Model for dynamics in supercooled water
Abstract
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 simplepointcharge model water at supercooled temperatures, and to apply this model to analyze high resolution inelastic xray scattering data of water in the future. The ISF of the center of mass of low temperature water computed from 10 Mstep molecular dynamics (MD) data shows clearly timeseparated twostep relaxation with a welldefined plateau inbetween. We interpret this result as due to the formation of a stable hydrogenbonded, tetrahedrally coordinated cage around a typical molecule in low temperature water. We thus model the longtime cage relaxation by the wellknown Kohlrausch form exp[(t/τ)^{β}] with an amplitude factor which is a kdependent DebyeWaller factor A(k), and treat the shorttime 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 [1A(k)]^{1/2}. We solve the generalized Enskog equation approximately but analytically by a Qdependent triple relaxation time kinetic model. This kinetic model was previously shown to account for the large k behavior of RayleighBrillouin scattering from moderately dense, simple fluids. We find that our model fits well with the MD generated collective as well as singleparticle ISFs. For the shorttime collisional dynamics, we fix values of the hard sphere diameter σ and pair correlation function at contact g(σ), without introducting any adjustable parameters. The calculated ISFs reproduce the correct Brillouin peak frequencies at low k values. From the longtime dynamics, we deduce values of the DebyeWaller factor A(k), the Kohlrausch exponent β(k), and the cage relaxation time τ(k).
 Publication:

Physical Review E
 Pub Date:
 December 1999
 DOI:
 10.1103/PhysRevE.60.6776
 Bibcode:
 1999PhRvE..60.6776L
 Keywords:

 61.20.Ja;
 64.70.Pf;
 Computer simulation of liquid structure;
 Glass transitions