Mean-field and computer simulation study of a biaxial nematogenic lattice model mimicking shape amphiphilicity

The present Letter considers a biaxial nematogenic lattice model, involving particles of D-2h symmetry, whose centres of mass are associated with a 3-dimensional simple-cubic lattice; the pair potential is isotropic in orientation space, and restricted to nearest neighbours. Let the two orthonormal triads {u(j), j = 1, 2, 3} and {v(k), k = 1, 2, 3} define orientations of a pair of interacting particles, and let G(jk) = P-2(v(j) (.) u(k)), where P-2(...) denotes the second Legendre polynomial. By now, interaction models defined by suitable linear combinations of terms G(jk) have been studied for some time in the literature; a new and simplified form for them has recently been proposed by Sonnet, Virga and Durand [Phys. Rev. E 67 (2003) 061701]; the present potential follows their idea, but now uses different parameter values (pushing, so to speak, their simplification even further), i.e., it has an extreme biaxial mesogenic form which, by elementary geometrical identities, can be written in two equivalent ways phi = epsilon[-(G(11) + G(22)) + (G(12) + G(21))] = epsilon[-2(G(11) + G(22)) + G(33)], where epsilon denotes a positive quantity setting energy and temperature scales (i.e., T* = k(B)T/epsilon). A mean-field analysis predicts the existence of a direct second-order transition between biaxial and isotropic phases; Monte Carlo simulations qualitatively confirm the prediction. Some thirty years ago, Alben [J. Chem. Phys, 59 (1973) 4299] suggested the possibility of producing biaxial nematic order by mixing rod-like and disc-like (mesogenic) molecules; the idea was investigated theoretically in a number of cases, but so far no experimental realisation has been observed. On the other hand, "shape amphiphlic" mesogens, containing both rod-like and disc-like parts covalently bonded together, have been synthesised in the last few years, although thermotropic biaxial nematic behaviour has not been experimentally detected in these pure compounds either. The present interaction model can be seen as a simple and extreme approximation to such a behaviour, favouring parallel orientation of rod moieties, parallel orientation of disc moieties, and mutual perpendicular orientations between rods and discs. (C) 2004 Elsevier B.V. All rights reserved.