Numerical Study of the Isotropic-Nematic Phase Transition in Liquid Crystals Using the String Method (Communications in Computational Physics, 2018)
We consider a system of liquid crystal modeled by hard spherocylinders. Incertain range of the pressure, the system exhibits two metastable phases: the isotropicphase and the nematic phase. In the isotropic phase, the spherocylinders are randomlypacked. In contrast, the spherocylinders are well-ordered in the nematic phase. Theisotropic-nematic phase transition is a rare event because it involves the crossing ofenergy barrier(s). This makes direct simulations, e.g. using molecular dynamics, ofthe transition event infeasible. In this paper, we study the phase transition in a coarse-grainedspace formed by two collective variables: the order parameter of the spherocylindersand the volume of the system. We compute the free energy in the collectivevariable space, the minimum free energy path (MFEP) between the isotropic phase andthe nematic phase, and the transition state. Our results reveal the multilayer structureof the critical nucleus. The nucleus will grow further and evolve to the nematic phaseafter it crosses the energy barrier.
Keywords: Phase transition; liquid crystal; order parameter; collective variables; string method