Casimir force between colloidal particles immersed in a critical polymer blend

Abstract

We consider here a low-density assembly of spherical colloids immersed in a mixture of two incompatible polymers A and B. We assume that, near the consolute point Tc of the host mixture, colloids adsorb preferentially A polymer. The preferential adsorption has as a consequence that particles aggregate in the nonpreferred B phase. We aim at the computation of the induced force F(r), responsible for this aggregation, as a function of the interparticle distance r. To achieve this, use is made of a field-theoretical approach based on ψ4 theory, where the field ψ is simply the composition fluctuation (order parameter). Combining this approach with the standard cumulants method, we first demonstrate that the effective pair potential is proportional to the two-point correlation function of the host mixture. Second, very close to the critical point, we find that the effective force is universal and decays with interparticle distance r>d0 according to: F(r)/kBTc=−(64π2/27)Nd02/r3, where N is the common polymerization degree of polymers and d0 is the particle diameter. Incidentally, this force is similar to the van der Waals one between two parallel plates.