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Nonlinear electrophoresis of dielectric and metal spheres in a nematic liquid crystal


Electrophoresis is a motion of charged dispersed particles relative to a fluid in a uniform electric field1. The effect is widely used to separate macromolecules, to assemble colloidal structures and to transport particles in nano- and microfluidic devices and displays2,3,4. Typically, the fluid is isotropic (for example, water) and the electrophoretic velocity is linearly proportional to the electric field. In linear electrophoresis, only a direct-current (d.c.) field can drive the particles. An alternating-current (a.c.) field is more desirable because it makes it possible to overcome problems such as electrolysis and the absence of steady flows5,6. Here we show that when the electrophoresis is performed in a liquid-crystalline nematic fluid, the effect becomes strongly nonlinear, with a velocity component that is quadratic in the applied voltage and has a direction that generally differs from the direction of linear velocity. The new phenomenon is caused by distortions of the liquid-crystal orientation around the particle that break the fore–aft (or left–right) symmetry. The effect makes it possible to transport both charged and neutral particles, even when the particles themselves are perfectly symmetric (spherical), thus allowing new approaches in display technologies, colloidal assembly and separation, microfluidic and micromotor applications.

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Figure 1: Nonlinear electrophoresis in a d.c. field.
Figure 2: A.c. electrophoresis in the nematic liquid crystal.
Figure 3: Electrophoretic motion of DDMAC-coated borosilicate spheres.
Figure 4: Spherical particles with normal anchoring in a nematic liquid crystal with quadrupolar or dipolar symmetry of director distortions.


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We are grateful to L. Tortora for help with surface functionalization of the particles and discussions. The research was supported by NSF DMR 0906751.

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Authors and Affiliations



Experimental strategy was designed by O.D.L. Initial d.c. and a.c. field experiments for dielectric spheres were performed by O.P.P. The d.c. and a.c. field experiments for dielectric and metallic spheres, experiments with non-uniform director and analysis of data were performed by I.L. The paper was written by O.D.L.

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Correspondence to Oleg D. Lavrentovich.

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The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Figure 1 and legend and legends for Supplementary Movies 1-2. (PDF 137 kb)

Supplementary Movie 1

This movie, which relates to figure 2b in the main paper, shows the motion of silica spheres (5μm diameter) coated with OTS - see Supplementary Information file for full legend. (MOV 1208 kb)

Supplementary Movie 2

This movie, which relates to figure 2d in the main paper, shows the motion of borosilicate spheres (17μm diameter) coated with DDMAC - see Supplementary Information file for full legend. (MOV 649 kb)

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Lavrentovich, O., Lazo, I. & Pishnyak, O. Nonlinear electrophoresis of dielectric and metal spheres in a nematic liquid crystal. Nature 467, 947–950 (2010).

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