheets is a positive integer including zero.
2. The sum of fractions of interlayers is unity. That is for any hydration layer i the fraction of interlayers in that hydration layer θi follows:
1 =?𝜃.
2
.37
Eq 33
3. The water content in hydration layer i is the volume of a single monolayer multiplied with i:
𝑊. = 𝑖 ∗𝑊4 Eq 34
4. Restriction 3 does not apply to the highest hydration layer. The hydration potential for the DA equation (Eq 11) results in full occupancy of the highest hydration state, which cannot be guaranteed as was previously mentioned. Thus to accommodate for the isomorphic nature of the material the highest hydration layer is equal to- or less than the value proposed by Eq 34. 5. The intercalation is progressive and exclusive. This means that for every bilayer that forms the interlayer must first have been a monolayer and when a new hydration layer forms the old is erased, i.e. if a monolayer becomes a bilayer it is no longer a monolayer. The calculation example for a trilayer system can be seen in Paper I Eq 8-11, here Eq 35-37.
𝜃Q =𝑤Q𝑊Q
Eq 35
28
𝜃( =𝑤( −
23 ∗ 𝑤Q𝑊(
Eq 36
𝜃4 =𝑤4 −
𝑤( −23 ∗ 𝑤Q2 − 𝑤Q3𝑊4
Eq 37
𝜃7 = 1 − 𝜃4 − 𝜃( − 𝜃Q Eq 38
These restrictions are used with the DA equation (Eq 10) to describe the total amount of intercalated water (Paper I eq 6).
By optimization of the parameters in the DA equation (Eq 10) restricted by the conditions mentioned and those of the DoDo equation (Eq 8) the combined water adsorption is fitted to experimental data. The resulting parameter values are used to plot the combined adsorption and that of the individual components as a function of humidity (Figure 3, Paper I SI Figure S2, Figure 9).
The adsorption resulting from intercalation can be further divided and plotted as hydration layer fraction (θ) where the formation and decay are modelled as a function of humidity (Figure 4).
Figure 4. The calculated layer distribution of homoionic MMT.
From the hydration layer fractions it is possible to estimate the basal spacing of the material as a function of hydration. By multiplying the fraction of hydration layers with the corresponding known basal spacing the resulting sum is a prediction of measured basal spacing.
Two issues need to be considered with these basal spacing predictions. It has been shown by Ferrage et al14 that the basal spacing of a hydration state in Montmorillonite is hydration sensitive, and any such prediction should be corrected for humidity. In addition to this it is likely that there are discrepancies between predicted and measured basal spacing as the results from the model
30
scales linearly with the fractions. This is not necessarily the case for experimental data as e.g. the crystallinity might increase for a higher hydration state resulting in a higher signal relative to the same fraction of another hydration state (Figure 5).
Figure 5. Average basal spacing of homoionic MMT. Solid lines correspond to the calculated values.
It should be noted that all examples given have been for adsorption data. The model also function to desorption which results in the inclusion of the Kr term in the DoDo equation (Eq 8) whereas the different energies of desorption are accounted for by a shift to higher energies in the DA equation (Eq 10).
The application of the model to Birnessite in Paper II validates that the model is not material specific but appears to also model the intercalation of other layered materials which adheres to similar adsorption mechanics.
It should also be noted that the DA equation (Eq 10) is not exclusive for water, the same can however not be stated for the DoDo equation (Eq 8). It was specifically developed for the adsorption of water with all relevant functions thereof, thus it cannot be guaranteed to function for other adsorbates. Appropriate modification of the α and β term may permit modelling but that will likely depend on the adsorbate. This can however be resolved by the modular nature of the model. If necessary, the DoDo component can be replaced by an adsorption model that can model the external adsorption for the relevant vapour pressures.
Lastly, there is the issue of the adsorption potential for the DA equation (Eq 11). As was stated earlier the adsorption deviates from Henry’s Law behaviour as the vapour pressure approaches zero. This being the case, the majority of adsorption for the samples in this thesis occurs at higher pressures. The interaction energy E in these systems designates the interaction of water with the internal surfaces and cations in-between the layers of the material, this filling or intercalation however necessitates the swelling of the material. The counteracting force of the layer-to-
layer attraction alters the characteristic energy and delays the major onset of adsorption to higher pressures. Assuming similar mechanics for layered materials, where the adsorption is delayed by a layer collapsing potential the problem is largely counteracted. It should however be taken into consideration if attempting to model very low pressures.
Intercalation of water as predicted from MCR decomposition of spectral series The adsorption of water for Montmorillonite and Birnessite was recorded by FTIR measurements in addition to gravimetric data. For both materials the adsorption showed clear trends of increasing signal in the stretching and bending region of water, with the opposite observed for dehydration (not shown) as is to be expected. (Figure 6-Figure 7).
Figure 6. FTIR spectra of water adsorbing on Birnessite divided into the (a) O-H stretching, (b) water bending and (c) Mn-O-H bending.
Figure 7. FTIR spectra of water adsorbing on MMT divided into the (a) OH stretching, (b) water bending and (c) Si-O stretching.
32
As the two materials show a similar adsorption process there are similarities in the O-H bending and stretching region. These shift in spectra due to the increasing hydration and resulting intercalation indicates that the hydration process can be monitored with FTIR. In the case of Birnessite a MCR analysis of the spectra was performed (Figure 8). By comparing the shape of component C0 in Figure 8 to that of the 0W component in Figure 8. Concentration profiles of Birnessite obtained from chemometric analysis of FTIR spectra. Divided into adsorption (squares) and desorption (circles). a similar shape can be seen albeit the decay of the C0 component is more rapid and is calculated in an experiment with lower maximum humidity. The discrepancy between the figures can be attributed to Figure 8. Concentration profiles of Birnessite obtained from chemometric analysis of FTIR spectra. Divided into adsorption (squares) and desorption (circles). illustrating the hydration state distribution whereas Figure 8 illustrates the concentration where component C1 and C2 can be likened to 1W and the condensation water. However, the inaccuracy of the comparison is made clear when observing the higher humidity distribution. The near complete loss of the C0 and C1 component means that no water is in the interlayer, yet there is no dry material either. Instead a more accurate description is that the C2 component is Birnessite with a 1W hydration layer with external water adsorbed. Due to how the hydration layer distribution is calculated there is no known way of including the water contribution of the non-intercalated water, and as a consequence there is no known method to convert the concentration profile into a hydration layer distribution.
The strength of the concentration profile is that the spectra correlated to the components are a representation of the material, thus any information found in the spectra describe how the sample transitions between the states described by the spectra. The concentration profile thus describe how the behaviour of the sample changes, not the formation and decay of hydration states even if similarities occur. It can be seen in the stretching region of Figure 6-6 how the relative portion of water corresponding to water-water interaction increases indicating the increasing presence of liquid like water. In cases like that of δ-Birnessite the water adsorbs in a liquid like manned even at the lowest humidity level, the method can thus not yield detailed information of the interlayer. Instead it show the importance of the particle size as the significantly smaller particles adsorbs external water quickly as is also supported by the adsorption model (Figure 9).
If a method of conversion between the hydration distribution and the concentration profile was to be found it can be used to perform cross-comparisons between the methods to compliment their weaknesses. The accuracy of especially high hydration layers for the adsorption model could be increased and accurate spectra of pure hydration layers and non-intercalated
water could be produced by constraining the concentration profiles to converted hydration state distributions with included non-intercalated water. This however remains to be proven.
Figure 8. Concentration profiles of Birnessite obtained from chemometric analysis of FTIR spectra. Divided into adsorption (squares) and desorption (circles).
Figure 9. Modelled uptake and Hydration layer distribution of Birnessite.
34
Intercalation in multi-component systems In order to determine which force fields to use when simulating clay minerals or similar materials, such as zeolites, layered double hydroxides etc, with organic compounds, eight alcohols (Methanol, Ethanol, Propanol, Butanol, Hexanol, Octanol, Phenol and Ethylene Glycol) was intercalated into MMT. A method was created to simulate the equivalent systems and by comparing the resulting XRD profiles, experimental and theoretical.
From the simulated data the two closest stable states surrounding the experimental basal spacing and the simulation with the closest d001 was selected to be fitted to the experimental data (Figure 10). The 𝐺( factors and d001 predicted by the simulations were kept unmodified to determine the capability of each force field combination to predict the experimental data.
Figure 10. Theoretical 1D XRD profile (Red) of phenol from ClayFFMod with OPLS fitted to experimental data (Black). The lower curve is the residual from experimental – theoretical intensities (bottom line).
The results indicate that the best fit varies depending on the alcohol but from observing the summary of the goodness-of-fit (Rwp) in Table 1 conclusions can be made. It is possible to compare the accumulated sum of the Rwp for single force fields or combinations to determine which in general is closest. However there are issues with the Butanol, Hexanol and Octanol. Octanol in particular has a very high Rwp and by analysing FTIR and XRD profiles of the three (not shown) the
predicted XRD profiles are grossly inaccurate either here or when later attempting to optimize the 𝐺( factors. The FTIR confirms presence of water but the systems could not be accurately simulated. It is plausible that the low miscibility of the alcohols caused interstratification of layers not considered in the simulation such as pure water/alcohol layers.76 Due to the inability to accurately model Butanol, Hexanol and Octanol they are considered outliers.
When excluding the outliers it is noted that ClayFFMod gave the results, especially in combination with OPLS. GAFF produced the lowest overall Rwp of the alcohol force fields and was best when combined with INTERFACE and ClayFF, the GAFF-INTERFACE combination being a close second to ClayFFMod-OPLS.
Table 1. Summary of Rwp (in %) for all force field and alcohol combinations.
ClayFF ClayFFMod INTERFACE Alcohol CGenFF GAFF OPLS CGenFF GAFF OPLS CGenFF GAFF OPLS
Me 21.6 25.2 25.3 19.9 20.2 17.3 22.8 24.4 21.3 Et 12.8 9.0 9.9 13.5 8.5 9.7 8.5 9.0 11.0 Pr1 12.3 14.6 17.0 11.2 13.2 14.9 11.4 11.3 17.6
Bu 18.2 18.1 20.6 16.3 16.3 18.7 22.7 25.4 18.1 He 20.6 24.0 20.3 22.3 22.3 22.4 15.7 21.2 20.2 Oc 52.9 54.0 51.7 66.4 51.0 52.2 61.6 56.7 40.3 Gly 13.7 9.5 16.2 15.5 14.6 10.9 11.2 9.8 15.1
Ph 7.1 7.6 7.4 6.9 7.3 7.5 9.0 6.9 7.7
As was mentioned earlier there are significant differences between the partial charges and sizes for the force fields. This results in different predicted interlayers which explains differences in Rwp and d001 values.
When optimizing the 𝐺( factors to improve the fit it was found that the modification resulted in an overall improvement of the non-excluded alcohols (Table 2). The modification also led to a change in lowest Rwp combination to ClayFF-Gaff, INTERFACE-CGenFF and INTERFACE-GAFF in that order. However the cumulative Rwp of ClayFFMod-OPLS is not much higher.
36
Table 2 Summary of Rwp (in %) after G2 factor modification.
ClayFF ClayFFMod Interface Alcohol CGenFF GAFF OPLS CGenFF GAFF OPLS CGenFF GAFF OPLS
Me 16.1 16.9 17.4 15.7 15.5 16.9 16.3 16.9 15.8 Et 12.9 7.4 9.3 15.7 7.7 9.5 7.1 7.6 10.5
Pr1 7.0 8.6 11.8 8.5 10.0 8.9 7.0 8.4 17.0 Bu 20.3 20.0 19.3 22.2 20.7 19.6 18.0 33.5 18.7 He 17.4 13.1 18.4 23.4 12.4 14.9 20.8 18.8 20.3 Oc 29.0 31.0 46.5 31.2 28.4 29.9 29.8 31.7 29.6 Gly 10.9 7.0 13.2 12.7 12.1 10.5 9.0 7.8 12.3 Ph 5.7 5.7 6.1 6.2 5.9 5.9 6.6 5.8 5.7
A sensitivity analysis based upon random changes with respect to the atomic positions and loading of the interlayer materials used to compute the 𝐺( factors was made. By making 500 perturbations it was possible to on occasion find trends in related to certain atom types. In Figure 11 it can be seen how changing the amount and position of alcohol oxygen in the ClayFF-GAFF ethylene glycol simulation affected the goodness-of-fit. Trends are not observable in all atom types or simulations but Figure 11 is representative to the general trends observed, change in goodness of fit is primarily associated with changing relative loading whereas the shift in the z-direction induces no clear trend of improvement.
Figure 11. Change in position and relative loading (xP) of alcohol oxygen Oc in ethylene glycol simulated with ClayFF-GAFF.
Intercalation of CTAB in Montmorillonite The intercalation of CTAB differs from the intercalation of water and alcohol. This is due to the dissociation of CTAB into the CTA+ cation and Br- anion that initially performs cationic exchange with Montmorillonite. This process is similar to the intercalation of water and alcohols in that it absorbs in a stepwise manner with an initial formation of a monolayer followed by the formation of a bilayer with increasing concentrations in solution (Figure 12). When increasing the concentration of CTAB further, the intercalation method changes as the non-dissociated CTAB intercalates via hydrophobic interactions, with the altered polarity of the interlayer space resulting from the long hydrophobic tails of the CTA+ cations. This is made evident by the expanding interlayer decreasing following washing with ethanol that extracts the non-cationic exchanged CTAB molecules.
Figure 12. XRD diffractogram of CMMT with increasing concentration of CTAB (a) and the corresponding diffractogram after ethanol washing (b).
Prior to the formation of a pseudo-trilayer the Montmorillonite interlayer expanded to a basal spacing corresponding to an intermediate state of a bi- and trilayer formation. From a shift in the FTIR spectra of the alkyl chains (Figure 13) the increased basal spacing is attributed to the transition of a lateral (gauche) orientation of the alkyl chains to a trans orientation. That is, the alkyl chains shift from being positioned parallel to the clay sheet to a paraffin type orientation where the alkyl chains of the two monolayers interlock.
38
Figure 13. FTIR spectra of CMMT with increasing concentration of CTAB. (a) the asymmetric and symmetric CH2 stretching bands and (b) the respective bending. The dashed line is pure CTAB.
After treatment the CMMT illustrated a significant difference in the water uptake capacity (Paper IV, Figure 2) where the adsorption decreased. This is to be expected from the hydrophobic nature of CTAB but the adsorption found a minimum at 1.1 CEC of CTAB. This is attributed to the formations of micelles at higher loadings where the polar heads of the CTAB may interact with water. Further experiments were conducted with 3 additional solvents, ethanol, DMSO and Hexane. Attempting to intercalate the solvents lead to ethanol solubilizing and removing the interlayer content similar to the alcohol washing in Figure 12, whereas Hexane indicated no adsorption as the basal spacing remained unchanged. Exposure to DMSO resulted in an increased basal spacing, however this expansion when compared to earlier works indicate that a full layer was not adsorbed. It is instead interpreted that the interaction and intercalation of DMSO results in a reorientation of the CTA+ in the interlayer. The ability of DMSO to interact with the interlayer without removing intercalated material indicates that moderately polar compounds are preferable to use as solvents when attempting to intercalate other substances into the interlayer.
The ability of the organo-modified clay mineral to intercalate alizarin with DMSO was investigated to determine the effect of interlayer content on the ability to further intercalate compounds of interest. It was found that the intercalation into a bilayer system adsorbed greater amounts of alizarin relative to that of a monolayer system. The resulting swelling of the respective clay mineral samples
indicates a lateral monolayer of alizarin forming in the monolayer system whereas the bilayer system adsorbed significantly more. The expansion from a 1.8 nm basal spacing to 3.3 nm is attributed to the CTA+ alkyl chains rearranging to the paraffin type orientation to accommodate for the alizarin intercalating through interacting with the alkyl chains. The apparent lack of intercalation for the pseudo-trilayer systems indicates that the hydrophobically intercalated CTAB molecules inhibit the intercalation of alizarin even with the use of DMSO solvent.
40
Conclusion and Future research In this thesis the interlayer space of layered materials and the adsorption of water, alcohols and large hydrophobic molecules is studied. The main focus is on the intercalation process, how to model it, how to predict it and the consequences of intercalation.
In Paper I a model is developed to predict the adsorption process of water in the clay mineral Montmorillonite. Samples were hydrated and dehydrated using DVS where the FTIR spectra, BET, XRD diffractograms and gravimetric data was collected. The model developed is optimized to fit the gravimetric data and the results of the model are used to calculate a predicted basal spacing. Comparison of the model and experimental data indicates that the model is valid for describing the adsorption and desorption of water, with a specific focus on the intercalation process. This is continued in Paper II where Birnessite is hydrated and dehydrated in a similar matter to Paper I and has similar measurements. The model developed in Paper I is used to model the adsorption on Birnessite, thus indicating that the model is applicable to other materials. No part of the model is specific to the adsorbents, although the Do & Do component was developed for the adsorption of water. Further research is needed to determine if it is necessary to replace this component with a model that predicts the surface adsorption and condensation of other adsorbates.
MCR was used to analyse the FTIR spectra collected for Paper II. The information that can was obtained is comparable to that of the model but rather than directly measuring the formation of the hydration layers it detects the changing nature of the sample and the adsorbate. This changing nature can be related to the hydration layers but is not identical. It is possible that a means to convert a concentration profile into a hydration layer distribution or the reverse can be found, but no such conversion method is known.
In Paper III the results of MD simulations of clay-water-alcohol systems were compared to corresponding experimental data. The force fields INTERFACE, ClayFF and ClayFFMod were used to describe the clay mineral whereas CGenFF, GAFF and OPLS/aa were used to describe the intercalated alcohols. By combining the force fields eight different primary alcohols in the clay-water-alcohol systems were simulated, methanol, ethanol, propanol, butanol, hexanol, octanol phenol and ethylene glycol. Stable states were found by calculating immersion energies and selecting states close to experimental values.
Theoretical XRD profiles where generated and fitted to experimental data with 1D XRD-modelling. The results indicated that the combination ClayFFMod-
OPLS gave the most accurate prediction. Upon modifying the 𝐺( factors to improve wellness-of-fit ClayFF-GAFF gave the best result with ClayFFMod-OPLS giving slightly worse results with the fifth lowest residuals. By performing sensitivity analysis of the systems, it is found that in general shift of atom types have no clear trend of improvement, this is however found by altering the relative loadings.
The method used was unable to simulate alcohols with low miscibility, it is plausible that there is interstratification of layers not considered in the method. Further research is required to determine the cause.
The nature of the interlayer space of MMT is highly dependent on the concentration of CTAB upon the creation of CMMT. The concentration not only affects the basal spacing of the mineral but also intercalation pathways and the arrangement of the intercalated material. As a consequence of material arrangement the intercalated content can increase greatly. It is determined that higher concentrations of CTAB lead to a “self-sealing” of the clay mineral preventing further intercalation of CTAB and other molecules. It stands to reason that the arrangement, intercalation mechanism and material arrangement all has an effect on other potential molecules to be adsorbed, such as medical drug compounds. This is compounded with the selection of solvent where it appears that solvents with moderate polarity such as DMSO is prone to intercalation. The work proposed would form a basis for CMMT creation to determine the effect on adsorption of such agents and to what extent the different factors affected by CTAB concentration would affect different classes of such compounds.
42
Acknowledgement First of all I would like to express my gratitude to all of those whom have helped, supported and worked with me.
I have met many new friends and I’ve had the honour of sharing educational, enlightening and humorous moments with people from all around the world. I’ve learnt more about the world around me and myself than ever before in this period of my life. I owe this to a great many people but more than anyone I owe to my group members, past and current. So I would like to especially express my thanks to my supervisors Michael Holmboe and Jean-François Boily and of all of those who have played an important role in my thesis: Junhyung, Mark, Magda, Hussein, Andy, Nahom, Andras, Tan, Merve, Andrey and Knut.
I would also like to express my thanks to the Umeå faculty of science and technology for them funding my PhD studies.
Lastly I would like to thank all whom work in the department of chemistry. So many of you have taken the role of a teacher for me even long before I started my PhD.
Thank you!
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