Chemical Transformations of Nanocrystals: Theory and Molecular Simulation

Many of the intriguing optical, electronic, and mechanical properties of nanoparticles and their assemblies are strongly influenced by their size, shape, and composition. The range of different nanoparticles accessible by direct synthesis, however, is currently limited. Post-synthetic modification is thus an important avenue for chemists to tailor the properties of nanocrystals and to guide their assembly into functional materials. Yet, tuning such properties as nanocrystal shape and composition is often difficult because procedures for doing so take place far from equilibrium. In this thesis, we will discuss the progress we have made in understanding two such processes using statistical mechanical theory and computer simulation: (i) chemical etching, which produces concentration-dependent transformations of nanocrystal shape, and (ii) cation exchange, in which spontaneous swapping of ions of different identities effects compositional change. For nanocrystal etching, we propose a simple kinetic model of etching which emphasizes the interplay between the concentration of etchant in the surrounding solution and the local energetics of the crystal surface. Monte Carlo simulations of this model reproduce experimentally observed etching trajectories over a broad range of parameters. We explain the observed transient nanocrystal shapes in terms of a balance between the external driving force for etching and the coordination number of nanocrystal surface atoms. Anisotropic particles such as nanorods present shape transformations which this kinetic model is unable to capture on its own. When we introduce additional kinetic moves which allow for mass transfer across the nanocrystal surface, we are able to capture nanorod shape transformations. Our microscopic explanation for this success invokes Ostwald ripening between distinct crystal facets on the nanoparticle surface. For cation exchange, we develop an elastic Ising model which highlights the role of elastic strain due to lattice mismatch between different cation species. In its bulk incarnation, Monte Carlo simulations of this model reveal rich phase behavior featuring modulated order and surprising coexistence scenarios. These result from the extensive cost for coexistence between elastic phases. Based on this observation, we combine mean field theory with a modified Maxwell construction to predict a phase diagram which captures key features of our simulations. If we switch to an ensemble where the net composition can fluctuate freely, the behavior of our model is vastly different. In lieu of modulated order, there is a single, mean-field critical point associated with spontaneous symmetry breaking of the net composition. We show that the long-ranged interactions responsible for this behavior arise naturally upon integrating out mechanical fluctuations. Mean field theory applied to the resulting effective Hamiltonian quantitatively captures both the thermodynamics and kinetics observed in Monte Carlo simulations. For nanocrystals, which break translational symmetry, a straightforward extension of mean field theory yields similarly accurate results. We further interrogate nanocrystal energetics by diagonalizing the nanocrystal effective Hamiltonian and its corresponding spin correlation function, revealing surface-localized soft modes. Detailed knowledge of nanocrystal energetics informs a nonequilibrium kinetic model for ion exchange focusing on surface exchange reactions and bulk diffusion of ions. Kinetic Monte Carlo simulations of this model for different choices of parameters reproduce a variety of nanocrystal morphologies seen in cation exchange experiments. Overall, our findings in this thesis demonstrate that the interplay between thermodynamics, kinetics, and geometry is key in determining the outcomes of nonequilibrium nanocrystal transformations