Nonsingular walls in plane cholesteric layers

Abstract

The structure of a straight interface (wall) between regions with differing values of the pitch in planar cholesteric layers with finite strength of the surface anchoring is investigated theoretically. It is found that the shape and strength of the anchoring potential influences essentially the structure of the wall and a motionless wall between thermodynamically stable regions without a singularity in the director distribution in the layer can exist for sufficiently weak anchoring only. More specifically, for the existence of such a wall the dimensionless parameter Sd = K22/Wd (where W is the depth of the anchoring potential, K22 is the elastic twist modulus and d is the layer thickness) should exceed its critical value, which is dependent on the shape of the anchoring potential. General equations describing the director distribution in the wall are presented. Detailed analysis of these equations is carried out for the case of infinitely strong anchoring at one surface and finite anchoring strength at the second layer surface. It is shown that the wall width L is directly dependent upon the shape and strength of the anchoring potential and that its estimate ranges from d to (dLp)1/2 (where Lp = K22/W is the penetration length), corresponding to different anchoring strengths and shape potentials. The dependence of the director distribution in the wall upon all three Frank elastic moduli is analytically found for some specific limiting cases of the model anchoring potentials. Motion of the wall is briefly investigated and the corresponding calculations performed under the assumption that the shape of a moving wall is the same as a motionless one. It is noted that experimental investigation of the walls in planar cholesteric layers can be used for the determination of the actual shape of surface anchoring potentials.

Cano-Grandjean Wedge at Weak Surface Anchoring

“…Quite recently another phenomena connected to the shape of the anchoring potential were studied. These are the temporal dynamics of the pitch jump [2,10] and the motion of a non-singular wall dividing the areas of different values of the pitch in a planar CLC layer [11,12,13]. These studies revealed also the dependence of the temporal evolution of the jump on the shape and the strength of anchoring for a relatively weak surface anchoring.…”

“…It happens that at If the described jump happens in a limited area of the layer surface the director distribution over the layer surface become inhomogeneous and the wall (interface between the configurations with N and N þ 1 half-turns of the director) occurs. Typically [12] the wall thickness Cano-Grandjean Wedge at Weak Anchoring 267 along the layer surface is much less than the layer thickness. The wall begins its motion in the direction of the N configuration, because the free energy of the N configuration per a unit layer area is higher than the corresponding value for the N þ 1 configuration [11,12].…”

“…These studies revealed also the dependence of the temporal evolution of the jump on the shape and the strength of anchoring for a relatively weak surface anchoring. More over, the distribution of director in the non-singular wall (moving or motionless) is also dependent on the shape of surface anchoring potential [12].…”

Weak Anchoring Effects in Nematic Liquid Crystals

“…if the director at the surface coincides with the easy direction. Recently, however, Belyakov et al [3][4][5] proposed an alternative form for a weak anchoring energy density that is particularly relevant to twist geometries. In our notation, this alternative version may be written as…”

“…The physical motivation for the B form of surface energy is largely driven by pitch 'jumps' in cholesteric liquid crystals where the twist of the director is dominant and is related to the twist elastic constant K 2 [3][4][5]. By considering simple series expansions, it can be shown that the RP and B energies almost coincide when the actual surface twist angle is close to the easy direction / Ã .…”