Phase Behavior of Binary Polymer Blends

Before discussing the phase behavior of ternary nanoparticle/polymer/polymer mixtures it is useful to briefly recall the fundamentals governing the phase behavior of binary polymer blends. The simplest model describing phase behavior of such 

The Flory-Huggins interaction parameter, Xab. has the meaning of mixing enthalpy divided by the absolute temperature. Sometimes, it is related to solubility parameters of polymers A and B via the following expression [36, 37]  

However, in practice, to fit experimental phase diagrams, one has to make x a more complex (often, non-monotonic) function of T. Sometimes, researchers use a concentration-dependent Flory-Huggins interaction parameter - while this is clearly contrary to the spirit of the original Flory-Huggins theory, it can be useful to successfully fit experimental diagrams (see, e.g.. Reference [38]). For more detailed discussion see, for example. References [38-40]. 

The above theory is based on the idea of incompressible polymer melt. Various alternative formalisms have been proposed where free energy explicitly depended on the pressure and the densities of pure components (see, e.g., Ruzette et ol. [41])  

Still have not found widespread application. Below, we will be mainly using the classical incompressible Flory-Huggins theory and consider its possible extensions when nanopartides are introduced into the system. 

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Exploring physical phenomena, such as phase separation, this book provides methods to design polymer blends and predict the phase behavior of binary polymer blends using desktop computers. 

In order to determine the phase behavior of heterogeneous polymer blends, phase diagrams are usually constructed in terms of the interaction parameter Xi2 and the composition or temperature and composition. Figure 3.2a represents the dependence of AG on as computed from the Flory-Huggins equation (Eq. (3.14)) for a symmetric binary blend (rj = V2 = r). The curves are shown for different values of Xi2> which is the only relevant parameter in the Flory-Huggins equation. For exothermic or adiabatic mixing G =J [Pg.101]

Effective compatibilization of binary polymer blends by addition of a copolymer reduces the dispersed particles size and Vj [Anastasiadis et al, 1987 Wu, 1987 Patterson et ai, 1971]. An illustration is shown on Figure 4.15. The effect of compatibilizer addition is similar to the emulsification of the classical emulsions. In the former systems, the compatibilizer effect on the drop size and Vj follows the same behavior as the emulsion drop size reduction upon addition of a surfactant. The latter behavior is usually described as the titration curve that characterizes the surfactant efficiency. The shape of the titration curve depends on the type of emulsifier and the emulsification process, e.g., mixing time and equipment. However, the amount of emulsifier to saturate the interface also depends on the affinity of emulsifier to the dispersed phase, the size of the dispersion, the orientation of the emulsifier at the interface and its ability to prevent flocculation and coalescence [Djakovic et al., 1987]. A similar behavior is to be expected for polymer blends upon addition of a compatibilizer. 

Ternary Blends. Discussion of polymer blends is typically limited to those containing only two different components. Of course, inclusion of additional components may be useful in formulating commercial products. The recent Hterature describes the theoretical treatment and experimental studies of the phase behavior of ternary blends (10,21). The most commonly studied ternary mixtures are those where two of the binary pairs are miscible, but the third pair is not. There are limited regions where such ternary mixtures exhibit one phase. A few cases have been examined where all three binary pairs are miscible however, theoretically this does not always ensure homogeneous ternary mixtures (10,21). 

One of the most commonly used criteria for establishing the phase behavior in amorphous binary polymer blends is the presence of one or more T s. If the blend is one-phase, a single... 

A general summary of the topic phase diagrams of polymers is given by Porter RS, Jonza JM, KimuraM, DesperCR, George ER (1989) A Review of Phase Behavior in Binary Blends Amorphous, Crystalline, Liquid Crystalline, and On Transreaction. Polymer Eng Sd 29 55-62. 

In the vicinity of the critical point of a binary mixture one observes universal behavior, which mirrors the divergence of the correlation length of composition fluctuations. The universal behavior does not depend on the details of the system but only on the dimensionahty of space and the type of order parameter. Therefore, binary polymer blends fall into the same imiversality class as mixtures of small molecules, metalHc alloys, or the three-dimensional Ising model, hi the vicinity of the critical point, Xc = 2 for a symmetric blend [ 14], the difference of the composition of the two coexisting phases—the order parameter m—vanishes like m - XcN), where the critical exponent... 

The model has,also,been applied to mixture of three random copolymers. Conditions for the enhancement of compatibility in polymer blends by the use of a third copolymer are examined as well as the influence of temperature in the phase behavior of ternary mixtures whose constituent binaries may show either UCST or LCST. These findings are, as yet, only theoretical and for space limitation they are not reproduced here. They will be, however, the subject of a forthcoming publication. 

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