Phase ordering in bulk uniaxial nematic liquid crystals

TL;DR

This paper investigates the phase-ordering kinetics of bulk uniaxial nematic liquid crystals, demonstrating an isomorphism with the O(2) model and deriving exact scaling functions that align with experimental and simulation data.

Contribution

It introduces a novel mapping between the nematic order parameter and a Gaussian field, revealing an exact scaling function and growth law within the Gaussian approximation.

Findings

The length scale grows as t^{1/2}.

Scaling functions match those of the O(2) model.

Results agree with experiments and simulations.

Abstract

The phase-ordering kinetics of a bulk uniaxial nematic liquid crystal is addressed using techniques that have been successfully applied to describe ordering in the O(n) model. The method involves constructing an appropriate mapping between the order-parameter tensor and a Gaussian auxiliary field. The mapping accounts both for the geometry of the director about the dominant charge 1/2 string defects and biaxiality near the string cores. At late-times t following a quench, there exists a scaling regime where the bulk nematic liquid crystal and the three-dimensional O(2) model are found to be isomorphic, within the Gaussian approximation. As a consequence, the scaling function for order-parameter correlations in the nematic liquid crystal is exactly that of the O(2) model, and the length characteristic of the strings grows as $t^{1/2}$. These results are in accord with experiment and simulation. Related models dealing with thin films and monopole defects in the bulk are presented and discussed.