Surface anchoring and dynamics of jump-wise director reorientations in planar cholesteric layers

A theoretical investigation is made into the dynamics of pitch jumps in cholesteric liquid-crystal layers having finite strength surface-anchoring conditions. A presentation is given of general formulations which connect the dynamics of pitch jumps with the key material parameters such as the viscosity, the specific form of the anchoring potential, and the dimensionless parameter S(d)=K(22)/Wd , where K22 is the elastic modulus, W is the depth of the anchoring potential, and d is the layer thickness. To illustrate the dependence of the pitch jump dynamics upon the shape and strength of the anchoring potential, we investigate two sets of different model surface-anchoring potentials for a jump mechanism that is connected with the slipping of the director at a surface over the barrier of the anchoring potential. Two types of "narrow" well potentials that are natural extensions of the more familiar "wide" potentials are considered: one type is based upon the well-known Rapini-Papoular potential and the other upon the B potential, introduced in Belyakov, Stewart, and Osipov, JETP 99, 73 (2004). Calculations for the unwinding (winding) of the helix in the process of the jump were performed to investigate the case of infinitely strong anchoring on one surface and finite anchoring on the other, which is important in applications. The results show that an experimental investigation of the dynamics of the pitch jumps will allow one to distinguish different shapes of the finite strength anchoring potential, and will, in particular, provide a means for determining whether or not the well-known Rapini-Papoular anchoring potential is the best suited potential relevant to the dynamics of pitch jumps in cholesteric layers with finite surface-anchoring strength.