Phase Behavior of Heterogeneous Patchy Particles

Patchy particles, characterized by limited valence and directional bonding, serve as versatile model systems for understanding the self-assembly of complex natural materials such as proteins, heteropolymers, and surfactants. Real-world systems, however, often exhibit heterogeneity in size, composition, sequence, or interaction motifs, that can strongly influence phase behavior but has been largely overlooked in prior studies. Here, we explore through molecular dynamics simulations the phase behavior of heterogeneous patchy particles by introducing variability in patch number and spatial arrangement. Directionality is quantified through a polarity metric that measures the asymmetry of patch distributions, while clustering analysis is used to evaluate the effective valence of each particle. Low polarity corresponds to nearly isotropic particles with symmetric patch distributions, while high polarity reflects strong directional asymmetry analogous to amphiphilic molecules or surfactants. Phase diagrams, mapped against mean polarity and volume fraction, reveal gas–liquid coexistence at low polarity and density, cluster fluids at high polarity, and percolating networks at elevated densities. Polarity acts as a key driver of the transition from gas–liquid separation to self-limiting cluster fluids: increasing polarity transforms isotropic spherical liquids into anisotropic structures that first fragment into irregular clusters, then evolve into rod-like aggregates (reminiscent of cylindrical micelles), and finally form tetrahedral clusters (analogous to spherical micelles). We further demonstrate that the mean patch number governs the progression from dispersed to clustered to fully aggregated phases, while broadening the distribution of patch numbers promotes gas–liquid separation, with high-patch particles preferentially condensing into liquid-like domains and low-patch particles remaining dispersed. Altogether, this study illuminates the pivotal role of heterogeneity in dictating phase behavior in systems with directional interactions and constrained valence, offering broader insights into diverse natural assemblies.