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). 

Due to vibrational anharmonicity, this transfer is resonant only for the K = 1 exchange, which has been considered in a previous section, but it remains, in the liquid, faster by several orders of magnitude than V-T relaxation for diatomics. Relaxation of highly excited I2 and Br2 close to the vibrational dissociation limit has been observed in the dense gas (at liquid densities). These indirect measurements of T, were correlated with the gas diffusion coefficient and should hence be more reasonably accounted for in the framework of an isolated binary interaction model. This interesting exjjerimental system raises the question of the influence of the change in molecular dimensions in higher excited states, due to anharmonicity, on the efficiency of collisional deexcitation. This question could jjerhaps be answered by more precise direct relaxation measurements. 

However, the simple binary interaction model is inadequate to study the sequence effects owing to its assumption of a random distribution. Assuming that the interaction energy parameters of all a-a and b-b pairs are equivalent and equal to zero and that all a-b interactions are equivalent to the average interaction parameter %ab, Balazs et al. [16] expressed xtotas the sum of the contribution of the composition Xcomp an(i the sequence distribution Xdistas follows ... 

Since PEC is a copolymer, description of its interaction with PS is more complex than if it were simply a homopolymer. Binary interaction models have been presented which suggest that copolymer miscibility with a homopolymer can be enhanced by endothermic interactions between the unlike repeat units of the copolymer (11-13). In its simplest form (11). the binary interaction model for the heat of mixing, AHaix, of a copolymer. A, containing repeat units 1 and 2, with a homopolymer, B, containing repeat units 3, is given by... 

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. 

Analysis of the kinetics of the recovery process in terms of r ,ax, To (see Fig. 13.2) provides a further means to quantitatively assess phase behavior (Ellis 1990 Hong et al. 1998). The structural dependence of these parameters has made it possible to investigate the phase behavior of blends containing aromatic polyamides (Ellis 1990). Despite the similarity in structure of the blend components and therefore the close proximity of the glass transition temperatures, Ellis was able to confirm the immiscibUity behavior predicted using the mean field binary interaction model (ten Brinke et al. 1983 Paul and Barlow 1984). 

The binary interaction model would be later shown to estimate an exothermic enthalpy of mixing for miscible blends. For stability at constant temperature and... 

Binary interaction model Intramolecular repulsions Copolymer-homopolymer miscibility Copolymer-copolymer miscibility Terpolymer-terpolymer miscibility Terpolymer-homopolymer miscibility Mean-field approach to obtain interaction parameters Spinodal and phase separation... 

B is preferred since its basis is always clearly a unit mixture of volume. The binary interaction model for the heat of mixing can be extended to multicomponent mixtures as follows ... 

FIGURE 3.1A Compositional window of miscibility in SAN-PMMA blends predicted by binary interaction model. 

In a similar manner, the blend of terpolymer A, styrene-methyl methacrylate-acrylonitrile, and polymer B, a different terpolymer with monomers styrene, methyl methacrylate, and acrylonitrile, can be studied using the binary interaction model and miscibility window obtained ... 

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. 

How would binary interaction model expect to fare for star polymers ... 

What is the role of the chain sequence distribution on the binary interaction model ... 

Can the binary interaction model be applied to block copolymer systems as it is applied to random copolymer systems ... 

The EOS of Sanchez and Lacombe in terms of reduced pressure, temperature, and density is a transcendental equation. In combining this equation with the free energy of mixing equation from the binary interaction model, is a numerical solution needed or can an analytical solution be obtained ... 

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. 

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