Variational Methods for Analyzing Phase Transitions in Chiral Liquid Crystals
Speaker:
Patricia Bauman, Purdue University
Date and Time:
Monday, August 25, 2003 - 2:30pm to 3:15pm
Location:
Fields Institute, Room 230
Abstract:
We introduce the Landau-de Gennes free energy used to model the transition between chiral nematic and smectic A liquid crystal phases. Within this mathematical framework, the physically observed growth behavior of the twist and bend Frank constants in the energy play a major role in bringing about the transition. We rigorously establish a transition regime separating the two phases, using variational techniques to analyze two competing effects: the layer formation of the smectic phase and the twist tendency of the chiral nematic phase. Our discussion will illustrate the analogies as well as the discrepancies in modeling and behavior between smectic A liquid crystals and superconducting materials described by the Ginzburg-Landau theory.