Space-Time Correlations in the Orientational Order Parameter and the Orientational Entropy of Water

TL;DR

This study explores the spatial and temporal correlations of local tetrahedral order in water using simulations, revealing a dynamic crossover at the Widom line and linking orientational entropy to relaxation times.

Contribution

It introduces correlation functions for local water structure, identifies a temperature-dependent change in correlations, and connects orientational entropy with dynamic behavior.

Findings

Correlation function C_Q(r) shows anticorrelation at high T and positive correlation below T_W.

Temporal autocorrelation C_Q(t) exhibits a two-step decay at low T.

Relaxation time τ_Q follows a non-Arrhenius to Arrhenius crossover at T_W.

Abstract

We introduce the spatial correlation function $C_Q(r)$ and temporal autocorrelation function $C_Q(t)$ of the local tetrahedral order parameter $Q\equiv Q(r,t)$. Using computer simulations of the TIP5P model of water, we investigate $C_Q(r)$ in a broad region of the phase diagram. First we show that $C_Q(r)$ displays anticorrelation at $r\approx 0.32$nm at high temperatures $T>T_W\approx 250$ K, which changes to positive correlation below the Widom line $T_W$. Further we find that at low temperatures $C_Q(t)$ exhibits a two-step temporal decay similar to the self intermediate scattering function, and that the corresponding correlation time $\tau_Q$ displays a dynamic crossover from non-Arrhenius behavior for $T>T_W$ to Arrhenius behavior for $T<T_W$. Finally, we define an orientational entropy $S_Q$ associated with the {\it local} orientational order of water molecules, and show that $\tau_Q$ can be extracted from $S_Q$ using an analog of the Adam-Gibbs relation.