Binary blend phase diagrams

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]

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]. 

Figure 27 Temperature - diblock concentration plane of the PB/PS blend phase diagram. The composition of the PB/PS homopolymer blend was the critical one of the binary blend. The right figure shows the Lifshitz part. Meaning of symbols (,) line of critical points with (-) the double critical point (() and (v) Lifshitz line between disordered and microemulsion phases (DpE and BpE droplet and bicontinuous microemulsion), respectively (B) transition from disordered to micro emulsion phase, ix) Lifshitz transition point LLT, (A) Ordering transition to lamellar phase. Erom Pipich, V. Schwahn, D. Willner, L. Phys. Rev. Lett. 2005, 94,117801 J. Chem. Phys. 2005, 123,124904-124916 ...

Fig. 6.35 Calculated constant y N ( = 12) phase diagram for a binary blend of a diblock and homopolymer with equal degree of polymerization (/ = 1) as a function of the volume fraction of homopolymer, 0h, and the composition of the diblock (/) (Matsen 1995ft). For clarity, only the largest biphasic regions are indicated.

Self-consistent field theory has been applied to analyse the phase behaviour of binary blends of diblocks by Shi and Noolandi (1994,1995), Matsen (1995a) and Matsen and Bates (1995). Mixtures of long and short diblocks were considered by Shi and Noolandi (1994) and Matsen (1995a), whilst Shi and Noolandi (1995) and Matsen and Bates (1995) calculated phase diagrams for blends of diblocks with equal degrees of polymerization but different composition. 

Fig. 6.46 Calculated phase diagram cube for binary blends of symmetric diblocks (equal degrees of polymerization) with xN = 20 (Shi and Noolandi 1995). The diblock compositions are denoted /,/2 and the blend composition as cf>.

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). 

Figure 17.13. Isosolid SFC temperature phase diagrams, as a funetion of blend eomposition, for binary systems eontaining FIMF-CB (A), MMF-CB (B) and AMF-CB (C).

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)...

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 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...

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.

Figure 27.1 shows a schematic phase diagram for binary blends showing the relationship between free energy of mixing AG ) and blend composition cp). For sample A, an immiscible system is obtained (AG j > 0), for sample B a fully miscible system is obtained in which AG < 0, and C represents a partially miscible system that satisfies AG < 0 for all compositions, but d AG Idcpi is lower than 0 at certain compositions, indicating that at these compositions the blend will be immiscible. 

---