Integral equation theory for the study of structure and thermodynamics and scaling-aggregation of droplets within Pickering emulsions versus the salt-concentration

In this work, we aim at the study of the statistical and thermal properties of the oil-in-water Pickering emulsions which are stabilized by strongly adsorbed charged nanoparticles on the surfaces of their droplets. In this study, we have adopted a pair-potential of Sogami-Ise type which is the sum of a repulsive part and an attractive one; and depends, in particular, on the saltconcentration. In this work, we were interested in two kinds of problems, namely (1) the determination of the structural and thermal properties of Pickering emulsions, and (2) the investigation of the scaling of cluster aggregation of the oil-droplets, as the salt-concentration is varied, keeping the other pertinent factors (surface-charge of oil-droplets, their size and density and bath temperature) fixed. For the two problems, we regarded the oil-droplets as monodisperse small spheres assimilated to charged soft-colloids. First, we have computed all of the structural properties (through the radial-distribution-function) versus the salt-concentration using the Integral-Equation Theory with the Hybridized-Mean-Spherical Approximation. Second, using the same numerical appoach, we have determined the thermal properties (through pressure, internal energy and isothermal compressibility). Finally, we have demonstraded that the oil-droplets aggregate has a fractal structure, with the help of an elaborated scaling model which was found to be in good agreement with Integral-Equation Theory.