Hexagonally perforated lamellar phases

The theoretically calculated phase diagrams of the mid 1990s agree remarkably well with the experimentally observed phase behavior of diblock copolymers. Figure4.2b shows the almost symmetric phase diagram of PS-fc-PI measured by Khandpur et al. in 1995 [10]. At that time it was still believed, that the semi-continuous hexagonally perforated lamellar phase, a combination of the lamellar and cylindrical phase, is a stable equilibrium phase. Later experimental and theoretical studies showed, that the HPL is a metastable structure or long-lived transition, but not an equilibrium structure [11]. Similarly, the Fddd was believed to exists as a metastable structure [12]. 

At very asymmetric compositions, the free-energy difference between the double-gyroid and hexagonally perforated lamellar (HPL) phases becomes very... 

A perforated lamellar phase (76% H4T4, 14% h) at equilibrium with a dilute micellar phase (19% H4T4, 0.04% I i) is found in box A . Lamellar and perforated lamellar crystals are observed at high surfactant concentrations (above 70"/o). Concentrated phases where the surfactant volume fraction lies between 60% and 70% show hexagonal structures, as observed from box B . No morphological order is observed for those systems where the inorganic concentration in the surfactant-rich phase is more than 40% (point C on Fig. 2). 

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. 

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... 

Figure 13.4 Phase diagram of a PS-PI diblock copolymer showing regions of BCC spheres (Im3m), hexagonal cylinders (HEX), laid gyroid, hexagonally perforated lamellae (HPL), lamellar (LAM), and disordered phases /pi is the volume fraction of polyisoprene. The dot-dash line represents the mean-field order-disorder transition based on the formula x = 71.4/T — 0.0857 with reference segment volume v — 144 A. (Reprinted with permission from Khandpur et al.. Macromolecules 28 8796. Copyright 1995, American Chemical Society.)...

A simple molecular model was used to simulate the equilibrium phase behaviour of hybrid materials for different inorganic precursors. Although some physical and chemical properties are not explicitly included in the model, it is possible to detect the general behaviour of the system such as the phase separation and the self-assembly of surfactants in hexagonal, lamellar or perforated lamellar structures. 

Hexagonally perforated layer (HPL) structure is one of the most complicated stmctures in polymers, particularly block copolymers. The HPL structure is known to be metastable and appears in limited temperature ranges between the stable lamellar and gyroid phases. HPL structure in polymers is known to be metastable and appears in limited temperature ranges between the stable lamellar and gyroid phases. Nevertheless,... 

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. 

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