Nonsingular walls in plane cholesteric layers

Abstract

The structure of a straight interface (wall) between regions with differing valuesof the pitch in planar cholesteric layers with finite strength of the surfaceanchoring is investigated theoretically. It is found that the shape and strengthof the anchoring potential influences essentially the structure of the wall and amotionless wall between thermodynamically stable regions without a singularity in thedirector distribution in the layer can exist for sufficiently weak anchoring only.More specifically, for the existence of such a wall the dimensionless parameterSd = K22/Wd (whereW is the depth of theanchoring potential, K22 is theelastic twist modulus and d is the layer thickness) should exceed its critical value, which is dependent onthe shape of the anchoring potential. General equations describing the directordistribution in the wall are presented. Detailed analysis of these equations iscarried out for the case of infinitely strong anchoring at one surface and finiteanchoring strength at the second layer surface. It is shown that the wall widthL isdirectly dependent upon the shape and strength of the anchoring potential and that its estimate rangesfrom d to (dLp)1/2 (where Lp = K22/W is the penetration length), corresponding to different anchoring strengths and shapepotentials. The dependence of the director distribution in the wall upon all three Frankelastic moduli is analytically found for some specific limiting cases of the model anchoringpotentials. Motion of the wall is briefly investigated and the corresponding calculationsperformed under the assumption that the shape of a moving wall is the same as amotionless one. It is noted that experimental investigation of the walls in planar cholestericlayers can be used for the determination of the actual shape of surface anchoring potentials.