We define a continuum energy functional that effectively interpolates between the mean-field Maier-Saupe energy and the continuum Landau-de Gennes energy functional and can describe both spatially homogeneous and inhomogeneous systems. In the mean-field approach the main macroscopic variable, the Q-tensor order parameter, is defined in terms of the second moment of a probability distribution function. This definition imposes certain constraints on the eigenvalues of the Q-tensor order parameter, which may be interpreted as physical constraints. We define a thermotropic bulk potential which blows up whenever the eigenvalues of the Q-tensor order parameter approach physically unrealistic values. As a consequence, the minimizers of this continuum energy functional have physically realistic order parameters in all temperature regimes. We study the asymptotics of this bulk potential and show that this model also predicts a first-order nematic-isotropic phase transition, whilst respecting the physical constraints. In contrast, in the Landau-de Gennes framework the Q-tensor order parameter is often defined independently of the probability distribution function, and the theory makes physically unrealistic predictions about the equilibrium order parameters in the low-temperature regime. Copyright © Taylor & Francis Group, LLC.
|Original language||English (US)|
|Number of pages||11|
|Journal||Molecular Crystals and Liquid Crystals|
|State||Published - Jul 20 2010|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: A. Majumdar is supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST) to the Oxford Centre for Collaborative Applied Mathematics. J. M. Ball is supported by EPSRC grants EP/E010288/1 and EP/E035027/1. The authors gratefully acknowledge helpful discussions with Geoffrey Luckhurst, Peter Palffy-Muhoray, Valery Slastikov and Tim Sluckin.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.