Perturbed hard sphere chain

For the calculations, different EoS have been used the lattice fluid (LF) model developed by Sanchez and Lacombet , as well as two recently developed equations of state - the statistical-associating-fluid theory (SAFT)f l and the perturbed-hard-spheres-chain (PHSC) theoryt ° . Such models have been considered due to their solid physical background and to their ability to represent the equilibrium properties of pure substances and fluid mixfures. As will be shown, fhey are also able to describe, if not to predict completely, the solubility isotherms of gases and vapors in polymeric phases, by using their original equilibrium version for rubbery mixtures, and their respective extensions to non-equilibrium phases (NELF, NE-SAFT, NE-PHSC) for glassy polymers. 

FEN Feng, W., Wen, H., Xu, Z., and Wang, W., Comparison of perturbed hard-sphere-chain theory with statistical associating fluid theory for square-well fluids, Ind. Eng. Chem. Res., 39, 2559, 2000. 

The perturbed-hard-sphere-chain (PHSC) equation of state is a hard-sphere-chain theory that is somewhat different to SAFT. It is based on a hard-sphere chain reference system and a van der Waals-type perturbation term using a temperature-dependent attractive parameter a(T) and a temperature-dependent co-volume parameter b(T). Song et ap-... 

Subsequently, various perturbation theories were developed which are also based on Eq. (3) but differ in the use of specific expressions for the different types of perturbations. Examples are the Perturbed Hard-Sphere-Chain Theory (PHSC) [64], as well as the models proposed by Chang and Sandler [65], Gil-ViUegas et al. [66], and Hino and Prausnitz [67]. 

The above-mentioned deficiencies of the Flory-Huggins theory can be alleviated, in part, by using the local-composition concept based on Guggenheim s quasichemical theory for the random mixing assumption and replacing lattice theory with an equation-of-state model (Prausnitz et al., 1986). More sophisticated models are available, such as the perturbed hard sphere chain (PHSC) and the statistical associating fluid theory (SAFT) (Caneba and Shi, 2002), but they are too mathematically sophisticated that they are impractical for subsequent computational efforts. 

The decisive advantage of the original Elory-Huggins theory [1] lies in its simplicity and in its ability to reproduce some central features of polymer-containing mixtures qualitatively, in spite of several unrealistic assumptions. The main drawbacks are in the incapacity of this approach to model reality in a quantitative manner and in the lack of theoretical explanations for some well-established experimental observations. Numerous attempts have therefore been made to extend and to modify the Elory-Huggins theory. Some of the more widely used approaches are the different varieties of the lattice fluid and hole theories [2], the mean field lattice gas model [3], the Sanchez-Lacombe theory [4], the cell theory [5], different perturbation theories [6], the statistical-associating-fluid-theory [7] (SAET), the perturbed-hard-sphere chain theory [8], the UNIEAC model [9], and the UNIQUAC [10] model. More comprehensive reviews of the past achievements in this area and of the applicability of the different approaches are presented in the literature [11, 12]. 

PHSC Perturbed Hard-Sphere-Chain Theory... 

Song Y, Lambert SM, Prausnitz JM (1994) A perturbed hard-sphere-chain equation of state for normal fluids and polymers. Ind Eng Chem Res 33 1047-1057... 

Additional examples of equation of state models include the lattice gas model (Kleintjens et al, [33,34], Simha-Somcynsky hole theory [35], Patterson [36], the cell-hole theory (Jain and Simha [37-39], the perturbed hard-sphere-chain equation of state [40,41] and the modified cell model (Dee and Walsh) [42]. A comparison of various models showed similar predictions of the phase behavior of polymer blends for the Patterson equation of state, the Dee and Walsh modified cell model and the Sanchez-Lacombe equation of state, but differences with the Simha-Somcynsky theory [43]. The measurement and tabulation of PVT data for polymers can be found in [44]. 

Contemporary Approaches. Numerous advanced theories have been formulated in the last decades to reproduce or even predict experimental findings for polymer containing mixtures. Most of them are particularly suitable for the description of some phenomena and special kinds of systems, but all have in common that they have lost the straightforwardness characterizing the Flory-Huggins theory. The following, incomplete collocation states some of the wider used approaches These are the different forms of the lattice fluid and hole theories (38), the mean field lattice gas model (39), the Sanchez-Lacombe theory(40), the cell theory (41), various perturbation theories (42), the statistical-associating-fluid-theory (43) (SAFT), the perturbed-hard-sphere chain theory (44), the... 

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