Interaction forces in quasi-two-dimensional charged dispersions

A “predictor-corrector” inversion of the Ornstein-Zernike equation has been presented for extracting the pair potential $u\left(r\right)\mathrm{}$ between colloidal particles from the radial distribution function $g\left(r\right)\mathrm{}$ or the static structure factor $S\left(q\right)\mathrm{}$ of dispersions confined to a single layer. The method, an extension of the three-dimensional analog presented earlier, is used to obtain $u\left(r\right)\mathrm{}$’s for recently published experimental data on confined dispersions. The results confirm unambiguously the existence of an attractive force in $u\left(r\right)\mathrm{}$, even for a set of data that has been described using a purely repulsive $u\left(r\right)\mathrm{}$ previously. We also illustrate the potential effect of experimental artifacts in imaging experiments that can lead to an apparent attraction in $u\left(r\right)\mathrm{}$ and offer an explanation for the persistence of attraction or its disappearance as a function of the distance between the plates used to confine the dispersions in the experiments.