Binary polymer blend, phase diagram

Figure 5.1. Schematic illustrations of the general types of polymer blend phase diagrams, for the simplest case of binary blends without the additional complications that are sometimes introduced by competing processes such as the crystallization of one of the components. The coefficients dg and d refer to the general functional form for %Ag given by Equation 5.7 [10].

This chapter summarizes the available data (x and / parameters) for polymer-polymer interactions in the melt state. The equations that are necessary to convert x parameters into binary homopolymer blend phase diagrams are also provided. We also summarize methods for predicting the properties of nanostructures with interfaces that are stabilized by the presence of block copolymers. 

Fig. 10.26 Schematic illustration of types of possible polymer blend phase diagrams, for binary blends where additional complications that can be introduced by competing processes (such as crystallization of a component) are absent. The coefficients di and d2 refer to a general functional form (as a function of temperature and component volume fractions) of the binary interaction parameter that quantifies deviations from ideal mixing (Courtesy Online resources)...

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]

Fig. 1. Temperature T vs volume fraction phase diagram of a binary polymer blend. Solid line denotes the coexistence curve (binodal) while the me dashed line marks the spinodal line. Binodal connects with spinodal at the critical point (( )c> Tc)...

Figure 3.25. Phase diagram of a binary polymer blend with miscibihty gap (UCST) and intersecting crystal/melt coexistence curve. The curve is extrapolated into the miscibility gap. Quenching routes A to D are explained in the text. For routes B and C, the quenching-induced phase...

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. 

Figure 15 (a) Phase diagram of a binary polymer blend N= 32) as obtained from Monte Carlo simulations of the bond fluctuation model. The upper curve shows the binodais in the infinite system the middle one corresponds to a thin film of thickness D=2.8/ e and symmetric boundary fields [wall = 0.16, both of which prefer species A (capillary condensation). The lower curve corresponds to a thin film with antisymmetric surfaces (interface localization/delocalization). The arrow marks the location of the wetting transition. Full circles mark critical points open circles/dashed line denotes the triple point, (b) Coexistence curves in the (T, A/y)-plane. Circles mark critical points, and the diamond indicates the location of the wetting transition temperature. It is indistinguishable from the temperature of the triple point. Adapted from Muller, M. Binder, K. Phys. Rev. 2001, 63, 021602. ... 

Fig. 1.14 Phase diagram of binary polymer blend with LCST (adapted from Higgins et al. 2010)...

A phase diagram of a binary polymer blend can be derived from the Tg of the demixed phases under the following conditions ... 

Using Figure 3.2 and the corresponding equations, it is possible to construct a phase diagram of a binary polymer blend in terms of Xizri and or, with the knowledge of temperature dependence of Xii, in terms of Tand (pi. Figure 3.3... 

Figure 14 Phase diagram for a binary polymer blend...

Matkar et al. have hypothesized what would happen to crystalline blend phase diagrams if one relaxes the last assumption of the Floty diluent theory of crystalline polymer solutions, namely, the complete rejection of polymeric solvent from the crystalline phase [66, 67]. In addition, Xu et al. have developed a new theory for a binary crystalline polymer blends based on a combination of liquid-liquid phase separation and solid-liquid phase transition by taking into consideration the coupling interaction between the solid crystal and amorphous liquid phase [71]. 

When a binary polymer blend (A-polymer and B-polymer) is rapidly quenched from one-phase to the two-phase region of the phase diagram (e.g., by a rapid temperature change), the system undergoes phase separation into A-rich and B-rich domains. It is often convenient to characterize the extent of phase separation by measuring the characteristic domain size as function of time, I(t). (Characteristic domain size could be defined as, for example, total volume divided by the total... 

Fig. 7. Phase diagram for a binary blend mixture of a flexible (A component) and a rigid (B component) polymers with NA = 200, N = 800, vA = vB = 1, and W B/kBTxAB = 0.4 as predicted by the RPA...

Qian, C. Mumby, S.J. Eichinger, B.E., "Phase Diagrams of Binary Polymer Solutions and Blends," Macromolecules, 24, 1655 (1991). 

The most basic question when considering a polymer blend concerns the thermodynamic miscibility. Many polymer pairs are now known to be miscible or partially miscible, and many have become commercially Important. Considerable attention has been focussed on the origins of miscibility and binary polymer/polymer phase diagrams. In the latter case, it has usually been observed that high molar mass polymer pairs showing partial miscibility usually exhibit phase diagrams with lower critical solution temperatures (LCST). 

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 16.5. Binary phase diagram at constant pressure, with the lower critical solution temperature,= LCST. The solid and broken lines indicate binodal and spinodal curves, respectively. The single phase, two meta-stable regions, and a spinodal region are shown. Majority of polymer blends (whose miscibility depends on specific interactions) shows this type of behavior.

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