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.

Advisor: Geissler, Phillip L