Pareto Fronts for Design: Optimizing Free Energy and Kinetic Accessibility for Self Assembling Colloids

Studies of short, self-assembling chains have uncovered many heuristic design principles for the formation of a target configuration. Among these principles is the fundamental trade-off between free energy and kinetic accessibility; high stability typically leads to low error correcting, and high error correcting typically leads to low stability. We quantitatively study this trade-off for the self-assembly of colloidal chains of 6 or 7 particles. We construct a model that allows for the efficient computation of ground state equilibrium probabilities and transition rates, for any set of design parameters. A genetic algorithm is then used to identify Pareto fronts for each ground state; parameter sets where neither equilibrium probability nor rate can be increased without decreasing the other. By examining the shape of the Pareto fronts, the minimal requirements for efficient self-assembly of a target state can be determined. We also discuss a sampling approach to extend these results to larger systems.