Nonequilibrium Variational Control Forces for Self-Limited Colloidal Assembly*

Materials with tunable functionalities can be synthesized bottom-up by controlled self-assembly of colloidal particles. Design principles that are rooted in thermodynamic principles and optimize specific interactions are often thwarted by kinetic limitations and confined to compact surface energy minimizing structures. We discuss a variational principle for the optimization of interparticle and nonequilibrium driving forces, which lead to robust assembly of self-limited clusters. Molecular dynamics simulations and a novel optimization strategy are used to solve for these optimal control forces. Our results expand the design space outside thermal equilibrium and provide new principles for tuning the dynamics of self-limited assembly in colloidal systems.