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E-International Scientific Research JournalISSN: 2094-1749 Volume: 2 Issue: 4, 2010INDUCED FORCES IN POLYMER BLENDSVERSUS TEMPERATURES. El Fassi, M. Benhamou, H. Ridouane, M. El YaznasniPolymer Physics and Critical Phenomena LaboratorySciences Faculty Ben M’sik, P.O. Box 7955, Casablanca, MoroccoAbstractWe re-examine <strong>the</strong> computation of <strong>the</strong> induced force experienced by colloidal p<strong>article</strong>simmersed in a binary mixture, made of two chemically incompatible polymers of highmolecular-weight.Such a force originates from <strong>the</strong> strong fluctuations of composition near <strong>the</strong>critical temperatureT c, and <strong>the</strong> fact that one polymer of <strong>the</strong> mixture prefers to be attracted bycolloids (critical adsorption). More precisely, we aim at a quantitative investigation of <strong>the</strong>temperature effect on <strong>the</strong> force expression, when one is far fromT c. To achieve calculations,we use <strong>the</strong> standard4ϕ -<strong>the</strong>ory, w<strong>here</strong> <strong>the</strong> field ϕ represents <strong>the</strong> composition fluctuation(order parameter). Combining this <strong>the</strong>ory with <strong>the</strong> standard cumulant method, we first findthat <strong>the</strong> effective pair-potential is <strong>the</strong> sum of two contributions, which are directly proportionalto <strong>the</strong> bulk two-point correlation functions constructed with fields ϕ and2ϕ , respectively.Second, taking advantage of <strong>the</strong> exactly known (mean-field) correlation functions, wedemonstrate that <strong>the</strong> expected force can be expressed in term of <strong>the</strong> modified Bessel functionsK 1 (z) and K 2 (z). Third, we show that <strong>the</strong> reduced induced force, D F(r) / kB T , is auniversal two-factor scaling function of <strong>the</strong> dimensionless variablesr / D andξ/ D, w<strong>here</strong> r is<strong>the</strong> inter p<strong>article</strong>-distance, ξ is <strong>the</strong> <strong>the</strong>rmal correlation length of <strong>the</strong> free polymer mixture andD is <strong>the</strong> scale-distanceD = d0N , w<strong>here</strong> d0is <strong>the</strong> p<strong>article</strong>s diameter and N <strong>the</strong>polymerization degree of chains. The essential conclusion is that, for high or low temperatures,<strong>the</strong> induced force becomes less important than that at <strong>the</strong> critical one.Keywords: Polymer blends, Colloids, Phase separation, Induced force, Temperature effects.IntroductionThe induced force generated by fluctuations of some physical entity is one of <strong>the</strong> mostfundamental discoveries of <strong>the</strong> last century. Already in 1948, Casimir predicted <strong>the</strong> attraction315

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