Pressure and temperature dependence of self-diffusion in water
The self-diffusion coefficient, D, for pure liquid water has been measured at temperatures between 275.2 and 498.2 K and at pressures up to 1.75 kbar by the proton spin echo method. Our values of D agree, where they overlap, with recently published data which, however, were measured mostly at low temperature and over rather narrow ranges of temperature.
The results are discussed in several ways. The Stokes–Einstein relation is found to be obeyed in the slipping boundary limit. The cubic cell model of Houghton accounts satisfactorily for the measured D values, particularly at higher temperatures. A simple test of a hard-sphere model is found to give poor agreement at lower temperatures but a modified hard-sphere theory seems to be more satisfactory. The activation analysis at constant density shows that water behaves very differently from non-associated liquids. It also suggests that an increase in both temperature and pressure leads to an increase in the fraction of free unbonded water molecules.
A free-volume analysis has led to a modified Arrhenius equation which involves pressure-dependent terms. This semi-empirical equation describes the results within experimental error and predicts a glass temperature at 115 K which is in reasonable agreement with the values obtained by other methods.