Chemical Physics Letters 389 (2004) 261–267

www.elsevier.com/locate/cplett

Simulation of hydrated Liþ-, Naþ- and Kþ-montmorillonite/polymernanocomposites using large-scale molecular dynamics

Pascal Boulet a,*,1, Peter V. Coveney a,*, Stephen Stackhouse b

a Centre for Computational Science, Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, UKb Department of Chemistry, Queen Mary, University of London, Mile End Road, London E1 4NS, UK

Received 26 September 2003; in final form 17 March 2004

Available online 13 April 2004

Abstract

We report a theoretical investigation of hydrated clay–polymer nanocomposites exchanged with Liþ, Naþ and Kþ. This work is

the result of the implementation of Teppen’s force field within a highly scalable molecular dynamics (MD) program called Large-

scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) with which, we performed large-scale MD simulations. The

results show that, in contradiction to the situation pertaining in the absence of polymer, the behaviour of Liþ and Naþ based

nanocomposites is quite distinct. Unlike Kþ and Naþ, the Liþ cations are observed to diffuse within the tetrahedral pockets of the

clay sheets as well as the centre of the galleries.

� 2004 Elsevier B.V. All rights reserved.

1. Introduction

To understand the behaviour of biological systems

molecular dynamics simulations must span very long

periods of time (between 1 and 100 ns is usually the

minimum to see interesting effects) relative to the very

small size of the integration time step (of the order of afemtosecond). This requirement stems from the size of

biological molecules, their solvation by water (meaning

models must be several tens or hundreds of thousand

atoms in size) and the fact that conformational motions,

and associated transport processes, take place on such

time scales. Although it is beginning to become common

practice to perform these so-called large-scale simula-

tions [1,2] in the field of computational molecular biol-ogy, to our knowledge this approach has not so far been

widely adopted in the context of nanocomposite mate-

rials. However, with the design of ever more powerful

* Corresponding authors. Fax: +44-20-7679-7463.

E-mail addresses: P.Boulet@ucl.ac.uk (P. Boulet), P.V.Coveney

@ucl.ac.uk (P.V. Coveney).1 Present address: Laboratoire de Physico-chimie de la Mati�ere

Condens�ee, UMR CNRS 5617, Universit�e Montpellier II, Place

Eug�ene Bataillon, 34095 Montpellier cedex 5, France.

0009-2614/$ - see front matter � 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.cplett.2004.03.084

computers, we are developing a growing ability to sim-

ulate more realistic systems using increasingly large

models, and clay–polymer nanocomposites are examples

whose complexity requires such simulations. These

nanocomposites have proved to be promising new ma-

terials, for instance, in the construction of batteries, as

potential electrolytes, heat refractors, and mechanicalstrength enhancers [3–5].

With the relentless development of ever more pow-

erful hardware, we have the opportunity to extend

computer simulation to even bigger and more complex

systems. However, while the increased raw computa-

tional speed is due to the evolution of hardware archi-

tecture, to fully harness this power for the purpose of

large-scale simulation new generations of algorithmsmust be used. Large-scale simulations are now amenable

thanks to the construction of such algorithms based on

spatial domain decomposition. These molecular dy-

namics (MD) programmes (LAMMPS) [6], NAMD [7])

show impressive improvement in terms of scalability

when compared to conventional MD codes and hence

dramatically reduce wallclock time for simulations. In

addition, related algorithms, such as rRESPA [8],SHAKE [9] or PPPM [10–13], further enhance the

ability of these codes to reach longer times.

262 P. Boulet et al. / Chemical Physics Letters 389 (2004) 261–267

This Letter concerns the implementation of the Tep-

pen force field within the scalable LAMMPS code and

reports on the performance of large-scale simulations on

poly(ethylene glycol)/Mþ-montmorillonite nanocom-

posites (where M is Li, Na and K, respectively). Wediscuss the results of these simulations, which point to

significant differences in certain properties of the nano-

composites containing different cations, and are cor-

roborated by experimental observations.

Fig. 1. Scaling properties of LAMMPS on a CRAY T3E-1200E cal-

culated using poly(ethylene oxide)diamine/Naþ-montmorillonite

nanocomposites containing 6486 and 17,296 atoms: (a) speedup¼ time

(N )/time (N1) and (b) efficiency¼ speedup* N1/N , where N is the

number of processors for the calculation and N1 is the number of

processors for the reference calculation (here N1¼ 1).

2. Implementation of the model

The Teppen force field [14,15] is a type II force field

that contains cross terms describing interaction energies

(bond–bond, angle–angle, middle-bond torsion and end-

bond-torsion) in addition to the usual bond, angle and

dihedral interaction terms. It is derived from the CFF91

[16] force field. It should be noted that a very similar

force field was previously published by Teppen et al. [17]

which proved to give accurate descriptions of varioustypes of clays. So far as the non-bonded van der Waals

interactions are concerned, Teppen’s force field uses a

9–6 potential of the form EvdW ¼ e ½2ðr=rÞ9 � 3ðr=rÞ6�,where r is the interatomic distance and e and r are pa-

rameters, instead of the usual 12–6 one.

The LAMMPS code [6], developed at Sandia Na-

tional Laboratories, is designed to perform very large-

scale molecular dynamics. This is achieved by usingspatial domain-decomposition techniques: the simula-

tion box is decomposed into sub-regions that are then

distributed across many individual processors. This al-

lows for the development of fast parallel algorithms that

make the program highly scalable: a bigger problem will

run nearly as efficiently as a small one, using a larger

number of processors. This is depicted in Fig. 1 for a

clay–polymer nanocomposite. The speedup propertiesof LAMMPS are shown in Fig. 1a. Ideally, a parallel

program should behave linearly with the number of

processors, namely, the speedup should be twice as large

if the number of processors is doubled. Linearity is de-

picted by the dashed line in Fig. 1a. Although LAM-

MPS does not behave linearly for the models presented

here (poly(ethyleneoxide)diamine/Naþ-montmorillonite

nanocomposites with 6486 and 17,296 atoms, respec-tively), the graph shows that it is more likely to behave

linearly as the number of atoms increases. In Fig. 1b is

depicted the LAMMPS efficiency that shows the high

scalability of the program. For example, the efficiency

amounts to nearly 0.78 on 16 processors of a CRAY

T3E-1200E for the small system (6486 atoms). The ef-

ficiency is even better (0.8) on 32 processors for a system

that is more than twice as large (17,296 atoms). Thebenefit of such scaling is that simulation times can be

reduced from weeks to a day or less of elapsed wall clock

time.

The bottleneck of fully atomistic MD is undoubtedly

the computation of long-range electrostatic interactions

because the convergence of the Coulomb sum is very

slow. This is achieved in LAMMPS using the particle–

particle particle mesh method (PPPM) [10–13] to cal-culate the Coulomb energies and forces for periodic

systems. This algorithm scales nearly linearly with the

size of the system, namely as N logN , where N is the

number of atoms [18].

Another limitation intrinsic to MD is the need for

very small integration timesteps. The rRESPA inte-

grator [8] has been implemented in LAMMPS in order

to further improve the performance of the program inthis respect. This multiple timescale technique imple-

ments a variety of timesteps that depend on the type

of interactions involved, with the intention of saving

CPU time: while the cheaper bonded and short range

non-bonded terms, which vary more quickly, are cal-

culated at every innermost loop, computationally

costly energy terms, namely the non-bonded long-

range electrostatic terms, can be computed four oreven eight times less often without loosing accuracy.

The PPPM and rRESPA algorithms were used in this

study.

3. Molecular dynamics simulation on small montmoril-

lonite clay systems

3.1. Swelling behaviour of Naþ-montmorillonite using

Teppen’s force field

The montmorillonite clay mineral is a 2:1 alumino-

silicate comprising an octahedral layer of alumina fused

P. Boulet et al. / Chemical Physics Letters 389 (2004) 261–267 263

between two tetrahedral layers of silica. The model we

used is a Wyoming-like montmorillonite in which iso-

morphic substitutions in the octahedral and tetrahedral

layers occur (aluminium and silicon atoms are replaced

by magnesium and aluminium, respectively). Thesecreate a net negative charge in the clay sheets that is

compensated by the presence of counterions in the in-

terlayer space. Naturally occurring cations are sodium

and calcium. They can easily be exchanged with other

types of cations (lithium, potassium or ammonium-

containing organic molecules). In this communication,

we report results on lithium, sodium and potassium

montmorillonite clays.The water swelling behaviour of clays is a well-known

phenomenon and has been widely studied in the past

both experimentally and theoretically [19–23]. There-

fore, as a benchmark for the current work, we imple-

mented the Teppen force field within LAMMPS and

calculated the swelling curve of the sodium-montmoril-

lonite for various water contents (from 0 to 300 mg/g of

clay). The dehydrated model consists of 652 atoms withstoichiometry [Al60Mg8][Si124O384H64]Na12. The simu-

lation was run by using an isobaric–isothermal (NPT)

ensemble at 300 K and a Nos�e–Hoover thermostat. 3-D

periodic boundary conditions were used to account for

electrostatic interactions. The system was equilibrated

for 20 ps and data were collected for another 100 ps. We

performed preliminary simulations to ascertain that 20

ps was long enough for the clay d-spacing (distancebetween two adjacent clay sheets) to reach a plateau of

equilibration.

These results are depicted in Fig. 2. Note that they are

obtained using a small (‘conventional’) system size for

direct comparison with other simulations and, conse-

quently, these should not be considered as large-scale

simulation results. The experimental results shown in

Fig. 2. Swelling curve of sodium-montmorillonite clay showing the

dependence of the d-spacing on the water content of the clay. Exper-

imental data from [19]. Monte Carlo simulations using an NPT en-

semble at 300 K (from [22]). Discover and LAMMPS data: this work.

Fig. 2 exhibit a hysteresis loop due to the fact that the

system was not completely equilibrated. Results from

previously published NPT Monte Carlo [22] and other

MD simulations performed by us using the Discover

program [24] (with an isobaric–isothermal ensemble at300 K) typically lie within this hysteresis loop. It is

noteworthy that the swelling curve calculated with

Discover was performed with the Teppen force field

using the same model size whereas for the Monte Carlo

simulation, the TIP4P force field was used for water. It

is now well-known from experiment [19,20] that the

hydration of the sodium-montmorillonite proceeds ac-

cording to a typical ‘step-jump behaviour’ that ariseswhen one, two and three layers of water molecules are

formed. This trend is well reproduced by similations

(Fig. 2) including LAMMPS with the Teppen force field.

3.2. Simulation of the Liþ-, Naþ- and Kþ-montmorillonite

clays

The interaction of the clay cations with their envi-ronment depends on non-bonding electrostatic and van

der Waals potentials. Since no parameters were avail-

able for the lithium cation within the Teppen force field,

the parameters that we have chosen for the van der

Waals potential are 0.003 kcalmol�1 for e and 3.25 �Afor r. Then, a new series of simulations were performed

to calculate the radial distribution function (RDF) be-

tween the alkali metal cations and their surroundingatoms. For this purpose, small system sizes were simu-

lated with LAMMPS to check the validity of our pa-

rameterisation of Liþ. For the sake of comparison, three

models were used, namely Liþ-montmorillonite, Naþ-montmorillonite and Kþ-montmorillonite, with and

without water. The RDF are depicted in Fig. 3. Both the

oxygen atoms of the clay and the oxygen of water

molecules (for hydrated clays) were selected to calculatethe RDF. The system was simulated with an isobaric–

isothermal ensemble controlled by a Nos�e–Hoover

thermostat at 300 K. The systems were equilibrated for

20 ps and the data were collected for 100 ps.

The RDF between the cations and the clay tetrahe-

dral oxygen atoms (Fig. 3a) of the dehydrated clays

clearly show structure. By contrast, for the hydrated

clays (Fig. 3b), this structure tends to disappear. Thiscan be explained as follows. In dehydrated clays, the

cations interact strongly with the clay sheets and are

trapped within stable potential wells. ‘Hopping’ from

site to site occurs only rarely on this timescale. In the

case of hydrated clays, the cations are solvated by water

and are more likely to diffuse within the clay galleries.

The lack of long-range structure in the RDF shows that,

on average, the counterions adhere less to the surface.This is further confirmed by the RDFs between the

counterions and the water molecules (Fig. 3c): they

clearly show a first sphere of coordination at about 2.0,

Fig. 3. Radial distribution functions (RDF) for Liþ, Naþ and Kþ-montmorillonite. RDF between ions and clay oxygen atoms for: (a)

dehydrated clays; (b) hydrated clays and (c) between ions and water

oxygen atoms for hydrated clays.

264 P. Boulet et al. / Chemical Physics Letters 389 (2004) 261–267

2.25 and 2.5 �A for Liþ, Naþ and Kþ, respectively, and asecond one at about 4.5–5.0 �A. Several experimental and

theoretical studies validate our results. In aqueous so-

lution [25] Liþ hydrates strongly and is surrounded by

an octahedral sphere of water coordination located at

about 1.9 �A. This was also found by Skipper et al. [26],

from neutron diffraction studies on hydrated Liþ-ver-miculite. These results show that when hydrated within

clays, Liþ behaves as in bulk water. Similar results toours were obtained for the hydrated Naþ-montmoril-

lonite system using Monte Carlo simulations [27]. In-

terestingly, the hydration behaviour of Liþ and Naþ

within confined environments has been shown to be

critical for the conductivity properties of these materials

[28]. Finally, compared to the small alkali cations, Kþ

has lower hydration energy, which explains the greater

distance of the first hydration sphere (Fig. 3c). Similarresults were obtained previously from Monte Carlo

simulations [29].

4. Large-scale molecular dynamics simulations

Subsequently, large scale simulations of the

poly(ethylene glycol)/Mþ-montmorillonite nanocom-

Table 1

Thermodynamics and structural data extracted from our large-scale molecu

Nanocomposites Total energy Kinetic energy P

Li )1.59490� 1106 � 7698 21429� 120 )Na )1.57175� 1106 � 1484 16018� 98 )K )1.57637� 1106 � 8388 16468� 130 )

Energies in kcalmol�1, temperature in K and d-spacing in �A.

posites (with M¼Li, Na and K, respectively) were

performed using LAMMPS. The models consist of 162,

72 and 90 organic molecules (for the Liþ, Naþ and Kþ

based nanocomposites, respectively) of formula

C18O10H38, and 486, 432 and 216 water molecules in-tercalated within a single layer of clay with stoichiom-

etry ([Al540Mg72][Si1152O3456H576]M108) per simulation

cell (M being the counterion). The total number of at-

oms is therefore 23,886, 17,784 and 18,324 for the

aforementioned nanocomposites, respectively. The sys-

tems were simulated for 1 ns using a NPT ensemble at

300 K and a Nos�e–Hoover thermostat. Data were col-

lected every 100 fs. The statistical averages for thecalculation of properties presented hereafter were eval-

uated from the last 800 ps of simulation, the first 200 ps

being required to achieve equilibration. Each computa-

tion ran for about 25 h on 64 processors of a CRAY

T3E-1200E.

In Table 1 are gathered the various energies (total,

potential and kinetic), the temperature and the d-spacing

together with their relative errors. They are informativefor checking the quality of the simulation. In all cases, it

can be seen that the relative errors are very small and

situated around 0.5%. This undoubtedly confirms that

the implementation within LAMMPS of the various

algorithms previously described is very stable.

The RDFs of the Liþ, Naþ and Kþ based nano-

composites are depicted in Fig. 4. The RDFs between

the cations and the water molecules are very similarwhen we compare the larger model (Fig. 4a) and the

smaller one presented in the previous section (Fig. 3c).

Large peaks are seen at about 2.0, 2.5 and 2.75 �A for

Liþ, Naþ and Kþ, respectively, denoting the position of

the first coordination sphere of solvation. However, the

second peaks, at about 5.0 �A, are much smaller: the

formation of a second sphere of solvation is less mani-

fest, no doubt due to the presence of polymers (see be-low). Indeed, the first sphere is slightly shifted to higher

distance.

For both the larger and the smaller models, the RDFs

between the cations and the clay tetrahedral oxygen

atoms are different: the RDF for the big model, depicted

in Fig. 4d, shows a much more ordered structure than

that of the small, hydrated system (Fig. 3b), especially

for the Kþ cation. This is due to the presence of poly-mers in the nanocomposite that prevents the diffusion of

the cations over a long distance [30]. Indeed, this is

confirmed by the fact that the cation-clay oxygen RDF

lar dynamics simulations

otential energy Temperature d-spacing

1.61640� 1106 � 7694 300.97� 1.68 18.009� 0.005

1.58777� 1106 � 1481 302.17� 1.85 16.928� 0.004

1.59284� 1106 � 8383 301.49� 2.40 14.043� 0.006

Fig. 5. Density profiles of the cations (Liþ, Naþ and Kþ), water

molecules and polymers within the poly(ethylene glycol)/Mþ-mont-

morillonite nanocomposites (where M is Li, Na and K, respectively)

calculated from large-scale molecular dynamics simulations. The

densities are plotted along the axis perpendicular to the clay sheets (c-axis of the simulation cell). The systems were simulated for 1 ns at 300

K using an NPT ensemble. The density profiles are averaged over 800

ps of each simulation. Density profiles for: (a) poly(ethylene glycol)/

Liþ-montmorillonite nanocomposite; (b) poly(ethylene glycol)/Naþ-montmorillonite nanocomposite; (c) poly(ethylene glycol)/Kþ-mont-

morillonite nanocomposite.

Fig. 4. Radial distribution functions (RDF) between the Liþ, Naþ and

Kþ cations and the various oxygen atoms in hydrated clay–polymer

nanocomposites computed from 1 ns of LAMMPS MD simulation at

300 K using an isobaric–isothermal ensemble: (a) RDF between the

cations and the water oxygen atoms; (b) between the cations and the

alcohol oxygen atoms of poly(ethylene glycol); (c) between the cations

and the ether oxygen atoms of poly(ethylene glycol); (d) between the

cations and the clay tetrahedral oxygen atoms.

P. Boulet et al. / Chemical Physics Letters 389 (2004) 261–267 265

of the nanocomposite is more similar to the cation-clay

oxygen RDF of the dehydrated clay (Fig. 3a). Finally,

the Liþ cation is more likely to get closer to the clay

surface than the other cations. This behaviour was also

demonstrated for the dehydrated PEO/Liþ-montmoril-

lonite using small-scale MD simulations [31] and in

NMR experiments [32]. It is assumed therefore that the

conductivity in these materials results in a succession ofLiþ jumps from one adsorption site to the next, a pro-

cess mediated by water and polymer molecules. Inter-

estingly, our results contrast with those obtained for

dehydrated PEO/Liþ- and PEO/Naþ-montmorillonite

systems [33]. Whereas, in these systems Naþ seems to get

closer to the clay surface than Liþ, the contrary occurs

within the hydrated systems. Furthermore, for Naþ, thedouble peak at 2.0 and 3.25 �A [33] visible in the dehy-drated clay is transformed into a single peak at 2.5 �Awhen the clay is hydrated.

In Figs. 4b and c are depicted the RDFs between the

cations and the oxygen atoms of the polymer. Com-

paring Fig. 4a with Figs. 4b and c, it can be seen that the

polymers play a similar role to the water molecules by

solvating the interlayer cations. Firstly, with respect to

the cations, the first water solvation shell is located atthe same distance as the first polymer solvation shell

(which includes both alcohol and ether oxygen atoms).

The lower intensity of the RDF of the polymer oxygen

atoms compared with that of water is due to the much

greater steric constraints associated with the polymer

oxygen atoms. Compared with the small water mole-

cules, fewer polymer based oxygen atoms can solvate the

cations. Second, in both cases two spheres of coordi-

nation are depicted at 2.0 �A and, to a less visible extentin the case of water, at about 5.0 �A. We can now explain

why the second sphere of water molecules around the

cations is more diffuse. The high density of oxygen

neighbours, which belong to water and polymers within

the first sphere of solvation has a high screening effect on

the central cations. The electrostatic effect exerted by the

cations at long distance is therefore weaker in a nano-

composite structure than in a merely hydrated clay, re-sulting to a more diffuse second sphere of solvation in

the case of nanocomposites. Finally, it is worthwhile to

note that the inner peak that dominates the cation-ether

oxygen atoms occurs in the K system (Fig. 4c). This is

expected as this ion is biggest and poly(ethylene glycol)

is known to wrap around Kþ ions very tightly.

We present in Fig. 5, a detailed description of the

structure of the poly(ethylene glycol)/Mþ-montmoril-lonite nanocomposites (where M is Li, Na and K, re-

spectively). This figure gives clear insight into the

position of the ions, water molecules and polymers

within the clay galleries and depicts the density of the

aforementioned compounds along an axis perpendicular

to the clay sheets. The density is averaged over 800 ps of

each simulation. The origin of the abscissa corresponds

to the mid-plane of the clay gallery.

266 P. Boulet et al. / Chemical Physics Letters 389 (2004) 261–267

The density profiles clearly provide complementary

information to the RDFs presented in Fig. 4. For the

Liþ based nanocomposite (Fig. 5a), the profile shows

that the cations can diffuse both into the tetrahedral

pockets of the clay surface (first peak at )8 �A), which isin agreement with experimental assumptions [32] and

with previous simulations [33], and into the middle of

the clay galleries. We then observe four layers of cations

within the interlayer. Between each of these four layers,

a monolayer of water molecules is ‘intercalated’ that

solvates the cations. No water molecules are seen to

diffuse between the cations and the clay sheets. Finally, a

clear double layer of poly(ethylene glycol) is observed toform within the gallery. This is, of course, consistent

with the calculated value of the d-spacing that we re-

ported in Table 1 for this nanocomposite (18.0 �A). This

value is usually considered as typical for a bilayer to

trilayer transition, which appears to be initiated by the

incipient formation of a third monolayer of water mol-

ecules in the mid-plane of the clay gallery. In the case of

the poly(ethylene glycol)/Naþ-montmorillonite nano-composite, we can see the formation of a bilayer of

polymers, but these layers are closer to each other than

in the case of the Liþ based composite (Fig. 5b). There is

a clear accompanying bilayer of water molecules; a bi-

layer of cations is also manifest with few Naþ cations

diffusing into the inner part of the clay gallery. As ex-

pected, the d-spacing of this material is smaller (16.9 �A)

than the Liþ one and is typical of what is commonlyreferred to as a bilayer. Finally, a monolayer of poly-

mers, located in the mid-plane of the clay gallery, is

observed in the poly(ethylene glycol)/Kþ-montmoril-

lonite system (Fig. 5c), as expected from the computed

d-spacing of 14.0 �A. No Kþ cations diffuse into the

middle of the gallery; they stay close to the clay sheet at

all times. A central layer of water molecules can be

observed, with two oxygen atom density maxima dis-placed equidistant from the mid-plane.

5. Conclusions

In this Letter, we have presented the results of our

initial work concerned with large-scale MD simulations

of clay–polymer nanocomposites, comparing someproperties of poly(ethylene glycol)/Mþ-montmorillonite

nanocomposites (with M¼Li, Na and K, respectively).

Each model contains about 20,000 atoms and was sim-

ulated for 1 ns. The Teppen force field, which has been

designed specifically to simulate the behaviour of clays,

has been implemented within the LAMMPS code. We

have demonstrated both the validity of this implemen-

tation and of additional potential parameters for thelithium cation. These large-scale simulations clearly

show that the cations are not only solvated by water but

also by polymers. In future developments, we plan to

compute the diffusion coefficients of the water mole-

cules, polymers and cations for these materials. For the

Kþ based nanocomposites, we have shown that a

monolayer is formed whereas for Naþ and Liþ one, a

polymer bilayer is observed. As already mentioned inprevious publications, the conductivity of Liþ based

nanocomposites is likely to occur by hopping of the Liþ

cations from site to site. Furthermore, we have also

shown that these cations are able to enter within the

tetrahedral sheet of the clay, in agreement with experi-

ments. Finally, the benefit of using a scalable molecular

dynamics code such as LAMMPS for these materials

applications is evident. It enables the study of muchlarger models, over long-time scales, within dramatically

reduced wall clock times. It is evidently now possible to

construct models at least one or two orders of magni-

tude larger than those described here that can exploit

current capabilities of leading supercomputers, where a

single simulation could be efficiently distributed over

thousands of processors.

Acknowledgements

The authors are indebted to Dr. Brian Teppen for

kindly providing us with his force field and to Dr Steve

Plimpton for helping us with aspects of LAMMPS in the

early stage of our work. We also thank Dr. David M.

Benoit for fruitful discussions. The calculations wereperformed at the CSAR supercomputing centre (Man-

chester, UK) on a CRAY T3E-1200E. The authors are

grateful to HEFCE for funding the SGI Onyx2 located

at University College London on which the small-scale

simulations were run. This work was funded by EPSRC

under Grant No. GR/R30907.

References

[1] I.H. Shrivastava, C.E. Capener, L.R. Forrest, M.S.P. Sansom,

Biophys. J. 78 (2000) 79.

[2] G. Groenhof, M.F. Lensink, H.J.C. Berendsen, J.G. Snijders,

A.E. Mark, Proteins 48 (2002) 202.

[3] E.P. Giannelis, Adv. Mater. 8 (1996) 29.

[4] P.C. Le Baron, Z. Wang, T.J. Pinnavaia, Appl. Clay Sci. 15 (1999)

11.

[5] M. Alexandre, P. Dubois, Mater. Sci. Eng. 28 (2000) 1.

[6] S.J. Plimpton, J. Comp. Phys. 117 (1995) 1.

[7] L. Kal�e, R. Skeel, M. Bhandarkar, R. Brunner, A. Gursoy, N.

Krawetz, J. Phillips, A. Shinozaki, K. Varadarajan, K. Schulten,

J. Comput. Phys. 151 (1999) 283.

[8] M.E. Tuckerman, B.J. Berne, G.J. Martyna, J. Chem. Phys. 97

(1992) 1990.

[9] G. Ciccotti, J.P. Ryckaert, Comput. Phys. Rep. 4 (1986) 345.

[10] R.W. Hockney, J. Eastwood, Computer Simulation using Parti-

cles, McGraw-Hill, New York, 1981.

[11] G. Rajagopal, R. Needs, J. Comp. Phys. 115 (1994) 399.

[12] B.A. Luty, M.E. Davis, I.G. Tironi, W.F. van Gunsteren, Mol.

Simul. 14 (1994) 11.

P. Boulet et al. / Chemical Physics Letters 389 (2004) 261–267 267

[13] A.Y. Toukmaji, J.A. Board Jr., Comp. Phys. Commun. 95 (1996)

73.

[14] B.J. Teppen, Private communication, 2000.

[15] B.J. Teppen, C.-H. Yu, S.Q. Newton, D.M. Miller, L. Sch€afer,

J. Mol. Struct. 445 (1998) 65.

[16] A.K. Rappe, W.A. Goddard, J. Chem. Phys. 95 (1991) 3358.

[17] B.J. Teppen, K. Rasmussen, P.M. Bertsch, D.M. Miller, L.

Sch€afer, J. Phys. Chem. 101 (1997) 1579.

[18] E.M. Pollock, J. Glosli, Comp. Phys. Commun. 95 (1996) 93.

[19] M.H. Fu, Z.Z. Zhang, P.F. Low, Clays Clay Miner. 38 (1990)

485.

[20] J.M. Cases, I. B�erend, G. Besson, M. Franc�ois, J.P. Uriot, F.

Thomas, J.E. Poirier, Langmuir 8 (1992) 2730.

[21] E.S. Boek, P.V. Coveney, N.T. Skipper, J. Am. Chem. Soc. 117

(1995) 12608.

[22] E.S. Boek, P.V. Coveney, N.T. Skipper, Langmuir 22 (1995) 4629.

[23] A.S. Bain, E.S. Boek, P.V. Coveney, S.J. Williams, M.V. Akbar,

Mol. Simul. 26 (2001) 101.

[24] Discover, Cerius2, version 4.2, San Diego, Accelrys, USA, 2001.

[25] G.W. Neilson, J.E. Enderby, Adv. Inorg. Chem. 34 (1989) 195.

[26] N.T. Skipper, M.V. Smalley, G.D. Williams, A.K. Soper, C.H.

Thompson, J. Phys. Chem. 99 (1995) 14201.

[27] V. Marry, P. Turc, T. Cartailler, D. Levesque, J. Chem. Phys. 117

(2002) 3454.

[28] N.J. Garc�ıa, J.C. Baz�an, Solid State Ionics 92 (1996) 139.

[29] S.-H. Park, G. Sposito, J. Phys. Chem. B 104 (2000) 4642.

[30] P. Boulet, A.A. Bowden, P.V. Coveney, A. Whiting, J. Mater.

Chem. 13 (2003) 2540.

[31] V. Kuppa, E. Manias, Chem. Mater. 14 (2002) 2171.

[32] D.-K. Yang, D.B. Zax, J. Chem. Phys. 110 (1999) 5325.

[33] E. Hackett, E. Manias, E.P. Giannelis, Chem. Mater. 12 (2000)

2161.