Apparent power-law behavior of water's isothermal compressibility and correlation length upon supercooling

The isothermal compressibility and correlation length of supercooled water obtained from small-angle X-ray scattering (SAXS) were analyzed by fits based on an apparent power-law in the temperature range from 280 K down to the temperature of maximum compressibility at 229 K. Although the increase in thermodynamic response functions is not towards a critical point, it is still possible to obtain an apparent power law all the way to the maximum values with best-fit exponents of gamma = 0.40 +/- 0.01 for the isothermal compressibility and nu = 0.26 +/- 0.03 for the correlation length. The ratio between these exponents is close to a value of approximate to 0.5, as expected for a critical point, indicating the proximity of a potential second critical point. Comparison of gamma obtained from experiment with molecular dynamics simulations on the iAMOEBA water model shows that it would be located at pressures in the neighborhood of 1 kbar. The high value and sharpness of the compressibility maximum observed in the experiment are not reproduced by any of the existing classical water models, thus inviting further development of simulation models of water.