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Statistical Mechanics and Dynamics of Liquids in and out of Equilibrium

  • Author(s): Hudson, Alexander;
  • Advisor(s): Chandler, David;
  • et al.

Liquids display an astonishing array of phenomena that, at first glance, seem to have little in common. In this thesis, we study two of these phenomena. The first is the hydrophobic effect, the well-known tendency of oil and water to demix and the driving force for biological assembly. The second is the glass transition, the process by which liquids cooled to very low temperatures become increasingly viscous until succumbing to structural arrest and displaying the rigidity of a solid with none of its microscopic ordering.

In the first part of this thesis, we expand upon our prior understanding of the hydrophobic effect. We study the behavior of water in the confined volume created by a pair of RNA helices at the inter-subunit interface of the bacterial ribosome, which provides an opportunity to apply our contemporary understanding of the hydrophobic effect, first detailed by Lum, Chandler, and Weeks almost twenty years ago, to a context that is less idealized than previously studied. We also discuss and improve upon computational models of hydrophobic solvation, expanding their applicability to more complicated solute geometries.

In the second part of this thesis, we study the glass transition from the perspective of the East model, a kinetically constrained lattice model of glass formers. We review and derive a number of results for East model glasses that we expect to emerge in more realistic, atomistic models of glass formers. We choose one such model and drive it out of equilibrium by cooling, forming a glass. We then check whether our East model predictions are correct. Of particular interest to us is whether inter-excitation correlations emerge out of equilibrium, a key prediction of the East model. Our atomistic results suggest that they do not, forcing us to reconsider our conceptual mapping between the highly abstract East model and more realistic models of glass formers.

The common thread in these seemingly disparate parts of the thesis is the importance of collective fluctuations in liquid-state phenomena. The hydrophobic effect is a physical consequence of liquid-vapor interfacial fluctuations near extended hydrophobic surfaces, while dynamics in supercooled liquids, the precursors to glasses, are dominated by small, collective motions of particles in an otherwise jammed material. The importance of fluctuations in these and other liquid-state phenomena make the tools of statistical mechanics particularly suitable to their study. In this thesis, we employ these tools in the service of furthering our understanding of the liquid state.

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