A. Deolia, A. Raman, R. Wagner
Purdue University,
United States
Keywords: nanomechanical measurements, photothermal AFM, cantilever mechanics, dynamics, heat transfer, vibrations
Summary:
Pyrotechnic shock loading of space systems, hypervelocity debris strikes on satellites, and high-frequency resonators expose polymer and polymer composites to forces with characteristic frequencies greater than 20 kHz. The Atomic Force Microscope (AFM) is well suited for material property characterization at these high frequencies. The smallest AFM cantilevers can push their fundamental resonance frequency up to a few MHz. Quasistatic AFM methods based on force-displacement curves or on force modulation can measure mechanical properties across a large fraction of the cantilever’s fundamental resonance frequency. Currently, practical issues related to forcing and calibration limit our ability to perform viscoelastic property characterization across a broad frequency range with AFM. Specifically, piezoelectric excitation suffers from the forest of peaks problem while photothermal and magnetic excitation modify the shape in which the cantilever vibrates, invalidating the commonly used optical lever calibration scheme. The implications of photothermally driven cantilever motion and its effect on material property measurement are unclear. We do not know the nature and extent of the effect of distributed thermal strain caused by the photothermal laser acting on the cantilever. Furthermore, lack of proper understanding of cantilever deflection shape complicates the use of the optical lever calibration scheme which assumes a particular deflection shape of the cantilever. In this work, we model the motion of a sub-resonance photothermally heated cantilever interacting with samples of varying mechanical properties and excitation parameters for large frequency bandwidth material property characterization. We perform parametric finite element simulations of the transient motion of a coated cantilever interacting with samples of varying young’s modulus and Hamaker constant, excitation location, and excitation frequency. The tip-sample interaction force is modeled using a modified Derjaguin-Muller-Toporov contact mechanics model that includes a combination of attractive long-range Van der Waals forces and a repulsive short-range Hertz contact force. We compare finite element simulation results with our prior experimental and analytical modeling results of a freely vibrating photothermally heated cantilever beam. These results give us an insight into the deflection shape of the cantilever in sub-resonance photothermal excitation under different experimental conditions and the implications this might have on the quantitative material property measurements. We validate our finite element modeling of the motion of a coated cantilever with prior work on static deflection of bimetallic cantilevers. This work can help extend the current measurement bandwidth of viscoelastic property measurement and offers a major upgrade on existing AFM systems equipped with photothermal excitation capability. Developing a better understanding of AFM microcantilever vibrating in the sub-resonance regime is crucial in many AFM imaging modalities such as force modulation microscopy, peak force tapping, and photothermal-off resonance tapping.