On the response of an ionic liquid to external perturbations and the calculation of shear viscosity

In this article, attention is directed to three related problems: (1) the response of the ionic liquid (IL) 1-hexyl-3-methylimidazolium chloride ([HMIM+][Cl-]) to different external perturbations, (2) the calculation of its shear viscosity, and (3) the investigation of the range of validity of linear response theory for these types of systems. For this purpose, we derive a set of equations linking bulk hydrodynamic predictions with microscopic simulations which are valid when linear response theory is applicable. As far as we are aware, this article reports results from the largest atomistic simulations ever performed on this liquid. Our study shows that even for systems with a box length as large as 0.03 mu the viscosities computed from perturbation frequencies compatible with this box size have not yet reached the bulk hydrodynamic limit. This is in sharp contrast with the case of other solvents such as water in which the hydrodynamic limit can be achieved by using perturbations on a length scale of typical molecular dynamics simulation box sizes. In order to achieve our goals, we comprehensively investigated how the IL relaxed upon weak external perturbations at different wavenumbers. We also studied the steady-state flow created by external shear acceleration fields. The short time behavior of instantaneous velocity profiles was compared with the results of linear response theory. The short time response appears to match the prediction from linear response theory, while the long time response deviates as the external field becomes stronger. From this study, the range on which a perturbation can be considered "weak" in the linear response sense can be established. The relaxation of initial velocity profiles was also examined and correlated to the decay of the transverse-current autocorrelation function. Even though none of our calculations reached the bulk hydrodynamic limit, we are able to make predictions for the shear viscosity of the bulk system at different temperatures which qualitatively agree with experimental data.