Interpretation of force curves in force microscopy

Since the introduction of force microscopy in 1986 as a tool for imaging insulators, it has increasingly been acclaimed as a quantitative probe of surface forces such as van der Waals, capillary, electrostatic, capacitive, double-layer, magnetic or adhesive forces. A plot of the force interaction between two surfaces - typically a tip mounted on a cantilever beam and a flat surface - as a function of relative tip-sample separation constitutes a force curve, and such measurements have been termed `force spectroscopy' (FS). We describe how to interpret force curves so as to gain information about (i) the instant of tip-sample contact, (ii) the magnitude and functional dependence of adhesive and long-range attractive forces for different tip/sample combinations, (iii) possible mechanisms of long-range force interaction (surface layers, fixed dipoles, patch charges), (iv) tip-sample contact area, which relates to the imaging mechanism in contact-mode force microscopy, (v) the elastic modulus and plasticity of thin and thick films, and (vi) how the pull-off force varies as a function of the maximum load. Van der Waals forces (in experiments with tips of high curvature) are masked by a longer-range attraction. The patch charge model gives the most promising explanation and the best fit to the data. The general shape of the force curve fits well to a semi-empirical formula that includes terms representing elastic repulsion, long-range attraction, and a transition region where surface forces and deformation significantly affect each other. From such empirical fits, values of contact area and of nanomechanical properties of thin films can be derived. For example, for the diamond-graphite system we found values of 0.3 J m-2 for the Dupre energy of adhesion and 4.7 GPa for the reduced elastic modulus, and a patch charge density of 10-5-10-6 electrons angstroms-2. Even at zero externally-applied load, the contact areas exceed atomic dimensions. We often find a surprising empirical relation between the pull-off force and the maximum load applied from when the specimens were placed in contact. The relationship is hard to explain but could perhaps yield information on the local nanotopography or surface chemistry of the tip-sample interface.