A study of Wertheim's thermodynamic perturbation theory (TPT1) for associating fluids with dispersive interactions: the importance of the association range

Abstract

A key approximation in the first-order thermodynamic perturbation theory (TPT1) of Wertheim is that once two association sites have formed a hydrogen bond, steric hinderance prevents a third site from approaching close enough to form a trimer at the bond location studied. We investigate the range and validity of this assumption of only one bond per pair of sites, which translates into the assumption of only dimer formation in the case of molecules with only one association site. We compare values for Wertheim's TPT1 obtained using the statistical associating fluid theory for potentials of variable range (SAFT-VR) with Monte Carlo simulations. Dealing with spherical square-well particles with one off-centre attractive square-well site, located a distance r _d = 0.25σ from the centre of the molecule and having a cut-off range of r _c, we show that the formation of trimers and higher s-mers is possible in the simulated fluid, and conclude that the formation of s-mers higher than dimers is a complex function of the site cut-off range r _c, interaction strength ε^hb*, the temperature T* and how densely packed the system is. In addition, we show that, in the case of a molecular model with square-well dispersive forces, the range of the square-well λ also affects the number of bonds forming at a site. Finally, we demonstrate the effect of higher s-mers on the phase behaviour of associating fluids. Thus when comparing analytical data from equations of state using the TPT1 of Wertheim and simulation results, for a meaningful comparison, care must be taken to ensure the site parameters (r _d, r _c) are chosen to ensure multiple bonding cannot occur in the simulation, or the simulations are performed in such a way that multiple bonding is prohibited.

Keywords:

• Wertheim's thermodynamic perturbation theory
• Associating fluids
• Dispersive interactions

Acknowledgements

We would like to thank the Molecular Systems Engineering group at Imperial College London, particularly Professor G. Jackson and Dr. A. Haslam, for useful discussions and suggestions, and the Department of Chemical Engineering at Imperial College London for a DTA studentship for HD.