ABSTRACT
A number of atomic force microscopy cantilevers have been exhaustively calibrated by a number of techniques to obtain both normal and frictional force constants to evaluate the relative accuracy of the different methods. These were of either direct or indirect character—the latter relies on cantilever resonant frequencies. The so-called Sader [Rev. Sci. Instrum. 70, 3967 (1999)] and Cleveland [Rev. Sci. Instrum. 64, 403 (1993)] techniques are compared for the normal force constant calibration and while agreement was good, a systematic difference was observed. For the torsional force constants, all the techniques displayed a certain scatter but the agreement was highly encouraging. By far the simplest technique is that of Sader, and it is suggested in view of this validation that this method should be generally adopted. The issue of the photodetector calibration is also addressed since this is necessary to obtain the cantilever twist from which the torsional force is calculated. Here a technique of obtaining the torsional photodetector sensitivity by combining the direct and indirect methods is proposed. Direct calibration measurements were conducted in liquid as well as air, and a conversion factor was obtained showing that quantitative friction measurements in liquid are equally feasible provided the correct calibration is performed.
ACKNOWLEDGMENTS
The authors acknowledge John Sader for the explanation of the trend in Fig. 4. The AFM was financed by a generous grant from the Knut and Alice Wallenberg foundation. The authors acknowledge a reviewer of the first version of this article for useful comments and bringing Ref. 14 to our attention. One of the authors (T.P.) acknowledges financial support from Swedish Research Council. Two of the authors (M.R. and N.N.) acknowledge support from BiMaC, the Biofibre Materials Centre at KTH and Biomime, the Swedish Centre for Biomimetic Fibre Engineering. One of the authors (M.R.) is a fellow of the Swedish Research Council.
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