Interaction energy density

FIGURE 11.12 Interaction energy density versus 4-methyl styrene content. (From Raboney, M., Gamer, R.T., Elspass, C.W., and Peiffer, D.G., Phase Behavior of Brominated Poly(Isobutylene-co-4-Methylstyrene)/ General Purpose Rubber Blends. Rubber Division, Proceedings of the American Chemical Society, Nashville, TN, Sept. 29-Oct. 2, 1998, Paper No. 36.)... 

When the interaction energy density is positive, equation 5 defines a critical temperature of the UCST type (Fig. la) that is a function of component molecular weights. The LCST-type phase diagram, quite common for polymer blends, is not predicted by this simple theory unless B is... 

We have now collected almost all the pieces required for a first version of COSMO-RS, which starts from the QM/COSMO calculations for the components and ends with thermodynamic properties in the fluid phase. Although some refinements and generalizations to the theory will be added later, it is worthwhile to consider such a basic version of COSMO-RS because it is simpler to describe and to understand than the more elaborate complete version covered in chapter 7. In this model we make an assumption that all relevant interactions of the perfectly screened COSMO molecules can be expressed as local contact energies, and quantified by the local COSMO polarization charge densities a and a of the contacting surfaces. These have electrostatic misfit and hydrogen bond contributions as described in Eqs. (4.31) and (4.32) by a function for the surface-interaction energy density... 

For such systems, the difference of the interaction energy density, AP, has been considered a measure of the binary interactions between polymeric segments, proportional to either Y, or B [Sanchez, 1989]. 

Instead of Xn interaction energy density, can be used both parameters are related by ... 

It is interesting to note that the temperature coefficient /It of the interaction energy density A is the largest and positive with PS/PVME blend, decreases with the copolymer blends in the reverse order to the above and finally... 

Table 2. Best fitting parameters for the polymer-polymer interaction energy density determined from fit to observed cloud points...

Roe and Zin analyzed the value of the polymer-polymer interaction energy density and its temperature dependence obtained in their work. Starting from the Flory equation-of-state theory they derived the following expression for A ... 

It should be noted that when the polymer sample employed is not strictly monodisperse, the A values evaluated from cloud point meaurements could entail some error. It has been shown that the error is more likely to affect the concentration dependence and temperature dependence of the interaction energy density. However, in this work, the pdydispersities of the copolymers used are moderate, ranging from 1.2 to 1.5, and also comparable among the several copolymers studied. In comparing the relative compatibility of various styrenic derivative copolymers with PVME, the conclusions drawn should be unaffected by any minor erros due to the differences in the molecular weight distributions. 

B interaction energy-density parameter that does not depend on the definition of a... 

Table 1 Interaction energy density of selected pol)rpropylene blends...

Enthalpies of mixing can be determined, in principle, calorimetrically but for polymer-polymer mixtures the inherent immiscibility of the components and lack of contacts between them means that these parameters cannot normally be determined directly. It is possible to estimate heats of mixing from mixtures of oligomeric analogues, which are often miscible by virtue of their greater entropy of mixing. The interaction energy density B, related to %aB 1 deter-... 

Figure 4.43 Melting point depression analysis to obtain the interaction energy density B for PEO-PU blends. The slope gives B = -14 J cm" ...

By using experimental values of the binary interaction parameters it is possible to calculate miscibility maps and therefore predict the phase behavior of poly-mer/copolymer, copolymer/copolymer, and more complex blends. A list of segment-segment interaction parameters and corresponding interaction energy densities,... 

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 interaction energy densities at the drying temperature of 150°C from the above analysis are Bams-mma= 0-12 cal/cc Bmma-an= 4.32 cal/cc Bams-an= 7.96 cal/cc. The larger values of 5, compared with values indicate possible EOS contributions. The compositional window of miscibility of copolymer-homopolymer blends of AMS-AN copolymer and PMMA homopolymer for the binary interaction parameter values obtained is shown in Figure 3.5. The B values are plotted as a function of AN composition in the copolymer for different volume fractions of the blend. 

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