Perturbed hard chain theory

The non-cubic equations of state are characterized by the use of a repulsive term that is based on the Camahan-Starling or on the HCB expressions already reported in Table 3. The attractive part is generally based on that derived from the perturbed hard chain theory (PHCT) [49], or from the statistical associating fluid theory SAFT [50, 51]. These approaches were the precursors of many theoretical attractive terms and consequently of different equations of... 

Donohue M.D., Prausnitz J.M., "Perturbed hard chain theory for fluid mixtures Thermodynamic properties for mixtures in natural gas and petroleum technology", AIChEJ. 1975, 24(5), 850. 

In the perturbed hard-chain theory (PHCT) of Beret and Prausnitz [14] and Donohue and Prausnitz [15], the reference fluid is modeled as chains of tangential hard spheres. Since the fluid is stiU composed of hard spheres, albeit bonded, the CS eos is applied with modification to account for the bonding. The hard-sphere-chain equation is... 

The S-S equation of state was recently modified to make it more suitable for gases as well as molten polymers in a wide range of pressure [Wang et al., 2006]. The authors used a modified partition function (from the perturbed hard-chain theory) and expression for the vibrational degree of freedom per molecule. For better fit to low-molecular-weight fluids, two constants, a and b, were introduced into the... 

Donohue, M.D., and Vimalchand, P. (1988) The perturbe -hard-chain theory - Extensions and Applications, Fluid Phase Equilibria 40, 185-211. 

Donahue and Prausnitz [23] developed the perturbed-hard chain theory (PHCT) based on perturbed hard-sphere theory for small molecules and Prigogine s theory for chain molecules. In order to account for attractive and repulsive forces among molecules, empirical parameters such as the c parameter were introduced by subsequent investigators. More accurate expressions for the repulsive and attractive forces were... 

Derive an expression for Hildebrandt solubility parameter as given by Equation (4.7) for the perturbed-hard chain theory (PCHT) EOS summarized as... 

Figure 4.3 Comparison of the measured composition of (methane + alkane) compared with composition estimates obtained from both the Peng-Robinson equation of state and the Simplified Perturbed Hard Chain Theory, (a), liquid-phase composition, and (b) vapour-phase composition. With permission from the American Chemical Society.

Donohue, M.D.andPrausnitz.J.M., 1978. Perturbed hard chain theory for fluid mixtures—Thermodynamic properties for mixtures in natnral-gas and petroleum technology. AIChE J., 24 849-860. 

High-pressure phase equilibria in systems of polymers, solvents, and supercritical gases are in almost all cases modeled using equations of state. A review of equations of state for polymer systems, including a discussion of their theoretical background, has been given by Lambert et al. [6]. One of the first equations of state that was used to model the high-pressure phase behavior of polymer-solvent systems was the Flory equation of state [11, 12]. Patterson and Delmas [10] showed that this equation of state can be used to describe both LCST and UCST phase behavior. The perturbed hard-chain theory (PCHT) was developed by Prausnitz and coworkers [57-59]. It can be considered as an improvement of the approach of Flory... 

Beret S, Prausnitz JM (1975) Perturbed hard-chain theory - equation of state for fluids containing small or large molecules. AIChE J 21(6) 1123-1132... 

Another approach for obtaining an equation of state is based on the partition function of a system derived firom statistical mechanics. One of these models is the Perturbed Hard-Chain Theory (PHCT) proposed by Beret and Prausnitz [6]. It was subsequently extended and modified by Cotterman et al. [7] and Morris et al. [8] as the Perturbed Soft-Chain Theory (PSCT). 

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