Polymerization phase diagram

Colloidal crystals . At the end of Section 2.1.4, there is a brief account of regular, crystal-like structures formed spontaneously by two differently sized populations of hard (polymeric) spheres, typically near 0.5 nm in diameter, depositing out of a colloidal solution. Binary superlattices of composition AB2 and ABn are found. Experiment has allowed phase diagrams to be constructed, showing the crystal structures formed for a fixed radius ratio of the two populations but for variable volume fractions in solution of the two populations, and a computer simulation (Eldridge et al. 1995) has been used to examine how nearly theory and experiment match up. The agreement is not bad, but there are some unexpected differences from which lessons were learned. 

In addition to all the metallic phase diagrams, a series of volumes devoted to ceramic systems have been published since 1964 by the American Ceramic Society and is still continuing. The original title was Phase Diagrams for Ceramists, now it is named Phase Equilibria Diagrams. Some 25,000 diagrams, binary and ternary mostly, have been published to date. There is no compilation for polymeric systems, since little attention has been devoted to phase diagrams in this field up to now. 

Fig. 8.8 The principle of the Dyson model. Each point in the phase diagram represents a possible composition of a molecular population. The horizontal axis is a, where (a+ 1) is the number of monomer types. On the vertical axis, b represents the quality factor of the polymeric catalysis. The transition region consists of populations which can have both an ordered and a disordered equilibrium state. In the death region there are only disordered states, while in the immortal region (in the Garden of Eden ), there is no disordered state (Dyson, 1988)...

Figure 14. The phase diagram of the gradient copolymer melt with the distribution functions g(x) = l — tanh(ciit(x —fo)) shown in the insert of this figure for ci = 3,/o = 0.5 (solid line), and/o — 0.3 (dashed line), x gives the position of ith monomer from the end of the chain in the units of the linear chain length. % is the Flory-Huggins interaction parameter, N is a polymerization index, and/ is the composition (/ = J0 g(x) dx). The Euler characteristic of the isotropic phase (I) is zero, and that of the hexagonal phase (H) is zero. For the bcc phase (B), XEuier = 4 per unit cell for the double gyroid phase (G), XEuier = -16 per unit cell and for the lamellar phases (LAM), XEuier = 0.

Interactions of such glassy polymeric particles should resemble the collisions of hard spheres. Phase diagrams of the type shown in Fig. 36 have been obtained for various polymer-organic solvent mixtures [85,94,345-353]. 

This section is primarily concerned with the behaviour of simple homo-polymers. The development of viscoelastic theory was intimately linked with the study of polymeric species. This area of activity has led the way in the development of rheological models and experimental design and so is a very important area for the proto-rheologist to understand. So far in this chapter we have taken the approach of developing phase diagrams from a rheological perspective in order to understand linear viscoelastic... 

In a system of significant interest to the present works, Graillard, et al. [62] studied the ternary phase diagrams of the systems polybutadiene-styrene-polystyrene and polybutadiene-block-polystrene-styrene-polystyrene. They showed that the presence of block copolymer increased the miscibility of the two poljrmers, as the styrene component polymerized. Similar effects are probable in the IPN s, as compared with the corresponding blends. 

Figure 2.36 Phase diagram for clay disks and polymers of different degrees of polymerization, T . Reprinted with permission from Y. Lyatskaya and A. C. Balazs, Macromolecules, Vol. 31, p. 6676. Copyright 1998 by the American Chemical Society.

Glass transition determinations Decomposition reaction Reaction kinetics Phase diagrams Dehydration reactions Solid-state reactions Heats of absorption Heats of reaction Heats of polymerization Heats of sublimation Heats of transition Catalysis... 

The most complete insights into the behavior of mixtures of nonpolymeriz-able lipids have come from the phase diagrams of these systems. These data have provided important reference points for the polymerizable lipid systems described next, even though few phase diagrams have been reported for polymerizable lipid mixtures. In spite of this deficiency the polymerization studies have... 

Figure 6 shows the phase diagram of a series of NIPA gels a part of which is ionized by introducing acrylic acid (AAc) as a comonomer [25]. The molar concentration of sodium acrylate was varied from 0 to 70 mM whereas the total molar concentration and crosslinker (BIS) concentration were kept at 700 mM and 81 mM, respectively. After the polymerization, the gel was washed with water. As shown in the figure, the transition temperature increases with inereas-... 

Silica and aluminum phosphate have much in common. They are isoelec-tronic and isostructural, the phase diagrams being nearly identical even down to the transition temperatures. Therefore, aluminum phosphate can replace silica as a support to form an active polymerization catalyst (79,80). However, their catalytic properties are quite different, because on the surface the two supports exhibit quite different chemistries. Hydroxyl groups on A1P04 are more varied (P—OH and A1—OH) and more acidic, and of course the P=0 species has no equivalent on silica. The presence of this third species seems to reduce the hydroxyl population, as can be seen in Fig. 21, so that Cr/AP04 is somewhat more active than Cr/silica at the low calcining temperatures, and it is considerably more active than Cr/alumina. 

The change of lyotropic l.c. behavior of a monomer in the hexagonal phase by polymerization has been described for the first time by Friberg et al. I07,108). A change from the hexagonal monomer phase to the lamellar phase of the polymer was observed and carefully identified. Complete phase diagrams of monomer and polymer, however, were not compared. 

Fig. 47. Phase diagram of the system water-polymeric surfactant (see Table 11,. No. 3)...

Fig. 2.43 Phase diagrams calculated (Hamley and Podneks 1997) within the Landau-Brazovskii approximation, applied to block copolymers by Fredrickson and Helfand (1987) (a) for a degree of polymerization N = 5 x 103, a direct transition between gyroid and dis phases occurs near f = 0.43 (b) for N = 106, there is no direct transition between these phases (Hamley and Podneks 1997).

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.

Fig. 6.43 Phase diagram for a ternary mixture of equal concentrations of A and B homopolymers and symmetric AB diblock (all with equal degrees of polymerization) computed by Holyst and Schick (1992). The Lifshitz tricritical point is shown at L, the line CL is that of continuous transitions from the disordered phase to coexisting A-rich and B-rich phases, and LG is the line of continuous transitions from the disordered to the lamellar phase. LD is the disorder line.

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>.

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