Inverse Thermodynamics: Designing Interactions for Targeted Phase Behavior

The traditional goal of <i>inverse self-assembly</i> is to design interactions that drive particles toward a desired target structure. However, achieving successful self-assembly also requires tuning the thermodynamic conditions under which the structure is stable. In this work, we extend the inverse design paradigm to explicitly address this challenge by developing a framework for <i>inverse thermodynamics</i>, i.e., the design of interaction potentials that realize specific thermodynamic behavior. As a step in this direction, using patchy particle mixtures as a model system, we demonstrate how precise control over both bonding topology and bond energetics enables the programming of targeted phase behavior. In particular, we establish design principles for azeotropic demixing and show how to create mixtures that exhibit azeotropy at any prescribed composition. Our predictions are validated through Gibbs-ensemble simulations [Panagiotopoulos, <i>Mol. Phys.</i> 1987, 61, 813-826]. These results highlight the necessity of coupling structural design with thermodynamic engineering, and provide a blueprint for controlling complex phase behavior in multicomponent systems.