Interaction force induced by composition fluctuations in confined polymer blends close to the consolute point

Abstract

We consider a critical binary mixture made of two incompatible polymers A and B, confined between two parallel plates 1 and 2, which are at a finite distance L from each other. We assume that the latter adsorb strongly both polymers at a temperature above the consolute point Tc. The strong fluctuations of composition generate an effective force between the two plates. Our aim is precisely the computation of such a force as a function of the separation L. Use is made of the standard ψ4–theory, where ψ is the composition fluctuation or order parameter. We show that the presence of surfaces can be taken into account by imposing two boundary conditions, which depend on the energy necessary to adsorb one monomer on the plates and the surface chemical potential change. For simplification, we choose two special boundary conditions: symmetric and asymmetric plates, depending on whether the plates have the same or opposite preferences for polymers A and B. We demonstrate that, in the strong adsorption limit and close the consolute point (T∼Tc), the resulting effective force becomes universal. For both symmetric and asymmetric plates, we find that the (attractive and repulsive) forces (per unit area) decrease with distance L according to a negative power law, Πa,r∼∓L−4, and we compute exactly the corresponding universal amplitudes.