Disentangling the impact of packing in colloidal and molecular self-assembly

Geometric packing is an oft-used causal mechanism for structure formation across many length scales – from the entropic ordering of colloidal nanoparticles to molecular co-crystallization of drug-like molecules. However, its exact role is hard-to-quantify, particularly in regimes where many competing forces can motivate nucleation, and evidently, crystallization. In this talk, I will first discuss the impact of geometric packing in systems where its effect should be most pronounced – hard, faceted nanoparticles that self-assemble based on volume exclusion alone. Using Maxwell relations, I will show that markers for "packing" behavior are absent in the regimes where self assembly occurs, pointing to packing as a correlative, rather than causal, force in the emergence of spontaneous order. I will then shift focus to crystallization in small-molecule systems, where the role of packing is still an open question and hard to pinpoint in analyses. Using physics-based machine learning representations and hybrid supervised-unsupervised models, I show how we can identify the role of enthalpic and geometric components in stabilizing (or destabilizing) these systems. I will end with an outlook on the future of physics-informed machine learning for understanding molecular packing, including future work directions.