Inverse design of self-assembling colloids via landscape engineering

This dissertation applies machine learning to the study of colloidal self-assembly to provide insights on the microscopic mechanisms driving assembly phenomena and drive towards a design framework capable of rationally manipulating the free energy landscape for self-assembly to derive building blocks that preferentially form into a target aggregate structure. The methodologies derived within are applicable to a wide class of self-assembly systems, both simulated and experimental, enabling a new frontier in the computer-aided design of self-assembling materials. The first portion of this dissertation focuses on the development of the many-body diffusion map and its application to the study of self-assembly. Diffusion map dimensionality reduction has shown great promise in the study of the low-dimensional folding landscapes inherent to protein folding. We extend this technique to handle multi-body systems via a graph-based distance measure that treats aggregate structure as a bonding network. In comparison to other techniques that utilize pathway engineering or heuristics, diffusion mapping of self-assembly systems is shown to systematically infer the low-dimensional manifold on which self-assembly occurs, detailing the structural pathway information and providing a framework for computation of both thermodynamic (what will form) and kinetic (how will it form) properties in a unified framework. We study this machine learning algorithm on the self-assembly and self-organization of three systems. In the first study we apply many-body diffusion maps to a double ring patchy colloid model shown to form discrete polyhedral aggregates by varying the angles of the different patchy rings. Our method is able to validate previous studies showing that self-assembly of icosahedral aggregates occurs along two competing assembly-pathways, and we use this self-assembly landscape to suggest patch-interaction design criteria for robust icosahedral assembly. In a second study, we apply our many-body diffusion map approach to particle-tracking experiments of Janus colloid self-assembly. This was to our knowledge the first attempt at machine learning collective order parameters and deriving assembly landscapes directly from experimental particle tracking data. Here we demonstrate the ability of our many-body diffusion map to provide insights on the affect experimental controls have on the self-assembly process, proving in line with our physical interpretation and extending to predict experimental systems to improve the yield or specificity of a targeted region of the self-assembly space. In our third study, we apply the diffusion map to the self-organization of a digital colloid, a discrete colloidal cluster capable of storing information by adopting certain configurations. Here we extract the important kinetic and thermodynamic information driving transitions between colloidal bit states, deriving the engineering design tradeoff between information stability and the energy required to write information. The second portion of this dissertation focuses on novel improvements to the sampling of diffusion map spaces to project free energy surfaces in the low-dimensional self-assembly landscape. The first part of this section proposes a novel extension of the diffusion map, so-called landmark diffusion maps, to enable the accurate and rapid embedding of out-of-sample points into a diffusion map landscape. Using this technique, we then propose a landscape engineering framework capable of manipulating the underlying free energy landscape for self-assembly to rationally design building blocks that aggregate into a desired structure. We use this design platform to study the self-assembly of the double ringed patchy colloid model, improving upon the expert-designed icosahedral building block's assembly rate by 76%, and then demonstrate that our technique can rapidly converge to new objective functions in the optimization of an octahedral forming patchy colloid