Generalized Coupling Parameter Expansion: Application to Square-Well and Lennard Jones Fluids

摘要

The coupling parameter expansion in thermodynamic perturbation theory ofsimple fluids is generalized to include the derivatives of bridge function. Weapplied seventh order version of the theory to Square-Well (SW) andLennard-Jones (LJ) fluids using Sarkisov Bridge function. In both cases, thetheory reproduced the radial distribution functions obtained from integralequation theory (IET) and simulations with good accuracy. Also, the methodworked inside the liquid-vapor coexistence region where the IETs are known tofail. In the case of SW fluids, the use of Carnahan-Starling expression forfree energy density of Hard-Sphere reference system has improved theliquid-vapor phase diagram (LVPD) over that obtained from IET. We also obtainedthe surface tension of SW fluids of various ranges. Results of present theoryand simulations are in good agreement. In the case of LJ fluids, the equationof state obtained from the present method matched with that obtained from IETwith negligible deviation. We also obtained LVPD of LJ fluid from virial andenergy routes and found that there is slight inconsistency between the tworoutes. The applications lead to the following conclusions. In cases wherereference system properties are known accurately, the present method givesresults which are very much improved over those obtained from the IET with thesame bridge function. In cases where reference system data is not available,the method serves as an alternative way of solving the Ornstein-Zernikeequation with a given closure relation with the advantage that solution can beobtained throughout the phase diagram with a proper choice of the referencesystem.