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Comments on the paper “A comprehensive modeling and vibration analysis of AFM microcantilevers subjected to nonlinear tip-sample interaction forces” by Sohrab Eslami and Nader Jalili
Ultramicroscopy 131 (2013) 92–93
Contents lists available at SciVerse ScienceDirect
Ultramicroscopy journal homepage: www.elsevier.com/locate/ultramic
Short communication
Comments on the paper “A comprehensive modeling and vibration analysis of AFM microcantilevers subjected to nonlinear tip-sample interaction forces” by Sohrab Eslami and Nader Jalili Ali Passian a,b,c,n, Laurene Tetard a, Thomas Thundat d a
Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA Department of Physics, University of Tennessee, Knoxville, TN 37996, USA c Department of Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, TN 37996, USA d Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alta., Canada T6G 2V4 b
art ic l e i nf o
a b s t r a c t
Available online 4 April 2013
This comment on the paper “A comprehensive modeling and vibration analysis of AFM microcantilevers subjected to nonlinear tip-sample interaction forces” by Sohrab Eslami and Jalili (2012) [1] aims to: (1) discuss and elucidate the concept of “virtual resonance” and thus (2) avert a misinterpretation of the experimental results and findings reported in the Tetard et al. Physical Review Letters 106, 180801 (2011) [2]. & 2013 Elsevier B.V. All rights reserved.
Keywords: Microscopy AFM MSAFM Imaging Nonlinear dynamics Nanomechanical forces
1. Comment In a recent Letter [3], Tetard et al. introduced a generalized approach to multifrequency atomic force microscopy (AFM) termed mode synthesizing AFM (MSAFM) with promising dynamic attributes for subsurface imaging [4]. The new modes of the MSAFM, or the synthesized modes, were shown to be a result of the nonlinear form of the probe-sample interaction force, giving rise to frequency mixing. Using a partial differential equation (PDE) description of the MSAFM, Tetard et al. showed that the multifrequency aspect of the dynamics of the MSAFM operation could be captured by assuming a semi-empirical nonlinear force [2,3,5]. The sum and difference frequency generation capitalized in the MSAFM operation [3], offers a number of dynamic advantages compared to traditional single or multifrequency microscopy [6,7], as demonstrated for example by the application of the MSAFM to biomass characterization [3,5]. An example of the versatility of the MSAFM is the experimental generation of an oscillation enhancement that was recently reported by Tetard et al. [2], an effect coined “virtual resonance”. Based on a careful measurement of this enhancement, the reported experimental results showed that, in principle, any synthesized mode of the MSAFM can respond in a resonance like fashion to a spectrally tuned external forcing, allowing the system n Corresponding author at: Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA. E-mail address: [email protected] (A. Passian).
0304-3991/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ultramic.2013.03.016
to exhibit useful amplitude at frequencies completely outside the “original” resonances of the system [2]. While the concept of virtual resonance was presented based solely on the experiments of Tetard et al. [2], a semi-analytical solution to the above mentioned PDE, based on the Euler–Bernoulli model of the cantilever probe, was also presented in the same article to verify that the nonlinearity in the proposed force form could indeed generate the difference frequency. In the paper by Eslami and Jalili [1], the subject of our Comment, instead of the Euler–Bernoulli model of the microcantilever probe, the Timoshenko model for the microcantilever oscillations is solved under the same assumptions as the ones described in [2]. The authors report that both the Timoshenko and the Euler–Bernoulli beam models “had acceptable representation of the realistic behavior of the AFM system.” However, here, with reference to Fig. 1, the following comments are made for the benefit of the readers. First, it is crucial to distinguish the oscillation mode of the probe at the engendered difference frequency (Fig. 1c) from the enhancement achieved at the virtual resonance (Fig. 1e). The former process (Fig. 1c) has alternatively been referred to as scanning nearfield ultrasonic holography (SNFUH) [8–12]. Even more crucial is to treat the tuning of the difference frequency to the resonance frequencies of the probe (Fig. 1d) as a completely separate dynamic effect from the probe oscillation during the tuning to the virtual resonance (Fig. 1e) [2,3]. The former process (Fig. 1d) has also been referred to as resonant difference-frequency atomic force ultrasonic microscopy (RDF-AFUM) in [13]. Therefore, our comment specifically points out the distinction of such frequency overlap (Fig. 1d) from
A. Passian et al. / Ultramicroscopy 131 (2013) 92–93
93
of the sample must be adequately taken into account. Since no sample dynamics is included in [1], the presented calculations by Eslami and Jalili [1] bear no information regarding subsurface microscopy, in particular within the framework of the MSAFM [2,3,4,13,14]. Experimentally, the capability of MSAFM as an approach for high-resolution noninvasive subsurface microscopy has been demonstrated through characterizing nanoparticles in macrophages and red blood cells [8,9] and plant cell walls of biomass [3,5]. As for subsurface models, while a simplified computational model predicting the variation in the sample surface traction and velocity as a result of embedded nanoparticles in a sample was presented in the Supplementary material associated with [3], interesting developments are also noted in the recent work of Verbiest et al. [4] and others [13,15].
Acknowledgments This work was sponsored by the BioEnergy Science Center (BESC) of the Oak Ridge National Laboratory (ORNL). Laurene Tetard would like to acknowledge partial support from the Wigner fellowship program. The BESC is a US Department of Energy (DOE) Bioenergy Research Center supported by the Office of Biological and Environmental Research in the DOE Office of Science. ORNL is managed by UT-Battelle, LLC, for the US DOE under contract DE-AC05-00OR22725. References
Fig. 1. Clarification of the various dynamic modes of the MSAFM [3]: difference and sum frequency generation and the concept of virtual resonance. (a) Single forcing on the probe only, similar to a semi-contact mode AFM imaging scheme, (b) single forcing on the sample, similar to an ultrasonic imaging scheme [14], (c) two single frequency forcings on the tip-sample system represents the simplest case of the mode synthesizing atomic force microscopy (MSAFM) [3] with the sum and difference frequency generation, (d) a special case of MSAFM, where the generated difference frequency coincides with the resonance frequency of the probe [13] and (e) the newly formed difference mode is amplified by exhibiting a resonance-like response when stimulated with a weak applied forcing [2].
the amplitude enhancement obtained using the virtual resonance (Fig. 1e) [2]. We note that it is not necessary for the MSAFM to produce a high resolution image at the generated difference frequency, neither does it require the overlap frequency just described [3]. Therefore, we reiterate that the virtual resonance considers the MSAFM system with all its synthesized frequencies as a new dynamic system, to which it assigns “new” resonances [2,3]. Following this distinction, what is referred to as “virtual …” in the article by Eslami et al., in fact only describes either the ordinary MSAFM oscillation at the difference frequency, or its overlap with the resonance frequencies of the probe, but not the virtual resonance. Second, it is constructive to note that in order to advance the understanding of subsurface microscopy, the mechanical excitation
[1] S. Eslami, N. Jalili, A comprehensive modeling and vibration analysis of AFM microcantilevers subjected to nonlinear tip-sample interaction forces, Ultramicroscopy 117 (2012) 31–45. [2] L. Tetard, A. Passian, S. Eslami, N. Jalili, R.H. Farahi, T. Thundat, Virtual resonance and frequency difference generation by van der Waals interaction, Physical Review Letters 106 (2011) 180801. [3] L. Tetard, A. Passian, T. Thundat, New modes for subsurface atomic force microscopy through nanomechanical coupling, Nature Nanotechnology 5 (2010) 105–109. [4] G.J. Verbiest, J.N. Simon, T.H. Oosterkamp, M.J. Rost, Subsurface atomic force microscopy: towards a quantitative understanding, Nanotechnology 23 (2012) 145704. [5] L. Tetard, A. Passian, R.H. Farahi, B.H. Davison, S. Jung, A.J. Ragauskas, A. L. Lereu, T. Thundat, Nanometrology of delignified Populus using mode synthesizing atomic force microscopy, Nanotechnology 22 (2011) 465702–465709. [6] J.R. Lozano, R. Garcia, Theory of multifrequency atomic force microscopy, Physical Review Letters 100 (2008) 076102. [7] R. Garcia, E.T. Herruzo, The emergence of multifrequency force microscopy, Nature Nanotechnology 7 (2012) 217–226. [8] L. Tetard, A. Passian, K.T. Venmar, R.M. Lynch, B.H. Voy, G. Shekhawat, V. P. Dravid, T. Thundat, Imaging nanoparticles in cells by nanomechanical holography, Nature Nanotechnology 3 (2008) 501–505. [9] L. Tetard, A. Passian, R.M. Lynch, B.H. Voy, G. Shekhawat, V.P. Dravid, T. Thundat, Elastic phase response of silica nanoparticles buried in soft matter, Applied Physics Letters 93 (2008) 133113. [10] O. Kolosov, K. Yamanaka, Nonlinear detection of ultrasonic vibrations in an atomic force microscope, Japanese Journal of Applied Physics 32 (1993) L095–L098. [11] M.T. Cuberes, H.E. Assender, G.A.D. Briggs, O. Kolosov, HFM of PMMA/rubber nanocomposites, Journal of Physics D: Applied Physics 33 (2010) 2347–2355. [12] G.S. Shekhawat, V.P. Dravid, Nanoscale imaging of buried structures via scanning near-field ultrasound holography, Science 310 (2005) 89–92. [13] S.A. Cantrell, J.H. Cantrell, P.T. Lillehei, Nanoscale subsurface imaging via resonant difference-frequency atomic force ultrasonic microscopy, Journal of Applied Physics 101 (2007) 114324. [14] O. Kolosov, R.M. Castell, C.D. Marsh, G.A.D. Briggs, Imaging the elastic nanostructure of Ge islands by ultrasonic force microscopy, Physical Review Letters 81 (1998) 1046–1049. [15] J.H. Cantrell, S.A. Cantrell, Analytical model of the nonlinear dynamics of cantilever tip-sample surface interactions for various acoustic atomic force microscopies, Physical Review B 77 (2008) 165409.
Contents lists available at SciVerse ScienceDirect
Ultramicroscopy journal homepage: www.elsevier.com/locate/ultramic
Short communication
Comments on the paper “A comprehensive modeling and vibration analysis of AFM microcantilevers subjected to nonlinear tip-sample interaction forces” by Sohrab Eslami and Nader Jalili Ali Passian a,b,c,n, Laurene Tetard a, Thomas Thundat d a
Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA Department of Physics, University of Tennessee, Knoxville, TN 37996, USA c Department of Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, TN 37996, USA d Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alta., Canada T6G 2V4 b
art ic l e i nf o
a b s t r a c t
Available online 4 April 2013
This comment on the paper “A comprehensive modeling and vibration analysis of AFM microcantilevers subjected to nonlinear tip-sample interaction forces” by Sohrab Eslami and Jalili (2012) [1] aims to: (1) discuss and elucidate the concept of “virtual resonance” and thus (2) avert a misinterpretation of the experimental results and findings reported in the Tetard et al. Physical Review Letters 106, 180801 (2011) [2]. & 2013 Elsevier B.V. All rights reserved.
Keywords: Microscopy AFM MSAFM Imaging Nonlinear dynamics Nanomechanical forces
1. Comment In a recent Letter [3], Tetard et al. introduced a generalized approach to multifrequency atomic force microscopy (AFM) termed mode synthesizing AFM (MSAFM) with promising dynamic attributes for subsurface imaging [4]. The new modes of the MSAFM, or the synthesized modes, were shown to be a result of the nonlinear form of the probe-sample interaction force, giving rise to frequency mixing. Using a partial differential equation (PDE) description of the MSAFM, Tetard et al. showed that the multifrequency aspect of the dynamics of the MSAFM operation could be captured by assuming a semi-empirical nonlinear force [2,3,5]. The sum and difference frequency generation capitalized in the MSAFM operation [3], offers a number of dynamic advantages compared to traditional single or multifrequency microscopy [6,7], as demonstrated for example by the application of the MSAFM to biomass characterization [3,5]. An example of the versatility of the MSAFM is the experimental generation of an oscillation enhancement that was recently reported by Tetard et al. [2], an effect coined “virtual resonance”. Based on a careful measurement of this enhancement, the reported experimental results showed that, in principle, any synthesized mode of the MSAFM can respond in a resonance like fashion to a spectrally tuned external forcing, allowing the system n Corresponding author at: Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA. E-mail address: [email protected] (A. Passian).
0304-3991/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ultramic.2013.03.016
to exhibit useful amplitude at frequencies completely outside the “original” resonances of the system [2]. While the concept of virtual resonance was presented based solely on the experiments of Tetard et al. [2], a semi-analytical solution to the above mentioned PDE, based on the Euler–Bernoulli model of the cantilever probe, was also presented in the same article to verify that the nonlinearity in the proposed force form could indeed generate the difference frequency. In the paper by Eslami and Jalili [1], the subject of our Comment, instead of the Euler–Bernoulli model of the microcantilever probe, the Timoshenko model for the microcantilever oscillations is solved under the same assumptions as the ones described in [2]. The authors report that both the Timoshenko and the Euler–Bernoulli beam models “had acceptable representation of the realistic behavior of the AFM system.” However, here, with reference to Fig. 1, the following comments are made for the benefit of the readers. First, it is crucial to distinguish the oscillation mode of the probe at the engendered difference frequency (Fig. 1c) from the enhancement achieved at the virtual resonance (Fig. 1e). The former process (Fig. 1c) has alternatively been referred to as scanning nearfield ultrasonic holography (SNFUH) [8–12]. Even more crucial is to treat the tuning of the difference frequency to the resonance frequencies of the probe (Fig. 1d) as a completely separate dynamic effect from the probe oscillation during the tuning to the virtual resonance (Fig. 1e) [2,3]. The former process (Fig. 1d) has also been referred to as resonant difference-frequency atomic force ultrasonic microscopy (RDF-AFUM) in [13]. Therefore, our comment specifically points out the distinction of such frequency overlap (Fig. 1d) from
A. Passian et al. / Ultramicroscopy 131 (2013) 92–93
93
of the sample must be adequately taken into account. Since no sample dynamics is included in [1], the presented calculations by Eslami and Jalili [1] bear no information regarding subsurface microscopy, in particular within the framework of the MSAFM [2,3,4,13,14]. Experimentally, the capability of MSAFM as an approach for high-resolution noninvasive subsurface microscopy has been demonstrated through characterizing nanoparticles in macrophages and red blood cells [8,9] and plant cell walls of biomass [3,5]. As for subsurface models, while a simplified computational model predicting the variation in the sample surface traction and velocity as a result of embedded nanoparticles in a sample was presented in the Supplementary material associated with [3], interesting developments are also noted in the recent work of Verbiest et al. [4] and others [13,15].
Acknowledgments This work was sponsored by the BioEnergy Science Center (BESC) of the Oak Ridge National Laboratory (ORNL). Laurene Tetard would like to acknowledge partial support from the Wigner fellowship program. The BESC is a US Department of Energy (DOE) Bioenergy Research Center supported by the Office of Biological and Environmental Research in the DOE Office of Science. ORNL is managed by UT-Battelle, LLC, for the US DOE under contract DE-AC05-00OR22725. References
Fig. 1. Clarification of the various dynamic modes of the MSAFM [3]: difference and sum frequency generation and the concept of virtual resonance. (a) Single forcing on the probe only, similar to a semi-contact mode AFM imaging scheme, (b) single forcing on the sample, similar to an ultrasonic imaging scheme [14], (c) two single frequency forcings on the tip-sample system represents the simplest case of the mode synthesizing atomic force microscopy (MSAFM) [3] with the sum and difference frequency generation, (d) a special case of MSAFM, where the generated difference frequency coincides with the resonance frequency of the probe [13] and (e) the newly formed difference mode is amplified by exhibiting a resonance-like response when stimulated with a weak applied forcing [2].
the amplitude enhancement obtained using the virtual resonance (Fig. 1e) [2]. We note that it is not necessary for the MSAFM to produce a high resolution image at the generated difference frequency, neither does it require the overlap frequency just described [3]. Therefore, we reiterate that the virtual resonance considers the MSAFM system with all its synthesized frequencies as a new dynamic system, to which it assigns “new” resonances [2,3]. Following this distinction, what is referred to as “virtual …” in the article by Eslami et al., in fact only describes either the ordinary MSAFM oscillation at the difference frequency, or its overlap with the resonance frequencies of the probe, but not the virtual resonance. Second, it is constructive to note that in order to advance the understanding of subsurface microscopy, the mechanical excitation
[1] S. Eslami, N. Jalili, A comprehensive modeling and vibration analysis of AFM microcantilevers subjected to nonlinear tip-sample interaction forces, Ultramicroscopy 117 (2012) 31–45. [2] L. Tetard, A. Passian, S. Eslami, N. Jalili, R.H. Farahi, T. Thundat, Virtual resonance and frequency difference generation by van der Waals interaction, Physical Review Letters 106 (2011) 180801. [3] L. Tetard, A. Passian, T. Thundat, New modes for subsurface atomic force microscopy through nanomechanical coupling, Nature Nanotechnology 5 (2010) 105–109. [4] G.J. Verbiest, J.N. Simon, T.H. Oosterkamp, M.J. Rost, Subsurface atomic force microscopy: towards a quantitative understanding, Nanotechnology 23 (2012) 145704. [5] L. Tetard, A. Passian, R.H. Farahi, B.H. Davison, S. Jung, A.J. Ragauskas, A. L. Lereu, T. Thundat, Nanometrology of delignified Populus using mode synthesizing atomic force microscopy, Nanotechnology 22 (2011) 465702–465709. [6] J.R. Lozano, R. Garcia, Theory of multifrequency atomic force microscopy, Physical Review Letters 100 (2008) 076102. [7] R. Garcia, E.T. Herruzo, The emergence of multifrequency force microscopy, Nature Nanotechnology 7 (2012) 217–226. [8] L. Tetard, A. Passian, K.T. Venmar, R.M. Lynch, B.H. Voy, G. Shekhawat, V. P. Dravid, T. Thundat, Imaging nanoparticles in cells by nanomechanical holography, Nature Nanotechnology 3 (2008) 501–505. [9] L. Tetard, A. Passian, R.M. Lynch, B.H. Voy, G. Shekhawat, V.P. Dravid, T. Thundat, Elastic phase response of silica nanoparticles buried in soft matter, Applied Physics Letters 93 (2008) 133113. [10] O. Kolosov, K. Yamanaka, Nonlinear detection of ultrasonic vibrations in an atomic force microscope, Japanese Journal of Applied Physics 32 (1993) L095–L098. [11] M.T. Cuberes, H.E. Assender, G.A.D. Briggs, O. Kolosov, HFM of PMMA/rubber nanocomposites, Journal of Physics D: Applied Physics 33 (2010) 2347–2355. [12] G.S. Shekhawat, V.P. Dravid, Nanoscale imaging of buried structures via scanning near-field ultrasound holography, Science 310 (2005) 89–92. [13] S.A. Cantrell, J.H. Cantrell, P.T. Lillehei, Nanoscale subsurface imaging via resonant difference-frequency atomic force ultrasonic microscopy, Journal of Applied Physics 101 (2007) 114324. [14] O. Kolosov, R.M. Castell, C.D. Marsh, G.A.D. Briggs, Imaging the elastic nanostructure of Ge islands by ultrasonic force microscopy, Physical Review Letters 81 (1998) 1046–1049. [15] J.H. Cantrell, S.A. Cantrell, Analytical model of the nonlinear dynamics of cantilever tip-sample surface interactions for various acoustic atomic force microscopies, Physical Review B 77 (2008) 165409.