Model for dynamics in supercooled water

We propose a phenomenological model for the intermediate scattering function (ISF) associated with density fluctuation in low temperature water. The motivation is twofold: to extract various physical parameters associated with the ISF computed from extended simple-point-charge model water at supercooled temperatures, and to apply this model to analyze high resolution inelastic x-ray scattering data of water in the future. The ISF of the center of mass of low temperature water computed from 10 M-step molecular dynamics (MD) data shows clearly time-separated two-step relaxation with a well-defined plateau in-between. We interpret this result as due to the formation of a stable hydrogen-bonded, tetrahedrally coordinated cage around a typical molecule in low temperature water. We thus model the long-time cage relaxation by the well-known Kohlrausch form exp[-(t/tau)(beta)] with an amplitude factor which is a k-dependent Debye-Waller factor A(k), and treat the short-time relaxation as due to molecular collisional motions within the cage. The latter motions can be described by the generalized Enskog equation, taking into account the confinement effect of the cage. We shall show that the effect of the confinement changes the collisional dynamics by modifying certain input parameters in the kinetic theory by a factor [1-A(k)](1/2). We solve the generalized Enskog equation approximately but analytically by a Q-dependent triple relaxation time kinetic model. This kinetic model was previously shown to account for the large k behavior of Rayleigh-Brillouin scattering from moderately dense, simple fluids. We find that our model fits well with the MD generated collective as well as single-particle ISFs. For the short-time collisional dynamics, we fix values of the hard sphere diameter sigma and pair correlation function at contact g(sigma), without introducing any adjustable parameters. The calculated ISFs reproduce the correct Brillouin peak frequencies at low k values. From the long-time dynamics, we deduce values of the Debye-Waller factor A(k), the Kohlrausch exponent beta(k), and the cage relaxation time tau(k).