Critical temperatures of real fluids from the extended law of corresponding states

Alfredo González-Calderón,Jorge Adrián Perera-Burgos,D P Luis

doi:10.1063/1.5123613

Abstract

The extended law of corresponding states was proposed based on the patterns observed in the second virial coefficient for potential models of variable range. In this work, we propose the use of this law, together with a generalized Lennard-Jones (or approximate nonconformal, ANC) potential, to predict the critical temperatures of real fluids. To this end, we first observe that the temperatures obtained from the scaling law are in agreement with those obtained from molecular simulations of ANC fluids. For short ranges, however, validation is performed by mapping the ANC fluid to the square well fluid because no simulation data have been reported for the former fluid for these ranges. Overall, the analysis shows the validity of the scaling law and the ANC potential for predicting critical temperatures for any range. With this in mind, the well depths of the effective binary potentials of atoms and molecules are rescaled to apply a correction for the three-body nonadditive interaction in order to determine the critical temperatures of fluids.

Highlights

The second virial coefficient (SVC) has been used mainly to describe the thermodynamic properties of real gases at low densities.1 This virial coefficient is relevant for the modeling of intermolecular binary potentials2 and the prediction of protein crystallization.3 the latter application leads to empirical observations that for spherical particles, as the interaction range varies, the virial coefficient remains constant at the critical temperature
This work aims to encourage the use of the scaling law as an alternative means of predicting the critical temperatures of atomic or molecular fluids
A generalized LJ potential is used in the Noro and Frenkel (NF) SVC; see Eq (3)

Summary

INTRODUCTION

The second virial coefficient (SVC) has been used mainly to describe the thermodynamic properties of real gases at low densities. This virial coefficient is relevant for the modeling of intermolecular binary potentials and the prediction of protein crystallization. the latter application leads to empirical observations that for spherical particles, as the interaction range varies, the virial coefficient remains constant at the critical temperature. This virial coefficient is relevant for the modeling of intermolecular binary potentials and the prediction of protein crystallization.3 The latter application leads to empirical observations that for spherical particles, as the interaction range varies, the virial coefficient remains constant at the critical temperature. 8, 10, and 11, it is well known that in the Baxter sticky limit, the SVC is equal to −4.696v0, which is different from the value −6v0 imposed in the scaling law for all ranges Despite this deviation, the predictions of the critical temperatures produce the correct results for the SW12 and mHCY9 fluids when the interaction range is considered to be less than 15% of the effective particle size. The authors of Ref. 15 presented critical temperatures for ANC fluids; in that work, they used an empirical quadratic function instead of the scaling law to fit the molecular simulation data.

BASIC EQUATIONS

PREDICTIONS OF CRITICAL TEMPERATURES

The ANC fluid and the scaling law

Application to real fluids

Findings

CONCLUSIONS