Copolymer blends binary interaction model

There are many examples known where a random copolymer Al, comprised of monomers 1 and 2, is miscible with a homopolymer B, comprised of monomer 3, even though neither homopolymer 1 or 2 is miscible with homopolymer 3, as illustrated by Table 2. The binary interaction model offers a relatively simple explanation for the increased likelihood of random copolymers forming miscible blends with other polymers. The overall interaction parameter for such blends can be shown (eg, by simplifying eq. 8) to have the form of equation 9 (133—134). 

Chlorinated polymers/Copolyester-aniides Recent studies (5) of blends of chlorinated polyeAylenes with caprolactam(LA)-caprolactone(LO) copolymers have been able to establish a correlation between miscibiUty and chemical structure within the framework of a binary interaction model. In some of the blends, both components have the ability to crystallize. When one or both of the components can crystallize, the situation becomes rather more complicated. Miscible, cystallizable blends may also undergo segregation as a result of the crystallization with the formation of two separate amorphous phases. Accordingly, it is preferable to investigate thermal properties of vitrified blends. Subsequent thermal analysis also produces exothermic crystallization processes that can obscure transitions and interfere with determination of phase behavior. In these instances T-m.d.s.c has the ability to separate the individual processes and establish phase behavior. 

Blends of various homopolymers with AMS-AN copolymers were systanatically examined for miscibility and phase separation temperatures in cases where LCST behavior was detected. The experimental data was used to calculate the interaction energy using the Sanchez-Lacombe lattice fluid equation of state theory. The analysis assumes that the experimental phase separation temperatures are represented using the spinodal curve and that the bare interaction energy density AP was found to be independent of temperature. Any dependence on the B interaction parameter with temperature stems frtrni compressibility effects. AP was determined as a function of cqxtlymer composition. AP,y values obtained for blends of the various homopolymers with AMS-AN copolymers woe then compared with corresponding ones obtained from SAN copolymers. Hwy-Huggins values were calculated from the experimental miscibility limits using the binary interaction model for comparison with AP,y values. 

The binary interaction model was applied to a system of copolymer-copolymer binary blend with common monomers in Section 3.3. The SAN/SAN blend, the compositional mismatch that can be tolerated to stay miscible, was calculated. A method to calculate the compositional window of miscibility for a terpolymer-terpolymer blend with common monomers was illustrated in Section 3.4. The RAND key can be used in an MS Excel spreadsheet to arrive at the compositional window of miscibility in computational time. The miscible regions for terpolymer-terpolymer binary blends with common monomers are shown in Figure 3.2. The compositional window of miscibility for terpolymer-homopolymer miscibility without any common monomers was calculated using a binary interaction model in Section 3.5. The system chosen for the illustration was TMPC/AMS-AN-MMA. 

Ternary blend using binary interaction model Gan et al. [18] found for certain copolymer compositions and volume fractions the ternary blend system of styrene acrylonitrile copolymer (SAN), polycarbonate (PC) homopolymer and polycaprolactone (PCL) was completely miscible. Develop the expression for binary interaction energy B for the ternary blend using binary interaction model. Is the intramolecular repulsion in the copolymer sufficient to drive miscibility with two other homopolymers without any common monomers ... 

D. R. Paul and J. W. Barlow, A binary interaction model for miscibility of copolymers in blends, Polymer, 25,487, 1984. 

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. 

This is a three-part book with the first part devoted to polymer blends, the second to copolymers and glass transition tanperatme and to reversible polymerization. Separate chapters are devoted to blends Chapter 1, Introduction to Polymer Blends Chapter 2, Equations of State Theories for polymers Chapter 3, Binary Interaction Model Chapter 4, Keesome Forces and Group Solubility Parameter Approach Chapter 5, Phase Behavior Chapter 6, Partially Miscible Blends. The second group of chapters discusses copolymers Chapter 7, Polymer Nanocomposites Chapter 8, Polymer Alloys Chapter 9, Binary Diffusion in Polymer Blends Chapter 10, Copolymer Composition Chapter 11, Sequence Distribution of Copolymers Chapter 12, Reversible Polymerization. 

A procedure for mapping the miscibility space of homopolymer-copolymer or copolymer-copolymer blends referred to as the mean field binary interaction model has proven to be quite useful. This approach was developed and pubhshed independently by three different laboratories [171-173].A number of papers [174—178] employing this approach have demonstrated excellent agreement of prediction with experiment. 

The window of miscibility in this case is an ellipse contained within the boundaries of the copolymer composition map. Additional examples of the mean field approach to predict the miscibility window for cop olymer-copolymer blends include SAN/SMMA, SMMA/MMA-AN and SAN/MMA-AN [188], amSAN/SAN and amSAN/SMA [202], SMMA/SMMA (different compositions) [203 ], SMA/tetramethyl Bis A polycarbonate [204], chlorinated PVC (different compositions), chlorinated polyethylene (different compositions and MMA-EMA (different compositions) [177] and SAN/NBR [205]. This approach has also been applied to ternary blends of PPO/PS/poly(o-chlorostyrene-co-p-chlorostyrene) [206]. The mean field binary interaction model approach was also successfully applied to polyamides based on various combinations of aliphatic and aromatic units [207]. 

A binary interaction model for miscibility of copolymers in blends. 

These three approaches have found widespread application to a large variety of systems and equilibria types ranging from vapor-liquid equilibria for binary and multicomponent polymer solutions, blends, and copolymers, liquid-liquid equilibria for polymer solutions and blends, solid-liquid-liquid equilibria, and solubility of gases in polymers, to mention only a few. In some cases, the results are purely predictive in others interaction parameters are required and the models are capable of correlating (describing) the experimental information. In Section 16.7, we attempt to summarize and comparatively discuss the performance of these three approaches. We attempt there, for reasons of completion, to discuss the performance of a few other (mostly) predictive models such as the group-contribution lattice fluid and the group-contribution Flory equations of state, which are not extensively discussed separately. 

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