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friction force microscopy is suitable. Contact scanning twists the AFM cantilever; the lateral photodetector difference measures friction and can distinguish the supported graphene and glass even if their heights are close. Acquire both trace and retrace and use half their lateral-signal difference to suppress slope-induced cross-talk. Keep the normal load low enough to avoid dragging or damaging the flake, control humidity and contamination, and calibrate torsional sensitivity if a quantitative coefficient of friction is required. An electrical connection is unnecessary.

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.

friction force microscopy records cantilever torsion caused by lateral tip–sample force. Choose the detector sign so that friction on a flat region contributes positively during a left-to-right trace. On a common laboratory-position axis, write the two signals schematically asHere $B$ is an offset and $G$ represents a slope-related lateral-force or detector cross-talk contribution. A reversed electronic convention reverses all plotted signs without changing the physical conclusions.

At the same controlled normal contact force $N$, the flat-region contribution is approximately $F_f=\mu N$. The lower perovskite structure plateaux give a larger trace–retrace separation than the upper inorganic surface, because their coefficient of kinetic friction is larger. Genuine friction reverses sign with scan direction, so a larger friction magnitude means a higher positive trace and a more negative retrace in this convention.

Sloped edges produce additional peaks or shoulders. The normal reaction to a slope has a lateral component, and the finite tip flank can contact the rim, so edge contrast is not a direct map of the local friction coefficient. With the two scans registered and load control maintained,The half-difference therefore emphasizes friction while the half-sum diagnoses common geometrical contributions. Real contact mechanics and imperfect registration can prevent exact cancellation. The bottom panel of the figure shows these two kinds of contrast separately.