Block copolymers gyroid structure

Figure 13.7 Transmission electron micrographs of a thin-sectioned PS-PI block copolymer gyroid phase (a) sectioned at an orientation showing the wagon-wheel three-fold projection of the cubic structure thi sectioned at an orientation showing the four-fold projection. (Reprinted with permission from Forster et al., Macromolecules 27 6922. Copyright 1994, American Chemical Society.)...

The best-known and simplest class of block copolymers are linear diblock copolymers (AB). Being composed of two immiscible blocks, A and B, they can adopt the following equilibrium microphase morphologies, basically as a function of composition spheres (S), cylinders (C or Hex), double gyroid (G or Gyr), lamellae (L or Lam), cf. Fig. 1 and the inverse structures. With the exception of the double gyroid, all morphologies are ideally characterized by a constant mean curvature of the interface between the different microdomains. 

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. 

In mean field theory, two parameters control the phase behavior of diblock copolymers the volume fraction of the A block /A, and the combined interaction parameter xTak- V. where Xab is the Flory-Huggins parameter that quantifies the interaction between the A and B monomers and N is the polymerization index [30], The block copolymer composition determines the microphase morphology to a great extent. For example, comparable volume fractions of block copolymer components result in lamella structure. Increasing the degree of compositional asymmetry leads to the gyroid, cylindrical, and finally, spherical phases [31]. 

For diblock copolymers, periodically arranged spheres (micelles), hexago-nally packed cylinders, and a lamellar phase have been observed [1]. A more complex bicontinuous cubic phase with QIasymmetry (gyroid structure) has also been identified. These supramolecular structures, with length scales on the order of 1 to 102 nm, may be controlled by changing the amount of solvent, the length of blocks, or the proportions of A and B monomeric units [128-131]. 

Also in bulk block copolymers microphase-separate into ordered liquid crystalline phases. A variety of phase morphologies such as lamellae (LAM), hexagonally ordered cylinders (HEX), arrays of spherical microdomains (BCC, FCC), modulated (MLAM) and perforated layers (FLAM), ordered bicontinuous structures such as the gyroid, as well as the related inverse structures have been documented. The morphology mainly depends on the relative block length. If, for instance, both blocks are of identical length, lamellar structures are preferred. 

Fig. 9. Self-organization structures of block copolymers and surfactants spherical micelles, cylindrical micelles, vesicles, fee- and bcc-packed spheres (FCC, BCC), hexagonaUy packed cylinders (HEX), various minimal surfaces (gyroid, F-surface, P-surface), simple lamellae (LAM), as well as modulated and perforated lamellae (MLAM, PLAM) (with permission from [5])...

Tri-block copolymer morphologies (a) Three-dimensional reconstruction of TEM images of gyroid structure in styrene isoprene styrene (Spontak, R. J. and Patel, N. P., Curr. Opin. Coll. Interface Sci, S, 334, 2000) Elsevier (b) TEM of lamellar edges in styrene butadiene styrene (Huy, T. A. et al.. Polymer, 44, 1237, 2000) Elsevier. 

Fig. 2.4 Different morphologies of block copolymers. From left to right an increasing fraction of the blue block, resulting in spherical, cylindrical, gyroid, lamellar, and the inverse structures, respectively. Adapted with the permission from Ref. [33]. Copyright 2010 American Chemical Society...

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