Water-like anomalies for core-softened models of fluids: One dimension

TL;DR

This paper investigates water-like anomalies in a one-dimensional core-softened fluid model, revealing how potential shape influences density and entropy anomalies, and identifying a critical point analog that affects thermodynamic response functions.

Contribution

It provides a detailed analysis of how specific 1D core-softened potentials produce water-like anomalies and identifies a critical point analog in the model, linking potential shape to anomalous behavior.

Findings

Certain two-step square well potentials produce density and entropy anomalies.

A critical point analog C' exists at T=0, influencing thermodynamic properties.

Anomalous behavior of compressibility and specific heat is observed near C'.

Abstract

We use a one-dimensional (1d) core-softened potential to develop a physical picture for some of the anomalies present in liquid water. The core-softened potential mimics the effect of hydrogen bonding. The interest in the 1d system stems from the facts that closed-form results are possible and that the qualitative behavior in 1d is reproduced in the liquid phase for higher dimensions. We discuss the relation between the shape of the potential and the density anomaly, and we study the entropy anomaly resulting from the density anomaly. We find that certain forms of the two-step square well potential lead to the existence at T=0 of a low-density phase favored at low pressures and of a high-density phase favored at high pressures, and to the appearance of a point $C'$ at a positive pressure, which is the analog of the T=0 ``critical point'' in the $1d$ Ising model. The existence of point $C'$ leads to anomalous behavior of the isothermal compressibility $K_T$ and the isobaric specific heat $C_P$.