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Inertial imaging with nanomechanical systems

Abstract

Mass sensing with nanoelectromechanical systems has advanced significantly during the last decade. With nanoelectromechanical systems sensors it is now possible to carry out ultrasensitive detection of gaseous analytes, to achieve atomic-scale mass resolution and to perform mass spectrometry on single proteins. Here, we demonstrate that the spatial distribution of mass within an individual analyte can be imaged—in real time and at the molecular scale—when it adsorbs onto a nanomechanical resonator. Each single-molecule adsorption event induces discrete, time-correlated perturbations to all modal frequencies of the device. We show that by continuously monitoring a multiplicity of vibrational modes, the spatial moments of mass distribution can be deduced for individual analytes, one-by-one, as they adsorb. We validate this method for inertial imaging, using both experimental measurements of multimode frequency shifts and numerical simulations, to analyse the inertial mass, position of adsorption and the size and shape of individual analytes. Unlike conventional imaging, the minimum analyte size detectable through nanomechanical inertial imaging is not limited by wavelength-dependent diffraction phenomena. Instead, frequency fluctuation processes determine the ultimate attainable resolution. Advanced nanoelectromechanical devices appear capable of resolving molecular-scale analytes.

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Figure 1: Superposition of resonator mode shapes.
Figure 2: Adaptive fitting for enhanced resolution and accuracy.
Figure 3: Mass and position analysis using published experimental data.
Figure 4: Size and shape analysis via frequency-shift measurements of droplet arrays.

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Acknowledgements

The authors acknowledge support from an NIH Director's Pioneer award (to M.L.R.), a Caltech Kavli Nanoscience Institute Distinguished Visiting Professorship (to J.E.S.), the Fondation pour la Recherche et l'EnseignementSuperieur, Paris (FRES; to M.L.R.), and the Australian Research Council grants scheme (P.M. and J.E.S.).

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Contributions

M.L.R. and J.E.S. supervised the project. J.E.S. provided the principal mathematical idea for mass measurement using mode superposition that was extended to imaging by M.L.R. The resulting theory was further developed by M.S.H., S.I.K., J.E.S., and M.L.R. Droplet measurements were conceived by J.E.S., performed by C.D.O., and supervised by P.M. and J.E.S. The paper was written by M.S.H., S.I.K., C.D.O., J.E.S., and M.L.R. The FE simulations were executed by M.S.H. and S.I.K. All authors analysed the data and contributed to the writing of the paper.

Corresponding authors

Correspondence to John E. Sader or Michael L. Roukes.

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The authors declare no competing financial interests.

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Hanay, M., Kelber, S., O'Connell, C. et al. Inertial imaging with nanomechanical systems. Nature Nanotech 10, 339–344 (2015). https://doi.org/10.1038/nnano.2015.32

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