Diffusion effects of hydrogen bond fluctuations. II. From the short to the long time regime in the translational dynamics of water

Abstract

To improve the quantitative agreement with the deviations from the predictions of Fick’s law, revealed by computer simulation, we develop a new theoretical model for translational diffusion of water. The time scale of hydrogen bond fluctuations can be comparable to that of the dynamics of translation velocity, and a tagged molecule of water might not have enough time to reach the diffusional regime before the establishment of new environmental conditions determined by hydrogen bond fluctuations. Thus we base our description on the modulation of the physical parameters determining the velocity time evolution rather than on the modulation of the diffusion coefficients. Computer simulation of water dynamics shows that the correlation function Fs(k,t)≡〈e−ik⋅r(0) eik⋅r(t)〉 is characterized by a fast decay at short times followed by a slower decay process. We show that this mainly depends on the velocity time evolution of molecules with two or three hydrogen bonds. We also show that the fitting parameters, within our theoretical modeling, lead to a satisfactory agreement with the time evolution of the velocity autocorrelation functions and their spectra, and also result in a remarkable quantitative agreement with the deviations from Fick’s law determined through computer simulation, except at high temperature.