{"id":859444,"date":"2026-06-11T08:18:19","date_gmt":"2026-06-11T08:18:19","guid":{"rendered":"https:\/\/www.europesays.com\/us\/859444\/"},"modified":"2026-06-11T08:18:19","modified_gmt":"2026-06-11T08:18:19","slug":"light-induced-quantum-friction-of-carbon-nanotubes-in-water","status":"publish","type":"post","link":"https:\/\/www.europesays.com\/us\/859444\/","title":{"rendered":"Light-induced quantum friction of carbon nanotubes in water"},"content":{"rendered":"<p>Preparation of SWCNTs<\/p>\n<p>If not stated otherwise, all chemicals were purchased from Sigma Aldrich (Germany). Unless specifically stated, all experiments were performed with (6,5)-enriched SWCNTs (Sigma Aldrich, Signis SG65i, CoMoCAT synthesis technology). For DNA-functionalized SWCNTs 150\u2009\u00b5l of 2\u2009mg\u2009ml\u22121 single-stranded DNA (for example, (GT)10) in 1\u00d7 PBS buffer (pH 7.4) was mixed with 75\u2009\u00b5l of 2\u2009mg\u2009ml\u22121 SWCNT in PBS and 75\u2009\u00b5l PBS, followed by tip sonication (Fisher Scientific, FB120, 120\u2009W, amplitude 35%, 9\u2009s pulse on and 1\u2009s off, 15\u2009min). The obtained solution was centrifuged for 30\u2009min at maximum speed (21,000g), the supernatant was collected, and the procedure was repeated two more times. The final supernatant was stored at 4\u2009\u00b0C until further experiments were performed. For (GT)10-SWCNT experiments in D2O, the PBS buffer was prepared with D2O instead of H2O.<\/p>\n<p>The separation\u00a0via aqueous two phase extraction (ATPE)\u00a0of (6,4)-SWCNTs was performed according to the following protocol<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 48\" title=\"Li, H., Gordeev, G., Garrity, O., Reich, S. &amp; Flavel, B. S. Separation of small-diameter single-walled carbon Nanotubes in one to three steps with aqueous two-phase extraction. ACS Nano 13, 2567&#x2013;2578 (2019).\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#ref-CR48\" id=\"ref-link-section-d80690512e1512\" rel=\"nofollow noopener\" target=\"_blank\">48<\/a>. (DOC)-SWCNTs were mixed with polyethylene glycol (PEG) (molecular weight 6\u2009kDa, 8% w\/v), dextran (Carl Roth, molecular weight 70\u2009kDa, 4% w\/v), and the surfactants DOC (0.025% w\/v), SDS (0.5% w\/w) and SC (ranging from 0.5% to 0.9% w\/w in 0.1% increments). The chiralities of SWCNTs in the two phases could be adjusted by adding HCl. Then, a one-step approach was used by adding a specific volume of HCl (hydrogen chloride) and NaClO (sodium hypochlorite) with 10\u201315% available chlorine for pH-driven and electronic separation, allowing the collection of monochiral (6,4)-SWCNTs in the bottom phase (B3). The solution was then dialysed (using a 300\u2009kDa dialysis bag, Spectra\/Por, Spectrum Laboratories) against a 1% DOC solution to remove dextran and obtain a stable 1% DOC-(6,4)-SWCNT solution.<\/p>\n<p>For DOC-SWCNTs, 150\u2009\u00b5l 2% (m\/v) DOC in H2O was mixed with 150\u2009\u00b5l of 2\u2009mg\u2009ml\u22121 SWCNTs (in H2O), followed by tip sonication and centrifugation similar to the conditions for (GT)10-SWCNTs preparation. The acquired supernatant was stored at 4\u2009\u00b0C. SDBS- and SC-functionalized SWCNTs were prepared according to the same procedure as DOC-SWCNTs.<\/p>\n<p>Quantum defect introduction was performed according to a previously developed protocol<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 49\" title=\"Mann, F. A., Galonska, P., Herrmann, N. &amp; Kruss, S. Quantum defects as versatile anchors for carbon nanotube functionalization. Nat. Protoc. 17, 727&#x2013;747 (2022).\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#ref-CR49\" id=\"ref-link-section-d80690512e1530\" rel=\"nofollow noopener\" target=\"_blank\">49<\/a>. Briefly, 20\u2009\u00b5l of 4\u2009mM 4-nitrobenzol diazonium tetrafluoroborate diazonium salt (dissolved in water) was added to 20\u2009ml of 10\u2009nM SDBS-SWCNTs solution. Then the mixture was irradiated with green light (550\u2009nm) while stirring for 15\u2009min. The obtained solution was mixed with the same volume of acetonitrile (ACN) and, consequently, the SWCNTs precipitated. The pellet was then washed with H2O two or three times to remove residual SDBS and ACN. Finally, the acquired precipitate was redispersed in 1% DOC by 15\u2009min tip sonication followed by centrifugation for 30\u2009min at 21,000\u00a0g. The collected supernatant was used for the experiments. The length of SWCNTs prepared by this procedure is about 600\u2009nm (ref.\u2009<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 25\" title=\"Ma, C. et al. Stochastic formation of quantum defects in carbon nanotubes. ACS Nano 17, 15989&#x2013;15998 (2023).\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#ref-CR25\" id=\"ref-link-section-d80690512e1539\" rel=\"nofollow noopener\" target=\"_blank\">25<\/a>).<\/p>\n<p>All samples were colloidally stable in aqueous solution without signs of aggregation as confirmed by absorbance (Extended Data Figs. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#Fig5\" rel=\"nofollow noopener\" target=\"_blank\">1a<\/a> and <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#Fig6\" rel=\"nofollow noopener\" target=\"_blank\">2<\/a>, and Supplementary Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">1<\/a>), one-dimensional (1D) (Extended Data Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#Fig5\" rel=\"nofollow noopener\" target=\"_blank\">1b,c<\/a>) and two-dimensional (2D) fluorescence spectroscopy (Supplementary Figs. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">2<\/a> and <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">3<\/a>) and atomic force microscopy (average SWCNT length of around 600\u2009nm; Supplementary Figs. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">4<\/a> and <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">5<\/a>). We also prepared chirality-pure (6,5)- and (6,4)-SWCNTs to exclude effects from impurities (Extended Data Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#Fig6\" rel=\"nofollow noopener\" target=\"_blank\">2<\/a> and Supplementary Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">1<\/a>).<\/p>\n<p>NIR spectroscopyOne-dimensional fluorescence spectra<\/p>\n<p>One-dimensional spectra of 0.5\u2009nM (GT)10-SWCNTs with or without analytes (2\u2009\u03bcM riboflavin and 100\u2009\u03bcM ascorbic acid in aqueous solution) or 0.5\u2009nM DOC-, SC- and SDBS-functionalized SWCNTs were measured in a custom-built setup based on an Olympus IX73 microscope and a solid-state laser (Quantum gem-561, 561\u2009nm). The emission spectra were captured with an Andor iDus InGaAs 491 array NIR detector coupled to a Shamrock 193i spectrometer (Andor Technology).<\/p>\n<p>Two-dimensional fluorescence spectra<\/p>\n<p>The same setup as for 1D spectra was used. However, to obtain 2D excitation\u2013emission spectra of 2\u2009nM SWCNTs in various surfactants and (GT)10-SWCNTs in 1\u2009\u00d7\u2009PBS (D2O) at pH 7.4, a monochromator (MSH150) equipped with an LSE341 light source (LOT-Quantum Design) was used for tunable excitation.<\/p>\n<p>FCS measurements<\/p>\n<p>FCS measurements were performed with a MicroTime 200 system (PicoQuant), equipped with pulsed lasers at 485\u2009nm (LDH-C-D-485) and 530\u2009nm (LDH-D-TA-530), an Olympus IX73 inverted confocal laser scanning microscope equipped with a 60\u00d7 water objective (Olympus, numerical aperture 1.2, UPlanSApo), and single-photon avalanche photodiodes (SPADs) detectors (Excelitas Technologies). We focused on (6,5)-SWCNTs because of the limited sensitivity of the detectors in our FCS setup in the NIR region &gt;1,100\u2009nm. Samples at a concentration of 1\u2009nM were excited with a pulsed laser at 485\u2009nm, operating at a frequency of 40\u2009MHz. DOC-(6,4)-SWCNTs showed weak emission when excited at 480\u2009nm. Consequently, we used the 532\u2009nm excitation. As the 532\u2009nm laser could not achieve higher power levels in pulsed mode, we used CW excitation at 532\u2009nm for this measurement, ensuring that the excitation power remained consistent. The emitted light was separated from the excitation light through a dichroic mirror (R405\/488\/532\/635, Semrock), passed through a 900-nm long-pass filter (Thorlabs) to block the excitation light, and then focused onto a 50-\u03bcm pinhole and directed to the SPAD detectors. For DOC-(6,4)-SWCNTs, a 800-nm long pass filter (Thorlabs) was used. The refractive index and viscosity corrections were done by adjusting the collar settings<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 50\" title=\"Chattopadhyay, K., Saffarian, S., Elson, E. L. &amp; Frieden, C. Measuring unfolding of proteins in the presence of denaturant using fluorescence correlation spectroscopy. Biophys. J. 88, 1413&#x2013;1422 (2005).\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#ref-CR50\" id=\"ref-link-section-d80690512e1612\" rel=\"nofollow noopener\" target=\"_blank\">50<\/a>.<\/p>\n<p>The autocorrelation function of the fluorescence intensity I is defined as<\/p>\n<p>$$G(\\tau )=\\frac{\\langle I(t)I(t+\\tau )\\rangle }{\\langle I{(t)}^{2}\\rangle }$$<\/p>\n<p>\n                    (1)\n                <\/p>\n<p> G(\u03c4) correlates the fluctuation of the intensity of a fluorophore at time t and after time lag \u03c4.<\/p>\n<p>Fluctuations arise because of the diffusive motion of the fluorophore through the 3D Gaussian confocal volume having widths wz and wxy. The correlation function corresponding to the diffusion is<\/p>\n<p>$${G}_{D}({\\tau })=\\frac{1}{N}{\\left[1+\\frac{{\\tau }}{{{\\tau }}_{D}}\\right]}^{-1}{\\left[1+\\frac{{\\tau }}{{w}^{2}{{\\tau }}_{D}}\\right]}^{\\frac{-1}{2}}$$<\/p>\n<p>\n                    (2)\n                <\/p>\n<p>where N is the total number of molecules in the confocal volume and \u03c4D is the diffusion time of that system. It is linked to the diffusion constant D by<\/p>\n<p>$${\\tau }_{D}=\\frac{{w}_{{xy}}^{2}}{4D}$$<\/p>\n<p>\n                    (3)\n                <\/p>\n<p>The structural parameter \\(w=\\frac{{w}_{x}}{{w}_{{xy}}}\\) was calibrated using the known Atto 488 dye (1\u2009nM) in water (Dt\u2009=\u2009400\u2009\u03bcm2\u2009s\u22121) (ref.\u2009<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 51\" title=\"Zhang, X. et al. Determination of equilibrium and rate constants for complex formation by fluorescence correlation spectroscopy supplemented by dynamic light scattering and Taylor dispersion analysis. Soft Matter 12, 8186&#x2013;8194 (2016).\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#ref-CR51\" id=\"ref-link-section-d80690512e2074\" rel=\"nofollow noopener\" target=\"_blank\">51<\/a>). The calculated excitation volume was 1.5\u2009fl.<\/p>\n<p>To analyse the FCS data, the software Igor Pro 6.34\u2009A and the following equation was used for fitting:<\/p>\n<p>$${G}_{D}(\\tau )=\\frac{1}{N}{\\left[1+\\frac{\\tau }{{\\tau }_{D}}\\right]}^{-1}{\\left[1+\\frac{\\tau }{{w}^{2}{\\tau }_{D}}\\right]}^{\\frac{-1}{2}}\\,\\left[1+\\frac{T}{1-T}\\exp {\\left(-\\frac{\\tau }{{\\tau }_{t}}\\right)}^{\\beta }\\right]$$<\/p>\n<p>\n                    (4)\n                <\/p>\n<p>where T is the fraction of the fluorescent molecules in the dark state and \\({{\\tau }}_{{t}}\\) signifies the corresponding lifetime. The stretching exponent \u03b2 is a marker for the degree of heterogeneity in the associated dynamics<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 52\" title=\"Haustein, E. &amp; Schwille, P. Fluorescence correlation spectroscopy: novel variations of an established technique. Annu. Rev. Biophys. 36, 151&#x2013;169 (2007).\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#ref-CR52\" id=\"ref-link-section-d80690512e2393\" rel=\"nofollow noopener\" target=\"_blank\">52<\/a>.<\/p>\n<p>FCS control experiments<\/p>\n<p>A control experiment under identical conditions was conducted with the dye Atto 488 (Supplementary Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">6a<\/a>) and showed a slight decrease in G(0) value but no change in the normalized autocorrelation functions and the diffusion time (Supplementary Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">6b<\/a>) under the same experimental conditions. This control experiment rules out effects from sample heating, which is known for surface-immobilized emitters<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 53\" title=\"Doose, S., Tsay, J. M., Pinaud, F. &amp; Weiss, S. Comparison of photophysical and colloidal properties of biocompatible semiconductor nanocrystals using fluorescence correlation spectroscopy. Anal. Chem. 77, 2235&#x2013;2242 (2005).\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#ref-CR53\" id=\"ref-link-section-d80690512e2414\" rel=\"nofollow noopener\" target=\"_blank\">53<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 54\" title=\"M&#xFC;ller, C. B. et al. Precise measurement of diffusion by multi-color dual-focus fluorescence correlation spectroscopy. Europhys. Lett. 83, 46001 (2008).\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#ref-CR54\" id=\"ref-link-section-d80690512e2417\" rel=\"nofollow noopener\" target=\"_blank\">54<\/a>. Furthermore, we verified that the temperature of the samples remained constant for both 10\u2009\u03bcW and 90\u2009\u03bcW (Supplementary Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">9<\/a>). Brightness of (GT)10-SWCNTs also increased linearly with laser power (Supplementary Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">7a<\/a>), indicating the absence of non-linear effects such as exciton\u2013exciton annihilation. The increase in the number of (apparent) fluorescent particles (Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#Fig1\" rel=\"nofollow noopener\" target=\"_blank\">1b<\/a>) from 3 to 9.3 in the confocal volume with higher laser power (Supplementary Table <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">1<\/a>) can be attributed to the relatively small quantum yield of NIR fluorophores such as SWCNTs (refs.\u2009<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 55\" title=\"Berger, F. J. et al. Brightening of long, polymer-wrapped carbon nanotubes by sp3 functionalization in organic solvents. ACS Nano 13, 9259&#x2013;9269 (2019).\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#ref-CR55\" id=\"ref-link-section-d80690512e2436\" rel=\"nofollow noopener\" target=\"_blank\">55<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 56\" title=\"Spreinat, A. et al. Quantum defects in fluorescent carbon nanotubes for sensing and mechanistic studies. J. Phys. Chem. C 125, 18341&#x2013;18351 (2021).\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#ref-CR56\" id=\"ref-link-section-d80690512e2439\" rel=\"nofollow noopener\" target=\"_blank\">56<\/a>), which means that they are not saturated by excitation. Moreover, the diffusion behaviour of (GT)10-SWCNTs could be reversibly switched by changing the excitation power (Supplementary Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">7b<\/a>). We also performed FCS measurements of chirality-purified (GT)10-(6,5)-SWCNTs and found that the diffusion behaviour was similar to that of the normal (GT)10-SWCNTs (Supplementary Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">8<\/a> and Supplementary Table <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">2<\/a>), which shows that sample purity is high in all cases and does not affect diffusivity.<\/p>\n<p>Although most FCS experiments employed pulsed excitation to collect more information (for example, lifetime), FCS using CW excitation showed the same results (Extended Data Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#Fig11\" rel=\"nofollow noopener\" target=\"_blank\">7a,b<\/a> and Supplementary Table <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">14<\/a>). This finding suggests that the diffusion behaviour of SWCNT (on the ms timescale) is less affected by the excitation timing (ps timescale) but rather the overall absorbed energy.<\/p>\n<p>As a control, to assess whether analytes induce aggregation or dissociation of SWCNTs, we measured the absorbance spectra. They remained unchanged for both analytes (Supplementary Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">13<\/a>). Thus, chemical manipulation affects diffusion the same way it affects exciton concentration (quantum yield). These results allow to exclude that the change in diffusion is an optical artefact. It is distinct from trapping of objects by light with optical tweezers<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 57\" title=\"Ashkin, A. Acceleration and trapping of particles by radiation pressure. Phys. Rev. Lett. 24, 156&#x2013;159 (1970).\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#ref-CR57\" id=\"ref-link-section-d80690512e2474\" rel=\"nofollow noopener\" target=\"_blank\">57<\/a>.<\/p>\n<p>We also investigated a 80% glycerol\/water mixture and observed almost no changes in diffusion (Extended Data Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#Fig7\" rel=\"nofollow noopener\" target=\"_blank\">3b<\/a> and Supplementary Table <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">4<\/a>). By contrast, for a 20% glycerol\/water mixture, we observed power-dependent changes in the diffusion constant similar to those of water (Extended Data Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#Fig7\" rel=\"nofollow noopener\" target=\"_blank\">3c<\/a> and Supplementary Table <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">5<\/a>). Previous THz spectroscopic studies demonstrated that when the glycerol concentration is below 20%, the number of water molecules hydrogen-bonded to glycerol continues to increase. By contrast, at concentrations above 40%, the number of hydrogen-bonded water molecules decreases because of the overlap of hydration shells<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 58\" title=\"Das Mahanta, D. et al. Local solvation structures govern the mixing thermodynamics of glycerol&#x2013;water solutions. Chem. Sci. 14, 7381&#x2013;7392 (2023).\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#ref-CR58\" id=\"ref-link-section-d80690512e2493\" rel=\"nofollow noopener\" target=\"_blank\">58<\/a>.<\/p>\n<p>To further understand the entanglement of excitation and diffusion in the FCS geometry, the random walk of SWCNTs in a box with a confocal laser volume was simulated (Supplementary Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">22<\/a>). The results (Supplementary Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">23<\/a>) qualitatively confirmed that changes in the diffusion by excitation of excitons in moving and rotating SWCNTs lead to the power-dependent changes of the autocorrelation functions observed in the experiments (Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#Fig1\" rel=\"nofollow noopener\" target=\"_blank\">1<\/a>).<\/p>\n<p>THz measurements<\/p>\n<p>The OPTP spectrometer was described in detail previously<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 36\" title=\"Hoberg, C. et al. Caught in the act: real-time observation of the solvent response that promotes excited-state proton transfer in pyranine. Chem. Sci. 14, 4048&#x2013;4058 (2023).\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#ref-CR36\" id=\"ref-link-section-d80690512e2519\" rel=\"nofollow noopener\" target=\"_blank\">36<\/a>. In summary, the system uses 50\u2009fs, 800\u2009nm laser pulses generated by a Ti:sapphire-amplified laser to produce a broadband THz probe pulse using a two-colour air plasma filament<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 59\" title=\"Xie, X., Dai, J. &amp; Zhang, X.-C. Coherent control of THz wave generation in ambient air. Phys. Rev. Lett. 96, 075005 (2006).\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#ref-CR59\" id=\"ref-link-section-d80690512e2523\" rel=\"nofollow noopener\" target=\"_blank\">59<\/a>. Part of the 800-nm-wavelength laser radiation is frequency-doubled in a BBO (beta barium borate) crystal to generate 400\u2009nm light, which serves as the optical pump. We measure the changes in THz absorption on optical excitation as a function of pump\u2013probe delay, \u0394t, between 0.25\u2009ps and 300\u2009ps by using a mechanical delay stage. To eliminate interference effects and the excitation of free charge carriers, we used a windowless, free-flowing jet with a thickness of 20\u2009\u03bcm as the sample<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 36\" title=\"Hoberg, C. et al. Caught in the act: real-time observation of the solvent response that promotes excited-state proton transfer in pyranine. Chem. Sci. 14, 4048&#x2013;4058 (2023).\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#ref-CR36\" id=\"ref-link-section-d80690512e2530\" rel=\"nofollow noopener\" target=\"_blank\">36<\/a>. An 80\u2009ml solution of SWCNTs (about 100\u2009nM) was circulated in the jet for 96\u2009h. A defoaming agent (BYK 025) was added to the reservoir to prevent foam generation. This defoaming agent remains as a thin film on the surface and does not interfere with the sample measurements. The THz field is detected using electro-optic sampling with a 100\u2009\u00b5m thin gallium phosphide (GaP) crystal. For further analysis, the electric fields are Fourier-transformed. The difference in THz transmission before and after optical excitation is expressed as \u0394mOD. Positive values indicate a decrease in transmission on optical excitation. The fluence of the blue light was varied from 50\u2009mJ\u2009cm\u22122 to 120\u2009mJ\u2009cm\u22122 and then to 200\u2009mJ\u2009cm\u22122. As a reference, we also measured pure water at a fluence of 200\u2009mJ\u2009cm\u22122. In the plots, we show data for a fluence of 200\u2009mJ\u2009cm\u22122, unless stated otherwise.<\/p>\n<p>Wide-field tracking of SWCNTs<\/p>\n<p>A 2.3\u2009\u00b5m Mylar thin film (TF\u2212125-225-F from Fluxana) was used as a spacer and placed between two glass cover slides to create a narrow flow-chamber-like volume. Subsequently, 50\u2009\u00b5l of a 0.1\u2009nM purified DOC-SWCNT solution was added. Single-walled carbon nanotube (SWCNT) tracking was performed using a custom-built setup. A 561\u2009nm laser (Cobolt Jive 500, 200\u2009mW, 100\u2009W\u2009cm\u22122) was coupled to an Olympus IX73 microscope equipped with a 100\u00d7 (UPlanSApo 100\u00d7\/1.35 Sil, Olympus) oil-immersion objective. Imaging in the NIR was performed with a InGaAs camera (Cheetah, Xenics 640, 640\u2009\u00d7\u2009512 pixel, thermoelectrically cooled). A dichroic mirror (VIS\/NIR, HC BS R785 lambda\/5 PV, F38-785, AHF) and a 900\u2009nm long-pass filter (FELH0900, Thorlabs) were installed in the beam path between the objective and the cameras. The NIR images were typically acquired at 7 frames per second (fps) with a 140\u2009ms exposure time. All analyses were conducted using Python 3.10.5. For particle tracking, the Python library trackpy was used to identify bright spots corresponding to individual SWCNTs. We analysed only traces above a certain length (typically 100 frames). The analysis determines the x and y centre-of-mass coordinates of particle positions. From the trajectories, we calculated the ensemble time-averaged mean squared displacement (MSD)<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 60\" title=\"Rehfeldt, F. &amp; Weiss, M. The random walker&#039;s toolbox for analyzing single-particle tracking data. Soft Matter 19, 5206&#x2013;5222 (2023).\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#ref-CR60\" id=\"ref-link-section-d80690512e2562\" rel=\"nofollow noopener\" target=\"_blank\">60<\/a>.<\/p>\n<p>Computation of friction and diffusion in water<\/p>\n<p>The classical atomistic molecular dynamics simulations were run with an open\u00a0source LAMMPS (Large-scale Atomic\/Molecular Massively Parallel Simulator)<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 61\" title=\"Thompson, A. P. et al. LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Comput. Phys. Commun. 271, 108171 (2022).\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#ref-CR61\" id=\"ref-link-section-d80690512e2574\" rel=\"nofollow noopener\" target=\"_blank\">61<\/a> to estimate the interfacial friction coefficient and diffusion of graphene and (6,5)-SWCNTs in explicit water. The models for graphene slab (2.5\u2009\u00d7\u20092.6\u2009nm2) with 1,600 water molecules and (6,5)-SWCNTs (3\u2009\u00d7\u20093\u2009\u00d7\u20094.1\u2009nm3) with 1,100 water molecules systems were created in Material Studio<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 62\" title=\"Module, F. Material Studio v.6.0 (Accelrys, 2011).\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#ref-CR62\" id=\"ref-link-section-d80690512e2582\" rel=\"nofollow noopener\" target=\"_blank\">62<\/a>. For the calculation of the interfacial friction, the graphene system used is periodic in the x\u2013y directions and non-periodic in the direction perpendicular to the surface, whereas all the CNT systems are 3D periodic with an infinite nanotube along the axial direction. Both non-polarizable and polarizable systems are analysed with harmonic consistent valence forcefield (CVFF)<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 63\" title=\"Dauber-Osguthorpe, P. et al. Structure and energetics of ligand binding to proteins: escherichia coli dihydrofolate reductase-trimethoprim, a drug-receptor system. Proteins Struct. Funct. Bioinform. 4, 31&#x2013;47 (1988).\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#ref-CR63\" id=\"ref-link-section-d80690512e2593\" rel=\"nofollow noopener\" target=\"_blank\">63<\/a> and interface force field-CVFF (IFF-CVFF)<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 64\" title=\"Heinz, H., Lin, T. -J., Mishra, R. K. &amp; Emami, F. S. Thermodynamically consistent force fields for the assembly of inorganic, organic, and biological nanostructures: the INTERFACE force field. Langmuir 29, 1754&#x2013;1765 (2013).\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#ref-CR64\" id=\"ref-link-section-d80690512e2597\" rel=\"nofollow noopener\" target=\"_blank\">64<\/a> parameters, respectively (Supplementary Table <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">17<\/a>), which use 12-6 LJ potential for the van der Waals interactions. In the non-polarizable model, the carbon atom C is neutral and only has LJ interactions with the water, whereas in the polarizable model, each carbon is decorated with two flexible negatively charged dummy atoms that mimic the \u03c0-orbitals and are perpendicular to the plane of C atoms. The dummy atoms are connected by harmonic bonds and angle restraints (Supplementary Table <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">17<\/a> for parameters). A similar simple model to include the metal polarization, which consists of a LJ potential and a harmonically coupled core\u2013shell charge pair for every atom has been recently developed and proved to reproduce the classical image potential of adsorbed ions as well as surface, bulk and aqueous interfacial properties in agreement with experiments<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 44\" title=\"Geada, I. L., Ramezani-Dakhel, H., Jamil, T., Sulpizi, M. &amp; Heinz, H. Insight into induced charges at metal surfaces and biointerfaces using a polarizable Lennard-Jones potential. Nat. Commun. 9, 716 (2018).\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#ref-CR44\" id=\"ref-link-section-d80690512e2607\" rel=\"nofollow noopener\" target=\"_blank\">44<\/a>. Here, two layers of virtual atoms sandwich the carbon layer in between to form a single graphene sheet or SWCNTs (Extended Data Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#Fig12\" rel=\"nofollow noopener\" target=\"_blank\">8a,b<\/a>). The dummy atoms mimic the \u03c0-electron cloud and add polarizability to the carbon atoms<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 43\" title=\"Dharmawardhana, C. C. et al. Reliable computational design of biological-inorganic materials to the large nanometer scale using interface-FF. Mol. Simul. 43, 1394&#x2013;1405 (2017).\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#ref-CR43\" id=\"ref-link-section-d80690512e2615\" rel=\"nofollow noopener\" target=\"_blank\">43<\/a>. The polarizable carbon carries a partial positive charge (+2\u03b4) and the two dummy atoms carry a negative half charge (\u2212\u03b4), so the overall C atom is neutral. However, there is an additional dipole contribution to each C atom. Hence, polarizable graphene\/SWCNTs also have a columbic interaction with the surrounding water.<\/p>\n<p>The Green Kubo (GK) friction coefficient has been calculated to estimate the strength of the interfacial interaction of water with the graphitic surfaces<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 65\" title=\"Falk, K., Sedlmeier, F., Joly, L., Netz, R. R. &amp; Bocquet, L. Molecular origin of fast water transport in carbon nanotube membranes: superlubricity versus curvature dependent friction. Nano Lett. 10, 4067&#x2013;4073 (2010).\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#ref-CR65\" id=\"ref-link-section-d80690512e2628\" rel=\"nofollow noopener\" target=\"_blank\">65<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 66\" title=\"Thiemann, F. L., Schran, C., Rowe, P., M&#xFC;ller, E. A. &amp; Michaelides, A. Water flow in single-wall nanotubes: oxygen makes it slip, hydrogen makes it stick. ACS Nano 16, 10775&#x2013;10782 (2022).\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#ref-CR66\" id=\"ref-link-section-d80690512e2631\" rel=\"nofollow noopener\" target=\"_blank\">66<\/a> (Extended Data Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#Fig14\" rel=\"nofollow noopener\" target=\"_blank\">10e<\/a>), according to the formula<\/p>\n<p>$${\\lambda }_{\\mathrm{GK}}=\\frac{1}{{An}{K}_{{\\rm{B}}}T}{\\int }_{0}^{\\infty }\\langle \\mathrm{FL}({\\rm{t}})\\mathrm{FL}(0)\\rangle $$<\/p>\n<p>\n                    (5)\n                <\/p>\n<p>where A is the area of the surface, n is the number of dimensions (n\u2009=\u20092 for graphene and 1 for CNT), KB is the Boltzmann constant, T is the temperature and FL is the lateral force acting on the surface for graphene or the force along the axial direction for the CNT. The integral of the autocorrelation of FL is used to compute the GK friction coefficient as per equation (<a data-track=\"click\" data-track-label=\"link\" data-track-action=\"equation anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#Equ5\" rel=\"nofollow noopener\" target=\"_blank\">5<\/a>). The friction coefficient for non-polarizable graphene and (6,5)-SWCNT was computed with the CVFF parameters, and for polarizable graphene and (6,5)-SWCNTs was computed with the IFF-CVFF polarizable model<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 44\" title=\"Geada, I. L., Ramezani-Dakhel, H., Jamil, T., Sulpizi, M. &amp; Heinz, H. Insight into induced charges at metal surfaces and biointerfaces using a polarizable Lennard-Jones potential. Nat. Commun. 9, 716 (2018).\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#ref-CR44\" id=\"ref-link-section-d80690512e2743\" rel=\"nofollow noopener\" target=\"_blank\">44<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 64\" title=\"Heinz, H., Lin, T. -J., Mishra, R. K. &amp; Emami, F. S. Thermodynamically consistent force fields for the assembly of inorganic, organic, and biological nanostructures: the INTERFACE force field. Langmuir 29, 1754&#x2013;1765 (2013).\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#ref-CR64\" id=\"ref-link-section-d80690512e2746\" rel=\"nofollow noopener\" target=\"_blank\">64<\/a>.<\/p>\n<p>We observe a higher friction coefficient of around 6.5\u2009\u00d7\u2009104\u2009N\u2009s\u2009m\u22123 at the graphene interface with the polarizable model as compared with 2\u2009\u00d7\u2009104\u2009N\u2009s\u2009m\u22123 for non-polarizable graphene, which is also the typical value observed with other force fields<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 4\" title=\"Bui, A. T., Thiemann, F. L., Michaelides, A. &amp; Cox, S. J. Classical quantum friction at water&#x2013;carbon interfaces. Nano Lett. 23, 580&#x2013;587 (2023).\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#ref-CR4\" id=\"ref-link-section-d80690512e2764\" rel=\"nofollow noopener\" target=\"_blank\">4<\/a>. Notably, the value for the friction coefficient obtained with our polarizable model is in very good agreement with the ab initio estimates of 4.5\u2009\u00d7\u2009104\u2009N\u2009s\u2009m\u22123 (ref.\u2009<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 66\" title=\"Thiemann, F. L., Schran, C., Rowe, P., M&#xFC;ller, E. A. &amp; Michaelides, A. Water flow in single-wall nanotubes: oxygen makes it slip, hydrogen makes it stick. ACS Nano 16, 10775&#x2013;10782 (2022).\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#ref-CR66\" id=\"ref-link-section-d80690512e2773\" rel=\"nofollow noopener\" target=\"_blank\">66<\/a>) and 9.5\u2009\u00d7\u2009104\u2009N\u2009s\u2009m\u22123 (ref.\u2009<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 67\" title=\"Tocci, G., Joly, L. &amp; Michaelides, A. Friction of water on graphene and hexagonal boron nitride from Ab Initio methods: very different slippage despite very similar interface structures. Nano Lett. 14, 6872&#x2013;6877 (2014).\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#ref-CR67\" id=\"ref-link-section-d80690512e2783\" rel=\"nofollow noopener\" target=\"_blank\">67<\/a>) obtained with revPBE-D3 and optB88-vdw functional, respectively (Extended Data Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#Fig12\" rel=\"nofollow noopener\" target=\"_blank\">8e<\/a>). We also observed that the friction coefficient increases for water in contact with the external surface of SWCNTs from 6.5\u2009\u00d7\u2009104\u2009N\u2009s\u2009m\u22123 for the non-polarizable model, to 15\u2009\u00d7\u2009104\u2009N\u2009s\u2009m\u22123 for the polarizable model. The result for the polarizable model is in good agreement with ab initio molecular dynamics results from a previous study<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 67\" title=\"Tocci, G., Joly, L. &amp; Michaelides, A. Friction of water on graphene and hexagonal boron nitride from Ab Initio methods: very different slippage despite very similar interface structures. Nano Lett. 14, 6872&#x2013;6877 (2014).\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#ref-CR67\" id=\"ref-link-section-d80690512e2801\" rel=\"nofollow noopener\" target=\"_blank\">67<\/a>. Hence, the new polarizable model permits reproducing electronic structure level accuracy at the cost of simple classical force field simulations, introducing the interaction of the polarizable electron cloud with the polar solvent. With the new and improved IFF-CVFF polarizable model, we also estimated the diffusion behaviour of (6,5)-SWCNTs. The latest IFF-CVFF polarizable graphite model (Supplementary Table <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">17<\/a>) has been validated with rigour by reproducing bulk properties such as density and bulk modulus, and interfacial properties such as surface energy, hydration energy and water contact angle, which are in excellent agreement with experimental observations and are suitable for model graphitic materials in various applications.<\/p>\n<p>The diffusion constant was computed with a (6,5)-SWCNT of length 4.1\u2009nm placed inside a cubical 3D periodic box of 140,000 water molecules modelled with flexible SPC parameters (CVFF). After pre-equilibration of the simulation box in an isothermal\u2013isobaric (NPT) ensemble, the simulation trajectory was run for another 20\u2009ns with a timestep of 0.5\u2009fs, and a coordinate snapshot was generated every 1\u2009ps. The (6,5)-SWCNT was end-capped with hydrogen atoms and allowed to diffuse inside the box unconstrained with the NPT ensemble at 298\u2009K and 1\u2009atm. Hydrogen parameters are borrowed from the CVFF models. The trajectory was analysed to compute the MSD of the centre of mass of the SWCNT with time. The slope (m) of the MSD compared with time plot was used to evaluate the diffusion constant D\u2009=\u2009m\/6. The diffusion constant was calculated for both non-excited and excited SWCNTs.<\/p>\n<p>The process of exciting the SWCNT, in molecular dynamic simulations with a classical potential, is modelled by introducing an exciton by the addition of an axial dipole along the SWCNT axis, as described in the main text. The charges of 44 virtual\/dummy (pi cloud) atoms are modified by \u00b1\u00a00.005\u00a0e so that the total charge is 0.22\u00a0e (44 virtual sites\u2009\u00d7\u20090.005\u00a0e per virtual site) in the polarizable case, whereas, for the non polarizable SWCNT model, the annular each region is composed of 22 carbon atoms with a charge of \u00b1\u00a00.01\u00a0e each to generate the excited state nanotube (Extended Data Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#Fig13\" rel=\"nofollow noopener\" target=\"_blank\">9<\/a>). This initial choice was motivated by introducing a moderate perturbation to maintain the stability of the simulation system and avoid crashing by overpolarization. Exact \u00b1\u00a01 would correspond to exactly one exciton present always throughout the experiment. However, smaller values are more likely because of lower exciton density (due to the average of excited and non-excited time periods in pulsed as well as CW excitation schemes and the longer SWCNT length in experiments). We also investigated the friction coefficient for dipole-free excitation of the SWCNT (Extended Data Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#Fig14\" rel=\"nofollow noopener\" target=\"_blank\">10<\/a>, Supplementary Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"supplementary material anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#MOESM1\" rel=\"nofollow noopener\" target=\"_blank\">21<\/a>), in which the two outer rings (blue) carry an additional \u22120.005\u00a0e charge on the 44 atoms in each ring, behaving as a delocalized electron. The delocalized hole is modelled using a central ring (red) composed of 44 atoms, each carrying an extra charge of +\u00a00.01\u00a0e. In this charge configuration, the SWCNT dipole moment is negligible compared with the excited configuration shown in Extended Data Fig. <a data-track=\"click\" data-track-label=\"link\" data-track-action=\"figure anchor\" href=\"http:\/\/www.nature.com\/articles\/s41586-026-10632-2#Fig13\" rel=\"nofollow noopener\" target=\"_blank\">9<\/a>, in which two rings describe a delocalized exciton. The polarizable nature of the electron cloud and excitons is analysed using molecular dynamics. The dynamic nature is captured mildly by separate simulations with 1\u2009nm and 2\u2009nm dipoles, then averaging the MSD. The true translational nature of the exciton along the length of the SWCNT is beyond the scope of molecular dynamics runs, as these studies require (1) extremely long SWCNTs that are hundreds of nanometres long and (2) a special implementation of varying charges with time on atoms in standard simulators such as LAMMPS, both of which are beyond the scope of this work.<\/p>\n","protected":false},"excerpt":{"rendered":"Preparation of SWCNTs If not stated otherwise, all chemicals were purchased from Sigma Aldrich (Germany). Unless specifically stated,&hellip;\n","protected":false},"author":3,"featured_media":859445,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_share_on_mastodon":"0"},"categories":[8],"tags":[197635,66619,10046,10047,77404,15104,159,67,132,68],"class_list":["post-859444","post","type-post","status-publish","format-standard","has-post-thumbnail","category-science","tag-carbon-nanotubes-and-fullerenes","tag-excited-states","tag-humanities-and-social-sciences","tag-multidisciplinary","tag-nanoscience-and-technology","tag-optical-spectroscopy","tag-science","tag-united-states","tag-unitedstates","tag-us"],"share_on_mastodon":{"url":"https:\/\/pubeurope.com\/@us\/116730495582018993","error":""},"_links":{"self":[{"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/posts\/859444","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/comments?post=859444"}],"version-history":[{"count":0,"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/posts\/859444\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/media\/859445"}],"wp:attachment":[{"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/media?parent=859444"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/categories?post=859444"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/tags?post=859444"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}