Three new branched chain equations of state based on Wertheim's perturbation theory

In this work, we present three new branched chain equations of state (EOS) based on Wertheimsperturbation theory. The first represents a slightly approximate general branched chain solution ofWertheims second order perturbation theory (TPT2) for athermal hard chains, and the second representsthe extension of first order perturbation theory with a dimer reference fluid (TPT1-D) tobranched athermal hard chain molecules. Each athermal branched chain EOS was shown to give improvedresults over their linear counterparts when compared to simulation data for branched chainmolecules with the branched TPT1-D EOS being the most accurate. Further, it is shown that thebranched TPT1-D EOS can be extended to a LennardJones dimer reference system to obtain anequation of state for branched LennardJones chains. The theory is shown to accurately predictthe change in phase diagram and vapor pressure which results from branching as compared to experimentaldata for n-octane and corresponding branched isomers