Evaluation of mixing and combining rules for asymmetric Lennard–Jones chain mixtures: Effect of segment diameter, energy interaction, and chain length

Abstract

Equations of state (EOS) capable of accurately representing the thermodynamic properties of chain molecules are of academic and industrial interest. In many cases, the systems of interest are composed by highly asymmetrical molecules, i.e., of different chain length, segment diameter, and segment interaction energy. The aim of this work is to evaluate mixing and combining rules (M&CR) for a SAFT-type equation of state. In the first part of this work, M&CR from literature are used together with the Wertheim Thermodynamic Polymerization Theory, in its dimer version, to calculate thermodynamic properties and then compare to those from molecular simulations. A data bank of compressibility factor and residual internal energy of Lennard–Jones chain asymmetrical mixtures was prepared for this purpose. In order to perform a systematic evaluation of M&CR, the one-fluid mixing rule (1FMR) and van der Waals one-fluid approximation (vdW1F) were coupled with the Berthelot combining rule (CR) and different CR for segment diameter, including Lorentz, Chen et al. [J. Chen, J. Lu, Y. Li, Fluid Phase Equilib. 140 (1997) 37], and a CR with one adjustable parameter. Results from comparisons with simulated data show that the 1FMR along with the Lorentz–Berthelot CR fails to represent thermodynamic properties of binary mixtures with simultaneous asymmetry in chain length and segment diameter. On the other hand, the density-dependent Chen et al. CR and vdW1F, only tested for Lennard–Jones sphere and hard-sphere chain asymmetrical mixtures, shows good performance in calculating compressibility factor and residual internal energy of asymmetrical mixtures of Lennard–Jones chains. The CR proposed in this work, with one optimized parameter, presented even better results than the Chen et al. CR, allowing a better description of simulated data employing a simpler rule.