(581e) Low-Dimensional Thermodynamic Models for Self and Directed Assembly of Small Ensembles of Colloidal Particles

Self and directed assembly of colloidal particles into crystalline objects is an emerging area of scientific interest that finds applications in manufacturing of photonic crystals and other meta-materials. Quantitatively accurate models of the thermodynamics and dynamics of these systems are essential to producing defect-free crystals. Robust methods for controlling the assembly of these crystals would require reduced dimension process-models that link the particle-level dynamics of the colloids to the actuator states. In this paper, we describe the building of such models for two systems comprising 10-100 micron sized silica particles in aqueous solution that employ either a temperature-tunable depletion interaction potential or externally applied electric field as a mechanism to promote the assembly process. We model the assembly process using coarse-grained representations, based on the Fokker-Planck equation, which can capture both the dynamics and the equilibrium properties of these small clusters. We use diffusion maps (DMaps), a machine learning technique to identify the slow, low-dimensional manifolds in these systems. The DMap coordinates are correlated against a set of candidate order parameters (OPs) to identify a suitable choice of observables. The DMap technique is sensitive to the nature of defects observed in these two systems and this is manifest in the correlations with OPs.  We construct free energy and diffusivity landscapes in the chosen OPs that serve as reduced order models for process control policy maps providing an optimal route to defect-free crystals.