1. Accurate Modelling of Defect Creation and Control
R. James, E. Willman, S.E. Day and F.A. Fernández
UCL Electronic and Electrical Engineering,
Torrington Place, London, WC1E 7JE
Abstract
In conventional LC displays and in many other liquid crystal devices, defects or disclinations are unwanted and traditionally regarded as detrimental to the device performance. However, the appearance and movement of defects are essential to the operation of certain devices. Furthermore, the LC structure produced by the presence of a defect can be used to advantage in the device design. Consequently, accurate modelling of the creation and evolution of defects is essential to the design and analysis of devices that exploit these effects. Some bistable display structures, like the Zenithal Bistable Display (ZBD) and the Post Aligned Bistable Nematic (PABN) display depend on the creation of defects and their movement to switch between the stable states. These devices rely on the distortion of the liquid crystal in the proximity of a fixed grating on a surface for the transition between a continuous and a defect state.
In the Pi cell defect lines and loops separate topologically distinct domains that may be shrunk or grown by varying the applied voltage. High resolution devices might be able to exploit such abrupt changes between topologically distinct states through the precise electrical control of defect lines. Precise control over the process of defect creation and movement could then be used to create abrupt changes of bulk liquid crystal orientation that can be of use in phase modulation devices. Furthermore, together with the interaction between defects and particles immersed in the liquid crystal, a precise control of the evolution of defects could provide the means to manipulate these particles within a liquid crystal cell.
Conventional display devices can be designed and optimized with the use of numerical modelling, which is made straightforward by the simplifying assumptions such geometries permit. Assumptions typically include a constant order parameter approximation, which prohibits the proper treatment of defects, strong anchoring and negligible flow. However, for cases where defects play an important role, these assumptions are no longer applicable and modelling is made difficult. The aim of our work is to explore some of the possibilities brought upon by the accurate control of defect creation and their movement. To this end, we use a finite element formulation based on the Landau-de Gennes free energy formulation, to calculate the dynamic behaviour of the liquid crystal orientation and degree of order. The completeness of this description is a necessity when simulating defects and their associated trajectories. Included in this model is the flow of the liquid crystal and the interaction between the liquid crystal and alignment surfaces, to which the liquid crystal may weakly or strongly adhere.
Stable Hybrid Aligned State
Stable Vertical State
Voltage is applied across the top electrode and the 2 grounded bottom electrodes. A defect pair forms at the peak of the grating. The +1/2 defect stays fixed at the top while the -1/2 defects migrates towards the trough.
Voltage is applied across bottom electrodes. Top electrode is left floating.
A defect pair is formed above the electrodes, towards the right hand side.
The +1/2 defect descends towards the electrode and gets smeared along the alignment area, on the electrode (a region of biaxiality is formed there). The -1/2 defect raises towards the peak of the grating and annihilates the +1/2 defect there
Voltage is removed. Leaves a HAN state with +1/2 and -1/2 defects at the peak and trough of the grating
Voltage is removed. The +1/2 defect above the lower electrodes is expelled from there and raises towards the trough of the grating where it annihilates the -1/2 defect there leaving the stable vertical state (without defects)
Defect Induced Bistability
Generation and evolution of defects can be used to switch this structure between two different stable states, without relying on flexoelectric effects.
Bulk Switching due to Electrically Induced Defects
Switching due to defects in tall, narrow LC cells.
Closely spaced small electrodes can be used to generate defects that will move through the cell and induce bulk alignment.
The electric field produced by the electrodes is confined to the vicinity of the electrodes.
Example:
HAN cell 1.5 mm tall, 1 mm wide
For voltages below 5.6 V no defects are generated and the switching is confined to a narrow layer above the electrodes.
After applying 5.6 V or more a defect pair is generated between the electrodes.
The –1/2 defect migrates up to reach a position above the electrodes determined by the voltage and the electrode separation leaving a planar aligned region above.
If the voltage is then reduced the –1/2 defect comes down and the +1/2 defect moves up and into a position between the electrodes, maximizing the planar aligned region, which is larger for a lower voltage. Below a certain threshold (0.8 V in this case) the defects annihilate each other.
5.6 V applied – after 50 ms
Steady State (15 ms)
Steady State (voltage reduced to 0.8 V)
Interaction with Particles
Proposition: Particles immersed in the LC interact with defects and this interaction can be used to manipulate the particles via the control of defect movement.
Defects around particles and their interaction
Particles of 0.5 mm diameter
Homeotropic alignment on particles
Immersed in planar (horizontal) aligned LC
Deformation energy versus separation
Separation in mm
Deformation Energy (a.u.)
Separation