Abstract
We discuss mathematical and physical aspects of the phase transition from nematic to smectic A liquid crystals. The first approach deals with analyzing a model obtained from the Maier-Saupe theory of nematic by taking into account that elongated liquid crystal molecules present distinguishable ends. Moreover, we represent long range microscopic interactions by means of nonlocal free energy functionals. The smectic configurations emerge as solutions of the extended nematic theory, through a modulation process. The second part of the article deals with energy minimization of the de Gennes free energy for smectic A* liquid crystals, and with the study of uniform twist grain boundary (TGB) structures. The goal is to mathematically justify parameter regions of the phase diagram of the transition between nematic and smectic A liquid crystals. Both approaches complement each other from the point of view that, while the first one deals with mechanisms causing layer arrangements, the second approach focuses on how chirality and layer effects interact, in a system with preassumed periodicity. The A* notation refers to chiral liquid crystals.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1273-1288 |
| Number of pages | 16 |
| Journal | Mathematical and Computer Modelling |
| Volume | 34 |
| Issue number | 12-13 |
| DOIs | |
| State | Published - Nov 5 2001 |
Bibliographical note
Funding Information:Liquid crystal molecules present elongated, rod-like shapes, that in the nematic phase tend to follow a preferred direction of alignment. The lower temperature smectic A phase presents orientational as well as one-dimensional positional order, with molecules arranged in layer structures Calderer has been supported by a grant from the National Science Foundation, Contract. No. DMS-9704714, 1997-2000.
Keywords
- Chirality
- Liquid crystal
- Modulation
- Nematic
- Polarization
- Smectic A