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The dynamic response of an oscillating microcantilever with a gold-coated tip interacting with dissimilar functionalized silica surfaces was studied in electrolyte solutions with pH ranging from 4 to 9. Silica surfaces were chemically modified, yielding dissimilar surfaces with -Br, -NH(2), and -CH(3) functional group terminations. The relative hydrophobicity of the surfaces was characterized by contact angle measurements. The surface charge of the functionalized surfaces was first probed with commonly used static AFM measurements and serves as a reference to the dynamic response data. The amplitude and phase of the cantilever oscillation were monitored and used to calculate the effective interaction stiffness and damping coefficient, which relate to the electrical double layer interactions and also to distance-dependent hydrodynamic damping at the solid/water interface. The data for the dynamic response of the AFM over silica surfaces as a function of chemical functionalization and electrolyte pH show that the effective stiffness has a distinctive dependence on the surface charge of functionalized silica surfaces. The hydrodynamic damping also correlates strongly with the relative hydrophobicity of the surface. The data reported here indicate that interfacial properties can be strongly affected by changing the chemical composition of surfaces.

This paper presents an event-driven, discrete-in-time feedback strategy for tracking and stabilizing naturally occurring periodic oscillations in the probe-tip dynamics of atomic force microscope (AFM) cantilevers in tapping-mode operation. Specifically, robust dynamic tracking and stabilization is achieved by the imposition of discrete changes in the vertical offset between the cantilever support and the sample surface based on an estimated linearization of the system dynamics about a dynamically generated reference trajectory. Here, use is made not only of the oscillation amplitude, as is typical in commercial control implementations for AFMs, but also of the instantaneous phase information. It is shown that stabilization and desirable performance during surface scanning is possible, even in the presence of uncertainty and limited state access. In particular, the methodology enables robust tracking and use of low-contact-velocity periodic system responses that are unstable in the absence of control.

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SUMMARYThis paper develops a rigorous control paradigm for regulating the near-grazing bifurcation behavior of limit cycles in piecewise-smooth dynamical systems. In particular, it is shown that a discrete-in-time linear feedback correction to a parameter governing a state-space discontinuity surface can suppress discontinuity-induced fold bifurcations of limit cycles that achieve near-tangential intersections with the discontinuity surface. The methodology ensures a persistent branch of limit cycles over an interval of parameter values near the critical condition of tangential contact that is an order of magnitude larger than that in the absence of control. The theoretical treatment is illustrated with a harmonically excited damped harmonic oscillator with a piecewise-linear spring stiffness as well as with a piecewise-nonlinear model of a capacitively excited mechanical oscillator.