(455d) Fast Monte Carlo Simulation of Liquid Crystal Nanodroplets by Theoretically-Informed Metropolis Sampling of Alignment-Tensor Fields
We have developed a fast theoretically informed Monte Carlo simulation method for liquid crystals, which works on multiple scales of coarse-graining, and have applied it to describe the morphology of nematic droplets of nanoscopic size. The method relies on stochastic changes to the alignment-tensor field Q(r) that describes the state of the liquid crystal inside the droplet, which are accepted on the basis of sampling criteria dictated by the desired free energy functional F[Q(r)] of the system. We take F to consist of the usual sum of bulk and surface terms and represent the liquid crystal configuration Q(r) in terms of a radial-basis-function interpolation.
By realizing that different values of parameter β in the Boltzmann factor exp(-β ΔF) correspond to different levels of the coarse-graining length-scale L, Monte Carlo methods capable of sampling simultaneously multiple values of β, such as parallel-tempering or replica exchange, become particularly useful for multi-scale descriptions of the system, while also accelerating sampling of the system's phase space.
We apply this method to predict the phase diagram of liquid-crystal morphologies inside nematic droplets over a range of nanoscopic sizes and anchoring conditions. A comparison to previous results, from particle-based molecular dynamics and Ginzburg-Landau continuum methods, reveals excellent agreement with past work and serves to highlight the improved performance of our proposed approach.