The Thermodynamic Basis of Polymer Solubility

FIGURE 7.2 Lattice model of solubility (a) low molecular weight solute (b) polymeric solute. O = Solvent O = Solute. 

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Interaction characteristics in polymer-related areas frequently make use of solubility parameters (16). While the usefulness of solubility parameters is undeniable, there exists the limitation that they need to be estimated either by calculation or from indirect experimental measurements. The thermodynamic basis of IGC serves a most useful purpose in this respect by making possible a direct experimental determination of the solubility parameter and its dependence on temperature and composition variables. Price (17) uses IGC for the measurement of accurate % values for macromolecule/vapor pairs, which are then used for the evaluation of solubility parameters for a series of non-volatile hydrocarbons, alkyl phthalates, and pyrrolidones. It may be argued that IGC is the only unequivocal, experimental route to polymer solubility parameters, and that its application in this regard may further enhance the practical value of that parameter. Guillet (9) also notes the value of IGC in this regard. 

The systems selected for evaluation are the PDMS-C02 system studied by Gerhardt et al. (1997, 1998) and PS-gas systems studied by Kwag et al. (1999). Properties for these systems are listed in Table 11.1. The variation in physical properties between these systems provides a very broad basis for evaluating the rheological properties of polymer-gas systems. The PDMS C02 system exhibits a favorable thermodynamic affinity between the polymer and dissolved gas, and provides the opportunity to evaluate the rheology of melts with very high dissolved gas content (up to 21 wt %). Carbon dioxide is much less soluble in polystyrene than in PDMS, so the PS-C02... 

When using this approach to polymer solubility, we need to remember that the basis is thermodynamics. In other words, this approach gives information about the energetics of solubility, but does not give any insight in the kinetics of the process. In order to promote rapid dissolution, it may be more helpful to employ a solvent that is less good thermodynamically, but that consists of small, compact molecules that readily diffuse into the polymer and hence dissolve the polymer more quickly. 

The empirical nature of is obvious, and it would be helpful to replace y by parameters having a sound basis in thermodynamic or statistical mechanical considerations. Recent efforts by Fowkes [40] to relate y to the dispersion forces between molecules at the interface have been especially promising in leading to tractable equations. An interesting direct correlation has been recently pointed out to us by Gar don [49] between the value of y of a solid polymer and the Hildebrand solubility parameter, 6, which is defined as the square root of the molar energy density—i.e., 6 = n/1E/p A simple consideration of the Young equation and the definition of y indicates that when cos 0=1,... 

The principles of polymer fractionation by solubility or crystallization in solution have been extensively reviewed on the basis of Hory-Huggins statistical thermodynamic treatment [58,59], which accounts for melting point depression by the presence of solvents. For random copolymers the classical Flory equation [60] applies ... 

Depending on the purposes and operating eonditions of polymer material processing, the opposite demands to solubility of low-moleeular-mass liquids in polymers exist. The produets of polymer materials designed for use in eontact with solvents should be stable against relative adsorption of these liquids. On the eontrary, the well dissolving polymer solvents are necessary to produce the polymer films. The indispensable condition of creation of the plasticized polymer systems (for example, rubbers) is the high thermodynamic compatibility of plasticizers with the polymer basis of material. 

Prior to Harwood s work, the existence of a Bootstrap effect in copolymerization was considered but rejected after the failure of efforts to correlate polymer-solvent interaction parameters with observed solvent effects. Kamachi, for instance, estimated the interaction between polymer and solvent by calculating the difference between their solubility parameters. He found that while there was some correlation between polymer-solvent interaction parameters and observed solvent effects for methyl methacrylate, for vinyl acetate there was none. However, it should be noted that evidence for radical-solvent complexes in vinyl acetate systems is fairly strong (see Section 3), so a rejection of a generalized Bootstrap model on the basis of evidence from vinyl acetate polymerization is perhaps unwise. Kratochvil et al." investigated the possible influence of preferential solvation in copolymerizations and concluded that, for systems with weak non-specific interactions, such as STY-MMA, the effect of preferential solvation on kinetics was probably comparable to the experimental error in determining the rate of polymerization ( 5%). Later, Maxwell et al." also concluded that the origin of the Bootstrap effect was not likely to be bulk monomer-polymer thermodynamics since, for a variety of monomers, Flory-Huggins theory predicts that the monomer ratios in the monomer-polymer phase would be equal to that in the bulk phase. 

A thermodynamic model was recently proposed to calculate the solubility of small molecules in assy polymers. This model is based on the assumption that the densiQr of the polymer matrix can be considered as a proper order parameter for the nonequilibrium state of the system (7). In this chapter, the fundamental principles of the model are reviewed and the relation of the model to the rheological properties of the polymeric matrix is developed. In particular, a unique relation between the equilibrium and non-equilibrium properties of the polymer-penetrant mixture can be obtained on the basis of a simple model for the stress-strain relationship. 

In this respect, the in silico prediction of the thermodynamic mixing behavior of different polymer-drug/excipient mixtures is of central interest. A common approach to cope with this problem is the calculation of the solubility parameters according to Hildebrand or Hansen [9-12], which is standard in the development of polymer mixtures [13]. The use of highly developed force fields as the basis of any MD simulation software enables the calculation of solubility parameters with accuracy comparable to those measured experimentally by inverse gas chromatography [14], and an increasing number of other statistical quantitative property relationships between simulated and experimental values are established [15-18]. 

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