Lamellar tilt

The SmC analog nature of the lyotropic phase was demonstrated by the observation of characteristic textures associated with the thermotropic SmC phase, such as broken fan-shaped texture, schlieren texture, zigzag defects, spontaneous tilt domains in the surface-stabilized state and pitch lines. Further evidence was provided by X-ray experiments. The two-dimensional dififaction pattern of an aligned sample confirms that the phase is lamellar, tilted and fluid. 

The formation of this instability can be understood qualitatively from scaling rules. Consider a block copolymer material between two plane parallel electrodes, where the lamellar microstructure is aligned parallel to the electrodes. The electrostatic energy can be reduced by a tilt in the lamellar layers, for example, by a ripple distortion as shown for a cholesteric in Figure 13. If the ripple has amplitude a and transverse wavelength A, the electrostatic free energy is reduced by an amount that scales with the square of the lamellar tilt away from horizontal ... 

Figure 13 Peterlin s model of molecular slip, lamellar tilt, and fracture of lamellae into crystalline blocks converting a lamellar morphology into a fibrillar one.

Many compounds, including clay minerals, form needle- or plateshaped crystals. With finely dispersed minerals, the electron diffraction method can give a special kind of diffraction pattern, the texture pattern, which contains a two dimensional distribution of a regularly arranged set of 3D reflections [2], Specimens of fine-grained lamellar or fiber minerals, prepared by sedimentation from suspensions onto supporting surfaces or films, form textures in which the component microcrystals have a preferred orientation. Texture patterns of lamellar crystals tilted with respect to the electron beam are called oblique texture electron diffraction patterns [1]. 

Crystallization from the melt often leads to a distinct (usually lamellar) structure, with a different periodicity from the melt. Crystallization from solution can lead to non-lamellar crystalline structures, although these may often be trapped non-equilibrium morphologies. In addition to the formation of extended or folded chains, crystallization may also lead to gross orientational changes of chains. For example, chain folding with stems parallel to the lamellar interface has been observed for block copolymers containing poly(ethylene), whilst tilted structures may be formed by other crystalline block copolymers. The kinetics of crystallization have been studied in some detail, and appear to be largely similar to the crystallization dynamics of homopolymers. 

There is no comprehensive theory for crystallization in block copolymers that can account for the configuration of the polymer chain, i.e. extent of chain folding, whether tilted or oriented parallel or perpendicular to the lamellar interface. The self-consistent field theory that has been applied in a restricted model seems to be the most promising approach, if it is as successful for crystallizable block copolymers as it has been for block copolymer melts. The structure of crystallizable block copolymers and the kinetics of crystallization are the subject of Chapter 5. 

The potential for novel phase behaviour in rod-coil block copolymers is illustrated by the recent work of Thomas and co-workers on poly(hexyl iso-cyanate)(PHIC)-PS rod-coil diblock copolymers (Chen etal. 1996). PHIC, which adopts a helical conformation in the solid state, has a long persistence length (50-60 A) (Bur and Fetters 1976) and can form lyotropic liquid crystal phases in solution (Aharoni 1980). The polymer studied by Thomas and co-workers has a short PS block attached to a long PHIC block. A number of morphologies were reported—wavy lamellar, zigzag and arrowhead structures—where the rod block is tilted with respect to the layers, and there are different alternations of tilt between domains (Chen et al. 1996) (Fig. 2.37). These structures are analogous to tilted smectic thermotropic liquid crystalline phases (Chen et al. 1996). 

Early work predicted smectic (or lamellar) ordering in rod-coil copolymers (Semenov 1991 Semenov and Vasilenko 1986). In liquid crystals, a smectic A phase is a lamellar phase where the molecules are, on average, parallel to the layer normal. In a smectic C phase, the molecules are tilted with respect to this direction. The imbalance in interfacial area per chain for a rod or coil can lead to tilting of chains to maintain uniform density. Semenov (1991) constructed a phase diagram for rod-coil copolymers in which second-order phase transitions... 

Lattice Model Carlo simulations of a block copolymer confined between parallel hard walls by Kikuchi and Binder (1993,1994) revealed a complex interplay between film thickness and lamellar period. In the case of commensurate length-scales (f an integral multiple of d), parallel ordering of lamellae was observed. On the other hand, tilted or deformed lamellar structures, or even coexistence of lamellae in different orientations, were found in the case of large incommensurability. Even at temperatures above the bulk ODT, weak order was observed parallel to the surface and the transition from surface-induced order to bulk ordering was found to be gradual. The latter observations are in agreement with the experimental work of Russell and co-workers (Anastasiadis et al. 1989 Menelle et al. 1992) and Foster et al. (1992). 

By adding the function u(x) to the phase factor in (4) one can describe departures from the planar (lamellar, one-dimensional) layer arrangement, which is characteristic for the 2D structures. The first term in (3) is the smectic layer compressibility energy. It is zero when layers are of the equilibrium thickness. If cx(T) > 0, the second term in (3) requires the director to be along the smectic layer normal (the smectic-A phase). If c (T) < 0, this term would prefer the director to lie in the smectic plane. So the last term in (3) is needed to stabilize a finite tilt of the director with respect to the smectic layer normal. In addition this term gives the energy penalty for the spatial variation of the smectic layer normal. 

The stability analysis [32] of the lamellar (one-dimensional) structure shows that it is stable only for weak coupling between the splay of polarization and molecular tilt. When Kv is larger than some critical value, layers start to undulate. 

Fig. 13 In the general tilt structure stronger lamellarization is predicted by the theoretical model and also observed experimentally. Left, the layer structure in the Blrev-type phase right, the lamellar structure in the higher temperature general tilt structure...

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