la048479m_CrossLinks_Spinodal_Langmuir - Langmuir 2005, 21,...

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Free Energy of Mixing of Cross-Linked Polymer Blends Chowdhury K. Mamun Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712 Received June 20, 2004. In Final Form: November 1, 2004 Freeenergyofmixingofcross-linkedpolymerblendsisderived,asamodificationtotheFlory - Huggins - de Gennes free energy functional for linear polymer blends. The latter arrives from the assumption of mean-field, short-range thermal interactions among ideal Gaussian chains. However, upon cross-linking a linear chain, the chain no longer remains Gaussian; new chain architectures belying the threadlike image of linear chains emerge. Fractal dimensions of these nonlinear chain clusters convene and command new entropic interactions. Topological constraints by cross-links introduce long-range nonequilibrium elastic forces. Relatively shorter range steric repulsions between fractal network surfaces may arrive if cross-linking is carried out inside the blend’s thermodynamically unstable region. Modified free energy has been used to highlight experiments on phase instability of cross-linked polymer blends. 1. Introduction Polymer science is an astoundingly active area of interdisciplinary research in soft condensed matter phys- ics.Topologicalconstraintsofferedbycross-linksarevery well perceived in polymer science; the consequent loss of conformational entropy of cross-linked chains is almost a platitude to mention. Yet phase diagrams of cross-linked polymerblendsarevirtuallyunknown. 1 Onemaysurmise that cross-linking in theory would increase the Flory - Huggins interaction parameter l and thus aggravate the phase instability. But there is also staggering evidence that cross-linking inhibits macrophase separations. 1 It would appear that the nature of forces s short and long range s unleashed by cross-linking is the pivotal feature, which a mere enhancement of the interaction parameter cannot address. (Enhancement of the interaction param- eter would blur its already dubious distinction as a predominantly energetic phenomenon. Cross-linking seems to rally mainly entropic interactions.) Moreover, cross- linked blends often show spatial patterns inside the miscibility gap and multiple peaks in their dynamic structurefunctions,quiteincongruouswithresultscoming from an enthalpic adjustment. The first step toward understanding cross-linked systems would be to discern their free energies: what may constitute them? What follows next is a quite simple, yet effective formulation of this free energy with underlying physics adequately outlined. This formulation, however platitudinous to mention,wouldaddresschieflyphaseinstabilityinbinary polymer blends in which one chain species is cross-linked onto itself for whatever reason application dictates. (Of course, the blend ought to have a miscibility gap over certain thermodynamic coordinates for the instability to set in, but at the same time the free energy expression is applicable to miscible regions as well. Phase instability
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la048479m_CrossLinks_Spinodal_Langmuir - Langmuir 2005, 21,...

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