35 research outputs found
Interpreting motion and force for narrow-band intermodulation atomic force microscopy
Intermodulation atomic force microscopy (ImAFM) is a mode of dynamic atomic
force microscopy that probes the nonlinear tip-surface force by measurement of
the mixing of multiple tones in a frequency comb. A high cantilever
resonance and a suitable drive comb will result in tip motion described by a
narrow-band frequency comb. We show by a separation of time scales, that such
motion is equivalent to rapid oscillations at the cantilever resonance with a
slow amplitude and phase or frequency modulation. With this time domain
perspective we analyze single oscillation cycles in ImAFM to extract the
Fourier components of the tip-surface force that are in-phase with tip motion
() and quadrature to the motion (). Traditionally, these force
components have been considered as a function of the static probe height only.
Here we show that and actually depend on both static probe height
and oscillation amplitude. We demonstrate on simulated data how to reconstruct
the amplitude dependence of and from a single ImAFM measurement.
Furthermore, we introduce ImAFM approach measurements with which we reconstruct
the full amplitude and probe height dependence of the force components
and , providing deeper insight into the tip-surface interaction. We
demonstrate the capabilities of ImAFM approach measurements on a polystyrene
polymer surface.Comment: 12 pages, 7 figure
Dynamic Calibration of Higher Eigenmode Parameters of a Cantilever in Atomic Force Microscopy Using Tip-Surface Interactions
We present a theoretical framework for the dynamic calibration of the higher
eigenmode parameters (stiffness and optical lever responsivity) of a
cantilever. The method is based on the tip-surface force reconstruction
technique and does not require any prior knowledge of the eigenmode shape or
the particular form of the tip-surface interaction. The calibration method
proposed requires a single-point force measurement using a multimodal drive and
its accuracy is independent of the unknown physical amplitude of a higher
eigenmode.Comment: 4 pages, 4 figure
Imaging high-speed friction at the nanometer scale
Friction is a complicated phenomenon involving nonlinear dynamics at
different length and time scales[1, 2]. The microscopic origin of friction is
poorly understood, due in part to a lack of methods for measuring the force on
a nanometer-scale asperity sliding at velocity of the order of cm/s.[3, 4]
Despite enormous advance in experimental techniques[5], this combination of
small length scale and high velocity remained illusive. Here we present a
technique for rapidly measuring the frictional forces on a single asperity (an
AFM tip) over a velocity range from zero to several cm/s. At each image pixel
we obtain the velocity dependence of both conservative and dissipative forces,
revealing the transition from stick-slip to a smooth sliding friction[1, 6]. We
explain measurements on graphite using a modified Prandtl-Tomlinson model that
takes into account the damped elastic deformation of the asperity. With its
greatly improved force sensitivity and very small sliding amplitude, our method
enables rapid and detailed surface mapping of the full velocity-dependence of
frictional forces with less than 10~nm spatial resolution.Comment: 7 pages, 4 figure
Intermodulation electrostatic force microscopy for imaging surface photo-voltage
We demonstrate an alternative to Kelvin Probe Force Microscopy for imaging
surface potential. The open-loop, single-pass technique applies a low-frequency
AC voltage to the atomic force microscopy tip while driving the cantilever near
its resonance frequency. Frequency mixing due to the nonlinear capacitance
gives intermodulation products of the two drive frequencies near the cantilever
resonance, where they are measured with high signal to noise ratio. Analysis of
this intermodulation response allows for quantitative reconstruction of the
contact potential difference. We derive the theory of the method, validate it
with numerical simulation and a control experiment, and we demonstrate its
utility for fast imaging of the surface photo-voltage on an organic
photo-voltaic material.Comment: 4 pages, 3 figures, peer-reviewed, preprin
The Role of Nonlinear Dynamics in Quantitative Atomic Force Microscopy
Various methods of force measurement with the Atomic Force Microscope (AFM)
are compared for their ability to accurately determine the tip-surface force
from analysis of the nonlinear cantilever motion. It is explained how
intermodulation, or the frequency mixing of multiple drive tones by the
nonlinear tip-surface force, can be used to concentrate the nonlinear motion in
a narrow band of frequency near the cantilevers fundamental resonance, where
accuracy and sensitivity of force measurement are greatest. Two different
methods for reconstructing tip-surface forces from intermodulation spectra are
explained. The reconstruction of both conservative and dissipative tip-surface
interactions from intermodulation spectra are demonstrated on simulated data.Comment: 25 pages (preprint, double space) 7 figure
On modeling and measuring viscoelasticity with dynamic Atomic Force Microscopy
The interaction between a rapidly oscillating atomic force microscope tip and
a soft material surface is described using both elastic and viscous forces with
a moving surface model. We derive the simplest form of this model, motivating
it as a way to capture the impact dynamics of the tip and sample with an
interaction consisting of two components: interfacial or surface force, and
bulk or volumetric force. Analytic solutions to the piece-wise linear model
identify characteristic time constants, providing a physical explanation of the
hysteresis observed in the measured dynamic force quadrature curves. Numerical
simulation is used to fit the model to experimental data and excellent
agreement is found with a variety of different samples. The model parameters
form a dimensionless impact-rheology factor, giving a quantitative physical
number to characterize a viscoelastic surface that does not depend on the tip
shape or cantilever frequency.Comment: 13 pages, 7 figure