PDE Seminar Smectic energies and existence theorems for liquid crystals

2008-06-23 16:30 - 2008-06-23 17:30
Faculty of Science Building #8 Room 309
Daniel Phillips (Department of Mathematics, Purdue University)
Smectic C liquid crystals form layered structures with a welldefined layer thickness, where the layers are made up of rod likeliquid crystal molecules, each of which tends to tilt from thelayer normal by an angle $\theta$. Liquid crystal configurationsare described by a pair $(\psi,\textbf{n})$. The director field$\textbf{n})$ is a unit vector field representing the distributionof the molecules' long axes. $\psi$ is a complex order parametergiving the layer structure. We investigate a 2nd order freeenergy, the Chen-Lubensky energy. We prove the existence ofminimizing pairs representing stable configurations. We furthershow how minimizing this energy tends to enforce the fixed layerthickness and tilt angle, and favor certain types of layer bending.