We consider a crosslinked polymer blend made of two polymers of different chemical nature. We suppose that such a system incorporates small colloidal particles, which prefer to be attracted by one polymer, close to the spinodal temperature. This is the so-called critical adsorption. As assumption, the particle diameter, d 0 , is considered to be small enough in comparison with the size of microdomains (mesh size) ξ * ∼ an 1/2 , with a -the monomer size and n -the number of monomers between consecutive crosslinks. The critical fluctuations of the crosslinked polymer mixture induce a pair-potential between particles located in the non-preferred phase. The purpose is the determination of the Casimir pair-potential, U2(r), as a function of the interparticle distance r. To achieve calculations, use is made of an extended de Gennes field theory that takes into account the colloid-polymer interactions. Within the framework of this theory, we first show that the pair-particle is attractive. Second, we find for this potential the exact form:, with the known universal amplitudes AH > 0 and BH > 0 (the Hamaker constants). This expression clearly shows that the pair-potential differs from its homologue with no crosslinks only by the two exponential factors exp(−r/ξ * ) and exp(−2r/ξ * ). The main conclusion is that the presence of reticulations reduces substantially the Casimir effect in crosslinked polymer blends.

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 ϕ 4 -theory, where the field ϕ is the order parameter or composition fluctuation.

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In this paper, we report on the computation of the induced forces in crosslinked polymer blends, with immersed small colloidal particles (nanoparticles) or confi ned to two parallel plates (fi lm). We assume that the particles or the walls prefer to be attracted by one polymer, close to the spinodal temperature where a microphase separation takes place. This is the so-called " critical adsorption " . As an assumption, the particle diameter or the fi lm thickness is considered to be small enough in comparison with the size of microdomains ( " mesh size " ). The critical fl uctuations of the crosslinked mixture induce a pair potential between particles located in the nonpreferred phase or between the confi ning walls. The purpose is to recall how this Casimir pair potential can be determined, as a function of the interparticle distance or the walls separation. To achieve calculations, use is made of an extended de Gennes model that takes into account the colloid-polymer and polymer-wall interactions. Finally, the obtained results are compared to those relatively to uncrosslinked polymer blends in the same geometries, and the main conclusion is that the induced force is reduced by the presence of permanent crosslinks.