Abstract
We prove that the Euler–Bernoulli elastic beam theory can be reliably used to describe the dynamics of an atomic force microscope cantilever during the far from equilibrium snapto contact event. In conventional atomic force microscope operation, forceseparation curves are obtained by postprocessing voltage versus time traces produced by measuring one point on the cantilever close to the hanging end. In this article, we assess the validity of the Euler–Bernoulli equation during the snaptocontact event. The assessment is based on a direct comparison between experiment and theory. The experiment uses Doppler vibrometry to measure displacement versus time for many points along the long axis of the cantilever. The theoretical algorithm is based on a solution of the Euler–Bernoulli equation to obtain the full shape of the cantilever as a function of time. The algorithm uses as boundary conditions, experimentally obtained information only near the hanging end of the cantilever. The solution is obtained in a manner that takes into account nonequilibrium motion. Within experimental error, the theory agrees with experiment indicating that the Euler–Bernoulli theory is appropriate to predict the cantilever kinematics during snaptocontact. Since forces on the tip can be obtained from the instantaneous shape of the cantilever, this work should allow for computation of tipsample forces during the snaptocontact event from a conventional forcedistance measured input.
Supplementary
Supplementary
Original language  English 

Number of pages  9 
Journal  Nanotechnology 
Volume  31 
Issue number  18 
DOIs  
Publication status  Published  14 Feb 2020 
Bibliographical note
provisional acceptance date added, based on publication informationKeywords
 cantilever
 AFM
 Dynamics
Fingerprint Dive into the research topics of 'Euler–Bernoulli theory accurately predicts atomic force microscope cantilever shape during nonequilibrium snaptocontact motion'. Together they form a unique fingerprint.
Equipment

Interface Analysis Centre (IAC)
Keith Hallam (Manager)
Interface Analysis CentreFacility/equipment: Facility