A one-dimensional model with water-like anomalies and two phase transitions

TL;DR

This paper introduces a one-dimensional water-like model combining long-range attraction and step potential interactions, revealing two phase transitions and anomalies characteristic of water through analytical and numerical analysis.

Contribution

It presents a novel one-dimensional model that captures water-like anomalies and phase transitions, extending understanding of water's thermodynamic behavior in simplified systems.

Findings

The model exhibits two phase transitions: liquid-gas and high-density to low-density liquid.

Water-like anomalies such as density and response function irregularities are observed.

The phase behavior depends on the potential well parameters.

Abstract

We investigate a one-dimensional model that shows several properties of water. The model combines the long-range attraction of the van der Waals model with the nearest-neighbor interaction potential by Ben-Naim, which is a step potential that includes a hard core and a potential well. Starting from the analytical expression for the partition function, we determine numerically the Gibbs energy and other thermodynamic quantities. The model shows two phase transitions, which can be interpreted as the liquid-gas transition and a transition between a high-density and a low-density liquid. At zero temperature, the low-density liquid goes into the crystalline phase. Furthermore, we find several anomalies that are considered characteristic for water. We explore a wide range of pressure and temperature values and the dependence of the results on the depth and width of the potential well.