Non‐equilibrium molecular‐dynamics measurement of the Leslie coefficients of a Gay–Berne nematic liquid crystal

Abstract

Using non‐equilibrium molecular‐dynamics (MD) simulations, we have measured the six Leslie coefficients of a nematic liquid crystal composed of molecules interacting via the Gay–Berne potential. In the presence of a simple shear flow, an alignment field is applied to control the molecular orientation and a uniform director is stabilized in the central region of the channel in which the liquid crystal is confined and sheared. With the director tuned by varying the applied field, a number of orientational states are stabilized in the presence of the shear flow and various viscous stress components are measured in these states of differently oriented directors. The six Leslie coefficients α _i are determined by interpreting the MD measurement data for viscous stress according to the constitutive relations in the Ericksen–Leslie–Parodi theory. Our measurement of the Leslie coefficients shows the Parodi relation α₂+α₃ = α₆−α₅ is well satisfied. Given the values of the Leslie coefficients, liquid crystal orientations are evaluated for different alignment fields and shear rates, and then compared with those directly measured in MD simulations, demonstrating a quantitative agreement. Our simulation results show that in the Gay–Berne nematic liquid crystal, the viscous stress and the coupling between orientation and flow are well described by the Ericksen–Leslie–Parodi theory.

Acknowledgements

Numerical computations were performed on a Beowulf cluster in the Center for Computational Science and Engineering of Peking University. T. Qian was partially supported by the Hong Kong RGC grant CA05/06.SC01. P. Zhang was partially supported by the special funds for Major State Research Projects 2005CB321704 and the National Science Foundation of China for Distinguished Young Scholars 10225103 and 20490222.