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Modeling the free energy functional at the fluid-solid transition in classical many-particle systems
The problem of phase equilibrium in colloidal and classical atomistic systems is of great interest in modern micro/nano fabrication and self-assembly processes. Systems with specific potential interactions are increasingly being developed and knowledge of their phase diagrams would aid in their use in materials applications. The conventional methods of using simulations and experiments to evaluate phase equilibrium are costly, especially for fluid-solid equilibrium. One way to address this problem is to improve the accuracy of theories, such as classical density functional theory (cDFT), that predict thermodynamic properties at the fluid-solid transition with modest computational cost. In such a program the challenges are of two kinds, viz. (1) the development of a new cDFT formulation to treat fluid-solid equilibrium, especially with regard to the higher order multi-body interaction terms in the free energy expression and (2) finding a more accurate numerical method to solve the cDFT equations. In our work we develop several numerical and inversion methodologies to meet these challenges, including closure relations that capture the higher order terms in the free energy expansion. We find that these closures are qualitatively and quantitatively very different from their liquid state analogs found in the Ornstein-Zernike integral equation theory. Specifically, we discover new closure relations applicable to the fluid-solid transition in hard-sphere, soft-repulsive and Lennard-Jones potentials. We further discuss the universal nature of these closures for different interaction potentials and explore the breadth of their applicability and future prospects.
Verma, Anurag, "Modeling the free energy functional at the fluid-solid transition in classical many-particle systems" (2012). Doctoral Dissertations Available from Proquest. AAI3498373.