Sampling Free Energy Landscapes of Ionic Colloidal Crystal Systems using Machine-Learned Proxy Collective Variables

Abstract

Charged colloids coated with a polymer brush can be designed to preferentially self-assemble into different crystal structures by varying easy-to-tune experimental conditions. For a given set of conditions, we have observed in experiments and simulations a distribution of thermodynamically (meta)stable self-assembled crystal structures. Properly quantifying the free energy landscape of these colloidal systems is essential for rationally choosing conditions to preferentially target particular crystal structures. For some of the structures we have formed, standard crystalline order parameters are not able to differentiate between crystals or between crystals and amorphous aggregates. We show that local environment similarity descriptors are able to distinguish the relevant metastable states, but are too expensive for use in biased MD simulations. Here, we adopt an approach from machine-learned interaction potentials showing that SE(3)-equivariant transformer networks can serve as an efficient-to-evaluate machine-learned proxy. As a result, we can compute the relative free energies of accessible colloidal structures as a function of different experimentally-relevant physical knobs that can steer our system between two observed crystal types. As an example application, we then show how changing surface potentials of positive and negative colloids while maintaining the same attractive energy can shift which crystal structure is favored.