Interaction parameters, miscibility, blended polymer thermodynamics

In a fundamental sense, the miscibility, adhesion, interfacial energies, and morphology developed are all thermodynamically interrelated in a complex way to the interaction forces between the polymers. Miscibility of a polymer blend containing two polymers depends on the mutual solubility of the polymeric components. The blend is termed compatible when the solubility parameter of the two components are close to each other and show a single-phase transition temperature. However, most polymer pairs tend to be immiscible due to differences in their viscoelastic properties, surface-tensions, and intermolecular interactions. According to the terminology, the polymer pairs are incompatible and show separate glass transitions. For many purposes, miscibility in polymer blends is neither required nor de-... 

The first is to develop thermodynamic issues to understand the complex phase behavior of polymer blends. Experimental determination of miscibility regions provides the individual segmental interaction parameters necessary for predictions of various phase equilibria. 

The spontaneous mixing of the two polymers will transpire at a rate which reflects the degree of miscibility of the system. As X approaches the critical value for phase separation, "thermodynamic slowing down" of the interdiffusion will occur [12]. The rate of increase of the scattering contrast reflects the proximity of the system to criticality, as well as the strong composition dependence of the glass transition temperature of the blend. Extraction of a value for either the self diffusion constants [13,14] or the interaction parameter is not feasible from the presently available data. 

IGC was used to determine the thermodynamic miscibility behavior of several polymer blends polystyrene-poly(n-butyl methacrylate), poly(vinylidene fluoride)-poly(methyl methacrylate), and polystyrene-poly(2,6-dimethyl-1,4-phenylene oxide) blends. Specific retention volumes were measured for a variety of probes in pure and mixed stationary phases of the molten polymers, and Flory-Huggins interaction parameters were calculated. A generally consistent and realistic measure of the polymer-polymer interaction can be obtained with this technique. 

In Eq 2.86 k and b are ratios of, respectively, ACp s and densities of polymers 1 and 2, and is the thermodynamic binary interaction parameter. Thus, the relation makes it possible to compute the interaction parameter of miscible blends from T vs. composition dependence. 

It has been known for more than a century that impurities reduce the melting point. This observation has been used to determine the molecular weight of the contaminant by Raoult in 1882-5. Nearly a hundred years later, this concept was used to calculate the thermodynamic binary interaction parameter, from the melting point depression of a crystalline polymer in miscible blend with low concentration of another polymer. The relation is usually used in the simplified form for very high molecular weight components [Nishi and Wang, 1975, 1977] ... 

The crystallization of blends tends to depend on the level of mutual miscibility of the components. In miscible blends, the general result is that suppression or otherwise of crystallization with miscibility is dependent on the relative glass transition temperatures of both phases [33, 34]. For example, in a blend of an amorphous and semicrystalline polymer, if the amorphous material has the higher Tg, the miscible blend will also have a higher Tg than that of the semicrystalline homopolymer and, at a given temperature, the mobility and thus the efficacy of the semicrystalline phase molecules to crystallize is reduced. The converse is often true if the amorphous phase has a lower glass transition. Effects such as chemical interactions and other thermodynamic considerations also play a role and the depression of the melting point in a miscible blend can be used to determine the Flory interaction parameter x [40]. 

Several interesting observations relate to such thermodynamic measurements. For example, the exothermic effects, associated with phase separation in LCST-type polymer blends, showed a correlation between the exothermic enthalpy and the interactions between the components (Natansohn 1985) however, the specific interaction parameter xn was not calculated. In another example, there are definitive correlations between the thermodynamic and the transport properties (see Chap. 7, Rheology of Polymer Alloys and Blends ). Thermodynamic properties of multiphase polymeric systems affect the flow, and vice versa. As discussed in Chap. 7, Rheology of Polymer Alloys and Blends , the effects of stress can engender significant shift of the spinodal temperature, AT = 16 °C. While at low stresses the effects can vary, i.e., the miscibility can either increase or decrease. 

PBSA and PVPh are miscible crystalline/amorphous polymer blends. Miscibility of PBSA/PVPh blends was evidenced by the single composition-dependent glass-transition temperature over the entire blend compositions. The negative polymer-polymer interaction parameter, obtained from the melting depression of PBSA, indicates that PBSA/PVPh blends are thermodynamically miscible. 

The binary interactirMi generally refers to the interactions between polymer-polymer and polymer-solvent The nature of solvent-polymer interaction plays an important role in the miscibility of blends. Many thermodynamic properties of polymer solutions such as solubility, swelling behavior, etc., depend on the polymer-solvent interaction parameter (y). The quantity was introduced by Flory and Huggins. Discussions of polymer miscibility usually start with Flory-Huggins equation for free energy of mixing of a blend (refer to Chap. 2, Thermodynamics of Polymer Blends ). 

The thermodynamic basis to explain miscibility in polymer blends is an exothermic heat of mixing as entropic contributions are small for such systems. Intramolecular repulsions may be an important factor in realizing exothermic heat of mixing. The application of binary interaction model to predict a compositional window of miscibility for copolymer/homopolymer blends, terpolymer blends with common monomers, copolymer blends with common monomers, is illustrated. A 6 X parameter expression for free energy of mixing for two copolymers with four monomers is described. The spinodal is derived from stability and miscibility considerations. The physical meaning behind concave and convex curvature of phase envelopes is described. 

Predictive models for drug-polymer miscibility have been introduced, and they are largely derived from solution thermodynamics. Lattice-based solution models, such as the F-H theory, can be used to assess miscibility in drug-polymer blends, for which the F-H interaction parameter can be considered as a measure of miscibility. In addition, solubility parameter models can be used for this purpose. The methods used to estimate interaction parameters include melting point depression and the determination of solubility parameters using group contribution theory. 

There are several factors that are either not included or assumed to be unimportant in the Stockmayer-Kennedy theory. Hydrodynamic interactions between two chains in a block copolymer are not included in the theory. This can be a serious omission, especially when dealing with low-molecular-weight diblock copolymers, such as the SI diblock copolymers considered above. Intermolecular (thermodynamic) interactions between chemically dissimilar chains are also neglected. Inclusion of such interactions can be important, especially when the chemical affinity between two chemically dissimilar chains is rather poor, such as the case in the SI diblock copolymers considered here. In Chapter 7, which discusses the rheology of miscible polymer blends, we pointed out the importance of the segmental interaction parameter in the prediction of the linear... 

Miscibility in polymer blends is controlled by thermodynamic factors such as the polymer-polymer interaction parameter [8,9], the combinatorial entropy [10,11], polymer-solvent interactions [12,13] and the "free volume effect [14,15] in addition to kinetic factors such as the blending protocol, including the evaporation rate of the solvent and the drying conditions of the samples. If the blends appear to be miscible under the given preparation conditions, as is the ca.se for the blends dcscibcd here, it is important to investigate the reversibility of phase separation since the apparent one-phase state may be only metastable. To obtain reliable information about miscibility in these blends, the miscibility behavior was studied in the presence and absence of solvents under conditions which included a reversibility of pha.se separation. An equilibrium phase boundary was then obtained for the binary blend systems by extrapolating to zero solvent concentration. 

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