Density functional theory for simple molecular fluids

Abstract

We formulate a density functional theory for the one particle densities and thermodynamic properties of a one component molecular fluid. In such a fluid the orientation as well as the position of a particle is a relevant variable. We derive exact integro-differential equations which the density-orientation distributions obey. We make a truncated multipole expansion of these distributions and reformulate the theory in terms of the coefficients of this expansion. For slowly varying densities and small anisotropy the Helmholtz free energy can be expanded as a series involving density gradients and local anisotropy coefficients (order parameters). The coefficients of this expansion are directly proportional to moments of the Ornstein-Zernike direct correlation functions, as in theories of simple fluids. The theory is applied to the liquid-vapour interface and some formally exact results for the surface tension are derived. Using the gradient-order-parameter expansion we develop a tractable approximation scheme for the surface properties. We use this scheme to derive the general form of the local anisotropy near the interface of a fluid containing dumbell-like or disc-like molecules. Other possible applications of the general formalism to problems involving molecular fluids and liquid crystals are briefly mentioned.