Block ordered phases

Shi A C, Noolandi J and Desai R C 1996 Theory of anisotropic fluctuations in ordered block copolymer phases Macromolecules 29 6487... 

T. Pusztai, L. Granasy. Monte Carlo simulation of first-order phase transformations with mutual blocking of anisotropically growing particles up to all relevant orders. Phys Rev B 57 14110, 1998. 

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]. 

Nb02.5 and this was described in detail in elegant papers by Anderson (1970, 1973). Ordered phases are based on shear structures, with parallel CS planes (double crystallographic shear) separating the blocks of the ReOs lattice. Ternary and intergrowth block structures have been discovered by extensive HRTEM... 

The association of block copolymers in a selective solvent into micelles was the subject of the previous chapter. In this chapter, ordered phases in semidilute and concentrated block copolymer solutions, which often consist of ordered arrays of micelles, are considered. In a semidilute or concentrated block copolymer solution, as the concentration is increased, chains begin to overlap, and this can lead to the formation of a liquid crystalline phase such as a cubic phase of spherical micelles, a hexagonal phase of rod-like micelles or a lamellar phase. These ordered structures are associated with gel phases. Gels do not flow under their own weight, i.e. they have a finite yield stress. This contrasts with micellar solutions (sols) (discussed in Chapter 3) which flow readily due to a liquid-like organization of micelles. The ordered phases in block copolymer solutions are lyotropic liquid crystal phases that are analogous to those formed by low-molecular-weight surfactants. 

This chapter is concerned with experiments and theory for semidilute and concentrated block copolymer solutions.The focus is on the thermodynamics, i.e. the phase behaviour of both micellar solutions and non-micellar (e.g. swollen lamellar) phases. The chapter is organized very simply Section 4.2 contains a general account of gelation in block copolymer solutions. Section 4.3 is concerned with the solution phase behaviour of poly(oxyethylene)-containing diblocks and tri-blocks. The phase behaviour of styrenic block copolymers in selective solvents is discussed in Section 4.4. Section 4.5 is then concerned with theories for ordered block copolymer solutions, including both non-micellar phases in semidilute solutions and micellar gels. There has been little work on the dynamics of semidilute and concentrated block copolymer solutions, and this is reflected by the limited discussion of this subject in this chapter. 

Ordered phases in poly(oxyethylene)/poly(oxypropylene) block copolymer solutions... 

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). 

Self-consistent field theory (SCFT, see Sections 2.3.3 and 3.4,2) has recently been applied to the phase behaviour of ordered micellar solutions. Noolandi et al. (1996) compared continuum SCFT to the lattice version of this theory for triblock copolymers such as the Pluronics in aqueous solution. From a different viewpoint, this work represents an extension of the SCFT employed by Hong and Noolandi (1981, 1983) and Matsen and Schick (1994) for the phase behaviour of block copolymer melts to block copolymers in solution. The approximations introduced by the adoption of a lattice model are found to lead to some significant differences in the solution phase behaviour compared with the continuum theory, as illustrated by Fig. 4.44. For example, the continuum theory predicts ordered phases for Pluronic L64 (PE013PP03oPEO 3), whereas the lattice theory (neglecting polydispersity) predicts none. 

The physics of the glass transition in block copolymers are essentially the same as those of homopolymers, and little experimental attention has been devoted to this aspect. Ordered phases in block copolymer melts can be vitrified by cooling below the glass transition temperature of a glassy block, and indeed this is often the method for preparing samples for transmission electron... 

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