Inverse Design and Analysis of Crystallization Pathways of Colloidal Systems

Abstract

The ability to produce particles on the nano-scale that self-assemble into soft materials with specifically targeted properties is a promising avenue for a completely new class of materials with novel applications. New synthesis routes and increased computational resources have led to the proposition, modeling, simulation, and experimental realization of a whole plethora of new particle types, including but not limited to faceted polyhedra, Janus particles, lock-and- key particles, and self-propelled particles. The inverse design problem of engineering particles for targeted self-assembly is challenging because of the large available design space. Unlike atoms which are more easily classified by their composition and energy state, nanoparticles can be almost arbitrarily shaped and interactions between particles can be further modulated to various degrees, for example with complete or partial surface coatings.

One of the main determinants of material properties is the breaking of symmetries manifested in the formation of crystal structures. In Chapter II of this dissertation, I present a computational method for the optimization of isotropic pair potentials (IPPs) as a general model for the effective interaction between colloidal particles. Using this method, which is based on the minimization of the relative entropy, I optimize IPPs for various simple and complex crystal structures, including simple cubic (cP1), body-centered cubic (cI2), face-centered cubic (cF4), β-tin tI4-Sn (tI4), diamond (cF8), A15-type cP8-Cr3Si (cP8), σ-phase tP30-CrFe (tP30), and clathrate-I cP54-K4Si23 (cP54). Reducing the design space to IPPs allows us to explore it more effectively, however solutions found in this way still need to be mapped to a physical model for experimental synthesis.

Chapter III is a study of crystallization pathways, including pathways of some of the models presented in Chapter II. I developed and applied an unsupervised machine learning (ML) workflow for the analysis of self-assembly pathways, which allows us to make observations about the general mechanism of, as well as identify local particle environments that play a role in, the nucleation and growth of the crystal structure. I observe two-step nucleation for all tested crystal structures at moderate supercooling and can demonstrate that random fluctuations of local order play a crucial role in mediating nucleation and growth.

In Chapter IV, I present signac, a software framework that assists researchers in managing their computational data and implementing workflows that operate on that data. The signac framework was originally designed and implemented by me and has since its early inception matured into an open-source project with a team of core maintainers and many internal and external contributors and users. Recent work has been focused on enabling the implementation of more complex workflows and increasing the user base, which is facilitated by an affiliation of the project with the NumFOCUS organization.

Chapter V provides guidelines on how to efficiently develop robust and reusable software within an academic research environment. These guidelines are presented in the form of a heuristic named lazy refactoring, which in essence priorities the incremental development of working solutions over general complete solutions. Determining the correct scope and Application Program Interface (API) for general solutions from scratch is typically much more difficult compared to refactoring existing partial solutions.

I conclude this dissertation with a general summary of the presented work and provide a brief outlook on potential future research directions.