Integral equation theory of polydisperse colloidal suspensions using orthogonal polynomial expansions

A procedure is described for the calculation of the generalized pair distribution function g(r,sigma,sigma'), where sigma is a molecular random variable with distribution f(sigma), using generalized integral equations familiar from simple liquid theory. The method is based on expansions of all sigma-dependent functions in the orthogonal polynomials p(j)(sigma) associated with the weight f(sigma) and is computationally efficient. To illustrate the procedure, calculations are made for a charge-stabilized, polydisperse colloidal suspension with Schulz distribution of diameters sigma. The method can be immediately generalized to fluids with internal degrees of freedom, for which f(sigma) must itself be self-consistently determined.