Thermodynamically self-consistent integral equation theory for pair-correlation functions of molecular fluids-II

Abstract

A closure for the pair-correlation functions of molecular fluids is described in which the hypernetted-chain and the Percus–Yevick approximations are “mixed” as a function of interparticle separation. An adjustable parameter α in the mixing function is used to enforce thermodynamic consistency, by which it is meant that identical results are obtained when the equations of state are calculated via the virial and compressibility routes, respectively. The mixed integral equation for the pair-correlation functions has been solved for two model fluids: (i) a fluid of the hard Gaussian overlap model, and (ii) a fluid the molecules of which interact via a modified Gay–Berne model potential. For the modified Gay–Berne fluid we have slightly modified the original Gay–Berne potential to study the effect of attraction on hard core systems. The pair-correlation functions of the isotropic phase which enter in the density-functional theory as input informations have been calculated from the integral equation theories for these model fluids. We have used two different versions of the density-functional theory known as the second order and modified weighted-density-functional theory to locate the isotropic-nematic (I–N) transitions and calculate the values of transition parameters for the hard Gaussian overlap and modified Gay–Berne model fluids. We have compared our results with those of computer simulations wherever they are available. We find that the density-functional theory is good to study the I–N transition in molecular fluids if the values of the pair-correlation functions in the isotropic phase are accurately known.