Constructing Free Energy Landscapes in Interfacial Colloidal Systems Using a Fokker-Planck Formalism

The self- and directed- assembly of colloidal (nano- to micro- scale) particles into structures within materials and devices is an emerging paradigm with wide-ranging technological impact. However, the ability to create a target structure with an acceptably small level of defects is still lacking; systems too easily become dynamically arrested in undesired disordered, or defect-rich, states. We have been exploring a synergistic combination of recent advances in digital microscopic imaging techniques with free energy calculation methods to create free energy landscapes that could be used in monitoring and controlling self-assembly. Following recent computational work by Y.G. Kevrekidis and co-workers, we analyze short-time trajectories of an assembling colloidal system (as obtained by a microscopy experiment) and extract the coefficients of the Fokker-Planck equation that describes the underlying probability distribution function. We show examples for two types of problems. In the first, the stochastic variables are simply the real-space positions of a single colloidal particle associating with a structural surface feature. In the second, a small set of order parameters are used as the stochastic variables in a many-particle system undergoing directed assembly into a crystalline object.