Research ArticleCONDENSED MATTER PHYSICS

Electrostatically controlled surface boundary conditions in nematic liquid crystals and colloids

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Science Advances  20 Sep 2019:
Vol. 5, no. 9, eaax4257
DOI: 10.1126/sciadv.aax4257
  • Fig. 1 Characterization of the platelets’ size and orientation in nematic LC.

    SEM micrographs of platelets before (A) and after (B) SiO2 coating. (C) TEM micrograph of particles. The inset shows the SiO2 layer, visible at the platelet’s edge as a thin gray stripe. (D) Schematic of the platelets showing a core, SiO2 coating, and Si-PEG layer. (E to H) Optical micrographs of platelets with conic (E), planar (F and G), and perpendicular (H) surface anchoring under crossed polarizer P and analyzer A without (left) and with (right) a retardation plate γ in a nematic cell. (I to L) Schematic diagrams of n(r) (green lines) around platelets with conic (I and J), planar (K), and perpendicular (L) anchoring. Inset in (J) is a schematic of conic degenerate boundary conditions. (M to P) Experimental sequence of optical micrographs, with elapsed time marked, showing reorientation of platelets with planar anchoring when a magnetic field B ≈ 480 G is applied normal to the image planes. Insets show schematics of n(r) around a platelet 1 at sn0||B in (M) and sn0B in (P).

  • Fig. 2 Measurement of tilt angle.

    (A) Texture of a nematic LC cell with substrates covered with platelets, with conic surface anchoring caused by surface charging; the inset shows n(r) around half-integer disclinations connected by a surface wall defect, indicative of conic boundary conditions. (B) Corresponding schematic of LC alignment with director tilted to the surface normal s.

  • Fig. 3 Characterization of translational and rotational diffusion of platelets.

    Translational (A to D) and rotational (E to G) diffusion of platelets in a nematic LC. (A to C) Dt of a platelet with (A) perpendicular, (B) planar, and (C) conical boundary conditions in a planar cell with in-plane n0; black and red dashed lines in (C) show a normal to the platelet and a direction of maximum displacements, respectively. Magnetic field B ≈ 480 G in (B) and (C) keeps the orientation platelet’s s parallel to the field of view. (D) Dt of a platelet with planar surface anchoring in a homeotropic cell; red and blue plots show Dt with respect to the cell and particle coordinate frames, respectively. Inset micrographs in (A) to (D) show the actual platelets undergoing diffusion. (E) Orientational fluctuations δθ of a tilted platelet in (C) with respect to its preferred orientation θe versus time t obtained at τ = 67 ms. (F) Histograms of angular displacements Δθ and Δβ obtained at τ = 67 ms, respectively, in planar and homeotropic cells. The solid blue and green lines are Gaussian fits. (G) Angular mean square displacement 〈Δθ2〉 versus lag time τ in a planar cell. A solid red line is a fit of experimental data (black filled circles) with 〈Δθ2(τ)〉. (H) Histogram of platelet orientations obtained at τ = 67 ms during ~10 min.

  • Fig. 4 Effect of ionic content of LC medium.

    (A) Schematic diagram of the LC alignment (an ellipsoid) at the surface (blue); ep, eef, and elc show the easy axes determined by interactions with the polymer capping, electrostatic interactions, and the LC alignment resulting from their competition, respectively. Φ is an electric potential varying over the thickness of the double layer, and r is a distance from the platelet surface. A red arrow shows the direction of EDL. Positive and negative charges are shown by green and yellow filled circles, respectively. The right-side insets schematically show the density of a positive charge (green spheres) at the platelet surface in as-purchased and doped 5CB. (B to D) Distributions of orientation for platelets in a planar cell when dispersed in pure 5CB (B) and salt-doped 5CB for NaCl concentrations of 1 nmol/ml (C) and 0.1 nmol/ml (D). Insets in (B) and (C) are optical micrographs of platelets at orientation, tilted and parallel to n0 in the respective LC media. (E) Change of θ with time for a platelet in pure 5CB due to absorption of ions from the atmosphere. (F) Distributions of platelet orientations showing discrete increments in the angle θ. The red line is a Gaussian fit of the central part of a distribution shown in (E) corresponding to the completed step during the change of the orientation.

  • Fig. 5 Self-assembled colloidal lattice formed by platelets.

    (A) Upconversion luminescence confocal image and (B) schematic of a self-assembled colloidal lattice of charged platelets with perpendicular anchoring in a planar cell. The measured (defined on schematics) parameters of the rhombic lattice: a = b ≈ 3 μm, ϕ ≈ 100°. (C and D) Schematics of 2D assemblies in a nematic LC for platelets with tilted (C) and planar (D) boundary conditions. Insets in (C) and (D) show the experimental fragments of corresponding assemblies, where θe ≈ 34°, a ≈ 2.1 μm, b ≈ 3.7 μm, and ϕ ≈ 56° in (C) and θe ≈ 0°, a = b ≈ 2.5 μm, and ϕ ≈ 68° in (D).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/9/eaax4257/DC1

    Supplementary Text

    Table S1. Physical parameters of 5CB.

    Table S2. Variations of Debye screening with ionic concentration.

    Table S3. Variations of Debye screening with time.

    Fig. S1. Variation of equilibrium conic angle and angular distribution with surface charge on the platelets.

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Text
    • Table S1. Physical parameters of 5CB.
    • Table S2. Variations of Debye screening with ionic concentration.
    • Table S3. Variations of Debye screening with time.
    • Fig. S1. Variation of equilibrium conic angle and angular distribution with surface charge on the platelets.

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