Variations of the helix in thin planar cholesteric layers influenced by surface anchoring

Abstract

Unwinding (winding) of a helix in thin planar cholesteric layers induced by the varying external parameters (temperature, electric or magnetic field) and its dependence on the surface anchoring are theoretically investigated for the defectless mechanism of the cholesteric pitch jumps connected with a slipping of the director on the surface through the anchoring potential barrier. Earlier investigations of the problem performed for the case of the temperature variations showed strong dependence of the relevant phenomena on the anchoring potential (two sets of model anchoring potentials were considered). However the field dependence of the pitch variations was examined only for the Rapini-Papoular (R- P) anchoring potential. We performed investigation of the problem for two types anchoring potentials, R-P - potential and so called B-potential and found a qualitatively different behavior of the pitch in applied field for the different types of potential. The parameter S_d = K₂₂/(dW) (where K₂₂ is the twist constant, W is the height of the anchoring potential and d is the sample thickness) governs the "pitch versus applied field (temperature)" dependence. The field dependences of the pitch are calculated for a planar cholesteric layer with infinite strength of anchoring at one surface and finite strength of anchoring at the second one for the R-P and B-surface anchoring potentials. It is found that for the B-potential the pitch jumps and hysteresis of these jumps exists at any strength of anchoring opposite to the case of the R-P-potential for which the jumps and hysteresis exist for sufficiently strong anchoring only when S_d<1. In particular it is shown that the critical field of the complete helix unwinding E_c, in a thin layer may be as essentially lower than the critical field in a bulk cholesteric so larger than this field and for some range of the relevant to the problem parameters the helix unwounded by the field remains to be unwounded after removing of the field.