Generalized thermodynamic perturbation theory for polyatomic fluid mixtures. I. Formulation and results for chemical potentials

Abstract

For general mixtures of polyatomic molecules and their constituent atoms, we first rigorously derive an exact statistical mechanical result relating the background pair correlation function y(1,2,…,m) to a certain excess chemical potential difference involving its components, βΔμe, extending and generalizing our previous results. Second, using only thermodynamic methods, we develop a perturbation theory for the equation of state (EOS) which involves βΔμe; we then express this EOS in an alternative form involving y(1,2,…,m). The latter form coincides with results recently obtained by Zhou and Stell using a different approach and with the EOS of the Wertheim first-order perturbation theory (TPT1); our approach explicitly exposes the underlying thermodynamic approximations involved. Third, we show for the case of tangent fused-hard sphere (FHS) systems, under the approximation that βΔμe is independent of composition, that implementation of the former form of the theory yields results analytically equivalent to those obtained from the Boublik–Nezbeda (BN) EOS; and that the alternative implementation is only slightly less accurate, due to a (numerically small) internal inconsistency in this EOS. This sheds light on the remarkable accuracy obtained for several previous implementations of TPT1 for such systems. We present new computer simulation results for a particular ternary tangent FHS heteronuclear diatomic mixture, which support the approximation that βΔμe for mixtures of such molecules is nearly composition independent. Finally, for several FHS mixture model systems, we test the Lewis–Randall rule and several other approximations for calculation of the mixture chemical potentials. The Lewis–Randall rule is generally superior for the individual chemical potentials, and is competitive for βΔμe.

The A in SAFT: developing the contribution of association to the Helmholtz free energy within a Wertheim TPT1 treatment of generic Mie fluids

“…The Wertheim TPT1 treatment therefore provides a route to the separate contributions to the EOS for both reversible association (e.g., resulting from intermolecular HB) and for molecules formed from bonded segments. A consideration of mixtures of associating monomers can also be employed to provide a reliable description of the thermodynamic properties of heteronuclear dimers [59,60], trimers [61,62], and generic molecules formed from segments of different type [55,[62][63][64][65][66][67][68][69][70][71]; such a formalism has been invaluable in the recent development of group-contribution approaches for heteronuclear molecules based on the SAFT EOS, allowing for the separate chemical moieties to be considered explicitly [72][73][74][75][76][77][78].…”

Equation of state and critical behavior of polymer models: A quantitative comparison between Wertheim’s thermodynamic perturbation theory and computer simulations

“…A similar equation has been derived in a rather more formal way recently 49 for the particular case of infinitely short ranged association potentials. The derivation we have employed is based on the thermodynamic cycle presented by Zhou and Stell 47 , which allows to extend their previous result to finite range potentials.…”

Extending Wertheim’s perturbation theory to the solid phase of Lennard-Jones chains: Determination of the global phase diagram

“…We summarize the main ideas contained within Wertheim's theory by following the formulation introduced by Zhou and Stell. [30][31][32] Let us assume that we have a certain number, N ref , of spherical monomer particles within a certain volume V at temperature T, and that these particles interact through a spherical pair potential u ref (r). In this work the pair potential u ref (r) is the Lennard-Jones potential with parameters and ⑀.…”