We demonstrate, for the first time, confinement of the orientation of micron-sized graphitic flakes to a well-defined plane. We orient and rotationally trap lipid-coated highly ordered pyrolytic graphite (HOPG) micro-flakes in aqueous solution using a combination of uniform magnetic and AC electric fields and exploiting the anisotropic diamagnetic and electrical properties of HOPG. Measuring the rotational Brownian fluctuations of individual oriented particles in rotational traps, we quantitatively determine the rotational trap stiffness, maximum applied torque and polarization anisotropy of the micro-flakes, as well as their dependency on the electric field frequency. Additionally, we quantify interactions of the micro-particles with adjacent glass surfaces with various surface treatments. We outline the various applications of this work, including torque sensing in biological systems. IntroductionMicro-and nano-particles of carbon such as graphene/graphite platelets and carbon nanotubes have unique electrical, magnetic, optical and mechanical properties that, combined with their biocompatible nature and their chemical and biological functionalization capability, make them very attractive for numerous applications. The controlled manipulation and orientation of such micro/nano-particles over macroscopic length-scales has interesting applications for batteries and energy storage devices 1 , for opto-electronic devices, including recently developed magnetically and electrically switched graphene-based liquid crystals 2-5 , and for the creation of novel artificial composite materials with tailored anisotropic properties such as conductive polymers and gels 6 , material reinforcements 7 , materials for thermal management solutions 8 , hydrophobic coatings, infra-red absorbing coatings, etc. The controlled orientation of graphene-based micro/nano-particles can aid the synthesis of large-scale monocrystalline graphene composites 9,10 and can lead to advances in template-mediated synthesis, for instance to induce the ordered deposition of organic molecules 11 .In this paper, we demonstrate, for the first time, confinement of the orientation of graphitic micro-flakes to a well-defined plane using a novel magneto-electrical approach for fully controlling micro-particle orientation. We orient and rotationally trap soluble, biocompatible, lipid-coated micro-particles of highly ordered pyrolytic graphite (HOPG) in aqueous solution. Our scheme takes advantage of the anisotropic diamagnetic and electrical properties of HOPG micro-flakes (graphene layer stacks) 12 to orient them parallel to a plane defined by two perpendicular fields: a vertical static magnetic field (∼ 240 mT); and a horizontal, linearly polarized electric field (∼ 2 × 10 4 V/m) oscillating at frequencies above 10 MHz. Our inexpensive set-up is made from one permanent magnet and two thin wire electrodes, involving no micro-fabrication. While we demonstrate our scheme on HOPG,

SignificanceThis paper presents the magnetic transport of diamagnetic graphite microparticles in water solutions. Given the dominance of viscous drag forces at the microscale, moving a microparticle that is submerged in liquid is comparably as hard as moving a macroparticle within dense honey. While diamagnetism is a weak magnetic property, for graphite it can be exploited to generate useful transport in liquid. The contactless magnetic control of biocompatible micrographite, together with graphite’s unique physical properties, opens up possibilities for applications in sensing, analysis, synthesis, and diagnosis in chemistry, biology, medicine, and physics.

Graphitic micro-particles are commonly coated with thin layers to generate stable aqueous dispersions for various applications. Such particles are technologically interesting as they can be manipulated with electric fields. Modeling the electrical manipulation of submerged layered micro-particles analytically or numerically is not straightforward. In particular, the generation of reliable quantitative torque predictions for electro-orientation experiments has been elusive. The traditional Laplace model approximates the coated particle by an ellipsoid with a confocal ellipsoidal layer and solves Laplace's equation to produce convenient analytical predictions. However, due to the non-uniformity of the layer thickness around the ellipsoid, this method can lead to incorrect torque predictions. Here we present a new theoretical dual-ellipsoid Laplace model that corrects the effect of the non-uniform layer thickness by calculating two layered ellipsoids, each accounting for the correct layer thickness along each relevant direction for the torque. Our model describes the electro-orientation of submerged lipid-coated graphitic micro-particles in the presence of an alternating current (AC) electric field and is valid for ellipsoids with moderate aspect ratios and coated with thin shells. It is one of the first models to generate correct quantitative electric torque predictions. We present model results for the torque versus frequency and compare them to our measurements for lipid-coated highly ordered pyrolytic graphite (HOPG) micro-flakes in aqueous NaCl solution at MHz frequencies. The results show how the lipid shell changes the overall electrical properties of the micro-flakes so that the torque is low at low frequencies and increases at higher frequencies into the MHz regime. The torque depends critically on the lipid-shell thickness, the solution conductivity and the shape of the particle, all of which can be used as handles to control the response of the particles. Our model is useful to predict the frequencies at which electro-orientation can be observed in dilute dispersions and the reduction in torque caused by the shell.