Extension of Wertheim's thermodynamic perturbation theory to include higher order graph integrals

This work extends Wertheim's Thermodynamic Perturbation Theory (TPT) to include dimer-dimer graphs, i.e., we extend the theory beyond the so-called single-chain approximation. The theory is referred to as thermodynamic perturbation dimer theory. We provide a graph-theoretical derivation of the additional dimer-dimer term and resum the graphs in terms of 3- and 4-particle correlation functions. It is shown how orientationally averaged (hard-sphere) correlation functions can be obtained by Monte Carlo simulation. The 4-particle correlation function, which arises from the additional order term, is adjusted to results of molecular (hard-sphere) dimer fluid simulations. A new equation of state for linear, flexible hard chain fluids is obtained. The predictions of the compressibility factor and the second virial coefficient of the new theory show a better agreement to results from molecular simulations compared as compared to TPT1 and TPT2. We compare the results of the derived theories with simulated data of chains with length ν = 4, 8, 16, and 64 and show that simply considering higher orders of the regular TPT is not sufficient to describe the low-density behavior of longer chains.