Theory of Systems of RodIike Particles: II. Thermotropic systems with orientation-dependent interactions

Abstract

A system of rigid, inpenetrable, rodlike molecules subject to orientation-dependent mutual attractions is treated by extension of the theory presented in the preceding paper. This energy is formulated, for a system at constant volume, by considering interactions between pairs of segments in contact, rather than in terms of interactions between entire molecules. The orientation-dependent energy between a pair of segments is taken to be proportional to cos² Ψ_ij, where Ψ_ij is the angle between the principal axes of their polarizability tensors, assumed to be cylindrically symmetric with respect to the molecular axis. A characteristic temperature T∗ measures the intensity of these interactions. The orientational energy of the system as a whole is of the form derived by Maier and Saupe. The orientation distribution with respect to the domain axis and the partition function are formulated with T∗ and the axial ratio x as parameters, Steric effects of molecular shape asymmetry, embodied in x, are of foremost importance. The reduced temperature [Ttilde]_ni = T_ni/xT∗ at which the nematic-isotropic transition takes place in the neat liquid decreases with decrease in x below its athermal limit x_erit = 6.417 for [Ttilde]^–1 _ni = 0. Both the entropy difference between isotropic and nematic phases and the orientational heat capacity C^p, are monotonic through the transition; C_p, diverges at a temperature appreciably above T_nl, where the metastable anisotropic state becomes unstable. Comparison of theory with experiments on those nematogens whose molecules can be approximated by rigid rods lends encouragement to the prospect of relating characteristics of the nematic-isotropic transition to molecular structure.