Effect of weak anchoring on the generalized Freedericksz transition in nematics

Abstract

The Oseen-Frank theory of curvature elasticity of nematic liquid crystals is used to investigate the occurrence of magnetic field-induced static periodic domains for weak anchoring of the nematic director at the sample boundaries. Planar and oblique director orientations are studied for different inclinations of a magnetic field applied in a plane normal to the initial director orientation. Comparison with results for rigid anchoring shows that weak anchoring can profoundly influence the formation of the periodic distortion. These results may be relevant to nematics of high elastic anisotropy, such as polymer nematics. The results are stated in some detail for symmetric anchoring ; consequences of asymmetric anchoring are briefly examined. It appears that it may not be possible to adapt results of this work to the case of nematics exhibiting a smectic phase via a simple symmetry transformation used earlier

Electric field induced static modulated structures in nematics

“…As demonstrated experimentally by Lonberg and Meyer [11] in this case the distortion that occurs above a threshold is not HD but a periodic deformation (PD) having the direction of periodicity normal to the (no, H) plane. It has been suggested theoretically [12][13][14][15][16] that PD may be suppressed by the proper choice of field direction, director anchoring strengths, initial director tilt relative to the sample boundaries etc.…”

Generalized Fréedericksz transition in nematics. Geometrical threshold and quantization in cylindrical geometry

“…The continuum theory does not rule out the occurrence of PD in nematics close to a smectic transition [4,6,7,14] where K2 > Kl, provided that the field is now applied in the twist geometry (parallel to the plates and normal to no, no being parallel to the sample planes) ; there appears to be a symmetry transformation connecting this case to the opposite case of K, > K2. The range of existence (ROE) of PD may depend critically on the magnitude of director anchoring energy at the sample boundaries [11,12,15,16]. When the ground state no is uniformly twisted (twisted nematic), PD may occur as one of two orthogonal modes when H is applied normal to the plates [17].…”

“…Though the finiteness of anchoring energy must be taken into account in any realistic calculation [11,12,15,16], the rigid anchoring hypothesis is adopted in this work for the sake of simplicity. Then, the boundary conditions to be satisfied at the two surfaces can be written down for the different cases as follows : Geometry 1 ; n r = 1 ; Geometry 2 ; n r = 0 ; ny, = 1 ; Geometry 3 ; nr = 0 = n,y ;…”

Magnetic field induced generalized Freedericksz transition in a rigidly anchored simple twisted nematic

“…These authors have also concluded, by using different forms of a simple expression for the surface free energy density [15a, b] that weak director anchoring may considerably affect the relative occurrences of PD and HD. The results of [13,14] have been generalized and presented in some detail in [16].…”

“…The director has been assumed to be rigidly anchored at the boundaries. Recent studies [13,14,16] have shown the importance of weak anchoring in determining the relative occurrence of PD and HD in PUS. Undoubtedly, finiteness of anchoring energy will considerably influence the domain of existence of PD wrt HD.…”