Density Fluctuations in Water and in Simple Fluids

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Abstract
The method of Fisher and Adamovich for obtaining the second order fluctuation of the particle number in a microscopic volume, and the correlation between such fluctuations in adjacent regions, has been modified to permit integration directly over x-ray scattering intensities instead of over the derived radial distribution function. With the new method and the more extensive x-ray data which are now available computations have been carried out for water at room temperature and at 200°C. In the former case the correlations are found to be essentially zero at all distances greater than two molecular diameters, in contrast to the results of Fisher and Adamovich, in which sizeable positive correlations appeared at distances up to and exceeding 30 Å. On comparing the density fluctuations in cold water with those calculated for Percus-Yevick liquids of appropriate hard-sphere diameters it is found that the two curves can be made to fit well except in the range 2.5 Å<D<8 Å, where no fit is possible (D = diameter of volume element). It is also found that for the Percus-Yevick liquid for which σ3ρ = 0.633 the fluctuations exceed the thermo-dynamic-limit value (〈 δ NG2/ N̄G 〉 = ρ k T κT) for all volumes less than (75 σ)3 where ρ is the number density, σ the hard-sphere diameter, and κT the isothermal compressibility. The method of integrating over x-ray scattering intensities has also been used with data for argon and krypton at several temperatures, with results in good agreement with expectation. The fluctuations in cold water are discussed from the point of view of their bearing on the problem of water structure. It is concluded that they could in principle be accounted for in terms either of an interstitial or of a ``continuum'' model.