Simha-Somcynsky theory, polymer thermodynamics

For the description and prediction of thermodynamic data, e.g. volumetric and compositional derivatives of thermodynamic functions of state, many theoretical models are available. The Simha-Somcynsky theory can be considered to be very succesful if one is interested in the quantitative description of thermodynamic properties. Especially, for the equation of state properties this has been shown on many occasions. For the phase behavior of polymer systems, the theory hasn t been evaluated yet in great detail. In this contribution the influence of composition, temperature and molar mass distribution of the polymer is studied for the system polystyrene/cyclohexane. 

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. 

Some theoretical equations of state (EOS) based on the statistical thermodynamic theory have also been developed and are often used to predict the volume swelling of polymers due to gas dissolution at equilibrium condition, such as the Sanchez and Lacombe (SL) EOS [19-21], the Simha and Somcynsky (SS) EOS [22], and SAFT [23-24]. However, those theories need to be verified rigorously with experimentally measured data. 

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