Electromigration of microspheres in nematic liquid crystals I. Dierking, * G. Biddulph, and K. Matthews School of Physics and Astronomy, University of Manchester, Schuster Building Oxford Road, Manchester M13 9PL, United Kingdom Received 9 August 2005; revised manuscript received 7 October 2005; published 4 January 2006 Application of an electric field to microspheres, dispersed in a nematic liquid crystal host material, causes particle translation along the direction of the average long molecular liquid crystal axis, i.e., the director. We have determined the stability regime of linear particle displacement in the parameter space of electric field amplitude and frequency for various applied electric wave forms and demonstrate a linear relationship between microsphere velocity and applied electric field amplitude. For increasing frequency the particle velocity ex- hibits a maximum before motion slowly vanishes. Addition of a small amount of an ionic dopant is shown to largely increase the stability region of linear microsphere motion, with particle velocities increasing until saturation is observed for increasing ion dopant concentration. It is presumed that the particle velocity is related to the surface charges adsorbed on the dispersed particles. Also the dynamics of occasionally observed two- and three-particle clusters is discussed. DOI: 10.1103/PhysRevE.73.011702 PACS numbers: 61.30.-v, 82.45.-h, 45.50.-j I. INTRODUCTION The study of the motion of particles, dispersed in a fluid medium while subjected to an electric field, has been a long- standing topic in science. The phenomenon, named electro- phoresis, covers the rotational as well as the translation mo- tion of particles and is used in a wide variety of applications ranging from analytical chemistry and biology 1 all the way to display technologies 2. First investigations go back to the 19th century when Weiler reported on a field-induced translation of chininsulfate particles in turpentine-oil 3, and Quincke discussed the rotation of solid particles in a liquid subjected to constant electric fields 4. It took almost a cen- tury to describe this rotation theoretically 5 and was later linked to bifurcation behavior 6. Nevertheless, electro- phoresis is mainly discussed in relation to translational par- ticle motion in isotropic liquids. For small amplitudes this motion proceeds with a velocity proportional to the electric field, v = E, where  is the electrophoretic mobility. For spherical particles the motion is directed parallel to the di- rection of the applied electric field. Considerable theoretical work has been reported for static 7 and alternating 8 elec- tric fields, spheroidal 9 and slender particles 10,11, as well as particles with a nonuniform charge distribution 12,13. It was pointed out that in the case of nonspherical particles the velocity vector does not need to be parallel to the applied electric field vector 7. Electric field induced particle motion in an isotropic matrix seems to be largely understood. It is thus surprising that only very little work in this di- rection has been reported for liquid crystals, because the mo- tion of microspheres can lead towards techniques of mi- crorheology 14–16, especially for the determination of the viscosity anisotropy on a microscopic scale 17. This would be a true advancement in liquid crystal viscosity determina- tion over the classic macroscopic measurements of Kneppe and Schneider 18 more than two decades ago. To date, experimental reports of micron-sized particles in liquid crystals often concentrate on the large volume fraction regime 19,20, while studies of individual microsphere mi- gration in thermotropic liquid crystals have so far been largely qualitative. Circular motion along macroscopic tra- jectories was reported for the isotropic and cholesteric N *  phases 21, while linear motion along the layer plane was observed for the smectic phases 16,21. For such transla- tions a certain threshold voltage must be exceeded when ap- plying symmetric fields, while it has been reported that asymmetric fields lead to threshold-less motion 21. For all cases it is important to notice that the macroscopic particle motion in liquid crystals takes place in a plane perpendicular to the applied electric field direction. This is in contrast to the parallel motion discussed for the electrophoresis of spherical particles in isotropic liquids. The dynamic behavior of microspheres in anisotropic flu- ids, subjected to electric fields, is obviously rather compli- cated. It displays a strikingly rich variety of particle motions: rotation, translation, and irregular movement, all depending on the investigated liquid crystal phase, the applied external conditions and the aggregation status of the particles. To our knowledge there is no theoretical model available to describe such behavior. Even the cause of translational motion of spherical particles in liquid crystals perpendicular to the ap- plied field direction seems to be largely unclear, although it has been proposed that this may be linked to a varied local charge distribution around rotating particles 16. In this pa- per we will concentrate on the translational motion of uni- form microspheres in the simplest of all liquid crystal phases: the nematic phase under unidirectional boundary conditions, exhibiting solely orientational order. II. EXPERIMENT The liquid crystal employed in this investigation was the commercially available and well-known room-temperature *Author to whom correspondence should be addressed. Electronic address: ingo.dierking@manchester.ac.uk PHYSICAL REVIEW E 73, 011702 2006 1539-3755/2006/731/0117026/$23.00 ©2006 The American Physical Society 011702-1