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Landau theory for biaxial nematic liquid crystals with two order parameter tensors

De Matteis, G. and Sonnet, A.M. and Virga, E.G. (2008) Landau theory for biaxial nematic liquid crystals with two order parameter tensors. Continuum Mechanics and Thermodynamics, 20 (6). pp. 347-374. ISSN 0935-1175

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We present a phenomenological theory for the homogeneous phases of nematic liquid crystals constituted by biaxial molecules. We propose a general polynomial potential in two macroscopic order parameter tensors that reproduces the mean-field phase diagram confirmed by Monte Carlo simulations [De Matteis et al. in Phys Rev E 72:041706 (2005)] and recently recognized to be universal [Bisi et al. in Phys Rev E 73:051709 (2006)] for dispersion force molecular pair-potentials enjoying the D 2h symmetry. The requirement that the phenomenological theory comply uniquely with this phase diagram reduces considerably the admissible phenomenological coefficients, both in their number and in the ranges where they can vary.