Viscosity Anomalies and Violations of the Stokes-Einstein Equation in Molecular Simulations of Water

Abstract

The behavior of water at supercooled temperatures, in particular the anomalous behavior of several of its properties, is a topic that is still not completely understood, and thus it is an active field of research. Specifically the shear viscosity anomaly, in which viscosity increases as density decreases, has not been fully explored. In this thesis, we ran molecular dynamics simulations to calculate viscosity using the Green-Kubo formalism, and delineated the region in water's phase diagram where viscosity behaves anomalously. Another focus of this thesis was to investigate the Stokes-Einstein relation, which relates the viscosity and the self-diffusion coefficient. This relation, although derived for the simple case of a supramolecular spherical particle in a fluid continuum, has been successfully applied to a large variety of systems. However, the Stokes-Einstein relation fails in the supercooled region, and the microscopic mechanisms behind this violation are not fully understood. Therefore, using molecular simulations, we also calculated the diffusivity of water in addition to the viscosity, in order to study further the region of temperatures and densities in which this relation breaks down. Moreover, it is common in the literature to calculate relaxation times as substitutes for the viscosity in simulations, since viscosity is computationally intensive. This thesis also analyses the validity of these substitutes or proxies for viscosity, and specifically we focus on the structural and stress relaxation times. Regarding the viscosity anomaly, we found that the region of anomalous behavior is located approximately between 0.9 and 1.15 g/cm3 and below around 290 K. We constructed a dome that delineates the anomaly, which can help comprehend the behavior of water's viscous properties. On the other hand, we effectively found that the Stokes-Einstein relation breaks down at supercooled temperatures, whereas at high temperatures the relation is obeyed. We constructed a graph that delimits the region in water's phase diagram where the relation is violated. We found that the relations between the structural and stress relaxation times with viscosity are non-trivial. The structural relaxation time was found to be a better substitute for viscosity at high temperatures and densities than the stress relaxation time. However, at low temperatures the latter seems to follow the violation of Stokes- Einstein qualitatively better than the structural relaxation time. The results suggest that it is important to be particularly careful when using any type of relaxation time as a substitute for viscosity. In summary, this thesis has studied two topics that are of current interest in the field of supercooled liquids, and both were applied to the specific case of water. Through molecular dynamics simulations, we have been able to calculate and analyze the viscosity anomaly and the Stokes-Einstein violation in water, in the hope that the results will shed light on these matters.