Polymer fluids hard-core chains

Here, the term A includes the contribution of interaction entropy (Floiy 1970). Such a contribution can be miderstood from the concept of compressible free volume in the fluids. When two fluids are mixed with each other, part of molecules of one species enters the free volume of another species, and then the total volume is not a simple addition of the two individual components. Yamakawa made an approximate estimation from the expansion theory (Yamakawa 1971). Prigogine attributed this contribution to a combinatorial contribution of molecular geometry and a non-combinatorial contribution of molecular stmctures, and proposed an equation-of-state theory (Prigogine 1957b). Hory, Orwell and Vrij further considered the contribution of free volume, and employed separate parameters to describe the hard-core volume and surface contacts of chain units (Flory et al. 1964 Flory 1965 OrwaU and Rory 1967). This work makes the equation of state fit better to the e erimental results, and derives the so-called Flory-Orwell-Vrij equation of state for pure polymers, as given by... 

The basic theory of star polymer fluids developed by Grayce and Schweizer is general in its ability to treat polymer models of variable chemical detail. For simplicity, we discuss the theory in the context of the tangent, semiflexible chain model. As true for most of the results discussed in Section VIII, the bare bending energy is set equal to zero, and pure hard-core interactions (athermal or good solvent conditions) are employed in numerical studies carried out so far. 

As a general comment on the recent polymer integral equation work, we note that applications to date have focused primarily on the structure (intra- and intermolecular) and equation of state (based on a virial or free energy route) of the simple hard core, tangent jointed chain model of polymer solutions and melts. How tractable and generalizable the various approaches are for treating semiflexible and/or atomistic models of macromolecular fluids is unclear for most theories. Little, or no, work has... 

Finally, we mention an interesting recent study by Chandler that extended the Gaussian field-theoretic model of Li and Kardar to treat atomic and polymeric fluids. Remarkably, the atomic PY and MSA theories were derived from a Gaussian field-theoretic formalism without explicit use of the Ornstein-Zernike relation or direct correlation function concept. In addition, based on an additional preaveraging approximation, analytic PRISM theory was recovered for hard-core thread chain model fluids. Nonperturbative applications of this field-theoretic approach to polymer liquids where the chains have nonzero thickness and/or attractive forces requires numerical work that, to the best of our knowledge, has not yet been pursued. 

Although we believe much progress has been made based on the PRISM theory approach, there remain important basic theoretical issues that require continuing attention in the future. The most obvious is the question of closure approximation. Even for the purely repulsive or hard-core polymer fluid, improved closures are desirable. Results for diatomic and polymer fluids based on the diagramatically proper Chandler-Silbey-Ladanyi (CSL) formulation of RISM theory have been obtained by Yethiraj based on the site-site PY closure. Unfortunately, for chain molecules this approach does not represent an... 

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