Lasse Lavikainen

DissertationsDepartment of ChemistryUniversity of Eastern Finland

No. 137 (2016)

107/2011 KASANEN Jussi: Photocatalytic TiO2-based multilayer coating on polymer substrate for use in self-cleaning applications

108/2011 KALLIO Juha: Structural studies of Ascomycete laccases – Insights into the reaction pathways109/2011 KINNUNEN Niko: Methane combustion activity of Al2O3-supported Pd, Pt, and Pd-Pt catalysts:

Experimental and theoretical studies110/2011 TORVINEN Mika: Mass spectrometric studies of host-guest complexes of glucosylcalixarenes111/2012 KONTKANEN Maija-Liisa: Catalyst carrier studies for 1-hexene hydroformulation: cross-linked

poly(4-vinylpyridine), nano zinc oxide and one-dimensional ruthenium polymer112/2012 KORHONENTuulia: Thewettabilitypropertiesofnano-andmicromodifiedpaintsurfaces113/2012 JOKI-KORPELAFatima:Functionalpolyurethane-basedfilmsandcoatings114/2012 LAURILA Elina: Non-covalent interactions in Rh, Ru, Os, and Ag complexes115/2012 MAKSIMAINEN Mirko: Structural studies of Trichoderma reesei, Aspergillus oryzae and

Bacillus circulans sp. alkalophilus beta-galactosidases – Novel insights into a structure-function relationship

116/2012 PÖLLÄNEN Maija: Morphological, thermal, mechanical, and tribological studies of polyethylene compositesreinforcedwithmicro–andnanofillers

117/2013 LAINEAnniina:Elementaryreactionsinmetallocene/methylaluminoxanecatalyzedpolyolefinsynthesis

118/2013 TIMONENJuri:Synthesis,characterizationandanti-inflammatoryeffects ofsubstitutedcoumarinderivatives

119/2013 TAKKUNEN Laura: Three-dimensional roughness analysis for multiscale textured surfaces: Quantitative characterization and simulation of micro- and nanoscale structures

120/2014 STENBERG Henna: Studies of self-organizing layered coatings121/2014 KEKÄLÄINEN Timo: Characterization of petroleum and bio-oil samples by ultrahigh-resolution

Fourier transform ion cyclotron resonance mass spectrometry122/2014 BAZHENOV Andrey: Towards deeper atomic-level understanding of the structure of magnesium

dichloride and its performance as a support in the Ziegler-Natta catalytic system123/2014 PIRINEN Sami: Studies on MgCl2/ether supports in Ziegler–Natta catalysts for ethylene

polymerization124/2014 KORPELA Tarmo: Friction and wear of micro-structured polymer surfaces125/2014 HUOVINEN Eero: Fabrication of hierarchically structured polymer surfaces126/2014 EROLA Markus: Synthesis of colloidal gold and polymer particles and use of the particles in

preparation of hierarchical structures with self-assembly127/2015 KOSKINEN Laura: Structural and computational studies on the coordinative nature of halogen

bonding128/2015 TUIKKA Matti: Crystal engineering studies of barium bisphosphonates, iodine bridged ruthenium

complexes, and copper chlorides129/2015JIANGYu: Modificationandapplicationsofmicro-structuredpolymersurfaces130/2015 TABERMAN Helena: Structure and function of carbohydrate-modifying enzymes 131/2015KUKLINMikhailS.:Towards optimizationofmetaloceneolefinpolymerizationcatalystsvia

structuralmodifications:acomputationalapproach132/2015SALSTELAJanne:Influenceofsurfacestructuringonphysicalandmechanicalpropertiesof

polymer-cellulose fibercompositesandmetal-polymercompositejoints133/2015 CHAUDRI Adil Maqsood: Tribological behavior of the polymers used in drug delivery devices134/2015 HILLI Yulia: The structure-activity relationship of Pd-Ni three-way catalysts for H2S suppression135/2016 SUN Linlin: The effects of structural and environmental factors on the swelling behavior of

Montmorillonite-Beidellite smectics: a molecular dynamics approach136/2016 OFORI Albert: Inter- and intramolecular interactions in the stabilization and coordination of

palladium and silver complexes: DFT and QTAIM studies

The structure and surfaces of2:1 phyllosilicate clay minerals

Lasse Lavikainen: The structure and surfaces of 2:1 phyllosilicate clay minerals

137

The structure and surfaces of2:1 phyllosilicate clay minerals

Lasse Lavikainen

Department of ChemistryUniversity of Eastern Finland

Finland

Joensuu 2016

Lasse Lavikainen Department of Chemistry, University of Eastern Finland P. O. Box 111, FI 80101 Joensuu, Finland

Supervisors Prof. Tapani Pakkanen, University of Eastern Finland, Joensuu, Finland

Referees Prof. Hannu Häkkinen, University of Jyväskylä, Jyväskylä, Finland Prof. Kari Laasonen, Aalto University, Espoo, Finland

Opponent Prof. Risto Laitinen, University of Oulu, Oulu, Finland

To be presented with the permission of the Faculty of Science and Forestry of the University of Eastern Finland for public criticism in Auditorium N100, Yliopistokatu 7, Joensuu, on 13th of May, 2016, at 12 o’clock noon.

Copyright © 2016 Lasse Lavikainen ISBN: 978-952-61-2122-2 (PDF) ISBN: 978-952-61-2091-1 (print) ISSN: 2242-1033

Grano Oy Jyväskylä Jyväskylä 2015

4

Lasse LavikainenDepartment of Chemistry, University of Eastern FinlandP. O. Box 111, FI 80101 Joensuu, Finland

SupervisorsProf. Tapani Pakkanen, University of Eastern Finland, Joensuu, Finland

RefereesProf. Hannu Häkkinen, University of Jyväskylä, Jyväskylä, FinlandProf. Kari Laasonen, Aalto University, Espoo, Finland

OpponentProf. Risto Laitinen, University of Oulu, Oulu, Finland

To be presented with the permission of the Faculty of Science and Forestry of theUniversity of Eastern Finland for public criticism in Auditorium N100, Yliopistokatu 7,Joensuu, on 13th of May, 2016, at 12 o’clock noon.

Copyright © 2016 Lasse Lavikainen

ISBN: 978-952-61-2091-1ISSN: 2242-1033

Grano Oy JyväskyläJyväskylä 2015

3

AbstractPhyllosilicate clay minerals are the main constituent of clays. The great structuralvariability of phyllosilicates has enabled their use in various industrial and domesticapplications but, on the other hand, has also made the characterization of their structuresdifficult. This difficulty not only arises from their heterogenic composition but also fromuncertainties related to anisotropy and the internal heterogeneity of their structures. Thedevelopment of specifically tailored phyllosilicate applications is hindered by theseuncertainties, thus research is required to reveal the structural features of phyllosilicates.This is the purpose of this thesis, the emphasis being on the clay mineralmontmorillonite.

Montmorillonite is a planar 2:1 phyllosilicate that belongs to the group of smectites. It isthe main component of bentonite clay, which is used as a filler, binder andadsorbent/absorbent in various applications, including the planned use as a buffer materialfor long-term nuclear waste disposal. The fundamental key features that impart tomontmorillonite its characteristic physicochemical behaviour are its structure and surfaces.These were studied computationally according to density functional theory.

Montmorillonite particles are formed by stacking mineral layers. These layers arenegatively charged due to the presence of isomorphous substitutions with a lower nuclearcharge. Typically, Mg(II) for Al(III) substitutions are present in montmorillonite, but alsoAl(III) for Si(IV) may appear to a lesser extent. Due to being the origin of layer charge,the interaction, arrangement and electrostatic nature of the substitutions were studied. Thefindings show that the substitutions repulse each other and tend to disperse in the layerstructure where they effectively resemble negative point-like charges.

The negative layer charge of montmorillonite is compensated for by inclusion of cationsbetween the layers. These positively charged atoms are rather loosely bound,exchangeable and maintain the cohesion of montmorillonite particles by drawing thelayers together with electrostatic forces. For these relevant reasons, cation–surfaceinteraction in the interlayer space of montmorillonite was inspected by using Na(I) andCa(II) as representative species. First, the obtained results demonstrate that cation–surface interaction energies depend linearly on cation–substitution inverse distances inthe periodic lattice. Secondly, the results show that substitution density and substitutiontype have little effect on cation–surface interaction strength in montmorillonite, althoughcertain trends were found.

The surface area of a montmorillonite particle is dominated by interlayer surfaces, butthe presence of chemically active surfaces at layer edges should not be ignored. Thestructure of edge surfaces is not well understood, hence the stability of a wide range ofdifferent edge surfaces was surveyed. Various edge surfaces were found to be similar instability, but it is further suggested on the basis of free energy estimation that the edgesobtained by cleaving the fewest bonds are the most stable. It is predicted that the (110)and (010) edge surfaces dominate and yield a hexagonally shaped particle.

4

List of original publicationsThis thesis is a summary of publications I–III.

I Lavikainen, L. P.; Tanskanen, J. T.; Schatz, T.; Kasa, S.; Pakkanen, T. A.Montmorillonite interlayer surface chemistry: effect of magnesium ion substitutionon cation adsorption. Theor. Chem. Acc. 2015, 134:51.

II Lavikainen, L. P.; Hirvi, J. T.; Kasa, S.; Schatz, T.; Pakkanen, T. A. Stability ofdioctahedral 2:1 phyllosilicate structures based on pyrophyllite models. Theor.Chem. Acc. 2015, 134:112.

III Lavikainen, L. P.; Hirvi, J. T.; Kasa, S.; Pakkanen, T. A. Interaction of octahedralMg(II) and tetrahedral Al(III) substitutions in aluminum-rich dioctahedralsmectites. Theor. Chem. Acc. 2016, 135:85.

Author’s contributionThe key ideas in publications I–III are based on conversations between the author andthe supervisors and the co-authors. The author has the main responsibility in the writingof the manuscripts and has carried out all computational work.

7

ContentsAbstract .............................................................................................................................. 4List of original publications .............................................................................................. 6Author’s contribution ........................................................................................................ 6Contents ............................................................................................................................. 7Abbreviations .................................................................................................................... 8

1. Introduction ................................................................................................................... 91.1 Background ............................................................................................................. 91.2 The scope of interests ............................................................................................ 121.3 The aims and approach ......................................................................................... 14

2. Models and methods.................................................................................................... 152.1 Model design ......................................................................................................... 152.2 Computational methods ........................................................................................ 16

3. Structure – Mg(II)- and Al(III)-substitutions ............................................................. 183.1 Systematic model design ....................................................................................... 183.2 The interaction of the substitutions....................................................................... 20

4. Interlayer surfaces – electrostatistics and cations ........................................................... 234.1 Electrostatic potential of interlayer surfaces ........................................................ 234.2 Electrostatic nature of Mg(II)- and Al(III)-substitutions ..................................... 244.3 Effect of substitution composition on cation–surface interaction .......................... 274.4 Effect of Mg–Mg distance on system energetics ................................................. 33

5. Edge surfaces – structure and stability ....................................................................... 355.1 Cleavage method ................................................................................................... 355.2 Cleavage energies .................................................................................................. 375.3 Particle shape ......................................................................................................... 38

6. Conclusions ................................................................................................................. 39

Acknowledgements ......................................................................................................... 41References ....................................................................................................................... 42

5

Contents

Abstract .............................................................................................................................. 3 List of original publications ............................................................................................... 4 Author’s contribution ......................................................................................................... 4 Contents ............................................................................................................................. 5 Abbreviations ..................................................................................................................... 6

1. Introduction .................................................................................................................... 7 1.1 Background .............................................................................................................. 7 1.2 The scope of interests .......................................................................................... 10 1.3 The aims and approach .......................................................................................... 12

2. Models and methods .................................................................................................... 13 2.1 Model design .......................................................................................................... 13 2.2 Computational methods ......................................................................................... 14

3. Structure – Mg(II)- and Al(III)-substitutions .............................................................. 16 3.1 Systematic model design ....................................................................................... 16 3.2 The interaction of the substitutions. .................................................................... 18

4. Interlayer surfaces – electrostatistics and cations ................................................................ 21 4.1 Electrostatic potential of interlayer surfaces ......................................................... 21 4.2 Electrostatic nature of Mg(II)- and Al(III)-substitutions ..................................... 22 4.3 Effect of substitution composition on cation–surface interaction ............................. 25 4.4 Effect of Mg–Mg distance on system energetics .................................................. 31

5. Edge surfaces – structure and stability ...................................................................... 33 5.1 Cleavage method ................................................................................................... 33 5.2 Cleavage energies .................................................................................................. 35 5.3 Particle shape ...................................................................................................... 36

6. Conclusions ............................................................................................................... 37

Acknowledgements .......................................................................................................... 39 References ........................................................................................................................ 40

6

AbbreviationsT Tetrahedral sheet

O Octahedral sheet

Mg-substitution Mg(II) for Al(III) ion substitution in octahedral sheet

Al-substitution Al(III) for Si(IV) ion substitution in tetrahedral sheet

IR Infrared spectroscopy

NMR Nuclear magnetic resonance spectroscopy

EXAFS Extended X-ray absorption fine structure

DFT Density functional theory

PBE Perdew–Burke–Ernzerhof exchange–correlation functional

PAW Projector augmented wave

ESP Electrostatic potential

MMT Montmorillonite

9

1. Introduction1.1 Background

Clay is a naturally occurring material, which becomes plastic when wet and hardenswhen dried or fired. It is mainly composed of fine-grained clay minerals that impart toclay its characteristic properties but may also contain other associated phases, such asquartz and organic matter.1 The commonly known clay minerals are planarphyllosilicates, which are utilized in millions of tons per year for industrial applicationsand domestic products worldwide. These include ceramics, cosmetics, pharmaceutics,foods, beverages, packaging, composites, catalysis, drilling fluids and buffer materials.The wide applicability of phyllosilicates can be attributed to their general inertness,stability and flow properties, but also to their specific reactivity, catalytic activity andadsorption capacity.2

The particles of planar phyllosilicates are formed by stacking mineral layers, which arefurther composed of connected silicate and aluminium(hydr)oxide sheets runningparallel to each other. These sheets are often referred to as tetrahedral (T) and octahedral(O) on the basis of their atomistic building blocks, which consist of silicon oxidetetrahedrons and aluminium(hydr)oxide octahedrons. The T:O ratio of layer structure isused to classify phyllosilicates into 1:1 (TO) and 2:1 (TOT) layer types. This thesis isconcerned with 2:1 phyllosilicates (Figure 1), to which the majority of clay mineralsbelong.

Figure 1. The structure of non-substituted 2:1 phyllosilicate: pyrophyllite.

8

AbbreviationsT Tetrahedral sheet

O Octahedral sheet

Mg-substitution Mg(II) for Al(III) ion substitution in octahedral sheet

Al-substitution Al(III) for Si(IV) ion substitution in tetrahedral sheet

IR Infrared spectroscopy

NMR Nuclear magnetic resonance spectroscopy

EXAFS Extended X-ray absorption fine structure

DFT Density functional theory

PBE Perdew–Burke–Ernzerhof exchange–correlation functional

PAW Projector augmented wave

ESP Electrostatic potential

MMT Montmorillonite

7

1. Introduction1.1 Background

Clay is a naturally occurring material, which becomes plastic when wet and hardenswhen dried or fired. It is mainly composed of fine-grained clay minerals that impart toclay its characteristic properties but may also contain other associated phases, such asquartz and organic matter.1 The commonly known clay minerals are planarphyllosilicates, which are utilized in millions of tons per year for industrial applicationsand domestic products worldwide. These include ceramics, cosmetics, pharmaceutics,foods, beverages, packaging, composites, catalysis, drilling fluids and buffer materials.The wide applicability of phyllosilicates can be attributed to their general inertness,stability and flow properties, but also to their specific reactivity, catalytic activity andadsorption capacity.2

The particles of planar phyllosilicates are formed by stacking mineral layers, which arefurther composed of connected silicate and aluminium(hydr)oxide sheets runningparallel to each other. These sheets are often referred to as tetrahedral (T) and octahedral(O) on the basis of their atomistic building blocks, which consist of silicon oxidetetrahedrons and aluminium(hydr)oxide octahedrons. The T:O ratio of layer structure isused to classify phyllosilicates into 1:1 (TO) and 2:1 (TOT) layer types. This thesis isconcerned with 2:1 phyllosilicates (Figure 1), to which the majority of clay mineralsbelong.

Figure 1. The structure of non-substituted 2:1 phyllosilicate: pyrophyllite.

8

The structural composition of 2:1 phyllosilicates varies greatly in nature. The mostimportant variations are isomorphic substitutions, which are elements that appear in theplace of aluminium or silicon without causing significant changes to the layer structure.Substitutions with a lower positive nuclear charge in relation to unsubstituted atomsgenerate a negative net layer charge. This charge is compensated for by the inclusion ofcations, i.e. positively charged atoms, between the layers, in the interlayer space.Depending on the layer charge and the type of cations, the interlayer space may alsocontain a variable amount of water.3

The great variety of 2:1 phyllosilicates is classified into separate groups on the basis ofthe layer charge and interlayer material. The layer charge generally shows selectivitytowards a certain type of interlayer material, which is why the layer charge and theinterlayer material serve as a convenient base for the classification. The further divisionof phyllosilicates into sub-groups is based on the character of their octahedral sheet: intrioctahedral phyllosilicates, all atomic sites in the octahedral sheet are occupied,whereas in dioctahedral phyllosilicates, such as in Figure 1, every third octahedral siteremains vacant. The ideal species in each sub-group are finally identified on the basis oftheir chemical composition (Table 1).4

Table 1. The classification of planar 2:1 phyllosilicates.4

Layercharge*

Interlayer material Group Octahedralcharacter

Example ofspecies

0 None Talc-pyrophyllite Trioctahedral TalcDioctahedral Pyrophyllite

0.4–1.2 Hydrated exchangeablecations

Smectite Trioctahedral SaponiteDioctahedral Montmorillonite

1.2–1.8 Hydrated exchangeablecations

Vermiculite Trioctahedral VermiculiteDioctahedral Vermiculite

1.7–2.0 Non-hydrated monovalent 50%) cations

True (flexible) mica Trioctahedral PhologopiteDioctahedral Muscovite

1.2–1.7 Non-hydrated mono- ordivalent cations

Interlayer-deficientmica

Trioctahedral IlliteDioctahedral Wonesite

2.6–4.0 Non-hydrated divalent 50%) cations

Brittle mica Trioctahedral ClintoniteDioctahedral Margarite

Variable Hydroxide sheet Chlorite Trioctahedral ClinochloreDioctahedral DonbassiteDi,trioctahedral Cookeite

*Approximate negative net charge per anionic O20(OH)4 formula unit

11

Phyllosilicates, for which the layer charge ranges between 0.4–1.2 per anionic O20(OH)4

formula unit, belong to the group of smectites. The smectites can be considered as lowlycharged 2:1 phyllosilicates with a high swelling capacity in the presence of water. Theextraordinary swelling behaviour of these minerals is based on their layer charge, whichis just high enough to attract hydratable cations, such as Na(I) and Ca(II), into theinterlayer space and to render the interlayer surfaces hydrophilic. These structuralfeatures of smectites enable water to overcome the electrostatic and van der Waalsinteractions keeping the layers together and to penetrate into the interlayer space. Theinflow of water expands the distance between the layers, and the clay is said to swell.Regardless of the structural similarity with smectites, phyllosilicates with higher layercharge are known to exhibit only limited swelling or do not swell at all. This is theconsequence of stronger electrostatic interactions between the positively chargedinterlayer cations and the negatively charged layers, which pull the layers into morefirmly stacked particles.3,5

Perhaps the most widely known smectite-rich and highly swelling clay is bentonite. It isused as a filler, binder and adsorbent/absorbent in various applications, includingplanned use as a buffer material for long-term nuclear waste disposal.2,6-8 Despite itsindustrial importance, bentonite might be best known from cat-litter or cosmetics. Themain component in bentonite is the clay mineral montmorillonite. It is a dioctahedralspecies of smectites characterized by the appearance of Mg(II) substitutions in the placeof Al(III) in the octahedral sheet. In other words, there are octahedral Mg(II) for Al(III)substitutions. The ideal species, however, is rare in nature, and therefore it is notuncommon that substitutions characteristic of other smectites are also present inmontmorillonite. These often include tetrahedral Al(III) for Si(IV) and octahedralFe(II/III) for Al(III), which are characteristic of beidellite and nontronite, respectively(Figure 2).9,10

Figure 2. A compositional triangle of montmorillonite, beidellite and nontronite. The designemphasizes the characteristic substitutions of these ideal end-members.

10

The structural composition of 2:1 phyllosilicates varies greatly in nature. The mostimportant variations are isomorphic substitutions, which are elements that appear in theplace of aluminium or silicon without causing significant changes to the layer structure.Substitutions with a lower positive nuclear charge in relation to unsubstituted atomsgenerate a negative net layer charge. This charge is compensated for by the inclusion ofcations, i.e. positively charged atoms, between the layers, in the interlayer space.Depending on the layer charge and the type of cations, the interlayer space may alsocontain a variable amount of water.3

The great variety of 2:1 phyllosilicates is classified into separate groups on the basis ofthe layer charge and interlayer material. The layer charge generally shows selectivitytowards a certain type of interlayer material, which is why the layer charge and theinterlayer material serve as a convenient base for the classification. The further divisionof phyllosilicates into sub-groups is based on the character of their octahedral sheet: intrioctahedral phyllosilicates, all atomic sites in the octahedral sheet are occupied,whereas in dioctahedral phyllosilicates, such as in Figure 1, every third octahedral siteremains vacant. The ideal species in each sub-group are finally identified on the basis oftheir chemical composition (Table 1).4

Table 1. The classification of planar 2:1 phyllosilicates.4

Layercharge*

Interlayer material Group Octahedralcharacter

Example ofspecies

0 None Talc-pyrophyllite Trioctahedral TalcDioctahedral Pyrophyllite

0.4–1.2 Hydrated exchangeablecations

Smectite Trioctahedral SaponiteDioctahedral Montmorillonite

1.2–1.8 Hydrated exchangeablecations

Vermiculite Trioctahedral VermiculiteDioctahedral Vermiculite

1.7–2.0 Non-hydrated monovalent 50%) cations

True (flexible) mica Trioctahedral PhologopiteDioctahedral Muscovite

1.2–1.7 Non-hydrated mono- ordivalent cations

Interlayer-deficientmica

Trioctahedral IlliteDioctahedral Wonesite

2.6–4.0 Non-hydrated divalent 50%) cations

Brittle mica Trioctahedral ClintoniteDioctahedral Margarite

Variable Hydroxide sheet Chlorite Trioctahedral ClinochloreDioctahedral DonbassiteDi,trioctahedral Cookeite

*Approximate negative net charge per anionic O20(OH)4 formula unit

9

Phyllosilicates, for which the layer charge ranges between 0.4–1.2 per anionic O20(OH)4

formula unit, belong to the group of smectites. The smectites can be considered as lowlycharged 2:1 phyllosilicates with a high swelling capacity in the presence of water. Theextraordinary swelling behaviour of these minerals is based on their layer charge, whichis just high enough to attract hydratable cations, such as Na(I) and Ca(II), into theinterlayer space and to render the interlayer surfaces hydrophilic. These structuralfeatures of smectites enable water to overcome the electrostatic and van der Waalsinteractions keeping the layers together and to penetrate into the interlayer space. Theinflow of water expands the distance between the layers, and the clay is said to swell.Regardless of the structural similarity with smectites, phyllosilicates with higher layercharge are known to exhibit only limited swelling or do not swell at all. This is theconsequence of stronger electrostatic interactions between the positively chargedinterlayer cations and the negatively charged layers, which pull the layers into morefirmly stacked particles.3,5

Perhaps the most widely known smectite-rich and highly swelling clay is bentonite. It isused as a filler, binder and adsorbent/absorbent in various applications, includingplanned use as a buffer material for long-term nuclear waste disposal.2,6-8 Despite itsindustrial importance, bentonite might be best known from cat-litter or cosmetics. Themain component in bentonite is the clay mineral montmorillonite. It is a dioctahedralspecies of smectites characterized by the appearance of Mg(II) substitutions in the placeof Al(III) in the octahedral sheet. In other words, there are octahedral Mg(II) for Al(III)substitutions. The ideal species, however, is rare in nature, and therefore it is notuncommon that substitutions characteristic of other smectites are also present inmontmorillonite. These often include tetrahedral Al(III) for Si(IV) and octahedralFe(II/III) for Al(III), which are characteristic of beidellite and nontronite, respectively(Figure 2).9,10

Figure 2. A compositional triangle of montmorillonite, beidellite and nontronite. The designemphasizes the characteristic substitutions of these ideal end-members.

10

1.2 The scope of interests

The focus of this thesis covers three interconnected key areas, all related to the structureand surfaces of montmorillonite, smectites or 2:1 phyllosilicates in general. A briefintroduction follows.

The first interest of this thesis deals with the appearance of substitutions in the layerstructure of montmorillonite. The substitutions are the fundamental origin of the layercharge which impact on several properties of smectites, including cation exchangecapacity,11,12 swelling behaviour13,14 and flow properties.14 The substitutions under thescope are octahedral Mg(II) for Al(III) and tetrahedral Al(III) for Si(IV), which arefurther referred to as Mg- and Al-substitutions, for convenience, respectively. Theoctahedral Fe(II/III) for Al(III) substitutions, although commonly present in iron-richmontmorillonites, have been excluded from the study due to their complex oxidation-reduction behaviour15 and because they require a dedicated study for comprehensiveunderstanding.

The earlier studies on Mg- and Al-substitutions in 2:1 phyllosilicates have focused ontheir relative arrangement in the presence of interlayer cations. The statistical analysesof reverse Monte–Carlo simulations16-20 at finite temperatures and density functionaltheory calculations21-23 have shown that these substitutions tend to disperse in the layerstructure and exhibit at least close-range ordering behaviour. The experimental studies,including IR,24 NMR25 and EXAFS24 measurements, and IR/NMR combined withreverse Monte-Carlo simulations,17-19 have generally provided similar indications.Although the exact results have varied with composition, which may also include iron,at least the lack of Mg- and Al-substitutions in the neighbouring positions has beenrealized. However, none of these studies have been dedicated to the compositional rangeof montmorillonite or substitution–substitution interactions alone, which is whyadditional studies on the subject are still worthwhile.

The second interest lies in the interlayer surfaces of montmorillonite, which define theboundaries and chemical environment for the interlayer material. Since these surfacesare formed by silicate sheets with valence saturated atoms, they are generally consideredas stable and inert surfaces. However, the electrostatic charge of these surfaces isrendered highly negative due to the appearance of substitutions in the layer structure.Consequently, the interactions between the interlayer material and the interlayer surfacesare largely electrostatic, particularly since the interlayer material involve cations ormolecules with permanent dipole moment, such as water.

According to the experimental observations26-28 and theoretical studies29-37 of smectitesand vermiculites, the interlayer cations may interact with the interlayer surfaces as fullyhydrated complexes or adsorb directly on the layer surfaces. The complexes are oftenobserved close to the substitutions, and the direct adsorption is the most probable in thevicinity of Al-substitutions. The exact outcome is found to be dependent not only on thehydration tendency of the cations and the water content of the interlayer space, but also

13

on the number and location of the substitutions. Obviously, the substitutions and therelated layer charge play a major role in the behaviour of cations, but so far the exactnature of this charge has not been discussed in detail – except for the next few studies.

On the basis of semi-empirical extended Hückel calculations,38 it has been suggested thatthe negative net charge generated by Mg- and Al-substitutions does not fully reside onthe substitution site due to bonding interactions. Instead, the charge is found to bedeposited in significant amounts to other atoms, mostly on the neighbouring and next-neighbouring atoms. This charge deposition implies that a substitution does notcorrespond to a negative point-like charge but to an array of charges. Derived from theextended Hückel calculations, this kind of charge array was used in the followingtheoretical study39 to further demonstrate how the substitutions generate a negativedefect potential on the interlayer surface. Thus, interlayer cation–surface interaction maybe expected to not only be dependent on the position of the substitutions but also on theirelectrostatic nature. These reasons make it interesting to revisit the subject and to inspectcation–surface interaction energetics within the compositional range of montmorillonite.

The third and final subject under the scope is the structure of edge surfaces. Thesenarrow surfaces confine the dimensions of the layer structure and are found at the edgesof the particle (Figure 1). Even though the surface area of edges is smaller than that ofthe interlayer surfaces,40 the edges show considerable chemical activity due to valenceunsaturated atoms, i.e. broken bonds, present on the surface. The edges are known toimpact on several physicochemical properties of phyllosilicates: they exhibit pH-dependent surface charge,41-49 influence on the flocculation and colloidal behaviour ofthe particles,42,50 participate in the sorption of ionic species,51-54 interact withenvironmental water,44,49,55 and are the primary frontier through which the aciddissolution of the particles progress.41,56 The edge surfaces are difficult to isolate forexperimental measurements and may exhibit various structures due to the complexgeometry of the phyllosilicate layers. It is not surprising that the structure of the edgesurfaces is not well understood.

Only a few theoretical studies on the stability of the edge surfaces exist. The earlyestimations based on the periodic bond chain theory have suggested that the mostprobable edge structures border the (110) and (010) atomistic planes.57 The givenindexing refers to the Miller-indices in an orthogonally assigned layer unit cell.58 Thelater computational studies based on classical potentials55,59 and density functionaltheory calculations43,55 have supported the stability of the (110) edge surface but alsoindicated that different edge surfaces are close to similar in stability. Although thesecomputational studies have provided valuable information, they have largely beenlimited to a few different edge surfaces and/or classical potential based calculations. Theexact results have also been varied, and therefore the studies are not yet conclusive.

12

1.2 The scope of interests

The focus of this thesis covers three interconnected key areas, all related to the structureand surfaces of montmorillonite, smectites or 2:1 phyllosilicates in general. A briefintroduction follows.

The first interest of this thesis deals with the appearance of substitutions in the layerstructure of montmorillonite. The substitutions are the fundamental origin of the layercharge which impact on several properties of smectites, including cation exchangecapacity,11,12 swelling behaviour13,14 and flow properties.14 The substitutions under thescope are octahedral Mg(II) for Al(III) and tetrahedral Al(III) for Si(IV), which arefurther referred to as Mg- and Al-substitutions, for convenience, respectively. Theoctahedral Fe(II/III) for Al(III) substitutions, although commonly present in iron-richmontmorillonites, have been excluded from the study due to their complex oxidation-reduction behaviour15 and because they require a dedicated study for comprehensiveunderstanding.

The earlier studies on Mg- and Al-substitutions in 2:1 phyllosilicates have focused ontheir relative arrangement in the presence of interlayer cations. The statistical analysesof reverse Monte–Carlo simulations16-20 at finite temperatures and density functionaltheory calculations21-23 have shown that these substitutions tend to disperse in the layerstructure and exhibit at least close-range ordering behaviour. The experimental studies,including IR,24 NMR25 and EXAFS24 measurements, and IR/NMR combined withreverse Monte-Carlo simulations,17-19 have generally provided similar indications.Although the exact results have varied with composition, which may also include iron,at least the lack of Mg- and Al-substitutions in the neighbouring positions has beenrealized. However, none of these studies have been dedicated to the compositional rangeof montmorillonite or substitution–substitution interactions alone, which is whyadditional studies on the subject are still worthwhile.

The second interest lies in the interlayer surfaces of montmorillonite, which define theboundaries and chemical environment for the interlayer material. Since these surfacesare formed by silicate sheets with valence saturated atoms, they are generally consideredas stable and inert surfaces. However, the electrostatic charge of these surfaces isrendered highly negative due to the appearance of substitutions in the layer structure.Consequently, the interactions between the interlayer material and the interlayer surfacesare largely electrostatic, particularly since the interlayer material involve cations ormolecules with permanent dipole moment, such as water.

According to the experimental observations26-28 and theoretical studies29-37 of smectitesand vermiculites, the interlayer cations may interact with the interlayer surfaces as fullyhydrated complexes or adsorb directly on the layer surfaces. The complexes are oftenobserved close to the substitutions, and the direct adsorption is the most probable in thevicinity of Al-substitutions. The exact outcome is found to be dependent not only on thehydration tendency of the cations and the water content of the interlayer space, but also

11

on the number and location of the substitutions. Obviously, the substitutions and therelated layer charge play a major role in the behaviour of cations, but so far the exactnature of this charge has not been discussed in detail – except for the next few studies.

On the basis of semi-empirical extended Hückel calculations,38 it has been suggested thatthe negative net charge generated by Mg- and Al-substitutions does not fully reside onthe substitution site due to bonding interactions. Instead, the charge is found to bedeposited in significant amounts to other atoms, mostly on the neighbouring and next-neighbouring atoms. This charge deposition implies that a substitution does notcorrespond to a negative point-like charge but to an array of charges. Derived from theextended Hückel calculations, this kind of charge array was used in the followingtheoretical study39 to further demonstrate how the substitutions generate a negativedefect potential on the interlayer surface. Thus, interlayer cation–surface interaction maybe expected to not only be dependent on the position of the substitutions but also on theirelectrostatic nature. These reasons make it interesting to revisit the subject and to inspectcation–surface interaction energetics within the compositional range of montmorillonite.

The third and final subject under the scope is the structure of edge surfaces. Thesenarrow surfaces confine the dimensions of the layer structure and are found at the edgesof the particle (Figure 1). Even though the surface area of edges is smaller than that ofthe interlayer surfaces,40 the edges show considerable chemical activity due to valenceunsaturated atoms, i.e. broken bonds, present on the surface. The edges are known toimpact on several physicochemical properties of phyllosilicates: they exhibit pH-dependent surface charge,41-49 influence on the flocculation and colloidal behaviour ofthe particles,42,50 participate in the sorption of ionic species,51-54 interact withenvironmental water,44,49,55 and are the primary frontier through which the aciddissolution of the particles progress.41,56 The edge surfaces are difficult to isolate forexperimental measurements and may exhibit various structures due to the complexgeometry of the phyllosilicate layers. It is not surprising that the structure of the edgesurfaces is not well understood.

Only a few theoretical studies on the stability of the edge surfaces exist. The earlyestimations based on the periodic bond chain theory have suggested that the mostprobable edge structures border the (110) and (010) atomistic planes.57 The givenindexing refers to the Miller-indices in an orthogonally assigned layer unit cell.58 Thelater computational studies based on classical potentials55,59 and density functionaltheory calculations43,55 have supported the stability of the (110) edge surface but alsoindicated that different edge surfaces are close to similar in stability. Although thesecomputational studies have provided valuable information, they have largely beenlimited to a few different edge surfaces and/or classical potential based calculations. Theexact results have also been varied, and therefore the studies are not yet conclusive.

12

1.3 The aims and approach

The purpose of this thesis is to reveal the structural key features of montmorillonite,smectites and 2:1 phyllosilicates in general. The aim is to determine how Mg- and Al-substitutions interact and distribute in the layer structure, what is their electrostatic natureand how do they affect interlayer cation–surface interaction. In addition, the mostprobable and dominant edge surface structures are pursued. A knowledge of thesefeatures improves our understanding of the structural characteristics of montmorilloniteand provides detailed information for future research and modelling of montmorilloniteparticles.

The presented studies have been performed computationally with density functionaltheory, based on the theories of physics and quantum mechanics. This approach allowsa detailed and systematic investigation of montmorillonite’s structural features deepdown at atomic and electronic levels. Similar experimental studies would be timeconsuming and/or difficult, if not outright impossible. This is due to the structuralheterogeneities and anisotropy of montmorillonite and bentonite clay, the limitations ofcurrent experimental methods and the very small particle size of montmorillonite, whichis often measured in tens or hundreds of nanometres.60

15

2. Models and methods2.1 Model design

To calculate properties of a material, a representative model of its structure is required.Since the structure of a solid matter consists of repeating patterns of atoms, a model maybe constructed from a small piece of that structure. This piece may then be replicated ineach direction in space to create a periodic lattice, which is an infinite system made ofrepeating units or sequences. Although the dimensions of a real solid are not infinite,they approach infinite in relation to the size of an atom. The smallest repeating unit of asystem is referred to as a unit cell, whereas a larger repeating unit made from severalunit cells is referred to as a supercell.

The structure of 2:1 phyllosilicate layers was modelled with a supercell consisting offour trans-vacant pyrophyllite-like Al4Si8O20(OH)4 unit cells (Figure 3). The supercellhad a c2/m space-group symmetry and its lattice vectors, which define the dimensionsof the supercell, were fixed at 90-degrees, i.e. kept orthogonal. The optimization of thelattice vectors was performed for different compositions, as described in thesupplementary information of Publication III. The length of the lattice vector c was keptfixed at 10 Å. This value is large enough to avoid overlapping of the adjacent layers,leaves enough space for the cations to occupy the interlayer space and is close to theexperimentally measured values of dried smectites.61

Figure 3. The model layer structure viewed from the side along a-direction (left) and from thetop along c-direction (right). The solid lines represent the boundaries of the model supercell andthe dotted lines represent the boundaries of the smaller unit cells.

14

1.3 The aims and approach

The purpose of this thesis is to reveal the structural key features of montmorillonite,smectites and 2:1 phyllosilicates in general. The aim is to determine how Mg- and Al-substitutions interact and distribute in the layer structure, what is their electrostatic natureand how do they affect interlayer cation–surface interaction. In addition, the mostprobable and dominant edge surface structures are pursued. A knowledge of thesefeatures improves our understanding of the structural characteristics of montmorilloniteand provides detailed information for future research and modelling of montmorilloniteparticles.

The presented studies have been performed computationally with density functionaltheory, based on the theories of physics and quantum mechanics. This approach allowsa detailed and systematic investigation of montmorillonite’s structural features deepdown at atomic and electronic levels. Similar experimental studies would be timeconsuming and/or difficult, if not outright impossible. This is due to the structuralheterogeneities and anisotropy of montmorillonite and bentonite clay, the limitations ofcurrent experimental methods and the very small particle size of montmorillonite, whichis often measured in tens or hundreds of nanometres.60

13

2. Models and methods2.1 Model design

To calculate properties of a material, a representative model of its structure is required.Since the structure of a solid matter consists of repeating patterns of atoms, a model maybe constructed from a small piece of that structure. This piece may then be replicated ineach direction in space to create a periodic lattice, which is an infinite system made ofrepeating units or sequences. Although the dimensions of a real solid are not infinite,they approach infinite in relation to the size of an atom. The smallest repeating unit of asystem is referred to as a unit cell, whereas a larger repeating unit made from severalunit cells is referred to as a supercell.

The structure of 2:1 phyllosilicate layers was modelled with a supercell consisting offour trans-vacant pyrophyllite-like Al4Si8O20(OH)4 unit cells (Figure 3). The supercellhad a c2/m space-group symmetry and its lattice vectors, which define the dimensionsof the supercell, were fixed at 90-degrees, i.e. kept orthogonal. The optimization of thelattice vectors was performed for different compositions, as described in thesupplementary information of Publication III. The length of the lattice vector c was keptfixed at 10 Å. This value is large enough to avoid overlapping of the adjacent layers,leaves enough space for the cations to occupy the interlayer space and is close to theexperimentally measured values of dried smectites.61

Figure 3. The model layer structure viewed from the side along a-direction (left) and from thetop along c-direction (right). The solid lines represent the boundaries of the model supercell andthe dotted lines represent the boundaries of the smaller unit cells.

14

The edge surface models were cleaved from the periodic layer structure represented bya single unit cell with a ~10 Å vacuum cap between the layers. The cleaved edge surfaceswere also separated by a ~10 Å vacuum cap, thus the obtained models resembled aninfinite stripe that were 18.2–25.7 Å thick (Figure 4). The vacuum caps isolate the edgesurfaces from each other and minimize possible effects associated with layer stacking,i.e. the rotations and translations of the layers in relation to each other, which in naturealso depend on the interlayer material. A more detailed description of the edge surfacemodels is given in Publication II.

Figure 4. An example of edge surface model and its periodic images.

2.2 Computational methods

The modelling of atoms and their interactions were performed with density functionaltheory (DFT). The practical applicability of this method is based on the Hohenberg–Kohn–Sham theory, which allows the calculation of the ground state energy of electronicstructures on the basis of electron density only – the computationally demandingquantum mechanical interactions between electrons do not need to be evaluatedindividually. Instead, the interactions are included into an effective potential, known asthe exchange–correlation potential, which describes the energy dependency of theseinteractions on the electron density. How the exchange–correlation potential is exactlyevaluated depends on the formulation of the density functional in use.62,63 For thepurposes of this thesis, the exchange–correlation functional by Perdew–Burke–Ernzerhof (PBE)64,65 was chosen.

17

To calculate with DFT, a description of electron density is also required. This isconstructed with a basis set, which is a collection of mathematical functions. One wayto select the appropriate functions is to mimic the shapes of electron orbitals around eachatom, but according to Bloch’s theorem naturally periodic functions may also be used tomimic plane waves in a periodic atomic lattice.66 The latter approach was adopted in thisthesis with the Projector Augmented Wave (PAW) -method, which is a numericalconstruction of computationally efficient but accurate plane waves.67,68

The actual calculations were performed with the Vienna ab-initio simulation package(VASP).69-72 Earlier studies have shown that the PBE and PAWs, as implemented in theVASP, have provided close to experimental bond lengths and lattice vectors formontmorillonite and pyrophyllite.37,73 The PAWs were used to explicitly describe thevalence electrons of all elements and the electrons on the lower shell p-orbital of thegroup 1–2 elements, i.e. Na, Ca and Mg. The number of plane wave basis functions waslimited with a kinetic energy cut-off value of 525 eV. The Brillouin zone was sampledwith a single gamma-point in the supercell calculations, whereas a doubled k-pointdensity was applied in the [100] and [130] directions for the edge surface relatedcalculations. The Monkhorst–Pack grid74 was used to distribute the k-points throughoutthe Brillouin zone. The electronic structures were iterated until a convergence of 10-5 eVwas reached, and the atomic geometries were optimized until the residual forces wereless than 0.01 eV/Å per atom. The parameters were tested to provide converged latticevectors and total energies for the studied systems.

16

The edge surface models were cleaved from the periodic layer structure represented bya single unit cell with a ~10 Å vacuum cap between the layers. The cleaved edge surfaceswere also separated by a ~10 Å vacuum cap, thus the obtained models resembled aninfinite stripe that were 18.2–25.7 Å thick (Figure 4). The vacuum caps isolate the edgesurfaces from each other and minimize possible effects associated with layer stacking,i.e. the rotations and translations of the layers in relation to each other, which in naturealso depend on the interlayer material. A more detailed description of the edge surfacemodels is given in Publication II.

Figure 4. An example of edge surface model and its periodic images.

2.2 Computational methods

The modelling of atoms and their interactions were performed with density functionaltheory (DFT). The practical applicability of this method is based on the Hohenberg–Kohn–Sham theory, which allows the calculation of the ground state energy of electronicstructures on the basis of electron density only – the computationally demandingquantum mechanical interactions between electrons do not need to be evaluatedindividually. Instead, the interactions are included into an effective potential, known asthe exchange–correlation potential, which describes the energy dependency of theseinteractions on the electron density. How the exchange–correlation potential is exactlyevaluated depends on the formulation of the density functional in use.62,63 For thepurposes of this thesis, the exchange–correlation functional by Perdew–Burke–Ernzerhof (PBE)64,65 was chosen.

15

To calculate with DFT, a description of electron density is also required. This isconstructed with a basis set, which is a collection of mathematical functions. One wayto select the appropriate functions is to mimic the shapes of electron orbitals around eachatom, but according to Bloch’s theorem naturally periodic functions may also be used tomimic plane waves in a periodic atomic lattice.66 The latter approach was adopted in thisthesis with the Projector Augmented Wave (PAW) -method, which is a numericalconstruction of computationally efficient but accurate plane waves.67,68

The actual calculations were performed with the Vienna ab-initio simulation package(VASP).69-72 Earlier studies have shown that the PBE and PAWs, as implemented in theVASP, have provided close to experimental bond lengths and lattice vectors formontmorillonite and pyrophyllite.37,73 The PAWs were used to explicitly describe thevalence electrons of all elements and the electrons on the lower shell p-orbital of thegroup 1–2 elements, i.e. Na, Ca and Mg. The number of plane wave basis functions waslimited with a kinetic energy cut-off value of 525 eV. The Brillouin zone was sampledwith a single gamma-point in the supercell calculations, whereas a doubled k-pointdensity was applied in the [100] and [130] directions for the edge surface relatedcalculations. The Monkhorst–Pack grid74 was used to distribute the k-points throughoutthe Brillouin zone. The electronic structures were iterated until a convergence of 10-5 eVwas reached, and the atomic geometries were optimized until the residual forces wereless than 0.01 eV/Å per atom. The parameters were tested to provide converged latticevectors and total energies for the studied systems.

16

3. Structure – Mg(II)- and Al(III)-substitutionsThe interaction of octahedral Mg-substitutions and tetrahedral Al-substitutions wasstudied within the compositional range of smectites. The goal was to determine howthese substitutions interact and distribute in the layer structure. The typical Mg-substitutions for montmorillonite were studied in the range of 0.25–1.25 substitutionsper unit cell, which equals to 1–5 substitutions per model supercell. The less commonAl-substitutions and the mix of Mg/Al-substitutions were studied only at thecomposition of 0.50 substitutions per unit cell, i.e. two substitutions per supercell. Adetailed description of the study and models is given in Publication III.

3.1 Systematic model design

The arrangement of substitutions can be studied by varying their positions andcalculating the total energy of each arrangement. In principle, all the possiblearrangements should to be studied to extract complete information from the system. Thedifficulty in such an approach is that the number of the arrangements becomesexponentially larger as the size and complexity of the system increases. One solution isto use methods based on random sampling, such as Monte Carlo simulations, but a largenumber of calculations is still required to provide adequate sampling density. For thisreason, atomic interactions in the latter methods are often described with classicalpotentials, which trade computational accuracy for efficiency. However, both accuracyand efficiency was to be maintained in this thesis, thus a third approach was chosen: asystematic model design. A limited but representative set of different arrangements wereselected with certain principles. An explanation follows.

The smallest building block of the layer is the structural unit, which consists of twotetrahedral sites and one octahedral site (Figure 5). In the systematic model design, thesubstitutions were introduced to these structural units in several chain-like or cluster-likearrangements, where the minimum distance between the substitutions was kept fixed.The minimum distance was measured in terms of structural units and increased in stepsto generate arrangements with more dispersed substitutions. In the 0th (nearest)neighbour arrangements, the substitutions occupied the same structural unit, whereas inthe 1st neighbour arrangements, the substitutions occupied the neighbouring structuralunits. Similarly, in the 2nd, 3rd and 4th neighbour arrangements, the substitutions occupiedstructural units in the 2nd, 3rd and 4th neighbouring positions, respectively. Theserelationships between structural units are demonstrated in Figure 5, and examples ofsuch arrangements are given in Figure 6.

The designed arrangements are referred to by substitution composition per unit cell, suchas Al0.50, and arrangement code, such as 4b. The number in the arrangement code refers tothe distance between substitutions as nth neighbours and the alphabet specifies thesubstitution configuration, i.e. the relative arrangement of substitutions. The arrangementcode 2-3 indicates a mix of 2nd and 3rd neighbours. The additional superscript ( ), if present,indicates that Al-substitutions occupy different tetrahedral sheets.

19

Figure 5. The model supercell viewed along a-direction (left) and along c-direction (right). Purpleindicates one of the structural units. On the right, the relationship of structural units as nth

neighbours is demonstrated with dashed arrows.

Figure 6. Examples of nth neighbouring substitutions. Mg- and Al-substitutions are representedby orange and green, respectively. The model supercells are viewed along c-direction.

The substitutions in the layer structure generate a negative net layer charge. Tocompensate for this charge, a homogenous background charge was adopted throughoutthe model supercell, instead of explicit interlayer cations. With this method,substitution–substitution interactions could be decoupled from interlayer cation–cationand cation–substitution interactions. While the adoption of the background charge mightbe less justified for highly charged, non-swelling and tightly stacked phyllosilicatespecies, it may be viewed as a generalization of the interlayer space of smectites, wherethe cations are hydratable, relatively mobile and exchangeable. In addition, thebackground charge simplifies the study, since the type and number of cations, theirhydration state and relative arrangement can be ignored. Consequently, the data obtainedfrom this study is only related to substitution–substitution interactions and provide adifferent perspective in comparison to earlier studies.

18

3. Structure – Mg(II)- and Al(III)-substitutionsThe interaction of octahedral Mg-substitutions and tetrahedral Al-substitutions wasstudied within the compositional range of smectites. The goal was to determine howthese substitutions interact and distribute in the layer structure. The typical Mg-substitutions for montmorillonite were studied in the range of 0.25–1.25 substitutionsper unit cell, which equals to 1–5 substitutions per model supercell. The less commonAl-substitutions and the mix of Mg/Al-substitutions were studied only at thecomposition of 0.50 substitutions per unit cell, i.e. two substitutions per supercell. Adetailed description of the study and models is given in Publication III.

3.1 Systematic model design

The arrangement of substitutions can be studied by varying their positions andcalculating the total energy of each arrangement. In principle, all the possiblearrangements should to be studied to extract complete information from the system. Thedifficulty in such an approach is that the number of the arrangements becomesexponentially larger as the size and complexity of the system increases. One solution isto use methods based on random sampling, such as Monte Carlo simulations, but a largenumber of calculations is still required to provide adequate sampling density. For thisreason, atomic interactions in the latter methods are often described with classicalpotentials, which trade computational accuracy for efficiency. However, both accuracyand efficiency was to be maintained in this thesis, thus a third approach was chosen: asystematic model design. A limited but representative set of different arrangements wereselected with certain principles. An explanation follows.

The smallest building block of the layer is the structural unit, which consists of twotetrahedral sites and one octahedral site (Figure 5). In the systematic model design, thesubstitutions were introduced to these structural units in several chain-like or cluster-likearrangements, where the minimum distance between the substitutions was kept fixed.The minimum distance was measured in terms of structural units and increased in stepsto generate arrangements with more dispersed substitutions. In the 0th (nearest)neighbour arrangements, the substitutions occupied the same structural unit, whereas inthe 1st neighbour arrangements, the substitutions occupied the neighbouring structuralunits. Similarly, in the 2nd, 3rd and 4th neighbour arrangements, the substitutions occupiedstructural units in the 2nd, 3rd and 4th neighbouring positions, respectively. Theserelationships between structural units are demonstrated in Figure 5, and examples ofsuch arrangements are given in Figure 6.

The designed arrangements are referred to by substitution composition per unit cell, suchas Al0.50, and arrangement code, such as 4b. The number in the arrangement code refers tothe distance between substitutions as nth neighbours and the alphabet specifies thesubstitution configuration, i.e. the relative arrangement of substitutions. The arrangementcode 2-3 indicates a mix of 2nd and 3rd neighbours. The additional superscript ( ), if present,indicates that Al-substitutions occupy different tetrahedral sheets.

17

Figure 5. The model supercell viewed along a-direction (left) and along c-direction (right). Purpleindicates one of the structural units. On the right, the relationship of structural units as nth

neighbours is demonstrated with dashed arrows.

Figure 6. Examples of nth neighbouring substitutions. Mg- and Al-substitutions are representedby orange and green, respectively. The model supercells are viewed along c-direction.

The substitutions in the layer structure generate a negative net layer charge. Tocompensate for this charge, a homogenous background charge was adopted throughoutthe model supercell, instead of explicit interlayer cations. With this method,substitution–substitution interactions could be decoupled from interlayer cation–cationand cation–substitution interactions. While the adoption of the background charge mightbe less justified for highly charged, non-swelling and tightly stacked phyllosilicatespecies, it may be viewed as a generalization of the interlayer space of smectites, wherethe cations are hydratable, relatively mobile and exchangeable. In addition, thebackground charge simplifies the study, since the type and number of cations, theirhydration state and relative arrangement can be ignored. Consequently, the data obtainedfrom this study is only related to substitution–substitution interactions and provide adifferent perspective in comparison to earlier studies.

18

3.2 The interaction of the substitutions

The calculated total energies of the substitution arrangements were compared. Thelowest energy arrangement at each substitution composition was treated as the energyreference in relation to which the energies of other arrangements were reported. Theresults clearly show that the relative energies of the arrangements decrease as thedistance between the substitutions increases (Figures 8A–G). The variations in thearrangement energies are significant, up to 109 kJ/mol, and largely depend onsubstitution–substitution distances measured in structural units. In other words, thesubstitutions repulse each other.

However, the distance property is one dimensional, which is why it cannot explain theenergy differences between substitution configurations, such 2a–2h in Figure 8c. Forimproved description, the degree of clusterization, i.e. the radial density of substitutions,must also be accounted for. A simple way to demonstrate this is to plot the relativeenergies of the nth neighbour arrangements against the average number of nth neighboursin the models. In Figure 7, such a plot is presented for the 2nd neighbour arrangementsof the Figure 8C configurations (2a–2h). The plot shows close to linear dependencybetween these properties, and the positive slope of the fitted line further supports therepulsive behaviour of the substitutions. Similar plots may be constructed for any nth

neighbour arrangements for any of the studied compositions.

Figure 7. The relative energies of the 2nd neighbour arrangements against the average number ofthe 2nd neighbours for Mg1.00-composition (Figure 8c).

Finally, the arrangement energies of different compositions with the same substitutiondensity (0.50 per unit cell) were found to follow a similar trend (Figure 8A and Figures8E–G). Notable differences only arise when the substitutions occupy structural unitsclose to each other. This is clearly evident if the 1st neighbour arrangements of Mg-substitutions (Figure 8A) and Al-substitutions (Figure 8E) are compared.

21

Figure 8. Relative energies of the substitution arrangements with different compositions: Mg-substitutions (A-D), Al-substitutions (E-F) and mixed Mg/Al-substitutions (G). The relativeenergies of geometry deformations are also presented (H). Each bar is labelled with anarrangement code, and bold font highlights the labels of the energy minimum reference systems.The Mg0.25-composition is excluded from the figure since only one possible arrangement existswithin the model supercell of that system.

20

3.2 The interaction of the substitutions

The calculated total energies of the substitution arrangements were compared. Thelowest energy arrangement at each substitution composition was treated as the energyreference in relation to which the energies of other arrangements were reported. Theresults clearly show that the relative energies of the arrangements decrease as thedistance between the substitutions increases (Figures 8A–G). The variations in thearrangement energies are significant, up to 109 kJ/mol, and largely depend onsubstitution–substitution distances measured in structural units. In other words, thesubstitutions repulse each other.

However, the distance property is one dimensional, which is why it cannot explain theenergy differences between substitution configurations, such 2a–2h in Figure 8c. Forimproved description, the degree of clusterization, i.e. the radial density of substitutions,must also be accounted for. A simple way to demonstrate this is to plot the relativeenergies of the nth neighbour arrangements against the average number of nth neighboursin the models. In Figure 7, such a plot is presented for the 2nd neighbour arrangementsof the Figure 8C configurations (2a–2h). The plot shows close to linear dependencybetween these properties, and the positive slope of the fitted line further supports therepulsive behaviour of the substitutions. Similar plots may be constructed for any nth

neighbour arrangements for any of the studied compositions.

Figure 7. The relative energies of the 2nd neighbour arrangements against the average number ofthe 2nd neighbours for Mg1.00-composition (Figure 8c).

Finally, the arrangement energies of different compositions with the same substitutiondensity (0.50 per unit cell) were found to follow a similar trend (Figure 8A and Figures8E–G). Notable differences only arise when the substitutions occupy structural unitsclose to each other. This is clearly evident if the 1st neighbour arrangements of Mg-substitutions (Figure 8A) and Al-substitutions (Figure 8E) are compared.

19

Figure 8. Relative energies of the substitution arrangements with different compositions: Mg-substitutions (A-D), Al-substitutions (E-F) and mixed Mg/Al-substitutions (G). The relativeenergies of geometry deformations are also presented (H). Each bar is labelled with anarrangement code, and bold font highlights the labels of the energy minimum reference systems.The Mg0.25-composition is excluded from the figure since only one possible arrangement existswithin the model supercell of that system.

20

The presented results suggest that the introduction of the substitutions produce structuraltension due the larger size of the substitutions in comparison to unsubstituted atoms.Since the lattice vectors were relaxed for each substitution composition, this tension islikely to be internal and related to geometry deformations around the substitutions.

To verify the latter assumption, a series of geometry deformation arrangement modelswere designed. These models were identical to the optimized model structures of themixed Mg/Al-substitution arrangements (Mg0.25Al0.25), except that the substitutions werereplaced with unsubstituted atoms. The trick was to conserve the structural deformationsproduced by the Mg- and Al-substitutions and to optimize the electron densities of thesystems only. The calculations confirmed that the relative energies of the geometrydeformations alone (Figure 8h) produce close to a similar trend with the relative energiesof the actual Mg/Al-substitution arrangements (Figure 8g). Notable deviations in theenergies appear only for the 0th and 1st neighbour arrangements. However, this isexpected since the orbital interactions of atoms between neighbouring deformedpositions are non-optimal for the geometry deformation arrangements and differ fromthe actual Mg/Al-substituted arrangements.

23

4. Interlayer surfaces – electrostatistics and cationsThe effect of Mg- and Al-substitutions on the electrostatic properties of interlayersurfaces and cation–surface interaction was studied within the compositional range ofsmectites. The aim was to find out and rationalize how the interlayer cation–surfaceinteraction is affected by the substitutions and layer charge. The presented study is basedon Publication I but modified and expanded further by using the models and parameterscomparable to Publication III.

4.1 Electrostatic potential of interlayer surfaces

The interlayer surfaces of smectites are formed by tetrahedral silicate sheets, which arenearly hexagonal, ditrigonal atomic frameworks (Figure 9A). The interlayer material ofsmectites is in contact with these surfaces, thus it is useful to inspect the electrostaticproperties of these surfaces under the influence of Mg- and Al-substitutions. This can beperformed visually by mapping electrostatic potential (ESP) on the electron densityisosurface of Mg-substituted (Figure 9B) and Al-substituted (Figure 9C) models. AnESP describes the amount of energy released when a positive unit charge is brought to apoint of interest from an infinite distance. Thus, the most negative ESP areas attractpositively charged cations most strongly.

Figure 9. (A) Atomic framework of the model silicate surface. The big and small black spheresrepresent silicon and oxygen atoms, respectively. The ditrigonal cavities that correspond to cationadsorption sites are labelled with numbers. (B) ESP mapped on the model isosurface under theinfluence of Mg-substitution which is located at the indicated position, below the surface. Redand blue colours indicate the negative and positive end of the ESP, respectively. The hydroxylgroups below the ditrigonal cavities are also rendered. (C) Similar to B, but mapped under theinfluence of Al-substitution which is located at the indicated position.

22

The presented results suggest that the introduction of the substitutions produce structuraltension due the larger size of the substitutions in comparison to unsubstituted atoms.Since the lattice vectors were relaxed for each substitution composition, this tension islikely to be internal and related to geometry deformations around the substitutions.

To verify the latter assumption, a series of geometry deformation arrangement modelswere designed. These models were identical to the optimized model structures of themixed Mg/Al-substitution arrangements (Mg0.25Al0.25), except that the substitutions werereplaced with unsubstituted atoms. The trick was to conserve the structural deformationsproduced by the Mg- and Al-substitutions and to optimize the electron densities of thesystems only. The calculations confirmed that the relative energies of the geometrydeformations alone (Figure 8h) produce close to a similar trend with the relative energiesof the actual Mg/Al-substitution arrangements (Figure 8g). Notable deviations in theenergies appear only for the 0th and 1st neighbour arrangements. However, this isexpected since the orbital interactions of atoms between neighbouring deformedpositions are non-optimal for the geometry deformation arrangements and differ fromthe actual Mg/Al-substituted arrangements.

21

4. Interlayer surfaces – electrostatistics and cationsThe effect of Mg- and Al-substitutions on the electrostatic properties of interlayersurfaces and cation–surface interaction was studied within the compositional range ofsmectites. The aim was to find out and rationalize how the interlayer cation–surfaceinteraction is affected by the substitutions and layer charge. The presented study is basedon Publication I but modified and expanded further by using the models and parameterscomparable to Publication III.

4.1 Electrostatic potential of interlayer surfaces

The interlayer surfaces of smectites are formed by tetrahedral silicate sheets, which arenearly hexagonal, ditrigonal atomic frameworks (Figure 9A). The interlayer material ofsmectites is in contact with these surfaces, thus it is useful to inspect the electrostaticproperties of these surfaces under the influence of Mg- and Al-substitutions. This can beperformed visually by mapping electrostatic potential (ESP) on the electron densityisosurface of Mg-substituted (Figure 9B) and Al-substituted (Figure 9C) models. AnESP describes the amount of energy released when a positive unit charge is brought to apoint of interest from an infinite distance. Thus, the most negative ESP areas attractpositively charged cations most strongly.

Figure 9. (A) Atomic framework of the model silicate surface. The big and small black spheresrepresent silicon and oxygen atoms, respectively. The ditrigonal cavities that correspond to cationadsorption sites are labelled with numbers. (B) ESP mapped on the model isosurface under theinfluence of Mg-substitution which is located at the indicated position, below the surface. Redand blue colours indicate the negative and positive end of the ESP, respectively. The hydroxylgroups below the ditrigonal cavities are also rendered. (C) Similar to B, but mapped under theinfluence of Al-substitution which is located at the indicated position.

22

As is evident on the basis of Figures 9B and 9C, the most negative ESP areas (red colour)locate on the surface oxygens in the vicinity of the substitutions. It is also evident thatthe Mg-substitution generates a more smoothly distributed negative surface charge thanthe Al-substitution. This is because the Mg-substitution locates below the surface in theoctahedral sheet and its negative net charge appears to be projected on a larger area. Dueto its location, the Mg-substitution also renders the ESP of the connected hydroxyloxygens in the octahedral sheet more negative, which can be observed through ditrigonalcavity number 3, as denoted in Figure 9A.

Another noteworthy detail observed in the latter ESP maps is the positive potential (bluecolour) produced by the hydroxyl hydrogens in the octahedral sheet. This potentialreduces the negativity of every third surface oxygen, which is well visible in Figure 9C:two surface oxygens connected to the Al-substitution appear as red, while one remainsalmost yellow due to the positive potential of hydroxyl hydrogen seen through theditrigonal cavity number 4.

The ESP maps presented in Figures 9B and 9C are calculated for negatively chargedsystems in the presence of homogenous background charge. Instead, in Publication I,the ESP map under the influence of two Mg-substitutions per supercell were calculatedas a non-charged system. According to analysis of electron density distributions, thecharged systems were found to produce a more realistic outcome if compared to a systemwith explicit interlayer cations. However, the differences are rather small, and bothapproaches are valid for qualitative inspection of ESP.

4.2 Electrostatic nature of Mg(II)- and Al(III)-substitutions

The ESP maps of Figures 9B and 9C clearly visualize that the negative net layer chargeis highest in the vicinity of the substitutions. This is obviously explained by the negativenet charge originating from the substitutions with a lower positive nuclear charge.However, as was discussed in the introduction of this thesis, this negative net chargemay be significantly deposited to other atoms due to orbital interactions. Consequently,the nature of the substitutions as charge deficits may be more complicated than formallyexpected and cannot be observed in detail on the basis of ESP maps only. Thus, a moredetailed analysis of the charge distributions was made.

A quantitative charge distribution analysis was performed with the Bader method.75-77 Inthis method, the electron density is partitioned between atoms along density gradientlines and through bond critical points where the density gradient is zero. When thepartitioned electron density around each atom is combined with its positive nuclearcharge, atomic partial charges are obtained. These were calculated for the charged Mg-and Al-substituted systems and are reported in Table 2 on a statistical basis. In Table 2,the Al-substitutions are denoted as Al(subs) and the oxygens have been classified intofour different categories based on their chemical environment: bridging oxygen (Ob),bridging oxygen connected to substitution (Obs), hydroxyl oxygen (Oh) and hydroxyloxygen connected to substitution (Ohs).

25

Table 2. Calculated atomic partial charges for the Mg- and Al-substituted systems.

Mg-substituted system Al-substituted systemAtom Formal* Mean Dev** Min Max Mean Dev** Min MaxSi +4 +3.20 0.003 +3.20 +3.19 +3.20 0.004 +3.20 +3.19Al(subs) +3 +2.46Al +3 +2.50 0.002 +2.50 +2.49 +2.50 0.001 +2.50 +2.50Mg +2 +1.74H +1 +0.59 0.006 +0.60 +0.58 +0.59 0.005 +0.60 +0.58Ob -2 1.61 0.017 1.56 1.64 1.62 0.020 1.57 1.66Obs -2 1.63 0.012 1.62 1.64 1.62 0.022 1.59 1.65Ohs -2 1.41 0.000 1.41 1.41Oh -2 1.42 0.007 1.42 1.44 1.42 0.015 1.40 1.45*Formal charge of the species; **standard deviation

The analysis of partial charges indicate that the substitutions are the only significantcharge defects in the layer structure, while the charge of other atoms is distributed closeto homogenously throughout the layer on an atomic basis. In other words, thesubstitutions resemble negative point-like charges. The charge of the Mg- and Al-substitutions are found to be 0.76 and 0.74 elementary units less positive thanunsubstituted Al and Si, respectively, thus very similar in their nature. The results areclosely in-line with Publication I, where the Bader analysis was performed for a systemwith two Mg-substitutions and explicit interlayer cations, Na(I) and Ca(II).

To test the effect of the substitutions on cation–surface interaction, an interlayer Na(I)cation was used as a charged probe. The position of Na(I) was varied on the surfaces ofFigure 9B and 9C models by assuming that its position is located in the centers ofditrigonal cavities (Figure 9A), as justified in Publication I, due to the cumulativenegative potential of the surrounding oxygens. Total energies were calculated for eachstructure optimized configuration. According to Coulomb’s law (Equation 1), theinteraction energy (E) between point charges i and j is linearly proportional to their unitcharges (q) and their inverse distances ( 1/r), while Coulomb’s constant (k) andelementary charge (e) are constants:

rqqkeE ji

12 (1)

Thus if Na(I) and the substitutions behave like point charges i and j, the cation–surfaceinteraction energies should depend linearly on cation–substitution inverse distances,

1/r, assuming also that electric permittivity remains comparable between the models.To test this relation, the calculated total energies of Na(I) configurations were plotted ona relative scale against 1/r (Figure 10).

24

As is evident on the basis of Figures 9B and 9C, the most negative ESP areas (red colour)locate on the surface oxygens in the vicinity of the substitutions. It is also evident thatthe Mg-substitution generates a more smoothly distributed negative surface charge thanthe Al-substitution. This is because the Mg-substitution locates below the surface in theoctahedral sheet and its negative net charge appears to be projected on a larger area. Dueto its location, the Mg-substitution also renders the ESP of the connected hydroxyloxygens in the octahedral sheet more negative, which can be observed through ditrigonalcavity number 3, as denoted in Figure 9A.

Another noteworthy detail observed in the latter ESP maps is the positive potential (bluecolour) produced by the hydroxyl hydrogens in the octahedral sheet. This potentialreduces the negativity of every third surface oxygen, which is well visible in Figure 9C:two surface oxygens connected to the Al-substitution appear as red, while one remainsalmost yellow due to the positive potential of hydroxyl hydrogen seen through theditrigonal cavity number 4.

The ESP maps presented in Figures 9B and 9C are calculated for negatively chargedsystems in the presence of homogenous background charge. Instead, in Publication I,the ESP map under the influence of two Mg-substitutions per supercell were calculatedas a non-charged system. According to analysis of electron density distributions, thecharged systems were found to produce a more realistic outcome if compared to a systemwith explicit interlayer cations. However, the differences are rather small, and bothapproaches are valid for qualitative inspection of ESP.

4.2 Electrostatic nature of Mg(II)- and Al(III)-substitutions

The ESP maps of Figures 9B and 9C clearly visualize that the negative net layer chargeis highest in the vicinity of the substitutions. This is obviously explained by the negativenet charge originating from the substitutions with a lower positive nuclear charge.However, as was discussed in the introduction of this thesis, this negative net chargemay be significantly deposited to other atoms due to orbital interactions. Consequently,the nature of the substitutions as charge deficits may be more complicated than formallyexpected and cannot be observed in detail on the basis of ESP maps only. Thus, a moredetailed analysis of the charge distributions was made.

A quantitative charge distribution analysis was performed with the Bader method.75-77 Inthis method, the electron density is partitioned between atoms along density gradientlines and through bond critical points where the density gradient is zero. When thepartitioned electron density around each atom is combined with its positive nuclearcharge, atomic partial charges are obtained. These were calculated for the charged Mg-and Al-substituted systems and are reported in Table 2 on a statistical basis. In Table 2,the Al-substitutions are denoted as Al(subs) and the oxygens have been classified intofour different categories based on their chemical environment: bridging oxygen (Ob),bridging oxygen connected to substitution (Obs), hydroxyl oxygen (Oh) and hydroxyloxygen connected to substitution (Ohs).

23

Table 2. Calculated atomic partial charges for the Mg- and Al-substituted systems.

Mg-substituted system Al-substituted systemAtom Formal* Mean Dev** Min Max Mean Dev** Min MaxSi +4 +3.20 0.003 +3.20 +3.19 +3.20 0.004 +3.20 +3.19Al(subs) +3 +2.46Al +3 +2.50 0.002 +2.50 +2.49 +2.50 0.001 +2.50 +2.50Mg +2 +1.74H +1 +0.59 0.006 +0.60 +0.58 +0.59 0.005 +0.60 +0.58Ob -2 1.61 0.017 1.56 1.64 1.62 0.020 1.57 1.66Obs -2 1.63 0.012 1.62 1.64 1.62 0.022 1.59 1.65Ohs -2 1.41 0.000 1.41 1.41Oh -2 1.42 0.007 1.42 1.44 1.42 0.015 1.40 1.45*Formal charge of the species; **standard deviation

The analysis of partial charges indicate that the substitutions are the only significantcharge defects in the layer structure, while the charge of other atoms is distributed closeto homogenously throughout the layer on an atomic basis. In other words, thesubstitutions resemble negative point-like charges. The charge of the Mg- and Al-substitutions are found to be 0.76 and 0.74 elementary units less positive thanunsubstituted Al and Si, respectively, thus very similar in their nature. The results areclosely in-line with Publication I, where the Bader analysis was performed for a systemwith two Mg-substitutions and explicit interlayer cations, Na(I) and Ca(II).

To test the effect of the substitutions on cation–surface interaction, an interlayer Na(I)cation was used as a charged probe. The position of Na(I) was varied on the surfaces ofFigure 9B and 9C models by assuming that its position is located in the centers ofditrigonal cavities (Figure 9A), as justified in Publication I, due to the cumulativenegative potential of the surrounding oxygens. Total energies were calculated for eachstructure optimized configuration. According to Coulomb’s law (Equation 1), theinteraction energy (E) between point charges i and j is linearly proportional to their unitcharges (q) and their inverse distances ( 1/r), while Coulomb’s constant (k) andelementary charge (e) are constants:

rqqkeE ji

12 (1)

Thus if Na(I) and the substitutions behave like point charges i and j, the cation–surfaceinteraction energies should depend linearly on cation–substitution inverse distances,

1/r, assuming also that electric permittivity remains comparable between the models.To test this relation, the calculated total energies of Na(I) configurations were plotted ona relative scale against 1/r (Figure 10).

24

Figure 10. Calculated Na(I) configuration energies plotted on a relative scale against cation–substitution inverse distances. On the left, the plot is for the Mg-substituted system of Figure 9B.On the right, the plot is for the Al-substituted system of Figure 9C. The labels refer to cationpositions in ditrigonal cavities, as denoted in Figure 9A.

The plots of Figure 10 show close to a linear relationship between the plotted propertiesand confirm the role of Mg- and Al-substitutions as negative point-like charges attractinginterlayer cations. The slopes of the fitted lines in Figure 10 have similar values, -241.5and -243.9 kJ Å mol-1, thus further indicating that the electrostatic nature of Mg- and Al-substitutions is similar. In Publication I, the same relationship was demonstrated to holdtrue for a system consisting of two Mg-substitutions and one Ca(II) cation.

The presented plots in Figure 10 are subject to some dispersion, mostly because of theapproximations made in the evaluation of inverse distances. The exact evaluation iscomplicated, since 1/r is infinite and divergent in a periodic lattice. Due to this reason,and for the purposes of this thesis, the summation of inverse distances was performed upto a cut-off radius of 50 Å. To compensate for the artefacts of the cut-off radius, thenumber of 1/r terms in the summation was truncated, starting from the smallest term, toequalize the upper limit of summation between systems with different cationconfigurations. This task was carried out with a custom made code which also excludeddouble-counting and self-interaction of the species in the periodic lattice. A simplifiedexample of the procedure follows.

27

In Figure 11, the evaluation of inverse distances is schematically illustrated for a twodimensional lattice with two different configurations. The black square represents theunit cell, whereas grey squares represents its periodic images. The blue dot is the positivecharge of interest, which interacts with the negative charges represented by red dots. Theinteraction of the blue dot with its own periodic images is always constant, hence itsperiodic images have been removed as redundant. The inverse distances from the bluedot to the red dots are evaluated up to the cut-off radius, R. Within the cut-off radius, theconfiguration on the left contains 9 red dots, whereas the configuration on the rightcontains only 8 red dots – the circled red dot remains outside of the cut-off radius. Tomake the net interactions experienced by the blue dot in both configurations morecomparable, the number of red dots has to be equalized within the cut-off radius: on theleft, the red dot closest to the cut-off limit, i.e. furthest from the blue dot, is crossed outfrom the evaluation. As a result, 8 red dots remain in both configurations and the numberof 1/r terms in 1/r is identical – the biased number of red dots due to the cut-off radiusis eliminated.

Figure 11. Evaluation of inverse distances for a set of two different dot configurations in aschematic two dimensional lattice.

4.3 Effect of substitution composition on cation–surface interaction

The effect of substitution composition on cation–surface interaction was studied withinthe range of 0.25–1.25 Mg-substitutions per unit cell, whereas for Al-substitutions anda mix of Mg/Al-substitutions, only the density of 0.50 substitutions per unit cell wasstudied. The compositional range is identical to the study of substitution interactionspresented in Section 3 and Publication III, from which the energy minimum substitutionarrangement models were used – i.e. the substitutions were maximally dispersed in themodels. The layer charge was compensated for by a multiple, charge equivalent numberof interlayer cations, using Na(I) or Ca(II) as representative species.

26

Figure 10. Calculated Na(I) configuration energies plotted on a relative scale against cation–substitution inverse distances. On the left, the plot is for the Mg-substituted system of Figure 9B.On the right, the plot is for the Al-substituted system of Figure 9C. The labels refer to cationpositions in ditrigonal cavities, as denoted in Figure 9A.

The plots of Figure 10 show close to a linear relationship between the plotted propertiesand confirm the role of Mg- and Al-substitutions as negative point-like charges attractinginterlayer cations. The slopes of the fitted lines in Figure 10 have similar values, -241.5and -243.9 kJ Å mol-1, thus further indicating that the electrostatic nature of Mg- and Al-substitutions is similar. In Publication I, the same relationship was demonstrated to holdtrue for a system consisting of two Mg-substitutions and one Ca(II) cation.

The presented plots in Figure 10 are subject to some dispersion, mostly because of theapproximations made in the evaluation of inverse distances. The exact evaluation iscomplicated, since 1/r is infinite and divergent in a periodic lattice. Due to this reason,and for the purposes of this thesis, the summation of inverse distances was performed upto a cut-off radius of 50 Å. To compensate for the artefacts of the cut-off radius, thenumber of 1/r terms in the summation was truncated, starting from the smallest term, toequalize the upper limit of summation between systems with different cationconfigurations. This task was carried out with a custom made code which also excludeddouble-counting and self-interaction of the species in the periodic lattice. A simplifiedexample of the procedure follows.

25

In Figure 11, the evaluation of inverse distances is schematically illustrated for a twodimensional lattice with two different configurations. The black square represents theunit cell, whereas grey squares represents its periodic images. The blue dot is the positivecharge of interest, which interacts with the negative charges represented by red dots. Theinteraction of the blue dot with its own periodic images is always constant, hence itsperiodic images have been removed as redundant. The inverse distances from the bluedot to the red dots are evaluated up to the cut-off radius, R. Within the cut-off radius, theconfiguration on the left contains 9 red dots, whereas the configuration on the rightcontains only 8 red dots – the circled red dot remains outside of the cut-off radius. Tomake the net interactions experienced by the blue dot in both configurations morecomparable, the number of red dots has to be equalized within the cut-off radius: on theleft, the red dot closest to the cut-off limit, i.e. furthest from the blue dot, is crossed outfrom the evaluation. As a result, 8 red dots remain in both configurations and the numberof 1/r terms in 1/r is identical – the biased number of red dots due to the cut-off radiusis eliminated.

Figure 11. Evaluation of inverse distances for a set of two different dot configurations in aschematic two dimensional lattice.

4.3 Effect of substitution composition on cation–surface interaction

The effect of substitution composition on cation–surface interaction was studied withinthe range of 0.25–1.25 Mg-substitutions per unit cell, whereas for Al-substitutions anda mix of Mg/Al-substitutions, only the density of 0.50 substitutions per unit cell wasstudied. The compositional range is identical to the study of substitution interactionspresented in Section 3 and Publication III, from which the energy minimum substitutionarrangement models were used – i.e. the substitutions were maximally dispersed in themodels. The layer charge was compensated for by a multiple, charge equivalent numberof interlayer cations, using Na(I) or Ca(II) as representative species.

26

Evaluation of cation–surface interactions

Multiple cations may occupy the ditrigonal cavities of the model supercells with variousconfigurations. They are attracted by the substitutions but simultaneously repel eachother. The energy of such point-like charge systems depends linearly on the net 1/r,which consists of an attractive part and a repulsive part. The attractive part can beevaluated by summing cation–substitution inverse distances within the cut-off radius, asdescribed before. Similarly, the repulsive part can be evaluated by summing cation–cation inverse distances. To account for different charges and interaction strengths, bothattractive and repulsive parts must be scaled by the product of the unit charges q of theinteracting species. For the substitutions, the value of qj is taken as -1, whereas for thecations, the value of qi is taken as the formal charge, i.e. +1 for Na(I) and +2 for Ca(II).Finally, the net 1/r is evaluated by subtracting the repulsive part from the attractivepart according to Equation 2:

rqq

rqq

r iiji111 (2)

In equation 2, the product of qiqj is taken as an absolute value to set the attractive part,i.e. the first term, positive, from which the repulsive part, i.e. the second term, issubtracted. By this definition, the higher the net 1/r is for a cation configuration, themore favourable that configuration is in energy. In Publication I, this dependency wasdemonstrated to be linear in the case of two Mg-substitutions and two Na(I) cations,similarly to Figure 10. This information may be used as a tool for qualitative evaluationof cation configuration energies in different systems.

A grid-based code was developed, which generated all the possible cation configurationsfor the studied systems and evaluated the related net 1/r values. In the evaluation, theinterlayer cations were constrained in the grid points set in the centers of ditrigonalcavities, approximately 1 Å above the surface oxygens. The evaluated net 1/r valuesare presented in descending order for Na(I) and Ca(II) configurations in differentlysubstituted systems in Figures 12 and 13, respectively. The cation configurationsassociated with the evaluated values are designated with comma separated numbers.These numbers refer to the cation occupied ditrigonal cavities within the modelsupercells, as denoted in Figure 9A. Note that the absolute net 1/r values are onlycomparable within the same system but not between different systems.

The evaluated 1/r values provide a qualitative estimate on the cation configurationenergies within differently substituted systems. According to Figure 12, increasingsubstitution density increases the number of possible Na(I) configurations and smoothensthe estimated energy (colour) differences. However, this only applies up to a substitutiondensity of 1.00 per unit cell, after which the increased Na(I) population limits the numberof configurations. For Ca(II), Figure 13 show less configurations with more discretenessin the energy distributions. The discreteness is emphasized by Al-substitutions, also in thecase of Na(I), since their charge is effectively more localized.

29

Figure 12. Evaluated net 1/r values for Na(I) configurations in differently substituted systems.The configurations outlined with a box were selected for DFT calculations, according to whichthe energy minimum configurations are highlighted in green.

3 8.225 2, 6 24.520 4, 7 24.435 3, 8 24.486 3, 7 24.437 1, 6, 7 56.171 1, 4, 7, 8 102.953 1, 2, 5, 7, 8 164.6404 8.183 4, 7 24.501 3, 7 24.404 1, 6 24.455 4, 7 24.431 1, 6, 8 56.168 1, 3, 4, 7 102.950 1, 3, 4, 7, 8 164.6306 8.176 3, 8 24.501 2, 5 24.380 4, 7 24.455 3, 8 24.430 2, 5, 8 56.146 1, 6, 7, 8 102.943 1, 3, 5, 7, 8 164.6255 8.158 3, 7 24.466 3, 8 24.369 3, 7 24.454 2, 5 24.395 2, 5, 7 56.145 2, 4, 7, 8 102.923 1, 4, 5, 7, 8 164.6232 8.096 2, 5 24.460 2, 6 24.344 2, 6 24.450 1, 6 24.394 2, 6, 7 56.126 1, 3, 7, 8 102.922 1, 5, 6, 7, 8 164.6211 8.091 1, 6 24.459 2, 3 24.331 6, 7 24.431 2, 6 24.378 2, 6, 8 56.123 1, 3, 4, 8 102.921 1, 2, 4, 7, 8 164.6197 8.071 4, 8 24.455 2, 7 24.324 6, 8 24.423 4, 8 24.342 4, 7, 8 56.114 2, 3, 4, 7 102.920 2, 5, 6, 7, 8 164.6118 8.062 2, 7 24.415 2, 4 24.322 4, 8 24.406 6, 7 24.329 3, 7, 8 56.109 1, 2, 3, 8 102.912 1, 3, 6, 7, 8 164.598

2, 3 24.413 4, 8 24.319 2, 5 24.401 3, 6 24.328 6, 7, 8 56.105 1, 2, 4, 7 102.910 1, 2, 3, 7, 8 164.598 6, 7 24.413 1, 6 24.308 3, 6 24.382 1, 5 24.328 2, 3, 8 56.101 1, 3, 6, 8 102.902 1, 4, 6, 7, 8 164.597 3, 6 24.412 3, 6 24.265 2, 7 24.362 2, 7 24.328 1, 5, 8 56.098 1, 4, 6, 8 102.902 2, 3, 4, 7, 8 164.597 2, 8 24.409 3, 4 24.264 7, 8 24.357 2, 3 24.326 1, 5, 7 56.098 1, 3, 6, 7 102.901 2, 3, 5, 7, 8 164.591 2, 4 24.408 1, 5 24.263 2, 8 24.353 5, 7 24.305 1, 3, 8 56.098 1, 4, 6, 7 102.901 1, 2, 6, 7, 8 164.591 6, 8 24.408 3, 5 24.260 4, 6 24.343 3, 5 24.304 5, 7, 8 56.078 3, 4, 7, 8 102.893 2, 4, 5, 7, 8 164.590 4, 6 24.406 6, 7 24.257 5, 7 24.342 1, 7 24.302 3, 6, 7 56.064 2, 3, 7, 8 102.892 1, 2, 5, 6, 7 164.578 7, 8 24.324 4, 6 24.255 5, 8 24.333 1, 3 24.301 3, 6, 8 56.061 2, 3, 4, 8 102.890 1, 3, 4, 5, 7 164.568 3, 4 24.321 1, 3 24.255 1, 7 24.327 4, 6 24.281 1, 4, 7 56.060 2, 5, 7, 8 102.882 2, 3, 6, 7, 8 164.565 1, 5 24.319 5, 7 24.253 1, 5 24.325 6, 8 24.281 2, 4, 7 56.059 2, 6, 7, 8 102.882 1, 2, 3, 4, 7 164.564 1, 7 24.313 4, 5 24.251 1, 8 24.318 2, 4 24.280 2, 3, 7 56.056 1, 5, 7, 8 102.881 2, 4, 6, 7, 8 164.564 5, 7 24.313 2, 8 24.248 2, 3 24.313 2, 8 24.280 1, 3, 7 56.053 1, 2, 4, 8 102.880 1, 3, 5, 6, 7 164.563 1, 3 24.312 1, 7 24.247 3, 5 24.293 4, 5 24.257 3, 5, 8 56.039 1, 2, 3, 7 102.879 1, 4, 5, 6, 7 164.562 3, 5 24.312 1, 4 24.245 5, 6 24.292 5, 8 24.257 3, 5, 7 56.039 2, 3, 6, 8 102.872 1, 2, 3, 5, 7 164.559 1, 8 24.308 1, 2 24.186 1, 3 24.278 1, 4 24.254 5, 6, 7 56.035 1, 3, 5, 8 102.872 1, 2, 4, 5, 7 164.558 5, 8 24.308 7, 8 24.183 2, 4 24.274 1, 8 24.254 5, 6, 8 56.032 2, 4, 6, 8 102.872 1, 2, 5, 6, 8 164.557 1, 4 24.306 6, 8 24.181 4, 5 24.253 7, 8 24.253 2, 5, 6 56.026 1, 4, 5, 8 102.871 1, 3, 4, 5, 8 164.547 4, 5 24.306 5, 8 24.177 1, 4 24.238 3, 4 24.251 4, 6, 7 56.025 1, 2, 5, 8 102.871 1, 3, 4, 6, 7 164.542 5, 6 24.280 1, 8 24.171 3, 4 24.228 5, 6 24.218 4, 6, 8 56.022 2, 5, 6, 8 102.871 1, 3, 5, 6, 8 164.541 1, 2 24.266 5, 6 24.135 1, 2 24.189 1, 2 24.202 2, 7, 8 56.017 2, 3, 6, 7 102.871 1, 4, 5, 6, 8 164.540

1, 7, 8 56.017 1, 3, 5, 7 102.871 1, 2, 3, 5, 8 164.537 1, 4, 8 56.012 1, 2, 6, 8 102.870 1, 2, 4, 5, 8 164.536 2, 4, 8 56.011 2, 4, 6, 7 102.870 2, 3, 4, 5, 7 164.535 3, 4, 7 55.999 1, 5, 6, 8 102.870 1, 2, 3, 6, 7 164.533 4, 5, 8 55.996 1, 4, 5, 7 102.870 1, 2, 4, 6, 7 164.531 4, 5, 7 55.996 1, 2, 5, 7 102.870 2, 3, 5, 6, 7 164.530 1, 5, 6 55.978 2, 5, 6, 7 102.870 2, 4, 5, 6, 7 164.528 3, 4, 8 55.952 1, 2, 6, 7 102.869 3, 4, 5, 7, 8 164.523 1, 2, 5 55.939 1, 5, 6, 7 102.869 1, 3, 4, 6, 8 164.520 2, 3, 6 55.934 3, 6, 7, 8 102.843 1, 2, 3, 4, 8 164.520 1, 3, 6 55.931 4, 6, 7, 8 102.843 3, 5, 6, 7, 8 164.518 3, 5, 6 55.919 2, 3, 5, 8 102.842 4, 5, 6, 7, 8 164.516 1, 2, 6 55.919 3, 4, 6, 8 102.841 2, 3, 4, 5, 8 164.513 2, 3, 5 55.910 2, 4, 5, 8 102.841 1, 2, 3, 6, 8 164.511 1, 3, 5 55.907 2, 3, 5, 7 102.840 1, 2, 4, 6, 8 164.510 1, 4, 6 55.893 3, 4, 6, 7 102.840 2, 3, 4, 6, 7 164.509 2, 4, 6 55.892 2, 4, 5, 7 102.840 2, 3, 5, 6, 8 164.508 1, 2, 7 55.886 1, 3, 4, 6 102.829 2, 4, 5, 6, 8 164.507 1, 2, 8 55.886 3, 5, 7, 8 102.813 3, 4, 6, 7, 8 164.497 4, 5, 6 55.876 4, 5, 7, 8 102.812 2, 3, 4, 6, 8 164.487 1, 4, 5 55.866 3, 4, 5, 8 102.811 3, 4, 5, 6, 7 164.461 2, 4, 5 55.865 3, 4, 5, 7 102.810 3, 4, 5, 6, 8 164.440 3, 4, 6 55.833 3, 5, 6, 8 102.801 1, 3, 4, 5, 6 164.407 3, 4, 5 55.806 4, 5, 6, 8 102.801 1, 2, 3, 5, 6 164.398 2, 3, 4 55.748 3, 5, 6, 7 102.800 1, 2, 4, 5, 6 164.397 1, 3, 4 55.745 4, 5, 6, 7 102.800 2, 3, 4, 5, 6 164.374 1, 2, 3 53.767 2, 3, 4, 6 102.799 1, 2, 3, 4, 6 159.989 1, 2, 4 53.718 1, 3, 4, 5 102.798 1, 2, 3, 4, 5 154.804

1, 2, 3, 6 102.7891, 3, 5, 6 102.7891, 2, 4, 6 102.7891, 4, 5, 6 102.7881, 2, 5, 6 102.7882, 3, 4, 5 102.7682, 3, 5, 6 102.7581, 2, 4, 5 102.7582, 4, 5, 6 102.7581, 2, 7, 8 102.7325, 6, 7, 8 102.7323, 4, 5, 6 102.7281, 2, 3, 5 99.4181, 2, 3, 4 97.303

Mg0.25 Al0.50 Mg0.75 Mg1.25Mg1.00Mg0.50Mg0.25Al0.25Al0.50

28

Evaluation of cation–surface interactions

Multiple cations may occupy the ditrigonal cavities of the model supercells with variousconfigurations. They are attracted by the substitutions but simultaneously repel eachother. The energy of such point-like charge systems depends linearly on the net 1/r,which consists of an attractive part and a repulsive part. The attractive part can beevaluated by summing cation–substitution inverse distances within the cut-off radius, asdescribed before. Similarly, the repulsive part can be evaluated by summing cation–cation inverse distances. To account for different charges and interaction strengths, bothattractive and repulsive parts must be scaled by the product of the unit charges q of theinteracting species. For the substitutions, the value of qj is taken as -1, whereas for thecations, the value of qi is taken as the formal charge, i.e. +1 for Na(I) and +2 for Ca(II).Finally, the net 1/r is evaluated by subtracting the repulsive part from the attractivepart according to Equation 2:

rqq

rqq

r iiji111 (2)

In equation 2, the product of qiqj is taken as an absolute value to set the attractive part,i.e. the first term, positive, from which the repulsive part, i.e. the second term, issubtracted. By this definition, the higher the net 1/r is for a cation configuration, themore favourable that configuration is in energy. In Publication I, this dependency wasdemonstrated to be linear in the case of two Mg-substitutions and two Na(I) cations,similarly to Figure 10. This information may be used as a tool for qualitative evaluationof cation configuration energies in different systems.

A grid-based code was developed, which generated all the possible cation configurationsfor the studied systems and evaluated the related net 1/r values. In the evaluation, theinterlayer cations were constrained in the grid points set in the centers of ditrigonalcavities, approximately 1 Å above the surface oxygens. The evaluated net 1/r valuesare presented in descending order for Na(I) and Ca(II) configurations in differentlysubstituted systems in Figures 12 and 13, respectively. The cation configurationsassociated with the evaluated values are designated with comma separated numbers.These numbers refer to the cation occupied ditrigonal cavities within the modelsupercells, as denoted in Figure 9A. Note that the absolute net 1/r values are onlycomparable within the same system but not between different systems.

The evaluated 1/r values provide a qualitative estimate on the cation configurationenergies within differently substituted systems. According to Figure 12, increasingsubstitution density increases the number of possible Na(I) configurations and smoothensthe estimated energy (colour) differences. However, this only applies up to a substitutiondensity of 1.00 per unit cell, after which the increased Na(I) population limits the numberof configurations. For Ca(II), Figure 13 show less configurations with more discretenessin the energy distributions. The discreteness is emphasized by Al-substitutions, also in thecase of Na(I), since their charge is effectively more localized.

27

Figure 12. Evaluated net 1/r values for Na(I) configurations in differently substituted systems.The configurations outlined with a box were selected for DFT calculations, according to whichthe energy minimum configurations are highlighted in green.

3 8.225 2, 6 24.520 4, 7 24.435 3, 8 24.486 3, 7 24.437 1, 6, 7 56.171 1, 4, 7, 8 102.953 1, 2, 5, 7, 8 164.6404 8.183 4, 7 24.501 3, 7 24.404 1, 6 24.455 4, 7 24.431 1, 6, 8 56.168 1, 3, 4, 7 102.950 1, 3, 4, 7, 8 164.6306 8.176 3, 8 24.501 2, 5 24.380 4, 7 24.455 3, 8 24.430 2, 5, 8 56.146 1, 6, 7, 8 102.943 1, 3, 5, 7, 8 164.6255 8.158 3, 7 24.466 3, 8 24.369 3, 7 24.454 2, 5 24.395 2, 5, 7 56.145 2, 4, 7, 8 102.923 1, 4, 5, 7, 8 164.6232 8.096 2, 5 24.460 2, 6 24.344 2, 6 24.450 1, 6 24.394 2, 6, 7 56.126 1, 3, 7, 8 102.922 1, 5, 6, 7, 8 164.6211 8.091 1, 6 24.459 2, 3 24.331 6, 7 24.431 2, 6 24.378 2, 6, 8 56.123 1, 3, 4, 8 102.921 1, 2, 4, 7, 8 164.6197 8.071 4, 8 24.455 2, 7 24.324 6, 8 24.423 4, 8 24.342 4, 7, 8 56.114 2, 3, 4, 7 102.920 2, 5, 6, 7, 8 164.6118 8.062 2, 7 24.415 2, 4 24.322 4, 8 24.406 6, 7 24.329 3, 7, 8 56.109 1, 2, 3, 8 102.912 1, 3, 6, 7, 8 164.598

2, 3 24.413 4, 8 24.319 2, 5 24.401 3, 6 24.328 6, 7, 8 56.105 1, 2, 4, 7 102.910 1, 2, 3, 7, 8 164.598 6, 7 24.413 1, 6 24.308 3, 6 24.382 1, 5 24.328 2, 3, 8 56.101 1, 3, 6, 8 102.902 1, 4, 6, 7, 8 164.597 3, 6 24.412 3, 6 24.265 2, 7 24.362 2, 7 24.328 1, 5, 8 56.098 1, 4, 6, 8 102.902 2, 3, 4, 7, 8 164.597 2, 8 24.409 3, 4 24.264 7, 8 24.357 2, 3 24.326 1, 5, 7 56.098 1, 3, 6, 7 102.901 2, 3, 5, 7, 8 164.591 2, 4 24.408 1, 5 24.263 2, 8 24.353 5, 7 24.305 1, 3, 8 56.098 1, 4, 6, 7 102.901 1, 2, 6, 7, 8 164.591 6, 8 24.408 3, 5 24.260 4, 6 24.343 3, 5 24.304 5, 7, 8 56.078 3, 4, 7, 8 102.893 2, 4, 5, 7, 8 164.590 4, 6 24.406 6, 7 24.257 5, 7 24.342 1, 7 24.302 3, 6, 7 56.064 2, 3, 7, 8 102.892 1, 2, 5, 6, 7 164.578 7, 8 24.324 4, 6 24.255 5, 8 24.333 1, 3 24.301 3, 6, 8 56.061 2, 3, 4, 8 102.890 1, 3, 4, 5, 7 164.568 3, 4 24.321 1, 3 24.255 1, 7 24.327 4, 6 24.281 1, 4, 7 56.060 2, 5, 7, 8 102.882 2, 3, 6, 7, 8 164.565 1, 5 24.319 5, 7 24.253 1, 5 24.325 6, 8 24.281 2, 4, 7 56.059 2, 6, 7, 8 102.882 1, 2, 3, 4, 7 164.564 1, 7 24.313 4, 5 24.251 1, 8 24.318 2, 4 24.280 2, 3, 7 56.056 1, 5, 7, 8 102.881 2, 4, 6, 7, 8 164.564 5, 7 24.313 2, 8 24.248 2, 3 24.313 2, 8 24.280 1, 3, 7 56.053 1, 2, 4, 8 102.880 1, 3, 5, 6, 7 164.563 1, 3 24.312 1, 7 24.247 3, 5 24.293 4, 5 24.257 3, 5, 8 56.039 1, 2, 3, 7 102.879 1, 4, 5, 6, 7 164.562 3, 5 24.312 1, 4 24.245 5, 6 24.292 5, 8 24.257 3, 5, 7 56.039 2, 3, 6, 8 102.872 1, 2, 3, 5, 7 164.559 1, 8 24.308 1, 2 24.186 1, 3 24.278 1, 4 24.254 5, 6, 7 56.035 1, 3, 5, 8 102.872 1, 2, 4, 5, 7 164.558 5, 8 24.308 7, 8 24.183 2, 4 24.274 1, 8 24.254 5, 6, 8 56.032 2, 4, 6, 8 102.872 1, 2, 5, 6, 8 164.557 1, 4 24.306 6, 8 24.181 4, 5 24.253 7, 8 24.253 2, 5, 6 56.026 1, 4, 5, 8 102.871 1, 3, 4, 5, 8 164.547 4, 5 24.306 5, 8 24.177 1, 4 24.238 3, 4 24.251 4, 6, 7 56.025 1, 2, 5, 8 102.871 1, 3, 4, 6, 7 164.542 5, 6 24.280 1, 8 24.171 3, 4 24.228 5, 6 24.218 4, 6, 8 56.022 2, 5, 6, 8 102.871 1, 3, 5, 6, 8 164.541 1, 2 24.266 5, 6 24.135 1, 2 24.189 1, 2 24.202 2, 7, 8 56.017 2, 3, 6, 7 102.871 1, 4, 5, 6, 8 164.540

1, 7, 8 56.017 1, 3, 5, 7 102.871 1, 2, 3, 5, 8 164.537 1, 4, 8 56.012 1, 2, 6, 8 102.870 1, 2, 4, 5, 8 164.536 2, 4, 8 56.011 2, 4, 6, 7 102.870 2, 3, 4, 5, 7 164.535 3, 4, 7 55.999 1, 5, 6, 8 102.870 1, 2, 3, 6, 7 164.533 4, 5, 8 55.996 1, 4, 5, 7 102.870 1, 2, 4, 6, 7 164.531 4, 5, 7 55.996 1, 2, 5, 7 102.870 2, 3, 5, 6, 7 164.530 1, 5, 6 55.978 2, 5, 6, 7 102.870 2, 4, 5, 6, 7 164.528 3, 4, 8 55.952 1, 2, 6, 7 102.869 3, 4, 5, 7, 8 164.523 1, 2, 5 55.939 1, 5, 6, 7 102.869 1, 3, 4, 6, 8 164.520 2, 3, 6 55.934 3, 6, 7, 8 102.843 1, 2, 3, 4, 8 164.520 1, 3, 6 55.931 4, 6, 7, 8 102.843 3, 5, 6, 7, 8 164.518 3, 5, 6 55.919 2, 3, 5, 8 102.842 4, 5, 6, 7, 8 164.516 1, 2, 6 55.919 3, 4, 6, 8 102.841 2, 3, 4, 5, 8 164.513 2, 3, 5 55.910 2, 4, 5, 8 102.841 1, 2, 3, 6, 8 164.511 1, 3, 5 55.907 2, 3, 5, 7 102.840 1, 2, 4, 6, 8 164.510 1, 4, 6 55.893 3, 4, 6, 7 102.840 2, 3, 4, 6, 7 164.509 2, 4, 6 55.892 2, 4, 5, 7 102.840 2, 3, 5, 6, 8 164.508 1, 2, 7 55.886 1, 3, 4, 6 102.829 2, 4, 5, 6, 8 164.507 1, 2, 8 55.886 3, 5, 7, 8 102.813 3, 4, 6, 7, 8 164.497 4, 5, 6 55.876 4, 5, 7, 8 102.812 2, 3, 4, 6, 8 164.487 1, 4, 5 55.866 3, 4, 5, 8 102.811 3, 4, 5, 6, 7 164.461 2, 4, 5 55.865 3, 4, 5, 7 102.810 3, 4, 5, 6, 8 164.440 3, 4, 6 55.833 3, 5, 6, 8 102.801 1, 3, 4, 5, 6 164.407 3, 4, 5 55.806 4, 5, 6, 8 102.801 1, 2, 3, 5, 6 164.398 2, 3, 4 55.748 3, 5, 6, 7 102.800 1, 2, 4, 5, 6 164.397 1, 3, 4 55.745 4, 5, 6, 7 102.800 2, 3, 4, 5, 6 164.374 1, 2, 3 53.767 2, 3, 4, 6 102.799 1, 2, 3, 4, 6 159.989 1, 2, 4 53.718 1, 3, 4, 5 102.798 1, 2, 3, 4, 5 154.804

1, 2, 3, 6 102.789 1, 3, 5, 6 102.789 1, 2, 4, 6 102.789 1, 4, 5, 6 102.788 1, 2, 5, 6 102.788 2, 3, 4, 5 102.768 2, 3, 5, 6 102.758 1, 2, 4, 5 102.758 2, 4, 5, 6 102.758 1, 2, 7, 8 102.732 5, 6, 7, 8 102.732 3, 4, 5, 6 102.728 1, 2, 3, 5 99.418 1, 2, 3, 4 97.303

Mg0.25 Al0.50 Mg0.75 Mg1.25Mg1.00Mg0.50Mg0.25Al0.25Al0.50

28

Figure 13. Evaluated net 1/r values for Ca(II) configurations in differently substituted systems.The configurations outlined with a box were selected for DFT calculations, according to whichthe energy minimum configurations are highlighted in green.

Selection of cation configurations for DFT calculations

Based on the evaluated net 1/r values, four different cation configurations per systemwere selected for DFT calculations. The emphasis of the selected configurations was seton the highest evaluated net 1/r values to make sure that the configurationcorresponding to or close to the global energy minimum is found. Instead, theconfigurations with the lowest evaluated net 1/r values were represented only by oneconfiguration for the sole purpose of estimating the range of configurational energies foreach system. In Figures 12 and 13, the selected configurations are outlined with a boxand the energy minimum configurations according to the DFT calculations arehighlighted in green. The energy minimum configurations do not necessarily match thehighest evaluated net 1/r values since small shifts in the cation positions occurred due tothe structural optimization in the DFT calculations, as described in Publication I.

Calculation of cation–surface interaction energies

The adsorption process of n cations (X) with formal charge q on the interlayer surfacesof montmorillonite (MMT) which contain nq substitutions may be presented via thefollowing reduction–oxidation reaction equation:

n X + MMT X MMT

2 32.372 3 32.263 6 32.363 7 32.275 3, 8 95.5826 32.369 2 32.263 7 32.347 3 32.273 4, 7 95.5797 32.319 7 32.249 8 32.329 6 32.218 1, 6 95.5373 32.315 4 32.244 3 32.249 2 32.214 4, 8 95.4578 32.308 6 32.129 2 32.225 4 32.179 3, 7 95.4554 32.305 5 32.120 5 32.184 8 32.179 2, 5 95.4161 32.169 1 32.109 4 32.169 1 32.174 2, 6 95.3525 32.169 8 32.097 1 32.156 5 32.168 1, 5 95.351

1, 8 95.121 6, 8 95.121 1, 7 95.119 6, 7 95.119 1, 3 95.116 3, 6 95.116 1, 4 95.116 4, 6 95.116 2, 8 95.061 5, 8 95.060 2, 7 95.058 5, 7 95.058 2, 3 95.056 3, 5 95.055 2, 4 95.055 4, 5 95.055 7, 8 94.862 3, 4 94.854 5, 6 94.753 1, 2 94.732

Al0.50 Al0.50 Mg0.50 Mg1.00Mg0.25Al0.25

31

In this reaction, n number of non-charged species X adsorb on the interlayer surfaces ofnon-charged, electron-deficient montmorillonite and donate nq electrons to the layerstructure. As a result, the montmorillonite layer is reduced into a negatively charged ionand X species are oxidized into positively charged cations which remain associated withmontmorillonite to maintain the total charge neutrality. The total energy change, Etot,associated with this reaction may be written as the total energy difference between thereactants and products:

(X)(MMT))MMTX(tot nEEEE nq-qn (3)

Division of this equation by n yields the average reaction energy per species X, EX:

(X)(MMT))MMTX(X E

nEEE

nq-qn (4)

The fraction in the above equation describes the average interaction energy betweenspecies X and montmorillonite interlayer surfaces, whereas the final term, E(X),describes the energy of species X outside of montmorillonite. Since the interest of thisstudy is within the interlayer space of montmorillonite, EX may be treated as a constant(energy of species X in vacuum) and excluded from the equation as redundant. Theremaining equation that now describes the average cation–surface interaction energywill be referred to as E:

nEEE

nq-qn (MMT))MMTX( (5)

To calculate E for Na(I) and Ca(II), the energy terms in Equation 5 are substituted withthe total energies obtained from DFT calculations. )MMTX( nq-q

nE is the total energyof a montmorillonite model with a selected cation configuration, whereas (MMT)Ecorresponds to the total energy of the same model but in a non-charged state and withoutcationic species. The n is simply the number of charge compensating cations within themodel supercell. The sign of E is always negative for the presented calculations, whichindicates that energy is released, i.e. the system is stabilized by the introduction ofcations.

The results

The obtained E for Na(I) and Ca(II) based on the minimum energy cationconfigurations are presented in Tables 3–4 with different substitution compositions. Thevalues for E are given per elementary charge unit, and therefore the E values for Ca(II)have been divided by a factor of 2. The red bars included in the tables graphicallyrepresent E below –400 kJ mol-1 e-1 and help in comparison of the values. The rangeindicates the estimated energy difference between the minimum and maximum energycation configurations for the systems and is given in the E units.

30

Figure 13. Evaluated net 1/r values for Ca(II) configurations in differently substituted systems.The configurations outlined with a box were selected for DFT calculations, according to whichthe energy minimum configurations are highlighted in green.

Selection of cation configurations for DFT calculations

Based on the evaluated net 1/r values, four different cation configurations per systemwere selected for DFT calculations. The emphasis of the selected configurations was seton the highest evaluated net 1/r values to make sure that the configurationcorresponding to or close to the global energy minimum is found. Instead, theconfigurations with the lowest evaluated net 1/r values were represented only by oneconfiguration for the sole purpose of estimating the range of configurational energies foreach system. In Figures 12 and 13, the selected configurations are outlined with a boxand the energy minimum configurations according to the DFT calculations arehighlighted in green. The energy minimum configurations do not necessarily match thehighest evaluated net 1/r values since small shifts in the cation positions occurred due tothe structural optimization in the DFT calculations, as described in Publication I.

Calculation of cation–surface interaction energies

The adsorption process of n cations (X) with formal charge q on the interlayer surfacesof montmorillonite (MMT) which contain nq substitutions may be presented via thefollowing reduction–oxidation reaction equation:

n X + MMT X MMT

2 32.372 3 32.263 6 32.363 7 32.275 3, 8 95.5826 32.369 2 32.263 7 32.347 3 32.273 4, 7 95.5797 32.319 7 32.249 8 32.329 6 32.218 1, 6 95.5373 32.315 4 32.244 3 32.249 2 32.214 4, 8 95.4578 32.308 6 32.129 2 32.225 4 32.179 3, 7 95.4554 32.305 5 32.120 5 32.184 8 32.179 2, 5 95.4161 32.169 1 32.109 4 32.169 1 32.174 2, 6 95.3525 32.169 8 32.097 1 32.156 5 32.168 1, 5 95.351

1, 8 95.121 6, 8 95.121 1, 7 95.119 6, 7 95.119 1, 3 95.116 3, 6 95.116 1, 4 95.116 4, 6 95.116 2, 8 95.061 5, 8 95.060 2, 7 95.058 5, 7 95.058 2, 3 95.056 3, 5 95.055 2, 4 95.055 4, 5 95.055 7, 8 94.862 3, 4 94.854 5, 6 94.753 1, 2 94.732

Al0.50 Al0.50 Mg0.50 Mg1.00Mg0.25Al0.25

29

In this reaction, n number of non-charged species X adsorb on the interlayer surfaces ofnon-charged, electron-deficient montmorillonite and donate nq electrons to the layerstructure. As a result, the montmorillonite layer is reduced into a negatively charged ionand X species are oxidized into positively charged cations which remain associated withmontmorillonite to maintain the total charge neutrality. The total energy change, Etot,associated with this reaction may be written as the total energy difference between thereactants and products:

(X)(MMT))MMTX(tot nEEEE nq-qn (3)

Division of this equation by n yields the average reaction energy per species X, EX:

(X)(MMT))MMTX(X E

nEEE

nq-qn (4)

The fraction in the above equation describes the average interaction energy betweenspecies X and montmorillonite interlayer surfaces, whereas the final term, E(X),describes the energy of species X outside of montmorillonite. Since the interest of thisstudy is within the interlayer space of montmorillonite, EX may be treated as a constant(energy of species X in vacuum) and excluded from the equation as redundant. Theremaining equation that now describes the average cation–surface interaction energywill be referred to as E:

nEEE

nq-qn (MMT))MMTX( (5)

To calculate E for Na(I) and Ca(II), the energy terms in Equation 5 are substituted withthe total energies obtained from DFT calculations. )MMTX( nq-q

nE is the total energyof a montmorillonite model with a selected cation configuration, whereas (MMT)Ecorresponds to the total energy of the same model but in a non-charged state and withoutcationic species. The n is simply the number of charge compensating cations within themodel supercell. The sign of E is always negative for the presented calculations, whichindicates that energy is released, i.e. the system is stabilized by the introduction ofcations.

The results

The obtained E for Na(I) and Ca(II) based on the minimum energy cationconfigurations are presented in Tables 3–4 with different substitution compositions. Thevalues for E are given per elementary charge unit, and therefore the E values for Ca(II)have been divided by a factor of 2. The red bars included in the tables graphicallyrepresent E below –400 kJ mol-1 e-1 and help in comparison of the values. The rangeindicates the estimated energy difference between the minimum and maximum energycation configurations for the systems and is given in the E units.

30

Table 3. E for Mg-systems.

Table 4. E for Mg-, Al- and Mg/Al-systems.

The results show that E is clearly more negative for Na(I) than for the moreelectronegative Ca(II). The variations in E are rather small between differentlysubstituted systems, up to 32 kJ mol-1 e-1 for Na(I) and 18 kJ mol-1 e-1 for Ca(II). Forcomparison, the energy differences between cation configurations within each systemare higher, up to 36 kJ mol-1 e-1 for Na(I) and up to 40 kJ mol-1 e-1 for Ca(II). Despite thesmall differences in E, some important trends arose.

In Table 3, E is given for systems with varying Mg-substitution density. Interestingly,the E of Na(I) is found to increase with an increasing substitution density, whereas theopposite behaviour is indicated for Ca(II). The behaviour of Na(I) is explained by the 1:1ratio between Na(I) and the substitutions, which allows the flexible distribution of Na(I)over the most negatively charged surface areas – there is one Na(I) to compensate for thenegative net charge of each substitution. However, an increasing number of substitutionsand Na(I) reduce the relaxation capabilities of the surface, thus E is increased. UnlikeNa(I), divalent Ca(II) is unable to interact optimally with the surface of a system with alow density of dispersed substitutions. Thus, when the average distance between Ca(II)and the substitutions is decreased by the increasing substitution density, the interactionsbecome more optimal and the E of Ca(II) is decreased.

Cation System RangeNa(I) Mg0.25 573 36Na(I) Mg0.50 570 20Na(I) Mg0.75 567 27Na(I) Mg1.00 558 7Na(I) Mg1.25 558 11Ca(II) Mg0.50 500 13Ca(II) Mg1.00 511 49

E (kJ mol-1 e-1)

Cation System RangeNa(I) Al0.50 591 33Na(I) Al0.50 585 31Na(I) Mg0.25Al0.25 576 30Na(I) Mg0.50 570 20Ca(II) Al0.50 518 32Ca(II) Al0.50 511 34Ca(II) Mg0.25Al0.25 518 37Ca(II) Mg0.50 500 13

E (kJ mol-1 e-1)

33

In Table 4, E is given for systems with different combinations of Mg- and Al-substitutions. The substitution density is constant, i.e. 0.50 per unit cell. As could beexpected, the trend of the E values for Na(I) and Ca(II) depend on the distribution ofsubstitutions between tetrahedral and octahedral sheets: the lowest E values areobtained with Al-substitutions in the same tetrahedral sheet, whereas the highest Evalues are obtained with Mg-substitutions in the octahedral sheet. However, a partialexception in the trend is observed for Ca(II) in the case of the Mg0.25Al0.25-system.Although half of the substitutions in this system locate in the octahedral sheet, the E ofthis system is identical with the Al0.50-system, where all of the substitutions locate in thesame tetrahedral sheet. This is likely related to the structural tension produced by the Al-substitutions in the same tetrahedral sheet, that hinders the surface relaxation aroundCa(II) and increases E. The effect also applies to Na(I), but since two Na(I) can interactwith the dispersed Al-substitutions more efficiently, the interactions compensate for thehindered surface relaxation and no deviation in the trend of E is observed.

In Tables 3–4, the range of cation configuration energies are generally found to followan opposite trend with E. In other words, the range of cation configuration energies isfound to decrease when E increases. The trend can be rationalized on the basis ofsurface charge distribution which becomes more homogenous when the substitutiondensity or the proportion of substitutions in the octahedral sheet is increased. Theincrease of surface charge homogeneity decreases the total energy difference betweencation configurations.

4.4 Effect of Mg–Mg distance on system energetics

To complement the presented results, the effect of substitution–substitution distance oncation–surface interaction and system stability was studied. This was performed brieflywith 0.50 Mg-substitutions per unit cell. The Mg–Mg distance was varied in stepsbetween the 1st and 4th neighbouring positions, and the energy minimum configurationswere determined for interlayer cations at each step, as described in Section 4.3. The exactpositions or arrangements of the substitutions were based on the energy minimumconfigurations, i.e. 1b, 2a, 3a and 4b, as obtained from Figure 8A in Section 3.2. Finally,

E for Na(I) and Ca(II) were calculated along with the stabilities of the systems (Tables5 and 6). The E corresponds to cation–surface interaction energy as defined in Section4.3, whereas the stabilities describe total energy differences between the whole systemson a relative scale. In other words, the calculated stabilities are affected by both cation–substitution and substitution–substitution interactions.

Table 5. Effect of Mg–Mg distance on E (kJ mol-1 e-1) of Na(I) and Ca(II).

Mg-arrangement 1b 2a 3a 4bNa(I) 566 568 568 570Ca(II) 509 519 512 500

32

Table 3. E for Mg-systems.

Table 4. E for Mg-, Al- and Mg/Al-systems.

The results show that E is clearly more negative for Na(I) than for the moreelectronegative Ca(II). The variations in E are rather small between differentlysubstituted systems, up to 32 kJ mol-1 e-1 for Na(I) and 18 kJ mol-1 e-1 for Ca(II). Forcomparison, the energy differences between cation configurations within each systemare higher, up to 36 kJ mol-1 e-1 for Na(I) and up to 40 kJ mol-1 e-1 for Ca(II). Despite thesmall differences in E, some important trends arose.

In Table 3, E is given for systems with varying Mg-substitution density. Interestingly,the E of Na(I) is found to increase with an increasing substitution density, whereas theopposite behaviour is indicated for Ca(II). The behaviour of Na(I) is explained by the 1:1ratio between Na(I) and the substitutions, which allows the flexible distribution of Na(I)over the most negatively charged surface areas – there is one Na(I) to compensate for thenegative net charge of each substitution. However, an increasing number of substitutionsand Na(I) reduce the relaxation capabilities of the surface, thus E is increased. UnlikeNa(I), divalent Ca(II) is unable to interact optimally with the surface of a system with alow density of dispersed substitutions. Thus, when the average distance between Ca(II)and the substitutions is decreased by the increasing substitution density, the interactionsbecome more optimal and the E of Ca(II) is decreased.

Cation System RangeNa(I) Mg0.25 573 36Na(I) Mg0.50 570 20Na(I) Mg0.75 567 27Na(I) Mg1.00 558 7Na(I) Mg1.25 558 11Ca(II) Mg0.50 500 13Ca(II) Mg1.00 511 49

E (kJ mol-1 e-1)

Cation System RangeNa(I) Al0.50 591 33Na(I) Al0.50 585 31Na(I) Mg0.25Al0.25 576 30Na(I) Mg0.50 570 20Ca(II) Al0.50 518 32Ca(II) Al0.50 511 34Ca(II) Mg0.25Al0.25 518 37Ca(II) Mg0.50 500 13

E (kJ mol-1 e-1)

31

In Table 4, E is given for systems with different combinations of Mg- and Al-substitutions. The substitution density is constant, i.e. 0.50 per unit cell. As could beexpected, the trend of the E values for Na(I) and Ca(II) depend on the distribution ofsubstitutions between tetrahedral and octahedral sheets: the lowest E values areobtained with Al-substitutions in the same tetrahedral sheet, whereas the highest Evalues are obtained with Mg-substitutions in the octahedral sheet. However, a partialexception in the trend is observed for Ca(II) in the case of the Mg0.25Al0.25-system.Although half of the substitutions in this system locate in the octahedral sheet, the E ofthis system is identical with the Al0.50-system, where all of the substitutions locate in thesame tetrahedral sheet. This is likely related to the structural tension produced by the Al-substitutions in the same tetrahedral sheet, that hinders the surface relaxation aroundCa(II) and increases E. The effect also applies to Na(I), but since two Na(I) can interactwith the dispersed Al-substitutions more efficiently, the interactions compensate for thehindered surface relaxation and no deviation in the trend of E is observed.

In Tables 3–4, the range of cation configuration energies are generally found to followan opposite trend with E. In other words, the range of cation configuration energies isfound to decrease when E increases. The trend can be rationalized on the basis ofsurface charge distribution which becomes more homogenous when the substitutiondensity or the proportion of substitutions in the octahedral sheet is increased. Theincrease of surface charge homogeneity decreases the total energy difference betweencation configurations.

4.4 Effect of Mg–Mg distance on system energetics

To complement the presented results, the effect of substitution–substitution distance oncation–surface interaction and system stability was studied. This was performed brieflywith 0.50 Mg-substitutions per unit cell. The Mg–Mg distance was varied in stepsbetween the 1st and 4th neighbouring positions, and the energy minimum configurationswere determined for interlayer cations at each step, as described in Section 4.3. The exactpositions or arrangements of the substitutions were based on the energy minimumconfigurations, i.e. 1b, 2a, 3a and 4b, as obtained from Figure 8A in Section 3.2. Finally,

E for Na(I) and Ca(II) were calculated along with the stabilities of the systems (Tables5 and 6). The E corresponds to cation–surface interaction energy as defined in Section4.3, whereas the stabilities describe total energy differences between the whole systemson a relative scale. In other words, the calculated stabilities are affected by both cation–substitution and substitution–substitution interactions.

Table 5. Effect of Mg–Mg distance on E (kJ mol-1 e-1) of Na(I) and Ca(II).

Mg-arrangement 1b 2a 3a 4bNa(I) 566 568 568 570Ca(II) 509 519 512 500

32

Table 6. Effect of Mg–Mg distance on the stability of Na(I) and Ca(II) systems (kJ/mol).

Mg-arrangement 1b 2a 3a 4bNa(I) +33 +8 +4 0*Ca(II) +42 0* +11 +33*Energy minimum reference

The results presented in Table 5 show that the E of Na(I) decreases slightly as the Mg–Mg distance increases, whereas the E of Ca(II) is at minimum when the Mg-substitutions occupy the 2nd neighbouring positions. The results show similarities withthe trend of the E that was obtained for different Mg-substitution compositions (Table3). This is explained by the fact that the increasing substitution density effectivelyreduces the average distance between the substitutions.

Interestingly, the calculated stabilities for the systems in Table 6 also follow similartrends to the E values presented in Table 5. This means that the Na(I) containing systemis the most stable when the Mg-substitutions are maximally dispersed, i.e. in the 4th

neighbouring positions, whereas the Ca(II) containing system is the most stable whenthe substitutions occupy the 2nd neighbouring positions. Importantly, the energydifferences between the calculated stabilities are much less than the energy differencesbetween the studied Mg-substitution arrangements in Section 3 (Figure 8A). This impliesthat the electrostatic cation–substitution interactions significantly compensate for thesubstitution–substitution repulsion and even stabilize the 2nd neighbouring Mg-positionsin the case of divalent Ca(II). Therefore, the type of cations in the interlayer space affectthe distribution of substitutions on a thermodynamic basis. These effects in combinationwith evolution, dynamics and the kinetics of the system may explain randomness ordifferences in the structure of montmorillonite and smectites in general.

35

5. Edge surfaces – structure and stabilityThe stability of edge surface structures was studied with pyrophyllite models to predictthe most probable edges exhibited by phyllosilicate particles. Pyrophyllite is a non-substituted dioctahedral 2:1 phyllosilicate and may be viewed as a generalization of othersimilar phyllosilicates, especially with low substitution densities, such asmontmorillonite. A detailed description of the study is presented in Publication II.

5.1 Cleavage method

The stability of pyrophyllite edges was determined by cleaving a pyrophyllite layer inseveral ways parallel to high atomic density lattice planes (Figure 14). Each cleavageresulted in two edge surfaces with broken bonds. Since such surfaces are unstable andreactive, they were terminated formally neutral by hydroxylation and protonation. Theprocess of termination was presented as a dissociative sorption of water on the cleavededges. Water was chosen as the terminating agent since the hydrogen to oxygen ratio inthe edge termination is 2:1 and it is likely the terminating agent in nature as well – thedissociative sorption of water has been studied on a variety of metal oxides, such assilica78, alumina79 and magnesium oxide.80 Water has also been used to describe thetermination of pyrophyllite in earlier studies.43,55,59

The process of cleavage and edge termination may be described as a reaction betweenthe pyrophyllite layer and water by the following equation:

n bulk + x H2O 2 edge–(H2O)x

In this reaction, a periodic pyrophyllite layer consisting of n bulk unit cells is cleavedand reacts with x water molecules that yield two terminated edge surface structures. Thecleavage energy, E, associated with this reaction may be written as the energydifference between the reactants and products, which on the basis of representativemodels takes the following form:

LxE nEEEE

2O)H((bulk)(edge2)(edge1) 2 (6)

E(edge1) and E(edge2) are the total energies of the edge models, whereas E(bulk) andE(H2O) are the total energies of the pyrophyllite unit cell and liquid water, respectively.The coefficients n and x are integers that preserve the stoichiometry of the reactionequation above. The L normalizes E with respect to length of cleavage and is equal to thewidth of the edge model repeating unit. The division by 2 accounts for two identical edgesurfaces in the edge model set-up. If E is even further divided by 2, edge surface energiesare obtained. However, the latter does not apply to asymmetric cleavages labeled with anasterix (*) in Figure 14. These cleavages correspond to two distinct terminated edgesurfaces for which only average surface energies can be determined.

34

Table 6. Effect of Mg–Mg distance on the stability of Na(I) and Ca(II) systems (kJ/mol).

Mg-arrangement 1b 2a 3a 4bNa(I) +33 +8 +4 0*Ca(II) +42 0* +11 +33*Energy minimum reference

The results presented in Table 5 show that the E of Na(I) decreases slightly as the Mg–Mg distance increases, whereas the E of Ca(II) is at minimum when the Mg-substitutions occupy the 2nd neighbouring positions. The results show similarities withthe trend of the E that was obtained for different Mg-substitution compositions (Table3). This is explained by the fact that the increasing substitution density effectivelyreduces the average distance between the substitutions.

Interestingly, the calculated stabilities for the systems in Table 6 also follow similartrends to the E values presented in Table 5. This means that the Na(I) containing systemis the most stable when the Mg-substitutions are maximally dispersed, i.e. in the 4th

neighbouring positions, whereas the Ca(II) containing system is the most stable whenthe substitutions occupy the 2nd neighbouring positions. Importantly, the energydifferences between the calculated stabilities are much less than the energy differencesbetween the studied Mg-substitution arrangements in Section 3 (Figure 8A). This impliesthat the electrostatic cation–substitution interactions significantly compensate for thesubstitution–substitution repulsion and even stabilize the 2nd neighbouring Mg-positionsin the case of divalent Ca(II). Therefore, the type of cations in the interlayer space affectthe distribution of substitutions on a thermodynamic basis. These effects in combinationwith evolution, dynamics and the kinetics of the system may explain randomness ordifferences in the structure of montmorillonite and smectites in general.

33

5. Edge surfaces – structure and stabilityThe stability of edge surface structures was studied with pyrophyllite models to predictthe most probable edges exhibited by phyllosilicate particles. Pyrophyllite is a non-substituted dioctahedral 2:1 phyllosilicate and may be viewed as a generalization of othersimilar phyllosilicates, especially with low substitution densities, such asmontmorillonite. A detailed description of the study is presented in Publication II.

5.1 Cleavage method

The stability of pyrophyllite edges was determined by cleaving a pyrophyllite layer inseveral ways parallel to high atomic density lattice planes (Figure 14). Each cleavageresulted in two edge surfaces with broken bonds. Since such surfaces are unstable andreactive, they were terminated formally neutral by hydroxylation and protonation. Theprocess of termination was presented as a dissociative sorption of water on the cleavededges. Water was chosen as the terminating agent since the hydrogen to oxygen ratio inthe edge termination is 2:1 and it is likely the terminating agent in nature as well – thedissociative sorption of water has been studied on a variety of metal oxides, such assilica78, alumina79 and magnesium oxide.80 Water has also been used to describe thetermination of pyrophyllite in earlier studies.43,55,59

The process of cleavage and edge termination may be described as a reaction betweenthe pyrophyllite layer and water by the following equation:

n bulk + x H2O 2 edge–(H2O)x

In this reaction, a periodic pyrophyllite layer consisting of n bulk unit cells is cleavedand reacts with x water molecules that yield two terminated edge surface structures. Thecleavage energy, E, associated with this reaction may be written as the energydifference between the reactants and products, which on the basis of representativemodels takes the following form:

LxE nEEEE

2O)H((bulk)(edge2)(edge1) 2 (6)

E(edge1) and E(edge2) are the total energies of the edge models, whereas E(bulk) andE(H2O) are the total energies of the pyrophyllite unit cell and liquid water, respectively.The coefficients n and x are integers that preserve the stoichiometry of the reactionequation above. The L normalizes E with respect to length of cleavage and is equal to thewidth of the edge model repeating unit. The division by 2 accounts for two identical edgesurfaces in the edge model set-up. If E is even further divided by 2, edge surface energiesare obtained. However, the latter does not apply to asymmetric cleavages labeled with anasterix (*) in Figure 14. These cleavages correspond to two distinct terminated edgesurfaces for which only average surface energies can be determined.

34

Figure 14. The (010), (130), (110) and (100) lattice planes in an orthogonally assignedpyrophyllite unit cell viewed along c-direction (big figure). The studied cleavages are viewedparallel to these lattice planes from the side of the layer (small figures). In the big figure, theoctahedral sheet is represented with a stick-ball model, whereas the tetrahedral sheets closer andfurther from the viewer are represented by dark and light grey tetrahedrons, respectively.

In addition to E, Gibbs free-energies of cleavage, G, were also estimated at 298 K.The estimation was based on an assumption that the entropy loss related to water sorptionis the determining factor for relative edge stability. The modeling studies of calcite81,82

and magnesium oxide80 surfaces have suggested that the contribution of entropy to thefree energy of water sorption is significant. On this basis, the energy terms in Equation6 were substituted with approximated Gibbs free-energies, G, as follows: G(bulk) E(bulk); G(edge) E(edge); G(H2O) E(H2O) S°(H2O)T, where S°(H2O) is theexperimental standard entropy of liquid water (70 J/K)83 and T is the temperature (298K). Note that if the water would be taken as gas, the contribution of entropy would bemuch higher in the estimation.

37

5.2 Cleavage energies

The calculated E and estimated G for the minimum energy edge structure geometriesare plotted versus sorbed water in Figure 15. Some of the cleavages in Figure 15 areassociated with a label (dw) which indicates that a water molecule was desorbed fromone of the cleaved edges as a result of structure optimization and surface relaxation. Thedesorbed water molecules were treated as non-sorbed water, hence the amount of sorbedwater for the labelled cleavages is less than ideally expected.

Figure 15. E (left) and G (right) plotted versus sorbed H2O per Å of cleavage.

According to E, the (110)A, (010)C, (100)A and (130)A cleavages correspond to themost stable edges parallel to each studied lattice plane. However, the range of E valuesis found to be very small, only about 10 kJ Å-1 mol-1, hence the most stable edgestructures cannot be predicted with certainty on the basis of E only. Instead, on thebasis of G, the range of cleavage energies is wider, approximately 35 kJ Å-1 mol-1,and the cleavage energies increase with the density of sorbed water. As a result, the moststable edges correspond to cleavages associated with the lowest density of sorbed water.Parallel to each studied lattice plane, these are (110)A, (010)A, (100)A and (130)A.Incidentally, the edges predicted by G are the same as predicted by E, except for(010)A which clearly supersedes (010)C in the cleavage energy on the basis of G.

36

Figure 14. The (010), (130), (110) and (100) lattice planes in an orthogonally assignedpyrophyllite unit cell viewed along c-direction (big figure). The studied cleavages are viewedparallel to these lattice planes from the side of the layer (small figures). In the big figure, theoctahedral sheet is represented with a stick-ball model, whereas the tetrahedral sheets closer andfurther from the viewer are represented by dark and light grey tetrahedrons, respectively.

In addition to E, Gibbs free-energies of cleavage, G, were also estimated at 298 K.The estimation was based on an assumption that the entropy loss related to water sorptionis the determining factor for relative edge stability. The modeling studies of calcite81,82

and magnesium oxide80 surfaces have suggested that the contribution of entropy to thefree energy of water sorption is significant. On this basis, the energy terms in Equation6 were substituted with approximated Gibbs free-energies, G, as follows: G(bulk) E(bulk); G(edge) E(edge); G(H2O) E(H2O) S°(H2O)T, where S°(H2O) is theexperimental standard entropy of liquid water (70 J/K)83 and T is the temperature (298K). Note that if the water would be taken as gas, the contribution of entropy would bemuch higher in the estimation.

35

5.2 Cleavage energies

The calculated E and estimated G for the minimum energy edge structure geometriesare plotted versus sorbed water in Figure 15. Some of the cleavages in Figure 15 areassociated with a label (dw) which indicates that a water molecule was desorbed fromone of the cleaved edges as a result of structure optimization and surface relaxation. Thedesorbed water molecules were treated as non-sorbed water, hence the amount of sorbedwater for the labelled cleavages is less than ideally expected.

Figure 15. E (left) and G (right) plotted versus sorbed H2O per Å of cleavage.

According to E, the (110)A, (010)C, (100)A and (130)A cleavages correspond to themost stable edges parallel to each studied lattice plane. However, the range of E valuesis found to be very small, only about 10 kJ Å-1 mol-1, hence the most stable edgestructures cannot be predicted with certainty on the basis of E only. Instead, on thebasis of G, the range of cleavage energies is wider, approximately 35 kJ Å-1 mol-1,and the cleavage energies increase with the density of sorbed water. As a result, the moststable edges correspond to cleavages associated with the lowest density of sorbed water.Parallel to each studied lattice plane, these are (110)A, (010)A, (100)A and (130)A.Incidentally, the edges predicted by G are the same as predicted by E, except for(010)A which clearly supersedes (010)C in the cleavage energy on the basis of G.

36

5.3 Particle shape

The equilibrium shape of the pyrophyllite particle was predicted on the basis of E andG. This was performed with the Wulff-construction method84,85 in which the surface

energy of a constant volume particle is minimized with respect to total surface area. Boththe E and G based constructions yielded close to identical hexagonal particle shapesdominated by (110) and (010) edges, while (100) edges are present only marginally(Figure 16). In both constructions, the (110) and (100) edges correspond to the (110)Aand (100)A cleavages, respectively, whereas the (010) edges appear with differentstructures: the E based construction predicts a structure that corresponds to the (010)Ccleavage, whereas the G based construction predicts a structure that corresponds tothe (010)A cleavage. The (130) edges do not appear at all in the constructions since theyare superseded by the more stable (110) and (010) edges.

The commonly observed morphologies for well crystallized phyllosilicate particles varyfrom hexagonal and rhombic shapes to elongated laths and fibers.40,43,56,86,87 The rhombicparticles are comprised of (110) edges, whereas the laths or even thinner fibers may beviewed as stretched hexagons: they are comprised of elongated (010) and shorter (110)edges which may be accompanied by (100) edges at the tips (Figure 16). Interestingly,it has been suggested that the laths and fibers of illites and mixed layer illite–smectitesare metastable kinetic products that result from the faster formation of (010) faces andtransform over time into a more stable hexagonal shape.86,87

Figure 16. Predicted, close to hexagonal shape of a pyrophyllite particle (left) and othercommonly observed phyllosilicate particle shapes (right) viewed along c-direction with similarorientation.

39

6. ConclusionsThis study has examined the structure and surfaces of planar 2:1 phyllosilicates. Theemphasis was on clay mineral montmorillonite which belongs to the group of smectitesand is the main component of bentonite clay. The scope of this study focused on theinteraction and arrangement of Mg- and Al-substitutions, their electrostatic nature andthe effect on interlayer cation surface interaction. Na(I) and Ca(II) were used asrepresentative interlayer cation species. The studied layer structure compositionsincluded 0.25 1.25 Mg-substitutions per unit cell, whereas the compositions for the Al-substitutions and a mix of Mg/Al-substitutions were limited to 0.50 per unit cell. Inaddition, the stability of various edge surfaces was determined based on pyrophyllitemodels.

The Mg- and Al-substitutions are found to repulse each other in the layer structure. Thisrepulsion is due to the larger size of the substitutions in comparison to unsubstituted atoms,which produce structural deformations and internal structural tension. To largely relax thistension, the substitutions must occupy 3rd or further neighbouring positions in the layerstructure. Therefore, the 0th, 1st and 2nd neighbouring positions are unlikely occupied inroom temperature on a thermodynamic basis. However, as demonstrated with the Mg-substituted systems, electrostatic cation substitution interactions effectively reducesubstitution substitution repulsion or even overcome it in the presence of divalent Ca(II)which is able to stabilize the 2nd neighbouring positions. These findings explain why theMg-substitutions have not been observed in the 1st neighbouring positions and providesupport and perspective for earlier studies.

In the layer structure, the substitutions are found to be the only significant charge defectsand resemble negative point-like charges. They carry approximately 75 % of the negativenet layer charge, whereas 25 % of the charge is deposited elsewhere in the layer. Hence,not only do the substitutions tend to disperse in the layer structure but so does a portionof the layer charge. Even so, most of the negative net charge still resides on thesubstitutions, which is why the distribution of interlayer surface charge is heavilyinfluenced by the positions of the substitutions. The interlayer cation surface interactionenergies are found to correlate linearly with cation substitution inverse distances in aperiodic lattice, in accordance with the negative point-like charge nature of thesubstitutions and Coulomb’s law.

The calculated cation surface interaction energies vary between 558–573 kJ mol-1 e-1

for Na(I) and 500–511 kJ mol-1 e-1 for Ca(II) in the range of 0.25–1.25 Mg-substitutionsper unit cell. Thus, the density of Mg-substitutions has only a small effect on interlayercation surface interaction. Instead, a slightly higher effect is obtained if the type ofsubstitutions is changed from Mg-substitutions to Al-substitutions at the composition of0.50 substitution per unit cell: the calculated cation surface interaction energies varybetween 570–591 kJ mol-1 e-1 for Na(I) and 500–518 kJ mol-1 e-1 for Ca(II). The lattereffect, however, may be expected to have a minimal impact in montmorillonites due tothe relatively low composition of Al-substitutions.9,10

38

5.3 Particle shape

The equilibrium shape of the pyrophyllite particle was predicted on the basis of E andG. This was performed with the Wulff-construction method84,85 in which the surface

energy of a constant volume particle is minimized with respect to total surface area. Boththe E and G based constructions yielded close to identical hexagonal particle shapesdominated by (110) and (010) edges, while (100) edges are present only marginally(Figure 16). In both constructions, the (110) and (100) edges correspond to the (110)Aand (100)A cleavages, respectively, whereas the (010) edges appear with differentstructures: the E based construction predicts a structure that corresponds to the (010)Ccleavage, whereas the G based construction predicts a structure that corresponds tothe (010)A cleavage. The (130) edges do not appear at all in the constructions since theyare superseded by the more stable (110) and (010) edges.

The commonly observed morphologies for well crystallized phyllosilicate particles varyfrom hexagonal and rhombic shapes to elongated laths and fibers.40,43,56,86,87 The rhombicparticles are comprised of (110) edges, whereas the laths or even thinner fibers may beviewed as stretched hexagons: they are comprised of elongated (010) and shorter (110)edges which may be accompanied by (100) edges at the tips (Figure 16). Interestingly,it has been suggested that the laths and fibers of illites and mixed layer illite–smectitesare metastable kinetic products that result from the faster formation of (010) faces andtransform over time into a more stable hexagonal shape.86,87

Figure 16. Predicted, close to hexagonal shape of a pyrophyllite particle (left) and othercommonly observed phyllosilicate particle shapes (right) viewed along c-direction with similarorientation.

37

6. ConclusionsThis study has examined the structure and surfaces of planar 2:1 phyllosilicates. Theemphasis was on clay mineral montmorillonite which belongs to the group of smectitesand is the main component of bentonite clay. The scope of this study focused on theinteraction and arrangement of Mg- and Al-substitutions, their electrostatic nature andthe effect on interlayer cation surface interaction. Na(I) and Ca(II) were used asrepresentative interlayer cation species. The studied layer structure compositionsincluded 0.25 1.25 Mg-substitutions per unit cell, whereas the compositions for the Al-substitutions and a mix of Mg/Al-substitutions were limited to 0.50 per unit cell. Inaddition, the stability of various edge surfaces was determined based on pyrophyllitemodels.

The Mg- and Al-substitutions are found to repulse each other in the layer structure. Thisrepulsion is due to the larger size of the substitutions in comparison to unsubstituted atoms,which produce structural deformations and internal structural tension. To largely relax thistension, the substitutions must occupy 3rd or further neighbouring positions in the layerstructure. Therefore, the 0th, 1st and 2nd neighbouring positions are unlikely occupied inroom temperature on a thermodynamic basis. However, as demonstrated with the Mg-substituted systems, electrostatic cation substitution interactions effectively reducesubstitution substitution repulsion or even overcome it in the presence of divalent Ca(II)which is able to stabilize the 2nd neighbouring positions. These findings explain why theMg-substitutions have not been observed in the 1st neighbouring positions and providesupport and perspective for earlier studies.

In the layer structure, the substitutions are found to be the only significant charge defectsand resemble negative point-like charges. They carry approximately 75 % of the negativenet layer charge, whereas 25 % of the charge is deposited elsewhere in the layer. Hence,not only do the substitutions tend to disperse in the layer structure but so does a portionof the layer charge. Even so, most of the negative net charge still resides on thesubstitutions, which is why the distribution of interlayer surface charge is heavilyinfluenced by the positions of the substitutions. The interlayer cation surface interactionenergies are found to correlate linearly with cation substitution inverse distances in aperiodic lattice, in accordance with the negative point-like charge nature of thesubstitutions and Coulomb’s law.

The calculated cation surface interaction energies vary between 558–573 kJ mol-1 e-1

for Na(I) and 500–511 kJ mol-1 e-1 for Ca(II) in the range of 0.25–1.25 Mg-substitutionsper unit cell. Thus, the density of Mg-substitutions has only a small effect on interlayercation surface interaction. Instead, a slightly higher effect is obtained if the type ofsubstitutions is changed from Mg-substitutions to Al-substitutions at the composition of0.50 substitution per unit cell: the calculated cation surface interaction energies varybetween 570–591 kJ mol-1 e-1 for Na(I) and 500–518 kJ mol-1 e-1 for Ca(II). The lattereffect, however, may be expected to have a minimal impact in montmorillonites due tothe relatively low composition of Al-substitutions.9,10

38

The findings imply that the energetics of cation–surface interaction is dominated by thetype of cations and the external matrix rather than layer structure composition. This is in-line with the experimental observations that show that the K(I) retention capacity ofsmectites correlates linearly with the layer charge but does not depend on the relativecomposition of Al-substitutions.11 Similarly, the relative composition of Al-substitutionshas been observed to have no effect on the Na(I) retention capacity of smectites, whereasthe Cs(I) retention capacity has surprisingly been found to decrease with increasing relativecomposition of Al-substitutions. It has been suggested that the different behaviour of Na(I)and Cs(I) arises from different hydration tendencies which affect their interaction with theinterlayer surfaces.12 Therefore, interlayer water content, not included in this thesis,requires more attention with different types of cations.

The introduction of water into interlayer space reduces electrostatic cation–surface (orcation–substitution) interactions. The water does not only screen these interactions but alsoincreases cation–surface distances due to the formation of cation hydration complexes andswelling. Thus, in addition to cation electronegativity and entropy effects, permeability ofthe cation electric field through interlayer water and the hydration tendency of cationslikely play the key role in understanding the full scale of cation–surface interactionmechanics and dynamics. These factors are required in order to obtain a completeexplanation for why the selectivity of montmorillonite is higher for Ca(II) than for Na(I)88

although the calculated cation surface interaction energies in this thesis are morefavourable for Na(I). The latter factors are also relevant for understanding the swellingbehaviour, since interlayer cations bind the layers into particles via surface cation surfaceinteractions.

As for the stability of edge surfaces, the calculated cleavage energies indicate close tosimilar stability for various edge surfaces. Therefore, the entropy effects associated withedge–water reaction dynamics play an important role for relative edge stability. Basedon the estimated free energies, the edge surfaces obtained by cleaving the fewest bondsappear to be the most stable, since they require the fewest sorbed water molecules forsurface termination. It is predicted that the (110) and (010) edge surfaces are dominantand that they yield a hexagonally shaped particle, which matches with experimentalobservations for well crystallized phyllosilicates. Further investigations should focus onthe evaluation of the reaction dynamics at the edge–water interface with varying solventand layer structure compositions – without forgetting the need for experimentalevidence.

Overall, the studies presented in this thesis provide fundamental information on thestructural features of montmorillonite, smectites and 2:1 phyllosilicates in general. Theresults help to understand and narrow down uncertainties related to anisotropy and theinternal heterogeneity of these minerals. This knowledge is required to fully realize thecharacteristic properties and diverse dynamic behaviour of phyllosilicates and tofacilitate the development of specifically tailored phyllosilicate related applications.Furthermore, the results are directly applicable for modelling purposes, such as swellingpressure simulations of smectite particles performed in our research group.89

41

AcknowledgementsThe work presented here was conducted during 2014–2016 at the Department ofChemistry, at the University of Eastern Finland. Financial support provided by PosivaOy, Finnish Funding Agency for Technology and Innovation TEKES, and the EuropeanUnion/European Regional Development Fund (ERDF) for the “Sliding Surfaces” projectis gratefully acknowledged. The computations were made possible by use of the FinnishGrid Infrastructure resources. The molecular structures and surfaces were visualizedwith VESTA.90

I am personally grateful to the current and former members of our research group,namely my supervisors Tapani Pakkanen, Janne Hirvi and Jukka Tanskanen and mycolleagues Linlin Sun and Chian Ye Ling. You have provided me valuable feedback andthe framework to carry out this research. I would also like to thank our collaboratorsfrom Posiva Oy and B+Tech Oy, especially Seppo Kasa for all his efforts towards ourproject and Timothy Schatzs for lending a touch of his expertise. To all the people of theChemistry Department, Café luola and the special “Sauna Division”: kudos for sharingsome memorable and cheerful moments!

Finally, I want to thank my mom, my dad and my sister, for being such a great, lovingand encouraging family to grow up with. Your support over the years is trulyappreciated.

40

The findings imply that the energetics of cation–surface interaction is dominated by thetype of cations and the external matrix rather than layer structure composition. This is in-line with the experimental observations that show that the K(I) retention capacity ofsmectites correlates linearly with the layer charge but does not depend on the relativecomposition of Al-substitutions.11 Similarly, the relative composition of Al-substitutionshas been observed to have no effect on the Na(I) retention capacity of smectites, whereasthe Cs(I) retention capacity has surprisingly been found to decrease with increasing relativecomposition of Al-substitutions. It has been suggested that the different behaviour of Na(I)and Cs(I) arises from different hydration tendencies which affect their interaction with theinterlayer surfaces.12 Therefore, interlayer water content, not included in this thesis,requires more attention with different types of cations.

The introduction of water into interlayer space reduces electrostatic cation–surface (orcation–substitution) interactions. The water does not only screen these interactions but alsoincreases cation–surface distances due to the formation of cation hydration complexes andswelling. Thus, in addition to cation electronegativity and entropy effects, permeability ofthe cation electric field through interlayer water and the hydration tendency of cationslikely play the key role in understanding the full scale of cation–surface interactionmechanics and dynamics. These factors are required in order to obtain a completeexplanation for why the selectivity of montmorillonite is higher for Ca(II) than for Na(I)88

although the calculated cation surface interaction energies in this thesis are morefavourable for Na(I). The latter factors are also relevant for understanding the swellingbehaviour, since interlayer cations bind the layers into particles via surface cation surfaceinteractions.

As for the stability of edge surfaces, the calculated cleavage energies indicate close tosimilar stability for various edge surfaces. Therefore, the entropy effects associated withedge–water reaction dynamics play an important role for relative edge stability. Basedon the estimated free energies, the edge surfaces obtained by cleaving the fewest bondsappear to be the most stable, since they require the fewest sorbed water molecules forsurface termination. It is predicted that the (110) and (010) edge surfaces are dominantand that they yield a hexagonally shaped particle, which matches with experimentalobservations for well crystallized phyllosilicates. Further investigations should focus onthe evaluation of the reaction dynamics at the edge–water interface with varying solventand layer structure compositions – without forgetting the need for experimentalevidence.

Overall, the studies presented in this thesis provide fundamental information on thestructural features of montmorillonite, smectites and 2:1 phyllosilicates in general. Theresults help to understand and narrow down uncertainties related to anisotropy and theinternal heterogeneity of these minerals. This knowledge is required to fully realize thecharacteristic properties and diverse dynamic behaviour of phyllosilicates and tofacilitate the development of specifically tailored phyllosilicate related applications.Furthermore, the results are directly applicable for modelling purposes, such as swellingpressure simulations of smectite particles performed in our research group.89

39

AcknowledgementsThe work presented here was conducted during 2014–2016 at the Department ofChemistry, at the University of Eastern Finland. Financial support provided by PosivaOy, Finnish Funding Agency for Technology and Innovation TEKES, and the EuropeanUnion/European Regional Development Fund (ERDF) for the “Sliding Surfaces” projectis gratefully acknowledged. The computations were made possible by use of the FinnishGrid Infrastructure resources. The molecular structures and surfaces were visualizedwith VESTA.90

I am personally grateful to the current and former members of our research group,namely my supervisors Tapani Pakkanen, Janne Hirvi and Jukka Tanskanen and mycolleagues Linlin Sun and Chian Ye Ling. You have provided me valuable feedback andthe framework to carry out this research. I would also like to thank our collaboratorsfrom Posiva Oy and B+Tech Oy, especially Seppo Kasa for all his efforts towards ourproject and Timothy Schatzs for lending a touch of his expertise. To all the people of theChemistry Department, Café luola and the special “Sauna Division”: kudos for sharingsome memorable and cheerful moments!

Finally, I want to thank my mom, my dad and my sister, for being such a great, lovingand encouraging family to grow up with. Your support over the years is trulyappreciated.

40

References1. Guggenheim, S.; Martin, R. T. Definition of clay and clay mineral: joint report of the AIPEA

nomenclature and CMS nomenclature committees. Clays Clay Miner. 1995, 43, 255-256.

2. Harvey, C. C.; Lagaly, G. In Developments in clay science; Bergaya, F., Theng, B. K. G.and Lagaly, G., Eds.; Elsevier Ltd: Oxford, UK, 2006; Vol. 1, pp 501-540.

3. Brigatti, M. F.; Galán, E.; Theng, B. K. G. In Developments in clay science; Bergaya, F.,Theng, B. K. G. and Lagaly, G., Eds.; Elsevier Ltd: Oxford, UK, 2006; Vol. 1; pp 19-48.

4. Guggenheim, S.; Adams, J. M.; Bain, D. C.; Bergaya, F.; Brigatti, M. F.; Drits, V. A.;Formoso, M. L. L.; Galán, E.; Kogure, T.; Stanjek, H. Summary of recommendations ofnomenclature committees relevant to clay mineralogy: Report of Association InternationalePour l’Etude des Argiles (AIPEA) nomenclature committee for 2006. Clays Clay Miner.2006, 54, 761-772.

5. Schoonheydt, R. A.; Johnston, C. T. In Developments in clay science; Bergaya, F., Theng,B. K. G. and Lagaly, G., Eds.; Elsevier Ltd: Oxford, UK, 2006; Vol. 1; pp 87-99.

6. P ikryl, R. In Expansive soils: recent advances in characterization and treatment; Al-Rawas, A. A., Goosen, M. F. A., Eds.; Taylor & Francis Group: London, UK, 2006; pp 48.

7. Pusch, R. Use of bentonite for isolation of radioactive waste products. Clay Miner. 1992,27, 353-361.

8. Posiva Oy. Final disposal. http://www.posiva.fi/en/final_disposal (accessed October 31,2015).

9. Emmerich, K.; Wolters, F.; Kahr, G.; Lagaly, G. Clay profiling: the classification ofmontmorillonites. Clays Clay Miner. 2009, 57, 104-114.

10. Wolters, F.; Lagaly, G.; Kahr, G.; Nueesch, R.; Emmerich, K. A comprehensivecharacterization of dioctahedral smectites. Clays Clay Miner. 2009, 57, 115-133.

11. Weir, A. H. Potassium retention in montmorillonites. Clay Miner. 1965, 6, 17-22.

12. Onodera, Y.; Iwasaki, T.; Ebina, T.; Hayashi, H.; Torii, K.; Chatterjee, A.; Mimura, H.Effect of layer charge on fixation of cesium ions in smectites. J. Contam. Hydrol. 1998, 35,131-140.

13. Laird, D. A. Influence of layer charge on swelling of smectites. Appl. Clay. Sci. 2006, 34,74-87.

14. Christidis, G. E.; Blum, A. E.; Eberl, D. D. Influence of layer charge and charge distributionof smectites on the flow behaviour and swelling of bentonites. Appl. Clay. Sci. 2006, 34,125-138.

15. Hadi, J.; Tournassat, C.; Ignatiadis, I.; Greneche, J. M.; Charlet, L. Modelling CECvariations versus structural iron reduction levels in dioctahedral smectites. Existingapproaches, new data and model refinements. J. Colloid Interface Sci. 2013, 407, 397-409.

43

16. Palin, E. J.; Dove, M. T.; Redfern, S. A. T.; Ortega-Castro, J.; Sainz-Díaz, C. I.; Hernández-Laguna, A. Computer simulations of cations order-disorder in 2:1 dioctahedralphyllosilicates using cation-exchange potentials and monte carlo methods. Int. J. QuantumChem. 2014, 114, 1257-1286.

17. Cuadros, J.; Sainz-Díaz, C. I.; Ramírez, R.; Hernández-Laguna, A. Analysis of Fesegregation in the octahedral sheet of bentonic illite-smectite by means of FTIR, 27Al MASNMR and reverse Monte Carlo simulations. Am. J. Sci. 1999, 299, 289-308.

18. Sainz-Díaz, C. I.; Cuadros, J.; Hernández-Laguna, A. Analysis of cation distribution in theoctahedral sheet of dioctahedral 2:1 phyllosilicates by using inverse Monte Carlo methods.Phys. Chem. Miner. 2001, 28, 445-454.

19. Palin, E. J.; Dove, M. T.; Redfern, S. A. T.; Bosenick, A.; Sainz-Diaz, C. I.; Warren, M. C.Computational study of tetrahedral Al–Si ordering in muscovite. Phys. Chem. Miner. 2001,28, 534-544.

20. Sainz-Diaz, C. I.; Palin, E. J.; Hernández-Laguna, A.; Dove, M. T. Octahedral cationordering of illite and smectite. Theoretical exchange potential determination and MonteCarlo simulations. Phys. Chem. Miner. 2003, 30, 382-392.

21. Hernández-Laguna, A.; Escamilla-Roa, E.; Timón, V.; Dove, M.; Sainz-Díaz, C. I. DFTstudy of the cation arrangements in the octahedral and tetrahedral sheets of dioctahedral 2:1phyllosilicates. Phys. Chem. Miner. 2006, 33, 655-666.

22. Ortega-Castro, J.; Hernández-Haro, N.; Dove, M. T.; Hernández-Laguna, A.; Sainz-Díaz,C. I. Density functional theory and Monte Carlo study of octahedral cation ordering ofAl/Fe/Mg cations in dioctahedral 2:1 phyllosilicates. Am. Mineral. 2010, 95, 209-220.

23. Escamilla-Roa, E.; Hernández-Laguna, A.; Sainz-Díaz, C. I. Cation arrangement in theoctahedral and tetrahedral sheets of cis-vacant polymorph of dioctahedral 2:1 phyllosilicatesby quantum mechanical calculations. Am. Mineral. 2013, 98, 724-735.

24. Vantelon, D.; Pelletier, M.; Michot, L. J.; Barres, O.; Thomas, F. Fe, Mg and Al distributionin the octahedral sheet of montmorillonites. An infrared study in the OH-bending region.Clay Miner. 2001, 36, 369-379.

25. Herrero, C. P.; Sanz, J. Short-range order of the Si, Al distribution in layer silicates. J. Phys.Chem. Solids 1991, 52, 1129-1135.

26. Skipper, N. T.; Soper, A. K.; Smalley, M. V. Neutron diffraction study of calciumvermiculite: hydration of calcium ions in a confined environment. J. Phys. Chem. 1994, 98,942-945.

27. Skipper, N. T.; Smalley, M. V.; Williams, G. D. Direct measurement of the electric double-layer structure in hydrated lithium vermiculite clays by neutron diffraction. J. Phys. Chem.1995, 99, 14201-14204.

28. Slade, P. G.; Stone, P. A.; Radoslovich, E. W. Interlayer structures of the two-layer hydratesof Na- and Ca-vermiculites. Clays Clay Miner. 1985, 33, 51-61.

29. Sposito, G.; Skipper, N. T.; Sutton, R.; Park, S.; Soper, A. K.; Greathouse, J. A. Surfacegeochemistry of the clay minerals. Proc. Natl. Acad. Sci. 1999, 96, 3358-3364.

42

References1. Guggenheim, S.; Martin, R. T. Definition of clay and clay mineral: joint report of the AIPEA

nomenclature and CMS nomenclature committees. Clays Clay Miner. 1995, 43, 255-256.

2. Harvey, C. C.; Lagaly, G. In Developments in clay science; Bergaya, F., Theng, B. K. G.and Lagaly, G., Eds.; Elsevier Ltd: Oxford, UK, 2006; Vol. 1, pp 501-540.

3. Brigatti, M. F.; Galán, E.; Theng, B. K. G. In Developments in clay science; Bergaya, F.,Theng, B. K. G. and Lagaly, G., Eds.; Elsevier Ltd: Oxford, UK, 2006; Vol. 1; pp 19-48.

4. Guggenheim, S.; Adams, J. M.; Bain, D. C.; Bergaya, F.; Brigatti, M. F.; Drits, V. A.;Formoso, M. L. L.; Galán, E.; Kogure, T.; Stanjek, H. Summary of recommendations ofnomenclature committees relevant to clay mineralogy: Report of Association InternationalePour l’Etude des Argiles (AIPEA) nomenclature committee for 2006. Clays Clay Miner.2006, 54, 761-772.

5. Schoonheydt, R. A.; Johnston, C. T. In Developments in clay science; Bergaya, F., Theng,B. K. G. and Lagaly, G., Eds.; Elsevier Ltd: Oxford, UK, 2006; Vol. 1; pp 87-99.

6. P ikryl, R. In Expansive soils: recent advances in characterization and treatment; Al-Rawas, A. A., Goosen, M. F. A., Eds.; Taylor & Francis Group: London, UK, 2006; pp 48.

7. Pusch, R. Use of bentonite for isolation of radioactive waste products. Clay Miner. 1992,27, 353-361.

8. Posiva Oy. Final disposal. http://www.posiva.fi/en/final_disposal (accessed October 31,2015).

9. Emmerich, K.; Wolters, F.; Kahr, G.; Lagaly, G. Clay profiling: the classification ofmontmorillonites. Clays Clay Miner. 2009, 57, 104-114.

10. Wolters, F.; Lagaly, G.; Kahr, G.; Nueesch, R.; Emmerich, K. A comprehensivecharacterization of dioctahedral smectites. Clays Clay Miner. 2009, 57, 115-133.

11. Weir, A. H. Potassium retention in montmorillonites. Clay Miner. 1965, 6, 17-22.

12. Onodera, Y.; Iwasaki, T.; Ebina, T.; Hayashi, H.; Torii, K.; Chatterjee, A.; Mimura, H.Effect of layer charge on fixation of cesium ions in smectites. J. Contam. Hydrol. 1998, 35,131-140.

13. Laird, D. A. Influence of layer charge on swelling of smectites. Appl. Clay. Sci. 2006, 34,74-87.

14. Christidis, G. E.; Blum, A. E.; Eberl, D. D. Influence of layer charge and charge distributionof smectites on the flow behaviour and swelling of bentonites. Appl. Clay. Sci. 2006, 34,125-138.

15. Hadi, J.; Tournassat, C.; Ignatiadis, I.; Greneche, J. M.; Charlet, L. Modelling CECvariations versus structural iron reduction levels in dioctahedral smectites. Existingapproaches, new data and model refinements. J. Colloid Interface Sci. 2013, 407, 397-409.

41

16. Palin, E. J.; Dove, M. T.; Redfern, S. A. T.; Ortega-Castro, J.; Sainz-Díaz, C. I.; Hernández-Laguna, A. Computer simulations of cations order-disorder in 2:1 dioctahedralphyllosilicates using cation-exchange potentials and monte carlo methods. Int. J. QuantumChem. 2014, 114, 1257-1286.

17. Cuadros, J.; Sainz-Díaz, C. I.; Ramírez, R.; Hernández-Laguna, A. Analysis of Fesegregation in the octahedral sheet of bentonic illite-smectite by means of FTIR, 27Al MASNMR and reverse Monte Carlo simulations. Am. J. Sci. 1999, 299, 289-308.

18. Sainz-Díaz, C. I.; Cuadros, J.; Hernández-Laguna, A. Analysis of cation distribution in theoctahedral sheet of dioctahedral 2:1 phyllosilicates by using inverse Monte Carlo methods.Phys. Chem. Miner. 2001, 28, 445-454.

19. Palin, E. J.; Dove, M. T.; Redfern, S. A. T.; Bosenick, A.; Sainz-Diaz, C. I.; Warren, M. C.Computational study of tetrahedral Al–Si ordering in muscovite. Phys. Chem. Miner. 2001,28, 534-544.

20. Sainz-Diaz, C. I.; Palin, E. J.; Hernández-Laguna, A.; Dove, M. T. Octahedral cationordering of illite and smectite. Theoretical exchange potential determination and MonteCarlo simulations. Phys. Chem. Miner. 2003, 30, 382-392.

21. Hernández-Laguna, A.; Escamilla-Roa, E.; Timón, V.; Dove, M.; Sainz-Díaz, C. I. DFTstudy of the cation arrangements in the octahedral and tetrahedral sheets of dioctahedral 2:1phyllosilicates. Phys. Chem. Miner. 2006, 33, 655-666.

22. Ortega-Castro, J.; Hernández-Haro, N.; Dove, M. T.; Hernández-Laguna, A.; Sainz-Díaz,C. I. Density functional theory and Monte Carlo study of octahedral cation ordering ofAl/Fe/Mg cations in dioctahedral 2:1 phyllosilicates. Am. Mineral. 2010, 95, 209-220.

23. Escamilla-Roa, E.; Hernández-Laguna, A.; Sainz-Díaz, C. I. Cation arrangement in theoctahedral and tetrahedral sheets of cis-vacant polymorph of dioctahedral 2:1 phyllosilicatesby quantum mechanical calculations. Am. Mineral. 2013, 98, 724-735.

24. Vantelon, D.; Pelletier, M.; Michot, L. J.; Barres, O.; Thomas, F. Fe, Mg and Al distributionin the octahedral sheet of montmorillonites. An infrared study in the OH-bending region.Clay Miner. 2001, 36, 369-379.

25. Herrero, C. P.; Sanz, J. Short-range order of the Si, Al distribution in layer silicates. J. Phys.Chem. Solids 1991, 52, 1129-1135.

26. Skipper, N. T.; Soper, A. K.; Smalley, M. V. Neutron diffraction study of calciumvermiculite: hydration of calcium ions in a confined environment. J. Phys. Chem. 1994, 98,942-945.

27. Skipper, N. T.; Smalley, M. V.; Williams, G. D. Direct measurement of the electric double-layer structure in hydrated lithium vermiculite clays by neutron diffraction. J. Phys. Chem.1995, 99, 14201-14204.

28. Slade, P. G.; Stone, P. A.; Radoslovich, E. W. Interlayer structures of the two-layer hydratesof Na- and Ca-vermiculites. Clays Clay Miner. 1985, 33, 51-61.

29. Sposito, G.; Skipper, N. T.; Sutton, R.; Park, S.; Soper, A. K.; Greathouse, J. A. Surfacegeochemistry of the clay minerals. Proc. Natl. Acad. Sci. 1999, 96, 3358-3364.

42

30. Boek, E. S.; Coveney, P. V.; Skipper, N. T. Monte Carlo molecular modeling studies ofhydrated Li-, Na-, and K-smectites: understanding the role of potassium as a clay swellinginhibitor. J. Am. Chem. Soc. 1995, 117, 12608-12617.

31. Chang, F.-C.; Skipper, N. T.; Sposito, G. Computer simulation of interlayer molecularstructure in sodium montmorillonite hydrates. Langmuir 1995, 11, 2734-2741.

32. Chang, F.-C.; Skipper, N. T.; Sposito, G. Monte Carlo and molecular dynamics simulationsof interfacial structure in lithium-montmorillonite hydrate. Langmuir 1997, 13, 2074-2082.

33. Chang, F.-C.; Skipper, N. T.; Sposito, G. Monte Carlo and molecular dynamics simulationsof electrical double-layer structure in potassium-montmorillonite hydrates. Langmuir 1998,14, 1201-1207.

34. Greathouse, J.; Sposito, G. Monte Carlo and molecular dynamics studies of interlayerstructure in Li(H2O)3-smectites. J. Phys. Chem. B 1998, 102, 2406-2414.

35. Suter, J. L.; Boek, E. S.; Sprik, M. Adsorption of a sodium ion on a smectite clay fromconstrained ab initio molecular dynamics simulations. J. Phys. Chem. C 2008, 112, 18832-18839.

36. Mignon, P.; Ugliengo, P.; Sodupe, M.; Hernandez, E. R. Ab initio molecular dynamics studyof the hydration of Li+, Na+ and K+ in a montmorillonite model. Influence of isomorphicsubstitution. Phys. Chem. Chem. Phys. 2010, 12, 688-697.

37. Berghout, A.; Tunega, D.; Zaoui, A. Density functional theory (DFT) study of the hydrationsteps of Na+/ Mg2+/ Ca2+/ Sr2+/ Ba2+-exchanged montmorillonites. Clays Clay Miner. 2010,58, 174-187.

38. Bleam, W. F.; Hoffmann, R. Isomorphous substitution in phyllosilicates as anelectronegativity perturbation: its effect on bonding and charge distribution. Inorg. Chem.1988, 27, 3180-3186.

39. Bleam, W. F. The nature of cation-substitution sites in phyllosilicates. Clays Clay Miner.1990, 38, 527-536.

40. Hassan, M. S.; Villieras, F.; Gaboriaud, F.; Razafitianamaharavo, A. AFM and low-pressureargon adsorption analysis of geometrical properties of phyllosilicates. J. Colloid InterfaceSci. 2006, 296, 614-623.

41. Bickmore, B. R.; Rosso, K. M.; Nagy, K. L.; Cygan, R. T.; Tadanier, C. J. Ab initiodetermination of edge surface structures for dioctahedral 2:1 phyllosilicates: implicationsfor acid-base reactivity. Clays Clay Miner. 2003, 51, 359-371.

42. Tombácz, E.; Szekeres, M. Colloidal behavior of aqueous montmorillonite suspensions: thespecific role of pH in the presence of indifferent electrolytes. Appl. Clay Sci. 2004, 27, 75-94.

43. Churakov, S. V. Ab initio study of sorption on pyrophyllite: structure and acidity of the edgesites. J. Phys. Chem. B 2006, 110, 4135-4146.

44. Churakov, S. V. Structure and dynamics of the water films confined between edges ofpyrophyllite: a first principle study. Geochim. Cosmochim. Acta 2007, 71, 1130-1144.

45

45. Bourg, I. C.; Sposito, G.; Bourg, A. C. M. Modeling the acid–base surface chemistry ofmontmorillonite. J. Colloid Interface Sci. 2007, 312, 297-310.

46. Delhorme, M.; Labbez, C.; Caillet, C.; Thomas, F. Acid–base properties of 2:1 clays. I.Modeling the role of electrostatics. Langmuir 2010, 26, 9240-9249.

47. Yan, L.; Englert, A. H.; Masliyah, J. H.; Xu, Z. Determination of anisotropic surfacecharacteristics of different phyllosilicates by direct force measurements. Langmuir 2011, 27,12996-13007.

48. Liu, X.; Cheng, J.; Sprik, M.; Lu, X.; Wang, R. Surface acidity of 2:1-type dioctahedral clayminerals from first principles molecular dynamics simulations. Geochim. Cosmochim. Acta2014, 140, 410-417.

49. Liu, X.; Lu, X.; Meijer, E. J.; Wang, R.; Zhou, H. Atomic-scale structures of interfacesbetween phyllosilicate edges and water. Geochim. Cosmochim. Acta 2012, 81, 56-68.

50. Keren, R.; Sparks, D. L. The role of edge surfaces in flocculation of 2:1 clay minerals. SoilSci. Soc. Am. J. 1995, 59, 430-435.

51. Scheidegger, A. M.; Lamble, G. M.; Sparks, D. L. Investigation of Ni sorption onpyrophyllite: an XAFS study. Environ. Sci. Technol. 1996, 30, 548-554.

52. Undabeytia, T.; Morillo, E.; Maqueda, C. Adsorption of Cd and Zn on montmorillonite inthe presence of a cationic pesticide. Clay Miner. 1996, 31, 485-490.

53. Kremleva, A.; Martorell, B.; Kruger, S.; Rosch, N. Uranyl adsorption on solvated edgesurfaces of pyrophyllite: a DFT model study. Phys. Chem. Chem. Phys. 2012, 14, 5815-5823.

54. Strawn, D. G.; Palmer, N. E.; Furnare, L. J.; Goodell, C.; Amonette, J. E.; Kukkadapu, R.K. Copper sorption mechanisms on smectites. Clays Clay Miner. 2004, 52, 321-333.

55. Martins, D. M. S.; Molinari, M.; Gonçalves, M. A.; Mirão, J. P.; Parker, S. C. Towardmodeling clay mineral nanoparticles: the edge surfaces of pyrophyllite and their interactionwith water. J. Phys. Chem. C 2014, 118, 27308-27317.

56. Bickmore, B. R.; Bosbach, D.; Hochella JR., M. F.; Charlet, L.; Rufe, E. In situ atomic forcemicroscopy study of hectorite and nontronite dissolution: implications for phyllosilicateedge surface structures and dissolution mechanisms. Am. Mineral. 2001, 86, 411-423.

57. White, N. G.; Zelazny, L. W. Analysis and implications of the edge structure of dioctahedralphyllosilicates. Clays Clay Miner. 1988, 36, 141-146.

58. Drits, V. A.; Guggenheim, S.; Zviagina, B. B.; Kogure, T. Structures of the 2:1 layers ofpyrophyllite and talc. Clays Clay Miner. 2012, 60, 574-587.

59. Bleam, W. F.; Welhouse, G. J.; Janowiak, M. A. The surface coulomb energy and protoncoulomb potentials of pyrophyllite {010}, {110}, {100}, and {130} edges. Clays ClayMiner. 1993, 41, 305-316.

44

30. Boek, E. S.; Coveney, P. V.; Skipper, N. T. Monte Carlo molecular modeling studies ofhydrated Li-, Na-, and K-smectites: understanding the role of potassium as a clay swellinginhibitor. J. Am. Chem. Soc. 1995, 117, 12608-12617.

31. Chang, F.-C.; Skipper, N. T.; Sposito, G. Computer simulation of interlayer molecularstructure in sodium montmorillonite hydrates. Langmuir 1995, 11, 2734-2741.

32. Chang, F.-C.; Skipper, N. T.; Sposito, G. Monte Carlo and molecular dynamics simulationsof interfacial structure in lithium-montmorillonite hydrate. Langmuir 1997, 13, 2074-2082.

33. Chang, F.-C.; Skipper, N. T.; Sposito, G. Monte Carlo and molecular dynamics simulationsof electrical double-layer structure in potassium-montmorillonite hydrates. Langmuir 1998,14, 1201-1207.

34. Greathouse, J.; Sposito, G. Monte Carlo and molecular dynamics studies of interlayerstructure in Li(H2O)3-smectites. J. Phys. Chem. B 1998, 102, 2406-2414.

35. Suter, J. L.; Boek, E. S.; Sprik, M. Adsorption of a sodium ion on a smectite clay fromconstrained ab initio molecular dynamics simulations. J. Phys. Chem. C 2008, 112, 18832-18839.

36. Mignon, P.; Ugliengo, P.; Sodupe, M.; Hernandez, E. R. Ab initio molecular dynamics studyof the hydration of Li+, Na+ and K+ in a montmorillonite model. Influence of isomorphicsubstitution. Phys. Chem. Chem. Phys. 2010, 12, 688-697.

37. Berghout, A.; Tunega, D.; Zaoui, A. Density functional theory (DFT) study of the hydrationsteps of Na+/ Mg2+/ Ca2+/ Sr2+/ Ba2+-exchanged montmorillonites. Clays Clay Miner. 2010,58, 174-187.

38. Bleam, W. F.; Hoffmann, R. Isomorphous substitution in phyllosilicates as anelectronegativity perturbation: its effect on bonding and charge distribution. Inorg. Chem.1988, 27, 3180-3186.

39. Bleam, W. F. The nature of cation-substitution sites in phyllosilicates. Clays Clay Miner.1990, 38, 527-536.

40. Hassan, M. S.; Villieras, F.; Gaboriaud, F.; Razafitianamaharavo, A. AFM and low-pressureargon adsorption analysis of geometrical properties of phyllosilicates. J. Colloid InterfaceSci. 2006, 296, 614-623.

41. Bickmore, B. R.; Rosso, K. M.; Nagy, K. L.; Cygan, R. T.; Tadanier, C. J. Ab initiodetermination of edge surface structures for dioctahedral 2:1 phyllosilicates: implicationsfor acid-base reactivity. Clays Clay Miner. 2003, 51, 359-371.

42. Tombácz, E.; Szekeres, M. Colloidal behavior of aqueous montmorillonite suspensions: thespecific role of pH in the presence of indifferent electrolytes. Appl. Clay Sci. 2004, 27, 75-94.

43. Churakov, S. V. Ab initio study of sorption on pyrophyllite: structure and acidity of the edgesites. J. Phys. Chem. B 2006, 110, 4135-4146.

44. Churakov, S. V. Structure and dynamics of the water films confined between edges ofpyrophyllite: a first principle study. Geochim. Cosmochim. Acta 2007, 71, 1130-1144.

43

45. Bourg, I. C.; Sposito, G.; Bourg, A. C. M. Modeling the acid–base surface chemistry ofmontmorillonite. J. Colloid Interface Sci. 2007, 312, 297-310.

46. Delhorme, M.; Labbez, C.; Caillet, C.; Thomas, F. Acid–base properties of 2:1 clays. I.Modeling the role of electrostatics. Langmuir 2010, 26, 9240-9249.

47. Yan, L.; Englert, A. H.; Masliyah, J. H.; Xu, Z. Determination of anisotropic surfacecharacteristics of different phyllosilicates by direct force measurements. Langmuir 2011, 27,12996-13007.

48. Liu, X.; Cheng, J.; Sprik, M.; Lu, X.; Wang, R. Surface acidity of 2:1-type dioctahedral clayminerals from first principles molecular dynamics simulations. Geochim. Cosmochim. Acta2014, 140, 410-417.

49. Liu, X.; Lu, X.; Meijer, E. J.; Wang, R.; Zhou, H. Atomic-scale structures of interfacesbetween phyllosilicate edges and water. Geochim. Cosmochim. Acta 2012, 81, 56-68.

50. Keren, R.; Sparks, D. L. The role of edge surfaces in flocculation of 2:1 clay minerals. SoilSci. Soc. Am. J. 1995, 59, 430-435.

51. Scheidegger, A. M.; Lamble, G. M.; Sparks, D. L. Investigation of Ni sorption onpyrophyllite: an XAFS study. Environ. Sci. Technol. 1996, 30, 548-554.

52. Undabeytia, T.; Morillo, E.; Maqueda, C. Adsorption of Cd and Zn on montmorillonite inthe presence of a cationic pesticide. Clay Miner. 1996, 31, 485-490.

53. Kremleva, A.; Martorell, B.; Kruger, S.; Rosch, N. Uranyl adsorption on solvated edgesurfaces of pyrophyllite: a DFT model study. Phys. Chem. Chem. Phys. 2012, 14, 5815-5823.

54. Strawn, D. G.; Palmer, N. E.; Furnare, L. J.; Goodell, C.; Amonette, J. E.; Kukkadapu, R.K. Copper sorption mechanisms on smectites. Clays Clay Miner. 2004, 52, 321-333.

55. Martins, D. M. S.; Molinari, M.; Gonçalves, M. A.; Mirão, J. P.; Parker, S. C. Towardmodeling clay mineral nanoparticles: the edge surfaces of pyrophyllite and their interactionwith water. J. Phys. Chem. C 2014, 118, 27308-27317.

56. Bickmore, B. R.; Bosbach, D.; Hochella JR., M. F.; Charlet, L.; Rufe, E. In situ atomic forcemicroscopy study of hectorite and nontronite dissolution: implications for phyllosilicateedge surface structures and dissolution mechanisms. Am. Mineral. 2001, 86, 411-423.

57. White, N. G.; Zelazny, L. W. Analysis and implications of the edge structure of dioctahedralphyllosilicates. Clays Clay Miner. 1988, 36, 141-146.

58. Drits, V. A.; Guggenheim, S.; Zviagina, B. B.; Kogure, T. Structures of the 2:1 layers ofpyrophyllite and talc. Clays Clay Miner. 2012, 60, 574-587.

59. Bleam, W. F.; Welhouse, G. J.; Janowiak, M. A. The surface coulomb energy and protoncoulomb potentials of pyrophyllite {010}, {110}, {100}, and {130} edges. Clays ClayMiner. 1993, 41, 305-316.

44

60. Cadene, A.; Durand-Vidal, S.; Turq, P.; Brendle, J. Study of invidual Na-montmorilloniteparticles size, morphology, and apparent charge. J. Colloid Interface Sci. 2005, 285, 719-730.

61. Tsipursky, S. I.; Drits, V. A. The distribution of octahedral cations in the 2:1 layers ofdioctahedral smectites studied by oblique-texture electron diffraction. Clay Miner. 1984, 19,177-193.

62. Perdew, J. P.; Ruzsinszky, A. Fourteen easy lessons in density functional theory. Int. J.Quantum Chem. 2010, 110, 2801-2807.

63. Sousa, S. F.; Fernandes, P. A.; Ramos, M. J. General performance of density functionals. J.Phys. Chem. A 2007, 111, 10439-10452.

64. Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple.Phys. Rev. Lett. 1996, 77, 3865-3868.

65. Perdew, J. P.; Burke, K.; Ernzerhof, M. Errata: generalized gradient approximation madesimple. Phys. Rev. Lett. 1997, 78, 1396-1396.

66. Martin, R. M. Electronic structure: basic theory and practical methods; CambridgeUniversity Press: Cambridge, 2004; pp 236-239.

67. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 1994, 50, 17953-17979.

68. Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wavemethod. Phys. Rev. B 1999, 59, 1758-1775.

69. Kresse, G.; Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. Rev. B 1993,47, 558-561.

70. Kresse, G.; Hafner, J. Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium. Phys. Rev. B 1994, 49, 14251-14269.

71. Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculationsusing a plane-wave basis Set. Phys. Rev. B 1996, 54, 11169-11186.

72. Kresse, G.; Furthmüller, J. Efficiency of ab-initio total energy calculations for metals andsemiconductors using a plane-wave basis set. Comput. Mat. Sci. 1996, 6, 15-50.

73. Voora, V. K.; Al-Saidi, W.; Jordan, K. D. Density functional theory study of pyrophylliteand M-montmorillonites (M = Li, Na, K, Mg, and Ca): role of dispersion interactions. J.Phys. Chem. A 2011, 115, 9695-9703.

74. Monkhorst, H. J.; Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B1976, 13, 5188-5192.

75. Bader, R. Atoms in molecules: a quantum theory; Oxford University Press: Oxford, USA,1990.

76. Tang, W.; Sanville, E.; Henkelman, G. A grid-based bader analysis algorithm without latticebias. J. Phys.: Condens. Matter 2009, 21, 084204.

47

77. Arnaldsson, A.; Tang, W.; Chill, S.; Henkelman, G.; Sanville, E.; Voss, J.; McNellis, E.;Dyer, M.; Lebegue, S.; Janos, A.; Aubert, E. Code: bader charge analysis, version 0.28a;University of Texas, USA, 2012. http://theory.cm.utexas.edu/henkelman/code/bader/

78. Mahadevan, T. S.; Garofalini, S. H. Dissociative chemisorption of water onto silica surfacesand formation of hydronium ions. J. Phys. Chem. C 2008, 112, 1507-1515.

79. Kirsch, H.; Wirth, J.; Tong, Y.; Wolf, M.; Saalfrank, P.; Campen, R. K. Experimentalcharacterization of unimolecular water dissociative adsorption on -alumina. J. Phys. Chem.C 2014, 118, 13623-13630.

80. Alvim, R. S.; Borges, I.; Costa, D. G.; Leitão, A. A. Density-functional theory simulation ofthe dissociative chemisorption of water molecules on the MgO(001) surface. J. Phys. Chem.C 2012, 116, 738-744.

81. Kerisit, S.; Parker, S. C. Free energy of adsorption of water and metal ions on the {1014}calcite surface. J. Am. Chem. Soc. 2004, 126, 10152-10161.

82. Rahaman, A.; Grassian, V. H.; Margulis, C. J. Dynamics of water adsorption onto a calcitesurface as a function of relative humidity. J. Phys. Chem. C 2008, 112, 2109-2115.

83. Lide, D. R., Ed. CRC Handbook of chemistry and physics; CRC Press: Boca Raton, Florida,USA, 2004; pp 5-18.

84. Wulff, G. Zur frage der geschwindigkeit des wachstums undder auflosung derkrystalflachen. Z. Krystallogr. 1901, 34, 499-530.

85. Zucker, R. V.; Chatain, D.; Dahmen, U.; Serge, H.; Carter, W. C. New software tools forthe calculation and display of isolated and attached interfacial-energy minimizing particleshapes. J. Mater. Sci. 2012, 47, 8290-8302.

86. Bauer, A.; Velde, B.; Gaupp, R. Experimental constraints on illite crystal morphology. ClayMiner. 2000, 35, 587-597.

87. Güven, N. Mica structure and fibrous growth of illite. Clays Clay Miner. 2001, 49, 189-196.

88. Rytwo, G.; Banin, A.; Nir, S. Exchange reactions in the Ca-Mg-Na-montmorillonite system.Clays Clay Miner. 1996, 44, 276-285.

89. Sun, L.; Ling, C. Y.; Lavikainen, L. P.; Hirvi, J. T.; Kasa, S.; Pakkanen, T. A. Influence oflayer charge and charge location on the swelling pressure of dioctahedral smectites. 2016,submitted for publication.

90. Momma, K.; Izumi, F. VESTA 3 for three-dimensional visualization of crystal, volumetricand morphology data. J. Appl. Crystallogr. 2011, 44, 1272-1276.

46

60. Cadene, A.; Durand-Vidal, S.; Turq, P.; Brendle, J. Study of invidual Na-montmorilloniteparticles size, morphology, and apparent charge. J. Colloid Interface Sci. 2005, 285, 719-730.

61. Tsipursky, S. I.; Drits, V. A. The distribution of octahedral cations in the 2:1 layers ofdioctahedral smectites studied by oblique-texture electron diffraction. Clay Miner. 1984, 19,177-193.

62. Perdew, J. P.; Ruzsinszky, A. Fourteen easy lessons in density functional theory. Int. J.Quantum Chem. 2010, 110, 2801-2807.

63. Sousa, S. F.; Fernandes, P. A.; Ramos, M. J. General performance of density functionals. J.Phys. Chem. A 2007, 111, 10439-10452.

64. Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple.Phys. Rev. Lett. 1996, 77, 3865-3868.

65. Perdew, J. P.; Burke, K.; Ernzerhof, M. Errata: generalized gradient approximation madesimple. Phys. Rev. Lett. 1997, 78, 1396-1396.

66. Martin, R. M. Electronic structure: basic theory and practical methods; CambridgeUniversity Press: Cambridge, 2004; pp 236-239.

67. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 1994, 50, 17953-17979.

68. Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wavemethod. Phys. Rev. B 1999, 59, 1758-1775.

69. Kresse, G.; Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. Rev. B 1993,47, 558-561.

70. Kresse, G.; Hafner, J. Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium. Phys. Rev. B 1994, 49, 14251-14269.

71. Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculationsusing a plane-wave basis Set. Phys. Rev. B 1996, 54, 11169-11186.

72. Kresse, G.; Furthmüller, J. Efficiency of ab-initio total energy calculations for metals andsemiconductors using a plane-wave basis set. Comput. Mat. Sci. 1996, 6, 15-50.

73. Voora, V. K.; Al-Saidi, W.; Jordan, K. D. Density functional theory study of pyrophylliteand M-montmorillonites (M = Li, Na, K, Mg, and Ca): role of dispersion interactions. J.Phys. Chem. A 2011, 115, 9695-9703.

74. Monkhorst, H. J.; Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B1976, 13, 5188-5192.

75. Bader, R. Atoms in molecules: a quantum theory; Oxford University Press: Oxford, USA,1990.

76. Tang, W.; Sanville, E.; Henkelman, G. A grid-based bader analysis algorithm without latticebias. J. Phys.: Condens. Matter 2009, 21, 084204.

45

77. Arnaldsson, A.; Tang, W.; Chill, S.; Henkelman, G.; Sanville, E.; Voss, J.; McNellis, E.;Dyer, M.; Lebegue, S.; Janos, A.; Aubert, E. Code: bader charge analysis, version 0.28a;University of Texas, USA, 2012. http://theory.cm.utexas.edu/henkelman/code/bader/

78. Mahadevan, T. S.; Garofalini, S. H. Dissociative chemisorption of water onto silica surfacesand formation of hydronium ions. J. Phys. Chem. C 2008, 112, 1507-1515.

79. Kirsch, H.; Wirth, J.; Tong, Y.; Wolf, M.; Saalfrank, P.; Campen, R. K. Experimentalcharacterization of unimolecular water dissociative adsorption on -alumina. J. Phys. Chem.C 2014, 118, 13623-13630.

80. Alvim, R. S.; Borges, I.; Costa, D. G.; Leitão, A. A. Density-functional theory simulation ofthe dissociative chemisorption of water molecules on the MgO(001) surface. J. Phys. Chem.C 2012, 116, 738-744.

81. Kerisit, S.; Parker, S. C. Free energy of adsorption of water and metal ions on the {1014}calcite surface. J. Am. Chem. Soc. 2004, 126, 10152-10161.

82. Rahaman, A.; Grassian, V. H.; Margulis, C. J. Dynamics of water adsorption onto a calcitesurface as a function of relative humidity. J. Phys. Chem. C 2008, 112, 2109-2115.

83. Lide, D. R., Ed. CRC Handbook of chemistry and physics; CRC Press: Boca Raton, Florida,USA, 2004; pp 5-18.

84. Wulff, G. Zur frage der geschwindigkeit des wachstums undder auflosung derkrystalflachen. Z. Krystallogr. 1901, 34, 499-530.

85. Zucker, R. V.; Chatain, D.; Dahmen, U.; Serge, H.; Carter, W. C. New software tools forthe calculation and display of isolated and attached interfacial-energy minimizing particleshapes. J. Mater. Sci. 2012, 47, 8290-8302.

86. Bauer, A.; Velde, B.; Gaupp, R. Experimental constraints on illite crystal morphology. ClayMiner. 2000, 35, 587-597.

87. Güven, N. Mica structure and fibrous growth of illite. Clays Clay Miner. 2001, 49, 189-196.

88. Rytwo, G.; Banin, A.; Nir, S. Exchange reactions in the Ca-Mg-Na-montmorillonite system.Clays Clay Miner. 1996, 44, 276-285.

89. Sun, L.; Ling, C. Y.; Lavikainen, L. P.; Hirvi, J. T.; Kasa, S.; Pakkanen, T. A. Influence oflayer charge and charge location on the swelling pressure of dioctahedral smectites. 2016,submitted for publication.

90. Momma, K.; Izumi, F. VESTA 3 for three-dimensional visualization of crystal, volumetricand morphology data. J. Appl. Crystallogr. 2011, 44, 1272-1276.

Lasse Lavikainen

DissertationsDepartment of ChemistryUniversity of Eastern Finland

No. 137 (2016)

107/2011 KASANEN Jussi: Photocatalytic TiO2-based multilayer coating on polymer substrate for use in self-cleaning applications108/2011 KALLIO Juha: Structural studies of Ascomycete laccases – Insights into the reaction pathways109/2011 KINNUNEN Niko: Methane combustion activity of Al2O3-supported Pd, Pt, and Pd-Pt catalysts: Experimental and theoretical studies110/2011 TORVINEN Mika: Mass spectrometric studies of host-guest complexes of glucosylcalixarenes111/2012 KONTKANEN Maija-Liisa: Catalyst carrier studies for 1-hexene hydroformulation: cross-linked poly(4-vinylpyridine), nano zinc oxide and one-dimensional ruthenium polymer112/2012KORHONENTuulia:Thewettabilitypropertiesofnano-andmicromodifiedpaintsurfaces113/2012JOKI-KORPELAFatima:Functionalpolyurethane-basedfilmsandcoatings114/2012 LAURILA Elina: Non-covalent interactions in Rh, Ru, Os, and Ag complexes115/2012 MAKSIMAINEN Mirko: Structural studies of Trichoderma reesei, Aspergillus oryzae and Bacillus circulans sp. alkalophilus beta-galactosidases – Novel insights into a structure-function relationship116/2012 PÖLLÄNEN Maija: Morphological, thermal, mechanical, and tribological studies of polyethylene compositesreinforcedwithmicro–andnanofillers117/2013LAINEAnniina:Elementaryreactionsinmetallocene/methylaluminoxanecatalyzedpolyolefin synthesis118/2013TIMONENJuri:Synthesis,characterizationandanti-inflammatoryeffectsofsubstitutedcoumarin derivatives119/2013 TAKKUNEN Laura: Three-dimensional roughness analysis for multiscale textured surfaces: Quantitative characterization and simulation of micro- and nanoscale structures120/2014 STENBERG Henna: Studies of self-organizing layered coatings121/2014 KEKÄLÄINEN Timo: Characterization of petroleum and bio-oil samples by ultrahigh-resolution Fourier transform ion cyclotron resonance mass spectrometry122/2014 BAZHENOV Andrey: Towards deeper atomic-level understanding of the structure of magnesium dichloride and its performance as a support in the Ziegler-Natta catalytic system123/2014 PIRINEN Sami: Studies on MgCl2/ether supports in Ziegler–Natta catalysts for ethylene polymerization124/2014 KORPELA Tarmo: Friction and wear of micro-structured polymer surfaces125/2014 HUOVINEN Eero: Fabrication of hierarchically structured polymer surfaces126/2014 EROLA Markus: Synthesis of colloidal gold and polymer particles and use of the particles in preparation of hierarchical structures with self-assembly127/2015 KOSKINEN Laura: Structural and computational studies on the coordinative nature of halogen bonding128/2015 TUIKKA Matti: Crystal engineering studies of barium bisphosphonates, iodine bridged ruthenium complexes, and copper chlorides129/2015JIANGYu:Modificationandapplicationsofmicro-structuredpolymersurfaces130/2015 TABERMAN Helena: Structure and function of carbohydrate-modifying enzymes 131/2015KUKLINMikhailS.:Towardsoptimizationofmetaloceneolefinpolymerizationcatalystsvia structuralmodifications:acomputationalapproach132/2015SALSTELAJanne:Influenceofsurfacestructuringonphysicalandmechanicalpropertiesof polymer-cellulosefibercompositesandmetal-polymercompositejoints133/2015 CHAUDRI Adil Maqsood: Tribological behavior of the polymers used in drug delivery devices134/2015 HILLI Yulia: The structure-activity relationship of Pd-Ni three-way catalysts for H2S suppression135/2016 SUN Linlin: The effects of structural and environmental factors on the swelling behavior of Montmorillonite-Beidellite smectics: a molecular dynamics approach136/2016 OFORI Albert: Inter- and intramolecular interactions in the stabilization and coordination of palladium and silver complexes: DFT and QTAIM studies

The structure and surfaces of2:1 phyllosilicate clay minerals

Lasse Lavikainen: The structure and surfaces of 2:1 phyllosilicate clay minerals

137