The origin of viscosity as seen through atomic level stress correlation function

The atomic level origin of viscosity and of various relaxation times is of primary interest in the field of supercooled liquids and the glass transition. Previously, by starting from the Green-Kubo expression for viscosity and by decomposing it into correlation functions between local atomic level stresses, we showed that there is a connection between shear stress waves and viscosity, and that the range of propagation of shear waves is also the range that is relevant for viscosity. Here, the behavior of the atomic level stress correlation function at different temperatures is discussed in more detail. The comparison of different time scales of the system shows that the long time decay of the stress correlation function (τ(S)) is approximately three times shorter than the long time decay of the intermediate self-scattering function (τ(α)), while the the Maxwell relaxation time (τ(M)) is approximately five times shorter than τ(α). It is demonstrated how different timescales of the stress correlation function contribute to the Maxwell relaxation time. Finally, we discuss the non-trivial role of periodic boundary conditions.