Damping mechanism in dynamic force microscopy

Friction and nonlinear dynamics

The nonlinear dynamics associated with sliding friction forms a broad interdisciplinary research field that involves complex dynamical processes and patterns covering a broad range of time and length scales. Progress in experimental techniques and computational resources has stimulated the development of more refined and accurate mathematical and numerical models, capable of capturing many of the essentially nonlinear phenomena involved in friction.

The role of the tip in non-contact atomic force microscopy dissipation images of ionic surfaces

In this paper we use simulations to investigate the role of the tip in nc-AFM measurements of dissipated energy. Using a virtual AFM we simulate the experiment focusing on the atomic scale energy dissipation on an NaCl(100) flat surface. The non-conservative interaction was treated with the theory of dynamic response and all the calculations were carried out using an atomistic model; several sets of tips were tested using ionic crystals (NaCl, KBr, MgO), each in different configurations (ideal, vacant, divacant, doped). Using an MgO-doped tip we were able to calculate a dissipation signal comparable to what is typically measured in experiments. It was not possible to see any dissipation with ideal tips, although they still have a significant interaction with the surface and give atomic contrast in the frequency shift signal. The effect of the scanning speed on measured frequency shift and dissipation is also calculated and discussed.

Calcium-dependent Open/Closed Conformations and Interfacial Energy Maps of Reconstituted Hemichannels

Using an atomic force microscope, we have studied three-dimensional molecular topography and calcium-sensitive conformational changes of individual hemichannels. Full-length (non-truncated) Cx43 hemichannels (connexons), when reconstituted in lipid bilayer, appear as randomly distributed individual particles and clusters. They show a lack of preferential orientation of insertion into lipid membrane; in a single bilayer, connexons with protrusion of either the extracellular face or the large non-truncated cytoplasmic face are observed. Extracellular domains of these undocked hemichannels are structurally different from hemichannels in the docked gap junctional plaques examined after their exposure by force dissection or chemical dissection. Calcium induced a reversible change in the extracellular pore diameter. Hemichannels imaged in a physiological buffer with 1.8 mm Ca(+2) had the pore diameter of approximately 1.8 nm, consistent with the closed channel conformation. Reducing Ca(+2) concentration to approximately 1.4, 1, and 0 mm, which changes hemichannels from the closed to open conformation, increased the pore diameter to approximately 2.5 nm for approximately 27, 74, and 100% of hemichannels, respectively. Thus, open/close probability of the hemichannel appears to be [Ca(2+)]-dependent. Computational analysis of the atomic force microscopy phase mode imaging reveals a significantly higher interfacial energy for open hemichannels that results from the interactions between the atomic force microscope probe and the hydrophobic domains. Thus, hydrophobic extracellular domains of connexins regulate calcium-dependent conformational changes.

Characterization of distance-dependent damping in tapping-mode atomic force microscopy force measurements in liquid

We have used a spectral analysis method to characterize changes in the local damping coefficient for an acoustically driven cantilever as it approaches a hard surface in liquid. We show a significant distance dependence of the damping coefficient (and associated quality factor) that must be accounted for to achieve successful theoretical reproduction of experimental tapping-mode force curves. We model the cantilever dynamics using a forced damped harmonic oscillator model and solve the equation of motion using the method of finite differences. Experiments in solutions of differing viscosities show that bulk viscous damping is not the source of the system dissipation, while simulations of the cantilever dynamics including adhesion hysteresis also eliminate this as the origin of the dissipation. We conclude that frictional dissipation that occurs with the intermittent contact is the likely source of dissipation in the system. Our results identify a semiquantitative means of interpreting tapping-mode force curves on nondeformable surfaces in liquid.

Interplay between nonlinearity, scan speed, damping, and electronics in frequency modulation atomic-force microscopy

Numerical simulations of the frequency modulation atomic force microscope, including the whole dynamical regulation by the electronics, show that the cantilever dynamics is conditionally stable and that there is a direct link between the frequency shift and the conservative tip-sample interaction. However, a soft coupling between the electronics and the nonlinearity of the interaction may significantly affect the damping. A resonance between the scan speed and the response time of the system can provide a simple explanation for the spatial shift and contrast inversion between topographical and damping images, and for the extreme sensitivity of the damping to a tip change.

Energy dissipation in atomic force microscopy and atomic loss processes

Atomic scale dissipation is of great interest in nanomechanics and atomic manipulation. We present dissipation measurements with a linearized, ultra-small amplitude atomic force microscope which is capable of measuring dissipation at chosen, fixed separations. We show that the dynamic dissipation in the noncontact regime is of the order of a few 10-100 meV per cycle. This dissipation is likely due to the motion of a bistable atomic defect in the tip-surface region. In the contact regime we observe dc hysteresis associated with nanoscale plasticity. We find the hysteretic energy loss to be 1 order of magnitude higher for a silicon surface than for copper.