Model for dynamics in supercooled water

We propose a phenomenological model for the intermediate scattering functio n (ISF) associated with density fluctuation in low temperature water. The m otivation is twofold: to extract various physical parameters associated wit h the ISF computed from extended simple-point-charge model water at superco oled temperatures, and to apply this model to analyze high resolution inela stic 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-defin ed plateau in-between. We interpret this result as due to the formation of a stable hydrogen-bonded, tetrahedrally coordinated cage around a typical m olecule in low temperature water. We thus model the long-time cage relaxati on 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 cane. T he latter motions can be described by the generalized Enskog equation, taki ng into account the confinement effect of the cage. We shall show that the effect of the confinement changes the collisional dynamics by modifying cer tain input parameters in the kinetic theory by a factor [1-A(k)](1/2). We s olve the generalized Enskog equation approximately but analytically by a Q- dependent triple relaxation time kinetic model. This kinetic model was prev iously shown to account for the large k behavior of Rayleigh-Brillouin scat tering from moderately dense, simple fluids. We find that our model fits we ll with the MD generated collective as well as single-particle ISFs. For th e short-rime collisional dynamics, we fix values of the hard sphere diamete r sigma and pair correlation function at contact g(sigma), without introduc ting any adjustable parameters. The calculated ISFs reproduce the correct B rillouin 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). [S1063-651X(99)13412-3].