Disordered phase, block copolymers

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. 

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... 

An A-B diblock copolymer is a polymer consisting of a sequence of A-type monomers chemically joined to a sequence of B-type monomers. Even a small amount of incompatibility (difference in interactions) between monomers A and monomers B can induce phase transitions. However, A-homopolymer and B-homopolymer are chemically joined in a diblock therefore a system of diblocks cannot undergo a macroscopic phase separation. Instead a number of order-disorder phase transitions take place in the system between the isotropic phase and spatially ordered phases in which A-rich and B-rich domains, of the size of a diblock copolymer, are periodically arranged in lamellar, hexagonal, body-centered cubic (bcc), and the double gyroid structures. The covalent bond joining the blocks rests at the interface between A-rich and B-rich domains. 

The mean-field SCFT neglects the fluctuation effects [131], which are considerably strong in the block copolymer melt near the order-disorder transition [132] (ODT). The fluctuation of the order parameter field can be included in the phase-diagram calculation as the one-loop corrections to the free-energy [37,128,133], or studied within the SCFT by analyzing stability of the ordered phases to anisotropic fluctuations [129]. The real space SCFT can also applied for a confined geometry systems [134], their dynamic development allows to study the phase-ordering kinetics [135]. 

The structure factor diverges at a spinodal point defined by 1 (xN)s = F(x, f) where x is given by eqn 2.10 with q = q. The spinodal for block copolymers is close to, but not identical to, the ODT (except for symmetric block copolymers in mean field theory) and defines the stability limit of the disordered phase. 

X = A + BIT, where A and B are constants). Thus S(q )should change linearly with 1/7. t his was indeed observed by Hashimoto etal. (1983b) at high temperatures however, at a temperature associated with the transition from the homogeneous disordered phase to the ordered phase, a deviation from linear behaviour was found. Such deviations are now ascribed to the effects of composition fluctuations (Bates et al. 1988 Lodge et al. 1996), and the crossover from linear to non-linear dependence of S(q ) on 1/7 does not correspond to the order disorder transition, rather the mean-field to non-mean-field transition (see Section 2.2.1 for block copolymer melts). 

Fig. 6.3 Schematic phase diagram for lamellar PS-PB diblocks in PS homopolymer (volume fraction 0h). where the homopolymer Mv is comparable to that of the PS block (Jeon and Roe 1994). L is a lamellar phase, I, and I2 are disordered phases, M may correspond to microphase-separated copolymer micelles in a homopolymer matrix. Point A is the order-disorder transition.The horizontal lines BCD and EFG are lines where three phases coexist at a fixed temperature and are lines of peritectic points. The lines BE and EH denote the limit of solubility of the PS in the copolymer as a function of temperature.

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