(Color online) Schematics of the experimental setup for both noncontact force (left) and noncontact friction measurements. The actuation of the cantilever in the force measurement is directed to be perpendicular to the plane defined by the sample surface in either static (force) or dynamic (gradient) modes. For the friction measurement, the cantilever is vertically situated with respect to the sample surface.
(Color online) Forces acting on the cantilever as a function of the applied voltage for the ideal case (a), where a single value of describes the parabola minima at all distances, and for the nonideal case of a distance-dependent (b). Parabola measurements showing a condition of properly and improperly determined energy minima are indicated by dotted and solid lines, respectively. The bottom curve illustrates the degree of overestimation of the force curve as a result of an “off the path” condition away from the proper minima.
Equations describing electric interactions and their respective parabola curvatures in three distinct AFM operation modes: (1) static mode, in which a deflection of a cantilever is measured and related to the actual force , (2) dynamic mode, in which the frequency shift of the cantilever is monitored, yielding the gradient of the force interaction , and (3) friction mode, in which the quality factor of the cantilever resonance is monitored and used to quantify the overall dissipative interaction . All three AFM modes reveal some aspects of the electromagnetic interactions between the tip and the sample, but they do not necessarily yield the same experimental information, such as characterizations of the distance-varying CPD and the asymptotic limits. Furthermore, each of the operation modes underscores a different physical mechanism of the interaction, making it difficult to compare among different sets of measurements.
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