``Free Volume'' and the Viscosity of Liquid Water

Abstract

The viscosity of liquid water between −10° and +150°C (Psat=4.7 atm) is expressed by the equation: η=A exp[B/ (T−T0)], in which A = 290 μp, B = 510°, and T0 = 150°K. The true temperature-independent activation energy for viscous flow is E = RB = 1020 cal/mole. The ``free volume'' representation uses the equation η=A exp(1/f), in which the free-volume fraction, f=vf/vl, increases linearly with temperature above the theoretical zero point, T0. Thus, f=(T−T0)/B. It evolves that f coincides with the volume fraction of unbonded water molecules, as defined by a structural model reported recently by Némethy and Scheraga. This empirical correlation between the viscosity and the structure of liquid water demonstrates the effects of internal structural rearrangements, which are not directly reflected in changes in the total volume. The implications regarding the effects of temperature and pressure on viscosity and other relaxation processes, particularly in hydrogen-bonded, structured liquids, are discussed.