Casimir Force between Nanoparticles Immersed in a Crosslinked Polymer Blend

S. El Fassi, M. Benhamou, M. Boughou, H. Kaidi, M. El Yaznasni and H. Ridouane Laboratoire de Physique des Polymères et Phénomènes Critiques , Faculté des Sciences Ben M'sik, P.O. Box 7955, Casablanca, Morocco

Received: January 30, 2010; in final form July 22, 2010

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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, d0, is considered to be small enough in comparison with the size of microdomains (mesh size) ξ* ~ an1/2, 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: U2 (r)/kB T = - AH(d0/r )2 exp ( - r/ξ* ) - BH(d0/r)4 exp(-2r/ξ*), 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.

DOI: 10.12693/APhysPolA.118.606 PACS numbers: 61.25.Hq, 64.75.+g, 82.70.Gg