Casimir force between colloidal particles immersed in a critical polymer blend

摘要

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 T-c 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 psi(4) theory, where the field psi 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 > d(0) according to: F(r)/k(B)T(c) = -(64pi(2)/27)Nd-0(2)/r(3), where N is the common polymerization degree of polymers and d(0) is the particle diameter. Incidentally, this force is similar to the van der Waals one between two parallel plates. (C) 2003 American Institute of Physics. [References: 62]