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

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.

Directional locking in deterministic lateral-displacement microfluidic separation systems.

We analyze the trajectory of suspended spherical particles moving through a square array of obstacles, in the deterministic limit and at zero Reynolds number. We show that in the dilute approximation of widely separated obstacles, the average motion of the particles is equivalent to the trajectory followed by a point particle moving through an array of obstacles with an effective radius. The effective radius accounts for the hydrodynamic as well as short-range repulsive nonhydrodynamic interactions between the suspended particles and the obstacles, and is equal to the critical offset at which particle trajectories become irreversible. Using this equivalent system we demonstrate the presence of directional locking in the trajectory of the particles and derive an inequality that accurately describes the "devil's staircase" type of structure observed in the migration angle as a function of the forcing direction. We use these results to determine the optimum resolution in the fractionation of binary mixtures using deterministic lateral-displacement microfluidic separation systems as well as to comment on the collision frequencies when the arrays of posts are utilized as immunocapture devices.