Lamellar interface

There are two primary types of lamellar interfaces in multiphase TlAl TlAl/TlAl interfaces between two twin-related lamellae with LIq structures, and TlAl/TiaAl interfaces between lamellae with Llo and DOig structures, respectively. In the former case the interfacial planes are (111) and (l 10) vectors in adjacent lamellae are parallel. In the latter caseJnterfacial planes are (111) in TlAl and (0001) in TigAl and (l lO) and 1120) vectors in adjacent lamellae are parallel. 

Similarly, in studies of lamellar interfaces the calculations using the central-force potentials predict correctly the order of energies for different interfaces but their ratios cannot be determined since the energy of the ordered twin is unphysically low, similarly as that of the SISF. Notwithstcinding, the situation is more complex in the case of interfaces. It has been demonstrated that the atomic structure of an ordered twin with APB type displacement is not predicted correctly in the framework of central-forces and that it is the formation of strong Ti-Ti covalent bonds across the interface which dominates the structure. This character of bonding in TiAl is likely to be even more important in more complex interfaces and it cannot be excluded that it affects directly dislocation cores. 

Dorset, D.L. (2000). Electron crystallography of the polymethylene chain. 4. Defect distribution in lamellar interfaces of paraffin sohd solutions Z. Krist. 215,190-198. 

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. 

Small-angle scattering intensity in the high angle (q) region can be analysed to provide information on interface thickness (e.g. the lamellar interface thickness block in copolymer melts or core-corona interface widths in micelles). For a perfectly sharp interface, the scattered intensity in the POrod regime falls as q A (Porod 1951). For an interface of finite width this is modified to... 

The orientation of crystalline stems with respect to the lamellar interface in block copolymers is a subject of ongoing interest and controversy. In contrast to homopolymers, where folding of chains occurs such that stems are perpendicular to the lamellar interface, the parallel orientation has been observed for block copolymers crystallized from the heterogeneous melt. It is not yet clear whether this is always the preferred orientation, or whether chains can crystallize perpendicular to the lamellar plane, for example when crystallization occurs from the homogeneous melt or from solution. 

Fig. 5.12 Model for the lamellar organization in semicrystalline PE-PVCH diblocks crystallized from the ordered melt (Hamley et al. 1996b). The PE chains are folded with stems parallel to the lamellar interface. The convention for labelling of the axis system with respect to the shear direction is also indicated.

However, the situation may be converted in the y-3 form, in which the presence of two cw-double bonds may stabilize the chain-chain interactions of the linoleic acid leaflet, prohibiting the transformation into more stable forms of P or P as illustrated in Figure 9B. For this reason, the A5 value of y of SLS is much larger than those of Y of SOS and SRS. Furthermore, A5 of SLS y is as large as P forms of SOS. Mechanistically, the transformation from y to P or P is associated with an inclined chain arrangement with respect to the lamellar interface (10), which might be prohibited by the chain-chain interactions of the linoleoyl leaflets in SLS. 

Chain orientation parallel to the lamellar interface was also reported for PE-PEE diblocks crystallized from the ordered melt [40]. In subsequent work, the chain orientation in a PE-PS diblock was investigated (here the ethyl branch density in PE was reduced to essentially zero) [41 ]. The PE stems were again par-... 

Chain folds can exist in equilibrium in block copolymers, in contrast to homopolymers, because of the finite cross-sections of the blocks at the lamellar interface, which have to be matched if space is to be filled at normal densities. The equilibrium fold diagram has been mapped ont for PEO-based block copolymers in the melt (163) and in solution (164). Noneqnilibrinm states of highly folded chains can also be trapped kinetically (164,165). 

Besides the introduction of an enthalpic contribution, the elastic energy terms of the spheres or cylinders located at lamellar interfaces have to be changed in the corresponding expressions for spheres or cylinders in a diblock copol5mier For a lamellar B block, there is no gain of conformational entropy upon mixing of the A and C blocks within this simple model. In addition the mixing entropy of the jimction points Sj at the AB and BC interfaces has to be considered as another... 

Fig. 30. Scheme of blends of various lamellar ABC and AC block copolymers forming the cylinder at lamellar interface and noncentrosymmetric lamellae. Weight ratios of the blends are indicated in the figure (OSO4, see Table 1). 

B block in symmetric S-B-M block copolymers, where B forms spheres [150,158] or cylinders at the lamellar interface between S and M, the corresponding polystyrene-block-poly(ethylene-co-butylene)-block-poly(methyl methacrylate) S-EB-M forms a hexagonal morphology, where S cylinders are surrounded by EB rings in an M matrix [150,159] (Figure 9). 

This morphological transition is induced by a change of the interfacial tensions between the middle block and the end blocks. While the interfacial tension between S and B is close to the one between B and M, the situation changes strongly for S and EB, and EB and M. This leads to a displacement of the spheres or cylinders at the lamellar interface in the S-B-M block copolymers and induces curvature into the interface between the outer blocks. This scenario is schematically shown for an ABC triblock terpolymer in Eigure 10. 

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