Frank-Oseen Theory Research Articles

The Freedericksz Transition in a Spatially Varying Magnetic Field

Much is known about the Freedericksz transition induced by uniform electric and magnetic fields in nematic liquid crystals. In this work, we are interested in the effects of a spatially varying field on the transition. Specifically, we study the director configuration in a homeotropic nematic cell in a spatially varying magnetic field with cylindrical symmetry. The experiment is conducted with a ring magnet which provides a radial magnetic field with magnitude monotonically decreasing to zero at the center. The nematic cell is positioned in the central plane of the ring, with the cell normal parallel to the ring normal. Interference patterns of the nematic cell between crossed polarizers were observed. The director configuration in the nematic cell is modeled with Frank–Oseen theory, and the computed interference pattern from the simulated director field are compared with experiment. We conclude that if the magnetic field strength varies with position in the plane of the cell, there is no Freedericksz transition.

Scaling of the elastic contribution to the surface free energy of a nematic liquid crystal on a sawtoothed substrate

We characterize the elastic contribution to the surface free energy of a nematic liquid crystal in the presence of a sawtooth substrate. Our findings are based on numerical minimization of the Landau-de Gennes model and analytical calculations on the Frank-Oseen theory. The nucleation of disclination lines (characterized by non-half-integer winding numbers) in the wedges and apexes of the substrate induces a leading order proportional to q ln q to the elastic contribution to the surface free-energy density, with q being the wave number associated with the substrate periodicity.

A density functional study of a twisted nematic cell and its relation to the Frank–Oseen theory

The numerical results for the twist angle profile xi(z) across a slab-shaped nematic cell obtained from a density functional theory (DFT) are compared to the predictions of the macroscopic Frank-Oseen theory. The latter theory predicts that xi"(z)=0, and this is also seen to be the case for the DFT results. These do, however, verify the Frank-Oseen relation, lambda+/-W+/-=K2, between the de Gennes extrapolation length (lambda+/-), the anchoring energy per unit area of the (+/-) cell wall (W+/-), and the elastic constant of the nematic for twist deformations (K2), only if W+/- is nonlinearly related to the amplitude of the anchoring term of the DFT.

Orientational phase transition and the solvation force in a nematic liquid crystal confined between inhomogeneous substrates.

A nematic liquid crystal confined between two identical flat solid substrates, with an alternating stripe pattern of planar and homeotropic anchoring, is studied in the framework of the Frank-Oseen theory. By means of numerical minimization of the free energy functional we study the effect of the sample thickness D on the location of the phase transition between a uniform alignment, either planar or homeotropic, and a distorted nematic texture. The solvation force f due to distortions of the nematic director is also studied. It is found that f is always attractive, and for D small compared to the periodicity of the surface structure it exhibits two distinct asymptotic behaviors: f approximately -D(-1/2) or f approximately -D(-1), depending on the relation between D and the extrapolation lengths.

Disclination Loop in Mori-Nakanishi Ansatz: Role of the Divergence Elasticity

Energetic stability of loop defects in nematic liquid crystal is analyzed using Mori-Nakanishi ansatz and Frank-Oseen theory with non-zero K 24 divergence term. The ratio of the bulk and divergence elastic constants defines a characteristic material length, which is the equilibrium radius a* of the disclination ring. Positive K 24 forces the ring to shrink.

Nematic bend-splay elasticity near the nematic-smectic-Atransition

Magnetic-field-induced bend-splay deformation experiments are presented which show that the linear Frank-Oseen theory of nematic curvature elasticity is valid near a continuous nematic-smectic-$A$ transition where smectic fluctuations dominate the bend elasticity. The results are compared with the Chu-McMillan criterion for the limit of linear response based on the smectic-$A$ superconductivity analogy. It is shown that the success of the linear theory may be due to the unexpectedly small values of the longitudinal and transverse correlation lengths found in recent x-ray experiments.