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quantitative nanomechanical mapping can image the flake without an electrical return path. Repeated AFM force curves provide surface topography, adhesion and deformation or effective elastic modulus channels. The step and differences in tip–surface interaction can distinguish graphene from glass. For an atomically thin supported sheet the contact response is strongly substrate dependent, so fitting a three-dimensional half-space contact model does not directly measure the intrinsic in-plane Young's modulus of free graphene. Calibrate the cantilever spring constant, deflection sensitivity and tip radius, use small loads, and compare bare substrate. The manufacturer's description specifies the force-curve origin of the mechanical channels.^[ref]

Three suitable approaches give complementary contrast. tapping-mode atomic force microscopy supplies surface topography and an oscillation-phase image. It reduces lateral drag and is often effective for soft block copolymer domains. Its phase contrast depends on elastic response, adhesion, dissipation and operating setpoint together: a bright phase domain is not automatically the stiffer polymer. Check contrast as amplitude and setpoint change and use a known reference.

quantitative nanomechanical mapping fits the repulsive portions of many AFM force curves and separately maps effective elastic modulus, adhesion and deformation. It directly addresses the stiffness difference and limits maximum force. Its quantitative result depends on tip radius, force calibration, contact model, loading rate and film thickness; domains narrower than the contact footprint are mixed and the substrate can dominate a thin film. Use small indentation, substrate controls and a suitable viscoelastic interpretation.

friction force microscopy can reveal domains with different frictional and adhesive response, using torsional deflection during contact scans. It is simple and sensitive to surface chemistry, but continuous shear may deform or displace soft domains, and slope/topography can contaminate the lateral signal. Acquire trace–retrace pairs at several low normal loads and check reproducibility. Use a mechanical-modulus map to test the stiffness assignment; phase or friction contrast alone does not uniquely identify stiffness or chemical composition.

In quantitative nanomechanical mapping, the operational adhesion is the magnitude of the most attractive force immediately before detachment on a calibrated retraction curve:Here $k_c$ is the cantilever spring constant and ${\delta }_c$ its deflection after baseline subtraction. The area between approach and retraction relates to dissipated work, whereas the minimum force is a force, not an energy. Chemical attraction, Van der Waals forces and ambient-water capillary bridges can all contribute. Match loading rate and peak load, calibrate deflection sensitivity and $k_c$, compare clean reference surfaces, and control humidity; otherwise different maps may reflect different tips or capillary conditions rather than different specimens.