# Repulsive Force for Micro- and Nano-Non-Contact Manipulation
## 1 Introduction  
Non-contact micro-nanomanipulation or micro-sorting consists the manipulation or sorting of microparticles using forces generated via a long range physical field (magnetic field, electrostatic field, acoustic field). The behavior and the design of the devices are significantly modified by the well-known scale effects [1]. When the scale reduces, the physical effects' magnitude is drastically modified: when the lengths are divided by 10, the volume effects (e.g., weight mass) are divided by \(10^{3}\), and the surface forces (e.g., van der Waals force) are divided only by \(10^{2}\). Therefore, the effect of gravity thus decreases more rapidly than the effect of surface forces during miniaturization [2]. Hence, on the microscale, the surface forces are predominant compared to the weight and the objects which tend to stick to the surfaces (e.g., adhesion [3]). Therefore, the manipulation (movement and position) of a micro-object is usually performed without touching it, but instead by using the proposed \"non-contact manipulation\" to avoid adhesion disturbance [4]. These manipulation methods are usually propelled by electrostatic [5], laser-induced thermal gradient [6], optical trapping [7, 8], magnetic [8, 9], or thermocapillary [10] forces. This article presents a new way to perform micromanipulation using electrostatic forces. In this field, the electric field is usually generated by (micro)electrodes placed in a liquid in order to induce dielectrophoresis (DEP) [11], optically induced dielectrophoresis (ODEP) [12],electro-rotation [13], or electrophoresis [14]. Indeed, applying a voltage on electrodes induces charges generating an electric field up to the electrodes. The microparticles located in the electric field experience a force of several tens of micrometers away from the electrodes depending on the applied electric field generated by the charges of the electrodes, the particle's size, and electrical properties. This general principle is usually used to sort particles [12; 15]. The objective of this paper is to propose a new way to control non-contact manipulations based on electric fields. Indeed, we propose to generate electrophoretic force using electric charges based on chemical principles in spite of generating electric charges generated with an external voltage. Concretely, a local chemical functionalization (typically amine groups) enables to locally concentrate electric charges generating an electric field up to the substrate in the liquid [16]. In order to be usable, the electric field generated by chemical functions has to be able to induce significant electrostatic forces on microparticles on a long range (typically greater than one micron). We demonstrate below the highly impacted interaction distance by the scale effect, showing that nanoparticles and microparticles have significant different behaviors. In nanoscale, the repulsive forces between colloids and a flat surface were already measured by different researchers in liquid media. The measures of repulsion forces enable to identify the hydration force [17] or electrostatic repulsions in inorganic solvents with different types of spheres glued on atomic force microscope (AFM) tips: alumina or silica [18], silicon nitrite [19], and gold [20] tips. More recently, some repulsive electrostatic forces have been measured in water [21]. In all these cases, the size of the sphere diameter is less than \(5\,\mathrm{\SIUnitSymbolMicro m}\) and the interaction distance is near \(20\,\mathrm{nm}\). Our paper focuses on larger microspheres whose diameters are higher than several micrometers. We demonstrate below the possibility to generate significant electrostatic forces on these microparticles over a long range (around tenth micron). Section 2 introduces the materials and methods used in the technical parts. Section 3 reports some experimental force measurement illustrating the long-range interaction forces. Section 4 focuses on a model of the force whose comparison with experiments is described in Section 5.