A scheme for solving the plane-plane challenge in force measurements at the nanoscale

Non-contact interaction between two parallel flat surfaces is a central paradigm in sciences. This situation is the starting point for a wealth of different models: the capacitor description in electrostatics, hydrodynamic flow, thermal exchange, the Casimir force, direct contact study, third body confinement such as liquids or films of soft condensed matter. The control of parallelism is so demanding that no versatile single force machine in this geometry has been proposed so far. Using a combination of nanopositioning based on inertial motors, of microcrystal shaping with a focused-ion beam (FIB) and of accurate in situ and real-time control of surface parallelism with X-ray diffraction, we propose here a "gedanken" surface-force machine that should enable one to measure interactions between movable surfaces separated by gaps in the micrometer and nanometer ranges.