No anomalous scaling in electrostatic calibrations for Casimir force measurements

Abstract

In a recent paper (Phys. Rev. A78, 020101(R) (2008)

Hydrodynamic force measurements under precisely controlled conditions: Correlation of slip parameters with the mean free path

“…49 and 50, the possibility to simultaneously measure both the Casimir force and the hydrodynamic force allows us to rule out systematic effects. In a previous work, 50 for example, we have utilized the same setup described in Sec. III to study the dependence of the Casimir force on the dielectric properties of the boundaries under experimental conditions for which the hydrodynamic drag was supposed to stay constant.…”

“…Finally, the conversion factor ξ that relates the AFM output signal to the measured force requires accurate calibration. As we have demonstrated recently, 50 all of these problems may be tackled simultaneously by means of an in situ dynamic electrostatic calibration method. The latter allows for the determination and compensation of the contact potential (residual V 0 < 50 μV) at each position d pz , an accurate calibration of the conversion factor (error <0.01 %), and the extraction of d 0 for every data set (error ∼0.5 nm, due to thermal drift within one sweep).…”

“…By holding the quantity V 2 AC /d small and constant for all separations throughout the experiments, the corresponding bending of the cantilever is limited to 50 pm. 50 Therefore, we can assume the sensor response to be constant over almost the entire range of distances approached in the experiment. It has to be noted that at smallest separations d < 80 nm both the hydrodynamic and Casimir forces result in cantilever deflections of more than 1 nm, which gives rise to a systematic error, forcing us to exclude the data taken in this regime from the fits.…”

Distance upon contact: Determination from roughness profile

“…In Casimir force measurements d 0 is determined using electrostatic calibration. In this case the force dependence on the separation is known, and one can determine the absolute separation ͑see resent discussions [16][17][18] ͒. Even when the distance is not counted from the point of contact 16,17,19 local realization of roughness as shown in this paper will contribute to uncertainty of the absolute separation.…”

“…In the experiments 13,14,17,19,22 the sphere attached to a cantilever or an optical fibre approaches the plate. Assuming that the sphere is large, R ӷ d, the local distance is…”