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Casimir Force between Nanoparticles Immersed in a Crosslinked Polymer Blend

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El Fassi S., Benhamou M., Boughou M., Kaidi H., El Yaznasni M., Ridouane H.

issue 4

606-612

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, U_2 (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: U_2(r)/k_{B}T = - A_{H}(d_0/r)^2 exp(-r/ξ*) - B_{H}(d_0/r)^4 exp(-2r/ξ*), with the known universal amplitudes A_{H} > 0 and B_{H} > 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.

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1 Acta Physica Polonica A

1 2010

1 Benhamou M.

1 Boughou M.

1 El Fassi S.

1 El Yaznasni M.

1 Kaidi H.

1 Ridouane H.

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Casimir Force between Nanoparticles Immersed in a Crosslinked Polymer Blend