On the force between two metallic plates of a gripper immersed in a nonpolar fluid D. Dantchev, K. Kostadinov Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev St. Bl. 4, 1113 Sofia, Bulgaria Abstract We analyse, as a function on the temperature T and the chemical potential µ , the total force (,,) tot F T L µ between two metallic plates of a gripper separated at a distance L from each other and immersed in a nonpolar fluid which can be liquid, or gas. In our approach we take into account the direct substrate-substrate van der Waals interaction, the van der Waals interactions between the molecules of the fluid with the other molecules of the fluid as well as with the constituent elements of the substrate, and the interaction between the plates generated by the fluctuations of the density of the fluid (i.e., the Casimir force). We suppose that both plates are equal and strongly prefer the liquid phase of the fluid. Under such boundary conditions both the direct plate-plate van der Waals interaction, as well as the Casimir force, are forces of attraction of the plates toward each other. In the phase space (temperature, chemical potential), we identify the regions where the net interaction force is the strongest. It turns out that these regions are close to the bulk critical point of the fluid µ µ = = ( , ) c c T T , and near the so-called capillary condensation regime µ < ∆ = ,( / )( / ) (1) c B T T La kT O , with µ µ µ ∆ = − < 0 c and a the characteristic distance between the molecules of the fluid. These regions shall be avoided in order to prevent sticking of the plates of the gripper on each other. Keywords: grippers, van der Waals forces, Casimir effect, thin films 1. Introduction Handling and fixing of micro parts reliably and precisely is the main bottleneck in micro assembly and is far from being solved today. Further handling and fixing strategies must be developed taking into account the forces appearing in small distances between the gripper’s plates and the micro object or between the object and a surface to taken off or to be placed on. Also the environmental influences are usually not mastered yet and they have to be studied. Tools for assisting the robot in micro assembly tasks are not available today. Components such as micro part feeders and miniature grippers for micro objects also put some problems of interaction in small distances with micro objects that should be studied in order to find ways to control these operations. In this article we study the force between two metallic plates of a gripper immersed in nonpolar fluid. If a fluid is confined by parallel plates at a distance L (see Fig. 1) and is in contact with a particle reservoir with a chemical potential μ and temperature T, the grand canonical potential ( , , ) ex T L µ Ω of the fluid in excess to its bulk value ( , ) bulk AL T ω µ depends on L. Then the effective force tot F between the plates normalized per cross sectional area A is ( , , ) ( , , ) ex tot B T L F T L kT L ω µ µ ∂ =− ∂ , (1) where kB is the Boltzmann’s constant, ( , , ) ( , , ) ( , ) ( , , )/ ex bulk ex T L T L L T T L A ω µ ω µ ω µ µ = − =Ω (2) is the excess grand canonical potential per cross sectional area A, ( , , ) ( , , ) T L A T L µ ω µ Ω = is the total grand canonical potential, and ( , ) bulk T ω µ is the density of the bulk grand canonical potential. Besides temperature T, chemical potential μ, and film thickness L, the force also depends on which boundary conditions the surfaces impose on the system. The order near the surfaces can be either reduced or -- which is the generic case for liquids confined by solid substrates – increased due to effective surface fields generated by the confinement. The latter case is known as (+,+) boundary conditions (for a more precise definition see below). For this case, the schematic phase diagram of a fluid film with thickness L is shown in Fig. 2. In order to calculate the effective force between the Fig. 1. The total and the Casimir force acting on the plates of a gripper. Note that they both are forces of attraction, i.e. the Casimir force causes stronger attraction between the plates. © 2008 Cardiff University, Cardiff, UK. Published by Whittles Publishing Ltd. All rights reserved. S. Dimov and W. Menz (Eds.) Multi-Material Micro Manufacture