Nematics Volterra process

There is a simple process to produce a disclination rotate the directors on two slips respectively by uq and wo and make lo — luo = w. Thus the same disclination line is produced. The process is named the de Gennes-Friedel process. One can prove that the de Gennes-Friedel process is equivalent to the Volterra process for nematic liquid crystals. The operation Pv of the Volterra process can in fact be divided into the translation and rotation steps, i.e., first, translate the directors (T) and then rotate them around themselves (IV). The latter is actually the de Gennes-Friedel process. In other words... 

The Volterra process for creating a loop, i.e., a closed disclination line, in a nematic is as follows. Let S be the surface enclosed by the loop L. Call the two sides of the surface and S . Rotate the molecules in contact with... 

The Volterra process for creating these disclinations is the same as for nematic disclinations. For the screw disclination the plane of cut is parallel to the cholesteric twist axis while for the edge disclination it is perpendicular to it. 

The major part of the arrows directed to the right in Fig. 8.12a correspond to the initial orientation of the director no in the planar nematic slab. However, the part of the slab shown by arrows directed to the left is virtually taken from the sample by some mysterious force , turned about axis Q through angle n and put back into the slab. After this operation called Volterra process, the director is everywhere again parallel to no due to the no = —no symmetry and such a structure in each of the two parts (initial and turned) is topologically stable. However, in the close proximity of the plane 2" ", on the scale of molecular size, the director changes its orientation by... 

Figure 15. The Volterra process applied to a nematic liquid. A planar section limited by a line normal to the director n allows the two lips Si and S2 to be separated by an angle 7t (b), and nematic material to be added to obtain the disclination structure (c). An initial matter subtraction creates two lips Si and Sj (d), both rotated by an angle kH (e) and restuck to obtain another disclination (0-...

The core structure of cholesteric discli-nations was interpreted by K16man and Frie-del [2, 3]. The rotation vector considered in the Volterra process is normal to the cholesteric axis and is either parallel to the molecules or normal to them, this resulting in a core structure that is either continuous, with a longitudinal nematic alignment of directors in the core (A disclinations), or discontinuous (t disclinations), with a singular line of the type encountered in non-twisted nematic liquids. 

In the so-called Volterra process [65], the topological defects of these disclinations can be visualized as follows If the nematic material is cut by a plane parallel to the di-... 

As for achiral disclinations, the Volterra process may be used to create screw or edge disclinations by cutting parallel or perpendicular, respectively, to the chiral nematic twist axis. 

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