We consider here a low density assembly of colloidal particles immersed in a critical polymer environment mixture of two chemically incompatible polymers. We assume that, near the critical point of the free mixture, the colloids prefer to be surrounded by a polymer (critical adsorption). Consequently, there is a reversible colloidal aggregation in the non-preferred phase, due to the existence of an attractive Casimir force at long distance between the particles. This aggregation is a phase transition driving the colloidal system from diluted phases to dense phases, like the usual gas - liquid transition. We are interested in a quantitative survey on a phase diagram of colloid submerges. We assume that the positions of the particles are disordered and that the disorder is extinct and follows a Gaussian distribution.
We emphasize that the present work is a natural extension of that, relative to simple liquid mixtures incorporating colloids.
In this article, we were interested in calculating the interaction force between colloids immersed in a critical mixture of two polymers of different chemical nature. We assumed that the colloidal particles prefer to be contacted rather by one of the two polymers (critical adsorption), close to the critical temperature. As a result, the particles in the non-preferred phase aggregate, and we were concerned with the calculation of the induced force (or Casimir), which is responsible for this aggregation. This force results from strong fluctuations in composition close to the critical point. We point out that the results presented in this article must be regarded as a natural extension of the previous results, which concern by the calculation of the force induced between two parallel adsorptive planes, and which delimit a critical mixture of two incompatible polymers.el-kaber hachem 2, PhD
Journal of Chemical Physics
J. Chem. Phys. 122, 244913 (2005)