Ordered copolymers phase equilibrium-temperature

In order to apply Equation (5.12), an expression for dG > is obtained in terms of the volume fraction of the component in the blend, copolymer composition, temperature, and pressure. Phase equilibrium is established. Equation (5.11) must be satisfied by any single phase that is stable with respect to the alternative of splitting into two phases. It requires that the Gibbs free energy for an equilibrium state be the minimum value with respect to all possible changes at the given temperature, T, and pressure, P. Two cases are shown in Figure 5.1 ... 

For a specific polymer, critical concentrations and temperatures depend on the solvent. In Fig. 15.42b the concentration condition has already been illustrated on the basis of solution viscosity. Much work has been reported on PpPTA in sulphuric acid and of PpPBA in dimethylacetamide/lithium chloride. Besides, Boerstoel (1998), Boerstoel et al. (2001) and Northolt et al. (2001) studied liquid crystalline solutions of cellulose in phosphoric acid. In Fig. 16.27 a simple example of the phase behaviour of PpPTA in sulphuric acid (see also Chap. 19) is shown (Dobb, 1985). In this figure it is indicated that a direct transition from mesophase to isotropic liquid may exist. This is not necessarily true, however, as it has been found that in some solutions the nematic mesophase and isotropic phase coexist in equilibrium (Collyer, 1996). Such behaviour was found by Aharoni (1980) for a 50/50 copolymer of //-hexyl and n-propylisocyanate in toluene and shown in Fig. 16.28. Clearing temperatures for PpPTA (Twaron or Kevlar , PIPD (or M5), PABI and cellulose in their respective solvents are illustrated in Fig. 16.29. The rigidity of the polymer chains increases in the order of cellulose, PpPTA, PIPD. The very rigid PIPD has a LC phase already at very low concentrations. Even cellulose, which, in principle, is able to freely rotate around the ether bond, forms a LC phase at relatively low concentrations. 

Fig. 47a-d. Hartree approximation for the free energy density fH(A) of a symmetrical diblock copolymer melt plotted vs the amplitude A of a concentration wave with q = q. For high temperatures (X < Xo) only the disordered phase (A = 0) existsfa). Aty0 N the limit of metastability of the lamellar ordering in the disordered phase appears (b), two metastable minima at A 0 develop, which become stable for % = %t- (c). Forx > X, the disordered state(A = 0) is only metastable (d), the lamellar phase being in stable thermal equilibrium. From Fredrickson and Binder [61]... 

In diblock copolymer melts, the free energy of a micro-phase-separated state can be shown to favor ordered domain structures where the mutual organization of A-and B-domains form regular lattices. The equilibrium structure depends on the relative size of the respective polymer blocks, the overall polymer size and the temperature (or rather the product xN of the Flory-Huggins interaction parameter and the degree of polymerization). 

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