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Liquid crystals with curved substrates

Liquid crystal displays

Liquid-crystal (LC) displays consist of a LC layer confined between two surfaces that impose a preferred orientation of the average molecular direction n(r). Current nematic displays rely on voltage-induced reorientation of the director within the bulk LC layer.

Recently, textured surfaces (on scales of the order of 1 micro m) were designed for patterned alignment of LC [1, 2], opening possibilities for an improved performance of LC cells.

Geometrically-controlled twist transitions in nematic cells [3]

We considered in particular the twist cell proposed in a recent experiment, where the nematic is confined between a flat and a sinusoidal grating surface [1, 3]. In the experiment a voltage-controlled twist (VCT) effect highly sensitive to the surface properties of the cell (grating geometry and anchoring strength) has been reported, for gratings on the scale of tenths of micro m. These twist displays exhibit excellent viewing angle characteristics, that are important in technological applications.

For large negative values of the anchoring strength W 1, the grating surface induces normal orientation of the nematic.

Upon increasing W 1 a first instability occurs when the director field becomes nearly uniform resulting from the competition of two effects: the anchoring energy favoring homeotropic alignment, and the elastic energy favoring homogeneous alignment at the grated surface.

As W 1 becomes positive, the nematic orientation changes continuously to follow the sinusoidal shape of the boundary.

Beyond a certain threshold, the bulk bending energy of this deformation is comparable with a bulk twist deformation and a new instability occurs. Owing to the degeneracy of the planar anchoring, the sinusoidal and the twisted configurations have approximately the same surface free energy.

The twist instability depends strongly on the geometry of the cell.

The approximate analytical results (thin lines) and the exact numerical results (bold lines) are shown in Figure 2. To favor twist configurations we used K 11 =K 33 =2K 22. This set of elastic constants corresponds very closely to the nematic LC cell used in Ref. [1]. The contour plot (Fig. 2(a)) represents the critical anchoring stregth W 1c – i.e., the onset of the twist instability – for a given cell geometry (A , q=2π/L). From this figure one infers that W 1c diverges for a set of geometrical parameters of the cell. This set delimits a range of parameters for which the nematic orientation will never twist. Outside this region, for larger values of A and q, a twisted nematic director may occur for small values of W 1c D / K 11.

References

1. G. P. Bryan-Brown, C. V. Brown, I. C. Sage, and V. C. Hui, Nature 392, 365 (1998).
2. V. K. Gupta and N. L. Abbott, Science 276, 1533 (1997); B.-W. Lee and N. A. Clark, Science 291, 2576 (2001); R. R. Shah and N. L. Abbott, Science 293, 1296 (2001).
3. Geometrically-controlled twist transitions in nematic cells P. Patrício, M. M. Telo da Gama and S. Dietrich, Phys. Rev. Lett., Vol. 88, 245502 (2002).
   Berreman and de Gennes first considered grating surfaces to explain azimuthal anchoring by elastic effects only. Since then, several studies about undulated surfaces have been carried out. However, a systematic study covering the whole range of operating parameters described in the experiment was lacking.