is availed to obtain the thermodynamic properties of chain fluids [36]. Based on these
concepts, the reference interaction site mode (RISM) [37, 38], originally developed for
small molecules was extended to polymers (polymer reference interaction site model or
PRISM) by Curro and Schweizer [39, 40, 41]. PRISM provides a good representation
of the segment-segment structure of the chain fluid, however, the description of the
thermodynamics are often poor [42]. In addition, there are ambiguities regarding the
closure equations to be used for specific systems. Other integral equation approaches
for hard chain fluids have been developed by Chiew [43] (using Percus-Yevick clo-
sure together with chain connectivity constraints) and Chang and Sandier [44] (by
solving Wertheim’s integral equation theory [26, 27, 28, 29]). Recently, the polymer
mean spherical approximation (PMSA) integral equation theory has been used by
Kalhuzhnyi et. al. [45] to obtain the thermodynamic properties of chains of Yukawa
spheres.
One of the most accurate descriptions of the phase behavior of polymer systems
had been achieved with EOS based on Wetheim’s TPTl [26, 27, 28, 29] for associ-
ating atomic fluids. The molecules of these associating atomic fluids have spherical
hard cores with off-centered associating sites on them. TPTl accurately describes
the phase behavior and thermodynamics of associating atomic fluids with multiple
association sites. Chapman et. al. [46, 47] extended TPTl to mixtures of associating
atomic fluids and derived an EOS for hard chain fluids by taking the limit of complete
association between the associating spheres. The EOS labeled as statistical associ-
13