Dimensionality dependence of the Kauzmann temperature: A case study using bulk and confined water

The Kauzmann temperature (T_K) of a supercooled liquid is defined as the temperature at which the liquid entropy becomes equal to that of the crystal. The excess entropy, the difference between liquid and crystal entropies, is routinely used as a measure of the configurational entropy, whose vanishing signals the thermodynamic glass transition. The existence of the thermodynamic glass transition is a widely studied subject, and of particular recent interest is the role of dimensionality in determining the presence of a glass transition at a finite temperature. The glass transition in water has been investigated intensely and is challenging as the experimental glass transition appears to occur at a temperature where the metastable liquid is strongly prone to crystallization and is not stable. To understand the dimensionality dependence of the Kauzmann temperature in water, we study computationally bulk water (three-dimensions), water confined in the slit pore of the graphene sheet (two-dimensions), and water confined in the pore of the carbon nanotube of chirality (11,11) having a diameter of 14.9 Å (one-dimension), which is the lowest diameter where amorphous water does not always crystallize into nanotube ice in the supercooled region. Using molecular dynamics simulations, we compute the entropy of water in bulk and under reduced dimensional nanoscale confinement to investigate the variation of the Kauzmann temperature with dimension. We obtain a value of T_K (133 K) for bulk water in good agreement with experiments [136 K (C. A. Angell, Science 319, 582-587 (2008) and K. Amann-Winkel et al., Proc. Natl. Acad. Sci. U. S. A. 110, 17720-17725 (2013)]. However, for confined water, in two-dimensions and one-dimension, we find that there is no finite temperature Kauzmann point (in other words, the Kauzmann temperature is 0 K). Analysis of the fluidicity factor, a measure of anharmonicity in the oscillation of normal modes, reveals that the Kauzmann temperature can also be computed from the difference in the fluidicity factor between amorphous and ice phases.