Atomic force microscopy spring constant determination in viscous liquids

The spring constant of cantilever in atomic force microscopy (AFM) is often calibrated from thermal noise spectra. Essential for accurate implementation of this thermal noise method is an appropriate fitting function and procedure. Here, we survey the commonly used fitting functions and examine their applicability in a range of environments. We find that viscous liquid environments are extremely problematic due to the frequency dependent nature of the damping coefficient. The deviations from the true spring constant were sometimes more than 100% when utilizing the fit routines built into the three investigated commercial AFM instruments; similar problems can arise with homebuilt AFMs. We discuss the reasons for this problem, especially the limits of the fitting process. Finally, we present a thermal noise based procedure and an improved fit function to determine the spring constant with AFMs in fluids of various viscosities.