Investigation of rheology and computation of viscosity of liquids at low temperatures

Abstract

In this thesis we explore different methods of calculating the viscosity using molecular dynamics simulations. We initially investigated three methods, namely Green Kubo relation, Helfand moment method and the shear simulations using the SLLOD equations of motion. These simulations are performed in the canonical ensemble. Green Kubo and Helfand moment are equilibrium and strain rate independent methods while the SLLOD is the nonequilibrium method based on application of a shear flow and measuring the corresponding response in the form of steady state stress. The viscosity can then be estimated in the Newtonian regime as the ratio of the steady state stress to the applied strain rate. The standard Green Kubo formalism involves calculation of an autocorrelation function which is not very efficient. Green Kubo and Helfand moment methods are dependent on the stress relaxation time scales, which corresponds to the molecular relaxation time scales in dense gases and high temperature liquids. We then consider a new method for the computation of viscosity, namely through the use of differentiable simulations. We use the differential definition of the viscosity and differentiate the stress with respect to the strain rate to obtain the viscosity.