Investigating visco-elastic forces at the nanometer-scale is important to thecharacterization of soft materials. A quantitative force measurement can be ob-tained using an atomic force microscope (AFM) with a calibrated force transducer(the AFM cantilever). In this thesis, we discuss and evaluate simple methods ofcalibration and we use these calibrations to measure dynamic force quadraturecurves for both normal and in-plane tip-surface forces using Intermodulation AFM(ImAFM).

ImAFM utilizes the nonlinearity of the tip-surface force by measuring the mix-ing between two or more drive frequencies placed close to a resonance of the AFMcantilever. The intermodulation response at many mixing frequencies provides ad-ditional observables, useful for characterization of materials. We use ImAFM nearthe first flexural resonance to measure visco-elastic materials and we show that sur-face motion plays an important role in the analysis of soft samples. To explain ourmeasurements we derive a simple model where the surface position is described byan exponential relaxation when perturbed from its equilibrium. Through numericalsimulations of this model we explain experiments for many different soft sampleswith varying properties. We further apply the intermodulation technique to softsamples in liquid.

ImAFM at the first torsional resonance frequency induces motion of the tip in-plane with the surface, enabling friction measurements between the tip and sample.Due to the high torsional resonance frequency, the tip velocity can reach severalcm/s, many orders of magnitude higher than typical AFM friction measurements.By measuring the amplitude dependence of the dynamic force quadrature curves,we can resolve the transition between the tip sticking to the surface, through stick-slip to free sliding motion.