Arrays of charged (+/- 2 pi)-twist disclinations in ferroelectric liquid crystals

The notion of an electrostatic charge of (+/-2)-twist disclinations is used to approximate the evaluation of the electrostatic interaction energy amon g disclinations forming arrays in finite samples of ferroelectric chiral sm ectic C liquid crystals. Screening effects of free charges in a material su rrounding the disclination are taken into account by introducing a phenomen ological depolarisation factor. The electrostatic interaction energy is important in chiral smectic C mater ials with high values of the spontaneous polarisation when screening effect s of free charges are small. Then the electrostatic interaction leads to el imination of disclinations from the sample. When there is a high concentrat ion of free charges in the sample (smaller value of depolarisation factor), the electrostatic interaction energy is of the order of the elastic intera ction energy of disclinations what influences the equilibrium of disclinati on arrays in the sample. Two disclination configurations are considered. In the Brunet-Williams configuration the disclinations of opposite topologica l charge have also the opposite electrostatic charge so their attraction is augmented. This attraction can be balanced by the helical structure in the central part of the sample when the sample thickness is rather high. On the contrary, in the Glogarova-Pavel configuration the disclinations of opposite topological charge have the electrostatic charge of the same sign. The equilibrium in this configuration is either a balance of elastic attra ction and electrostatic repulsion if elastic and Coulomb forces are of the same order or it is governed by the value of the anchoring energy when elec trostatic interaction prevails over the elastic one.