Dee-Walsh equation

S.C. Davis, U.S. Patents 5,372,980, 13 Dec 1994, Appl. 03 June 1993, to Polysar G.T. Dee, D.J. Walsh, Equations of state for polymer liquids. Macromolecules 21, 811-815 (1988) A modified cell model equation of state for polymer liquids. Macromolecules... 

Dee, G. T., and Walsh, D. J., A modified cell model equation of state for polymer liquids,... 

Cell and hole models were used to formulate equations of state for polymer liquids or to discuss isothermal expansion and compressibility of the systems [Hory et al., 1964 Simha, 1977 Dee and Walsh, 1988]. In the models, chain segments are placed on lattice sites. All sites are completely occupied in cell models, and volume changes of the system are related solely to changes in cell volume. Hole models as used by Simha and Somcynsky allow for both lattice vacancies and changes in cell volume. 

UG Ougizawa, T., Dee, G.T., and Walsh, D.J., PVT properties and equation of state of polystyrene. Molecular weight dependence of the characteristic parameters in equation-of-state theories (experimental data by D.J. Walsh), Polymer, 30, 1675, 1989. 

Today, there are two principal ways to develop an equation of state for polymer solutions first, to start with an expression for the canonical partition function utilizing concepts similar to those used by van der Waals (e.g., Prigogine, Flory et al., Patterson, Simha and Somcynsky, Sanchez and Lacombe, Dee and Walsh,Donohue and Prausnitz, Chien et al. ), and second, which is more sophisticated, to use statistical thermodynamics perturbation theory for freely-jointed tangent-sphere chain-like fluids (e.g., Hall and coworkers,Chapman et al., Song et al. ). A comprehensive review about equations of state for molten polymers and polymer solutions was given by Lambert et al. Here, only some resulting equations will be summarized under the aspect of calculating solvent activities in polymer solutions. 

Derive an expression for Hildebrandt solubility parameter as given by Equation (4.7) for the model proposed by Dee and Walsh. The EOS as given by Equation (2.41) is summarized as... 

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]. 

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