Improved in situ spring constant calibration for colloidal probe atomic force microscopy

In colloidal probe atomic force microscopy (AFM) surface forces cannot be measured without an accurate determination of the cantilever spring constant. The effective spring constant k depends upon the cantilever geometry and therefore should be measured in situ; additionally, k may be coupled to other measurement parameters. For example, colloidal probe AFM is frequently used to measure the slip length b at solid/liquid boundaries by comparing the measured hydrodynamic force with Vinogradova slip theory (V-theory). However, in this measurement k and b are coupled, hence, b cannot be accurately determined without knowing k to high precision. In this paper, a new in situ spring constant calibration method based upon the residuals, namely, the difference between experimental force-distance data and V-theory is presented and contrasted with two other popular spring constant determination methods. In this residuals calibration method, V-theory is fitted to the experimental force-distance data for a range of systematically varied spring constants where the only adjustable parameter in V-theory is the slip length b. The optimal spring constant k is that value where the residuals are symmetrically displaced about zero for all colloidal probe separations. This residual spring constant calibration method is demonstrated by studying three different liquids (n-decanol, n-hexadecane, and n-octane) and two different silane coated colloidal probe-silicon wafer systems (n-hexadecyltrichlorosilane and n-dodecyltrichlorosilane).