Creation-cum-stabilization of the topological soft rail

In Chapter 5.5 we have seen how the director field develops when 5CB LC equilibrated to the nematic phase at room temperature, following the interplay of surface anchoring and long-range ordering [6]. At corners formed by two PDMS walls, the alignment encounters a situation of nonconformity, which is resolved by the elastic deformations of the director field.

In topological parlance, the deformations correspond to regions of topological rank 1/4 at each corner. The net topological charge is conserved through the creation of a singular line defect, of opposite strength and rank 1/2 within the nematic bulk. However, in absence of any flow, the defect line collapses towards the channel corners, shown by the image sequence in Fig. 6.33.

Figure 6.33: Time sequence of optical micrographs show the collapse of a disclination line towards a channel corner (top view). Time separation between images is 2 s. Scale bar: 5µm.

As suggested by the time sequence in Fig. 6.33, the bulk disclination is attracted towards a corner of the channel. The tendency of the defects to dwell near the walls can be overcome, however, by using electric fields [184] or, as demonstrated here, by the viscous drag forces resulting from a flow of the LC through the channel: At a local flow velocity ofv=8±2µm/s, the disclination line detached from the wall and stabilized within the flowing bulk. The elastic force Felastic (see Chapter 5.5) was effectively outweighed by a force Fviscous exerted on the line by the flowing medium. This is shown in the image sequence in Fig. 6.34a. The strength of the viscous force Fviscous was estimated to be ≈ 4 µN/m, derived from the relations by Ryskin-Kremenetsky [116] and Imura-Okano (see Chapter 2.7.3) [241]:

Figure 6.34: Laying down the ’soft rail’. (a) Micrograph time sequence showing a collapsed disclination line separating from the channel wall when flow is started. The black arrow points the disclination. Each image is separated by 2.5 s. (b) POM images of the stable disclination line within the nematic bulk. The relative orientation of the polarizers are shown in each micrograph. The director has complementary angles of reorientation about the defect line.

Scale bar: 50µm. (c) FCPM images showing the disclination cross-section for two different laser polarizations. (d) Director field cross-section reconstructed using POM and FCPM data.

The value of the rotational viscosity of nematic 5CB considered for the calculations here is γ1 =0.077 Pas (see Table 3.2). Taking into account the uncertainties in viscosity and elastic constants, as well as the fact that the flow-director coupling was neglected, it can be concluded that the Fviscous was strong enough to shift the static equilibrium position of the disclination line. With increasing flow speed, the disclination line was further shifted away from the wall, and was finally positioned close to the mid-plane, at v ≈ 18µm/s. Such a stabilized defect line is shown in shown in Fig. 6.34b. The disclination line then stretched along the entire length of the channel (shown in Fig. 6.34a) and was found to be stable for flow velocities of up tov≈ 200µm/s. The FCPM imaging across the defect cross-section (Fig. 6.34c) supports the flow-induced director field, stabilizing the disclination line within the nematic bulk (see Fig. 6.34d).

Figure 6.35: Generation of a disclination line while filling the channel. (a) Time sequence of polarized micrographs shows generation of a continuous disclination line, with the origin at the meniscus. (b) Magnified imaging close to the 5CB-air interface confirmed the origin of the disclination close to the glass surface. (c) Schematic of the possible director orientations close to the glass surface. At the 5CB-air interface, the molecules anchor perpendicularly, whereas in the upstream region, glass induces uniform planar anchoring, resulting in nucleation of the 1/2 defect, which is stabilized in the upstream portion due to the prevalent surface anchoring on the channel walls.

Alternatively, the disclination line could be laid by simply filling the channel with 5CB in the nematic phase (image sequence, Fig. 6.35a). The anchoring constraints on the channel walls and at the air-LC interface strongly support the evolution of a 1/2 disclination line along the channel, as presented in Fig. 6.35b. When the channel is filled up with 5CB in the nematic phase, the LC molecules anchor perpendicularly at the interface of air and 5CB [178]. The glass surface on the other hand induces uniform planar anchoring, orthogonal to the flow direction. This leads to a conflict between the two surface-induced boundary conditions. To accommodate the antagonistic anchoring, a topological defect of rank 1/2 is generated close to the nematic interface and the glass surface (Fig. 6.35b). This scenario was verified by focusing the microscope objective near the glass surface. Within the nematic bulk, sustenance of this spontaneously evolved defect is possible due to the surface anchoring present on the remaining parts of the channel walls (Fig. 6.34c). Effectively, this leads to a continuous disclination line originating at the leading meniscus and extends through the entire length of the filled channel.

Thus, by tailoring the surface and flow parameters appropriately, disclinations of arbitrary lengths can be created and stabilized within a microfluidic device.

Figure 6.36: Set of polarized micrographs of a continuous disclination line within a wide microchannel (w=500µm.) The defect line is typically unstable, exhibiting a wobbly motion in the transverse direction.

Clearly, the side walls of the microchannels possessing homeotropic anchoring, have a significant contribution in stabilization of the disclination line. Due care needs to be taken for determining the appropriate combination of the flow parameters and the channel dimensions.

It is plausible, that in sufficiently wide channels (high aspect ratio), the director stabilization falls short of adequate contribution from the side walls of the channel. This was observed in experiments with wide channels: In channels withw> 1000µm (d ≈50µm), the disclination line exhibited a wobbly motion in the transverse direction (Fig. 6.36). When similar flow speeds were applied within a channel ofw= 200µm, the defect line was found to be stable.

Furthermore, within extremely wide channelsw>3000µm, the defect was rarely observed.