Electric-field-induced transport of microspheres in the isotropic and chiral nematic phase of liquid crystals

The application of an electric field to microspheres suspended in a liquid crystal causes particle translation in a plane perpendicular to the applied field direction. Depending on applied electric field amplitude and frequency, a wealth of different motion modes may be observed above a threshold, which can lead to linear, circular, or random particle trajectories. We present the stability diagram for these different translational modes of particles suspended in the isotropic and the chiral nematic phase of a liquid crystal and investigate the angular velocity, circular diameter, and linear velocity as a function of electric field amplitude and frequency. In the isotropic phase a narrow field amplitude-frequency regime is observed to exhibit circular particle motion whose angular velocity increases with applied electric field amplitude but is independent of applied frequency. The diameter of the circular trajectory decreases with field amplitude as well as frequency. In the cholesteric phase linear as well as circular particle motion is observed. The former exhibits an increasing velocity with field amplitude, while decreasing with frequency. For the latter, the angular velocity exhibits an increase with field amplitude and frequency. The rotational sense of the particles on a circular trajectory in the chiral nematic phase is independent of the helicity of the liquid crystalline structure, as is demonstrated by employing a cholesteric twist inversion compound.

Figure 1

(a) Field amplitude-frequency stability regimes for circular and random motion of microspheres in the isotropic phase of a liquid crystal. (Black and red symbols indicate the boundaries between different motional behavior, lines are a guide to the eye.) (b) Exemplary circular microsphere trajectory in the plane of the liquid crystal sandwich cell.

Figure 2

Angular microsphere velocity as a function of (a) applied electric field amplitude at a constant frequency of $f=160\mathrm{Hz}$, and (b) frequency at constant electric field amplitude of $E=5\mathrm{V}/\mu \mathrm{m}$. The angular velocity ω increases with increasing field and is independent of frequency.

Figure 3

Diameter of the circular microsphere trajectory as a function of (a) electric field amplitude and (b) frequency, for the same experimental conditions as in Fig. 2. For both parameters the diameter decreases for increasing control parameter.

Figure 4

A fit of the experimental data for the isotropic phase to a rearranged Eq. (1) yields a critical field of approximately $E_{\mathrm{cr}}\approx 3\mathrm{V}/\mu \mathrm{m}$ and a Maxwell-Wagner relaxation time of about ${\tau }_{\mathrm{MW}}\approx 1\mathrm{s}$, in agreement with qualitative experimental observations.

Figure 5

Field amplitude-frequency stability regimes for linear, circular, and random motion of microspheres in a chiral nematic liquid crystal phase. (Black, red, and green symbols indicate the boundaries between different motional behavior, lines are a guide to the eye.)

Figure 6

Exemplary trajectory of a microsphere in the chiral nematic phase, subjected to relatively small fields at low frequencies $(E=2.7\mathrm{V}/\mu \mathrm{m},f=40\mathrm{Hz})$, leading to linear particle motion.

Figure 7

Linear microsphere velocity as a function of (a) electric field amplitude and (b) frequency, in the chiral nematic phase. While the velocity increases with increasing field, it decreases slightly with increasing frequency, which is in qualitative agreement with the particle motion observed in achiral nematic phases [9].

Figure 8

Exemplary trajectory of a microsphere in the chiral nematic phase, observed in the plane of the sandwich cell at slightly increased electric field amplitude as compared to Fig. 6 $(E=3.9\mathrm{V}/\mu \mathrm{m},f=40\mathrm{Hz})$, leading to circular particle motion. The onset of a domain structure in the texture indicates the onset of electrohydrodynamic effects in the liquid crystal. All electric-field-dependent measurements were performed below this onset.

Figure 9

Angular microsphere velocity in the chiral nematic phase as a function of (a) electric field amplitude at constant frequency of $f=40\mathrm{Hz}$ and (b) frequency at applied field $E=3.6\mathrm{V}/\mu \mathrm{m}$. For increasing control parameters the angular velocity increases in magnitude.

Figure 10

A fit of the experimental data for the chiral nematic phase to a rearranged Eq. (1) yields a critical field, which is still comparable to that of the isotropic phase, $E_{\mathrm{cr}}\approx 3\mathrm{V}/\mu \mathrm{m}$, but with an increased Maxwell-Wagner relaxation time to ${\tau }_{\mathrm{MW}}\approx 4\mathrm{s}$.

Figure 11

Texture series of the employed cholesteric twist inversion compound W46 to establish a possible relationship between direction of circular particle motion and helix sense. (a) Crystalline phase, (b) left-handed cholesteric phase with pitch jumps approaching the twist inversion temperature, (c) right-handed cholesteric phase with remains of oily streaks formed during the twist inversion, and (d) annealed right-handed cholesteric phase in Grandjean orientation. The cell gap is $d=6\mu \mathrm{m}$, planar anchoring conditions. Part (e) demonstrates the helical pitch inversion as a function of temperature, with negative values implying a left-handed helix and positive values a right-handed structure (after [42], reproduced by permission of Taylor & Francis).