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,σ,${\mathrm{\sigma }}^{\prime }$), where σ is a molecular random variable with distribution f(σ), using generalized integral equations familiar from simple liquid theory. The method is based on expansions of all σ-dependent functions in the orthogonal polynomials ${\mathit{p}}_{\mathit{j}}$(σ) associated with the weight f(σ) and is computationally efficient. To illustrate the procedure, calculations are made for a charge-stabilized, polydisperse colloidal suspension with Schulz distribution of diameters σ. The method can be immediately generalized to fluids with internal degrees of freedom, for whichf(σ) must itself be self-consistently determined. © 1996 The American Physical Society.