Interaction forces in charged colloids: Inversion of static structure factors

A simple, easily usable 'predictor-corrector' inversion method is presented for extracting the effective pair potential u(r) from static structure factor S(q) of colloidal dispersions and liquids. The method, based on the Ornstein-Zernike integral equation, replaces the unknown bridge function B(r) in the closure with an iteratively obtained hard-sphere bridge function Bd(r). The accuracy of the method is examined by direct determination of B(r) using simulations for extreme examples of pair potential appropriate for charged dispersions. An example of the application of the method to liquid metals is also presented. The results demonstrate the need for using S(q) over the full range of q's [especially S(q)"s for sufficiently low values of q] for obtaining the crucial details of u(r). They further show the fallacies associated with the previous analyses of S(q) that have fueled the controversy concerning the nature of interaction forces in charged colloids and suggest the types of data needed for extracting u(r) for colloidal, Coulombic, and simple fluids.