Propelling and spinning of microsheets in nematic liquid crystals driven by ac electric field

Dynamics of microparticles in isotropic liquids by transducing the energy of an applied electric field have been studied for decades. Recently, such studies in anisotropic media like liquid crystals have opened up new perspectives in colloid science. Here, we report studies on ac-electric-field-driven dynamics of microsheets in nematic liquid crystals. In planar aligned liquid crystals, with negative dielectric anisotropy, the microsheets are propelled parallel to the director. A steady spinning of the microsheets is observed in homeotropic cells with positive dielectric anisotropy liquid crystals. The velocity of propelling and the angular frequency of spinning depends on the amplitude and the frequency of the applied electric field. The electrokinetic studies of anisotropic microparticles are important as they are potential for applications in microfluidics and in areas where the controlled transport or rotation is required.

Figure 1

Optical microscopy image of hexagonal single crystal microsheets.

Figure 2

(Top view) Electric-field-driven propelling of a microsheet in a planar nematic cell with negative dielectric anisotropy liquid crystal (MLC 6608) (see Supplemental Material S1: video 1 [29]). (a–d) Sequence of CCD images of the microsheet taken at different times and at applied field, $E$= 2.8 V/$\mu \mathrm{m}$ and frequency, $f$= 1 kHz. Cell thickness $d$ = 15 $\mu \mathrm{m}$. Double-headed arrow at the right corner indicates the director and the electric field direction is out of plane.

Figure 3

(a) The time-dependent position of a microsheet at a fixed field strength $E=3.4\text{V}/\mu \text{m}$. (b) Electrophoretic velocity $v$ as a function of the applied electric field at a fixed frequency $f=1\text{kHz}$. Cell thickness $d=15\mu \text{m}$. The red line is the best fit to $v\propto E^2$. (Inset) The linear variation of $v$ with $E^2$.

Figure 4

Variation of velocity as a function of applied frequency at two different fixed field strengths, $E=3.2\text{V}/\mu \text{m}$ (green open circles) and $E=4\text{V}/\mu \text{m}$ (filled blue circles), respectively. Cell thickness $d=15\mu m$. The continuous red lines are the best fits to Eq. (1).

Figure 5

(a) Schematic top view of a microsheet in a planar aligned nematic at $E=0$. Here the plane of the microsheet is parallel to $x\text{−}y$ plane. The director field surrounding the microsheet is shown with dotted lines. (b) Schematic side view when the field is applied along the $z$ axis and $E>1\text{V}/\mu \text{m}$, the microsheet rotates along the $x$ axis and its plane becomes parallel to $x\text{−}z$. The black arrow indicates the transport direction of the microsheet.

Figure 6

Electric field response of microsheet at higher frequency ($f$ = 100 kHz). Applied field amplitude $E=3.5\text{V}/\mu \text{m}$. (b) The microsheet first rotates and the short axis of the sheet is now along the field direction. (c) The microsheet moves toward the bottom substrate and goes out of focus (see Supplemental Material S2: video 2). (d–f) Returning back to the previous position after switching off the field.

Figure 7

Electric-field-driven spinning of a microsheet in a homoetropic cell with 5CB nematic liquid crystal (see Supplemental Material S3: video 3). (a–f) Sequence of CCD images of the microsheet taken at different times at field amplitude $E=0.85\text{V}/\mu \text{m}$ and frequency, $f=1\text{kHz}$. $\widehat{n}$ is the director and the field direction is out of the plane. White arrows indicate the direction of rotation. Cell thickness $d=20\mu \text{m}$.

Figure 8

(a) Variation of angular frequency of spinning of a microsheet as a function of the applied electric field. The driving frequency is $f$= 1 kHz. The solid red line is the best fit to $\omega \propto E^2$. (Inset) Linear variation of $\omega$ with $E^2$. (b) Variation of angular frequency of spinning as a function of driving frequency of the field ($E$ = 1.5 V/$\mu \mathrm{m}$). Red line shows the best fit to $\omega \propto 1/f$.