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arXiv · 2306.17600

Phase separation in complex mixtures with many components: analytical expressions for spinodal manifolds

Arjen Bot·Erik van der Linden·Paul Venema
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Abstract

The phase behavior is investigated for systems composed of a large number of macromolecular components N, with N greater or equal to 2. Liquid-liquid phase separation is modelled 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 that 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 the composition of the co-existing 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 effects of polydispersity on phase behavior in fields like polymer or food science, and to liquid-liquid phase separation in the cytosol of living cells.

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Arjen Bot, Erik van der Linden, Paul Venema. 2023-06-30. Phase separation in complex mixtures with many components: analytical expressions for spinodal manifolds. https://doi.org/10.1021/acsomega.4c00339

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