Perforated layer structure

In recent years a number of so-called complex phases, such as the bicontinuous gyroid and perforated layer structures, have been identified. The former has been established as an equilibrium structure, whereas the latter seem to be metastable structures observed during transformations to and from the gyroid structure. 

The existence of a second class of complex phases, the modulated and perforated layer structures, has largely been explored by Bates and co-workers (Forster et al. 1994 Hamley et al. 1993, 1994 Khandpur et al. 1995 Schulz et al. 1996), who used SANS and TEM to investigate shear oriented structures. The thermally-induced phase transition from the lam to the hex phase in polyolefin diblocks was studied in detail by Hamley et al. (1993, 1994) using SANS, TEM and rheology. Intermediate hexagonal modulated lamellar (HML) and hexagonal perforated layer (HPL) structures were observed on heating PEP-PEE, PE-PEP and PE-PEE diblocks, where PEP is poly(ethylene-propylene), PEE is... 

Bicontinuous cubic phases have not, to date, been accounted for using SSL theory. The OBDD phase has been shown to be unstable with respect to lam and hex phases (Likhtman and Semenov 1994 Olmsted and Milner 1994a,b). As discussed above, it now appears that the OBDD was a misidentified gyroid phase however, SSL calculations for the gyroid structure have not been performed as yet. A perforated layer structure was found to be unstable by Fredrickson (1991), using SSL theory following Semenov s method. 

Fig. 2.47 Pseudostable perforated layer structure, observed following a quench from the lam to hex phase using a multimode analysis of the time-dependent Ginzburg-Landau equation, within the single-wavenumber approximation (Qi and Wang 1997). This structure results from the superposition of six BCC-type wavevectors.

The fact that the most unstable mode of a lamellar phase is infinitely degenerate in the x-y plane can be used to show that, when the lamellar phase is driven into other ordered phases, the kinetics of the transition proceeds through a long-lived intermediate modulated-layered state that may correspond to the experimentally observed perforated layered structures. If one direction of the most unstable mode is excited, it will lead to the undulation of the layers that eventually form cylindrical structures (Figure 8.5). However, because of the degeneracy of the fluctuation modes, it is most likely that more than one direction of the fluctuation modes will be excited, leading to the formation of a perforated layered structure (Figure 8.6). 

Figure 8.6 Three-dimensional contour plots showing the effects of the degeneracy of the most unstable modes. The parameters are the same as in Figure 8.4. It is obvious that the simultaneous excitation of the most unstable modes leads to a perforated layered structure. (Reproduced from M. Laradji et al. Macromolecules 30, 3242 (1997) Copyright (1997) with permission from the American Chemical Society).

Hexagonally perforated layer structure in block copolymers 453... 

For nearly symmetric compositions the unlike blocks form domains composed of alternating layers, known as lamellar phase (L). Slightly off-symmetry composition results in the formation of a different layered structure. The structure is known as perforated layers (PI) or catenoid phase. Despite an earlier assignment as an equilibrium phase, it is now known to be in a long-lived metastable state that facilitates the transition from I to G phases [9-14], The PL structure consists of alternating minority and majority component layers in which hexagonally packed channels of the majority component extend through the minority component. 

A sketch of the perforated lamellar morphology is depicted in Fig. 2. Depending on the point of view, the 2D projection exhibits different patterns perpendicular to the layers of the perforated lamellar structure the projection appears like a hexagonal honeycomb mesh (Fig. 2a). By contrast, the parallel view (Fig. 2b) leads to rows of spots. 

Fig. 2 Sketch of perforated layers (PL) or catenoid structure, a Projection direction perpendicular to layers of perforated lamellar structure appears as a hexagonal honeycomb mesh, b Projection parallel to layers appears as rows of dark spots resulting from cross section of parts. Sketch according to [15]. Copyright 2001 American Chemical Society...

The kinetics and mechanisms of the C —> G transition in a concentrated solution of PS-fr-PI in the PS-selective solvent di-n-butyl phthalate was studied [137,149]. An epitaxially transformation of the shear-oriented C phase to G, as previously established in melts [13,50,150], was observed. For shallow quenches into G, the transition proceeds directly by a nucleation and growth process. For deeper quenches, a metastable intermediate structure appears, with scattering and rheological features consistent with the hexag-onally perforated layer (PL) state. The C -> G transition follows the same pathways, and at approximately the same rates, even when the initial C phase is not shear-oriented. 

Fig. 2.3 Typical isothermal frequency scans for PE-PEE diblocks with indicated compositions in different ordered phases (Zhao ei at. 1996). Qualitative differences between the low frequency rheological response for distinct ordered structures similar to these are observed for other diblocks. S = BCC spheres, C = hex cylinders, G = Ia3d gyroid, HPL = hexagonal perforated layer, L = lamellae. (A) G (x) G . Structural assignments of the ordered phases were made using TEM and SAXS.

The effect of harmonics in the composition profile has been considered in Landau Brazovskii theory, as well as mean field theory. Olvera de la Cruz (1991) found a hexagonal perforated layer (HPL) structure to be stable for symmetric or nearly symmetric diblocks in addition to the classical phases. Recent work has... 

Fig. 6.6 TEM images of a catenoid lamellar hexagonal perforated layer (HPL) structure in a blend of a PS-PB diblock (M = 49.9kgmor1, 51wt% PS) and PS homopolymer M = 26 kg mol 1) and a total PS volume fraction fFS = 0.67 (Disko etal. 1993). The sample was annealed at 130 °C prior to microtoming (a) view parallel to the lamellae (b) view normal to the lamellae, showing hexagonal perforations in a PI lamella.

PPO repeating units self-assemble into a supramolecular honeycomb-like layered structure, in which perforations are filled by coil segments. When cast from dilute CHCR solution onto a carbon support film, honeycomb-like supramolecular structure was observed, as revealed by transmission electron microscopy (TEM), in which coil perforations are packed on a hexagonal symmetry with distances between perforations of approximately 10 nm (Figure 14a). 

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. 

Figure 28 Phase diagram of ABC star polymers with arm-length ratio 1 1with symmetric interaction parameters. Morphologies are lamella+sphere (L+S), five cylindrical structures in sectional view, perforated layer (PL), lamella + cylinder (L + C), columnar piled disk (CPD), and lamella in sphere (L-in-S). Reprinted from Gemma, T. Hatano, A. Dotera, T. MacromoleculesZOOZ, 35,3225. ...

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