Abstract
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 γ = 0.40 ± 0.01 for the isothermal compressibility and ν = 0.26 ± 0.03 for the correlation length. The ratio between these exponents is close to a value of ≈0.5, as expected for a critical point, indicating the proximity of a potential second critical point. Comparison of γ 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.
Highlights
Hyogo 679-5198, Japan † Electronic supplementary information (ESI) available
We want to give a brief validation of the temperature estimate given by Kim et al based on homogeneous nucleation rates, and a more detailed discussion on the temperature validation can be found in Section I of the ESI.† If we assume the temperature calibration by Kim et al to yield too low temperature estimates and instead assume the temperature to match the power-law fit of Speedy and Angell, it would mean that the lowest temperature given by Kim et al.[13] is close to 234 K
We studied the anomalous increase in isothermal compressibility and correlation length (x) of pure water upon supercooling from the data taken from Kim et al.[13]
Summary
The liquid–liquid critical point (LLCP) scenario[12] is the most supported scenario[13,14,15,16] among other models,[17,18,19] which potentially explains water’s anomalies In this scenario, the hypothesized singularity is explained as a second critical point between two local and fluctuating configurations in the liquid – a high-density liquid (HDL) and a low-density liquid (LDL). This study has been criticized[23] but all issues could be addressed.[24] Interestingly, the temperature of maxima in kT and x was found to be very close to the TS of 228 K that had been proposed earlier. The results and the best-fit exponents are compared with previous studies on kT and x at higher temperatures as well as MD simulations that together point to an LLCP located at a moderate positive pressure, in agreement with the estimation based on the value of kT.[13]
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