Universal Features in the Nematic Uniaxial-to-Biaxial Transition

Abstract

Recent experimental findings about new nematogenic molecules have reported thermally driven transitions to biaxial phases, which has revived the interest for macroscopic biaxiality. In particular, the simplified interaction model proposed by Straley for molecules endowed with D_2h symmetry has met renewed interest. In the scenario obtained for phases a unifying character can be captured. There exists a universal feature in the behaviour of one uniaxial order parameter, rebounding at the biaxial-to-uniaxial transition. This finding has been confirmed by means of a Monte-Carlo simulation. Moreover, the phase sequences and the order of the transitions are poorly influenced by one of the interaction parameters.

Keywords:

• biaxial
• minimax principle
• nematic liquid crystal

Acknowledgments

First of all, I need to acknowledge E. G Virga, G. De Matteis and S. Romano; this paper is based on the fruit of our collaboration. I am indebted to E. C. Gartland, Jr. for precious suggestions and enlightening discussions on the mean-field bifurcation analysis adopted in this paper, during our common stay at the IMA, Institute for Mathematics and its Applications, University of Minnesota, Minneapolis MN (USA), where part of this work was done. Financial support from both the Royal Society of London through the Project Biaxial liquid crystals: mathematical models and simulation and the Italian Ministry for Higher Education MIUR through the PRIN Grant No. 2004024508 is gratefully acknowledged. Last, but absolutely not least, my gratitude goes to G. R. Luckhurst, who prompted some of the exploration presented in this paper.