278100 Fast Monte Carlo Simulation of Liquid Crystal Nanodroplets by Theoretically-Informed Metropolis Sampling of Alignment-Tensor Fields

Wednesday, October 31, 2012: 9:24 AM
411 (Convention Center )
Juan Pablo Hernandez-Ortiz, Department of Materials and Bioengineering, Universidad Nacional de Colombia, Sede Medellin, Medellin, Colombia, Orlando Guzman, Departamento de Fisica, Universidad Autonoma Metropolitana-Iztapalapa, Mexico D. F., Mexico, Tyler Roberts, Department of Chemical and Biological Engineering, University of Wisconsin Madison, Madison, WI and Juan J. de Pablo, Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, WI

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.

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See more of this Session: Thermodynamics at the Nanoscale
See more of this Group/Topical: Engineering Sciences and Fundamentals