Temperature Dependence of the Elastic Constants for Biaxial Nematic Liquid Crystals

The elastic constants Kij of the Frank‐Oseen energy density for uniaxial nematic liquid crystals depend on the Maier‐Saupe order parameter S and hence on temperature. Longa et al. recently used an extended Landau‐Ginzburg‐de Gennes theory to expand the functions Kij(S) up to fourth order in S. Here, a similar procedure is applied for the elastic energy density of biaxial nematic liquid crystals. The three chiral and 15 achiral constants are expressed as fourth‐order polynomials in the order parameter S and the degree of biaxiality T. Via the temperature dependence of the quantities S and T also the temperature dependence of the elastic constants is fixed.