Liquid crystals with patterned molecular orientation as an electrolytic active medium

Transport of fluids and particles at the microscale is an important theme in both fundamental and applied science. One of the most successful approaches is to use an electric field, which requires the system to carry or induce electric charges. We describe a versatile approach to generate electrokinetic flows by using a liquid crystal (LC) with surface-patterned molecular orientation as an electrolyte. The surface patterning is produced by photoalignment. In the presence of an electric field, the spatially varying orientation induces space charges that trigger flows of the LC. The active patterned LC electrolyte converts the electric energy into the LC flows and transport of embedded particles of any type (fluid, solid, gaseous) along a predesigned trajectory, posing no limitation on the electric nature (charge, polarizability) of these particles and interfaces. The patterned LC electrolyte exhibits a quadratic field dependence of the flow velocities; it induces persistent vortices of controllable rotation speed and direction that are quintessential for micro- and nanoscale mixing applications.

Figure 1

Assembled microfluidic chamber. The chamber is bounded by two glass plates. One of them is a bare glass and the other has stripe indium tin oxide (ITO) electrodes separated by a gap $L=10$ mm. Both of them are coated with the photoalignment material. The width of each electrode is 3 mm. After the chamber is filled with the liquid crystal, it is sealed by an epoxy.

Figure 2

Photopatterning optical exposure setup. The light beam from the illumination lamp passes through the predesigned patterns of slits in the photomask and becomes polarized. The pattern image is then focused on the inner surfaces of the microfluidic LC chamber by the combination of two objective lenses.

Figure 3

Electrokinetic flows in LC electrolytes with unidirectionally periodic director patterns. (a)–(c) polscope textures of nematic cell with surface-imposed director patterns described by Eqs. (7a)–(7c), respectively; “+” and “−” show the charges separated by the electric field of the shown polarity; reversal of the field polarity reverses the polarity of the charges but the driving Coulomb force remains the same. (d)–(f) Corresponding LC flow velocity maps caused by an ac field directed along the horizontal $x$ axis. (g)–(i) Averaged $x$ component of the nematic velocity vs the distance along the $y$ axis, corresponding to the periodic director fields in (a)–(c), respectively.

Figure 4

Disclination pair (−1/2,1/2) pattern. (a) Designed (−1/2,1/2) director slits pattern; disclination −1/2 is core marked by a triangle and 1/2 core is marked by a semicircle. (b) Simulated polarizing microscopy texture of (−1/2,1/2) disclination pair. (c) Polarizing microscopy texture of the (−1/2,1/2) disclination pattern in the assembled and photoaligned cell. (d) Streamlines of electrokinetic flow caused by the ac electric field applied along the $x$ axis and visualized by fluorescent 200 nm tracers. P and A represent the polarizer and analyzer.

Figure 5

Nonlinear electrokinetic flows in LC electrolytes with pairs of topological defects. (a) polscope texture of a nematic cell with disclination −1/2 (core marked by a triangle) and 1/2 (core marked by a semicircle). (b) Map of spatially separated charges in a dc electric field. (c) Velocity of LC flows caused by an ac field $\left(E_0,0\right)$. (d) LC volume pumped per unit time along the $x$ axis, $Q_x\left(x\right)$, and along the $y$ axis, $Q_y\left(y\right)$. (e) Maximum elecrokinetic flow velocity vs distance $d$ between the disclinations.

Figure 6

Slit patterns representing disclination triplets. (a),(e) Designed slit patterns of (−1/2,1,−1/2) (a) and (1/2,−1,1/2) (e) disclinations. (b),(f) Simulated polarizing microscopy texture of (−1/2,1,−1/2) and (1/2,−1,1/2) disclinations. (c)(g) Polarizing microscopy texture of (−1/2,1,−1/2)and (1/2,−1,1/2)sets of disclinations; note the split character of the core of the integer-strength central defect. (d),(h) Streamlines of electrokinetic flow caused by (−1/2,1,−1/2) and (1/2,−1,1/2) sets, caused by the ac electric field applied along the horizontal direction in the plane of the figure. P and A the represent polarizer and analyzer.

Figure 7

Nonlinear electrokinetic flows in LC electrolytes with triplets of topological defects. (a) polscope texture of a nematic cell with three disclinations (−1/2,1,−1/2) (−1/2 core marked by a triangle, 1 core marked by a circle). (b) Corresponding velocity map of the nematic caused by the pattern in (a) caused by an ac electric field $\left(E_0,0\right)$. (c) Numerically simulated electrokinetic flow velocity map. (d) polscope texture of disclinations (1/2,−1,1/2), (1/2 core marked by a semicircle, −1 core marked by a square). (e) Corresponding velocity map caused by the pattern in (d). (f) Volume of nematic fluid pumped per unit time along the horizontal $x$ axis, $Q_x\left(x\right)$, and along the $y$ axis, $Q_y\left(y\right)$; the flow is of quadrupolar symmetry with four vortices and no pumping effect.

Figure 8

Nonlinear electrokinetic flows in LC electrolytes with patterns of two-dimensional lattice of topological defects. (a) Polarizing microscopy texture of a periodic array of disclinations. (b) polscope texture of the area indicated in (a). (c) Streamlines of electrokinetic flow caused by the ac electric field along the $x$ axis and visualized by fluorescent 200 nm tracers. (d) Corresponding velocity field in the same region. (e) Streamlines of electrokinetic flow caused by the ac electric field acting along the $y$ axis. (f) Corresponding velocity field.

Figure 9

Transport of cargo by patterned LCEK flows.(a),(b) Linear transport of two polystyrene particles of diameter $5 \mu \mathrm{m}$ in the LC with the periodic pattern shown in Fig. 3. (c),(d) Linear transport of an air bubble (profiled by a dashed circle) in the nematic chamber with periodic director pattern. (e)(f) LC flows carry a water droplet (marked by a small arrow) doped with the dye Brilliant Yellow in the nematic chamber with the (−1/2,1/2) disclination pattern shown in Fig. 5; the trajectory is shown by a curved arrow; the droplet is transported towards the core of the 1/2 disclination on the right-hand side and coalesces with another water droplet that is already trapped there.

Figure 10

Micromixing in a Y junction with photopatterned director distortions. (a) Y junction with a photoimprinted mixing pad (red square) that combines the LC with fluorescent particles (green), and pure LC (black). (b) polscope texture of the mixing pad. (c) Velocity maps within the mixing pad (Supplemental Material Movie S5 [23]). (d) Comparison of mixing efficiencies of passive diffusion and LCEK; the insets show the fluorescence microscopy textures of the mixing pad with the exposure time interval 550 s after the start of mixing.