Secondary minimum coagulation in charged colloidal suspensions from statistical mechanics methods

A statistical mechanics approach is applied to predict the critical parameters of coagulation in the secondary minimum for charged colloidal suspensions. This method is based on the solution of the reference hypernetted chain (RHNC) integral equation, and it is intended to estimate only the locus of the critical point instead of the full computation of the "gas-liquid" coexistence. We have used an extrapolation procedure due to the lack of solution of the integral equation in the vicinity of the critical point. Knowing that the osmotic isothermal compressibility of the colloidal system should ideally diverge in the critical point, we work out the critical salt concentration for which the inverse of the compressibility should be zero. This extrapolation procedure is more rapid than that previously proposed by Morales and co-workers [Morales, V.; Anta, J. A.; Lago, S. Langmuir 2003, 19, 475], and it is shown to give equivalent results. We also present experimental results about secondary minimum coagulation for polystyrene latexes and use our method to reproduce the experimental trends. The comparison between theory and experiment is quite good for all colloidal diameters studied.