Simha-Somcynsky theory, polymer

Nies, E., Stroeks, A., Simha, R., and Jain, R. K., LCST [lower critical solution temperature] phase behavior according to the Simha-Somcynsky theory apphcation to the n-hexane/polyethylene system. Colloid Polym. Sci., 268, 731-743 (1990). 

Curro, J. G., Lagasse, R. R., Simha, R., Application of the Simha-Somcynsky Theory to polymer glasses. Bulletin of the American Physical Society, 26, pp. 368-368 (1981). 

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. 

The hole theory offers an excellent basis to evaluate the phase behavior of polymer systems. The description of the spinodal conditions are almost quantitative without the introduction of empirical parameters. The cell free volume is very important for this quantitative success. The influence of polydispersity on the spinodal conditions in the Simha-Somcynsky theory is not restricted to the mass average molar mass. 

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]. 

Wang, M., Takishima, S., Sato, Y, and Masuoka, H., Modification of Simha-Somcynsky equation of state for small and large molecules. Fluid Phase Equilibria, 242. 10-18 (2006). Wang, W, Liu, X., Zhong, C., Twu, C. H., and Coon, J. E., Simplified hole theory equation of state for liquid polymers and solvents and their solutions, Ind. Eng. Chem. Res., 36, 2390-2398 (1997). 

Much of the work stems from Simha-Somcynsky (S-S) [1969] hole theory, developed originally to describe polymers in the liquid state. They introduced the free volume by using the formalism of vacant cells or holes in a lattice and developed an equation of state that could be used to calculate the fraction of sites occupied and hence the fractional free volume. As discussed in Chapter 6, the concept has been developed further by Simha and his co-workers. 

Experimental data from our laboratories will be shown for an extensive series of amorphous polymers with glass transitions between Tg = 200 and 500 K. We discuss the temperature dependence of the hole-size distribution characterized by its mean and width and compare these dependencies with the hole fraction calculated from the equation of state of the Simha-Somcynsky lattice-hole theory from pressure-volume-temperature PVT) experiments [Simha and Somcynsky, 1969 Simha and Wilson, 1973 Robertson, 1992 Utracki and Simha, 2001]. The same is done for the pressure dependence of the hole free-volume. The free-volume recovery in densified, and gas-exposed polymers are discussed briefly. It is shown that the holes detected by the o-Ps probe can be considered as multivacancies of the S-S lattice. This gives us a chance to estimate reasonable values for the o-Ps hole density. Reasons for its... 

Simha et al. have used the hole theory of Simha-Somcynsky (S-S) (Simha and Somcynsky 1969) as a starting point to develop further the idea of fi ee volume. In their vacant cells or holes in a polymer lattice constitute the fi ee volume arising from inefficient chain packing. An equation of state was developed to calculate the Iraction of occupied lattice sites and hence the fractional free volume. 

Free-volume theory is an improved cell or lattice model for the liquid state by introduction of vacancies in the lattice. In the free-volume theory, the Simha-Somcynsky equation of state of a polymer system is written as (10)... 

The Simha-Somcynski Hole Theory In the MFLG theory the effects of compressibility are related to the presence of vacancies on the lattice. On the other hand, in the EoS theory of Flory and coworkers a completely filled lattice is assumed and the pVT contributions are due to changes in the volume of the lattice sites or cells. Finally hole theories, which for polymer systems were initiated by Simha and... 

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. 

Other free volume theories such as those of Sanchez and Lacombe and Simha and Somcynski are based on a lattice model and all or part of the free volume arises from vacancies on the lattice, unlike the Flory theory where free volume arises from an overall increase in molecular separations. Such theories are discussed in the chapter on polymer solutions (Volume 2, Chapter 3) and have not been much used in relation to polymer mixtures. Their use may -well prove to be valuable since, especially using the theory of Simha and Somcynski, they much better describe the properties of the pure components. 

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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