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)

We consider here a low-density assembly of colloidal particles immersed in a critical polymer mixture of two chemically incompatible polymers. We assume that, close to the critical point of the free mixture, the colloids prefer to be surrounded by one polymer (critical adsorption). As result, one is assisted to a reversible colloidal aggregation in the nonpreferred phase, due the existence of a long-range attractive Casimir force between particles. This aggregation is a phase transition driving the colloidal system from dilute to dense phases, as the usual gas–liquid transition. We are interested in a quantitative investigation of the phase diagram of the immersed colloids. We suppose that the positions of particles are disordered, and the disorder is quenched and follows a Gaussian distribution. To apprehend the problem, use is made of the standardφ4 theory, where the field φ represents the composition fluctuation (order parameter), combined with the standard cumulant method. First, we derive the expression of the effective free energy of colloids and show that this is of Flory–Huggins type. Second, we find that the interaction parameter uu between colloids is simply a linear combination of the isotherm compressibility and specific heat of the free mixture. Third, with the help of the derived effective free energy, we determine the complete shape of the phase diagram (binodal and spinodal). The continuous “gas–liquid” transition occurs at some critical point. Finally, we emphasize that the present work is a natural extension of that, relative to simple liquid mixtures incorporating colloids.

July 2005

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