Stress tensor and viscosity of water: Molecular dynamics and generalized hydrodynamics results

The time correlation functions (CF’s) of diagonal and off-diagonal components of the stress tensor of water have been calculated at 245 and 298 K in a molecular dynamics (MD) study on 343 molecules in the microcanonical ensemble. We present results obtained at wave number k=0 and at a few finite values of k, in the atomic and molecular formalism. In all cases, more than 98% of these functions are due to the potential term of the stress tensor. At k=0, their main features are a fast oscillatory initial decay, followed by a long-time tail more apparent in the supercooled region. Bulk and shear viscosities, calculated via Green-Kubo integration of the relevant CF at k=0, are underestimated with respect to experimental data, mainly at low temperature, but their ratio (≊2) is correctly reproduced.

Both shear and bulk viscosity decrease as a function of k, the latter more rapidly, so that they become almost equal at ≊1 A${\mathrm{̊}}^{\mathrm{-}1}$. Also, both viscosities drop rapidly from their maximum at ω=0. This behavior has been related to the large narrowing observed in the acoustic band, mainly in the supercooled region. The infinite frequency bulk and shear rigidity moduli have been shown to be in fair agreement with the experimental data, provided the MD value used for comparison is that corresponding to the frequency range relevant to ultrasonic measurements. The MD results of stress-stress CF’s compare well with those predicted by Bertolini and Tani [Phys. Rev. E 51, 1091 (1995)] at k=0, by an application of generalized hydrodynamics [de Schepper et al., Phys. Rev. A 38, 271 (1988)] in the molecular formalism, to the same model of water (TIP4P) [Jorgensen et al., J. Chem. Phys. 79, 926 (1983)]. These CF’s are essentially equal in the atomic and molecular formalism, the only minor difference being restricted to the high frequency librational region of the shear function. By a comparison of atomic and molecular results, we show here that neglecting libration has no effect on the density-density and longitudinal current CF’s and very little effect on transverse properties. On the other hand, this study points out the importance of including the oscillation in the nearest-neighbor cage in the memory function of the longitudinal and transverse current CF. The oscillatory local motion turns out to play an important role in all CF’s and hence contributes significantly to the value of viscosity and of rigidity moduli.