Date of Award

Fall 2022

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Chemical and Environmental Engineering (ENAS)

First Advisor

Haji-Akbari, Amir

Abstract

Crystal nucleation occurs during the initial stages of crystallization and constitutes the emergence of sufficiently large crystalline regions– known as critical nuclei– within the metastable liquid or the supersaturated solution. Nucleation plays an important role in a wide variety of areas such as cloud microphysics, semiconductor and solar cell manufacturing and the production of pharmaceuticals. In the absence of any external impurity, nucleation proceeds via homogeneous nucleation. Heterogeneous nucleation over an external surface, however, is the predominant mode of nucleation on the planet due to the abundance of a wide variety of impurities or crystal nucle- ation agents (CNA’s). Despite its omnipresence, the microscopic details of crystal nucleation are far from fully understood, mainly due to the difficulties in probing nucleation with current experimental techniques that lack the required spatiotempo- ral resolution. Molecular dynamics (MD) simulations provide an avenue for probing the small length and time scales associated with crystal nucleation. Conventional MD simulations are, however, inefficient for sampling the free-energy barrier associ- ated with nucleation. Specialized sampling techniques such as forward flux sampling (FFS) are, therefore, needed to efficiently probe the kinetics and mechanism of crystal nucleation. In this thesis, we extensively discuss the implementation details, variants and past applications of FFS, and utilize its recently developed variant, jumpy FFS (jFFS), to probe the kinetics and mechanism of crystal nucleation for an important mode of atmospheric ice nucleation, known as contact freezing. Moreover, we system- atically probe the effect of finite system size on the kinetics and mechanism obtainedfrom crystal nucleation simulations. One of the most consequential occurrence of crystal nucleation is the formation of ice in the atmosphere. Contact freezing is a mode of atmospheric ice nucleation in which a dry ice nucleating particle (INP) collides with a water droplet and results in considerably faster heterogeneous nucleation as compared to immersion freezing in which the INP is completely immersed within the droplet. The microscopic origin of such an enhancement is, however, still a mystery. While earlier studies had attributed it to collision-induced transient perturbations, recent experiments point to the pivotal role of nanoscale proximity of the INP and the free interface, suggesting that the origin of contact freezing might be linked with the tendency of the free-interface to enhance homogeneous nucleation. Water is suspected of possessing this latter property, known as surface freezing. We simulate heterogeneous nucleation of ice within INP-supported nanofilms of two model water-like tetrahedral liquids with different surface freezing propensities and show that the nanoscale proximity of the INP and the free interface is indeed sufficient for inducing rate increases commensurate with those observed in contact freezing experiments, but only if the free interface is conducive to surface freezing as well. We analyze the nucleation mechanism and find that faster nucleation in contact freezing proceeds through the formation of hourglass-shaped critical nuclei that conceive at either interface. By developing a theoretical model based on classical nucleation theory we show that hourglass-shaped nuclei have a lower free energy of formation due to the synergy of nanoscale interfacial proximity and the modulation of the free-interfacial structure, which we find through structural characterization of the free-interface. We, therefore, provide new insights into the physics of contact freezing and further the evidence in support of a relationship between contact and surface freezing. To ensure that our simulations of contact freezing are free from artifacts– known as finite size effects– arising due to the finite size of the simulation box, we develop,for the first time, a rigorous set of heuristics for quantifying and avoiding finite size effects in crystal nucleation simulations within periodic boxes. We achieve this by systematically probing the dependence of heterogeneous ice nucleation rate on the surface area of the underlying ice nucleating particle (INP). We show that nucleation rates can strongly depend on the size of the INP due to unphysical interactions be- tween crystalline nuclei and their periodic images. We identify three distinct regimes for the dependence of rate on the INP dimension, L. For small INPs, the rate is a strong function of L due to artificial spanning of critical nuclei across the periodic boundary. We call this the spanning regime. For intermediate-sized INPs, however, critical nuclei are non-spanning but ’proximal’, i.e., they are close enough to their periodic images to fully structure the intermediary liquid, which is the liquid region present between a critical nucleus and its closest periodic image. Although such prox- imity can facilitate nucleation, its effects are offset by an artificial increase in density, resulting in smaller nucleation rates overall. For larger INPs, the critical nuclei formed are neither spanning nor proximal. Yet, we find that the rate is a weak function of L, with its logarithm scaling linearly with 1/L. We believe this to be a manifesta- tion of the system size dependence of intrinsic thermodynamic quantities relevant to nucleation. We develop a key heuristic which stipulates that finite size effects will be minimal if critical nuclei are neither spanning nor proximal, and if the intermediary liquid has a region that is structurally indistinguishable from the supercooled liquid under the same conditions. We also test this heuristic for homogeneous nucleation in the Lennard-Jones (LJ) liquid and find that while the prevalence of spanning critical nuclei is the primary indicator of finite size artifacts and fully describes the system size dependence of rate in the spanning regime, the measure of proximity discussed above is less consequential. We show that the formation of fragmented critical nuclei in the LJ liquid suggests that any structuring observed in the intermediary liquid is an artifact and does not represent the true diffuse solid-liquid interface. The dependence of rate on system size is therefore subtle for systems with negligible spanning nuclei, even if they have significant fraction of proximal nuclei. We also find that nucleation rates do not show any noticeable dependence on system size for larger systems, suggesting that the previously observed weak scaling of rate is likely system and nucleation mode dependent. We, therefore, verify the universal applicability of our heuristics to different modes of nucleation (homogeneous and heterogeneous) in different systems.

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