Mechanism of Viscous Flow in Water

Abstract

BY treating viscous flow, self-diffusion and dielectric relaxation as rate processes, it has been shown that in water the energies of activation associated with the foregoing processes not only exhibit the same temperature dependence but have identical values^1,2. The dielectric relaxation time τ of a polar liquid has been expressed in terms of the viscosity η by the Debye equation: where a is the molecular radius. Equation (1) does not hold for hydrogen-bond-associated liquids (such as 2-methyl heptan-3-ol and octan-1-ol)³, yet it holds for water, and the value of a = 1.4 Å obtained from a plot of τ⁻¹ against η/T agrees well with recently published data⁴. The foregoing findings can be explained with the aid of the ‘flickering cluster’ model for water, described by Frank and Wen⁵, on the basis that the time taken for a translational jump or a molecular re-orientation is less than the mean life-time of the clusters, which may be of the order of 10⁻¹¹ sec. Thus, in a discussion of viscous flow, the nature and concentration of non-hydrogen-bonded water must be considered a major factor. This is made possible by using the cluster model of Nemethy and Scheraga⁶. For ease in computation the clusters are taken to be spherical and, from a consideration of their total area and volume, the x_i parameters (mole fractions of i-bonded water) are calculated as functions of temperature. The molar volume of water, $V_{{\text{H}}_{\text{2}}\text{O}}$, is the sum of the volume of clusters, V_b, and the volume of dipolar water, V_u and it is given by: (In this representation of the molar volume of water lies one of the main differences between this model and that proposed by Frank and Quist, in whose gas hydrate type structures unbonded water molecules can only fill vacant sites in the clusters and therefore cannot contribute to $V_{{\text{H}}_{\text{2}}\text{O}}$ (ref. 10).) where V_b can be taken to be the extrapolated molar volume of ice, and V_u can be calculated at each temperature from a knowledge of x_i, $V_{{\text{H}}_{\text{2}}\text{O}}$ and V_b