Random copolymers, phase diagram

First, different data sets (away from and at binodal) must be scaled to the identical temperature and concentrations. This is possible for a few blends with (assumed) identical interaction parameter but characterized by different chain lengths (Na, Nb) and hence different phase diagrams. This method is used for isotopic polystyrene mixtures. If the parameter ySANs((t)) is linear with 1/T for each concentration < > then %SANS(=const, T) can be reasonably extrapolated to regions at or inside coexistence curve. We use this solution for olefinic blends composed of random copolymers E EE. Here the self-same mixtures are used in both bulk SANS samples and in profiled thin films. 

Figure 15 shows the phase diagram of block copolymers and random copolymers. For comparison, the phase diagram of a homopolymer having the same molecular weight is also shown in the figure. As we can see, the number of blocks on the polymer has a dramatic effect on the phase behavior. The... 

Fig. 15. Phase diagram of block copolymers and random copolymers. Circles are results for homopolymers squares are results for diblock copolymers diamonds are results for triblock copolymers up triangles are results for a mixture of A-B-A and B-A-B triblock copolymers left triangles are results for tetrablock copolymers X s are results for random copolymers with average sequence length 1 = 55 crosses are results for random copolymers with / = 20 asterisks are results for a completely random copolymer.

Thermodynamic equations are formulated for the isomorphic behavior of A-B type random copolymer systems, in which both A and B comonomer units are allowed to cocrystallize in the common lattices analogous to, or just the same as, those of the corresponding homopolymers poly(A) or poly(B). It is assumed that, in the lattice of poly (A), the B units require free energy relative to the A units and vice versa. On the basis of the derived thermodyn-amie equations, phase diagrams are proposed for the A-B random copolymers with cocrystallization. The melting point versus comonomer composition curve predicted by this diagram is very consistent with that experimentally observed for the P(3HB-co-3HV) copolymers, as shown in Fig. 21.1. It is suggested that the minor comonomer unit with a less bulky structure cocrystallize thermodynamically simpler than that with a more bulky structure. 

Rubbers and PESs are initially miscible with cyanate ester monomers. Phase separation occurs during the reaction. By plotting the phase diagrams (temperature vs. conversion), it is possible to compare the effects of chain ends and AN content in butadiene-acrylonitrile random copolymers and the effect of molar mass in PES. The cyanate ester monomer based on bisphenol A is a better solvent than DPEDC, and both dicyanates are better solvents than DGEBA. 

Fig. 11.18 The phase diagram of a conformationally symmetric diblock copolymer showing fully ordered phase forms, which in actual practice can often be randomly disordered (from Hamley (2004b) courtesy of Wiley).

Figure 7.22 represents a typical DSC ttace of copolymer melting. The poly(ethylene-co-vinyl acetate) is expected to follow a eutectic phase diagram. The melting temperature decreases from the value of the homopolymer, but the crystallinity decreases much more than expected from the small amount of noncrystallizable comonomer. Also, the crystallization of a eutectic component, required by an equilibrium phase diagram, seen for example in Fig. 7.1, is rarely observed in random copolymers with short repeating units, as in vinyl polymers. 

The almost 30 examples of phase diagrams of this section show that equilibrium is rare in copolymers. Nanophase separation is found frequently when partial crystallization occurs. Dissolutions are possible by randomizing the conformations and by chemical reaction. 

The phase diagram of linear coil-coil diblock copolymers (for instance PS-PI) has been extensivdy studied and is well established (see Figure 12, the PS-PI case)." This is for the case of cyclic block copolymers. However, theoretical modds using the Random Phase Approximation (RPA) model (see Figure 13) and simulations" predicted a transition from the disordered to an ordered phase (miao-phase separation) at/N, diblock copolymer as compared to the dassical result for linear diblocks for which/N, mRgt= 10.5, 1.95. 

The dominant process in this market segment is the Spheripol process by Basell. Similar to the dominance achieved by the Phillips process in HOPE, roughly one-third of the world s polypropylene is produced using the Spheripol process. The Spheripol process uses loop reactors. A small loop reactor is used to prepolymerize the catalyst the main polymerization, for homopolymer or random copolymer, takes place in one or two loop reactors. For impact copolymer production, a gas-phase reactor is required after the loop reactor because of the limited solubility of ethylene in liquid propylene. A typical flow diagram of the Spheripol process is shown in Figure 2.40. 

The phase diagrams of PO-type random copolymers may be more complex than those for homopolymers with different, but uniform, molecular structure. Thus, similar to SLCT, but simplified further, is the basic lattice cluster theory (BLCT). The version was developed for the random copolymers or random and block copolymer systems. 

F. 11 (a) Phase diagram showing the variation in critical adsorption strength = (ej /e ) — 1) with block length M. (b) Critical adsorption potential (CAP) versus composition p frandom copolymers. Solid line is a best fit of the theoretical prediction ej = /n[(expej + p — )//>] Here, CAP ej = 1.716. Symbols denote the CAP for multiblock copolymers with block size Af. Reprinted (adapted) with pmnission from [52]. Copyright 2008 American Chemical Society... 

The phase diagram for random copolymers with quenched disorder that gives the change in the critical adsorption potential, e, with changing percentage of the sticking A-monomers, p, has also been determined from extensive computer simulations carried out with the two employed models (cf. Fig. 11b). We observed... 

Four series of IPNs were polymerized, the compositions of which are given in Table 5.2. The underlined polymer was polymerized first. This was always the elastomer PEA (normal IPNs), except for series I (inverse series), where the plastic homopolymer PS or PMMA was polymerized first. The B in PEAB indicates that the PEA contained 1% butadiene as a comonomer to permit staining for electron microscopy. The letters E, L, P, and I denote elastomeric, leathery, plastic, and inverse series, respectively. In compositions containing both S- and MMA-mers, a random copolymer was formed with the indicated composition. The actual compositions employed can be portrayed with the aid of a pseudoternary phase diagram, as shown in Figure 5.1 for the normal IPNs. Only the border compositions (no random... 

Fig. 4. Theoretically predicted phase diagrams of diblock copolymer A/- B f melts in the plane of jjarameters yJV (y = Flory-Huggins parameter, N = chain length) and composition / [where f = NaKNa + JVb)], according to the Leibler (29) random phase approximation (a) and the BVedrickson-Helfand (30) Hartree approximation (b). Mesophases considered are the lamellar (LAM) phase, the hexagonal (HEX) phase where cylinders rich in the minority component are arranged periodically, a cross section perpendicular through the cylinders yielding a triangular lattice, and the body-centered cubic (BCC) lattice of spherical micelles. From Ref. 32.

Recently Koningsveld and Kleintjens made some numerical analyses of possible phase diagrams of three random copolymers, in particular with the aim of identifying conditions necessary for a given copolymer to act as a compatibilizer. They deduced that addition of copolymer 3 with the composition intermediate between the other two copolymers 1 and 2 would not in general induce compatibilization unless components 1 and 2 were already of fairly low molecular weight. 

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