Dislocation-disclination models

Solids of different classes, including polymers, are characterized typically with a complex non-uniform structure on various morphological levels and the presence of different local defects. The theoretical approaches describe the deformation of solid polymers via local defects in the form of dislocations (or dislocation analogies ) and disclinations, or in terms of dislocation-disclination models even for non-crystalline polymers [271-275, 292]. In principle, this presumes the localized character and jump-like evolution of polymer deformation at various levels. Meantime, the structural heterogeneity and localized microdeformation processes revealed in solids by microscopic or diffraction methods, could not be discerned typically in the mechanical (stress-strain or creep) curves obtained by the traditional techniques. This supports the idea of deformation as a monotonic process with a smoothly varying rate. Creep process has been investigated in the numerous studies in terms of average rates (steady-state creep). For polymers, as the exclusion. 

It has also been presumed that the magnitude of the kinetic units corresponds closely to the activation volume of deformation, as well as to the units in different kinds of motion, namely the rotation-translation displacement of a segment or several neighboring segments in a polymer. In addition to the molecular-kinetic model of deformation, the disclination [271], dislocation analogy [272,273], or dislocation-disclination [274,275] solid-state models of polymer deformation have also been discussed. 

Figure 10. Pairing of two disclination lines of opposite signs (lamellar details are not featured) (top) a less probable model for the core of a dislocation (middle) and focal line appearing on the dislocation in order to release locally deformation energy (bottom)...

The concept of defects came about from crystallography. Defects are dismptions of ideal crystal lattice such as vacancies (point defects) or dislocations (linear defects). In numerous liquid crystalline phases, there is variety of defects and many of them are not observed in the solid crystals. A study of defects in liquid crystals is very important from both the academic and practical points of view [7,8]. Defects in liquid crystals are very useful for (i) identification of different phases by microscopic observation of the characteristic defects (ii) study of the elastic properties by observation of defect interactions (iii) understanding of the three-dimensional periodic structures (e.g., the blue phase in cholesterics) using a new concept of lattices of defects (iv) modelling of fundamental physical phenomena such as magnetic monopoles, interaction of quarks, etc. In the optical technology, defects usually play the detrimental role examples are defect walls in the twist nematic cells, shock instability in ferroelectric smectics, Grandjean disclinations in cholesteric cells used in dye microlasers, etc. However, more recently, defect structures find their applications in three-dimensional photonic crystals (e.g. blue phases), the bistable displays and smart memory cards. 

Figure 9.9. Model structure of the two-brush defect i.e., dispiration, a combined defect of a wedge disclination and a screw dislocation.

Figure 28. Progressive disjunction of edge dislocations in cholesterics (left-handed twist). The open circles show the locus of vertical directors, (a) Planar model of a very thin thread , (b) First step of the disjunction into a At and a t dislocation, (c) Cross-section of a thin thread , with complete disjunction of the two disclinations and T , corresponding to a Burgers vector of length b = p 2. (d) Edge-dislocation of the type A A, with =p. (e) A X A pair with (>=3p.

This texture distribution is common, but corresponds to a rather schematic model, indicating that high-energy defects, such as disclinations, are found mainly in the vicinity of the isotropic transition. Other situations are observed in thick preparations of cholesterics, for example, where planar domains can be interrupted by walls of vertical layers (Fig. 34 c and d), due to edge dislocations disjoining into disclina-tion pairs (see Fig. 5 d). Despite these par-... 

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