Molecular-field-theory approach to the Landau theory of liquid crystals: Uniaxial and biaxial nematics

Biaxiality-induced magnetic field effects in bent-core nematics: Molecular-field and Landau theory

“…In this, the molecular interaction only depends on one relative biaxiality parameter, λ = u 222 /u 202 = u 202 /u 200 . We note that the notation λ for the biaxiality parameter is consistent with the usage of Luckhurst et al [15], but differs from that of Sonnet et al [24], and of Luckhurst et al [17]. A key simplification of the GMA, at least within molecular field theory, is that now there is only one combination of spherical harmonics J entering the theory [15,17].…”

“…Combining eqs. (14,17), together with eq. (9) the quantity J can be expressed self-consistently in terms of the scaled temperature T * and scaled external field V as follows:…”

“…Some of the present authors [16,17] have adopted an intermediate Landau-de Gennes strategy. In this approach, parameters in the Landau theory of a biaxial nematogen have been directly associated with quantities which occur in the molecular field theory.…”

“…We use the free energy expansion introduced by Luckhurst et al [17] to obtain the following order parameter expansion, truncated at fourth order:…”

“…In addition to studying the molecular field theory, we also derive a Landau-de Gennes expansion from the molecular field theory for uniaxial nematic formed from biaxial molecules in section III. The methodology is an extension of that developed by Katriel et al [16] for uniaxial nematic formed from uniaxial molecules, and later extended by Luckhurst et al [17] to study nematics formed from biaxial molecules. Using this method, we demonstrate that the cubic expansion coefficient B can be related to the molecular biaxiality.…”