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Document Type

Open Access Dissertation

Degree Name

Doctor of Philosophy (PhD)

Degree Program

Chemical Engineering

Year Degree Awarded


Month Degree Awarded


First Advisor

David M. Ford

Second Advisor

Dimitrios Maroudas

Subject Categories

Chemical Engineering | Materials Science and Engineering | Thermodynamics


Self and directed assembly of finite clusters (10 to 1000) of colloidal particles into crystalline objects is an emerging area of scientific interest that finds applica- tions in manufacturing of 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 that is far below the bulk limit. 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 mapping (DMaps), a machine learning technique, on raw trajectory data to identify slow, low-dimensional manifolds in the system dy- namics. Second, we identify convenient observables, or order parameters (OPs), that strongly correlate with 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 have applied this technique to two model systems in this work. The first system comprises 32 silica particles, which interact via a temperature-tunable depletion interaction potential. This system shows transitions between an expanded and condensed phase when the pair interaction strength is changed by a few kBT . The second system comprises 210 quasi-2D silica particles confined within quadrupole electrodes and the interaction strength, which is of the order of few kBT , is tuned by an externally applied electric field. This system shows interesting features like the formation and annealing of polycrystalline microstructures as the magnitude of the applied field is changed. We systematically compare and contrast the DMap analysis on both these model systems. We construct an optimal control policy map in the low-dimensional DMap coordinates using dynamic programming. The free energy and diffusivity landscapes along with the control policy map is used to robustly assemble perfect colloidal crystals.

We have also examined the phase behavior of the depletion potential system via a histogram-based simulation approach. We conducted replica exchange Monte Carlo simulations of these small colloidal clusters and generated potential energy histograms for various levels of the osmotic pressure that controls the interaction strength. By carefully tuning the osmotic pressure, we observed bimodal distributions in the potential energy space, which is indicative of coexistence between fluid-like and solid-like configurations. Quantitative analysis of these histograms yield phase coexistence curves for these small clusters and we report comparisons with bulk colloidal phase diagrams.