A method for the calibration of force microscopy cantilevers via hydrodynamic drag

A new method for the in situ and nondestructive calibration of cantilevers used in force microscopy employing hydrodynamics is described. Using the notion that the viscous drag on objects is scale invariant for similar Reynolds numbers, the drag on a 500:1 scale model of a typical cantilever was compared with that of the actual cantilever drag within the Stokes regime of laminar flow. The spring constant of the model cantilever was determined via static end loading with known masses, and the distributed load due to viscous drag was carried out in neat glycerol. A master curve of the ratio of distributed load to point load was determined as a function of distance from a horizontal surface. Similar curves were then obtained for actual cantilevers in water, the comparison of which to the master curve provided an estimate of the spring constant.