Computer Simulations of Nematic Defects

Abstract

The dynamics of nematic defects may not seem to be too important for device applications, if one knows how to avoid them. This may change in future, when disclinations can be used to store and process information, which appears possible due to their high entropy. The application of the differential equations of nemato-dynamics is however interesting from a theoretical point of view: it elucidates the capabilities and also the weaknesses of the present theory.

The numerical algorithm used here [1] is based on a dynamic equation for the alignment tensor a_μv, which takes the rotational diffusion, the influence of an orienting external field, and the Frank elasticity (in the one-coefficient approximation) into account. Flow processes are neglected.

First, I simulate the relaxation of randomly generated disclinations. The results are in accord with general topological laws [2] and with experimental observations. They demonstrate that disclination movement can occur as a pure reorientation process, without material flow. Second, the interesting behavior of disclinations subjected to an external field is investigated. It is found that the typical transient loops that occur during relaxation after a shear flow can be stopped from shrinking (and even caused to grow again) by an external electric field. I have confirmed this latter result by experiment [3]. As a more practical application of the numerical algorithm, the alignment and the relaxation of nematic droplets of spherical and ellipsoidal shape is simulated with different anchoring conditions at the boundary. The results may be helpful for modeling of the new PDLC (Polymer Dispersed Liquid Crystal) devices [4, 5].