Novel inverse methods for crystal self-assembly
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Inverse design methods are a promising new strategy to aid the discovery of materials with targeted properties. In this thesis, we employ two novel inverse design methods and apply it to the study of crystal self-assembly in two dimensions. In particular, we introduce a novel zero temperature (ground state -GS) analytical method and find effective interactions that stabilize targeted lattices by means of a constrained non-linear optimization. We demonstrate advantages of this new formulation by designing a square lattice to display increasing energetic differences over relevant lattice competitors and show that such constraints correlate with crystal thermal stability. However, these constraints also reduce density range representation of the target lattice in its phase diagram and suggests an inherent tradeoff in the constrained strategy. Having established a link between crystal property and constraint type, we design the snubsquare lattice by means of energetic constraints over close competitors and show this is in contrast to the design of the kagome lattice which required no such constraints. We then test the limits of the GS method and design the open and challenging truncated square (TS) and truncated hexagonal lattices (TH). Unlike the previous targets, these lattices require the inclusion of a large pool of competitor micro-phases that greatly complicate optimization. Nevertheless, we show the system is still solvable by judicious use of constraints and decision variables. Next, we use a novel relative entropy minimization approach (RE) and the GS method to explore the design space of particles interacting via a potential featuring a single attractive well. Specifically, we design a square, honeycomb and kagome lattice and show that we are able to infer a set of `design rules' from generalities of the resulting interactions in both methods. We validate these rules by designing the challenging TS and TH lattices and show that optimized interactions readily promote target assembly from the fluid state. Finally, we expand the RE method to accommodate multi-component systems and inverse design a variety of crystal binary mixtures featuring triangular, square as well as other intricate and open motifs. We demonstrate how binary systems can help achieve equivalent single component structures but with simpler underlying interactions. Further, we analyze the binary assembly process and find that self interactions act as a `primer' that place particles in the correct local positions while cross interactions, through system coupling, act as the `binder' that lock particles into the correct binary structure.