University of Minnesota
Aerospace Engineering and Mechanics
Spring 1999 Seminar Series

Modeling Studies of the Phase Transition Between Chiral Nematic and Smectic a Liquid Crystals

Prof. Maria-Carme Calderer

Department of Mathematics, Penn State University


This colloquium addresses the existence of minimizers of the Landau--de Gennes free energy for chiral smectic A liquid crystal materials (smectic A*). Such an energy is appropriate to describe the liquid crystal behavior near the transition temperature between the nematic and the smectic A phases. We are interested in liquid crystals exhibiting chiral structure above the transition temperature and smectic A layering below the transition. The leading mechanism underlying all the observed phenomena is the competition between the tendency of the molecules to form layers in the smectic phase and the helical twist arrangements preferred by the nematic chiral structures. The boundary conditions of the admissible fields include, both, strong and week anchoring. The energy that we study combines the general Landau form for second order phase transitions with the Oseen--Frank energy for liquid crystals. Such an energy was first proposed and studied by de Gennes, Lubensky and Renn exploring formal analogies with the Ginzburg--Landau energy modeling high $T_c$ superconductivity. The wave function and the director of the smectic A* theory correspond to the superconducting electron pair density and the magnetic potential, respectively. However, the fact that the liquid crystal director is subject to the unit length constraint is the source of fundamental mathematical differences between the two theories. Our discussion addresses phenomena such as the type I and type II behavior of both, liquid crystals and superconductors, the upper and lower critical parameter values, the corresponding length scales, the nucleation of one phase within the other, the Abrikosov phase of the superconductors and the twist grain boundary phase (TGB) of the liquid crystals. Some of the topics presented are joint work with P. Bauman, C. Liu, D. Phillips and L. Truskinovsky.

Friday, April 16, 1999
209 Akerman Hall
2:30-3:30 p.m.

Refreshments served after the seminar in 227 Akerman Hall.
Disability accomodations provided upon request.
Contact Kristal Belisle, Senior Secretary, 625-8000.