Bimodality of the viscoelastic response of a dense liquid and comparison with the frictional responses at short times

Abstract

While the time dependence of the friction on a tagged particle in a dense liquid has been investigated in great detail, a similar analysis for the viscosity of the medium and the interrelationship between the two has not been carried out. This is despite the close relation always assumed, both in theoretical and experimental studies, between friction and viscosity. In this article a detailed study of the time and frequency dependencies of the viscosity has been carried out and compared with those of the friction. The analysis is fully microscopic and is based on the mode coupling theory (MCT). It is found that for an argon like liquid near its triple point, the initial decay of the viscosity occurs with a time constant of the order of 100 fs, which is close to that of the friction. The frequency dependent viscosity shows a pronounced bimodality with a sharp peak at the low frequency and a broad peak at the high frequency; the usually employed Maxwell's relation fails to describe the peak at the high frequency. A surprising result of the present study is that both the bare and the MCT values of viscosity and friction individually sustain a ratio which is close to the value predicted by the Stokes relation, even when Navier-Stokes hydrodynamics itself seems to have little validity.