Thermodynamic properties and phase equilibria of branched chain fluids using first- and second-order Wertheim’s thermodynamic perturbation theory

Abstract

We present an extension of the statistical associating fluid theory (SAFT) for branched chain molecules using Wertheim’s first- and second-order thermodynamic perturbation theory with a hard-sphere reference fluid (SAFT-B). Molecules are formed by hard spherical sites which are tangentially bonded. Linear chains are described as freely jointed monomeric units, whereas branched molecules are modeled as chains with a different number of articulation points, each of them formed by three arms. In order to calculate the vapor–liquid equilibria of the system, we have considered attractive interactions between the segments forming the chain at the mean-field level of van der Waals. The Helmholtz free energy due to the formation of the chain is explicitly separated into two contributions, one accounting for the formation of the articulation tetramer, and a second one due to the formation of the chain arms. The first term is described by the second-order perturbation theory of Phan et al. [J. Chem. Phys. 99, 5326 (1993)], which has been proven to predict the thermodynamic properties of linear chain fluids in a similar manner to Wertheim’s approach. The formation of the chain arms is calculated at Wertheim’s first-order perturbation level. The theory is used to study the effect of the chain architecture on the thermodynamic properties and phase equilibria of chain molecules. The equation predicts the general trends of the compressibility factor and vapor–liquid coexistence curve of the system with the branching degree, in qualitative agreement with molecular simulation results for similar models. Finally, SAFT-B is applied to predict the critical properties of selected light alkanes in order to assess the accuracy of the theory. Experimental trends of the critical temperature of branched alkanes are qualitatively captured by this simple theory.