OF INTERLAYER AND SURFACE SPECIES OF LAYERED DOUBLE … · 2005-10-20 · volumes. Traditional diffraction methods have proven insufficient to adequately address these issues, but

$Page 1: OF INTERLAYER AND SURFACE SPECIES OF LAYERED DOUBLE … · 2005-10-20 · volumes. Traditional diffraction methods have proven insufficient to adequately address these issues, but$
R. James Kirkpatrick, Andrey G. Kalinichev, Jianwei Wang, Xiaoqiang Hou, and James E.Amonette (2005) molecular modeling of the vibrational spectra of interlayer and surface species oflayered double hydroxides: In The application of vibrational spectroscopy to clay minerals andlayered double hydroxides, CMS Workshop Lectures, Vol. 13, J. Theo Kloprogge ed., The ClayMineral Society, Aurora, CO, 239-285.

MOLECULAR MODELING OF THE VIBRATIONAL SPECTRAOF INTERLAYER AND SURFACE SPECIES OF LAYERED DOUBLE

HYDROXIDES

R. JAMES KIRKPATRICK, ANDREY G. KALINICHEV, JIANWEI WANG,XIAOQIANG HOU AND JAMES E. AMONETTE

CONTENTS 239

INTRODUCTION 240

MOLECULAR DYNAMICS MODELING 243

INTERATOMIC POTENTIALS 246

ANALYSIS OF ATOMIC VIBRATIONAL DYNAMICS FROM MDSIMULATIONS 250

EXPERIMENTAL FAR INFRARED SPECTRA OF LDH PHASES 254

COMPARISON OF CALCULATED AND OBSERVED DATA 258

Ca2Al-Cl LDH 259LiAl2-Cl LDH 264LiAl2-SO4 LDH 268Mg3Al-Cl LDH 273

POWER SPECTRA OF AQUEOUS SPECIES ASSOCIATEDWITH LDH SURFACES 277

CONCLUSIONS 280

ACKNOWLEDGEMENTS 280

REFERENCES

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MOLECULAR MODELING OF THE VIBRATIONAL SPECTRAOF INTERLAYER AND SURFACE SPECIES OF LAYERED DOUBLE

HYDROXIDES

R. JAMES KIRKPATRICK1, ANDREY G. KALINICHEV1, JIANWEIWANG1, XIAOQIANG HOU1 AND JAMES E. AMONETTE2

1 Department of GeologyUniversity of Illinois at Urbana-Champaign

Urbana, IL 61801, USA.

2 Environmental Molecular Sciences Laboratory, Pacific NorthwestNational Laboratory,P.O. Box 999, K8-96,

Richland, WA 99352, USA.

INTRODUCTION

Layered double hydroxides (LDHs), also known as hydrotalcite-likecompounds (HTs), anionic clays, and mixed-metal layered hydroxides(MMLHs), are unusual among oxide and hydroxide materials in having largepermanent positive layer charges and, consequently, large anion exchangecapacities. Interest in the LDH phases has increased rapidly in recent years dueto their role in a wide range of natural and hazardous waste environments, inPortland cements, and their use as catalysts, carriers for drugs, and othertechnological applications (e.g., Cavani et al., 1991; Basile et al., 2001). LDHscan be easily synthesized with a wide range of main (hydroxide) layer cationsand interlayer organic and inorganic anions (e.g., Miyata, 1975, 1983;Constantino et al., 1998; Newman and Jones, 1998; Choy et al., 1999). Thesematerials thus offer an excellent opportunity to investigate fundamentalstructural and dynamical properties of interlayer and surface species and areimportant models for understanding aqueous solutions confined in nano-pores(Kagunya, 1996; Kagunya et al., 1997; Kirkpatrick et al., 1999; Kalinichev etal., 2000; Wang et al., 2001, 2003; Hou et al., 2002, 2003; Kalinichev andKirkpatrick, 2002). The positive layer charge of LDHs provides importantcontrast with the negative layer charges typical of aluminosilicate clays.

The structures of most LDHs consist of single-layer metal hydroxidesheets alternating with interlayers that contain anions and water molecules (e.g.,Taylor, 1973; Bellotto et al., 1996; Newman and Jones, 1998). The hydroxidesheets develop positive charge by cation substitution, which is compensated bythe interlayer and surface anions (Fig. 1). In many LDHs, the hydroxide layercan be thought of as a trioctahedral, brucite-type sheet of composition[M+2(OH)2] in which some of the divalent cations are replaced by higher charge

Modeling of vibrational spectra

241

ca t ions . A typ i ca l s t ruc tu ra l fo rmula o f LDH i s[M11-x

+2M2x+3(OH)2] · Ax/n

-n · mH2O, where x is the fraction of trivalent cations(M2) in the structure, n is the anionic charge, and m is the number of watermolecules per formula unit. The main layers of LiAl2 LDHs, which have typicalstructural formulae of [LiAl2(OH)6] · A1/n

-n · mH2O, can be thought of asdioctahedral gibbsite sheets with Li occupying the vacancies. Again anionsoccupy interlayer and surface sites to compensate the positive layer charge andare accompanied by water molecules.

Figure 1. Crystal structure of Ca2Al-Cl layered double hydroxide, [Ca2Al(OH)6]Cl·2H2O (Friedel'ssalt). Green balls = Cl–, red balls = O of water or OH, white balls = H of water or OH,pink octahedra = Al of hydroxide layer, blue balls = Ca of hydroxide layer.

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Understanding of the chemical behavior and transport properties of theinterlayers and surfaces of LDHs and other layered structure materials requiresknowledge of the molecular scale structural environments of the interlayer andsurface species and their dynamical behavior on many length and time scales.Because of the diversity of structural and chemical environments in layeredmaterials, such data also provide a broad and important basis for understandingthe behavior and properties of water and aqueous fluids confined in nano-scalevolumes. Traditional diffraction methods have proven insufficient to adequatelyaddress these issues, but a wide range of spectroscopic, synchrotron-based X-rayscattering, and molecular computational methods are now making significantprogress in understanding interlayers and mineral-fluid interfaces (e.g., Brown etal., 1999).

Vibrational spectroscopy (Raman and infrared) has the potential tomake considerable contribution to this effort, but interpretation of the spectralfeatures related to interlayer and surface environments is often difficult due tocompositional complexity, structural disorder, and the wide range ofcomplicated, typically low frequency motions that contribute to the observedspectra. In contrast to the relatively simple metal-oxygen (M-O) and O-Hstretching, and M-O-M and H-O-H bending modes that often dominate the mid-and high-frequency spectra of hydrous oxides and hydroxides, many of themodes related to interlayer and surface species are essentially intermolecular.They often involve complex interactions among water molecules, interlayer orsurface ions, and the substrate oxide or hydroxide layer. Better understanding ofthem can provide otherwise unavailable insight into the interlayer structure anddynamics. Because the significance of LDHs is often related to their reactionand anion exchange properties, understanding the structure and dynamicalbehavior of their interlayer and surface species is key to understanding their rolein the earth and to advancing their technological applications. As for clays andother fine-grained materials, these issues can be most effectively addressed by acombination of spectroscopic and computational approaches.

Molecular dynamics computational modeling is proving to be anespecially effective tool in helping to unravel these complicated low frequencyvibrational, rotational and translational motions. The FIR spectra of LDHs andsimilar hydrous layered phases reflect both the low-frequency lattice vibrationsassociated with torsional motions of the hydroxide layer (e.g., Ruan et al., 2002)and intermolecular vibrations resulting from the complex combination ofrelatively weak hydrogen bonding interactions within the anion-water interlayersand between these interlayers and main hydroxide layers (Wang et al., 2003).The intermolecular modes involve the relative motions of interlayer species as awhole and may be either translational or librational (rotational) in origin. Thefrequencies of translational vibrations depend upon the total molecular mass,whereas the rotational vibrations are functions of molecular moments of inertiaand are expected to have higher intensity in the spectra (Finch et al., 1970).Vibrational spectroscopy has played an important role in understanding the


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structures of LDHs (Hernandez-Moreno et al., 1985; Kagunya et al., 1998; Frostet al., 2000; Kloprogge et al., 2001, 2002), but principal focus has been on thehigher frequency bands in the mid-infrared range (4000–400 cm-1) associatedwith vibrations of the octahedral layers and interlayer species.

Kagunya et al. (1998) studied several Mg/Al LDH compounds usingIR, Raman and inelastic neutron scattering (INS) techniques and theirvibrational mode analysis has provided an important basis for our studies ofLDH interlayers and surfaces. In their analysis, Kagunya et al. (1998) assumedthat all octahedral sites of the hydroxide layer have D3d symmetry, that there iscomplete cation disorder over these sites, and that there is only a single cationposition. Thus, their vibrational band assignments were based on those forsimple hydroxides such as Mg(OH)2. Al+3 and Mg+2, however, have quitedifferent charge to radius ratios (z/r), and there is good experimental evidencefor substantial short-range Mg/Al ordering on the octahedral sites of Mg/AlLDHs (Vucelic et al., 1987; Cai et al., 1994; Yao et al., 1998). The difference inz/r ratio is even more dramatic for the Ca2Al and LiAl2 LDH phases, leading tohigh degrees of cation ordering in both cases. Additionally, the network ofhydrogen bonds among the interlayer water molecules and anions and mainlayer OH-groups is known to be structurally and dynamically disordered(Kirkpatrick et al., 1999; Wang et al., 2001; Hou et al., 2002). The simplifyingassumptions of Kagunya et al. (1998), thus, limit the ability of their approach toeffectively assign and analyze the vibrational bands in the FIR region below400 cm-1. MD modeling methods are most useful in this region.

MOLECULAR DYNAMICS MODELING

Classical methods of molecular computer simulations includeMolecular Dynamics (MD) and Monte Carlo (MC) techniques and are highlydeveloped theoretically and in practice. Software is now widely available. Suchsimulations are neither experiment nor theory, and thus these “computerexperiments” can, to some extent, take on both theoretical and experimentaltasks and thereby bridge theoretical and experimental understanding. In bothcases the simulations are typically performed for a relatively small number ofparticles (atoms, ions, and/or molecules; 100 < N < 100,000) confined in a box(the simulation cell). The interparticle interactions are represented by a set ofinteratomic potentials, and it is generally assumed that the total potential energyof the system can be described as a sum of these interactions. The greatestchallenge in effectively undertaking molecular simulations is having a reliableway to model and calculate these interparticle interactions. In classicalmolecular simulations, the interaction potentials are often based on quantumchemical calculations but are empirically adjusted to reproduce a limited set ofexperimentally measurable properties of a few model materials over a limitedrange of conditions. In contrast, quantum chemical and more recent quantumMD methods calculate the properties of a chemical system ab initio, and,ideally, do not require even a limited preliminary knowledge of the system’s

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properties. However, quantum calculations are orders of magnitude morecomputationally intensive, and the classical methods of molecular simulationsremain the tools of choice for investigating large but molecular scalephenomena. We discuss interatomic potentials in detail below.

Molecular computer simulations generate a large number ofinstantaneous particle configurations and with the help of statistical mechanics,directly yield many useful thermodynamic, structural, and transport propertiesfrom the microscopic information about instantaneous atomic positions andvelocities. It is possible, for instance, to calculate pressure, temperature, internalenergy, heat capacity, interatomic distances, coordination numbers, radialdistribution functions, diffusion coefficients, and of central importance here, thespectra of vibrational, rotational and translational atomic motions for thesimulated systems. There are many excellent introductions to statistical physicsand molecular computer simulations (e.g., McQuarrie, 1976; Hansen andMcDonald, 1986; Allen and Tildesley, 1987; Frenkel and Smit, 1996; Balbuenaand Seminario, 1999). If only the thermodynamic and structural properties of thesystem are of interest, MC and MD methods give essentially equivalent results.However, MD simulations have the great advantage of allowing the study oftime-dependent phenomena, such as the spectra of atomic motions. Thus, wefocus here on the fundamental concepts and calculation of atomic vibrationalspectra using classical methods of molecular dynamics simulation.

In MD simulations, all individual particles in the simulation box aregiven initial positions and velocities, and the Newtonian equations of motion arenumerically integrated over time for all particles under the influence of theinteratomic potentials. The size of the time step for integration depends ontemperature, density, the masses of the particles, the interparticle potentials, thedetail of information sought, and the numerical stability of the integrationalgorithm. In the simulations discussed in this chapter, the time step is typicallyof the order of a femtosecond (1 fs = 10–15 s), and the dynamic trajectories of theparticles are usually followed for 104 to 106 time steps after a period ofthermodynamic pre-equilibration. The resulting record of the trajectories of theparticles (i.e. their positions and velocities, and if they are molecules theirorientations and angular velocities) is a complete description of the system in aclassical mechanical sense. The thermodynamic, structural, spectroscopic, andtransport properties of the system can then be calculated from the time averagesof these parameters. For example, the temperature is related to the average valueof the kinetic energy of all particles in the system:

TNk

mi i

i

N

==∑2

3 2

2

1B

v , (1)

where mi and v i are the masses and the velocities of the molecules, kB is theBoltzmann constant, and the angular brackets denote time-averaging along thedynamic trajectory of the system. Pressure can be calculated from the virial


245

theorem:

PNk T

V V i ii

N

= −

⋅

=∑B 1

3 1r F , (2)

where V is the volume of the simulation box and (ri·Fi) is the dot product of theposition and the force vectors for particle i. The heat capacity of the system canbe calculated from temperature fluctuations:

C R NT T

TV = −

−

−2

3

2 2

2

1(3)

where R is the universal gas constant.

Molecular dynamics simulations may be performed under a variety ofconditions and constraints, corresponding to different ensembles in statisticalmechanics. Many simulations use the microcanonical (NVE) ensemble, in whichthe number of particles (N), the volume (V), and the total energy (E) of thesystem remain constant during the simulation. These conditions are always truefor any closed mechanical system. Relationships (1)-(3) are valid for this case.Modifications of the MD algorithm allow use of the canonical (constant NVT) orisothermal-isobaric (constant NPT) ensembles. Relationships similar toEquations (1)-(3) and many others can be systematically derived for theseensembles. Allen and Tildesley (1987) and Frenkel and Smit (1996) provideexcellent introductions. Most of the simulations discussed here used NVT orNPT conditions.

One of the principal difficulties in MD simulation is that the number ofatoms is always much smaller than the Avogadro number, NA, characteristic ofmacroscopic systems. Many atoms are, thus, located near enough to the edge ofthe simulation cell that their potential fields reflect conditions outside the cell,and edge effects can significantly distort the results. Therefore, most workersuse so-called periodic boundary conditions to minimize edge effects andsimulate more closely the system’s bulk macroscopic properties. In practice, theapplication of periodic boundary conditions assumes the basic simulation box tobe surrounded by identical boxes infinitely in all three dimensions. Thus, if aparticle leaves the box through one side, its identical image enterssimultaneously through the opposite side.

Whether the properties of this relatively small, infinitely periodicsystem and the equivalent macroscopic system are the same depends in part onthe length scale over which the intermolecular potentials act and the propertyunder investigation. For short-range interactions, either spherical or “minimumimage” cutoff criteria are commonly used (Allen and Tildesley, 1987; Frenkeland Smit, 1996). The latter means that each molecule interacts only with theclosest image of all other particles in the simulation cell or its periodic replicas.

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However, all realistic potentials for ionic species in solids or aqueous solutionscontain long-range electrostatic (Coulombic) interactions, which decay only as1/r, where r is the interatomic distance. Ewald summation is considered the mostsatisfactory method for treating these long-range interactions (see, e.g., Allenand Tildesley, 1987; and Gale, 2002).

MD simulations involve averages taken over computational runs withfinite sizes and times and are thus subject to statistical errors. It is essential toestimate these in evaluating the results. The statistical uncertainties of simulatedproperties are usually estimated by the method of block averages (Allen andTildesley, 1987). The MD trajectory is subdivided into several non-overlappingblocks of equal length, and the averages of the desired properties are computedfor each block. If 〈A〉i is the mean value of a property A computed for block i,the variance δA of the mean value 〈A〉 for the entire simulation can be estimatedas

€

(δA)2 =1M

A i − A[ ]2

i=1

M

∑ , (4)

where M is the number of blocks. Strictly speaking, Equation (4) is valid only ifall 〈A〉i are statistically independent and show a normal Gaussian distribution.Thus, if the simulation is of insufficient length, these estimates should be takenwith caution, especially for the properties calculated from fluctuations, such asCV in Equation (3). Many MD software packages provide output of the timedependence of the running averages of the simulated properties, and these canbe very useful in evaluating statistical validity. One can roughly estimate thelimits of the statistical errors as the maximum variation of the running averagesduring the simulation.

INTERATOMIC POTENTIALS

The theory of MD modeling and development of computationalsoftware is well advanced, but much recent effort has been devoted todeveloping sets of interatomic potentials (”force fields”) for specificapplications. Indeed, it is no exaggeration to say that the potentials are now thekey to effective MD modeling. There are many approaches to force fielddevelopment, and each has important advantages for particular applications. Inall cases, the total interaction energy is described by a series of terms thataccount for the interactions between two or more species (atoms, ions,molecules). In many cases, the interaction potentials are based on quantumchemical calculations, but are often calibrated empirically using a wide range ofexperimental data including X-ray diffraction structural data and vibrationalspectra. One successful approach commonly used for inorganic solids is to


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explicitly define chemical bonds and a set of interatomic interaction termsdescribing these bonds (e.g., Hill and Sauer, 1994, 1995; Ermoshin et al.,1996a,b; Teppen et al., 1997; Bougeard et al., 2000). In this approach, all bondsin the structure are initially identified and evaluated for each possible nearestneighbor coordination. Recently, for instance, Teppen et al. (1997) successfullydeveloped a force field for clay phases that is based on rigorous analysis ofexperimental X-ray diffraction data and charge assignment from quantummechanical calculations. This set of potentials was successfully used to simulateseveral clay structures including gibbsite, kaolinite, pyrophyllite, and thesmectite beidellite.

This approach usually gives very accurate structural results, but itsapplication is often limited to simulations of materials with relatively well-known structures, because it requires a large number of force field parameters todescribe the bonded states. LDHs, clays, and their surfaces and interlayers,however, commonly have complex and incompletely or poorly characterizedstructures, low symmetries, large unit cells, and variable compositions. Thus,use of bonded force fields for them is often unsatisfactory, because it is difficultto transfer the numerous parameters of a bonded force field from models ofrelatively simple and well-understood materials to more complex systems withill-defined bond structures. Lack of the experimental data required to constrainall the parameters necessary for explicit description of all bonded interactionsleads to significant over-parameterization of the force field, thus making theentire set of force field parameters unreliable. For such complex situations, theforce field parameters must be readily transferable among simulations, and theoverall structure of the force field parameterization must be simple enough toallow calculations for disordered systems containing large numbers of particlesand to effectively capture their complex and often cooperative behavior. Inaddition, the force field must properly account for energy and momentumtransfer between the crystalline solid and the interfacial or interlayer fluid phase.

The MD simulations reported here use the newly developed CLAYFFforcefield (Cygan et al., 2004), which takes this approach. CLAYFF is a generalforce field specifically developed for the simulation of hydrated and multi-component mineral systems, such as clays and similar layered materials, and theinterfaces of these materials with aqueous solutions. It is based on a non-bonded, ionic description of the metal-oxygen interactions. All atoms arerepresented as point charges and are allowed complete translational freedomwithin this force field framework. Metal-oxygen interactions are based on asimple Lennard-Jones (12-6) potential function combined with a Coulombicdescription of the electrostatic interactions. The empirical parameters wereoptimized based on several well-known structures of simple metal oxide andhydroxide minerals. In this approach, the individual atoms do not have their fullformal charges, but rather so-called partial charges that empirically account forelectron transfer in covalent bonds. Oxygen atoms, for instance, typically havepartial charges of -0.8 to -1, rather than their formal value of -2. Cygan et al.

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(2004) derived these partial atomic charges from periodic density functionaltheory (DFT) quantum chemical calculations for several oxide, hydroxide, andoxyhydroxide model compounds with well-defined structures. The Lennard-Jones parameters, which determine the atomic sizes and short-range interactions,were empirically optimized based on experimental crystal structure refinementsof the model phases. Oxygen and hydroxyl charges vary depending on theiroccurrence in water molecules, hydroxyl groups, and bridging and substitutionenvironments. Explicit bonded interactions are used to describe only O-Hbonding in water molecules and hydroxyl groups, and the bonding in polyatomicdissolved species such as SO4

2-. In these cases, the bond stretching (e.g., O-H)and bond angle bending (e.g., H-O-H) interactions are simplified to include onlyharmonic terms.

In all MD simulations of hydrous systems the potential used to describewater is key, and there is a large body of research on this topic dating to the1970’s and even earlier. Several recent reviews discuss the history and currentstatus of MD simulations for water in detail (Robinson et al., 1996; Chialvo andCummings, 1999; Wallqvist and Mountain, 1999; Kalinichev, 2001; Guillot,2002). Here we use the SPC water model to describe H2O and OH (Berendsenet al., 1981). This model has been used successfully in a variety of molecularsimulations to evaluate water structure and properties (Berendsen et al., 1981;Berendsen et al., 1987; Van der Spoel, 1998) and for the interaction of waterwith hydroxide mineral surfaces (Kalinichev et al., 2000; Kalinichev et al.,2001; Kirkpatrick et al., 2001; Kalinichev and Kirkpatrick, 2002). Compared tomore complex water models such as TIP4P (Jorgensen et al., 1983) or BJH(Bopp et al., 1983), SPC is relatively simple. It has partial charges centereddirectly on each of the three atoms, and the short-range interactions arerepresented by a single oxygen-oxygen Lennard-Jones term. The flexibility ofthe H2O molecule is modeled by introducing O–H bond stretch and H–O–Hbond angle bend terms using the expressions determined by Teleman et al.(1987).

The total potential energy of a simulated system generally includescontributions from electrostatic (Coulombic) interactions, short-rangeinteractions (often referred to as the van der Waals term, VDW), and anybonded interactions:

BendAngleStretchBondVDWCoulTotal EEEEE +++= (5)

Coulombic and VDW interactions are excluded for bonded atoms. The energy ofelectrostatic interactions is inversely proportional to the distance between thecharges, rij , as described by the Coulomb law:

∑≠

=ji ij

jiCoul r

qqeE

o

2

4πε, (6)


249

where qi and qj are the atomic partial charges, e is the charge of the electron, andεo is the dielectric permittivity of vacuum (8.85419 x 10-12 F/m). The van derWaals term is represented by the conventional Lennard-Jones (12-6) functionand includes the short-range repulsion dominating the increase in energy as twoatoms closely approach each other and the attractive dispersion energy at largerinteratomic distances:

∑≠

−

=

ji ij

ij

ij

ijijVDW r

R

r

RDE

6

,0

12

,0,0 2

, (7)

where D0,ij and R0,ij are empirical parameters derived from the fitting of themodel to observed structural and physical property data. D0,ij, R0,ij, and thepartial atomic charges are the key parameters in the potentials. The VDWparameters between the unlike atoms are calculated according to the arithmeticmean rule for the distance parameter, R0, and the geometric mean rule for theenergetic parameter, D0 (e.g., Molecular Simulations, 1999):

2/)( ,0,0,0 jiij RRR += , (8)

jiij DDD ,0,0,0 = . (9)

In our calculations, all oxygen atoms are assigned VDW parameters identical tothose for the SPC oxygen atom (Berendsen et al., 1981).

CLAYFF has been successfully tested in MD simulations of a widerange of materials, and it shows good promise to evolve into a widely adaptableand broadly effective force field for molecular simulations of clays and otheraluminosilicate minerals, LDHs and other hydroxide phases, similar amorphousmaterials, mineral interlayers, aqueous fluids, and fluid-mineral interfacesincluding dissolved species (Cygan, 2001; Cygan et al., 2004; Kalinichev et al.,2000; Wang et al. 2001, 2003; Hou et al., 2002; Kalinichev and Kirkpatrick,2002). The applicability of this force field for the molecular modeling of LDHphases has recently found an additional justification in the thermochemicalmeasurements of Allada et al., (2002), who demonstrated that thethermodynamic properties of mixed layered hydroxides can be quite accuratelyestimated by treating them as a mixture of structurally similar binarycompounds. This mechanical-mixture approach works on the atomistic scalebecause the metal and anion coordination environments are structurally and,therefore, energetically similar to those in the simple phases used ascomponents. These are in many cass the same model phases that were used forCLAYFF parameterization (Cygan et al., 2004).

Importantly for the modeling of vibrational spectra described here,

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CLAYFF yields frequencies in the computed atomic power spectra that are insurprisingly good agreement with the observed FIR spectra, even though theforce field is simple, does not explicitly include most covalent bonds, and wasnot optimized to simulate either LDHs or the vibrational properties of anyphases. Thus, it is likely that future force fields will do even better at this task.Our principal purposes here are to describe the MD approach to calculating andinterpreting FIR spectra, to illustrate the information that can be obtained, and toencourage broader application of the methods.

The specific computational methods and algorithms used to carry outthe MD simulations presented below are described in detail elsewhere(Kalinichev et al., 2000, 2001; Hou et al., 2002; Kalinichev and Kirkpatrick,2002; Wang et al., 2003). The MD simulations were performed using periodicboundary conditions, Ewald summation to calculate long-range electrostaticcontributions to the potential energy, and a “spline cutoff” method to calculateshort-range VDW interactions (Molecular Simulations, 1999). NVT- or NPT-ensemble MD algorithms were used at T = 300 K and P = 1 bar. A time step of1.0 fs was used, and all simulated systems were allowed to relax and equilibrateduring 100 ps of MD simulation before the equilibrium dynamic trajectorieswere recorded for further statistical analysis of the structural and dynamiccharacteristics. To ensure thermodynamic equilibrium, the convergence of thetotal energy and its components, as well temperature, density, and atomic radialdistribution functions were carefully monitored during the equilibration period.The equilibrium dynamic trajectory of all atoms was recorded at intervals of 4-8 fs. This time resolution is sufficient to reliably calculate the atomic velocityautocorrelation functions (VACFs) and the corresponding power spectra in theFIR range.

ANALYSIS OF ATOMIC VIBRATIONAL DYNAMICS FROM MDSIMULATIONS

Connection between observed vibrational spectra and MD simulationscan be made by calculating either the power spectra of atomic motions averagedacross the entire MD trajectory or the frequencies of the normal modes ofvibration for one or more individual representative snapshots of a simulation.For the complex, low-frequency motions of hydrous interlayers and mineralsurfaces, we use principally the calculated power spectra. Normal mode analysisis useful principally as a visualization tool to observe the types of motion, but itcannot provide statistically meaningful quantitative information. The normalmode analysis technique most commonly used is standard (e.g., Lasaga andGibbs, 1988; Kubicki, 2001). First, the nearest local minimum of the totalpotential energy (Eq. 5) is found for a single configuration taken from the MD-simulated equilibrium trajectory. Once the optimized atomic configurationcorresponding to the local energy minimum is established, the computedpotential energy surface is approximated by a Taylor series truncated after the


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second term, and the frequencies of each of the 3N -6 normal modes ofvibrational are calculated in the harmonic approximation (N = number of atomsin the system). The vibrational analysis is achieved by diagonalizing thevibrational matrix:

ji

Total

ji

vibij qq

E

mmE

∂∂

∂=

21 (10)

kkkvibE UU λ= (11)

where mi is the mass of the i-th atom, qi is the displacement of this atom in the x-, y-, and z- directions, Uk is the k-th normal mode, and the eigenvalue, λk, isrelated to the vibrational frequencies by:

λk = (2πνk)2 . (12)

In addition to the limitations imposed by the harmonic approximation, the seriesof computed energy-minimized (i.e., effectively “frozen” at 0 K) atomicconfigurations used in the vibrational analysis of normal modes does notcompletely represent the phase space of a dynamic system at a finitetemperature. Thus, the normal mode calculations typically yield frequencies andintensities that are somewhat different than those obtained from the powerspectra. We used this method only as a visualization and interpretation aid.

In contrast, the power spectra computed from the MD-simulated atomictrajectories contain the entire distribution of the power of all atomic motions inthe system throughout the simulation as a function of frequency and with certainrestrictions can be compared to the observed vibrational spectra. The powerspectra are obtained as Fourier transformations of the so-called velocity auto-correlation function (VACF), which can be calculated directly from the MD-simulated dynamic trajectories of the atoms in the model system (e.g.,McQuarrie 1976; Kleinhesselink and Wolfsberg 1992):

Γ⋅=⋅=≡ ∫ dttCvv (t)(0))()0()(VACF vvvv , (11)

where the integration is performed over the entire phase space of the simulatedsystem, Γ.

Qualitatively, the VACF reflects the relative rate with which the systemor its individual atoms “forget” the velocities they had at a particular moment intime, indicated here as t = 0. Fourier transformation of the VACF then gives thespectral density of atomic motions, also called the vibrational density of states orthe power spectrum:

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dttt

P )cos((0)

)((0))(

02

ωω ∫∞ ⋅

=v

vv, (12)

Quantitatively, VACFs are calculated in MD simulations for each atomic typeas:

∑∑= =

+⋅=⋅≡ô

1 1ô

)()(1

)()0()(N

i

N

jijijvv ttt

NNttC vvvv (13)

where Nτ is the number of time averages (using different independent time-origins as t = 0), N is the number of atoms, and vj(t) the velocity of atom j attime t (Allen and Tildesley, 1987). The total system VACF is calculated over allatoms in the system, and the VACFs of individual atom types (e.g., Mg and O ofOH) are calculated for all atoms of a given type.

It is also possible to calculate the individual components of the VACFtensor for a given atom type, and thus analyze the anisotropy of the motion. Forlayered materials, we have found analysis of the three principal anisotropiccontributions, XX, YY, and ZZ, to be very informative. They provide insight intox-, y-, and z- projections of the velocity vectors and therefore the atomic motionsalong different crystallographic directions, greatly enhancing vibrational bandassignment and spectral interpretation. For all results reported here, the x- and y-components of the atomic velocities are parallel to the metal hydroxide layers,and the z-components are perpendicular to the layers. Thus, the XX and YYVACFs reflect the correlations of atomic motions within the plane parallel to thelayers of LDHs and the ZZ VACFs those perpendicular to the layers. As shownin Figures 2 and 3, all VACFs in the systems discussed here decay to zero withinseveral ps, providing spectral resolution of about 5–8 cm-1 in the FIR frequencyrange. The power spectra for light atoms such as hydrogen have lower absoluteresolution than those of other atoms. Figure 3 also shows that the high frequencyintramolecular stretching and bending modes of water molecules can be wellreproduced in such simulations. However, our discussion here focuses on theFIR range of frequencies 600 < ω < 0 cm-1 that reflect mainly the intermolecularmodes involving complex translational and librational motions of interlayerspecies in LDHs and the low-frequency lattice vibrations associated withtorsional motions of the metal-hydroxide sheets.

It is very important to note in comparing computed power spectra andexperimentally observed vibrational spectra that the two are not physicallyidentical, with the result that the calculated and experimental band intensitiescannot be directly compared. The total computed power spectrum includescontributions from all atomic motions recorded in the VACF. In contrast,experimental IR band intensities are related to fluctuations of the electric dipole


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moment due to atomic and molecular vibrations (McMillan and Hess 1988;Kagunya et al. 1998; Bougeard et al. 2000). However, since in the MDsimulations each moving atom bears a partial charge, all atomic motionscontribute to the fluctuations of the system’s electric dipole moment. Thus, thenumber of bands and their positions in the observed and computed spectra arestrongly related. However, the relative intensities of the individual bands cannotbe quantitatively compared using the methods described.

Figure 2. Calculated velocity autocorrelation functions, VACF, (left) and corresponding powerspectra (right) reflecting the dynamics of translational vibrations of Cl- ions in the interlayer ofLiAl2-Cl layered double hydroxide, [LiAl2(OH)6]Cl·1H2O. A similar spectrum for hydrated Cl- ion inbulk aqueous solution is shown for comparison as open circles. XX indicates motions parallel to thehydroxide layers, and ZZ motions perpendicular to these layers.

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Figure 3. Calculated velocity autocorrelation functions, VACF, (left) and corresponding powerspectra (right) reflecting the dynamics of translational, librational, and intramolecular vibrationalmotions of H atoms of water molecules in the interlayer of Ca2Al-Cl layered double hydroxide,[Ca2Al(OH)6]Cl·2H2O (Friedel's salt). XX indicates motions parallel to the hydroxide layers, and ZZmotions perpendicular to these layers. Bands near 3700 cm-1 reflect O-H stretching, bands, the bandnear 1500 cm-1 reflects H-O-H bending, and the lower frequency bands reflect librational motions, asdiscussed in the text.

EXPERIMENTAL FAR INFRARED SPECTRA OF LDH PHASES

The experimentally observed FIR spectra of LDHs provide a rich arrayof features that, in combination with the molecular modeling results, providesignificant information about the structure and dynamical behavior of interlayer


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water and anions. Focus here will be on understanding the similarities anddifferences between LDH interlayers and bulk water and aqueous solutions andon the effects of different hydroxide layer compositions. Figures 4, 5 and 6 showthe experimental FIR spectra for a range of Ca2Al, LiAl2, and Mg3Al LDHphases with different interlayer anions. Synthesis of these samples is describedin Kirkpatrick et al. (1999), Hou and Kirkpatrick (2000, 2002), and Hou et al.(2000a,b, 2002, 2003).

Figure 4. Experimental FIR spectra of Ca2Al LDH phases containing the indicated interlayer anions.Left panels show the 50 – 500 cm-1 portion of the spectra. Right panels show a vertically expandedview of the details of the low-intensity bands in the lower frequency range. Dashed and solid linesrepresent two sets of data collected using two different spectrometers. See text for description ofexperimental methods.

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Figure 5. Experimental FIR spectra of LiAl2 LDH phases containing the indicated interlayer anions.Left panels show the 50 – 500 cm-1 portion of the spectra. Right panels show a vertically expandedview of the details of the low-intensity bands in the lower frequency range. Dashed and solid linesrepresent two sets of data collected using two different spectrometers. See text for description ofexperimental methods.


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Figure 6. Experimental FIR spectra of Mg3Al LDH phases containing the indicated interlayer anions.Left panels show the 50 – 550 cm-1 portion of the spectra. Right panels show a vertically expandedview of the details of the low-intensity bands in the lower frequency range. Dashed and solid linesrepresent two sets of data collected using two different spectrometers. See text for description ofexperimental methods.

The FIR spectra were collected in transmission mode with Bruker IFS66v/S and IFS 66/S spectrometers using standard FT-IR techniques. Spectracould be readily obtained by pressing small amounts of powder onto one side ofa piece of Scotch tape. Figures 4, 5 and 6 contain full FIR spectra from ca. 50 to500 cm-1 and two vertically expanded spectra in the range below ca. 250 cm-1 tobetter illustrate the important low-intensity bands in this region. The spectrashown as dashed lines were collected with a Bruker IFS 66v/S instrument under

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vacuum conditions using a 23 µm Mylar® beam splitter, which is nearly opaquenear 150 cm-1 but is relatively sensitive at other frequencies between 25 and600 cm-1. The spectra shown as solid lines were collected with a Bruker IFS66/S instrument under N2 purge conditions using a 6 µm Mylar® beam splitter,for which sensitivity is optimal at 150 cm-1 and higher frequencies. The bandpositions and relative intensities in the two sets of spectra are in goodagreement.

All the spectra have quite similar overall character, and samples withthe same hydroxide layer composition yield many identical features. All spectracontain a set of relatively intense bands in the range above 300 cm-1 range thatare due principally to librational motions of water molecules and OH-groups(Wang et al., 2003). In the lower frequency range, there is a large number ofrelatively low intensity bands that are related to complex translational vibrationsof interlayer anions and water molecules or to complex, torsional motion ofcations and OH-groups of the main layer. The MD simulations discussed belowprovide insight into the motions responsible for all of these bands.

COMPARISON OF CALCULATED AND OBSERVED SPECTRA

Interpretation of the observed FIR spectra of LDH phases in terms ofinterlayer structure and specific types of molecular motion has previously beenquite difficult, because the interlayers have been poorly understood and becausethe molecular scale motions giving rise to the observed bands are complex. Suchdetailed interpretation is, however, key to connecting the observed spectra tointerlayer structure and dynamics. Comparison of the computed total powerspectra and individual atom power spectra, including their anisotropiccomponents, with the experimental spectra provide the basis for this. Our recentstructural studies of LDH interlayers using principally NMR spectroscopy andMD are also important starting points for these interpretations (Kirkpatrick etal., 1999; Hou and Kirkpatrick, 2000, 2002; Hou et al., 2000a,b, 2002, 2003).

Hydrogen bonding plays a key role in LDH phases, and understandingtheir H-bond networks is essential to understanding their structures anddynamics. The LDH layered structure allows the main-layer OH groups todonate H-bonds to the interlayer anions and H2O molecules, and the interlayerwaters can also form H-bonds between themselves and can donate H-bonds tothe interlayer anions (Figs. 1, 7, 10, 13, 16). Importantly, the relative weaknessof H-bonding interactions between the interlayer species and the hydroxidesheets compared to the much stronger M-OH bonds within the hydroxide sheetsleads to significant decoupling of their vibrational modes (Miyata, 1983;Hernandez-Moreno et al., 1985; Cavani et al., 1991; Kagunya et al., 1997;Kagunya et al., 1998; Wang et al., 2003). Thus, to a good approximation, we cantreat the hydroxide sheets and the interlayers as two separate substructures.


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Interlayer anions and water molecules could each have three translational modesin the interlayer H-bonding network, but two of these modes (XX and YY) can bedegenerate due to the symmetry of the layered structure. Water molecules couldalso have three librational modes associated with rotational motions of H2Ohindered by the H-bonding network. Because the molecular center of mass forH2O nearly coincides with the center of the oxygen atom, the translationalmodes of H2O are highly correlated with the motions of the O atom, whereas thelibrational modes are much more pronounced in the calculated power spectra ofthe hydrogen atoms.

Figure 7. (a) Local structural environment of Cl– ions and H2O molecules in the interlayer of Ca2Al-Cl layered double hydroxide, [Ca2Al(OH)6]Cl·2H2O (Friedel's salt). Color coding as in Figure 1.

Ca2Al-Cl LDH

Hydroxide-layer and interlayer structure. [Ca2Al(OH)6]Cl·2H2O, known ashydrocalumite or Friedel's salt, is an important LDH phase with a well-orderedCa,Al distribution in the hydroxide layer and a high degree of O,Cl ordering inthe interlayer. Because of its structural order and occurrence as relatively largecrystals, it is the only LDH phase for which a single crystal structure refinementis available (Terzis, et al., 1987). Thus, it is currently the best model compoundfor understanding the structure and dynamical behavior of interlayer and surfacespecies in less-ordered LDHs. Even though CLAFF was not optimized for

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[Ca2Al(OH)6]Cl·2H2O, or any other LDH phases, our simulation resultsreproduce the structure very well, a necessary requirement for an effective forcefield (Kalinichev et al., 2000, 2001; Kalinichev and Kirkpatrick, 2002).

Figure 7. (b) Contour map parallel to the hydroxide layers showing the time and space averagedatomic density for interlayer species of Friedel’s salt across the entire calculated MD trajectory. Bluedots and crosses are the Ca positions closest in the neighboring upper and lower hydroxide layers,respectively. Thick red contours are for O atoms of H2O molecules; thin black contours are for Hatoms of H2O molecules, and thick green contours are for interlayer Cl– ions. The restricted librationof the water molecules among three possible H-bonding configurations is readily seen in the three-lobed contours for the H-atoms of H2O

Due to the difference in size between Ca and Al, the Ca ions inFriedel’s salt are displaced ~0.6 Å from the middle of the hydroxide layers alongthe c-direction, with half of them shifted up and half shifted down in an orderedarrangement (Figs. 1 and 7a). This structure produces two different types ofpositively charged sites on the basal [Ca2Al(OH)6] surface to which Cl– or H2Omolecules can coordinate. (Water molecules bear a negative partial charge ontheir O atoms and behave in many ways like the anions.) One type of positivesite is located directly above the Ca cations that are displaced from the middle of


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the hydroxide layer toward the interlayer (Fig. 7a). In the Friedel’s salt interlayerall sites of this type are occupied by water molecules, which are displaced≈0.8 Å from the central plane of the interlayer by the electrostatic forces. Thiseffectively creates two sub-layers of H2O molecules associated, respectively,with Ca cations in the “upper” and “lower” hydroxide layers sandwiching aninterlayer and completing the unusual 7-fold coordination of each Ca site in thisstructure (Terzis et al., 1987; Kalinichev et al., 2000). The second type ofpositive site is located above Ca atoms shifted in the hydroxide layer away fromthe interlayer and is formed by three hydroxyl groups bending towards theinterlayer species (Figure 7a). In the Friedel’s salt interlayer, Cl- occupies allsites of this type (Terzis et al., 1987; Kalinichev et al, 2000; Kalinichev andKirkpatrick, 2002). Thus, each interlayer Cl- is coordinated by three OH groupsfrom the “upper” hydroxide layer, three OH groups from the “lower” hydroxidelayer and four hydrogens of neighboring H2O molecules, all through H-bonds.

The 10-coordinate arrangement of H-bonds to Cl– is well reproduced inour MD simulations, which also reveal significant dynamical disorder of thewater orientations that are not captured in the X-ray diffraction measurements(Kalinichev et al., 2000). The interlayer water molecules constantly undergolibrational motions (hindered hopping rotations) around an axis essentiallyperpendicular to the layers. This results in breaking and reformation of H-bondswith the neighboring Cl– anions. At any instant each water molecule is H-bonded to 2 Cl-, but because it hops among three possible pairs of Cl-, onaverage it is H-bonded to each one about 2/3 of the time. From the perspectiveof the Cl– ion, this results in a time-averaged nearly uniaxial symmetry.Although at any instant each Cl- is receiving an average of four H-bonds fromthe neighboring water molecules, averaged over time there are six H-bonds with2/3 occupancy. The time-averaged picture of the structural ordering in theFriedel’s salt is well illustrated by the atomic density contours on Figure 7b.These results are in excellent agreement with variable-temperature NMR(Kirkpatrick et al., 1999; Andersen et al., 2002) and synchrotron X-ray data(Rapin et al., 2002), which indicate a structural phase transition in this materialnear room temperature. This ability to model both structural and dynamicalaspects of these complex LDH systems has continued to be borne out throughoutour simulation efforts (Kalinichev et al., 2000, 2001; Hou et al., 2002;Kalinichev and Kirkpatrick, 2002; Wang et al., 2001, 2003).

Translational dynamics of interlayer species. The calculated power spectra forinterlayer Cl- and H2O in Friedel’s salt both show two bands of translationalmodes (Figure 8a). For water, the band centered near 80 cm-1 is associatedmainly with molecular motions parallel to the layering in the x-y plane (XX andYY components of the VACFs; inset to Figure 8a), and the band centered near210 cm-1 is due mainly to ZZ motions (inset to Figure 8a). Similar bands for theinterlayer Cl- are centered near 40 and 130 cm-1, respectively.

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Figure 8. Calculated power spectra of atomic motions in Ca2Al-Cl LDH. (a) Low frequencytranslational vibrations of Cl– ions and H2O molecules in the interlayer. The calculated powerspectrum of OH2O in bulk water is shown as open circles for comparison. H-bond stretching andbending are illustrated in the inset. (b) Librations (hindered rotations) of interlayer H2O moleculesand OH groups of the main hydroxide layers. The three librational modes of H2O are schematicallyillustrated in the insert. (c) Low frequency lattice vibrations of the [Ca2Al(OH)6] octahedra of themain hydroxide layers.


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In bulk water and ice, the two bands of translational vibrations centerednear 60 and 200 cm-1 are associated with the O···O···O bending and O···Ostretching of hydrogen bonds, respectively (e.g., Eisenberg and Kauzmann,1969). Water molecules in the first hydration shell of Cl- in bulk aqueoussolutions also have similar modes (Bopp, 1987). Because the interactions amongCl-, water and OH are due principally to H-bonding, all translational modes aredifferent combinations of the stretching and bending vibrations of the interlayerH-bonding network. The translations in the x-y plane are related mainly to thebending of H-bonds between OH and the interlayer species, whereas thetranslations in the z direction are related mainly to stretching of H-bondsbetween OH and the interlayer species. Smirnov and Bougeard (1999) haveobserved similar translational dynamics of interlayer H2O molecules in their MDsimulations of kaolinite.

Librational modes of H2O and OH. Water molecules have three possiblelibrational modes (hindered rotations around the molecular center of mass).These modes are schematically represented in the insert in Figure 8b and can bedescribed as twisting motion around an axis ζ corresponding to the bisector ofthe H-O-H angle (dipole axis), wagging motion around an axis η that isperpendicular to ζ in the plane of the molecule and parallel to the HH vector,and rocking motion around an axis ξ that is perpendicular to the plane of themolecule. Based only on the molecular moments of inertia around the differentaxes, the frequencies of the three librations for a free water molecule increase inthe order frock < ftwist < fwag. In MD simulations of bulk water (e.g., Heinzinger,1990; Lu et al., 1996), all three components of the simulated spectra overlapeach other over a wide frequency range between 300 and 700 cm-1, resulting inone broad librational band of the spectrum, in agreement with experimentalobservation (e.g., Eisenberg and Kauzmann, 1969). Due to the greater orderingand reduced mobility of water molecules in the LDH interlayers, the librationalbands of interlayer water are much narrower (Figure 8b).

The strong electrostatic attraction between negatively charged oxygenatoms of interlayer water molecules and Ca cations in the hydroxide layer makesthe Ca···OH2O bond direction the preferred axis for H2O librations. On the otherhand, the calculated distribution of instantaneous dihedral angles between the H-O-H plane of the water molecules and the (001) crystallographic plane exhibits adistinct maximum at about 50 degrees. In this orientation, hopping rotationalmotions of interlayer H2O molecules around the Ca···OH2O bond axis contributeto all three librational modes in Figure 8b.

Surprisingly, the librational spectrum of the hydroxyl groups (HOH) alsoshows three distinct peaks in the frequency range between 300 and 800 cm-1

(solid line in Fig. 8b). We associate the presence of these peaks with threestatistically distinguishable ranges of H-bonding strength between OH groupsand interlayer Cl- ions, possibly as the result of Cl- translational vibrations.

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Vibrational modes of the [Ca2Al(OH)6] octahedra. The principal normal modesof vibration for an ideal brucite-like structure occur at frequencies above the FIRrange studied here (Lutz et al. 1994). In LDHs, however, cation substitution andthe consequent structural distortion cause some modes related to the hydroxidesheet vibrations to occur at lower frequencies, in the FIR range (Kagunya et al.,1998; Wang et al., 2003). For Friedel’s salt, five of the most prominent modesoccur at about 70, 120, 180, 240 and 350 cm-1 in the calculated power spectrum(Fig. 8c), and are in good agreement with the vibrational bands observedexperimentally (Fig. 9). The principal types of motion for each of these modescan be deduced from the decomposition of the Ca, Al, and OOH power spectrainto XX, YY, and ZZ anisotropic components and normal mode analysis. Themode at 70 cm-1 involves Al moving principally in the x-y plane with Ca movingprincipally perpendicular to this in the z direction. We can describe this complexmotion as a combination of the A2u and Eu vibrational modes of an undistortedmetal hydroxide octahedron. A similar type of motion is responsible for themode at 120 cm-1, but with Al vibrating in the z direction and Ca in the x-yplane. The mode at 180 cm-1 is mainly due to Ca motions in the x-y plane (Ca-Eu). The mode at 350 cm-1 involves principally Al motions in the x-y plane withOH also cooperatively moving parallel to this plane (Al-Eu). OOH motions withXX, YY, and ZZ components of approximately equal intensity contribute to all ofthe modes at 70, 120, 180, 240 and 350 cm-1. In the experimental spectra the lasttwo modes are better resolved than in the total calculated spectrum and occur astwo distinct peaks at 260 and 320 cm-1. The lower frequency modes overlap thetranslational modes of the interlayer Cl- and H2O (Fig. 9a,b).

LiAl2-Cl LDH

Hydroxide-layer and interlayer structure. In the LiAl2 layered doublehydroxides, Li+ occupies the octahedral vacancies of a dioctahedral gibbsitesheet, and X-ray diffraction data indicate that the Li,Al distribution is highlyordered (Serna et al., 1982; Besserguenev et al., 1997). 7Li and 27Al NMR dataconfirm the Li,Al structure (Isupov et al., 1998). X-ray data provides limitedinformation about the structural environments and dynamical behavior ofinterlayer and surface species, but our recent 35Cl NMR experiments for theLiAl2(OH)6Cl·H2O phase have proven particularly useful for investigating theseissues (Hou et al., 2002).

MD calculations for LiAl2(OH)6Cl·H2O provide structural anddynamical insight that substantially improves interpretation of the X-ray, NMR,and FIR data, and agreement between the computed and observed vibrationalfrequencies are particularly good for this phase. Dynamically, the computationsshow the expected rapid (ca. 1011 Hz) librational hopping of the water moleculesamong possible H-bonding orientations and also relatively rapid diffusionalhopping of Cl- and water molecules among sites. The restricted libration of the


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Figure 9. Comparison of calculated power spectra for Ca2Al-Cl LDH (heavy line) with observed FIRspectra. Light dashed and solid lines represent two sets of experimental data collected using twodifferent spectrometers. See text for description of experimental methods.

water molecules is comparable to that observed for interlayer water in Ca2Al-Cland other LDH phase and is well illustrated by the multiple peaks for the H-atoms of individual water molecules in the atomic probability density contourplot (Figure 10a). Such plots are very useful for understanding interlayer andsurface structure and atomic motion, and the one in Figure 10a was obtained byplotting the instantaneous atomic positions over the entire 100 ps equilibriumMD trajectory. The calculated mean frequency of Cl- site hopping is of the orderof 3x108 Hz, and that for water about an order of magnitude faster. Althoughthese values are near the limits of statistical reliability for the calculations, theyare fully consistent with the experimentally observed peak narrowing in thevariable temperature 35Cl NMR data (Hou et al., 2002). The minimum hoppingfrequency from these data is of the order of 103 Hz.

Structurally, the results indicate a disordered but not randomarrangement of Cl- ions and H2O molecules in the interlayer. Unlike theinterlayer arrangement of H2O in the Ca2Al-Cl phase discussed above (formingtwo sub-layers due to coordination of the Ca of the hydroxide layer), the watermolecules in the LiAl2-Cl phase are all located in the middle the interlayer, andthe OH2O receives two H-bonds, one each from an OH-group on each side theinterlayer. Simultaneously, the water molecule donates its two H-bonds to twoCl- ions, which are located on several different types of sites all of which are atthe middle of the interlayer along the c-axis. Because of the eclipsed layer

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Figure 10. (a) Calculated of atomic probability density contour map in the plane of the interlayer(b, a*) of [LiAl2(OH)6]Cl·H2O. Contours: green = Cl-, red = O of water, thin black = H of water,thick black = H of OH of hydroxide layer below interlayer, pink = Al of hydroxide layer belowinterlayer, blue = Li of hydroxide layer below interlayer.

Figure 10. (b-c) Cl- and H2O structural environments in the interlayer of [LiAl2(OH)6]Cl·H2O. Cl-

ion is located in a distorted octahedral environment viewed from the direction parallel (b) andperpendicular (c) to the interlayer, respectively. Green balls = Cl-, red balls = O of water or OH,black balls = H of water or OH, pink octahedral = Al of hydroxide layer, blue balls = Li ofhydroxide layer (shown not to scale to improve visibility).


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stacking (Besserguenev et al., 1997), each water molecule is in a stable,distorted tetrahedral coordination (Figs. 10b,c) very similar to that in bulk liquidwater. This configuration orients the H-O-H plane the water molecules parallelto the interlayer, allowing it to donate H-bonds to the neighboring Cl- ions. Afew of the interlayer Cl- occupy sites that are near the vector connecting Liatoms in adjacent hydroxide layers and are comparable to the Cl- sites in thedehydrated phase, in which all Cl- are located exactly along the Li-Li vector.Most Cl-, however, are on distorted octahedral sites formed by H-bonds receivedfrom two OH-groups above, two OH-groups below and two H2O (Fig. 10b,c).The four OH-groups of this site form a rectangle due to the eclipsed layerstacking, and the mean Cl- position is near its center. The H-bonds from the twowater molecules are on an axis ca. 60o to the square of OH-groups, and theoctahedron is quite asymmetric and also dynamic due to the hopping libration ofthe H2O molecules.

The computed interlayer structure also provides an explanation for theunusual maximum 1/1 Cl/H2O ratio observed for LiAl2 LDHs. Other well-ordered LDH phases, most notably Friedel’s salt (CaAl2), have maximumH2O/Cl ratios of 2 (see above). In the interlayer of Friedel’s salt, all OH2O arecoordinated by Ca cations, and the OH-groups donate H-bonds only to the Cl-

ions, which at any instant are 10 coordinate (six OH and four H2O). In the LiAl2

phases, the OH2O cannot coordinate either Li or Al, and their positions arestabilized by the H-bonding network. Of the six OH-groups per formula unit,two are used to coordinate the one water and four to coordinate the one Cl-.Thus, there are no stable interlayer sites for substantial amounts of additionalwater. Indeed, in an MD simulation with an H2O/Cl ratio of 2/1, the structuredisaggregated.

Translational dynamics of interlayer species. The calculated frequencies of thetranslational vibrational motions of interlayer Cl- ions and H2O molecules in thepower spectrum of the LiAl2-Cl LDH phase (Fig. 11a) are very similar to thoseof the Ca2Al-Cl LDH, although due to the different orientation of interlayerwater molecules in the LiAl2 phase, the band near 90 cm-1 is now associatedmainly with molecular motions perpendicular to the layering (bending ofHOH···Cl···HO bonds), whereas the band centered near 210 cm-1 is due to H2Otranslational vibrations in the x-y plane (stretching of HOH···Cl bonds).

Vibrational modes of the [LiAl2(OH)6] octahedra. The seven most prominentmodes associated with vibrations of [LiAl2(OH)6] octahedra occur in thecalculated power spectrum at about 90, 140, 190, 280, 350, 450 and 570 cm-1

(Fig. 11b), and the computed and observed band frequencies are in excellentagreement (Fig. 12). Decomposition of the Li, Al, and OOH power spectra intotheir X X, Y Y, and ZZ components shows that the band at 570 cm-1 is acombination of A1g and Eu vibrational modes of Li ions (see the insert in Fig. 8cfor notation), the bands at 450 and 350 cm-1 Li-A2u with a contribution from Al-Eu, and the band near 280 cm-1 a purely Al-Eu mode. The lower frequency bands

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are due primarily to Al and Li motions in the z direction, with a lessercontribution from OOH motions in the x-y pane, OH-(Eu+Eg). The FIR spectrumof gibbsite contains a similar sequence of vibrational modes for Al(OH)6

octahedra (Ruan et al. 2002).

Figure 11. Calculated power spectra of atomic motions in [LiAl2(OH)6]Cl·H2O. See Figure 8 fornotation.

LiAl2-SO4 LDH

Hydroxide-layer and interlayer structure. The structure of the hydroxide layerof [Li2Al4(OH)12]SO4·nH2O is the same as that of the LiAl2-Cl phase, but due tothe presence of large divalent SO4

2- anions in the interlayer, the structure of theinterlayer is much more disordered. This disorder allows for a wider range ofhydration states (n) and leads to a different type of swelling behavior. Water-


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vapor sorption isotherms and relative-humidity-controlled powder X-raydiffraction data (Hou et al., 2003) show that near room humidity the equilibriumnumber of interlayer H2O molecules per anion is n ≈ 3.5. We have performedMD simulations for 0 ≤ n ≤ 6 in this phase, and the calculated layer expansionsare in good agreement with the experimental observations (Hou et al., 2003).We show only the results for n = 3 below for comparison with experimental FIRspectra (Fig. 5).

Figure 12. Comparison of calculated power spectra for [LiAl2(OH)6]Cl·H2O (heavy line) withobserved FIR spectra. Light dashed and solid lines represent two sets of data collected using twodifferent spectrometers. See text for description of experimental methods.

Structurally, the MD results show that the interlayer water molecules inthe LiAl2-SO4 phase form two sub-layers, in contrast to the single layer andplanar orientation in the LiAl2-Cl interlayer. The positions of water moleculesare controlled by their H-bonding to the negatively charged O atoms of sulfate(Fig. 13), rather than by their coordination to Ca in the hydroxide layer, as in theCa2Al-Cl phase (Fig. 1, 7). For n = 3 or 4 approximately 70% of all SO4

2- ionshave C2 orientation with two O-atoms on either side of the interlayer. About30% have C3 orientation with three O-atoms on one side of the interlayer andone on the other. The combined result of these effects is much greater positionaland orientational disorder than in either the LiAl2-Cl or Ca2Al-Cl phases.

Translational dynamics of interlayer species. The calculated power spectra forinterlayer SO4

2- and H2O in the LiAl2-SO4 LDH phase (Fig. 14a), are quitesimilar to those for the Ca2Al-Cl (Fig. 8a) and LiAl2-Cl (Fig. 11a) LDH phases.

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Both SSO4 and OSO4 show a low-frequency peak due to translational vibrations ofthe sulfate ions, with the OSO4 band showing significant broadening due to itsslow librational motions hindered by H-bonding interactions to the neighboringwater molecules and OH groups of the hydroxide layer. The bands near 450 cm-1

in Figure 14a are due to internal vibration of the S-O bonds, reflected in thepower spectra of both SSO4 and OSO4.

Figure 13. Calculated SO42– and H2O structural environments in the interlayer of LiAl2-SO4 LDH

phase, [Li2Al4(OH)12]SO4·3H2O.

Librational modes of H2O and OH. The bands for H2O and OH hinderedrotations in the LiAl2-SO4 phase (Fig. 14b) are much broader those of the Ca2Al-Cl and LiAl2-Cl phases, consistent with its greater structural disorder. Themaximum intensity of the librational bands for both H2O and OH are shifted tohigher frequencies (ω > 600 cm-1), indicating a generally greater strength of H-bonds to the divalent SO4

2- anion.

Vibrational modes of the [LiAl2(OH)6] octahedra. As expected from thedecoupling of the motions of the interlayer and hydroxide layer, the componentsof vibrational spectrum of the [LiAl2(OH)6] hydroxide layer are not verysensitive to interlayer composition (Figs. 14c and 11c). However, all bands aresomewhat broadened relative to the LiAl2-Cl phase, indicating strongerinteraction of the octahedral layer with divalent interlayer SO4

2-. Overallagreement between computed and experimental spectra is not as good in thiscase, with the experimental band near 400 cm-1 being represented by a shouldernear 450 cm-1 in the calculated spectrum (Fig. 15a). There is good agreementbelow 350 cm-1 (Fig. 15b).


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Figure 14. Calculated power spectra of atomic motions in [Li2Al4(OH)12]SO4·3H2O. See Figure 8 forthe notation.

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Figure 15. Comparison of calculated power spectra for [Li2Al4(OH)12]SO4·3H2O (heavy lines) withobserved FIR spectra (lighter lines). (a) Full FIR spectra. (b) Vertically amplified view showinglow-intensity details in the lower frequency range. Lighter dashed and solid lines represent two setsof data collected using two different spectrometers. See text for description of experimentalmethods.


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Mg3Al-Cl LDH

Hydroxide-layer and interlayer structure. The most detailed MD modeling studyof the FIR frequency range for LDH phases has been recently published for theMg3Al-Cl phase, Mg3Al(OH)8Cl·3H2O (Wang et al., 2003). The interlayerstructure of this phase (Fig. 16) bears some resemblance to those of both theCa2Al-Cl and LiAl2-Cl phases. As in the Ca2Al-Cl phase, interlayer watermolecules form two sub-layers, but only some of them are coordinated to Mg.Others are coordinated by OH groups, as in the LiAl2-Cl phase. This similaritymost prominently exhibits itself in the shapes and positions of the H2O and OHlibrational bands, as described below. Both H2O and Cl- are distributed betweenthe two sublayers in such a way that none of them is able to simultaneously formdirect H-bonds to both adjacent octahedral layers (Fig. 16a). This structuralarrangement is well illustrated by the computed atom-atom radial distributionfunctions and the integrated atomic coordination numbers (Wang et al., 2003).Each Cl- ion accepts on average ~2.5 H-bonds from the OH groups and ~4.0 H-bonds from neighboring H2O molecules. In contrast, in LiAl2-Cl LDH thesituation is just the opposite, with each Cl- accepting on average ~4.0 H-bondsfrom the OH groups of the main layers interlayer and only ~2.5 H-bonds fromwater molecules (Hou et al., 2002, see also Fig. 10b,c). However, the averagenearest neighbor (Cl···H) structural environment of Cl- is strikingly similar inboth cases and strongly resembles that of Cl- in bulk aqueous solution. Theaverage number of H-bonds to interlayer Cl- is ~6.5, and the average H-bonddistance is 2.21 Å, in excellent agreement with experimental neutron diffractiondata (Powell et al., 1993) and previous simulations for bulk aqueous solutions(Smith and Dang, 1994).

The average nearest-neighbor environment of the interlayer H2Omolecules is, however, somewhat different than in bulk liquid water(Fig. 16a,b). In the Mg3Al-Cl LDH interlayer, the oxygen atoms of the watermolecules accept on average ~1.3 H-bonds from the OH groups of the hydroxidelayers and ~0.6 H-bonds from other H2O molecules. Simultaneously, the watermolecules donate on average ~0.3 H-bonds to neighboring H2O molecules and~0.65 H-bonds to interlayer Cl-. This structure results in an average total of 3.8H-bonds per interlayer water molecule, significantly higher than the calculatedvalue of 3.2 for bulk liquid water (e.g., Kalinichev 2001) and close to the valueof 4.0 for ice.

Translational dynamics of interlayer species. The band frequencies in thecalculated power spectrum and observed FIR spectrum of[Mg3Al(OH)8]Cl·3H2O (Figures 17 and 18) are in good agreement, although notas good as for the LiAl2-Cl phase. The computed power spectrum for Mg3Al-Clcontains three major bands in the range from 325 to 450 cm-1, in goodqualitative agreement with the observed spectrum. The separation of these bandsfrom each other is greater in the computed spectrum, because the calculated

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Figure 16. A snapshot of the [Mg3Al(OH)8]Cl·3H2O structure illustrating the instantaneous structureof the H-bonding network in the interlayer. (a) Viewed along the [010] direction. Balls are Cl- ionsand V-shaped moieties are water molecules. The dashed lines represent H-bonds. The mainhydroxide layer is represented by Mg,Al octahedra and OH sticks. (b) Interlayer Cl- and H2Omolecules viewed along the [001] direction illustrating the disordered H-bonding between watermolecules and Cl-. The H2O-Cl- H-bonding is dynamically disordered, and water molecules hop(librate) among multiple possible orientations.


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frequencies of these bands are 20-50 cm-1 lower than the observed frequencies.As for the other LDH phases (Figs. 9b, 12b and 15b), there is a bettercorrespondence between the frequencies in the measured and calculated spectrain the lower frequency range (Fig. 18). For most bands, the observed andcomputed frequencies of Mg3Al-Cl LDH are nearly the same, but those at 145,157 and 180 cm-1 in the observed spectrum are shifted about 4-13 cm-1 to 132,153 and 171 cm-1 in the calculated spectrum.

Figure 17. Calculated power spectra of atomic motions in [Mg3Al(OH)8]Cl·3H2O. See Figure 8 forthe notation.

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Figure 18. Comparison of calculated power spectra for [Mg3Al(OH)8]Cl·3H2O (heavy line) withobserved FIR spectra. Lighter dashed and solid lines represent two sets of data collected using twodifferent spectrometers. See text for description of experimental methods.

As for the other LDH phases, the lower frequency (ω < 300 cm-1)vibrational modes of the interlayer species of the Mg3Al-Cl phase are bestvisualized as complex translational motions involving different combinations ofthe stretching and bending vibrations of the interlayer H-bonding network. Cl-

and OH2O have similar sizes and charges, and thus Cl- ions can substituterelatively easily for water molecules in this H-bonding network. Because theinteractions among Cl-, water and OH of the octahedral sheet are principally dueto H-bonding, these motions are comparable in many ways to those of water (seeFigs. 8a, 11a, 14a, and 17a). The OH2O bands centered near 60 cm-1 areassociated mainly with water motions parallel to the hydroxyl layer in the x-yplane (XX and YY components of the VACFs), whereas the band centered near200 cm-1 is due mainly to ZZ motions. Thus, the lower frequency translations inthe x-y plane are related mainly to the bending of H-bonds between OH and theinterlayer species, whereas the higher frequency translations in the z directionare related mainly to stretching of H-bonds between OH and the interlayerspecies. Interlayer Cl- has bands involving comparable motion near 40 cm-1

(mainly XX and YY motions) and 120 cm-1 (mainly ZZ motions). Cl- also has twoother bands that involve different styles of motion. The band at 80 cm-1 containsnearly equal contributions from the XX, YY and ZZ components, and thus at thisfrequency, interlayer water undergoes mainly translational vibrations in the x-yplane, and the Cl- vibrates equally in the x, y, and z directions. The broad bandcentered near 210 cm-1 is associated with Cl- translational motions mainly in the


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x-y plane, whereas at this frequency interlayer H2O molecules move mainly inthe z direction, and there is significant stretching of the H-bonds between waterand Cl-.

Vibrational modes of the [Mg3Al(OH)8] octahedra. As for other LDH phases,the spectral contributions due to the Mg, Al and OOH motions are stronglycorrelated (Fig. 17b). In the Mg3Al-Cl case, all atoms constituting the octahedrallayer have bands near 90, 170, and 330 cm-1. Al and Mg also have bands near250 cm-1, Mg and OOH have a band near 480 cm-1, Mg has a strong band near130 cm-1, and OOH has a band near 290 cm-1. For Mg (dashed line in Fig. 17b),the bands near 90 and 130 cm-1 are due to motions contributing to the Z Zcomponents of velocity, those near 250 and 480 cm-1 mainly to the XX/YYcomponents, and those near 330 and 170 cm-1 to all three. Similarly, for Al(thick solid line in Fig. 17b), the band near 170 cm-1 is due mainly to the ZZcomponent and those near 90, 250 and 330 cm-1 mainly to the XX /YYcomponents. For the OH groups (thin solid line in Fig. 17b), the bands near 480and 370 cm-1 are associated with the motions contributing mainly to the ZZcomponents, and the bands near 330, 290 and 170 cm-1 mainly to the XX/YYcomponents.

POWER SPECTRA OF AQUEOUS SPECIES ASSOCIATED WITH LDHSURFACES

The positive structural charge of the LDHs hydroxide sheets can becompensated by anions not only in the interlayer space but also on externalsurfaces. As for the interlayer species, MD modeling can be an effective tool toinvestigate the structural environments and dynamical behavior of surface-associated species. We present here the results of MD simulations of theinteractions between the surface of [Ca2Al(OH)6]Cl·2H2O LDH and aqueoussolutions containing NaCl, Na2SO4, and Na2CO3. To simulate the mineral-fluidinterface, the layer structure of Ca2Al-Cl LDH from previous simulations wascleaved parallel to the hydroxide layers [along (001)] within the interlayer. Thisexposes OH-groups on the surface, the normal case for such materials in contactwith water. The model surface was then brought into contact with a layer ofaqueous solution, and periodic boundary conditions were applied in all threedimensions to produce interface models containing 30-40 Å-thick solid layersand 30 Å-thick layers of aqueous solution between them. The thickness of thesolution layer was chosen to be sufficiently large to effectively exclude directinteraction between neighboring mineral-fluid interfaces created by the imposedperiodicity. The number of H2O molecules in the fluid layer was chosen toreproduce the density of the bulk aqueous solutions under ambient conditions(~1 g/cm3). The computational details of such simulations are discussed inKalinichev and Kirkpatrick (2002).

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We distinguish three types of surface-related molecular environmentsin the aqueous phase: 1) inner-sphere surface complexes – the ions directlycoordinated by atoms of the LDH surface; 2) outer-sphere surface complexes –the ions separated from the surface by one molecular layer of water; and 3) ionsin the bulk solution – ions separated from the surface by more than onemolecular layer of water. (We recognize that readily detectable effects of thesolid surface on the fluid structure often extend to ca. three molecular layers.)The number of ions present in the simulations was not sufficient to effectivelyprobe the macroscopic behavior of the diffuse (Gouy) layer near the surface,which can easily have a thickness comparable to that of the entire aqueous layerin our simulations, depending on solution composition.

Figure 19. Calculated power spectra of atomic motions for adsorbed aqueous species (H2O, Cl–,SO4

2–, CO32–) on the (001) surface of Ca2Al-Cl LDH.

Movement of individual atoms and molecular groups among inner-sphere, outer-sphere, and bulk environments is clearly observable on the 100 pstime scale of our simulations. With respect to the power spectra, thecharacteristic relaxation times of the atomic velocity autocorrelation functions


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for all species, however, are always at least an order magnitude less than thetypical lifetime on an individual surface site, justifying the classification aboveand the following analysis. For H2O and Cl–, the lifetimes as inner-spheresurface complexes are about 30-50 ps, whereas they are several times longer forCO3

2– and SO42– due to their larger masses and charges. For Cl– this estimate is

consistent with the rapid hopping of ions between surface-sorbed and solution-like sites (_ < 10-6 s) observed for pastes of Ca2Al-Cl LDH and water using 35ClNMR spectroscopy (Kirkpatrick et al., 1999, 2001).

The power spectra of atomic motions of inner-sphere surface species inthe FIR frequency range are generally intermediate between those of theircorresponding interlayer and bulk counterparts and contribute to the samevibrational bands in the total FIR spectra (Figure 19). Analysis of XX, YY and ZZcontributions to the CO3

2– and SO42– spectra indicates that both spend their time

on the surface with three oxygen atoms simultaneously receiving H-bonds fromthe surface OH-groups.

CONCLUSIONS

The combination of experimental far infrared spectroscopy andmolecular dynamics modeling is highly effective in probing the structure anddynamics of water molecules and ionic and molecular species to mineralinterlayers or adsorbed on the surfaces of layered minerals. These methodsdirectly probe the intermolecular and H-bonding interactions that dominate thesematerials. Molecular modeling techniques, such as those discussed in thischapter, aid significantly with band assignment to the complicated patterns ofatomic motions present in these complex situations and also with interpretationsof the many overlapping bands.

The principal limitation of this approach, which is characteristic of allsemi-empirical molecular modeling approaches, is the accuracy of theinteratomic potentials. The CLAYFF force field (Cygan et al., 2004) used in oursimulations was not specifically optimized to reproduce either the structure ofLDHs or their vibrational properties. Moreover, apart from the intramolecularharmonic stretching and bending terms for interlayer H2O molecules, oxyanionsand OH groups of octahedral layers, the force field model contains no explicitparameters related to interatomic bonding or vibration. Nevertheless, there isremarkably good agreement of the frequencies in the calculated power spectraand the experimentally measured FIR spectra for the LDH phases. These resultsclearly demonstrate that the combination of experimental vibrationalspectroscopy and molecular modeling has significant potential to help unravelthe details of the structural and dynamic behavior of aqueous systems inconfined environments such as interlayers of LDHs, clays, nano-pores ofzeolites, biomolecular systems, and other heterogeneous fluid media dominatedprimarily by hydrogen bonding.

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ACKNOWLEDGEMENTS

This research was supported by DOE Basic Energy Sciences GrantDEFGO2-00ER15028. Computation was partially supported by the NationalComputational Science Alliance (Grant EAR 990003N) and utilized NCSASGI/CRAY Origin 2000 computers and Cerius2-4.0 software package fromMolecular Simulations Inc. J. Wang also acknowledges the fellowship from theUniversity of Illinois at Urbana-Champaign. Fruitful discussions with Dr.R. T. Cygan about force field parameterization and Dr. Ping Yu about LDHstructure are most gratefully acknowledged. The far-infrared spectra werecollected at the W. R. Wiley Environmental Molecular Sciences Laboratory, anational scientific user facility sponsored by the U.S. Department of Energy'sOffice of Biological and Environmental Research and located at PacificNorthwest National Laboratory. PNNL is operated for the Department of Energyby Battelle.

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OF INTERLAYER AND SURFACE SPECIES OF LAYERED DOUBLE … · 2005-10-20 · volumes. Traditional diffraction methods have proven insufficient to adequately address these issues, but