Precise local control of liquid crystal pretilt on polymer layers by focused ion beam nanopatterning

Abstract

Background: The alignment of liquid crystals by surfaces is crucial for applications. It determines the director configuration in the bulk, its stability against defects and electro-optical switching scenarios. The conventional planar alignment of rubbed polymer layers can be locally flipped to vertical by irradiation with a focused ion beam on a scale of tens of nanometers. Results: We propose a digital method to precisely steer the liquid crystal director tilt at polymer surfaces by combining micrometer-size areas treated with focused ion beam and pristine areas. The liquid crystal tends to average the competing vertical and planar alignment actions and is stabilized with an intermediate pretilt angle determined by the local pattern duty factor. In particular, we create micrometer-sized periodic stripe patterns with this factor gradually varying from 0 to 1. Our optical studies confirm a predictable alignment of a nematic liquid crystal with the pretilt angle continuously changing from 0° to 90°. A one-constant model neglecting the difference between the elastic moduli reproduces the results quantitatively correctly. Conclusion: The possibility of nanofabrication of polymer substrates supporting an arbitrary (from planar to vertical) spatially inhomogeneous liquid crystal alignment opens up prospects of "imprinting" electrically tunable versatile metasurfaces constituting lenses, prisms and q-plates.

Keywords: focused ion beam nanopatterning; nematic liquid crystal; optical retardation; pretilt control; surface anchoring.

Figure 1

Schematic of a 2 μm periodic stripe pattern imprinted in the rubbed PI layer (rubbing direction shown by the white arrow) with the duty factor r gradually increasing downwards. The pattern comprises 220 periods, each corresponding to 16 pixels of the digital template. The discretized duty factor variation divides the pattern into 16 approximately equal areas (shown by the 16 shades of grey), corresponding to the indicated rational values of r. The insets show typical fragments of the scanning electron microscope images of the patterned PI.

Figure 2

Exemplary PLM images in crossed polarisers (oriented as indicated by the white arrows) of the LC cells with the FIB-patterned area of 2 μm periodicity and the gradual duty factor variation for different LC layer thickness values: 3.8 μm (a), 5.0 μm (b), 6.5 μm (c) and 13 μm (d)

Figure 3

(a) The relative optical retardation (a) measured at a wavelength of 546 nm, and the pretilt angle (b) as functions of the duty factor for the nematic LC layers of different thickness d above the areas patterned with different periodicity P as indicated in the legends. The dependences given by Equation 1 and Equation 2 within the one-constant approximation are shown by the solid lines. The numerically calculated dependence for the elastic constants of E7 nematic is shown in (a) by the dashed line.

Figure 4

Schematic of the LC orientation on the striped pattern: The molecules are anchored in-plane along the rubbing direction (white “R” arrow) by pristine PI (light yellow stripes) and orthogonally to the substrate by PI irradiated with FIB (middle darker stripe). The competing aligning actions are averaged by the LC elasticity at some distance from the substrate and establish a homogeneous polar angle θ determining the pretilt angle Θ.