Cooperative liquid-crystal alignment generated by overlaid topography

Nematic and smectic liquid crystals were introduced into μm-scale gaps between plates coated with polymer films nanoimprinted with parallel arrays of rectangular channels. Overlaying the channels on the two plates close enough at a slight angle produces a mosaic of alternating planar and homeotropic alignments and hybrid alignment, showing that complex liquid-crystal orientation patterns can be achieved by combining two simple topographic patterns. These alignment patterns are attributed to spatial variation of surface roughness and 3D topographic structure created by a sufficient proximity of the two patterns.

Figure 1

Topographically patterned cell structures. (a) AFM images of the polymer replica. The insets show the top surface of a channel separator (left) and the bottom surface of a channel (right), with rms roughnesses of 2 and 1 nm, respectively. The period of the channel array is $p$ $=$ 1.5 μm, with each channel width $w$ $=$ 0.8 μm and depth $d$ $=$ 0.5 μm; $s$ $=$ 0.7 μm is the width of the separator and $g$ is the cell gap. The channels are oriented along the $y$ axis. (b) Optical microscope image of an empty overlaid (inside the red box) cell in polarized light with both sets of channels aligned approximately along the $y$ direction. The broad horizontal bands are a Moiré pattern (period Π $=$ 45 μm), which is discontinuous at the gaps in the pattern array. (c) Cross sections of overlaid cells, with the channels positioned in phase ($I$) and out of phase ($O$).

Figure 2

DTLM images of 11CB cells with overlaid channels in the Sm$A$ phase. At left, the channels are rotated ∼45° from the analyzer, while at right, they are approximately along the analyzer. (a) A thick cell ($g$ $=$ 4.2 μm) shows only partial alignment of director field. The inset shows the uniform alignment in a thicker 8CB cell with 7-μm spacers in the Sm$A$ phase. The scale bar in the inset represents 200 μm. (b) A thinner cell ($g$ $=$ 0.8 μm) shows uniform alignment except near the pattern gaps. (c) A very thin cell ($g$ $=$ 0.2 μm) shows bright and dark bands, corresponding to the Moiré pattern in Fig. 1b. The inset shows similar bands of a very thin 8CB cell in the nematic phase. The scale bar in the inset represents 100 μm.

Figure 3

Nucleation and growth of needlelike domains at the isotropic-Sm$A$ phase transition of 11CB in a very thin cell. DTLM pictures were obtained at intervals of 15 s while cooling a cell with $g$ $=$ 0.2 μm from 53.1 to 53.0 °C at 0.02 °C/min. Smectic domains (numbered in their order of appearance) nucleate and stop growing at the center of dark bands in the cell. (a) Four nuclei are visible at $t$ $=$ 0. (b) The first set of needlelike smectic domains are now fully grown ($t$ $=$ ∼270 s). (c) Fresh set of domains are nucleated once the growth of the older needles are essentially complete ($t$ $=$ ∼300 s). The red and cyan dashed boxes mark respectively the areas originally shown in pictures (a) and (b). The inset shows for comparison the continuous growth of Sm$A$ domains in the somewhat thicker 11CB cell ($g$ $=$ 0.8 μm) shown in Fig. 2b. (d) Growth dynamics of individual nuclei. Notice the appearance of many fresh nuclei at 300 and 330 s, after the older needles are fully grown.

Figure 4

(a) DTLM image of a thin overlaid 11CB cell showing individual channels, with a bright central $I$ band, where the channels are mostly in phase, bounded by darker $O$ bands. The inset shows the intensity profile along the thin red line with $y$ axis 45° and 0° rotated relative to the analyzer. The director field of the defect is shown in the inset indicated with a cyan box with an arrangement of thin rhombi corresponding to the four possible combinations of the top and the bottom patterns. (b) Planar director field model. In both $I$ and $O$ bands, $n$ orients uniformly, parallel to the channels, shown here in cross sections along the two lines, indicated with letters $I$ and $O$, along $x$ direction in the blue box in (a). The tops of the separators are rougher than the bottoms of the channels. (c) Hybrid director field model. In $I$ bands, $n$ is uniformly pretilted by δ${}_1$ from $y$ direction in the channels and by δ${}_2$ from $z$ direction in the narrower gap between the separators. In $O$ band the director tilt is nonuniform, increasing between the channel bottom and the separator surface and giving hybrid alignment. (d) Director field in the blue box shown in (a) with regions where channels (separators) overlap are sketched in the white (dark blue). At the bottom of the figure, the overlap of channels (white area) shifts by a half pitch ($p$/2) at the center of the $O$ band.

Figure 5

Planar and homeotropic models on rough surface. A cross section of a rough surface along $x$ direction is sinusoidal, $z$ $=$ $A$sin($\mathit{qx}$), where $A$ and λ $=$ 2π/$q$ are the amplitude and the spatial period, respectively. (a) Director is tangential to the sinusoidal surface and shows bend deformation. (b) Director deviates from tangent of the surface and shows splay deformation.

Figure 6

Transition from planar alignment to alternation of planar and homeotropic alignments by the decrease of the cell gap. (a) The twist elastic energy in a thick cell is too large to keep the homeotropic configuration and the alignment is planar. (b) The twist elastic energy in a thin cell is small and the homeotropic anchoring on the top of separator maintains the alternation of planar and homeotropic alignment. Small pretilts are assumed in the director fields.

Figure 7

Topological transition of the director field in a thin cell. As the position moves along the channels from the center of $I$ band to that of $O$ band a transition from the alternation of alignment, (a) and (b), to a hybrid organization, (d) and (e), occurs at an intermediate position, (c) and (d). The blue curves represent contours of director field with 45° tilt from the $z$ axis.