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Rotational molecular dynamics in the RI phase of n-nonadecane
ELSEVIER
Physica B 234 236 (1997) 106-108
Rotational molecular dynamics in the
phase of n-nonadecane
L. Gonzalez Mac Dowell a, F. Guillaume b'*, J.-P. Ryckaert a, P. Girard b,c, V. Rodriguez b, A.-J. Dianoux c aPhysique statistique de la Mati~re Condens~e, CP223, ULB, 1050 Bruxelles, Belgium bLaboratoire de Spectroscopie Molkculaire et Cristalline, URA 124 CNRS, 351 cours de la Libbration, 33405 Talence Cedex, France CInstitut Laue-Langevin, B.P. 156, 38042 Grenoble Cedex 9, France
Abstract
Reorientational dynamics of n-nonadecane molecules in the RI phase have been investigated by means of molecular dynamics computer simulations (MD) and incoherent quasielastic neutron scattering (IQNS) techniques. Models based on jump process and rotational diffusionare compared with the calculated intermediate scattering functions and with the experimental spectra. A four-site jump model must be ruled out while a model based on a fourfold potential with two different barriers could be used to interpret the data succesfully. Keywords: Molecular systems; Quasielastic scattering; Computer modelling; Low-dimensional systems
Normal alkanes n-CnH2,+2 display disordered crystalline structures called 'rotator phases' between the fully ordered crystalline phase and the liquid phase. These rotator phases provide excellent prototypes to interpret at a microscopic level the dynamic and structural properties of more complex systems with aliphatic chains. N-nonadecane displays only one structural phase transition at Tt = 295.2K between the ordered crystal and the R~ rotator phase. In the RI phase (Fmmm, Z = 4), the n-nonadecane molecules form layers and the chain axes are perpendicular to the layers. The molecular dynamics of n-nonadecane chains in the R~phase has been investigated, among other techniques, by means of incoherent quasielastic neutron scattering (IQNS) [1] and molecular dynamics simulations (MD) [2]. The interpretation of the data was found to be in marked disagreement *Corresponding author.
as a model of jumps among 4 orientations was proposed in Ref. [2] and a model of reorientational diffusion in a two-fold potential was proposed in Ref. [1]. As shown in Ref. [2], the observed discrepancies could originate in the effect of the instrumental resolution (~90 peV) in the IQNS experiments. We have therefore undertaken a collaborative study of the molecular dynamics of n-nonadecane in the R~ phase and we will discuss here the models for the uniaxial reorientational dynamics of n-nonadecane in the R~ phase which could fit both IQNS and MD data. New IQNS experiments were performed on IN5 at the ILL (Grenoble, France) with instrumental resolutions of 20 and 80 ~teV. Semi-oriented polycrystalline samples were used following the procedure described in Ref. [1]. The MD simulations were performed as described in Ref. [2]. From the MD trajectories, the intermediate scattering law, IMD(Q, t), of the whole molecule has been
0921-4526/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved PII S092 1 - 4 5 2 6 ( 9 6 ) 0 0 8 9 8 - 8
L. Gonzalez Mac Dowell et al. / Physica B 234-236 (1997) 106-108
107
1 8 10.3
Cy 0.8 - e - 6 10"3 0.6 4 10.3
iy
2 10.3 1
0.4 0.2 "
I
I
-150 -100 -50
0
50
100
150
Fig. 1. Calculated orientational distribution function for the chain backbones at 300 K.
0
0
~ 50
= 100 Time / ps
2 ,~-1 150
Fig. 3. Comparison of IMD(Q, t) (symbols) with lj,mp(Q,t) (broken lines), l,~p(Q, t) (dotted lines) and l~iff(Q, t) (full lines).
b /jump(Q,t) with k and k' as free parameters gives
k
.a
k Fig. 2. Schematic representation for the jump model over four sites.
computed excluding the contribution due to intramolecular vibrations [2]. The orientational distribution function p(~b) deduced for the n-nonadecane molecules in R~ phase at 300 K, reported in Fig. 1, displays a four-peak structure suggesting in a first approximation a model of jumps among four equilibrium orientations, schematized in Fig. 2. From the total numbers of transitions that occurred across the a and b-axes of the crystal [2], the rate constants defined in Fig. 2 were found to be k = 0.020 and k' = 0.017 ps -1. As shown in Fig. 3, the theoretical intermediate scattering function 1jump(Q,t) for this four-sites jump model does not compare well with IMD(Q,t). In addition, the fit of
a slightly better agreement when comparing the theoretical intermediate scattering function to IMD(Q,t) but with k = 0.028 and k ' = 0.010ps -1. We have therefore fitted the same jump model to the experimental neutron scattering law Soxp(Q,co) and we have found k = 0.062 and k' = 0.025 ps- 1 at 302 K, with a bad agreement with IMD(Q, t) (see Fig. 3). This result suggests that a jump model is not appropriate for allowing comparisons to be made between MD and IQNS. Nevertheless, the effective orientational potential obtained in MD simulations seems to be rather different from the experimental one. We have also considered a model of rotational diffusion in a potential V(q~) = - kT In (p(~b)). The relevant correlation functions were obtained by calculating the eigenvalues and eigenvectors of the dynamical matrix obtained by discretization of p(q~). Applying this method to the simulation-derived function p(~b) (Fig. 1), the intermediate scattering law Idlff(Q, t) was fitted to IMD(Q, t) with the rotational diffusion coefficient D~ as a free parameter. A perfect agreement (shown in Fig. 3) between the model and the MD data was obtained for D r = 0.093 ps-1. This suggests that a model of rotational diffusion should be considered to interpret the molecular dynamics of n-nonadecane in the R~ phase. In conclusion, we have shown that a reorientational model based on jumps over four sites must be ruled out and that a model of rotational
108
L. Gonzalez Mac Dowell et al. / Physica B 234-236 (1997) 106-108
diffusion must be considered. We are currently analyzing the I Q N S data on the basis of such model and our preliminary results would suggest that a good fit could be achieved by considering a four-fold potential with non-equivalent barriers.
References [1] F. Guillaume, J. Doucet, C. Sourisseau and A.-J. Dianoux, J. Chem. Phys. 91 (1989) 2555. [2] J.-P. Ryckaert, M. Klein and I.R. McDonald, Mol. Phys. 83 (1994) 439.
Physica B 234 236 (1997) 106-108
Rotational molecular dynamics in the
phase of n-nonadecane
L. Gonzalez Mac Dowell a, F. Guillaume b'*, J.-P. Ryckaert a, P. Girard b,c, V. Rodriguez b, A.-J. Dianoux c aPhysique statistique de la Mati~re Condens~e, CP223, ULB, 1050 Bruxelles, Belgium bLaboratoire de Spectroscopie Molkculaire et Cristalline, URA 124 CNRS, 351 cours de la Libbration, 33405 Talence Cedex, France CInstitut Laue-Langevin, B.P. 156, 38042 Grenoble Cedex 9, France
Abstract
Reorientational dynamics of n-nonadecane molecules in the RI phase have been investigated by means of molecular dynamics computer simulations (MD) and incoherent quasielastic neutron scattering (IQNS) techniques. Models based on jump process and rotational diffusionare compared with the calculated intermediate scattering functions and with the experimental spectra. A four-site jump model must be ruled out while a model based on a fourfold potential with two different barriers could be used to interpret the data succesfully. Keywords: Molecular systems; Quasielastic scattering; Computer modelling; Low-dimensional systems
Normal alkanes n-CnH2,+2 display disordered crystalline structures called 'rotator phases' between the fully ordered crystalline phase and the liquid phase. These rotator phases provide excellent prototypes to interpret at a microscopic level the dynamic and structural properties of more complex systems with aliphatic chains. N-nonadecane displays only one structural phase transition at Tt = 295.2K between the ordered crystal and the R~ rotator phase. In the RI phase (Fmmm, Z = 4), the n-nonadecane molecules form layers and the chain axes are perpendicular to the layers. The molecular dynamics of n-nonadecane chains in the R~phase has been investigated, among other techniques, by means of incoherent quasielastic neutron scattering (IQNS) [1] and molecular dynamics simulations (MD) [2]. The interpretation of the data was found to be in marked disagreement *Corresponding author.
as a model of jumps among 4 orientations was proposed in Ref. [2] and a model of reorientational diffusion in a two-fold potential was proposed in Ref. [1]. As shown in Ref. [2], the observed discrepancies could originate in the effect of the instrumental resolution (~90 peV) in the IQNS experiments. We have therefore undertaken a collaborative study of the molecular dynamics of n-nonadecane in the R~ phase and we will discuss here the models for the uniaxial reorientational dynamics of n-nonadecane in the R~ phase which could fit both IQNS and MD data. New IQNS experiments were performed on IN5 at the ILL (Grenoble, France) with instrumental resolutions of 20 and 80 ~teV. Semi-oriented polycrystalline samples were used following the procedure described in Ref. [1]. The MD simulations were performed as described in Ref. [2]. From the MD trajectories, the intermediate scattering law, IMD(Q, t), of the whole molecule has been
0921-4526/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved PII S092 1 - 4 5 2 6 ( 9 6 ) 0 0 8 9 8 - 8
L. Gonzalez Mac Dowell et al. / Physica B 234-236 (1997) 106-108
107
1 8 10.3
Cy 0.8 - e - 6 10"3 0.6 4 10.3
iy
2 10.3 1
0.4 0.2 "
I
I
-150 -100 -50
0
50
100
150
Fig. 1. Calculated orientational distribution function for the chain backbones at 300 K.
0
0
~ 50
= 100 Time / ps
2 ,~-1 150
Fig. 3. Comparison of IMD(Q, t) (symbols) with lj,mp(Q,t) (broken lines), l,~p(Q, t) (dotted lines) and l~iff(Q, t) (full lines).
b /jump(Q,t) with k and k' as free parameters gives
k
.a
k Fig. 2. Schematic representation for the jump model over four sites.
computed excluding the contribution due to intramolecular vibrations [2]. The orientational distribution function p(~b) deduced for the n-nonadecane molecules in R~ phase at 300 K, reported in Fig. 1, displays a four-peak structure suggesting in a first approximation a model of jumps among four equilibrium orientations, schematized in Fig. 2. From the total numbers of transitions that occurred across the a and b-axes of the crystal [2], the rate constants defined in Fig. 2 were found to be k = 0.020 and k' = 0.017 ps -1. As shown in Fig. 3, the theoretical intermediate scattering function 1jump(Q,t) for this four-sites jump model does not compare well with IMD(Q,t). In addition, the fit of
a slightly better agreement when comparing the theoretical intermediate scattering function to IMD(Q,t) but with k = 0.028 and k ' = 0.010ps -1. We have therefore fitted the same jump model to the experimental neutron scattering law Soxp(Q,co) and we have found k = 0.062 and k' = 0.025 ps- 1 at 302 K, with a bad agreement with IMD(Q, t) (see Fig. 3). This result suggests that a jump model is not appropriate for allowing comparisons to be made between MD and IQNS. Nevertheless, the effective orientational potential obtained in MD simulations seems to be rather different from the experimental one. We have also considered a model of rotational diffusion in a potential V(q~) = - kT In (p(~b)). The relevant correlation functions were obtained by calculating the eigenvalues and eigenvectors of the dynamical matrix obtained by discretization of p(q~). Applying this method to the simulation-derived function p(~b) (Fig. 1), the intermediate scattering law Idlff(Q, t) was fitted to IMD(Q, t) with the rotational diffusion coefficient D~ as a free parameter. A perfect agreement (shown in Fig. 3) between the model and the MD data was obtained for D r = 0.093 ps-1. This suggests that a model of rotational diffusion should be considered to interpret the molecular dynamics of n-nonadecane in the R~ phase. In conclusion, we have shown that a reorientational model based on jumps over four sites must be ruled out and that a model of rotational
108
L. Gonzalez Mac Dowell et al. / Physica B 234-236 (1997) 106-108
diffusion must be considered. We are currently analyzing the I Q N S data on the basis of such model and our preliminary results would suggest that a good fit could be achieved by considering a four-fold potential with non-equivalent barriers.
References [1] F. Guillaume, J. Doucet, C. Sourisseau and A.-J. Dianoux, J. Chem. Phys. 91 (1989) 2555. [2] J.-P. Ryckaert, M. Klein and I.R. McDonald, Mol. Phys. 83 (1994) 439.