Association and phase transitions in simple models for biological and soft matter condensates

We investigate a set of design principles that link specific features ofinterparticle interactions to predictable structural and dynamicoutcomes in two-dimensional self-assembly, a framework relevant tosoft matter and biological condensates. Using extensive MolecularDynamics simulations of single- and two-component systems, wesystematically dissect how modifications to competing short-rangeattraction and long-range repulsion (SALR) potentials (both isotropicand anisotropic) serve as independent control parameters. Inparticular, we have focused on tuning the repulsive barrier height,decorating the attractive well with oscillatory components, and changing particle geometry. We demonstrate that these modifications dictate cluster sizedistributions, the degree of intra-cluster ordering, the geometry ofthe clusters, and thepropensity for inter-cluster crystallization. A key finding is thedecoupling of internal and global dynamics: oscillatory wells promotesolid-like order within clusters while maintaining liquid-like clustermobility. Furthermore, we show how asymmetric interactions in a binarySALR mixture can be designed to induce internal phase segregationwithin condensates. Complementing this, we observe that in anisotropicmodels in which the short rage component of the interaction stems fromthe presence of attractive patchy sites, stoichiometry and thegeometric distribution of the patches are essential to control self-assembly and cluster morphology, whereas long-range repulsion can beused to tune cluster size and polydispersity. The extractedprinciples provide a causal road-map for engineering self-assembledmaterials and a set of basic physical concepts for interpreting the complex phasebehavior of biomolecular condensates.