Boundary Mismatch Free Energy Links Activity Coefficients and Cooperativity in Molecular Solids

Predicting cooperative behavior and thermodynamic nonideality in heterogeneous molecular solids remains challenging because activity coefficients and collective phase behavior are typically treated within separate theoretical frameworks. Here, we show that both quantities can be interpreted as manifestations of a common boundary mismatch free energy associated with local structural incompatibility within the correlated crystalline environments. Using a minimal coarse-grained statistical-mechanical framework, the energetic penalty associated with boundary formation is shown to govern both excess chemical potential and correlation length, thereby linking activity coefficients to the cooperative domain size. Triacylglycerol (TAG) molecular solids are used as an experimentally accessible model system, because solid-state activity coefficients and cooperative melting behavior can be independently extracted from equilibrium melting transitions. Reanalysis of previously reported thermodynamic data reveals a crossover from entropy-dominated to mismatch-controlled behavior together with scaling consistent with an exponential dependence of cooperativity on the boundary mismatch free energy. The results suggest that activity coefficients in heterogeneous molecular solids encode information not only about thermodynamic nonideality but also about correlated structural organization, domain connectivity, and structural accommodation. More broadly, the framework provides a physical interpretation of cooperative behavior in terms of interfacial mismatch energetics and suggests that activity coefficients may serve as experimentally accessible probes of correlations and collective organization in hierarchical matter.