Computer simulation study of a nematogenic lattice model based on the Nehring-Saupe interaction potential

By now, nematogenic lattice models have been extensively studied in the literature; they usually involve cylindrically symmetric (uniaxial) particles and isotropic interaction potentials defined by even functions of the scalar products between unit vectors defining their orientations; anisotropic interaction potentials involving other scalar invariants, i.e. also depending on the orientations of the two particles with respect to the intermolecular vector, have been considered far less often. A model of the latter kind was proposed by Nehring and Saupe over 25 years ago; we have considered here its restriction to nearest neighbours, having the form W-jk = epsilon [- 3/2h(jk) + 1], h(jk) = (3a(j)a(k) - b(jk))(2), r = x(j) - x(k), s = r/\ r \, a(j) = u(j) . s, a(k) = u(k) . s, b(jk) = u(j) . u(k). Here the three-component vectors x(j) is an element of Z(3) define centre-of-mass coordinates of the particles, and ul, are three-component unit vectors defining their orientations; e is a positive quantity setting energy and temperature scales (i.e. T* = k(B)T/epsilon); this model is seen to be the anisotropic counterpart to the generic Lebwohl-Lasher lattice model. The model has been addressed by simulation; comparisons are reported with other anisotropic lattice models recently studied in the literature.