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.

Automated summary

Understanding the phase behavior of mixtures with many components is crucial for various applications, such as describing intracellular compartmentalization. This study investigates the phase ordering instabilities in a complex model that represents biological mixtures using random second virial coefficients. By manipulating the concentration of a few components, it is possible to change the nature of the instability and achieve demixing, highlighting the interplay between interaction complexity and entropic effects.