Period-Doubling Bifurcations in Atomic Force Microscopy

2009 ◽  
Author(s):  
Andrew J. Dick ◽  
Wei Huang
Keyword(s):  
Dynamic Response ◽  
Atomic Force Microscope ◽  
Period Doubling ◽  
Surface Force ◽  
Resonance Excitation ◽  
Force Model ◽  
Beam Model ◽  
Atomic Force ◽  
Local Material ◽  
Local Material Properties

The dynamic response of an atomic force microscope cantilever probe is studied for off-resonance excitation and interactions with a soft silicone rubber material. The dynamic response of the probe is simulated using a three-mode approximation of the Euler-Bernoulli beam model for excitation at two-and-a-half times the probe’s fundamental frequency. These simulations are conducted in order to reproduce the period-doubling bifurcation experimentally observed in the response of the probe of a commercial atomic force microscope. In order to duplicate this behavior, parameters within the surface force model are tuned to account for variations in the characteristics of the sample material. Through this work, the relationship between the sample material’s effective stiffness and the response behavior of the probe are studied in an effort to develop the means to identify the local material properties of a sample by characterize the nonlinear response of the probe.

Utilizing Off-Resonance and Dual-Frequency Excitation to Distinguish Attractive and Repulsive Surface Forces in Atomic Force Microscopy

2010 ◽  
Vol 6 (3) ◽  
Author(s):  
Andrew J. Dick ◽  
Santiago D. Solares
Keyword(s):  
Fundamental Frequency ◽  
Period Doubling ◽  
Qualitative Change ◽  
Surface Forces ◽  
Resonance Excitation ◽  
Atomic Interaction ◽  
Beam Model ◽  
Dual Frequency ◽  
Atomic Force ◽  
Frequency Excitation

A beam model is developed and discretized to study the dynamic behavior of the cantilever probe of an atomic force microscope. Atomic interaction force models are used with a multimode approximation in order to simulate the probe’s response. The system is excited at two-and-a-half times the fundamental frequency and with a dual-frequency signal consisting of the AFM probe’s fundamental frequency and two-and-a-half times the fundamental frequency. A qualitative change in the response in the form of period doubling is observed for the harmonic off-resonance excitation when significantly influenced by repulsive surface forces. Through the use of dual-frequency excitation, standard response characteristics are maintained, while the inclusion of the off-resonance frequency component results in an identifiable qualitative change in the response. By monitoring specific frequency components, the influence of attractive and repulsive surface forces may be distinguished. This information could then be used to distinguish between imaging regimes when bistability occurs or to operate at the separation distance between surface force regimes to minimize force levels.

Influence of Local Material Properties on the Nonlinear Dynamic Behavior of an Atomic Force Microscope Probe

2011 ◽  
Vol 6 (4) ◽  
Author(s):  
Wei Huang ◽  
Andrew J. Dick
Keyword(s):  
Atomic Force Microscope ◽  
Dynamic Behavior ◽  
Material Properties ◽  
Parametric Study ◽  
Period Doubling ◽  
Force Model ◽  
Atomic Force Microscope Probe ◽  
Atomic Force ◽  
The Relationship ◽  
Microscope Probe

In this paper, a study of the characteristics of period-doubling bifurcations in the dynamic behavior of an atomic force microscope probe for off-resonance excitation is presented. Using a three-mode approximation and excitation at two-and-a-half times the fundamental frequency, the relationship between the characteristics of the period-doubling bifurcation and the material properties is studied by using numerical simulations. Simulations are first used to successfully reproduce nonlinear response data collected experimentally by using a commercial atomic force microscope system and then to conduct a parametric study in order to examine the influence of variations in other system parameters on the relationship. These parameters are the excitation magnitude, the damping level, the cantilever stiffness, and the characteristics of the force model. Based upon the results of the parametric study, a new operation mode for obtaining localized material properties through an efficient scanning process is proposed. A preliminary scan simulation demonstrates the successful implementation of the relationship and its potential for providing localized material property information with nanoscale resolution.

Dynamic analysis of AFM by applying Timoshenko beam theory in tapping mode and considering the impact of interaction forces in a liquid environment

2014 ◽  
Vol 92 (6) ◽  
pp. 472-483 ◽  
Author(s):  
M. Damircheli ◽  
M.H. Korayem
Keyword(s):  
Dynamic Response ◽  
Atomic Force Microscope ◽  
Timoshenko Beam ◽  
Ambient Air ◽  
Beam Model ◽  
Timoshenko Beam Model ◽  
Interaction Forces ◽  
Liquid Environment ◽  
Atomic Force ◽  
Simulation Results

In an atomic force microscope (AFM), the cantilever vibrates by excitation at a frequency near the fundamental frequency, and the changes in vibration parameters, which result from the nonlinear forces of interaction between sample and cantilever tip, can be used as a tool to reveal the properties of the sample. To properly describe the images acquired by the AFM and to approximate the properties of the investigated sample, it is essential to use analytical and numerical models that can accurately simulate the dynamics of the cantilever and sample. For short beams, the Timoshenko model seems to be very accurate. Considering the fact that short beams (cantilevers) have many applications including the imaging of biological samples in liquid environments, the use of this theory seems to be necessary. In this paper, by employing the Timoshenko beam model, the effect of rotational inertia and shear deformation has been taken into consideration. The interaction forces between sample and cantilever in liquid, ambient air, and vacuum environments are quite different in terms of magnitude and formulation, and they play a significant role in the system’s dynamic response. These forces include hydrodynamic forces, electrostatic double layer force, etc. Using an accurate model for the interaction forces will improve the simulation results significantly. In this paper, the frequency response of the atomic force microscope has been investigated by applying the Timoshenko beam model and considering the forces of interaction between sample and tip in the air and liquid environments. The results indicate that the resonant frequency changes and cantilever vibration amplitude diminishes in a liquid environment compared to the air environment. The simulation results have good agreement with the experimental ones. The frequency responses for the attractive and repulsive regions in the two environments are compared and it is demonstrated that the dynamic response is highly dependent on the hydrodynamic and interaction forces in the liquid medium.

Localized Material Properties Through Nonlinear Dynamics Based Atomic Force Microscopy

2010 ◽  
Author(s):  
Wei Huang ◽  
Andrew J. Dick
Keyword(s):  
Atomic Force Microscopy ◽  
Material Properties ◽  
Period Doubling ◽  
Nonlinear Behavior ◽  
Separation Distance ◽  
Resonance Excitation ◽  
Current Effort ◽  
Force Microscopy ◽  
Atomic Force ◽  
Local Material Properties

Due to the intrinsic nonlinearity of the tip-sample interaction forces that are utilized in atomic force microscopy, nonlinear behavior can be observed even under the most ‘ideal’ conditions. While the standard operating modes of the atomic force microscope (AFM) have been developed to minimize this nonlinear behavior, the authors’ work focuses on utilizing a nonlinear response of the AFM probe associated with off-resonance excitation in order to measure local material properties of the sample. Previously, period-doubling bifurcations were identified and studied for an off-resonance excitation condition of two-and-a-half times the fundamental frequency. A relationship was identified between the characteristics of the qualitative response transition and the properties of the probe and sample. For a given probe, the critical separation distance where the period-doubling bifurcation occurs is influenced by the local modulus properties of the sample. This paper details the current effort studying this relationship with the goal of developing a new AFM operation mode for obtaining localized material properties by scanning the sample. The influence of different system parameters on this relationship is studied and preliminary simulation results are presented for a simple scanning process.

Heat Transfer Spectroscopy and “Heat Transfer-Distance” Curves

2008 ◽  
Author(s):  
Arvind Narayanaswamy ◽  
Sheng Shen ◽  
Gang Chen
Keyword(s):  
Heat Transfer ◽  
Radiative Transfer ◽  
Atomic Force Microscope ◽  
Near Field ◽  
Surface Force ◽  
Casimir Forces ◽  
Distance Curve ◽  
Transfer Distance ◽  
Atomic Force ◽  
Order Of Magnitude

Thermal radiative transfer between objects as well as near-field forces such as van der Waals or Casimir forces have their origins in the fluctuations of the electrodynamic field. Near-field radiative transfer between two objects can be enhanced by a few order of magnitude compared to the far-field radiative transfer that can be described by Planck’s theory of blackbody radiation and Kirchoff’s laws. Despite this common origin, experimental techniques of measuring near-field forces (using the surface force apparatus and the atomic force microscope) are more sophisticated than techniques of measuring near-field radiative transfer. In this work, we present an ultra-sensitive experimental technique of measuring near-field using a bi-material atomic force microscope cantilever as the thermal sensor. Just as measurements of near-field forces results in a “force distance curve”, measurement of near-field radiative transfer results in a “heat transfer-distance” curve. Results from the measurement of near-field radiative transfer will be presented.

Dynamic response of bridges under travelling loads

1993 ◽  
Vol 20 (2) ◽  
pp. 287-298 ◽  
Author(s):  
J. L. Humar ◽  
A. M. Kashif
Keyword(s):  
Dynamic Response ◽  
Rational Design ◽  
Weight Ratio ◽  
Experimental Investigations ◽  
Speed Ratio ◽  
Force Model ◽  
Beam Model ◽  
Dynamic Amplification Factor ◽  
Design Procedures ◽  
Dynamic Amplification

In spite of a number of analytical and experimental investigations on the dynamic response of bridges to moving vehicle loads, the controlling parameters that govern the response have not been clearly identified. This has, in turn, inhibited the development of rational design procedures. Based on an analytical investigation of the response of a simplified beam model traversed by a moving mass, the present study identifies the governing parameters. The results clearly show why attempts to correlate the response to a single parameter, either the span length or the fundamental frequency, are unsuccessful. Simple design procedures are developed based on relationships between the speed ratio, the weight ratio, and the dynamic amplification factors; and a set of design curves are provided. Key words: dynamic response of bridges, vehicle–bridge interaction, moving force model, moving sprung mass model, dynamic amplification factor.

Nano-Contact Force Calculation Method of Different Tip Radius of Curvature and the Specimen Surface of AFM

2015 ◽  
Vol 723 ◽  
pp. 952-957
Author(s):  
Guo Dong Cheng ◽  
Xiao Jing Yang
Keyword(s):  
Atomic Force Microscope ◽  
Contact Force ◽  
Calculation Model ◽  
Specimen Surface ◽  
Radius Of Curvature ◽  
Force Model ◽  
Atomic Force ◽  
Working Principle ◽  
Tip Radius ◽  
Force Calculation

Atomic Force Microscope (AFM) works by the force between the probe tip and specimen surface. The nanocontact force between the probe tip and specimen surface has an important influence on the detection surface. Base on the analysis of the working principle of the AFM and nanocontact force calculation model, according to Hamaker assumptions, using continuum method established the theoretical contact force model of the AFM tip. the contact force calculation methods of contact pressure in process has been obtained. The variation of the force between the probe tip and specimen surface has been found by calculation model and programming calculation of Matlab. Provide the basis for improving the accuracy of an atomic force microscope surface inspection and error analysis

Sign in / Sign up

Export Citation Format

Share Document