Composition Dependent Instabilities in Mixtures with Many Components

Understanding the phase behavior of mixtures with many components is important in many contexts, including as a key step toward a physics-based description of intracellular compartmentalization. Here, we study phase ordering instabilities in a paradigmatic model that represents the complexity of-e.g., biological-mixtures via random second virial coefficients. Using tools from free probability theory we obtain the exact spinodal curve and the nature of instabilities for a mixture with an arbitrary composition, thus lifting an important restriction in previous work. We show that, by controlling the concentration of only a few components, one can systematically change the nature of the spinodal instability and achieve demixing for realistic scenarios by a strong composition imbalance amplification. This results from a nontrivial interplay of interaction complexity and entropic effects due to the nonuniform composition. Our approach can be extended to include additional systematic interactions, leading to a competition between different forms of demixing as density is varied.