On the nature of long-range contributions to pair interactions between charged colloids in two dimensions

We perform a detailed analysis of solutions of the inverse problem applied to experimentally measured two dimensional radial distribution functions for highly charged latex dispersions. The experiments are carried out at high colloidal densities and under low-salt conditions. At the highest densities studied, the extracted effective pair potentials contain a long-range attractive part. At the same time, we find that for the best distribution functions available the range of stability of the solutions is limited by the nearest neighbour distance between the colloidal particles. Moreover, the measured pair distribution functions can be explained by purely repulsive pair potentials contained in the stable part of the solution. The machinery of statistical mechanics is designed to provide information on the structure of liquids from given interparticle interaction potentials. When solving the inverse problem of statistical mechanics, one hopes to find a unique interaction potential reproducing a measured distribution function [1, 2]. There are, however, always obstacles such as limited range and finite accuracy of the measured distributions, but also a number of numerical difficulties. No numerical procedure is able to fit the reference distribution exactly. Therefore, in practice, the inverse problem is always ill-posed and the uniqueness of the solution is not guaranteed. The problem becomes even more complicated at high particle densities where the spatial distributions are governed by packing effects. In this case, a wide range of effective potentials are projected onto a very tight space of radial distribution functions (rdfs), thus making it impossible to distinguish between the potentials of different shapes by comparing the pair distributions only. Another problem that occurs is particularly virulent in dense suspensions of charged colloids. It is related to the fact that a colloidal system is not a simple liquid with stateindependent pair interactions, but rather a complex system in which the colloidal interaction results from integrating out the microionic degrees of freedom [3–6]. As a result, a description