# Thermodynamic properties of the 3D Lennard-Jones/spline model

## TL;DR

This study systematically maps the thermodynamic properties of the Lennard-Jones spline model using simulations, revealing its critical points, phase coexistence, and limitations of existing theoretical models in accurately describing its behavior.

## Contribution

First comprehensive thermodynamic analysis of the LJ spline model, highlighting its phase behavior and evaluating the performance of perturbation theories.

## Key findings

- Critical point estimated at T_c^*=0.885, P_c^*=0.075.
- Peng-Robinson EOS well represents coexistence data.
- Perturbation theories overestimate critical parameters.

## Abstract

The Lennard-Jones (LJ) spline potential is a truncated LJ potential such that both the pair potential and the force continuously approach zero at $r_c \approx 1.74{\sigma}$. We present a systematic map of the thermodynamic properties of the LJ spline model from molecular dynamics and Gibbs ensemble Monte Carlo simulations. Results are presented for gas/liquid, liquid/solid and gas/solid coexistence curves, the Joule-Thomson inversion curve, and several other thermodynamic properties. The critical point for the model is estimated to be $T_c^*=0.885 \pm 0.002$ and $P_c^*=0.075 \pm 0.001$, respectively. The triple point is estimated to be $T_{tp}^*=0.547 \pm 0.005$ and $P_{tp}^*=0.0016 \pm 0.0002$. The coexistence densities, saturation pressure, and supercritical isotherms of the LJ/s model were fairly well represented by the Peng-Robison equation of state. We find that Barker-Henderson perturbation theory works less good for the LJ spline than for the LJ model. The first-order perturbation theory overestimates the critical temperature and pressure by about 10% and 90%, respectively. A second-order perturbation theory is not much better. Our assessment is that mean compressibility approximation gives a poor representation of the second-order perturbation term. Our main conclusion is that we at the moment do not have a theory or model that adequately represents the thermodynamic properties of the LJ spline system.