Method for measuring K₁₁/K₃₃ and ε_∥/ε_⊥ ratios of nematic liquid crystals with negative dielectric anisotropy

Abstract

For any nematic liquid crystal having a negative dielectric anisotropy ε _α, in a homeotropic texture sandwiched between two parallel plates with a sufficiently large distance L between them, and under a square external electric field excitation E ₀(t) = ±E ₀ and a static magnetic field H perpendicular to the plates, the applied external voltage V at the threshold of the electrohydrodynamic instability and the square S ² of the quantity S = qL/π are linear functions of the Fréedericksz transition voltage V _F . Here π/L is equal to the wave number of the distortion along the Z‐axis perpendicular to the walls and q is the wave number of distortion along any X‐direction perpendicular to the Z‐axis. S ² is also a linear function of voltage V. The two lines V _F (V _F) and V(V _F) intersect at a value of voltage V ₀ such that V = V _F  = V ₀, which depends only on frequency. With experimental measurements around the point V ₀, one may compute the ratio of the elastic constants, K ₁₁/K ₃₃ where K ₁₁ and K ₃₃ are the splay and bend elastic constants, respectively, and by combining the slopes of the two lines S ²(V _F) and S ²(V), one may obtain an estimate of the ratio of the dielectric constants ε_∥/ε_⊥.