Polymer solution thermodynamics solubility parameters

Grater, H. Schuster, R. H. Cantow, H.-J., "Thermodynamics of Polymer Systems. 5. Sorption and Mixing Properties of Selected Solutes and Solubility Parameters of Atactic Poly(Styrene) by Gas Chromatography," Polym. Bull., 14, 379 (1985). 

In the thermodynamics of polymer blends the solubility parameter is the most important parameter describing the miscibility between component polymers. However, this parameter is insufficient to explain the above finding. The samples were prepared in the form of film by casting from dimethyl formamide (DMF) solution. The values of solubility parameters are 14.7, 18.93, and 24,8x10 ... 

Diffusion Theory. The diffusion theory of adhesion is mostly applied to polymers. It assumes mutual solubility of the adherend and adhesive to form a true interpliase. The solubility parameter, the square root of the cohesive energy density of a material, provides a measure of the intemiolecular interactions occurring witliin the material. Thermodynamically, solutions of two materials are most likely to occur when the solubility parameter of one material is equal to that of the other. Thus, the observation that "like dissolves like." In other words, the adhesion between two polymeric materials, one an adherend, the other an adhesive, is maximized when the solubility parameters of the two are matched ie, the best practical adhesion is obtained when there is mutual solubility between adhesive and adherend. The diffusion theory is not applicable to substantially dissimilar materials, such as polymers on metals, and is normally not applicable to adhesion between substantially dissimilar polymers. 

Selectivity and productivity depend on sorption and diffusion. Sorption is dictated by thermodynamic properties, namely, the solubility parameter of the solute(s)/membrane material system. On the other hand, the size, shape, molecular weight of the solute, and the availability of inter/intra molecular free space of the polymer largely govern the second property, the diffusion coefficient. For an ideal membrane, both the sorption and diffusion processes should favor the chosen solute. If one step becomes unfavorable for a given solute the overall selectivity will be poor [28]. 

A thermodynamic method, more fitting to this chapter, has been proposed by Nauman et al. They claim a process for the separation of a physically mixed solid polymers by selective dissolution. They rely on the different polymer solubility characteristics. Tables of this property have been reported and are based on regular solution theory and Hildebrand solubility parameters. The core of the Nauman invention is to find suitable solvents to dissolve particular polymers under defined temperature and pressure conditions. A mixture of polymers is first added to one solvent, at a given temperature, in order to dissolve a particular polymer. The remaining polymer mixture is then treated at a higher temperature with the same solvent or with a different solvent. For clarity, two examples are taken from the patent."... 

At temperatures above Tg, the magnitude of Vg° is a measure of the solubility of the probe in the stationary phase. From the Flory-Huggins treatment of solution thermodynamics, one can obtain the x parameter, which is a measure of the residual free energy of interaction between the probe and the polymer QZ,. 18). 

There are some who question the usefulness of the Flory-Huggins solubility parameter for problems related to the solubilization of polymers, although it is agreed that it is useful for study of the thermodynamics of dilute solutions. Barton (1975) has referred to literature that cites its shortcomings as a practical criterion of solubility. Some of these are ... 

Hansen, C.M. and Beerbower, A., Solubility parameters, in Kirk-Othmer Encyclopedia of Chemical Technology, Suppl. VoL, 2nd ed., A. Standen, Ed., Wiley Interscience, New York, 1971, 889-910. Flory, P.J., Thermodynamics of polymer solutions. Discuss. Faraday Soc., 49, 7-29, 1970. 

Section 16.2 will discuss the concept and importance of the group-contribution (GC) approach in estimating two polymer properties, which are relevant for polymer solutions and blends the density and the solubility parameter. The GC technique is employed in several of the thermodynamic models discussed later in the chapter. 

Many properties of pure polymers (and of polymer solutions) can be estimated with group contributions (GC). Examples of properties for which (GC) methods have been developed are the density, the solubility parameter, the melting and glass transition temperatures, as well as the surface tension. Phase equilibria for polymer solutions and blends can also be estimated with GC methods, as we discuss in Section 16.4 and 16.5. Here we review the GC principle, and in the following sections we discuss estimation methods for the density and the solubility parameter. These two properties are relevant for many thermodynamic models used for polymers, e.g., the Hansen and Flory-Hug-gins models discussed in Section 16.3 and the free-volume activity coefficient models discussed in Section 16.4. 

The solubility parameter approach is a thermodynamically consistent theory and it has some links with other theories such as the van der Waals internal pressure concept, the Lennard-Jones pair potentials between molecules, and entropy of mixing concepts of the lattice theories. The solubility parameter concept has found wide use in industry for nonpolar solvents (i.e. solvent selection for polymer solutions and extraction processes) as well as in academic endeavor (thermodynamics of solutions), but it is unsuccessful for solutions where polar and especially hydrogen-bonding interactions are operating. 

The energy of vaporization is not accessible for polymers, but cohesive energy density of polymers can be determined from PVT-data. However, common ways for determining polymer solubility parameters use thermodynamic properties of polymer solutions and their relations to excess enthalpy or excess Gibbs energy per unit volume. These excess quantities are related to the (square) difference between the solubility parameters of solvents and polymers, i.e. (d -... 

The thermodynamic affinity between components of a solution is important for quantitative estimation of mutual solubility. The concept of solubility parameters is based on enthalpy of the interaction between solvent and polymer. Solubility parameter is the square root of the cohesive energy density, CED ... 

Adidharma and Radosz provides an engineering form for such a copolymer SAFT approach. SAFT has successfully applied to correlate thermodynamic properties and phase behavior of pure liquid polymers and polymer solutions, including gas solubility and supercritical solutions by Radosz and coworkers Sadowski et al. applied SAFT to calculate solvent activities of polycarbonate solutions in various solvents and found that it may be necessary to refit the pure-component characteristic data of the polymer to some VLE-data of one binary polymer solution to calculate correct solvent activities, because otherwise demixing was calculated. GroB and Sadowski developed a Perturbed-Chain SAFT equation of state to improve for the chain behavior within the reference term to get better calculation results for the PVT - and VLE-behavior of polymer systems. McHugh and coworkers applied SAFT extensively to calculate the phase behavior of polymers in supercritical fluids, a comprehensive summary is given in the review by Kirby and McHugh. They also state that characteristic SAFT parameters for polymers from PVT-data lead to... 

The convenience of use of solubility parameters has become the reason for easy integration with compatibility concepts. Any numerical description of interactions in polymer solutions requires the use of thermodynamic theories and interactions parameters. 

The idea of solubility parameters was first introduced by Hildebrand using the concept of regular solutions and was further developed by Scatchard [6,7]. Hildebrand s solubility parameter concept is based on Gibbs free energy relationship. Thermodynamically two compounds (e.g. polymer in solvent) do mix when the change in their free energy is negative ... 

Also a thermodynamic model based on the coupled Equation of State model and Flory-Huggins theory for polymer solutions was developed. The model parameters such as solubility-parameter of asphaltenes, molecular weight of asphaltenes, and molar volume of asphaltenes were obtained by fitting the model to experimental data. 

A thermodynamic model based on Flory-Huggins polymer-solution theory was developed and coupled with Equation of State model to predict the amount of asphaltene precipitation. The model prediction shows close agreement with the experimental data after regression of asphaltene properties such as molar volume, solubility parameter and molecular weight. The model, however, fails to account for the effect of large changes in the solubility parameters of the oil-solvent mixtures. 

Some implicit databases are provided within the Polymer Handbook by Schuld and Wolf or by Orwoll and in two papers prepared earlier by Orwoll. These four sources list tables of Flory s x-fiinction and tables where enthalpy, entropy or volume changes, respectively, are given in the literature for a large number of polymer solutions. The tables of second virial coefficients of polymers in solution, which were prepared by Lechner and coworkers (also provided in the Polymer Handbook), are a valuable source for estimating the solvent activity in the dilute polymer solution. Bonner reviewed vapor-hquid equilibria in concentrated polymer solutions and listed tables containing temperature and concentration ranges of a certain number of polymer solutions. Two CRC-handbooks prepared by Barton list a larger number of thermodynamic data of polymer solutions in form of polymer-solvent interaction or solubility parameters." ... 

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