Screw Volterra process

The helical structure of the c-director in the smectic C phase makes the defects different from those in the smectic C phase. As the Volterra process produces a screw dislocation, for example, along the z axis and the Burger vector b = d, it must be accompanied by a parallel wedge disclination in the c-director, in the form... 

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 equivalence just demonstrated for screw dislocations versus wedge x disclinations can be extended to edge dislocations (Figure 5.12) versus twist X disclinations and even further, to mixed dislocations and disclinations, for the simple reason that the two corresponding Volterra processes are the same. 

Figure 17. The Volterra process applied to cholesteric phases. The core structure is masked by a cylinder along the line L. (a, b) Edge and screw dislocation, (c-e) A section S limited by L, normal to the cholesteric axis, allows one to build either the edge dislocation (a) or a disclination (d), as in smectics (Fig. 16d and d"). (f, g) Construction of the opposite disclination. (Drawing made in collaboration with F. Livo-lant).

If we now apply the Volterra process, there are two possible ways to obtain a screw dislocation, as indicated in Fig. 22 b and c, when the length of the Burgers vector is p/2, the half-helicoidal pitch. In a simple model it is assumed that the directors... 

Along a circle nm, directors show a definite distribution that is coherent, with a uniform alignment within the horizontal plane (a"). When the Volterra process is applied along the cylinder axis to create screw dislocations (b or c), the rectangles ABA B are transformed into parallelograms (b or c ) and the distributions of the directors are changed along a transverse circle nm. This leads to two different patterns in the core (b" or c") when the molecules are assumed to remain horizontal. (Drawn in collaboration with F. Livolant.)... 

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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