Thermal Conductivity of Supercooled Water

TL;DR

This paper investigates the thermal conductivity behavior of supercooled water, exploring whether critical fluctuations near a hypothesized liquid-liquid critical point significantly affect it, and explains observed anomalies through thermodynamic property variations.

Contribution

The study applies mode-coupling theory to assess critical fluctuation effects on thermal conductivity, finding them negligible, and explains the conductivity's non-divergent behavior in supercooled water.

Findings

Thermal conductivity shows no divergence near the hypothesized critical point.

Thermal conductivity is predicted to have a minimum as temperature decreases.

Observed anomalies in thermodynamic properties explain the thermal conductivity behavior.

Abstract

The heat capacity of supercooled water, measured down to -37 {\deg}C, shows an anomalous increase as temperature decreases. The thermal diffusivity, i. e., the ratio of the thermal conductivity and the heat capacity per unit volume, shows a decrease. These anomalies may be associated with a hypothetical liquid-liquid critical point in supercooled water below the line of homogeneous nucleation. However, while the thermal conductivity is known to diverge at the vapor-liquid critical point due to critical density fluctuations, the thermal conductivity of supercooled water, calculated as the product of thermal diffusivity and heat capacity, does not show any sign of such an anomaly. We have used mode-coupling theory to investigate the possible effect of critical fluctuations on the thermal conductivity of supercooled water, and found that indeed any critical thermal-conductivity enhancement would be too small to be measurable at experimentally accessible temperatures. Moreover, the behavior of thermal conductivity can be explained by the observed anomalies of the thermodynamic properties. In particular, we show that thermal conductivity should go through a minimum as temperature is decreased, as Kumar and Stanley observed in the TIP5P model of water. We discuss physical reasons for the striking difference between the behavior of thermal conductivity in water near the vapor-liquid and liquid-liquid critical points.