Casimir force in confined polymer blends or ternary polymer solutions

This paper is devoted to a review of recent progresses concerning the computation of the Casimir force between two parallel plates delimitating a polymer blend or a ternary polymer solution (with a good solvent). We assume that, close to the consolute point, one or the two polymers of the mixture are strongly attracted by the plates (critical adsorption). For both systems, the induced force originates from the fluctuations of composition near the consolute point. In polymer blends case, it was found that the force decreases with separation L between the two plates as L-4, with a known universal amplitude. For ternary polymer solutions, however, it has been shown that the interaction force decays rather as L-3. This drastic change of the force expression is due to the presence of the good solvent, which gives rise to additional fluctuations of polymer concentration. To do calculations, for the two systems, use is made of the standard (phi(4)-theory, where the field (p is the order parameter or composition fluctuation.