Lamellar phase parallel/perpendicular orientation

Theory for the self- and tracer-diffusion of a diblock copolymer in a weakly ordered lamellar phase was developed by Fredrickson and Milner (1990). They modelled the interactions between the matrix chains and a labelled tracer molecule as a static, sinusoidal, chemical potential field and considered the Brownian dynamics of the tracer for small-amplitude fields. For a macroscopically-oriented lamellar phase, they were able to account for the anisotropy of the tracer diffusion observed experimentally. The diffusion parallel and perpendicular to the lamellae was found to be sensitive to the mechanism assumed for the Brownian dynamics of the tracer. If the tracer has sufficiently low molecular weight to be unentangled with the matrix, then its motion can be described by a Rouse model, with an added term representing the periodic potential (Fredrickson and Bates 1996) (see Fig. 2.50). In this case, motion parallel to the lamellae does not change the potential on the chains, and Dy is unaffected by... 

For a quenched lamellar phase it has been observed that G = G"scales as a>m for tv < tvQ. where tvc is defined operationally as being approximately equal to 0.1t and r is a single-chain relaxation time defined as the frequency where G and G" cross (Bates et al. 1990 Rosedale and Bates 1990). This behaviour has been accounted for theoretically by Kawasaki and Onuki (1990). For a PEP-PEE diblock that was presheared to create two distinct orientations (see Fig. 2.7(c)), Koppi et al. (1992) observed a substantial difference in G for quenched samples and parallel and perpendicular lamellae. In particular, G[ and the viscosity rjj for a perpendicular lamellar phase sheared in the plane of the lamellae were observed to exhibit near-terminal behaviour (G tv2, tj a/), which is consistent with the behaviour of an oriented lamellar phase which flows in two dimensions. These results highlight the fact that the linear viscoelastic behaviour of the lamellar phase is sensitive to the state of sample orientation. 

Locally oblate lyotropic elastomers with lamellar phase structure (L -phase) can be oriented by uniaxial compression, as outlined above for thermotropic smectic-A elastomers. Fischer et al. synthesized crosslinked polysiloxane elastomers carrying non-ionic amphiphilic side-groups attached with their hydrophobic end to the polymer backbone. They were able to compress elastomer samples between Teflon half-cylinders to about half of their original thickness. The orientation of the phase structure - except for some unoriented domains - was demonstrated by means of H-NMR spectroscopy on the directly deuterated samples as well as by X-ray scattering. The preferred orientation of the director, and hence the amphiphilic side chains, was found to be parallel to the axis of compression with the amphiphilic bilayers aligned perpendicularly [98, 99]. 

The orientation of crystalline stems with respect to the interface of the microstructure in block copolymers depends on both morphology and the speed of chain diffusion, which is controlled by block copolymer molecular weight and the crystallization protocol (i.e. cooling rate). In contrast to homopolymers, where folding of chains occurs such that stems are always perpendicular to the lamellar interface, a parallel orientation was observed for block copolymers crystallized from a lamellar melt phase perpendicular folding was observed in a cylindrical microstructure. Both orientations are shown in Fig. 8. Chain orientation can be probed via combined SAXS and WAXS on specimens oriented by shear or compression. In PE, for example, the orientation of (110) and (200) WAXS reflections with respect to Bragg peaks from the microstructure in the SAXS pattern enables the unit cell orientation to be deduced. Since PE stems are known to be oriented along the c axis, the chain orientation with respect to the microstructure can be determined. 

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