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Abstract
Recent measurements in a nematic liquid crystal formed by polyester compounds have given evidence of spontaneous macroscopic polar ordering. A mean-field theory for liquid crystals is built combining short-range, repulsive, steric forces with the average electric dipolar energy exchanged between molecules sharing the same excluded region. Such model is capable of identifying both uniaxial and biaxial polar phases. Under the assumption of a spheroidal shape for the molecules, and through a numerical bifurcation analysis, we assess the stability of phases upon two interaction parameters: the degree of intrinsic biaxiality, and the relative orientation of the permanent electric dipoles.
Acknowledgment
This work refers to and partly resumes a more thorough paper written with Prof. A. M. Sonnet and Prof. E. G. Virga; the author is in debt with them. This work was partly supported by Grants Progetto Giovani 2008 “Modelli multiscala per fluidi nanostrutturati” and Progetto Giovani 2009 “Effetti sterici in fluidi nanostrutturati polari” by GNFM (Gruppo Nazionale per la Fisica Matematica), Italy.