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Infrared nanosensors of piconewton to micronewton forces

Nature volume 637, pages 70–75 (2025)Cite this article

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Abstract

Mechanical force is an essential feature for many physical and biological processes1,2,3,4,5,6,7, and remote measurement of mechanical signals with high sensitivity and spatial resolution is needed for diverse applications, including robotics8, biophysics9,10, energy storage11 and medicine12,13. Nanoscale luminescent force sensors excel at measuring piconewton forces, whereas larger sensors have proven powerful in probing micronewton forces14,15,16. However, large gaps remain in the force magnitudes that can be probed remotely from subsurface or interfacial sites, and no individual, non-invasive sensor is capable of measuring over the large dynamic range needed to understand many systems14,17. Here we demonstrate Tm3+-doped avalanching-nanoparticle18 force sensors that can be addressed remotely by deeply penetrating near-infrared light and can detect piconewton to micronewton forces with a dynamic range spanning more than four orders of magnitude. Using atomic force microscopy coupled with single-nanoparticle optical spectroscopy, we characterize the mechanical sensitivity of the photon-avalanching process and reveal its exceptional force responsiveness. By manipulating the Tm3+ concentrations and energy transfer within the nanosensors, we demonstrate different optical force-sensing modalities, including mechanobrightening and mechanochromism. The adaptability of these nanoscale optical force sensors, along with their multiscale-sensing capability, enable operation in the dynamic and versatile environments present in real-world, complex structures spanning biological organisms to nanoelectromechanical systems.

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Fig. 1: Photon-avalanche-based nanoscale force sensors.
Fig. 2: Optical force sensing over four orders of magnitude by a single ANP.
Fig. 3: Sensitivity and cyclability of pre-ANP to ANP mechanobrightening.
Fig. 4: Ratiometric mechanochromism of dual-wavelength ANPs.

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Data availability

All data generated or analysed during this study, which support the plots within this paper and other findings of this study, are included in this published article and its Supplementary Information. Source data are provided with this paper.

Code availability

The code for modelling the force-dependent photon avalanche using the differential rate equations described in Supplementary Information is freely available on Zenodo at https://doi.org/10.5281/zenodo.13380752 (ref. 81).

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Acknowledgements

We thank K. W. C. Kwock and R. G. Stark for assistance with the set-up configuration. N.F.-M. acknowledges support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement number 893439, the US Department of State – IL Fulbright Scholarship Program, the Zuckerman–CHE STEM Leadership Program, the Israel Scholarship Education Foundation (ISEF), the ISEF – de Gunzburg International Science Fellowship Program, and the Weizmann Institute’s Women’s Postdoctoral Career Development Award. B.U. and P.J.S. acknowledge support by the National Science Foundation under grant number CHE-2203510. A.S. acknowledges the support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement number 895809 (MONOCLE). Work at the Molecular Foundry was supported by the Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under contract number DE-AC02-05CH11231. X.Q., B.E.C. and E.M.C. were supported in part by the Defense Advanced Research Projects Agency (DARPA) ENVision programme under contract HR0011257070, and C.L. and P.J.S. under DARPA ENVision contract HR00112220006. T.P.D. and P.J.S. also acknowledge support for scan-probe instrumentation and measurement capabilities from Programmable Quantum Materials, an Energy Frontier Research Center funded by the US DOE, Office of Science, Basic Energy Sciences (BES), under award DE-SC0019443.

Author information

Author notes

  1. Artiom Skripka

    Present address: Department of Chemistry, Oregon State University, Corvallis, OR, USA

Authors and Affiliations

  1. Department of Mechanical Engineering, Columbia University, New York, NY, USA

    Natalie Fardian-Melamed, Benedikt Ursprung, Changhwan Lee, Thomas P. Darlington & P. James Schuck

  2. The Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Artiom Skripka, Ayelet Teitelboim, Xiao Qi, Bruce E. Cohen & Emory M. Chan

  3. Nanomaterials for Bioimaging Group, Departamento de Física de Materiales, Facultad de Ciencias, Universidad Autόnoma de Madrid, Madrid, Spain

    Artiom Skripka

  4. Department of Physics and Astronomy, University of Utah, Salt Lake City, UT, USA

    Maoji Wang & Jordan M. Gerton

  5. Division of Molecular Biophysics and Integrated Bioimaging, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Bruce E. Cohen

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Contributions

Conceptualization: N.F.-M. and P.J.S. Experimental design: N.F.-M. and P.J.S. Experimental set-up: N.F.-M., B.U., T.P.D. and C.L. Mechano-optical measurements: N.F.-M., M.W., J.M.G. and P.J.S. Mechano-optical data analysis: N.F.-M., B.U. and C.L. Theoretical modelling and simulations: N.F.-M., E.M.C., A.S., C.L., P.J.S. and B.U. Advanced nanocrystal synthesis and structural characterization: A.S., A.T., X.Q., B.E.C. and E.M.C. Single-nanocrystal sample preparation: N.F.-M. and C.L. Paper writing: all authors.

Corresponding authors

Correspondence to Natalie Fardian-Melamed, Bruce E. Cohen, Emory M. Chan or P. James Schuck.

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Extended data figures and tables

Extended Data Fig. 1 Avalanche-shifting (7% Tm3+) ANP mechano-optics at the avalanching and saturation regimes.

a. Emission spectra as a function of applied force, for increasing excitation intensities, for single ANPs. At each excitation intensity, 100 force-dependent optical spectra are measured per 2.5 µN force ramp. The accessible force range (dashed line), and the relative brightness of the ANP (note different scales) for each excitation intensity correlate with avalanching behavior. b. Full compression cycles, each consisting of 100 emission intensity versus applied force data points, for single ANPs excited in their avalanching regime (27 kW cm−2) and saturation regime (85 kW cm−2). Each data point is derived from a single force-dependent optical spectrum (as in a and c). c. Two sequentially measured emission spectra (left) and their corresponding integrated intensities (right) as a function of applied force, for an ANP excited in its avalanching regime (18 kW cm−2). Error bars for integrated emission intensities are based on signal Poissonian statistics. The noise-defined resolution, retrieved from a full compression cycle (as in a and b), is depicted (P is photon counts (integrated intensity), F is force, P0 is the photon count at F = 0). Integration time is 3 s for all measurements.

Extended Data Fig. 2 Mechano-optical response of single avalanche-shifting (7% Tm3+) ANPs.

a. Excitation power dependence of the mechano-optical response of a single ANP. Each compression cycle (measured at a different excitation intensity) consists of 100 data points, derived from 100 force-dependent optical spectra measured at 3 s acquisition times. Force increment step size is 25nN. Excitation intensities and fitted graph equations (where P is emission intensity and F is force) for each compression cycle are depicted within the legend. b. Mechano-optical response cyclability of a single ANP. Repeating compression cycles measured for a single ANP at a specific excitation power (27 kW cm−2), for different acquisition times. Each compression cycle consists of 20 data points, derived from 20 force-dependent optical spectra measured at 2 s (cycles 1, 2) and 5 s (cycles 10, 11, 12) acquisition times. The force-dependent optical response is repeatable, for the 2.5-µN-force cycles applied. No photodegradation or plastic deformation is measured under these excitation and mechanical conditions, for up to 25 measured cycles per particle. The difference in apparent ambient particle brightness, and hence emission-force graphs, derives from the different acquisition times (noted for each cycle in the figure legend). Normalization by the acquisition time yields similar noise-equivalent sensitivity (NES) values for all cycles.

Extended Data Fig. 3 Cyclability of single (4% Tm3+) pre-ANP to ANP transitions.

a-b. Recurring compression cycles on a single pre-ANP excited at 52 kW cm−2 (a) and 41 kW cm−2 (b). For each cycle, once the particle reaches its maximal emission (at the same force value, within the measurement error), its emission decreases with force following an ANP response to force. Cycle number and fitted graph equations (where P is emission intensity and F is force) for each compression cycle are depicted within the legend. c-d. Excitation power dependent compression cycles for single pre-ANPs at the low-power regime (c) and at the high-power regime (d). Excitation intensities and fitted graph equations (where P is emission intensity and F is force) for each compression cycle are depicted within the legend. For each cycle, once the particle reaches its maximal emission (at the same force value, within the measurement error), its emission decreases with force following an ANP response to force. e. Emission increase force range of compression cycles #9, #10, and #11, of a pre-ANP measured at ~1,800 kW cm−2. a-e. Integration time per unit force was 3 s for all compression cycles.

Extended Data Fig. 4 Measurements and simulations of the 800 nm/700 nm -emission as a function of Tm3+ concentration.

a. Single particle spectra, measured for different Tm3+ concentration pre-ANPs/ANPs, at their respective saturation regimes (excitation wavelength: 1064 nm; excitation intensity: 376 kW cm−2 (4% Tm3+), 1,849 kW cm−2 (5% Tm3+), 517 kW cm−2 (15% Tm3+)). b. 800 nm / 700 nm -emission ratio as a function of Tm3+ concentration for different Tm3+ concentration pre-ANPs/ANPs, measured at their respective saturation regimes (excitation wavelength: 1064 nm; excitation intensity: 376 kW cm−2 (4% Tm3+), 1,849 kW cm−2 (5% Tm3+), 517 kW cm−2 (15% Tm3+)). Error bars are the standard deviations of three single-NP measurements. c. Photon avalanche differential rate equation (DRE) model simulations of the 800 nm / 700 nm -emission ratio as a function of Tm3+ concentration. The DRE simulations for the different Tm3+ concentrations were performed with the respective parameters (per Tm3+ concentration) extracted from fitting the emission versus excitation graphs measured at zero applied force (Supplementary Note 6, Table S3, and Fig. S5). Note that the DRE model predicts Tm3+ emissions from these levels up to a certain excitation threshold, above which other, higher-level, excited states are populated and thus must be taken into account. Any discrepancies between the simulated values here and the measured ones in a-b may be accounted for by adding DREs for higher levels (above 3F2). Other factors – such as determination of exact concentrations and hence energy transfer rates, or discernment of the precise 700 nm emission at lower concentrations and hence experimental 800 nm / 700 nm -emission ratios – may also reduce discrepancies between simulated and measured values. The DRE simulations show that higher cross-relaxation rates, attained at higher Tm3+ concentrations, decrease the 800 nm / 700 nm -emission ratio by: 1. Populating 3F4 at a faster rate, which, in turn, populates 3F3 at a faster rate by direct excited state absorption. 2. Depopulating 3H4 at a faster rate.

Extended Data Fig. 5 Mechano-optical response cyclability of single (15% Tm3+) piezochromic ANPs.

a. 800 nm and 700 nm integrated emission intensity versus applied force, for 4 consecutive force cycles, attained for a single piezochromic ANP. A total of up to 1.5 µN force was applied on the particle at each compression cycle. Each full compression cycle consists of 10–50 force-spectrum data points. Integration time per data point was: 3 s (cycle #1), 9 s (cycle #2), 20 s (cycle #3), and 30 s (cycle #4). b-e. Hyperspectral imaging of a single piezochromic ANP, before compression cycle #1 (b), #2 (c), and #9 (d), and after cycle #9 (e). Corresponding compression cycles displayed in f. Sampling time: 0.3 s. f. 800 nm / 700 nm -emission ratio versus applied force, for three force cycles, attained for a single piezochromic ANP (pre- and post-imaging in a-d). A total of 1 µN force was applied on the particle at each compression cycle. Each full compression cycle consists of 10–20 force-spectrum data points. Integration time per data point was: 30 s (cycle #1), 50 s (cycle #2), and 3 s (cycle #9). a-f. Excitation intensity: 1,131 ± 46 kW cm−2.

Extended Data Fig. 6 Mechano-optical response versus cycle # for single (15% Tm3+) piezochromic ANPs.

a. Mechano-optical response (percent change of the 800 nm / 700 nm -emission ratio versus applied force), for up to 9 compression cycles per particle, for 8 different piezochromic ANPs. b-d. Mechano-optical response (b), normalized initial (F = 0) brightness (c), and initial (F = 0) 800 nm / 700 nm -emission ratio (d) versus cycle #. Data are derived from 21 compression cycles on 8 piezochromic ANPs (excitation intensity: 1,131 ± 46 kW cm−2). Each compression cycle consists of 10–1000 emission versus force data points. Error bars depict the extrapolated errors derived from the 800 nm / 700 nm -emission ratio versus applied force fit values’ 95% confidence intervals, while compression cycles consisting of a lower number of emission-versus-force data points yield larger S.E.M.s. Data points in c are normalized to a 3 s integration time baseline (i.e., divided by their respective integration times, and multiplied by 3 s), so as to conform to data acquired for the other (pre-avalanching and avalanching) particles in this study – for comparison between particles (data in c was further normalized to a 1 s integration time baseline for NES derivation). Data in b, c, and d are colour-coded as in a (each colour represents a different single particle).

Extended Data Fig. 7 Measurements and simulations of the mechano-optical response of single (15% Tm3+) piezochromic ANPs.

Measured 800 nm / 700 nm -emission ratio (a) and percent change of the 800 nm / 700 nm -emission ratio (b) versus applied force, for 5 compression cycles originating from 5 different piezochromic ANPs (excitation intensity: 1,131 ± 46 kW cm−2). Integration time per data point was: 3 s (NP #1), 3 s (NP #2), 3 s (NP #3), 30 s (NP #4), and 50 s (NP #5). While their initial 800 nm / 700 nm -emission ratios differ by up to ±25% (full statistics in Extended Data Fig. 8), their mechanical response is similar. c. Photon avalanche DRE model simulations of the 15% Tm3+ piezochromic ANP force response. All DRE parameters are listed in Supplementary Note 6, Table S3. Zero-force simulation parameters are derived from fitting the excitation (at 1064 nm) versus emission (at 800 nm) data measured for piezochromic ANPs at ambient conditions (Supplementary Note 6, Fig. S5c). Force dependence of all of the nonradiative relaxation and cross-relaxation rates are derived from the equations listed in Supplementary Note 6. Calculations were performed for excitation intensities ca. 20-fold higher than threshold intensities, in line with the excitation power densities used for the piezochromic ANP measurements in this study.

Extended Data Fig. 8 Mechano-optical parameter distributions for single (15% Tm3+) piezochromic ANPs.

Initial (F = 0) 800 nm / 700 nm -emission ratio (a), noise-equivalent sensitivity (NES) (b), and force range (c) population distributions, along with their histogram Gaussian fits, for 21 compression cycles measured for 8 piezochromic ANPs (excitation intensity: 1,131 ± 46 kW cm−2). Each compression cycle consists of 10–1000 emission versus force data points, measured at different integration times (3–50 s). The normal distribution fits yield means and S.E.M.s of: I800 nm(F0) / I700 nm(F0) = 8.0 ± 0.7 (a), NES = 9.2 ± 2.0 nN Hz−1/2 (b), and Frange = 0.4 ± 0.04 µN (c).

Extended Data Fig. 9 Mechano-optical response and resolution as a function of integration time for single (15% Tm3+) piezochromic ANPs.

a. Mechano-optical response (percent change of the 800 nm / 700 nm -emission ratio versus applied force), for up to 9 compression cycles per particle, for 8 different piezochromic ANPs. b-d. Mechano-optical response (b), normalized initial (F = 0) brightness (c), and initial (F = 0) 800 nm / 700 nm -emission ratio (d) versus integration time. Data are derived from 21 compression cycles on 8 piezochromic ANPs. Data points in c are normalized to a 3 s integration time baseline (see Extended Data Fig. 6). Data in b, c, and d are colour-coded as in a (each colour represents a different single particle). e. Resolution of (15% Tm3+) piezochromic ANPs as a function of integration time. Resolutions are derived from 7 compression cycles on two 15% Tm3+ piezochromic ANPs with different initial (F = 0) brightnesses. a-e. Excitation intensity: 1,131 ± 46 kW cm−2. Each compression cycle consists of 10–1000 emission versus force data points. Error bars depict the extrapolated errors derived from the 800 nm / 700 nm -emission ratio versus applied force fit values’ 95% confidence intervals, while compression cycles consisting of a lower number of emission-versus-force data points yield larger S.E.M.s.

Extended Data Fig. 10 ANP (7% Tm3+) avalanche-shifting, pre-ANP (4% Tm3+) mechanobrightening, and piezochromic ANP (15% Tm3+) mechanochromism parameters versus excitation intensity.

Force range (a), force resolution (b), and noise-equivalent sensitivity (NES) (c), versus excitation intensity, derived from 26 compression cycles and 6 power-dependent compressions on six 4% Tm3+ pre-ANPs (grey), 23 compression cycles on nine 7% Tm3+ ANPs (teal), and 21 compression cycles on eight 15% Tm3+ piezochromic ANPs (purple). Different symbol shapes represent different single NPs. Each compression cycle consists of 10–1000 emission versus force data points, measured at 3 s (4% Tm3+), 3 s (7% Tm3+), and 3–50 s (15% Tm3+) integration times. Integration times for power-dependent compressions are 3–7 s per excitation power. Error bars represent S.E.M.s, propagated from the (integrated intensity versus force – for pre-ANPs and ANPs; 800 nm / 700 nm -emission ratio versus force – for piezochromic ANPs) linear fit value standard errors; compressions consisting of a lower number of emission-versus-force data points yield larger S.E.M.s. d. Summary of ICP-derived doping concentrations, TEM-derived NP sizes, and force measurement NES’s (mean ± standard deviation, for 3 single NPs measured at the same excitation intensity) for different sensing modalities.

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Fardian-Melamed, N., Skripka, A., Ursprung, B. et al. Infrared nanosensors of piconewton to micronewton forces. Nature 637, 70–75 (2025). https://doi.org/10.1038/s41586-024-08221-2

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