(247ai) Coarse-Grained Thermodynamic Models for Self and Directed Assembly of Small Ensembles of Colloidal Particles

Self and directed assembly of colloidal particles into crystalline objects is a topic of technological interest, as a route to produce photonic crystals and other meta-materials. Such assembly problems are also of fundamental scientific interest because they involve thermodynamically small systems, with number of particles (10 – 1000) that is far below the bulk limit. 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 poster presentation, we describe the building of such models for two thermodynamically small systems comprising 10-100 micron sized silica particles in aqueous solution.

The first system comprises 32 particles, which interact via a temperature-tunable depletion interaction potential. This system shows interesting phase behavior when the pair interaction strength is changed by a few kT. The second system contains 210 particles and their assembly is controlled by an externally applied electric field. This system shows interesting features like the formation and annealing of grain boundaries during the assembly process as the magnitude of the applied voltage is changed.

 We model the assembly process for both these systems 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.