| M.Sc Thesis | Department of Physics |
| Supervisor: | Prof. Akkermans Eric |
 | Full Thesis text |
This thesis derives analytically and calculates the existence and appearance of screw dislocations into a mesoscopic smectic A liquid crystal sample.
Screw dislocations have first been observed experimentally by Goodby et al (1989). A short time after Renn and Lubensky (1988) published their theoretical work describing the twist grain boundary phase, which includes such screw dislocations and is analogous to the Abrikosov vortex phase.
The theoretical basis of this work is the de Gennes analogy (1972) between the free energies of superconductors and the smectic A phases. This analogy enabled to implement the Bogomol’nyi method, for flat two-dimensional infinite superconductors at the dual point on infinite long cylindrical smectic A samples. These samples have to lie in an external twist field, which is parallel to the cylinder axis. For such systems the minimization of the energy obtained is topological. Moreover, for a cylinder of a finite mesoscopic radius it is possible to obtain an energy expression which includes the number of the residing screw dislocations. This makes it possible to determine the exact number of the screw dislocations in equilibrium as a function of the applied external twist field.
The value of the external field needed for the entrance of the first dislocation is calculated for a specific set of system parameter values and presented in a matching figure.