Asymptotic trends in thermodynamic perturbation theory

The development of transferable force fields for n-alkanes has enabled molecular-dynamics simulation of the reference (A0) and perturbation (A1,A2) terms in thermodynamic perturbation theory (TPT) over a broad range of chain length. The implied equations of state yield 9.1% average error in vapor pressure and 4.7% error in liquid density for compounds ranging from propane to triacontane. Further simulations extend to nC80, but there are no experimental data to which comparisons can be made. With reliable TPT terms from molecular simulation, it is possible to analyze the trends with respect to molecular weight. Each TPT contribution is shown to approach an asymptote in the long chain limit. The asymptotes and the approaches to them are quantitatively characterized. A0 and A1 approach their asymptotes at relatively short chain lengths (nC30). A2, on the other hand, approaches its asymptote slowly (nC80). Simulation-based TPT terms also permit unambiguous interpretation of the number of coarse-grained segments relative to the number of carbons in the chain. Previous attempts have relied on characterizations that included the repulsive and attractive contributions simultaneously in a manner susceptible to a cancellation of errors. In this work, the reference fluid alone provides the characterization and the result is shown to be consistent with expectations for the A1 term. The conclusion is that the number of carbons per segment approaches roughly 10 in the long chain limit, much larger than previously reported. A small adjustment to the chain contribution from Wertheim's [J. Stat. Phys. 42, 477 (1986)] TPT1 model is sufficient to provide quantitative accuracy for A0.