Colloidal aggregation in polymer blends
Abstract
We consider here a lowdensity 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 longrange attractive Casimir force between particles. This aggregation is a phase transition driving the colloidal system from dilute to dense phases, as the usual gasliquid 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 standard φ^{4} 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 FloryHuggins type. Second, we find that the interaction parameter u 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) in the (Ψ,u) plane, with Ψ as the volume fraction of immersed colloids. The continuous "gasliquid" transition occurs at some critical point K of coordinates (Ψ_{c}=0.5,u_{c}=2). Finally, we emphasize that the present work is a natural extension of that, relative to simple liquid mixtures incorporating colloids.
 Publication:

Journal of Chemical Physics
 Pub Date:
 June 2005
 DOI:
 10.1063/1.1943973
 Bibcode:
 2005JChPh.122x4913B
 Keywords:

 82.70.Dd;
 64.70.Fx;
 82.60.s;
 Colloids;
 Liquidvapor transitions;
 Chemical thermodynamics