Theoretical and Computational Studies of Condensed-Phase Phenomena: The Origin of Biological Homochirality, and the Liquid-Liquid Phase Transition in Network-Forming Fluids

Abstract

This dissertation describes theoretical and computational studies of the origin of biological homochirality, and the existence of a liquid-liquid phase transition in pure-component network-forming fluids. A common theme throughout these studies is the use of sophisticated computer simulation and statistical mechanics techniques to study complex condensed-phase phenomena.

In the first part of this dissertation, we use an elementary lattice model with molecular degrees of freedom, and satisfying microscopic reversibility, to investigate the effect of reaction reversibility on the evolution of stochastic symmetry breaking via autocatalysis and mutual inhibition in a closed system. We identify conditions under which the system’s evolution towards racemic equilibrium becomes extremely slow, allowing for long-time persistence of a symmetry-broken state. We also identify a “monomer purification” mechanism, due to which a nearly homochiral state can persist for long times, even in the presence of significant reverse reaction rates. Order of magnitude estimates show that with reasonable physical parameters a symmetry broken state could persist over geologically-relevant time scales.

In the second part of this dissertation, we study a chiral-symmetry breaking mechanism known as Viedma ripening. We develop a Monte Carlo model to gain further insights into the mechanisms capable of reproducing key experimental signatures associated with this phenomenon. We also provide a comprehensive investigation of how the model parameters impact the system’s overall behavior. It is shown that size-dependent crystal solubility alone is insufficient to reproduce most experimental signatures, and that some form of a solid-phase chiral feedback mechanism (e.g., agglomeration) must be invoked in our model.

In the third part of this dissertation, we perform rigorous free energy calculations to investigate the possibility of a liquid-liquid phase transition (LLPT) in the Stillinger-Weber (SW) model of silicon. A similar analysis is also presented for the generalized SW family of models by varying the “tetrahedrality” of the potential. Contrary to previously published findings, we do not find any evidence of the existence of an LLPT for SW silicon, nor for the generalized family of SW models over the range of parameters studied. Our results for the original parameterization of SW silicon are in semi-quantitative agreement with previous free energy calculations for this model, which were only provided at three state points. Explanations for the discrepancies between previous independent studies are provided, along with explicit demonstrations of how these discrepancies may have occurred.

Finally, in the fourth part of this dissertation, we perform free energy calculations to demonstrate the existence of an LLPT in the Jagla potential. We also utilize finite-size scaling analysis to calculate the surface tension associated with the LLPT. In addition to the thermodynamics of the model, we investigate the relaxation times for density and bond-orientational order and show that, contrary to assertions in the literature, the characteristic relaxation time of bond-orientational order is not orders of magnitude slower than that of density. We compare our results for the Jagla model with those found in the literature for the ST2 model of water (which has also been rigorously shown to exhibit an LLPT) in order to emphasize key similarities and differences between two models that exhibit pure-component liquid-liquid phase separation.