Elastic constants and dynamics in nematic liquid crystals

Abstract

In this paper, we present molecular dynamics calculations of the Frank elastic constants, and associated time correlation functions, in nematic liquid crystals. We study two variants of the Gay–Berne potential, and use system sizes of half a million molecules, significantly larger than in previous studies of elastic behaviour. Equilibrium orientational fluctuations in reciprocal ( k -) space were calculated, to determine the elastic constants by fitting at low | k |; our results indicate that small system size may be a source of inaccuracy in previous work. Furthermore, the dynamics of the Gay–Berne nematic were studied by calculating time correlation functions of components of the order tensor, together with associated components of the velocity field, for a set of wave vectors k . Confirming our earlier work, we found exponential decay for splay and twist correlations, and oscillatory exponential decay for the bend correlation. In this work, we confirm similar behaviour for the corresponding velocity components. In all cases, the decay rates, and oscillation frequencies, were found to be accurately proportional to k ² for small k, as predicted by the equations of nematodynamics. However, the observation of oscillatory bend fluctuations, and corresponding oscillatory shear flow decay, is in contradiction to the usual assumptions appearing in the literature, and in standard texts. We discuss the advantages and drawbacks of using large systems in these calculations.

Keywords:

• molecular dynamics
• nematic
• liquid crystal
• elastic constants
• hydrodynamics

Acknowledgements

Computer facilities were provided by Warwick University Centre for Scientific Computing. Support from the Engineering and Physical Sciences Research Council is gratefully acknowledged. We are grateful to an anonymous referee for comments on the first draft.

Disclosure statement

No potential conflict of interest was reported by the authors.