Pattern Formation in the Transient Periodic Splay Freedericksz Transition in a Nematic Liquid Crystal

1992 ◽  
Vol 31 (Part 1, No. 3) ◽  
pp. 858-861 ◽  
Author(s):  
Hiap Liew Ong
Keyword(s):  
Liquid Crystal ◽  
Pattern Formation ◽  
Nematic Liquid Crystal ◽  
Freedericksz Transition ◽  
Fréedericksz Transition

scholarly journals Bifurcation analysis of the twist-Fréedericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditions

2009 ◽  
Vol 20 (3) ◽  
pp. 269-287 ◽  
Author(s):  
FERNANDO P. DA COSTA ◽  
EUGENE C. GARTLAND ◽  
MICHAEL GRINFELD ◽  
JOÃO T. PINTO
Keyword(s):  
Magnetic Field ◽  
Liquid Crystal ◽  
Boundary Conditions ◽  
Nematic Liquid Crystal ◽  
Pitchfork Bifurcation ◽  
Critical Magnetic Field ◽  
Twist Boundary ◽  
Freedericksz Transition ◽  
Diamagnetic Anisotropy ◽  
Fréedericksz Transition

Motivated by a recent investigation of Millar and McKay [Director orientation of a twisted nematic under the influence of an in-plane magnetic field. Mol. Cryst. Liq. Cryst435, 277/[937]–286/[946] (2005)], we study the magnetic field twist-Fréedericksz transition for a nematic liquid crystal of positive diamagnetic anisotropy with strong anchoring and pre-twist boundary conditions. Despite the pre-twist, the system still possesses ℤ2 symmetry and a symmetry-breaking pitchfork bifurcation, which occurs at a critical magnetic-field strength that, as we prove, is above the threshold for the classical twist-Fréedericksz transition (which has no pre-twist). It was observed numerically by Millar and McKay that this instability occurs precisely at the point at which the ground-state solution loses its monotonicity (with respect to the position coordinate across the cell gap). We explain this surprising observation using a rigorous phase-space analysis.

scholarly journals Freedericksz Transition in Hybrid Aligned Nematic Liquid Crystal Cell

1984 ◽  
Vol 39 (6) ◽  
pp. 575-583 ◽  
Author(s):  
G. Barbero
Keyword(s):  
Liquid Crystal ◽  
Nematic Liquid Crystal ◽  
Polarization Plane ◽  
Liquid Crystal Cell ◽  
General Situation ◽  
Threshold Field ◽  
Freedericksz Transition ◽  
Crystal Cell ◽  
Fréedericksz Transition ◽  
The One

We analyse the Freedericksz transition and the flexoelectric deformation in a hybrid aligned nematic liquid crystal cell. We show that the threshold field for the first effect is smaller than that for a homogeneous sample. The calculations are made in the one constant approximation and in the general situation. Furthermore, in the adiabatic approximation we calculated the polarization plane rotation vs. the applied magnetic field, in the one constant approximation. A similar calculation is made for the flexoelectric effect. In particular we show that it is possible to extend the analysis to a situation of weak anchoring energy.

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