Three-dimensional director structures of defects in Grandjean-Cano wedges of cholesteric liquid crystals studied by fluorescence confocal polarizing microscopy

We use a nondestructive technique of fluorescence confocal polarizing microscopy to visualize three-dimensional director patterns of defects in Grandjean-Cano wedges filled with a cholesteric liquid crystal of pitch p=5 microm. Strong surface anchoring of the director causes a stable lattice of dislocations in the bulk. Optical slicing in the vertical cross sections of the wedges allows us to establish the detailed structure of dislocations and their kinks. Dislocations of Burgers vector b=p/2 are located in the thin part of the sample, very close to the bisector plane. Their cores are split into a pair of tau(-1/2) and lambda(+1/2) disclinations. Pairs of lambda(-1/2) and tau(+1/2) disclinations are observed when the b=p/2 dislocation forms a kink. The kinks along the b=p/2 dislocations change the level of dislocations by +/-p/4 and +/-p/2; these kinks are confined to the glide plane and are very long, (5-10) p. Above some critical thickness h(c) of the wedge sample, the dislocations are of Burgers vector b=p. They are often found away from the bisector plane. The core of b=p dislocations is split into a pair of nonsingular lambda(-1/2) and lambda(+1/2) disclinations. The kinks along the b=p dislocation are of a typical size p and form cusps in the direction perpendicular to the glide plane. At the cusp, lambda(-1/2) and lambda(+1/2) disclinations interchange ends. Other defect structures inlude "Lehmann clusters," i.e., dislocations of zero Burgers vector formed by two lambda(-1/2) and two lambda(+1/2) disclinations and dislocations of nonzero Burgers vector with a core split into more than two disclinations. We employ the coarse-grained Lubensky-de Gennes model of the cholesteric phase to describe some of the observed features. We calculate the elastic energy of a dislocation away from the core, estimate the energy of the core split into disclinations of different types, study the effect of finite sample thickness on the dislocations energy, and calculate the Peach-Koehler elastic forces that occur when a dislocation is shifted from its equilibrium position. Balance of the dilation/compression energy in the wedge and the energy of dislocations defines the value of h(c) and allows to estimate the core energy of the dislocations. Finally, we consider the Peierls-Nabarro mechanisms hindering glide of dislocations across the cholesteric layers. Because of the split disclination character of the core, glide is difficult as compared to climb, especially for b=p dislocations.