Beyond Arrhenius: Fluctuation Theory for Dynamics

Abstract

A long-standing challenge for simulation and experiment has been the accurate calculation ofactivation energies and activation volumes via Arrhenius analyses which typically require rate constants or dynamical timescales to be resolved over a wide-range of temperatures and pressures to high accuracy. Unfortunately, in some systems timescales can be non-Arrhenius; in others, the system can undergo fundamental changes with temperature (e.g. phase transitions, changing solubility). In this thesis, an extension of fluctuation theory from statistical mechanics is developed that allows for the direct calculation of derivatives of dynamical timescales with respect to temperature and pressure, from simulations at a single temperature and pressure. This allows for the direct calculation of activation energies and volumes without requiring the problematic temperature and pressure ranges involved in the traditional Arrhenius approach. Furthermore, these approaches allow for the decomposition of the activation energy into contributions from various molecular interactions to gain deeper mechanistic insight that is otherwise unavailable. Applications to a wide-range of dynamical timescales in liquid water (diffusion, reorientation, hydrogen bond exchanges, and spectral diffusion) are presented. We furthermore demonstrate the ability of these techniques to study water under supercooling and water under pressure, demonstrating that these derivatives can be used to predict the dependence of liquid structure and dynamical timescales with respect to pressure and temperature. We furthermore demonstrate that this method can be used to connect liquid structure and the observed dynamics in liquid water. Finally, we demonstrate that these approaches can be applied to other systems to glean useful, otherwise unobtainable information.