INTEGRAL-EQUATION THEORY OF POLYDISPERSE COLLOIDAL SUSPENSIONS USING ORTHOGONAL POLYNOMIAL-EXPANSIONS

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