Series Expansion of Distribution Functions in Multicomponent Fluid Systems

The equations of Kirkwood and Salzburg for distribution functions are generalized to multicomponent systems. The generalized equations serve to derive a recurrence relation between the coefficients of powers of particle number densities in a Maclaurin expansion of the distribution functions. This recurrence relation is then used to derive the general term in the expansion of the distribution functions in terms of modified irreducible integrals in multicomponent systems, which includes the original one-component expansion of Mayer and Montroll as a special case. The corresponding expansion of the potentials of average force is derived. The use of the new expansion is illustrated by a relatively simple derivation of the Fuchs expansion of the grand potential in multicomponent systems. Possible applications to ionic solutions, impurities in solids and x-ray diffraction in solutions of several solutes are briefly discussed. Some new formulas in the theory of cumulants (Thiele semi-invariants) are presented.