Theory of polar fluids. I

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Abstract
We examine a classical fluid composed of molecules which contain a polarizable electric dipole with finite permanent moment. The long-ranged dipolar and the short-ranged interactions are treated on a different footing by expanding relative to a reference system characterized by the absence of electrostatic interactions. Extensions of graph theoretical techniques developed in an earlier paper are used to analyse the pair distribution function and the dielectric constant. Reduction of the number of graphs and their complexity is effected by introducing renormalizations of the permanent moment and the polarizability. The analysis leads to the definition of a new function w(12), which is free of terms dependent on the shape of the sample. For polar, polarizable molecules the direct correlation function lacks translational invariance; its role as a basic quantity is ceded to w(12). The pair distribution function and the dielectric constant ε are expressed in terms of w(12) and two closely related functions. Attention is drawn to an unsolved problem in dielectric theory, and an alternative formula for ε is presented in the form of a conjecture. An approximation for ε is formulated for the case in which the short-ranged non-dipolar interactions are independent of the molecular orientations. A simplified version is solved analytically.