Speaker: David Ford, Professor, Department Head and Ralph E. Martin Endowed Leadership Chair in Chemical Engineering, University of Arkansas
Date: Monday, September 10th, 2018, 5:00PM-6:00PM
Location: SCEN 322

Title: Thermodynamics, dynamics, and control in the directed assembly of small ensembles of colloidal particles 

Abstract: Systems with a number of particles far below the bulk thermodynamic limit are increasingly of scientific and technological interest. Clusters comprising 10-1000 particles are particularly interesting; they are too small to be described by classical thermodynamics but have enough degrees of freedom to present a challenge for statistical mechanics. Furthermore, in the case of colloidal particles, such clusters can be assembled into structured meta-material objects that manipulate light. We present a formalism to model the thermodynamics and dynamics of colloidal clusters under the influence of external fields, and ultimately to control meta-material assembly processes through the real-time actuation of those fields. The formalism comprises three parts. High-dimensional data comprising trajectories of the particles in real time and space are analyzed by a machine learning technique called Diffusion Mapping, to identify a small number of order parameters (OPs) that sufficiently describe the data. A low-dimensional representation of the cluster thermodynamics and dynamics, based on either a Fokker-Planck equation or Markov state model, is then constructed in this set of OPs using information from short dynamic trajectories at different locations in the OP space. Finally, the low-dimensional model is used to construct a process control policy that provides the optimal choice of external field value at any point in the assembly process. We demonstrate this approach on two systems: a cluster of 32 colloidal particles interacting via a temperature-tunable depletion-based attraction, and a two-dimensional cluster of 210 colloidal particles in the AC electric field generated by a quadrupole microelectrode device. The 32-particle system showed behavior indicative of fluid-solid phase equilibrium at certain values of the attraction strength, as well as unique defects associated with one or more particles separating from the main cluster. The 210-particle system formed two-dimensional crystalline structures with defects similar to grain boundaries seen in bulk systems.

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