Nuclear quantum effects on the thermodynamic response functions of a polymorphic waterlike monatomic liquid

Abstract

Water and hydrogen are examples of substances proposed to exhibit a liquid-liquid critical point (LLCP) at conditions where nuclear quantum effects are relevant. The LLCP is usually accompanied by lines of maxima in density ρ and thermodynamic response functions, such as isothermal compressibility κ_{T} and isobaric heat capacity C_{P}, in the supercritical region of the P-T plane. In the case of water, the ρ- and κ_{T}-maxima lines can be accessed in experiments, while, instead, the LLCP has not been observed due to rapid crystallization. In this work, we study the nuclear quantum effects on a monatomic liquid that exhibits waterlike anomalous properties and a LLCP. By performing path-integral Monte Carlo simulations with different values of the Planck's constant h, we are able to explore how the location of the LLCP in the P-T plane and, in particular, the maxima lines in the supercritical region, shift as the system evolves from classical, h=0, to quantum, h>0. We find that as the quantum nature of the liquid (as quantified by h) increases and the atoms in the liquid become more delocalized, the LLCP shifts towards higher pressures and lower temperatures while the LLCP volume remains constant. Similar shifts (towards higher pressures and lower temperatures) are found in the case of the C_{P}- and κ_{T}-maxima lines. Instead, the ρ-maxima line extends towards higher temperatures and expands over a wider pressure interval as the liquid becomes more quantum. It follows that the nuclear quantum effects on the location of the LLCP may be estimated from the shift in C_{P}- and κ_{T}-maxima lines but not on measurements of the ρ-maxima line. Interestingly, nuclear quantum effects considerably alter the slope of the liquid-liquid coexistence line and C_{P}-maxima line in the P-T plane while the slope of the κ_{T}-maxima line along the Widom line is barely affected. We discuss briefly the implications of our results to the case of H_{2}O/D_{2}O.