Homeotropic microchannel with cylindrical micro-pillar

The soft lithography technique allows us to integrate micro-structures of different geome-tries and dimensions within the microchannel, e. g. micro-pillars of circular, and rectangular cross-sections. A schematic representation of such a microfluidic chip is shown in Fig. 5.7a.

In this section we shall look into simple linear channels with a rectangular cross-section and a cylindrical pillar placed at the middle of the channel. The depth of the channel,d, was varied between 8µm and 50 µm, and the pillar diameter 2rwas chosen between 10 µm and 60 µm (Fig. 5.7b). All our experiments were conducted withinw ≈ 100µm wide and sufficiently long (20 mm) channels. In Fig. 5.7a,x,y, and zdenote the flow direction, channel width and channel depth, respectively.

The equilibrium director configuration of nematic 5CB was studied for a range of aspect ratios (w/d) and pillar dimensions (r). Figure 5.8a shows micrographs of a (r,d,w) = (20, 40, 100) µm channel filled with nematic 5CB, and observed under white light and confocal microscopes. The white light micrograph (top) clearly shows the channel boundary and the

Figure 5.7: Microfluidic confinement with cylindrical micro-pillar. (a) Microchannel with a micron-sized cylindrical pillar positioned symmetrically in the flow path. (b) Schematic representation of the plan view and the cross-sectional view (xz plane position shown in the plan view). The channel and pillar surfaces possess homeotropic surface anchoring.r,w, and ddenote the pillar radius, channel width and depth, respectively.

cylindrical micro-pillar. When crossed polarizers were introduced, distinct dark and bright patterns were observed in the vicinity of the confining walls and the pillar surface. This is in accordance to the interference phenomenon discussed previously. Farther away from the pillar and the confining surfaces, the LC director field equilibrated without any elastic deformation.

The whole-field director configuration was further confirmed from the FCPM measurements (xy scan, laser polarized along y). As seen in the FCPM micrograph (Fig. 5.8a), a strong fluorescence signal is observed at the PDMS boundaries, whereas a weak signal is obtained from the rest of the channel. The lateral spread of the interference pattern at the surfaces varied with the channel depth. As is shown in Fig. 5.8b (top), no significant interference is observed within a channel of depthd≈10µm. The reduction in the number of the interference fringes within shallow channels additionally led to a sharp appearance of the channel and pillar boundaries. On the contrary, the interference pattern is significantly prominent in the (20, 40, 50)µm channel (Fig. 5.8b, bottom). By varying the aspect ratio (w/d> 1) of the channel, one can essentially tune the homeotropic coverage within the microchannels.

Figure 5.8c shows POM and FCPM images obtained in a (30, 40, 100)µm channel. The FCPM intensity distribution from the channel cross-section along sections1and2(Fig. 5.8d) clearly resolves the homeotropic orientation on the involved surfaces. Interestingly, the lateral spread of the bend deformation at the side walls, seen as the bright fluorescence signal, is wider in section1as compared to that in section2. This difference occurs due to larger elastic deformations effected by the micro-pillar. For a given aspect ratio, the larger the pillar size, the more significant is the elastic interaction. For example, a 40µm diameter pillar (Fig. 5.8a) reduced the lateral spread by ≈ 50%, whereas, the presence of a 60 µm pillar reduced the

Figure 5.8: POM and FCPM imaging of the confined NLC around the micro-pillar. Polarized micrographs are indicated by a pair of crossed arrows (polarizers atπ/4 to the channel length).

(a) From top: White light, polarized optical, and fluorescence confocal polarized micrographs (laser polarization at π/2 to the channel length, indicated by the double-headed arrow) of a (r,d,w)= (20, 40, 100)µm channel. 0 and 1 on the FCPM intensity scale bar correspond to director orientations parallel and perpendicular to the laser polarization direction. (b) From top: POM images of a (r,d,w)= (30, 10, 100) and (r,d,w)= (20, 40, 50)µm microchannel respectively. Note the reduction of the number of interference fringes in the shallow (r,d,w)= (30, 10, 100)µm channel. (c) POM and FCPM images of (r,d,w)=(30, 40, 100) microchan-nel.(d) FCPM imaging of theyzcross-sections along the lines1and2in (c). The polarization of the excitation laser is shown with the double-headed arrow.

spread further to≈75% (Fig. 5.8c). The overall confinement-induced behaviour, discussed so far, is generally observed also in presence of multiple pillars within a homeotropic matrix.

The director field around the micro-pillar, reconstructed from the POM and FCPM data, is shown in Fig. 5.9a and b. At the confining walls and the micro-pillar, LC molecules anchored homeotropically. Consequently, the director is normal to the xyplane away from the pillar, represented by black dots in Fig. 5.9b. In the vicinity of the side walls and the pillar, the director undergoes a transition from the in-plane to the out-of-plane orientation through the gradual bend deformation (indicated by the nail heads in Fig. 5.9b). Additionally, the director orientation around the micro-pillar preserves a rotational symmetry about its axis (z). Two possible director orientations about the yz plane – singular +1/2 defect loop (sharp pillar

Figure 5.9: Director configuration around the micro-pillars. (a) Reconstruction of the director field from the POM and FCPM images. Hatched lines depict the glass surface. Cross-sectional view (yz) through the pillar (shown in grey colour) shows two possible director orientations around it: singular +1/2 defect loop (top) or a non-singular director configuration (bottom).

Both configurations possess symmetry about the cylinderzaxis. (b) Schematic nail represen-tation of the director field on xyplane. The nail heads indicate director tilted partially into the image plane.

base), and the continuous non-singular director field (rounded pillar base) – are shown in Fig. 5.9a. Although symmetric projections of the above two cases are shown in Fig. 5.9a, asymmetric director configurations, as shown in Fig. 5.4, are also likely [195]. Typically in the experiments presented here, the non-singular configuration was observed long time after equilibration of 5CB from the isotropic to the nematic phase. The singular loop manifested itself typically at elevated temperatures (Fig. 5.10), under external perturbations, or due to pinning of the defect loop at surface irregularities.

Figure 5.10: Defect loop around a micro-pillar (r= 25µm) is observed through the sequence of optical micrographs, obtained during the transition of 5CB from isotropic to the nematic phase. Time proceeds along the black arrow. Different stages of the loop formation is pointed by the red arrow head on the micrographs. Time interval between the images is not uniform.