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Phase Separation in Complex Mixtures with Many Components: Analytical Expressions for Spinodal Manifolds
Arjen Bot1,2, Erik van der Linden2, Paul Venema2
1Unilever Foods Innovation Centre, Bronland 14, NL-6708 WH Wageningen, The Netherlands.
Abstract:
The phase behavior is investigated for systems composed of a large number of macromolecular components N, with N ≥ 2. Liquid-liquid phase separation is modeled using a virial expansion up to the second order of the concentrations of the components. Formal analytical expressions for the spinodal manifolds in N dimensions are derived, which simplify their calculation (by transforming the original problem into inequalities that can be evaluated numerically using linear programming techniques). In addition, a new expression is obtained to calculate the critical manifold and composition of the coexisting phases. The present analytical procedure complements previous attempts to handle spinodal decomposition for many components using a statistical approach based on random matrix theory. The results are relevant for predicting the effects of polydispersity on phase behavior in fields like polymer or food science and liquid-liquid phase separation in the cytosol of living cells.
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