Predictions of Dynamic Behavior under Pressure for Two Scenarios to Explain Water Anomalies

Abstract

Using Monte Carlo simulations and mean field calculations for a cell model of water we find a dynamic crossover in the orientational correlation time from non-Arrhenius behavior at high temperatures to Arrhenius behavior at low temperatures. This dynamic crossover is independent of whether water at very low temperature is characterized by a ''liquid-liquid critical point'' or by the ''singularity-free'' scenario. We relate to fluctuations of hydrogen bond network and show that the crossover found for for both scenarios is a consequence of the sharp change in the average number of hydrogen bonds at the temperature of the specific heat maximum. We find that the effect of pressure on the dynamics is strikingly different in the two scenarios, offering means to distinguish between them. DOI: 10.1103/PhysRevLett.100.105701 PACS numbers: 64.70.Ja, 05.40.ÿa, 64.70.qj Two different scenarios are commonly used to interpret the anomalies of water [1,2]: (i) The liquid-liquid critical point (LLCP) scenario hypothesizes that supercooled water has a liquid-liquid phase transition line that separates a low-density liquid (LDL) at low temperature T and low pressure P and a high-density liquid (HDL) at high T and P and terminates at a critical point C 0 [3]. From C 0 emanates the Widom line T W P, the line of maximum correlation length in the (T, P) plane. Response functions, such as the isobaric heat capacity C P , the coefficient of thermal expansion P , and the isothermal compressibility K T , have maxima along lines that converge toward T W P upon approaching C 0 [Figs. 1 and 2(a)]. (ii) The singularityfree (SF) scenario hypothesizes the presence of a line of temperatures of maximum density T MD P with negative slope in the (T, P) plane. As a consequence, K T and j P j have maxima that increase upon increasing P, as shown using a cell model of water. The maxima in C P do not increase with P, suggesting that there is no singularity [4] [ Fig. 2(b)].Above the homogeneous nucleation line T H P where data are available, the two scenarios predict roughly the same equilibrium phase diagram. Here we show that dynamic measurements should reveal a striking difference between the two scenarios. Specifically, the low-T dynamics depends on local structural changes, quantified by the variation in the number of hydrogen bonds, that are affected by pressure differently for each scenario. We find this result by studying-using Monte Carlo (MC) simulations and mean field calculations -a cell model which has the property that by tuning a parameter its predictions conform to those of either the LLCP or the SF scenario [5]. This cell model is based on the experimental observations that on decreasing P at constant T, or on decreasing T at constant P, (i) water displays an increasing local tetrahedrality where the sum is over NN cells, 0 < J < is the bond energy, a;b 1 if a b and a;b 0 otherwise, andwhere P k;' i denotes the sum over the IM bond indices (k, l) of the molecule i and J > 0 is the IM interaction energy with J < J, which models th...

A statistical mechanical theory for a two-dimensional model of water

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High-pressure studies with x-rays using diamond anvil cells

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