Phase diagrams of polymer blends

Phase diagrams of polymer blends and solutions (open symbols are binodals and filled symbols are spinodals). (a) Polymer blends of poly(vlnyl methyl ether) (A/ = 51 500 g mol ) and various molar masses of polystyrene (circles have Af = 10 000 g mol, squares have M = 20400 g moP, hexagons have M=5l 000 g mol , diamonds have A/ = 200000 g moP ), data from T. K. Kwei and T. T. Wang, in Polymer Blends, Vol. 1 (D. R. Paul and S. Newman, editors). Academic Press, 1978. (b) Polyisoprene solutions in dioxane------... 

The phase diagrams of polymer blends, the pseudo-binary polymer/polymer systems, are much scarcer. Furthermore, owing to the recognized difficulties in determination of the equilibrium properties, the diagrams are either partial, approximate, or built using low molecular weight polymers. Examples are fisted in Table 2.19. In the Table, CST stands for critical solution temperature — L indicates lower CST, U indicates upper CST (see Figure 2.15). 

FIGURE 16 General phase diagram of polymer blends, phase behavior can be monitored in the window between and T, areas enclosed by the curves are regions of phase instability. 

Generally, most polymer pairs of high molecular weight are immiscible in the range from glass transition temperature (Tg) to thermal decomposition temperature (T ). It is difficult to mix polymers at a molecular level even for polymer pairs with similar structures, e.g., polyethylene (PE) and polypropylene (PP). To discuss the thermodynamics for the miscibility and the phase diagram of polymer blends, the Flory-Huggins equation has been widely used (Flory 1953),... 

MIY Miyashita, N., Okada, M., and Nose, T., Critical exponents and phase diagram of polymer blend solutions Polystyrene/poly(methyl methaciylate)/d6-benzene system. Polymer, 35, 1038, 1994. 

Phase diagrams of polymer blends under atmospheric pressure are usually presented in terms of the variables 0a and T. Emanating from the discussed universal phase diagram in terms of x and 0a, these can be obtained by introducing into the consideration the temperature dependence of the Flory-Huggins parameter. This function, x( )> fhen solely determines the appearance. For different types of temperature dependencies x(T), different classes of phase diagrams emerge and we discuss them in this section. 

Typical of polymer blends is that phase separation occurs when the temperature is increased to a certain lower critical solution temperature (LCST) (Fig. 4.19). The upper critical solution temperature (UCST) behaviour predominates in systems with small-molecule solvents (Fig. 4.19). The equation-of-state theories can relatively adequately describe the phase diagrams of polymer blends. 

Fig. 14. Schematic phase diagram of a blend solution of immiscible polymers Pi and P2. A - initial blend solution, B - stability limit, C - onset of phase separation, D - slowing down of phase separation owing to enhanced viscosity...

Very recent Monte Carlo simulations and self consistent mean field calculations [223] have shown that wetting properties might be reflected in the phase diagram of a blend confined between symmetric selective surfaces Close to Tw a convex curvature is exhibited by the phase diagram on the side poor in preferentially adsorbed polymer. Also the temperature dependence of Ap changes around the wetting point Tsv. 

Another interesting application of HPTMC is encountered in the study of compressibility effects on the phase behavior of polymer blends. While much theoretical work has been devoted to describe the temperature dependence of miscibility for polymer blends, there are relatively few studies of the effect of pressure on miscibility. To a large extent, this is due to the fact that most theoretical models assume that polymer blends are incompressible. HPTMC can be used to determine the miscibility of blends as a function of pressure. Figure 11 shows the phase diagrams for two above-mentioned asymmetric polymer blends. For both of these systems, we can see that in... 

PC/ABS blend is an injection moldable material widely used for automotive parts. These blends, developed in 1960, can be prepared by simple meltmixing of PC with ABS, without any compatibilizer. In this early stage of polymer blends technology, the phase diagram of polymer/polymer mixture, the spinodal decomposition, and the effect of the flow fields were not seriously considered. Nowadays, using these concepts, one can describe the processes that are behind the simple melt-mixing . 

Hess, M. and Lopez, B. (1997) Phase diagrams of polymer liquid crystals and polymer liquid crystal blends relation to mechanical properties, in this volume. 

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. 

One can see that when p = I, this equation can be reduced to the Flory-Huggins-Scott equation for binary polymer blends. The lattice fluid theory can predict both UCST and LOST (lower critical solution temperature) types of phase diagrams for polymer blends, with further considerations of speciflc interactions (Sanchez and Balazs 1989), see more introductions about LOST in Sect. 9.1. 

Classical thermodynamics can be used to predict phase diagrams in polymer blends on the basis of Eq. (19.2). We present the governing equations assuming that x is only a function of T. The spinodal curve, i.e., the curve enclosing the region within which a homogeneous mixture is thermodynamically unstable, is given by... 

Fig. 8.17 Schematic representation of phase diagram in polymer blend with polymerization (a) monomer/polymer blend before polymerization, (b) polymer/polymer blend afto polymerization. Solid circle ( ) represents pol5anerization c

N.Y. Vaidya, C.D. Han, Temperature-composition phase diagrams of binary blends of block copolymer and homopolymer. Polymer 43 (2002) 3047-3059. 

Figure 1. Schematic diagram of polymer blend and diblock copolymer phase behavior for systems that exhibit a miscibility gap.

Figure 2.5. Generalized phase continuity diagram, of polymer blends, as controlled by viscosity, 17, and weight fraction, w, for polymers 1 and 2. At equal viscosities and weight fractions (marked point), or along idealized curve, some aspects of dual phase continuity may be initiated.

Polymer alloys and composites have become an attractive research field world-wide because of their practical and theoretical significance. Miscibility and phase separation arc the key topics in this field. With the development of criterion techniques for miscibility, complicated phase diagrams for polymer blends were obtained which cannot be explained by the... 

Phase diagrams of polymer-polymer blend systems and polymer-solvent mixtures can be constructed as a function of tanperature vs. composition. Two important factors need to be considered when constructing phase diagrams (1) equilibrium and (2) stability. It can be shown from the laws of thermodynamics and reversibility that the equilibrium sate of a closed systan is that state at which the total Gibbs free energy is a minimum with respea to aU possible changes at the given temperature and pressure. At equilibrium ... 

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