(605e) Fundamental Thermodynamic and Kinetic Models for Self-Assembly of Small Clusters of Colloidal Particles
The self-assembly of finite clusters 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 a number of particles (10 to 1000) that is far below the bulk limit. One assembly method involves the use of thermodynamic variables (e.g. temperature, depletant concentration) or external fields as actuators, to modify the level of interparticle attraction. Robust methods for assembling defect-free target structures will ultimately require reduced-dimension process models that link the particle-level dynamics of the colloids to the actuator states. We have developed a three-part strategy for developing such process models. First, we employ diffusion maps (DMaps) on raw trajectory data to identify slow, low-dimensional manifolds in the system dynamics. Second, we identify convenient observables, or order parameters (OPs), that strongly correlate with the low-dimensional DMap coordinates; this step may involve a feedback loop with the DMap process itself. Third, we use a Fokker-Planck or Smoluchowski formalism to build free energy and diffusivity landscapes in the OPs, which serve as our reduced-dimension process models. We demonstrate our strategy on two colloidal systems that have been synthesized and studied experimentally.