Inverse Design of Isotropic Pair Potentials for Colloidal Self-assembly

Abstract

The development and use of new materials have significantly shaped the development of society since ancient times. With the advances in the ability to make and modify nanoparticles and the improved understanding of material structure at different length scales through new characterization methods, we see a shift in materials development approaches from the traditional way of discovery and refinement towards the rational materials design of individual building blocks that can directly form a targeted material with specific properties. Among the different types of individual building blocks studied for self-assembly, isotropically interacting particles represent one conceptually simple case with vast possibilities. There has been much research in rational design with the hope to find the best pairwise particle interactions that can self-assemble different materials.

A key challenge in rational materials design is understanding the mechanisms that drive complex self-assembly. In colloidal systems, self-assembly behavior is determined by a delicate balance of energy and entropy. In the first part of this dissertation, I quantify the energy and entropy contributions in stabilizing self-assembled structures found in two families of isotropic pair interaction potentials and show that whereas most simple self-assembled structures we observe are determined energetically, complex self-assembled structures are largely entropy-stabilized. This work provides a definitive case where vibrational entropy alone can stabilize complex structures, without rotational entropy that is associated with complex shape, or configurational entropy that requires a multi-component system.

Many methods have been proposed to achieve rational materials design by searching for the optimum building block. In the rest of this dissertation, I will use the `digital alchemy' optimization method, a statistical optimization process that treats each design attribute as a fluctuating thermodynamic variable in an extended thermodynamic ensemble, to probe the inverse design problem and find different pair potentials for different target self-assembly behavior. In particular, I apply digital alchemy to the Oscillating Pair Potential (OPP) and the Fourier Potential (FP) to explore different design spaces in isotropic pair interaction systems to find optimal potentials that form different crystal structures. I show that the digital alchemy method can also be used to inversely design pair potentials to achieve target materials properties (here, bulk modulus) directly, without explicit knowledge of the structure--property relationship. The digital alchemy method used in this work can be generalized and applied to other target crystal structures or materials properties and used with any differentiable interaction potentials. It is my intent that these designed isotropic pair potentials motivate and guide future synthesis of new materials.