Copolymer disordered

Keywords Block copolymer Disordered micelles Fluctuation effect Order-disorder transition Self-consistent mean-field theory... 

Micellar structure has been a subject of much discussion [104]. Early proposals for spherical [159] and lamellar [160] micelles may both have merit. A schematic of a spherical micelle and a unilamellar vesicle is shown in Fig. Xni-11. In addition to the most common spherical micelles, scattering and microscopy experiments have shown the existence of rodlike [161, 162], disklike [163], threadlike [132] and even quadmple-helix [164] structures. Lattice models (see Fig. XIII-12) by Leermakers and Scheutjens have confirmed and characterized the properties of spherical and membrane like micelles [165]. Similar analyses exist for micelles formed by diblock copolymers in a selective solvent [166]. Other shapes proposed include ellipsoidal [167] and a sphere-to-cylinder transition [168]. Fluorescence depolarization and NMR studies both point to a rather fluid micellar core consistent with the disorder implied by Fig. Xm-12. 

It must be pointed out that deviations from such a simple relationship do occur. For example, since random copolymerisation tends to promote disorder, reduce molecular packing and also reduce the interchain forces of attraction, the Tg of copolymers is often lower than would be predicted by the linear relationship. Examples are also known where the Tg of the copolymer is higher than predicted. This could occur where hydrogen bonding or dipole attraction is possible between dissimilar comonomer residues in the chain but not between similar residues, i.e. special interchain forces exist with the copolymers. 

With block copolymers two types of effect have been observed. In some instances a transition corresponding to each block is observable whilst in other cases a single transition is observed, usually close to that predicted by a linear relationship even where random copolymers show large deviations. This is because the blocks reduce both the contacts between dissimilar comonomer residues and also the disorder of the molecules which occurs in random copolymer systems. 

Using the so-called "block copolymers (a block of Na A-monomers at one end is covalently bonded to a block of Nb B-monomers) one can also realize the analogy of order-disorder phenomena in metallic alloys with polymers one observes transitions from the disordered melt to mesophases with various types of long range order (lamellar, hexagonal, cubic, etc ). We shall not consider these phenomena here further, however... 

Microdomain stmcture is a consequence of microphase separation. It is associated with processability and performance of block copolymer as TPE, pressure sensitive adhesive, etc. The size of the domain decreases as temperature increases [184,185]. At processing temperature they are in a disordered state, melt viscosity becomes low with great advantage in processability. At service temperamre, they are in ordered state and the dispersed domain of plastic blocks acts as reinforcing filler for the matrix polymer [186]. This transition is a thermodynamic transition and is controlled by counterbalanced physical factors, e.g., energetics and entropy. 

FIGURE 5.17 Temperature versus G —the shear storage modulus at a frequency of 1.6 Hz for diblock copolymer poly(ethylene propylene)-poly(ethylethylene) (PEP-PEE). The order-disorder transition (ODT) calculated to be 291°C 1°C. (From Rosedale, J.H. and Bates, F.S., Macromolecules, 23, 2329, 1990. With permission of American Chemical Society.)... 

LeiblerL., Theory of microphase separation in block copolymers. Macromolecules, 13, 1602, 1980. Eoerster S., Khandpur A.K., Zhao J., Bates E.S., Hamley I.W., Ryan A.J., and Bras W. Complex phase behavior of polyisoprene-polystyrene diblock copolymers near the order-disorder transition. Macromolecules, 21, 6922, 1994. 

Hashimoto T., Order disorder transition in block copolymers. Thermoplastic Elastomers A Comprehensive Review (Legge N.R., Holden G., and Schroeder H.E., eds.), Hanser Publishers, Munich, 1987. Bianchi U. and Pedemonte E., Morphology of styrene butadiene styrene copolymer. Polymer, 11, 268, 1970. 

Reactive compatibilization can also be accomplished by co-vulcanization at the interface of the component particles resulting in obliteration of phase boundary. For example, when cA-polybutadiene is blended with SBR (23.5% styrene), the two glass transition temperatures merge into one after vulcanization. Co-vulcanization may take place in two steps, namely generation of a block or graft copolymer during vulcanization at the phase interface and compatibilization of the components by thickening of the interface. However, this can only happen if the temperature of co-vulcanization is above the order-disorder transition and is between the upper and lower critical solution temperature (LCST) of the blend [20]. 

Covalent polymeric networks which are completely disordered. Continuity of structure is provided by an irregular three-dimensional network of covalent links, some of which are crosslinks. The network is uninterrupted and has an infinite molecular weight. Examples are vulcanized rubbers, condensation polymers, vinyl-divinyl copolymers, alkyd and phenolic resins. 

Fig. 35 Phase diagrams AB miktoarm-star copolymers for n = 2, n = 3, n = 4 and n = 5. mean-field critical point through which system can transition from disordered state to Lam phase via continuous, second-order phase transition. All other phase transitions are first-order. From [112]. Copyright 2004 American Chemical Society...

Usually the discussion of the ODT of highly asymmetric block copolymers in the strong segregation limit starts from a body-centred cubic (bcc) array of the minority phase. Phase transitions were calculated using SOFT accounting for both the translational entropy of the micelles in a disordered micelle regime and the intermicelle free energy [129]. Results indicate that the ODT occurs between ordered bcc spheres and disordered micelles. 

Fig. 59 Phase diagram for blend consisting of two symmetric PS-6-PI block copolymers of different molecular weights in parameter space of temperature and fraction of higher molecular weight copolymer, . disordered state lamella A PS cylinder. From [179]. Copyright 2001 American Chemical Society... 

In what follows we will discuss systems with internal surfaces, ordered surfaces, topological transformations, and dynamical scaling. In Section II we shall show specific examples of mesoscopic systems with special attention devoted to the surfaces in the system—that is, periodic surfaces in surfactant systems, periodic surfaces in diblock copolymers, bicontinuous disordered interfaces in spinodally decomposing blends, ordered charge density wave patterns in electron liquids, and dissipative structures in reaction-diffusion systems. In Section III we will present the detailed theory of morphological measures the Euler characteristic, the Gaussian and mean curvatures, and so on. In fact, Sections II and III can be read independently because Section II shows specific models while Section III is devoted to the numerical and analytical computations of the surface characteristics. In a sense, Section III is robust that is, the methods presented in Section III apply to a variety of systems, not only the systems shown as examples in Section II. Brief conclusions are presented in Section IV. 

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