Analytical approach to V-shaped characteristics in antiferroelectric liquid crystal displays

Abstract

Not only in ferroelectric liquid crystal displays (LCDs), but also in antiferroelectric LCDs, grey levels are possible by actively addressing the 'continuous director rotation mode'. For ferroelectric LCDs this was shown qualitatively and quantitatively in previous articles. In this article it is shown that an exact analytical approach is also possible for antiferroelectric LCDs. In two consecutive layers the director orientations are symmetric, and at zero voltage they are in a splayed state. The conditions on alignment layer thickness and interaction coeYcients are related to those of ferroelectric liquid crystal but are easier to ful ll. Introductionuniform Q-theory, but that an exact analytical solution For antiferroelectric liquid crystals there has been is possible, at least in the bookshelf geometry, and if one discussion as to whether thresholdless V-shaped characneglects dielectric anisotropy. This is not always justi ed teristics are possible [1]. In this discussion an approxibut we think its in uence is negligible at the small mate theory, the so-called uniform Q-theory, plays an voltages where V-shape characteristics take place. important role [2], in which the orientation of the layer The derivation of the equations of motion and of the polarization is considered to be independent of the depth stationary states always starts from an energy expression. within the liquid crystal cell. This theory often gives a Two approaches are used in the literature. Either one qualitative insight into what is happening. The so-called solves the problem with a computer program without symmetrical up-state (SU) plays an important role in avoiding complexity, or alternatively, one tries to nd explaining V-shaped characteristic s [3]. If one has applied analytical solutions and so seeks to avoid non-essential a suYciently strong positive voltage, and thus has set complexity. Nakagawa [4] and De Meyere and Dahl [5] the liquid crystal in the ferroelectric up-state (FU) and have studied the shape of the chevron structure and tried then lets V gradually decrease, one rst goes over to to develop the most general energy expression. Sabater the SU-state, with the polarization in two successive and Oton [6, 7] also used a very general expression and layers symmetrical with respect to the eld direction. If include a chevron structure, bending and motion of the one succeeds in remaining in this state until V 5 0, an chevron tip, dielectric anisotropy, etc. The controversy alternating state (or antiferroelectric state) results, with over V-shaped switching in ferroelectrics and antiferroboth polarizations parallel to the electrodes. We shall electrics was not known at that time. In this respect call this state the continuous director rotation state the polar interaction with the alignment layers plays a (CDR) because it gives rise to the thresholdless V-shaped crucial role, and this was not included by Sabater and characteristics. If the liquid crystal does not remain Oton [6,7]. Fornier et al.[8] used a somewhat less in the SU-s...

Simulations of energy and switching in AFLCDs with different boundary conditions

“…Since then there has been an intensive experimental study of the behaviour of V-shaped switching, including the investigation of bulk optical properties [4], electrostatics [5] and the influence of ions [6]. Theoretical modelling of FLC [7,8] and AFLC thresholdless switching [9,10] have been presented with slightly different approaches; however the simulation results reach similar conclusions. In contrast to the simulation results there is so far no experimental evidence for V-shaped switching in AFLCs.…”

“…Since strong polar interaction is needed to obtain a V-shaped switching characteristic, it is clear that the uniform theory is not a good approximation for V-shape studies. We showed however that by using a fictitious negative non-polar interaction, c 1 v0, one could obtain V-shape, both in ferroelectric [7] and in antiferroelectric [10] liquid crystals; this is illustrated in figure 2 (a). One should also take into account that in the earlier publication [17] the thickness of the alignment layer was ignored.…”

“…if the directors in two consecutive layers are at opposite sides of the smectic cone. This energy is assigned to the two layers, thus there is no factor K. This also leads to the fact that KA of [10] plays the role of A in this article, and thus 2A will be reflected by 4A.…”

“…Non-stationary equations The energy expressions lead, according to EulerLagrange, to the following non-stationary equations [10]:…”

“…Under constant voltage over the cell, the energy of the cell is the Gibbs free energy with the expression [10]: (1)…”