Multiscale approach to nematic liquid crystals via statistical field theory
Abstract
We propose an approach to a multiscale problem in the theory of thermotropic uniaxial nematics based on the method of statistical field theory. This approach enables us to relate the coefficients A , B , C , L_{1}, and L_{2} of the Landaude Gennes free energy for the isotropicnematic phase transition to the parameters of a molecular model of uniaxial nematics, which we take to be a lattice gas model of nematogenic molecules interacting via a shortranged potential. We obtain general constraints on the temperature and volume fraction of nematogens for the Landaude Gennes theory to be stable against molecular orientation fluctuations at quartic order. In particular, for the case of a fully occupied lattice, we compute the values of the isotropicnematic transition temperature and the order parameter discontinuity predicted by (i) a continuum approximation of the nearestneighbor LebwohlLasher model and (ii) a LebwohlLashertype model with a nematogenic interaction of finite range. We find that the predictions of (i) are in reasonably good agreement with known results of Monte Carlo simulation.
 Publication:

Physical Review E
 Pub Date:
 August 2017
 DOI:
 10.1103/PhysRevE.96.022709
 arXiv:
 arXiv:1705.00168
 Bibcode:
 2017PhRvE..96b2709L
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 12 pages, 2 figures