Title: Quantitative Theories of Nanocrystal Growth Processes
Description: Nanocrystals are an important field of study in the 21st century. Crystallites that are nanometers in size have very different properties from their bulk analogs because quantum mechanical effects become dominant at such small length scales. When a crystallite becomes small enough, the quantum confinement of electrons in the material manifests as a size-dependence of the nanocrystal's properties. Electrical and optical properties such as absorbance, surface plasmon resonance, and photoluminescence are sensitive to the size of the nanocrystal and proffer an array of technological applications for nanocrystals in such fields as biological imaging, laser technology, solar power enhancement, LED modification, chemical sensors, and quantum computation.The synthesis of size-controlled nanocrystals is critical to using nanocrystal in applications for their size-dependent properties. The development of nanocrystal synthesis techniques has been its own entire field of study for two decades or more, and several successes have established novel, utilitarian protocols for the mass-production of nanocrystals with controlled size and very low polydispersity.

However, the experimental successes are generally poorly understood and no theoretical framework exists to explain the dynamics of these processes and how to better control or optimize them. It is the goal of this thesis to develop novel theories of nanocrystal synthesis processes to describe these phenomena in theoretical detail and extract meaningful correlations and driving forces that provide the necessary insight to improve the technology and enhance our understanding of nanocrystal growth. Chapter 4, 5 and 6 comprise all the novel research conducted for this thesis, with Chapters 1, 2 and 3 serving as necessary background to understanding the current state of the art. In Chapter 4, we develop a quantitative describe of the process of size focusing, in which a population of polydisperse nanocrystals, which are useless for applications, can be made more monodisperse by the injection of new crystallizable material. We derive mass balance equations that relate the rate of new-material generation to changes in the growth patterns of the nanocrystals.

Specifically, we determine that only when the rate of crystal-material production is sustained at a high level can size focusing occur and a monodisperse sample of nanocrystals be produced. Quantitative criteria are provided for how high the rate of production must be, and the quantitative effects on the nanocrystal size distribution function for various magnitudes of the production rate. The effect of the production rate on every facet of the size distribution function is evaluated analytically and confirmed numerically. Furthermore, through comparison of the theory to experimental data, it is determined that a typical nanocrystal synthesis accidentally correlates two variables that are critical to the phenomenon of size focusing. The unknowingly correlated variables have frustrated experimental investigations of the same insights we provided with theory. We recommend a new synthesis protocol that decouples the critical variables, and thus permit the quantitative control of nanocrystal size and polydispersity through theoretical relations, which can also be generalized for the a priori design and optimization of nanocrystal synthesis techniques.

In Chapter 5, a theoretical investigation of the growth of surfactant-coated nanocrystals is undertaken. The surfactants create a layer around the nanocrystal that has different transport properties than the bulk solution, and therefore has a strong effect on diffusion-limited growth of nanocrystals. This effect of a surfactant layer is investigated through the lens of the LSW theory of Ostwald ripening as well as through the lens of our own theory of size focusing from Chapter 4. The quantitative effect of a surfactant layer on the various growth processes of spherical nanocrystals is determined, with the result that size focusing can potentially be enhanced by the choice of an appropriate surfactant for a particular nanocrystal material. In addition to the kinetic studies of Chapter 4 and 5, a thermodynamic investigation of surfactant-coated nanocrystals is conducted in Chapter 6, with the goal of understanding the process known as "digestive ripening". In digestive ripening, a population of polydisperse gold nanocrystals is exposed to a strongly binding surfactant, at which point the nanocrystals spontaneously shrink and become highly monodisperse.

Different surfactants and different crystal materials can exhibit digestive ripening. Those same materials also have the capacity to be digested further from nanocrystals into molecular clusters that eliminate all crystalline material in favor of surfactant-crystal coordination. The outstanding question is, why does the spontaneous digestive ripening process appear to make large nanocrystals shrink to small nanocrystals, but it does not force small nanocrystals to shrink further to molecular clusters? We construct a full Gibbs free energy model, which we minimize under multiple constraints to obtain quantitative relations for what thermodynamic properties (such as the surfactant binding energy and the crystal-solvent surface energy) govern the existence and size-dependence of a thermodynamically stable nanocrystal. Through our model, we determine that a finite-size nanocrystal is only stable under two possible conditions: either the surfactant-crystal binding is stronger than the crystal-crystal binding and the system contains too few surfactants to form molecular clusters and thus "surfactant-lean" nanocrystals are created, or the surfactantsurfactant intermolecular interactions are sufficiently strong that the nanocrystal core is treated as a swollen micelle in a microemulsion and is stabilized by the surfactant tails' interactions.

Quantitative equations are provided that establish what trends and values are expected for experimental results. The results are inconclusive: there is no evidence supporting either conclusion because the available experimental data is insufficient. More accurately, many thermodynamically critical parameters (like the crystal surface energy) are unknown and are practically immeasurable in experimental systems. Speaking generally, the evidence for the surfactant-lean condition is moderately better than the evidence for the microemulsion condition, but in both cases the evidence is insufficient to make a solid conclusion. We therefore use our quantitative results of the thermodynamic investigation to make recommendations to experimentalists as to what trends and what nanocrystal growth processes we expect to observe in either thermodynamic case. While our results are inconclusive in and of themselves, they will be used to highlight the exact thermodynamic driving forces of the experimental systems.

We conclude by giving an overview of two new fields of study for theoretical descriptions of nanocrystal growth, specifically the growth of anisotropic nanocrystals and a practical theory for nanocrystal nucleation. Preliminary relations are constructed, with comments on what directions we expect the research to take and how the results would be useful in enhancing our understanding of nanocrystal growth behavior.