Inverse design methods for targeted self-assembly

In this thesis, we study the problem of what microscopic thermodynamic driving forces can stabilize target macroscopic structures. First, we demonstrate that inverse statistical mechanical optimization can be used to rationally design inter-particle interactions that display target open structures as ground states over a wide range of thermodynamic conditions. We focus on designing simple interactions (e.g., isotropic, convex-repulsive) that drive the spontaneous assembly of material constituents to low-coordinated ground states of diamond and simple cubic lattices. This is significant because these types of phases are typically accessible given more complex systems (e.g., particles with orientation-dependent attractive interactions) and for a narrow range of conditions. We subject the optimal interactions to stringent stability tests and also observe assembly of the target structures from disordered fluid states. We then use extensive free energy based Monte Carlo simulation techniques to construct the equilibrium phase diagrams for the model materials with interactions designed to feature diamond and simple cubic ground states, i.e., at zero temperatures. We find that both model materials, despite the largely featureless interaction form, display rich polymorphic phase behavior featuring not only thermally stable target ground state structures, but also a variety of other crystalline (e.g., hexagonal and body-centered cubic) phases. Next, we investigate whether isotropic interactions designed to stabilize given two-dimensional (2D) lattices (e.g., honeycomb or square) will favor their analogous three-dimensional (3D) structures (e.g., diamond or simple cubic), and vice versa. We find a remarkable transferability of isotropic potentials designed to stabilize analogous morphologies in 2D and 3D, irrespective of the exact interaction form, and we discuss the basis of this cross-dimensional behavior. Our results suggest that computationally inexpensive 2D material optimizations can assist in isolating rare isotropic interactions that drive the assembly of materials into 3D open lattice structures.