Imaging and measurement of elasticity and friction using the TRmode

Torsional and lateral vibrations of atomic force microscope (AFM) cantilevers can be used to measure elastic and frictional properties on a nanoscale. Recently a new dynamic operation mode called Torsional Resonance mode (TRmode) has been introduced. This paper describes the physical base of the TRmode and compares it to related dynamic AFM modes. In the theoretical part the torsional equation of motion of the cantilever beam is analysed. In the experimental part the contrast of images is interpreted based on the equation of motion. The route to quantitative measurements of contact stiffness, elastic moduli and friction is laid out.

[1]  Joseph A. Turner,et al.  Imaging of flexural and torsional resonance modes of atomic force microscopy cantilevers using optical interferometry , 2003 .

[2]  N. Amer,et al.  Simultaneous measurement of lateral and normal forces with an optical‐beam‐deflection atomic force microscope , 1990 .

[3]  Mark A. Lantz,et al.  Lateral stiffness of the tip and tip-sample contact in frictional force microscopy , 1997 .

[4]  O. Marti,et al.  Pulsed force mode: a new method for the investigation of surface properties , 1999 .

[5]  Hong-Ki Hong,et al.  Coulomb friction oscillator : Modelling and responses to harmonic loads and base excitations , 2000 .

[6]  Kazushi Yamanaka,et al.  Quantitative material characterization by ultrasonic AFM , 1999 .

[7]  P. Hansma,et al.  Using force modulation to image surface elasticities with the atomic force microscope , 1991 .

[8]  Robert W. Carpick,et al.  Lateral stiffness: A new nanomechanical measurement for the determination of shear strengths with friction force microscopy , 1997 .

[9]  Sokolov,et al.  Shear modulation force microscopy study of near surface glass transition temperatures , 2000, Physical review letters.

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

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

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

[13]  Ricardo Garcia,et al.  Dynamic atomic force microscopy methods , 2002 .

[14]  A. Spychalski-Merle.  Friction contrast in resonant cantilever vibration mode , 2000 .

[15]  Ryutaro Maeda,et al.  Evaluation of the Elastic Properties of a Cantilever Using Resonant Frequencies , 1997 .

[16]  Bharat Bhushan,et al.  Lateral force microscopy using acoustic friction force microscopy , 1999 .

[17]  Kazushi Yamanaka,et al.  Quantitative elasticity evaluation by contact resonance in an atomic force microscope , 1998 .

[18]  E. Meyer,et al.  Lateral-force measurements in dynamic force microscopy , 2002 .

[19]  Bharat Bhushan,et al.  On the nanoscale measurement of friction using atomic-force microscope cantilever torsional resonances , 2003 .

[20]  K. Yamanaka,et al.  Lateral Force Modulation Atomic Force Microscope for Selective Imaging of Friction Forces , 1995 .

[21]  O. Marti,et al.  Dynamic friction force measurement with the scanning force microscope , 1999 .

[22]  Ugo Andreaus,et al.  Friction oscillator excited by moving base and colliding with a rigid or deformable obstacle , 2002 .

[23]  A. Baró,et al.  Lock‐in technique for measuring friction on a nanometer scale , 1996 .

[24]  Hideki Kawakatsu,et al.  Mapping of lateral vibration of the tip in atomic force microscopy at the torsional resonance of the cantilever. , 2002, Ultramicroscopy.

[25]  Joseph A. Turner,et al.  Imaging using lateral bending modes of atomic force microscope cantilevers , 2004 .

[26]  J. Loubet,et al.  Normal and lateral modulation with a scanning force microscope, an analysis: implication in quantitative elastic and friction imaging , 1999 .

[27]  Joseph A. Turner,et al.  Sensitivity of flexural and torsional vibration modes of atomic force microscope cantilevers to surface stiffness variations , 2001 .

[28]  Kazushi Yamanaka,et al.  Ultrasonic Atomic Force Microscope with Overtone Excitation of Cantilever , 1996 .

[29]  C. Heiden,et al.  A lateral modulation technique for simultaneous friction and topography measurements with the atomic force microscope , 1994 .

[30]  Oleg Kolosov,et al.  Ultrasonic force microscopy for nanometer resolution subsurface imaging , 1994 .

[31]  B. Bhushan,et al.  Investigating ultra-thin lubricant layers using resonant friction force microscopy , 2005 .

[32]  H. Sturm,et al.  Use of scanning force microscopy studies with combined friction, stiffness and thermal diffusivity contrasts for microscopic characterization of automotive brake pads , 2002 .

[33]  Lionel Presmanes,et al.  Measurement of Young's modulus of nanocrystalline ferrites with spinel structures by atomic force acoustic microscopy , 2000 .

[34]  Robert W. Stark,et al.  Determination of shear stiffness based on thermal noise analysis in atomic-force microscopy: Passive overtone microscopy , 2001 .

[35]  V. Elings,et al.  Fractured polymer/silica fiber surface studied by tapping mode atomic force microscopy , 1993 .

[36]  M. Marcus,et al.  Phase imaging and the lever-sample tilt angle in dynamic atomic force microscopy , 2004 .

[37]  D. Maugis.  Adhesion of spheres : the JKR-DMT transition using a dugdale model , 1992 .

[38]  W. Arnold,et al.  Ultrasonic Modes in Atomic Force Microscopy , 2004 .

[39]  R. Williams,et al.  Imaging the elastic nanostructure of Ge islands by ultrasonic force microscopy , 1998 .

[40]  Mathias Göken,et al.  Imaging and measurement of local mechanical material properties by atomic force acoustic microscopy , 2002 .

[41]  Bharat Bhushan,et al.  A surface topography-independent friction measurement technique using torsional resonance mode in an AFM , 2004 .