Numerical Simulation of Elastic Anisotropy in Nematic Liquid Crystalline Polymers

Abstract

This chapter summarizes recent simulation work aimed at understanding elastic anisotropy in nematic liquid crystalline polymers (LCPs) based on a deterministic model that considers the three Prank elastic constants. A tensor expression of the so-called “texture field” is deduced so that the nematic symmetry is conserved automatically. In the absence of an external field, the evolution of the director field can be viewed as a process towards the state of zero elastic torque. The model forms the basis for improved understanding of the mesoscale structures and rheological phenomena of nematic LCPs. It has been tested in its ability to reproduce the Fréedericksz transitions, and simulations of thin LCP films clearly show the effect of elastic anisotropy on the microstructure evolution of the director field. In simulations of bulk samples disclination lines of strength half and escaped integer disclinations are observed. The distortion fields around the disclinations are found to depend on elastic anisotropy. If the twist constant is the lowest, as is the case for main chain LCPs, the disclination lines are predominantly of the twist type. Under shear flow, the simulation shows that the “log-rolling” orientation of the directors emerges for the tumbling nematics if the twist constant is smaller than the splay and the bend constants. The interaction of the wedge disclination pairs subject to a shear flow field is also simulated. The generation, multiplication and interaction of inversion wall defects during shearing have been revealed.