Shuiqing Hu

Equivalent point-mass models of continuous atomic force microscope probes

The theoretical foundations of dynamic atomic force microscopy (AFM) are based on point-mass models of continuous, micromechanical oscillators with nanoscale tips that probe local tip-sample interaction forces. In this letter, the authors present the conditions necessary for a continuous AFM probe to be faithfully represented as a point-mass model, and derive the equivalent point-mass model for a general eigenmode of arbitrarily shaped AFM probes based on the equivalence of kinetic, strain, and tip-sample interaction energies. They also demonstrate that common formulas in dynamic AFM change significantly when these models are used in place of the traditional ad hoc point-mass models.

Inverting amplitude and phase to reconstruct tip- sample interaction forces in tapping mode atomic force microscopy

Quantifying the tip-sample interaction forces in amplitude-modulated atomic force microscopy (AM-AFM) has been an elusive yet important goal in nanoscale imaging, manipulation and spectroscopy using the AFM. In this paper we present a general theory for the reconstruction of tip-sample interaction forces using integral equations for AM-AFM and Chebyshev polynomial expansions. This allows us to reconstruct the tip-sample interactions using standard amplitude and phase versus distance curves acquired in AM-AFM regardless of tip oscillation amplitude and in both the net attractive and repulsive regimes of oscillation. Systematic experiments are performed to reconstruct interaction forces on polymer samples to demonstrate the power of the theoretical approach.

Analytical formulas and scaling laws for peak interaction forces in dynamic atomic force microscopy

Determining the peak interaction force between an oscillating nanoscale tip and a sample surface has been a fundamental yet elusive goal in amplitude-modulated atomic force microscopy. Closed form analytical expressions are derived using nonlinear asymptotic theory for the peak attractive and repulsive forces that approximate with a high degree of accuracy the numerically simulated peak forces under ambient or vacuum conditions. Scaling laws involving van der Waals, chemical forces, nanoscale elasticity, and oscillator parameters are identified to demonstrate approximate similitude for the peak interaction forces under practical operating conditions.

Invited Article: VEDA: A web-based virtual environment for dynamic atomic force microscopy

We describe here the theory and applications of virtual environment dynamic atomic force microscopy (VEDA), a suite of state-of-the-art simulation tools deployed on nanoHUB (www.nanohub.org) for the accurate simulation of tip motion in dynamic atomic force microscopy (dAFM) over organic and inorganic samples. VEDA takes advantage of nanoHUBs cyberinfrastructure to run high-fidelity dAFM tip dynamics computations on local clusters and the teragrid. Consequently, these tools are freely accessible and the dAFM simulations are run using standard web-based browsers without requiring additional software. A wide range of issues in dAFM ranging from optimal probe choice, probe stability, and tip-sample interaction forces, power dissipation, to material property extraction and scanning dynamics over hetereogeneous samples can be addressed.

Frequency Domain Identification of Tip-sample van der Waals Interactions in Resonant Atomic Force Microcantilevers

Hamaker constants are characteristic material properties that determine the magnitude of the nonlinear van der Waals force between atoms, molecules and nanoscale aggregates of atoms. This paper explores the novel possibility of using Harmonic Balance based nonlinear system identification methods to extract from the nonlinear vibration spectrum of resonant atomic force silicon microcantilevers, the Hamaker constants between a few atoms at the tip of the microcantilever and graphite, gold and silicon carbide samples. First, the nonlinear dynamics of a diving board microcantilever coupled to the samples through van der Waals force potentials are investigated through a discretized model of the system. Next, the feasibility of using Harmonic Balance based nonlinear system identification techniques are demonstrated using simulations of the discretized model. Finally the method is implemented on an AFM system. The results indicate that the proposed method provides a novel alternative way to measure Hamaker constants and the measured results are within the range of known experimental data.

Nonlinear Tapping-Tip Dynamics in Atomic Force Microscopy

Tapping or intermittent contact atomic force microscopy (AFM) is widely used scanning probe techniques for high resolution imaging, manipulation and nanolithography. The presence of van der Waals forces and nanoscale impacts render highly nonlinear the dynamics of the AFM microcantilever while it operates in the tapping mode. A comprehensive nonlinear analysis of the nonlinear dynamics of AFM microcantilevers tapping on a nanostructure using the theoretical and computational tools of modern nonlinear dynamics has not yet been presented. Also, a rational connection between certain features of the tip-sample interaction potential and the nonlinear response has not been established satisfactorily. To address this problem, we have combined both experimental and nonlinear computational analysis of the tapping response of a microcantilever as a function of the excitation frequency. We show that this approach enables a comprehensive understanding of the nonlinear dynamic behavior observed in AFM experiments.Copyright