Modeling of Weak Anisotropic Anchoring of Nematic Liquid Crystals in the Landau–de Gennes Theory

Abstract

The anisotropic anchoring effect of a treated solid surface on a nematic liquid crystal is described in the Landau-de Gennes theory using a power expansion on the tensor-order parameter and two mutually orthogonal unit vectors. The expression has three degrees of freedom, allowing for independent assignment of polar and azimuthal anchoring strengths and a preferred value of the surface-order parameter. It is shown that in the limit for a uniaxial constant-order parameter, the expression simplifies to the anisotropic generalization of the Rapini-Papoular anchoring energy density proposed by Zhao et al. Experimentally measurable values with a physical meaning in the Oseen-Frank theory can be scaled and assigned to the scalar coefficients of the tensor-orderparameter expansion. Results of numerical experiments comparing the anchoring according to the study of Zhao et al. in the Oseen-Frank theory and the power expansion in the Landau-de Gennes theory are presented and shown to agree well. Index Terms-Anchoring, liquid crystal (LC).Eero Willman received the M.Eng. degree in electronic and electrical engineering from the Department of Electronic and Electrical Engineering, University College London, London, U.K., in 2003, where he is currently working toward the Ph.D. degree.His current research interests include computer modeling and development of modeling tools for the simulation of nematic-liquid-crystal devices.

The effect of anchoring on the nematic flow in channels

“…For lowG, the mass flow rate of the channel is very well represented by Eqn. (27). This agreement is seen close up to values ofG before the onset of the sudden jump in Φ, as illustrated in the inset of this figure.…”

“…(38) with Eqn. (27) shows that the low flow limit dΦ/dG is larger in the planar case, as is confirmed in figure (14). Hence we note that the linear term of Φ is dependent on the type of anchoring, while dependence on the strength of anchoring only arrives in the cubic term.…”

Liquid crystal alignment induced by micron-scale patterned surfaces

“…The tr(Q 2 ) term is an additional isotropic term that stabilizes the surface order parameter. Setting a = (W 1 + W 2 )/(6S s ) favors a surface order parameter equal to a value S s , whereas omitting it causes the linear terms to drive the surface order towards ±∞ [15]. In the present case, planar degenerate anchoring is assumed over the patterned surface.…”

“…Using the representation of the anchoring energy (5) described in Ref. [15], a value of W 1 = 1.5 × 10 −3 J/m was [38]. In the calculations, two different sets of elastic coefficients are used.…”

“…A commonly used surface energy term was proposed by Rapini and Papoular [12] and takes the form W 2 sin 2 α, where W is the strength of the anchoring and α is the angle the director makes with the direction favored by the surface or easy direction. Modifications and extensions to this formulation have been introduced in the past, allowing, for example, the description of anisotropic anchoring surfaces [13][14][15]. Nevertheless, the assumption of a simple sin 2 α type of variation in the energy remains popular.…”