(678d) Non-Equilibrium Colloidal Interactions and Chain Folding Dynamics in Time-Dependent Magnetic Fields

The ability to engineer colloidal assembly processes is of interest to produce ordered structures for meta-materials with exotic properties. Based on this motivation, much research has been conducted on colloidal crystallization at near equilibrium conditions. However, such systems are prone to kinetic barriers and traps as they transition from high free energy to low free energy states. The use of rotating magnetic fields is one approach that has been shown to produce two-dimensional crystals via non-equilibrium processes. Recent results from our group have shown that time averaged hydrodynamic and dipolar interactions in rotating magnetic fields significantly affect particle pairs and multi-particle configurations during these non-equilibrium, steady-state assembly processes. To better understand and characterize these interactions, we conduct optical microscopy and simulated computer experiments of two-particles and multiple particles in a rotating magnetic field at several magnitudes and frequencies. By fitting two-particle trajectories to the Fokker-Planck (FP) equation, we can calculate the effective free energy between colloids as well as the relative diffusivity. This approach can then be applied to a multiple particle system by fitting the FP equation to order parameters that describe how a chain folds and the particles rearrange to form a perfect crystal. The use of order parameters quantifies both statistical mechanical (pseudo free energy) and fluid mechanical (hydrodynamic) contributions. With the ability to measure and tune kT-scale colloidal interactions and quantitatively model how such interactions are connected to dynamically changing microstructures, we demonstrate the potential for control of the assembly, disassembly, and repair of colloidal crystals under steady state, time-dependent fields.