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A molecular dynamics study of modelcyanoadamantaneDAVID CATHIAUX a , FRANJO SOKOLI[Cgrave] a , MARC DESCAMPS b & AURÉLIEN PERERA ca Laboratore de Spectrochimie Infrarouge et Raman, UPR CNRS A2631L, Franceb Laboratoire de Dynamique et Structure des Matérieux Moléculaires, Université desSciences et Technologies de Lille 59655 Villeneuve d'Ascq Cedex, UFR de Physique, Bat.P5,Francec Laboratoire de Physique Théorique des Liquides, Université Pierre et Marie Curie, 4 PlaceJussieu, 75252, Paris edex 05, FrancePublished online: 01 Sep 2009.

To cite this article: DAVID CATHIAUX , FRANJO SOKOLI[Cgrave] , MARC DESCAMPS & AURÉLIEN PERERA (1999) A moleculardynamics study of model cyanoadamantane, Molecular Physics: An International Journal at the Interface Between Chemistryand Physics, 96:7, 1033-1042

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MOLECULAR PHYSICS, 1999, VOL. 96, No. 7, 1033-1042

A molecular dynamics study of model cyanoadamantane DAVID CATHIAUX' , FRANJO SOKOLIC' , MARC DESCAMPS2 and

AURELIEN PERERA3 Laboratore de Spectrochimie Infrarouge et Raman, UPR CNRS A2631L, and Laboratoire de Dynamique et Structure des Materieux Moleculaires, UFR de

Physique, Bat.P5, Universitk des Sciences et Technologies de Lille 59655 Villeneuve d'Ascq Cedex, France

Laboratoire de Physique Thkorique des Liquides, Universite Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France

(Received 27 April 1998; revised version accepted 16 November 1998)

A simple model for the cyanoadamantane molecule is proposed and investigated by molecular dynamics simulation. This model has the three phases (crystalline, plastic and fluid) within temperature ranges corresponding to those observed experimentally. An interesting aspect of the model is that the plastic phase has much faster rotational dynamics (by five orders of magnitude) than the true system. This feature opens the route for a molecular dynamics study of the eventual orientational glassy state, within times accessible to simulation methods. The preliminary study conducted in the present work is focused on the plastic and fluid phases. The static and dynamic properties are calculated for both phases and compared with them and with those accessible by experiment. This study confirms the overall adequacy of the proposed model. The general features found through this analysis reveal the nature of the rotational and translational dynamics in these two phases as well as their underlying differences.

1. Introduction The adamantane (ADM) CI0Hl6 and the family of its

derivatives CIOH15X, where X stands for one of the following substituents (Cl, F, I, Br, CN), are known to form a plastic crystal phase with dynamic disorder. Among them at least I-cyanoadamantane, CIOH15CN (denoted CN-ADM), is known to form an orientational glass with frozen orientational disorder [ 1,2]. CN-ADM is a molecule of C3v symmetry, obtained from ADM by a substitution of one hydrogen by a cyano group (CN), which is responsible for a high dipole moment. The ADM system has been studied intensively by molecular dynamics (MD) simulation [3-51. The main feature of the CN-ADM system is that it forms an orientational glass characterized by the calorimetric glass transition temperature T , = 170K [l], and which has been studied experimentally as a one-component material and in glassy binary mixtures [6]. Usually the plastic phase is the first step towards the generation of the orientational glass. In general, the study of glassy states by MD tech- niques is met by severe difficulties. Indeed, glassy states are characterized by extemely large relaxation times, which often lead to unreasonably long simulation times in order to capture the dynamic relaxation fea- tures. Moreover, the simulation of a small sample within periodic boundary conditions is threatened by ergodicity problems. As an example, the reorientational

time in the plastic CN-ADM is about 3 x 10-7s [7] while the usual M D timesteps are of the order of a femtosecond. It is then tempting to produce a model of CN-ADM that, in addition to having some of the global features of the real system as obtained by experi- ment, will also have faster rotational dynamics. Obtaining statistically reliable time correlation functions needs long M D runs, which in turn implies that a simple model must be used.

The aim of the present work is to build a model which shows qualitatively the same thermodynamic behaviour as the CN-ADM system over the correct temperature range. The adequacy of the model has been tested in the three phases by calculation of the corresponding structural and dynamical properties. More specifically, we focus our interest on the changes in the dynamics passing from the orientationally disordered (plastic) phase to the totally disordered (liquid) phase. The results provide an interesting picture concerning the evo- lution of the rotational-translational coupling in these two phases.

The experimental study of CN-ADM has been con- centrated mainly on the solid and plastic phases and the orientational glassy state. In particular, Raman spectral [l], X-ray [7] and neutron scattering [8] data are avail- able, and these provide a basis for testing the model used in MD simulations and its predictions. Indeed, MD

Mokcular Physics ISSN 00268976 print/ISSN 1362-3028 online 0 1999 Taylor & Francis Ltd http://www.tandf.co.uk/JNLS/mph.htrn

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1034 D. Cathiaux et al.

simulations can be used to calculate these quantities, and also to have a closer look at the dynamics involved in each of the phases, and thus they represent a powerful complementary tool.

2. Potential model The ADM molecule is fairly spherical in form, and the

presence of the cyano group is responsible for the high anisotropy of CN-ADM molecule. In order to model this anistropy, we propose here a simplified model of CN-ADM with just three sites instead of the full model with 27 atoms. The first site corresponds to the nitrogen atom, the second to the adjacent carbon atom and the last one (a supersite) to the whole ADM group. Site-site interactions are represented by an m - n Len- nard-Jones (LJ) potential:

where rinJP is a distance between site a on molecule i and site ,B on molecule j . The usual values for m and n are 12 and 6, respectively, except for the interactions between superatoms, which are represented by unusual values of exponents m and n (table 1). Indeed, the superposition of several LJ interactions will not necessarily be of the same form. In order to determine the new exponents we proceeded as follows. First, two CN-ADM mol- ecules, with the geometry given in [9], were placed par- allel to each other and then cyano groups were removed; the remaining 25 atoms were represented by LJ sites [lo]. One could also have taken the set of parameters for the Buckingham potential which reproduces the solid state properties of crystalline hydrocarbons [ 1 I]. The potential curve obtained by varying the distance between the centres of mass of the two groups of 25 atoms was fitted to the form given by equation (1). The corresponding values of m and n are given in table 1. The final value of the interaction energy parameter E

between the two supersites was obtained by fitting again the total energy to that obtained with the full model. The Lorentz-Berthelot composition rule was applied

Table 1. Parameters for the Lennard-Jones potentials.

Interaction (&/kB)/k d n m ) m n

N-N 85.41 0.325 12 6 c-c 37.17 0.355 12 6 Supersite-supersite 1000 0.63 16 10 N-C 56.34 0.34 12 6 N-supersi te 292.25 0.47 12 6 C-supersite 192.79 0.49 12 6

for interactions between two unlike sites. The LJ par- ameters for nitrogen and carbon were taken from [lo].

The CN-ADM molecule has a nonzero dipole moment along the cyano group axis. In order to improve the accuracy of the model described above we have added two partial charges of 0.712e, negative on the nitrogen atom and positive on the carbon atom. This charge distribution gives the correct value for the dipole moment (about -1.3 x lop2' Cm = -3.89D compared with the experimental value which is -3.92D).

The striking feature of this simplified model is obvious when comparing the CPU times spent in the MD simu- lations of the full and simplified models. The 27 atoms of the full CN-ADM model requires 5 s CPU time per MD step on a Cray C95 instead of 0.12s for the three- site model.

3. Simulation method and details The molecular dynamics simulations were performed

in the microcanonical ensemble [ N , V , E ] , with a fixed number of particles N = 256, molar volume V,, and internal energy E . The molar volume is obtained by requiring atmospheric pressure conditions. The timestep in the simulations was 1 fs. The equilibration runs were at least about lo4 timesteps and the production runs around lo5 steps. The effects due to the long range elec- trostatic contribution to the intermolecular potential were taken into account using Ewald summation. The MD runs were started from initial configurations corre- sponding to the face centred cubic (fcc) crystal lattice for the centres of mass of the molecules with antiferroelec- tric arrangement of their axes, i.e., mutually parallel in each plane and antiparallel for two molecules in neigh- bouring planes. Two different cases were considered: in the first the molecular axes were perpendicular to the plane (structure A), and in the second the molecular axes were perpendicular to the plane (structure B). These two structures were proposed in [7] to interpret the nature of the short range observed in the plastic crystal phase. It is important to realize at this point that our aim is not to simulate the crystalline solid phase itself (which is known to be a monoclinic crystal [12]). Indeed, such a simulation cannot be performed properly within the microcanonical ensemble, and a constant pressure method is required instead [ 131, mainly in order to allow for the crystal lattice par- ameters to change in the course of the simulation. How- ever, for the simulation of plastic and fluid phases, it is sufficient to impose the atmospheric pressure condition and consequently the corresponding volume changes can be determined properly with microcanonical ensemble simulation methods. It is important that the plastic phase obtained by melting the crystal is indepen- dent of the initial crystalline choice (although the transi-

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A molecular dynamics study of model cyanoadamantane 1035

n 7 200-

8 1901

mE 180- w

2 170- Figure 1. Energies and molar

obtained by MD simula- tion. The dotted line cor-

volumes for the two phases W

>' 160-

Table 2. Thermodynamic and dynamic properties obtained from MD simulations. Plastic phase thermodynamic points obtained starting from A (1,2,3,5) and B (4), and liquid points (6,7,8,9).

V M E M T P a ( F 2 ( 0 ) ) ( T 2 ( 0 ) ) Dt,,", ~ Melting

No. m3 mol-' kJ mol-' K MPa A N2 mol-' N2 m2 mol-' m2 s-' factor

hi

w- i w i w

H+-l m w

158.0 160.2 164.6 164.6 176.0 180.0 185.0 190.0 202.0

- 52.7908 - 50.443 1 -46.0201 - 45.9483 - 39.8988 -37.6455 -34.31 11 -31.9381 -26.7044

374f 11 9 % 1 l 10.16 404f11 5 f 1 1 10.20 454k 13 4 f 11 10.30 465 f 12 7 f 13 10.30 4 7 4 f 14 8 f 1 4 507k 13 6 f 13 551 f 13 1 2 f 14 582 f 14 1 2 f 14 648% 13 7 % 14

762 815 890 889 829 817 870 888 880

200 1 0 - l ~ 167 208 1 0 - l ~ 173 221 170 227 x 1 0 - l ~ 159 190 x lO- I9 1.59 x 0.8 193 x 2.38 x 0.4 197 1 0 - l ~ 2.62 x 1 0 - ~ 1.2 193 10- l~ 3.55 lop9 0.4 198 x 7.27 x 0.7

n - 3

8 -40 -30i m

tion temperature may depend on this choice). We note moreover that the plastic phase is experimentally observed to be in the fcc state, which is consistent with our finding by melting any of the two fcc initial crystal configurations A and B.

To determine whether the system was in the plastic crystal or the liquid state we used the fact that the trans- lational diffusion coefficient is equal to zero for the first phase and different from zero for the second. In addition we used the melting factor (the order parameter relative to the fcc lattice), which is of the order of N (the number

of particles in the simulation box) for the fcc structure and about 1 in the fluid phase.

The thermodynamics obtained from our MD simula- tions for nine different state points are presented in table 2 and figure 1 which shows the variation in molar internal energy EM and F'M as a function of tempera- ture. Horizontal error bars correspond to the fact that in MD simulations the volume and energy are fixed while the temperature is fluctuating. The vertical dotted line represents the experimental value of the temperature corresponding to the plastic-liquid phase transition of

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1036 D. Cathiaux et al.

CN-ADM at atmospheric pressure (T, = 458 K) [l]. The major conclusion we gather from these results is that the temperature ranges of the different phases obtained with our simplified model are well bracketed by those observed experimentally. The evidence for this is shown also in the next sections, where we study the The structures of the plastic and liquid phases structural and dynamical properties in detail, in order to obtained by the simulations were analysed with the

characterize the correct phase for each of the nine state points studied herein. For the data corresponding to the crystalline phase of this model see [13].

4. Results for the structural properties

t 0 *

uf n tl:

4

t u 8 3 :i uf n L

- 1 1 I I I I

4

0 . 6 0 . 8 1 . 0 1 . 2 1 , I4 1 ,‘6 1 e n

( n m ) (b)

Figure 2. The radial distribution functions RDFCM-CM (solid lines) and angular distributions (cos a(r)) (dotted lines) and (cos’ a(r) ) (dashed lines) for the three phases: (a) plastic phase at 404K and (b ) fluid phase at 582K. The upward arrows indicate the position of the fcc lattice vertices.

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A molecular dynamics study of model cyanoadamantane 1037

help of the following distribution functions: the radial distribution function between the centres of mass of the molecules (RDFCM-CM), the nitrogen-nitrogen radial distribution function (RDFN-N)r and finally the relative angular distribution of molecules (ADF) characterized by the first- and the second-order functions (cos a ( r ) ) and (cos2 a(r)) , respectively, where Q is the angle between the axes of two different molecules, and the orientational probability distributions (OPD) P(0) and P(q5) and $ being respectively the polar and the azi- muthal angles of the molecular axis measured in the laboratory frame).

The RDFCM-CM for the two phases are shown in figure 2. The upward arrows in figure 2 (a ) indicate the position of the first three groups of nearest neighbours in the FCC structure. At temperatures of 374 K, 404 K, 454K and 465K the equilibrium structure is an FCC lattice with respect to the position of the centres of mass of the molecules. This can be seen clearly from the RDFCM-CM given in figure 2 ( a ) for temperature T = 404K. We note that this structure is in agreement with that observed experimentally in the plastic phase [6 ] . ADFs of the first and the second order shown in figure 2 (a ) have general features characteristic of an orientationally disordered phase (as compared with those of the liquid phase given in figure 2 (b) . The zero asymptotic value for (cos a ( r ) ) is reached at about 1.1 nm, and that of (cos2 a ( r ) ) is about 30% faster (at about 0.8 nm). These two asymptotic values correspond to the isotropic distribution of the relative orientations. The RDFN-N is particularly sensitive to the orientations of the molecules because of the position of the nitrogen atom at the top of the molecule. The fact that the plastic phase is orientationally isotropic appears very clearly also in the RDFNbN (not represented) which has no par- ticular structure (this is true also for the RDFN-N of the liquid phase).

However, the OPDs for the plastic phase show that the molecules are preferentially oriented along the crystal axis, but with non-negligible probability for intermediate orientations, which is the consequence of the specific reorientational dynamics of this model. Then the orientational isotropy suggested by (cos a(r)) = 0, (cos2 ~ ( r - ) ) = 1/3 and the features of RDFN-N, as dis- cussed previously, simply reflect the symmetry of the orientational distribution with respect to the crystal axis. This orientational feature specific to the plastic phase has been observed also through neutron scattering experiments [8]. Moreover, the lattice spacing of the plastic phase measured experimentally at 293 K is 9.813(3)A [7], which is very close to the values observed in our simulations for the close temperatures (see table 2).

As mentioned before, the static structural functions give only indirect information about the dynamics. In the next section we present results about the dynamics and shed more light on the broad features revealed by our analysis above.

5. Results for the dynamic properties The time autocorrelation functions (ACF) are invalu-

able tools for studying translational and rotational dynamics in dense phases. The general form of an ACF of the vector property A( t ) is given by:

Some well known ACFs are associated to the individual molecular properties [14], as for example RACF (reor- ientation A = u, where u is the unit vector along the molecular axis) C,(t), VACF (velocity A = u) C,(t), WACF (angular velocity A = w) C,(t), FACF (force A = F) C,(t) and TACF (torque A = T) CT(t). By con- trast, TDACF (total dipole A = M) CM(t) measures a global property of the system. Our system being in thermodynamic equilibrium we have to deal with sta- tionary processes, so that the time appearing in the ACFs has only a relative meaning. The averaging is done over initial times. Unlike the global properties, the individual one is obtained by averaging also over all the molecules.

C,(t) gives the change of orientation for one molecule as a function of time. It is a single particle dynamic property. CM(t) is a collective dynamic property with M(t) = C21 ui(t), N being the total number of par- ticles. It should be noted that in that case the average is done N times less than in the case of an individual property.

C, ( t ) for plastic and liquid phase (figure 3) have an exponential form, which is the signature of an orienta- tional diffusion regime. The corresponding correlation time is 2 9 . 7 5 ~ s at 404K, 12 .10~s at 454K, both in the plastic phase, and 3.87 ps at 582 K in the liquid phase. We note that within the plastic phase itself there is an important variation in the reorientational correlation time. For short times in the fluid phase, typical free rotator behaviour is observed. This is less apparent for the plastic phase, suggesting that even for short times the individual rotational motions are coupled to those of the neighbours.

The correlation time of CM(t) at 404K is 7.1 ps, a value much smaller than that associated with C,(t) at the same temperature. It indicates that the long term collective reorientational motion is more decorrelated than the individual reorientational motion. In the plastic phase, the experimentally observed orientational corre- lation time at 293 K is about 3 x lop7 s [7], which is lo5

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1038 D. Cathiaux et al.

Figure 3. The time correla- tion functions C, ( t ) for the plastic phase at 404K (solid line) and 454K (dotted line), and the fluid at 582K (dashed line) and CM (t) for 404 K (dot-dashed line).

1 . 0

0 . 9

0 . 8

rA 0 . 7 V 4 a 0 . 6 fi

0 . 5 La

0 . 4

u 4 0 . 3 d

0 . 2

0 . 1

0 . 0 I l ' l ' l ' l ' l ' l ' l ' l ' l ' l

0 1 2 3 4 5 6 I 8 9 10

t i m e ( P S I

times longer than that found in this simulation. This fact allows the reorientational motions to be studied within times accessible by MD simulations. As a matter of fact, the fast relaxation timescales observed in our simula- tions are similar to that of another adamantane deriva- tive, Cl-ADM.

The zero-frequency (w = 0) values of the Fourier transforms (FT) of C,(t) and C,(t) (figure 4) are par- ticularly informative on the phase under study. In the plastic phase, for the first quantity one obtains a value different from zero, whereas it is exactly zero for the second one. Thus, there exists orientational diffusion in the plastic phase but no translational diffusion. The calculated values of the translational diffusion coeffi- cient are given in table 2. For the liquid phase, the zero-frequency values of both quantities are different from zero, as expected.

It is important to note that there are two types of rotational motion, a rapid one (libration), seen through the rotational density of states, and a tumbling motion, which appears through the orientational correlation function C,(t). The frequency plot in figure 4 shows that the rotational density of states peaks around 48cm-', a value quite close to that found by Raman spectroscopy [I] (50 cm-'). This good agreement shows that the dynamics of the small amplitude dipole motion are not much influenced by the peculiarities of the model, for which the objective is mainly to accelerate the large amplitude motion.

We observe that the plastic phase has a more pro- nounced negative tail for both C,(t) and C,(t), com-

pared with those for the liquid. This is no surprise since one expects the motions in the plastic phase to be more caged than in the liquid. The fact that the motions in the plastic phase are centred on higher fre- quencies than for the liquid can be explained by the higher rigidity of the cage in the former phase. The frequency plots show also that for both phases the rota- tional motions occur at higher frequencies than for the translational ones. It is interesting to note that, in the plastic phase, the translational motions appear to be more caged than the rotational ones, whereas the oppo- site seems to be true for the liquid (although with much smaller magnitude). This difference can be interpreted by noting that, in the liquid, the rotational diffusion is slaved to the translational one as the particle must rotate in order to translate among the neighbouring ones. This strong rotation-translation coupling is expected to be less important in the plastic phase, at least for the short term dynamics (less than Ips), characterized by strong return events, thus explaining the large negative tail in C,(t). The rotation-translational coupling in the plastic phase must involve collective cooperative motions, and thus can be seen only at larger spatial- temporal scales.

The normalized CF(t) and CT(t) plus their Fourier transforms are shown for both phases in figure 5 . There is almost no difference between CF(t) of both phases, indicating that the translational dynamical environment is very similar in both phases despite the large temperature difference involved. By contrast, CT (t) of the plastic phase shows the same high frequency shift

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A molecular dynamics study of model cyanoadamantane 1039

LL

wavenumber (cm-')

1 I I I Q , O 0 9 5 1 . 0 i , 5 2 , O

t i m e (ps)

(4

Figure

I 1 I I 1 0 , Q 0 , 5 1 1 0 1 9 5 2 , O

time (ps)

(b) The time correlation functions (a) C, ( t ) and (b) C, ( t ) and their Fourier transforms for the plastic (solid line) phase at

404 K and fluid (dotted line) phase at 582 K.

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1040 D. Cathiaux et al.

0,015,

0,010-

0 1 6 - u. 0 . 0 0 5 -

0 , 4 - L 0 ;f 0 , 2 -

wavenumber (cm-') . . . . I ._ . . . 010 -

- 0 , 2 -

- 0 , 4 I 1 1 1 0 , o o 0 , 2 5 0 , 5 0 0 , 7 5 1 , a 0

t i m e (ps)

(b) Figure 5 . The time correlation functions (a) C,(t) and (b) C,(t) and their Fourier transforms for the plastic and fluid phases. The

symbols are as for figure 4.

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A molecular dynamics study of model cyanoadamantane 1041

as observed in figure 4. The gross picture that emerges through figures 4 and 5, for the short term dynamics, is that in the liquid phase particles manage to diffuse over the boundaries of the cage by successive (correlated) rotations, whereas in the plastic phase they are more likely to bounce within the cage by small (uncorrelated) librations and translations.

From table 2 we see that the mean-square force and mean-square torque are discontinuous across the plastic-liquid transition, due to the increase in free volume available for each particle in the latter phase.

Figure 3 shows C,(t) for both the plastic and liquid phase at three different temperatures. In addition, CM( t ) is shown for the plastic phase at 404 K. As expected, we observe that a decrease in temperature leads to a slower decay of C,( t ) . It is intriguing to compare the behaviour of CM(t) at 404K (plastic phase) with that of C,(t) at 582K (liquid phase), which reveals that for short times the collective orientational relaxations in the plastic phase are slower than the individual molecular relaxa- tion in the liquid. This seems to be compatible with the picture of the plastic phase being an assembly of uncor- related librators, at least over a very short timescale. However, for times longer than 1.5ps a crossover between the two ACFs occurs, and CM(t) of the plastic becomes slower than C,(t) of the liquid, indicating that long term correlated collective motions are more im- portant in the plastic phase.

Comparing C,(t) and CM(t) in the plastic phase at 4MK, we observe that the collective correlations decay faster than the individual ones. A sizeable differ- ence between the relaxation times of C,(t) and CM(t) is observed at 404 K in figure 4. Specifically, the relaxation seen at q = 0 (C,(t)) appears to be much more rapid than that of the individual rotational motion (C,(t)) . The latter involves relaxation occurring at all q values. This behaviour seems to indicate that some slowing down in the rotational motion operates for q different from q = 0.

6. Conclusion A preliminary study of a model of CN-ADM by stan-

dard MD techniques shows that the model is reliable in the sense that it reproduces the correct phase behaviour over a wide temperature range, in agreement with experimental data. We have shown also that some of the structural features of the plastic phase, such as the preferred molecular orientations and the cell constants, are in good agreement with those found experimentally. Similarly, the agreement found in the rotational density of states between our model and that found by Raman spectroscopy indicates that this model is dynamically correct also. In this study, we have shown also that MD techniques are well adapted to pinpointing precisely

the different static and dynamic behaviour of the dif- ferent phases of our model system. We have shown how the detailed analysis of various autocorrelation functions allows one to tell the difference between the plastic phase and the liquid phase. Indeed, this differ- ence is obvious when examining the q = 0 and w = 0 properties (diffusion constants), but there seems to be little apparent difference between the short-medium term behaviour of the various autocorrelation functions of the two phases. A finer analysis of the caging effects and the transitional and rotational relaxations reveals that the translation-rotation coupling in both phases is quite different. In the liquid phase, this coupling occurs essentially in the short term dynamics, and expresses the fact that particles must rotate in order to translate out of the cage, whereas in the plastic phase this coupling is apparent mainly for long term and large scale dynamics, as it involves coupled collective motions.

In the real system, the kinetics of the rotational jumps between pockets is slow, the corresponding relaxation times are about TC = 3 x lop7 s [7]. These time scales are obviously unreachable by standard MD techniques. Our model system with much faster passage between the orientational pockets is then more suited to studying the plastic phase. Thus, in addition to representing an invaluable gain in terms of computation, this model is a good candidate for future studies of dynamics in the plastic phase and near the phase boundaries, and for localizing an eventual orientational glass near the plastic-solid phase boundary. Similar simplified models can be proposed for the whole family of substi- tuted ADM molecules. The determination of the global phase diagram of the CN-ADM model seems a reach- able goal with the present form. Further studies in these directions are in progress.

Institut du Dkveloppement et des Ressources en Informatique Scientifique is gratefully acknowledged for the CPU time allocation on the Cray machines.

References FOULON, M., AMOUREUX, J. P., SAUVAJOL, J. L., LEFEBVRE, J., and DESCAMPS, M., 1983, J . Phys. C, 16, 265. WILLART, J. F., DESCAMPS, M., and BENZAKOUR, N., 1996, J . chem. Phys., 104, 2508. MEYER, M., and CICCOTTI, G., 1985, Molec. Phys., 56, 1235. MEYER, M., MARPHIC, C., and CICCOTTI, G., 1986, Molec. Phys., 58, 723. CICOTTI, G., FERRARIO, M., MEMCO, E., and MEYER, M., 1987, Phys. Rev. Lett., 59, 2574. WILLART, J. F., DESCAMPS, M., BERTAULT, M., and BENZAKOUR, N., 1992, J . Phys. condensed Matter, 4, 9509.

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1042 A molecular dynamics study of model cyclnoadamantane

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