Determination of the interaction force between two adsorptive surfaces delimiting a critical binary polymer blend

We consider a mixture of two incompatible polymers A and B, confined between two parallel surfaces of the same chemical nature, separated by a distance L. It is assumed that both surfaces strongly adsorb one of the species (A) at high temperature. It is also assumed that a demixing transition occurs at a critical temperature T(c) below the adsorption temperature T(a). The strong adsorption implies that the composition of species A on surfaces is quenched even when the temperature is lowered. The presence of strong density fluctuations near the critical point induces an interaction between the surfaces. We reexamine this attractive force and determine its dependence with the thickness L, when the latter is smaller than the thermal correlation length. We find that, in the vicinity of the critical point, this force decreases with distance as L-4. We show that the corresponding amplitude is a universal number, independent of the value of the composition on surfaces, and we give its exact expression. Finally, we note that the present system may be considered as a typical model enabling one to understand qualitatively and quantitatively the flocculation of colloids embedded in critical binary polymer blends.