Dynamic self-assembly of colloids through periodic variation of inter-particle potentials

Abstract

A short-ranged and time-varying attraction drives self-assembly of colloidal crystals from a suspension of colloidal spheres. Brownian dynamics simulations of this process demonstrate that the envelope for self-assembly of large, low defect crystals is broadened dramatically when this attractive interaction is switched on and off periodically in time. This process is termed dynamic self-assembly because temporal control of the inter-particle potential requires injection and extraction of energy from the self-assembling materials. We develop a theory using non-equilibrium statistical mechanics to determine the rate at which particles cross a similarly switched energy barrier, and show that there is a switching rate that maximizes barrier crossing. While barrier crossing towards thermodynamic equilibrium is limited by the Kramers hopping rate, the rate of out-of-equilibrium barrier crossing can exceed this limit. In the context of self-assembly, barrier crossing is the rate limiting step and responsible for both defect formation and slow nucleation. This simple theory is used to explain the optimal switching rate observed in our simulations of dynamic self-assembly. Dynamic self-assembly via switched potentials enables growth of ordered phases without thermodynamic constraints on the assembly kinetics.