Viscosities of the Gay-Berne nematic liquid crystal.

We present molecular dynamics simulation measurements of the viscosities of the Gay-Berne phenomenological model of liquid crystals in the nematic and isotropic phases. The temperature-dependence of the rotational and shear viscosities, including the nonmonotonic behavior of one shear viscosity, are in good agreement with experimental data. The bulk viscosities are significantly larger than the shear viscosities, again in agreement with experiment. 61.30.-v, 61.30Cz,64.70Md Typeset using REVTEX 1 Ever increasing computer power has made simulations of simple, yet realistic molecular models of liquid crystals a feasible enterprise. With the aid of computers it is possible to study the effects of molecular shapes, sizes and interactions on macroscopic behavior.Three types of liquid crystal models have been used in simulation work. The first is the LebwohlLasher model [1], a lattice model for rotators. This model can be used to study the isotropicnematic transition as a rotational order-disorder transition in an effective crystalline solid. Another class of models which has received much attention and includes the translational degrees of freedom of a liquid crystal uses hard particles of various shapes which interact solely by excluded volume effects [2,3]. These hard body models exhibit very rich phase diagrams including smectic, columnar and cubatic phases. Finally, in recent years there has been considerable numerical study of the Gay-Berne (GB) system [4] which is a fluid of point-like particles, each carrying a unit vector û which mimics the long molecular axis. The particles interact via an anisotropic Lennard-Jones potential which depends on the relative orientation and location of a pair of molecules. This system displays rich behavior like the hard body models, but also includes attractive forces. These latter forces play an especially important role in the formation of smectic phases, which are more readily formed in the GB system than in the hard body models.. The GB model has also been extended to include chirality [5] and to model discotics [6]. Previous studies of the GB system have focused on the phase diagram [7–9] and singleparticle translational and rotational dynamics [10]. In this Letter we report on numerical measurements of the viscosities of the GB system. We find a number of results which indicate that the GB model exhibits the principal dynamical features of a real nematic liquid crystal. The temperature dependence of the shear viscosities and the rotational viscosity below the isotropic-nematic transition is qualitatively similar to what is observed in experiment [11–14], including the nonmonotonic behavior of one of the shear viscosities. The two bulk viscosities are an order of magnitude larger than the shear viscosities in agreement with ultrasonic measurements [15]. We also find that long-time correlations of the director exhibit the expected Brownian motion due primarily to the finite-size of our system. This motion 2 yields exceptionally good statistics for the rotational viscosity. The GB potential is modeled to give the best fit to the pair potential for a molecula consisting of a linear array of four equidistant Lennard-Jones centers with separation of 2σo between the first and fourth sites (subsequent work [9] examined different fits) The GB potential is given by, U(û1, û2, r) = 4ε(û1, û2, r)× [{ σo r − σ(û1, û2, r) + σo }12 − { σo r − σ(û1, û2, r) + σo }6] (1) where û1, û2 are unit vectors giving the orientations of the two molecules separated by the position vector r. The parameters ε(û1, û2, r) and σ(û1, û2, r) are orientation dependent and give the well depth and intermolecular separation where U = 0 respectively. The well depth is written as, ε(û1, û2, r) = εoε (û1, û2)ε (û1, û2, r) (2)