Relation between the Widom line and the dynamic crossover in systems with a liquid–liquid phase transition

TLDR

We investigate the relationship between dynamic and thermodynamic anomalies in two water models that exhibit a liquid–liquid critical point. The study employs two water models and the Jagla spherically symmetric two‑scale potential to probe how competing liquid structures generate the liquid–liquid critical point. Our results show that the dynamic crossover aligns with the Widom line defined by the specific‑heat maximum, indicating a general connection between liquid–liquid criticality and dynamic transitions, consistent with neutron‑scattering observations in confined water.

Abstract

We investigate, for two water models displaying a liquid–liquid critical point, the relation between changes in dynamic and thermodynamic anomalies arising from the presence of the liquid–liquid critical point. We find a correlation between the dynamic crossover and the locus of specific heat maxima \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}C_{P}^{{\mathrm{max}}}\end{equation*}\end{document} (“Widom line”) emanating from the critical point. Our findings are consistent with a possible relation between the previously hypothesized liquid–liquid phase transition and the transition in the dynamics recently observed in neutron scattering experiments on confined water. More generally, we argue that this connection between \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}C_{P}^{{\mathrm{max}}}\end{equation*}\end{document} and dynamic crossover is not limited to the case of water, a hydrogen bond network-forming liquid, but is a more general feature of crossing the Widom line. Specifically, we also study the Jagla potential, a spherically symmetric two-scale potential known to possess a liquid–liquid critical point, in which the competition between two liquid structures is generated by repulsive and attractive ramp interactions.