# 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*

*Abstract*

### 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.