Finite-element vibration analysis of tapping-mode atomic force microscopy in liquid.

Investigation of morphology and mechanical properties of biological specimens using atomic force microscopy (AFM) often requires its operation in liquid environment. Due to the hydrodynamic force, the vibration of AFM cantilevers in liquid shows dramatically different dynamic characteristics from that in air. A good understanding of the dynamics of AFM cantilevers vibrating in liquid is needed for the interpretation of scanning images, selection of AFM operating conditions, and evaluation of sample's mechanical properties. In this study, a finite element (FE) model is used for frequency and transient response analysis of AFM cantilevers in tapping mode (TM) operated in air or liquid. Hydrodynamic force exerted by the fluid on AFM cantilevers is approximated by additional mass and hydrodynamic damping. The additional mass and hydrodynamic damping matrices corresponding to beam elements are derived. With this model, numerical simulations are performed for an AFM cantilever to obtain the frequency and transient responses of the cantilever in air and liquid. The comparison between our simulated results and the experimentally obtained ones shows good agreement. Based on the simulations, different characteristics of cantilever dynamics in air and liquid are discussed.

[1]  F. Kienberger,et al.  Hydrodynamic damping of a magnetically oscillated cantilever close to a surface. , 2004, Ultramicroscopy.

[2]  Goodman,et al.  Roles of the attractive and repulsive forces in atomic-force microscopy. , 1991, Physical review. B, Condensed matter.

[3]  Jan Greve,et al.  Tapping mode atomic force microscopy in liquid , 1994 .

[4]  J. Sader.  Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope , 1998 .

[5]  Joseph A. Turner,et al.  Analysis of the high-frequency response of atomic force microscope cantilevers , 1997 .

[6]  Georg Schitter,et al.  State-space model of freely vibrating and surface-coupled cantilever dynamics in atomic force microscopy , 2004 .

[7]  Franz J. Giessibl,et al.  Forces and frequency shifts in atomic-resolution dynamic-force microscopy , 1997 .

[8]  Pascal Gallo,et al.  How does a tip tap? , 1997 .

[9]  Paul K. Hansma,et al.  Tapping mode atomic force microscopy in liquids , 1994 .

[10]  B. V. Derjaguin,et al.  Effect of contact deformations on the adhesion of particles , 1975 .

[11]  Hans-Jürgen Butt,et al.  Calculation of thermal noise in atomic force microscopy , 1995 .

[12]  W. Arnold,et al.  High-frequency response of atomic-force microscope cantilevers , 1997 .

[13]  Dror Sarid,et al.  Numerical simulations of a scanning force microscope with a large-amplitude vibrating cantilever , 1994 .

[14]  C. Siegerist,et al.  Reproducible Imaging and Dissection of Plasmid DNA Under Liquid with the Atomic Force Microscope , 1992, Science.

[15]  L. Wang,et al.  Analytical descriptions of the tapping-mode atomic force microscopy response , 1998 .

[16]  H. Hosaka,et al.  DAMPING CHARACTERISTICS OF BEAM-SHAPED MICRO-OSCILLATORS , 1995 .

[17]  B. Bhushan,et al.  Simulation of dynamic modes of atomic force microscopy using a 3D finite element model , 2006 .

[18]  Ute Rabe,et al.  Vibrations of free and surface‐coupled atomic force microscope cantilevers: Theory and experiment , 1996 .

[19]  Thomas Thundat,et al.  Harmonic response of near‐contact scanning force microscopy , 1995 .

[20]  Thomas Thundat,et al.  Transient response of tapping scanning force microscopy in liquids , 1996 .

[21]  H. Saunders,et al.  Finite element procedures in engineering analysis , 1982 .

[22]  D. J. Gorman.  Free vibration analysis of beams and shafts , 1975 .

[23]  G. Lévêque,et al.  Vibration of the cantilever in Force Modulation Microscopy analysis by a finite element model , 2003 .

[24]  C F Quate,et al.  Imaging crystals, polymers, and processes in water with the atomic force microscope. , 1989, Science.

[25]  L. Wang.  The role of damping in phase imaging in tapping mode atomic force microscopy , 1999 .