Subharmonic Pattern Formation in a Nematic Cell – A 1D Flexoelectric Model Approach

Abstract

The application of an AC electric field to a nematic liquid crystal cell produces two distinct instability pattern regimes, conductive or dielectric. Recently, asymmetric electric field waveforms have been shown to cause a period-doubling subharmonic bifurcation. We extend these calculations to include flexoelectricity in the one-dimensional case. We calculate the threshold values for the electric field strength determining the optimum oblique angle at which the roll patterns form. We find, in some areas of parameter space, the formation of oblique rolls is favoured over normal rolls. In addition we find cross-over points from normal to oblique rolls called Lifshitz points. These have been found in the subharmonic and dielectric regions of the linear stability diagram.

Keywords:

• Carr-Helfrich
• electrohydrodynamic instability
• flexoelectricity
• nematic
• pattern formation
• subharmonic dynamics

Notes

¹Dropping the tildas for convenience.

²Conversion between SI and cgs units is done using conversion tables found in Jackson [23] and Stewart [18].

³The 3 × 3 matrix of coefficients is now reduced to the 2 × 2 matrix [10].

Additional information

Notes on contributors

Jonathan Low

One of the authors, Jonathan Low, wishes to thank the Engineering and Physical Sciences Research Council (EPSRC) UK for funding and to thank Ralf Stannarius for both Mischung V liquid crystal data and for a visit to his research group in Magdeburg, Germany.