Macroscopic Length Scale of Water Super-Transport in Single Ultralong Carbon Nanotube

Macroscopic Length Scale of Water Super-Transport in Single Ultralong Carbon Nanotube | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Macroscopic Length Scale of Water Super-Transport in Single Ultralong Carbon Nanotube Silei Sun, Boyuan Shen, Jun Gao, Zhenxing Zhu, Fei Wei This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3267193/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The emergent nanofluidics promotes the exploration of the special hydrodynamics of fluid transport in a nano-sized flow domain 1–3 . Water, the most common fluid in the nature and human society, will form the ordered structures 4–7 by reducing the hydrogen bonding and transport ultra-fast in carbon nanotubes 8–16 . However, such behaviors have only been reported in the tubes with nano- or micro-meter lengths far away from what can be considered as the macroscopic scales. Here we establish a mass spectroscopy system to detect the super-transport of water and heavy water in individual ultralong carbon nanotubes with an enhancement ratio ε over 10 6 , two orders of magnitude higher than previous results. It indicates that the physics behind water super-transport is still efficient in a macroscopic length scale, where the effects of entrance/exit losses, surface energies, and temperature on the water super-transport can also be evaluated. Such a long transport system will reduce the contribution of entrance/exit effect to the total pressure drop to approach the intrinsic slippage resistance. This work not only extends the super-transport property of nanofluidics into macroscopic length scale, but also provide new hope to detect the intrinsic ultra-low friction on solid-liquid interface for a lossless mass transport in macroscopic applications. Nanoscience carbon nanotubes macro length water super-transport nanofluidics frictionless Figures Figure 1 Figure 2 Figure 3 Figure 4 Main The development of nanofluidics is accompanied by the exploration of various striking behaviors of fluids and particles confined in nano-scale channels and pores 17–25 , such as the enhanced mass transport, ionic correlations, selective permeability, and nonlinear hydrodynamics. These discoveries enlighten us the wide applications of nanofluidics in the ion detection, drug delivery, flow sensor, desalination, filtration, energy storage and biomimetic systems 26–32 . The water (H 2 O) and carbon nanotube (CNT) system provides an ideal model in nanofluidics for the mechanism and applications of enhanced mass transport 8–16 due to their well-defined structures and interfaces. However, there is still a leak of macroscopic-length evidence of such nanofluidics to date, which is an important step towards both the basic physics and real applications of super-transport. On the one hand, a longer transport distance will reduce the entrance/exit effect to reflect the intrinsic flow slippage on water-carbon interface. On the other hand, the extended time for transport allows us to measure it by new methods with a more reliable accuracy but lower time resolution, such as the mass spectroscopy (MS) for a quantitative molecular analysis. In the last decade, we developed the synthesis of ultralong CNTs by the chemical vapor deposition (CVD) 33,34 . Such ultralong CNTs maintain consistent chirality and defect-free structures for over half a meter length. Using these samples, we confirmed that many outstanding properties of ideal CNT structures, including the super-strength 35,36 , super-durability 37 and super-lubricity 38 , are still unexpectedly valid at the macroscopic length scales. Now, we are focusing on the super-transport of fluids in ultralong CNTs, which is closely related to the frictionless solid-liquid interfaces. In this work, a MS system is used to precisely measure small quantity changes of molecules passing through a single ultralong CNT. The transport time of water or heavy water (deuteroxide, D 2 O) in CNT can be obtained from the responses of ion current curves to estimate the velocities. A series of velocity data help us investigate the effects of surface energy, entrance/exit losses and interface slippage on the super-transport property of water through the CNT, as well as its temperature independence. In the centimeter-length CNT, we get the lowest friction coefficient λ and the highest enhancement ratio ε with two orders of magnitude of improvements, which can be predicted by the modified model and the previous data in references. The ultralong CNT was synthesized on a Si/SiO 2 substrate (see Materials and Methods) as shown in Supplementary Discussion 1, which can reach a centimeter length and have been proven to be perfectly constructed and defect-free 33–38 (Supplementary Discussion 2). Figure 1 a shows an atomic force microscopic (AFM) image of the single ultralong CNT that we studied in this work. The profile analysis of this AFM image (Fig. 1 b) was used to measure the diameter of this CNT. Consistent with previous studies 33–38 , the CNTs synthesized by this method are mainly double walled, further demonstrated by the transmission electron microscopy results in Supplementary Discussion 3. Electron diffraction analysis and resonant Raman-Rayleigh spectroscopy accurately identified the ultralong CNT indexed by (16,2)@(17,12). It indicates an inner radius of the CNT, R ≈ 0.67 nm, besides a similar outer radius of 0.99 nm to that measured by AFM. Figures 1 c, d are the true-color Rayleigh image and the Raman spectrum of this CNT, showing a consistent chirality and continuous defect-free structure (no visible D band indicating defects can be detected). The length of CNT was controlled by cutting it with a metal probe. Examples of the cutting process are given in Supplementary Discussion 4, where the cutting can also create an open end of CNT for water transport. Then the water transport properties of this CNT at a length of 1.6, 2.2 and 2.4 cm were studied by using a MS system to precisely detect the change of a micro amount of water passing through a single CNT. Figure 1 e shows the schematic set-up of the MS system for measuring water transport. The substrate with a CNT was sealed at the entrance of this MS system making the outside atmosphere and vacuum chamber only connected by the CNT (Supplementary Discussion 5). During the measurements, the D 2 O was used as probe molecules and injected into the chamber by a driving force of 1-atm pressure drop, in order to avoid the interference of H 2 O signals in the air (Supplementary Discussion 6). With the D 2 O feeding (defined as time zero) in the 1.6-cm CNT (Supplementary Table), Fig. 2 a shows the changing ion currents (corresponding to the quantity of each component detected in chamber) for N 2 (blue line), O 2 (red line) and D 2 O (black line), respectively. After a time interval ( ∆t 1 = 81.8 s, Supplementary Discussion 7), the ion currents for three components changed synchronously. The decreasing N 2 , O 2 and the increasing D 2 O indicate that the D 2 O molecules were squeezed through the CNT by internal-external pressure difference ∆P , and then the N 2 and O 2 molecules in the CNT were discharged, which is defined as the filling process. As a benchmark, the results of the unopened CNT in Supplementary Discussion 8 show no component change after the D 2 O feeding and prove the air tightness of this system. Then, at t = 850 s, the D 2 O was switched to H 2 O. After another time interval ( ∆t 2 = 13.8 s), only the ion current for D 2 O decreased. This reflects that the H 2 O passed through the CNT and extruded the D 2 O from the CNT, which is defined as the transport process. Meanwhile, there was no gas (air) leak during this water switching and transport process, indicating that the water keeps filling the CNT. It should be noticed that there is an obvious difference between Δt 1 and Δt 2 when the CNTs are encapsulated by air and water, that is, the filling and transport processes. In Fig. 2 b, we summarized the MS responses of the filling and transport processes in this CNT at different lengths, and the change of the time delay in MS response with the CNT length is shown in Fig. 2 c. Then, two sets of data points were fitted together with the origin, respectively. It can be seen that linear fitting is more reasonable compared with quadratic fitting, showing two different velocities of 2.24×10 − 4 and 1.43×10 − 3 m/s (calculated by the slopes of linear fitting). These results can be explained by the comparison among the Hagen-Poiseuille (HP) model, slippage HP (SHP) model and modified SHP (MSHP) model (considering both slippage and entrance/exit effect). Based on the HP model and SHP model, the velocities can be predicted as: where ΔP is the driving pressure of water transport, R and L are the radius and length of tube, and L s can also be expressed as a ratio of viscosity µ and friction coefficient λ ( L s = µ / λ ) considering the slippage on water-carbon interface. It is obvious that the Δt is proportional to the quadratic power of L in these two models. However, in the MSHP model that involves the losses at entrance/exit 39 , the total pressure drop can be divided into two parts (Supplementary Discussion 9). One is subject to the slippage and deduced from Eq. 2 . Another is contributed by the entrance/exit effect and estimated as πµCv/R , where the coefficient C represents the losses at entrance/exit 39,40 . Therefore, the relation between Δt and L in the MSHP model should be expressed as: where the first and second terms are linear and quadratic terms of L , respectively. According to the linear fitting in Fig. 2 c, it is worth noting that even in such an ultralong CNT, the entrance/exit effect on the velocity of water passing through CNT (expressed by the linear term in Eq. 3 ) is still dominant, which explains why the velocities of filling and transport processes will not change significantly as the L changes. Meanwhile, there is at least an order of magnitude difference between the velocities in the filling and transport processes. An essential difference between these two processes is that both the solid-liquid and solid-vapor interfaces exist in the filling process, while only a solid-liquid interface exist in the transport process. Therefore, the slowing filling process is attributed to the change in driving pressure ΔP caused by surface energies, which can be expressed as: where P 0 is the atmosphere (1.01×10 5 Pa), γ SV and γ SL are the surface energies for solid-vapor and solid-liquid interfaces, respectively, and γ SV - γ SL = σcosθ in the Young-Laplace equation (σ is the water surface tension and θ is the contact angle for water on CNT surface). In the transport process, the second term in Eq. 4 does not exist. Because ΔP is directly proportional to v in all models, we can estimate the contribution of surface energies (the second term in Eq. 4 ) according to two velocities measured in the filling and transport processes: $$\frac{{v}_{filling}}{{v}_{transport}}=\frac{{P}_{0}+\frac{2\left({\gamma }_{SV}-{\gamma }_{SL}\right)}{R}}{{P}_{0}}$$ 5 , where the calculated γ SV - γ SL =-2.85×10 − 5 J/m 2 , corresponding to a nearly vertical contact angle of 90.02°. This slightly hydrophobic CNT inner surface agrees with the molecular mechanism of water super-transport in narrow-diameter CNTs, since it has been widely reported that the water molecules can be linked in single file with dynamic hydrogen bonding during the filling process 41–43 . These results not only explain the slowdown of the filling process, but also help us to reveal the nano-scale capillarity with surface energies, while previous methods cannot provide this part of information. Furthermore, we studied whether such water super-transport in CNT was affected by temperature. After the room-temperature (R.T.) measurement of the 1.6-cm sample, we further tried to carry out the water transport experiments at different temperatures (40 and 60°C) for this sample. Although water evaporation and tightness decrease in this system prevent it from operating stably at higher temperatures, the temperature range from R.T. to 60 ℃ is enough to judge the temperature effect and meets most application conditions. Figure 3 a shows the MS responses of the filling and transport processes in this CNT at R.T., 40 and 60°C, respectively. We found that in such a temperature range, the time intervals of water filling and transport did not change dramatically. Converting them into the data of average velocities in Fig. 3 b, we noticed that in both the filling and transport processes, there is only a difference of average velocity up to 7.5%, which should be ignored under such a huge enhancement of super-transport. On the one hand, these results confirmed the repeatability of our experiments, and on the other hand, they also revealed the temperature independence of water transport in a certain range. The strong confinement of a 1.34-nm-diameter CNT on water molecules greatly limits their thermal motion within the temperature range as we studied in this work 7 so that the ordered structures and corresponding high transport velocity will be maintained. To describe the enhancement of water transport in this CNT, we review the models in Eqs. 1 – 3 . In following discussions, we only used the data for the transport process that exclude the pressure change caused by the surface energies. The water viscosity µ will not change by orders of magnitude and has little effect on the enhancement ratio ε (Supplementary Discussion 10). Therefore, ΔP and µ can be fixed as 1.01×10 5 Pa and 0.9×10 − 3 Pa·s, respectively. Putting the measured R and L of our CNT into Eq. 1 , the theoretical v HP is only 3.19×10 − 10 m/s. Therefore, the enhancement ratio ε = v/v HP is up to 4.48×10 6 in this work, nearly two orders of magnitude higher than the previous results 8–16 . Here we summarized the enhancement ratios ε versus the aspect ratios L/R of CNTs in these results (Fig. 4 a). Based on the MSHP model in Eq. 3 , the ε = v/v HP can be expressed as: $$\frac{1}{\epsilon }=\frac{1}{1+\frac{4\mu }{R\lambda }}+\frac{C\pi }{8}\bullet \left(\frac{R}{L}\right)$$ 6 , where two terms represent the contributions of slippage (first) and entrance/exit effect (second), respectively. The first term is independent of CNT length, while the second term reduces with CNT length, which means that the slippage will gradually dominate the ε in longer CNTs. As we have discussed that the second term is much larger than the first one even in our ultralong CNT (according to the linear fitting in Fig. 2 c), the ε should show a positive correlation with L/R as shown in Fig. 4 a. After ignoring the first term, a linear fitting gives a C value of 3.82 indicating the limited values of ε by the entrance/exit effect (the dash line in Fig. 4 a). The deviation of data points from linearity is mainly due to the difference in C value, which is caused by the different entrance/exit structures in these CNTs. Then, the dot lines show the slippage limit to the ε calculated by the first term, where R was fixed as 0.67 nm, and λ was set as 0.1, 1 and 10 Pa·s·m − 1 , respectively. These results provide a unified description of the historical data and the measurements in this work and explain why we can get the highest ε with two orders of magnitude of improvements in the CNT with a macroscopic length. Since increasing the CNT length will reduce the second term in Eq. 6 to make the slippage play a more important role in water transport, using longer CNTs for measurements may allow us to approach the slippage limit of ε and find the real λ (an intrinsic property of water-carbon interface) that gradually excludes the entrance/exit effect. For example, in the previous calculations of apparent λ values (using the SHP model in Eq. 2 ), the entrance/exit losses were usually not considered, as we summarized in Fig. 4 b. Putting our measured velocity into Eq. 2 , the slip length L s is only 7.56×10 − 4 m, corresponding to an ultra-low λ of 1.19 Pa·s·m − 1 (the lowest value reported). Overall, the apparent λ value shows a downward trend with the increase of CNT length L , and a linear relation between the logarithms of λ and L (log 10 λ and log 10 L ) was found in Fig. 4 b, indicating an inversely proportional relation between λ and L . The λ is only related to the water-carbon interface and cannot change by over six orders of magnitude. Thus, the decrease in λ with L is due to the weakening of entrance/exit effect relative to the slippage in ultralong tubes, as we have discussed on the ε in Fig. 4 a. If we attribute the resistance entirely to the entrance/exit losses and combine Eqs. 2 and 3 (see details in Supplementary Discussion 9), the apparent λ can be simplified as λ ≈ πµC /(2 L ), which is consistent with the dash line in Fig. 4 b. It is worth noting that our estimation of λ value (1.19 Pa·s·m − 1 ) is only an upper limit of its real value, because we have noticed that the entrance/exit effect is also dominant that still cannot be ignored in such centimeter-long CNTs. The measurement in a longer CNT, although it brings more difficulties in the synthesis and fabrication of samples, can further magnify the contribution of slippage to the overall losses to obtain a lower λ approaching the intrinsic water-carbon interface property, which is important for us to truly reveal the confined water structures, the friction between water and carbon, and the principles of nanofluidics. Meanwhile, these results also confirm that some quantum behaviors, such as the super-transport phenomenon in nanotube, may still exist when a certain dimension of the system reaches the macroscopic length scale. It motivates our further studies on other quantum behaviors using even longer CNTs, since the stronger quantum effects may be detected in such macroscopic materials when it is possible to ignore the interference of aperiodic local structures, such as terminations and defects. Materials and Methods Synthesis of ultralong CNTs The ultralong CNTs were prepared on a Si/SiO 2 substrate in a tube reactor using the CVD method. FeCl 3 ·nH 2 O powder (0.5 g) was preloaded on the substrate as the precursor for Fe particle catalysts. The precursor was reduced under the flow of Ar/H 2 (V Ar :V H2 =1:2; F total =100–200 sccm) to form Fe particles after heating up to 910°C. Then, the temperature was slowly increased to 1020°C and maintained for 20 min under H 2 /Ar protection. The CH 4 as carbon source was supplied with H 2 and H 2 O (V CH4 :V H2 =1:2.2; F total =75 sccm, with 0.5% H 2 O). After 120 min, the CNTs propagated to the enough lengths and were cooled down to be carefully kept for further transport measurements. Characterizations of ultralong CNTs The TEM images were obtained using a transmission electron microscope (JEM 2010, JEOL) operated at 120 kV. The SEM images were obtained using a high-resolution scanning electron microscope (JSM-7401, JEOL) at 1 kV. The Raman spectroscopy (HR 800, Horiba) was used to characterize and confirm the CNT structure. Combining it with the analysis in previous works 33–38 , the structural integrity of ultralong CNTs can be confirmed. The AFM image was obtained by the Dimension Icon (Bruker). These results provide an important basis for our research of water super-transport. Measurements of water transport The measurement set-up was established by assembling the transport system with the detection system (MS system). In the transport system, the substrate with single CNT was carefully attached to an O-shape ring by the sealant for high vacuum applications (Torr Seal, Agilent) and fixed in a specific flange. The air tightness of the total set-up was tested by the uncut samples as shown in Supplementary Fig. 13. The detection system consists of a vacuum chamber, a gas analyzer (GSD 320 Gas Analysis System, Pfeiffer Vacuum) and a pump. The gas analyzer provides the real-time ion currents of the target gas components with a minimum time interval of about 1.5 s between each detection. Declarations Data availability: The data supporting the findings of this study are available from the corresponding authors upon request. Competing interests: The authors declare no competing interests. Author contributions: B.S., Z.Z. and F.W. conceived the project. 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Supplementary Files supportinginformation.pdf Supporting Information for Macroscopic Length Scale of Water Super-Transport in Single Ultralong Carbon Nanotube Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3267193","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":226628912,"identity":"79588d9e-2556-47f5-abaf-1245ce44dedf","order_by":0,"name":"Silei Sun","email":"","orcid":"","institution":"Tsinghua University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Silei","middleName":"","lastName":"Sun","suffix":""},{"id":226628913,"identity":"74dbd4f9-36c7-4727-a14d-ff66750ecf01","order_by":1,"name":"Boyuan Shen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0klEQVRIiWNgGAWjYBACAwYGNiBlA8QJDBA2kVrSSNdymAQt5hLpzx583HHe3uB48gOGD2WHGfhnN+DXYjkjx9xw5pnbiRvOPDNgnHHuMIPEnQMEHHYjh02at+12gsGNBANm3rbDDAYSCYS0pD+T/tt2zh7I+MD8lzgtCWbSjG0HGDfcyDFgZiRGi2XPGzPJ3rbkxJln3hQc7DmXziNxg4AWc/b0ZxI/2+zs+Y6nb3zwo8xajn8GAS0MAkgKDgAxDwH1QMB/gLCaUTAKRsEoGOEAAJSORtFuaLl3AAAAAElFTkSuQmCC","orcid":"","institution":"Soochow University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Boyuan","middleName":"","lastName":"Shen","suffix":""},{"id":226628914,"identity":"fa073655-48f1-4fc2-a357-9d659e9a39b0","order_by":2,"name":"Jun Gao","email":"","orcid":"","institution":"Tsinghua University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Jun","middleName":"","lastName":"Gao","suffix":""},{"id":226628915,"identity":"4a8e60bb-6157-4b34-952e-53cf3b33b736","order_by":3,"name":"Zhenxing Zhu","email":"data:image/png;base64,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","orcid":"https://orcid.org/0000-0001-8060-0775","institution":"Tsinghua University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Zhenxing","middleName":"","lastName":"Zhu","suffix":""},{"id":226628916,"identity":"96adbb6a-a6cc-47d7-9d29-41f7732b59f0","order_by":4,"name":"Fei Wei","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA60lEQVRIiWNgGAWjYDAC5gMMEgwMNkAGGIFAAgEtbAkgLWkSJGs5LAG2kSgtBscYGG/8qDhfJ9/Oe/h1YZsdAz97jgHDzx14tTBb9py5LWFwmC/NemZbMoNkzxsDxt4zuLWY3e//Js3YBtTCzGNmzNvGzGBwI8eAmbENj5ZjDGzSjP/OScg3g7XUM9gTp6XhgATDYR7jx7xthxkMJAhosQf75Viy5IbDPGbMPOeO80iceVZwsBePFsk2UIjV2PHL958x/sxTVi3H35688cFPPFqQARsocnhArAPEaQDG5AdiVY6CUTAKRsHIAgAdYEZbZFKJRQAAAABJRU5ErkJggg==","orcid":"","institution":"Tsinghua University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Fei","middleName":"","lastName":"Wei","suffix":""}],"badges":[],"createdAt":"2023-08-16 01:21:40","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":true,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false,"coiExplicitlySet":false},"doi":"10.21203/rs.3.rs-3267193/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3267193/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":41793402,"identity":"60889cc8-e786-4705-9973-2363024d7705","added_by":"auto","created_at":"2023-08-18 23:59:54","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":128933,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSingle ultralong CNT for water transport measurements. a,b,\u003c/strong\u003e AFM image (\u003cstrong\u003ea\u003c/strong\u003e) and the corresponding profile analysis (\u003cstrong\u003eb\u003c/strong\u003e) to measure the outer diameter of an ultralong CNT. \u003cstrong\u003ec,d,\u003c/strong\u003e True-color Rayleigh image (\u003cstrong\u003ec\u003c/strong\u003e) and Raman spectrum (\u003cstrong\u003ed\u003c/strong\u003e) of this CNT. Scale bar, 10 mm. \u003cstrong\u003ee,\u003c/strong\u003e Schematic set-up of the water transport measurement.\u003c/p\u003e","description":"","filename":"Figure1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3267193/v1/540c09f0ab022d0f03f39f7e.jpg"},{"id":41793172,"identity":"22124b0b-a026-412f-b7a6-63836d01e58c","added_by":"auto","created_at":"2023-08-18 23:51:54","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":109500,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eMeasurement of the transport time of water in ultralong CNT. a\u003c/strong\u003e, Changes of N\u003csub\u003e2\u003c/sub\u003e (blue line), O\u003csub\u003e2\u003c/sub\u003e (red line) and D\u003csub\u003e2\u003c/sub\u003eO (black line) quantity shown as the ion currents detected by gas analyzer. The processes after the D\u003csub\u003e2\u003c/sub\u003eO and H\u003csub\u003e2\u003c/sub\u003eO feeding (measured as \u003cem\u003eΔt\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e and \u003cem\u003eΔt\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e) are defined as the filling and transport processes, respectively. \u003cstrong\u003eb,c,\u003c/strong\u003e Measuring the time intervals \u003cem\u003eΔt\u003c/em\u003e of water passing through the same CNT at different lengths during the filling and transport processes, respectively. The \u003cem\u003eΔt\u003c/em\u003e in \u003cstrong\u003ec\u003c/strong\u003e were obtained from the ion current curves in \u003cstrong\u003eb\u003c/strong\u003e (solid lines for 1.6 cm, dash lines for 2.2 cm, dot lines for 2.4 cm) and were used to calculate two velocities during the filling and transport processes using the near linear fitting (dash lines in \u003cstrong\u003ec\u003c/strong\u003e).\u003c/p\u003e","description":"","filename":"Figure2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3267193/v1/5c692ddfcef108efb53d875d.jpg"},{"id":41793174,"identity":"2c4ddf10-104f-4af9-b754-e5f01f34dd39","added_by":"auto","created_at":"2023-08-18 23:51:54","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":58555,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTemperature independence of the water transport in ultralong CNT. a\u003c/strong\u003e, Ion current curves to measure the transport time at different temperatures (solid lines for R.T., dash lines for 40 °C, dot lines for 60 °C). \u003cstrong\u003eb,\u003c/strong\u003e Calculated velocities during the filling and transport processes at different temperatures using the data in \u003cstrong\u003ea\u003c/strong\u003e.\u003c/p\u003e","description":"","filename":"Figure3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3267193/v1/724324edfb22a001271ba578.jpg"},{"id":41793403,"identity":"dba9aa32-0072-4501-89dd-1697d41b3b63","added_by":"auto","created_at":"2023-08-18 23:59:54","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":77453,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSummary of the enhancement of the water transport in CNTs. a, \u003c/strong\u003eEnhancement ratio \u003cem\u003eε \u003c/em\u003eof the water transport in CNTs. The dash line and dot lines show the limits of \u003cem\u003eε \u003c/em\u003eby the entrance/exit losses and the slippage, respectively. \u003cstrong\u003eb, \u003c/strong\u003eApparent friction coefficient \u003cem\u003eλ\u003c/em\u003e of the water-carbon interfaces. The dash line shows the prediction in the MSHP model when the total losses are dominated by those at the entrance/exit completely. The data of the previous studies were obtained from the references [8-16].\u003c/p\u003e","description":"","filename":"Figure4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3267193/v1/096c03f8ec431f70574441c7.jpg"},{"id":41793404,"identity":"bf186fca-10f1-4a3f-83ea-0379c80d214b","added_by":"auto","created_at":"2023-08-18 23:59:59","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":601009,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3267193/v1/3eca1c2b-5c18-4b84-96a4-e764ca562353.pdf"},{"id":41793176,"identity":"ef4e99c0-dd50-42bd-96da-59b028c46b53","added_by":"auto","created_at":"2023-08-18 23:51:54","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":1324055,"visible":true,"origin":"","legend":"\u003cp\u003eSupporting Information for\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMacroscopic Length Scale of Water Super-Transport in Single Ultralong Carbon Nanotube\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"supportinginformation.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3267193/v1/9a926e486e08640f307bdfe3.pdf"}],"financialInterests":"","formattedTitle":"\u003cp\u003e\u003cstrong\u003eMacroscopic Length Scale of Water Super-Transport in Single Ultralong Carbon Nanotube\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"Main","content":"\u003cp\u003eThe development of nanofluidics is accompanied by the exploration of various striking behaviors of fluids and particles confined in nano-scale channels and pores\u003csup\u003e17\u0026ndash;25\u003c/sup\u003e, such as the enhanced mass transport, ionic correlations, selective permeability, and nonlinear hydrodynamics. These discoveries enlighten us the wide applications of nanofluidics in the ion detection, drug delivery, flow sensor, desalination, filtration, energy storage and biomimetic systems\u003csup\u003e26\u0026ndash;32\u003c/sup\u003e. The water (H\u003csub\u003e2\u003c/sub\u003eO) and carbon nanotube (CNT) system provides an ideal model in nanofluidics for the mechanism and applications of enhanced mass transport\u003csup\u003e8\u0026ndash;16\u003c/sup\u003e due to their well-defined structures and interfaces. However, there is still a leak of macroscopic-length evidence of such nanofluidics to date, which is an important step towards both the basic physics and real applications of super-transport. On the one hand, a longer transport distance will reduce the entrance/exit effect to reflect the intrinsic flow slippage on water-carbon interface. On the other hand, the extended time for transport allows us to measure it by new methods with a more reliable accuracy but lower time resolution, such as the mass spectroscopy (MS) for a quantitative molecular analysis.\u003c/p\u003e \u003cp\u003eIn the last decade, we developed the synthesis of ultralong CNTs by the chemical vapor deposition (CVD)\u003csup\u003e33,34\u003c/sup\u003e. Such ultralong CNTs maintain consistent chirality and defect-free structures for over half a meter length. Using these samples, we confirmed that many outstanding properties of ideal CNT structures, including the super-strength\u003csup\u003e35,36\u003c/sup\u003e, super-durability\u003csup\u003e37\u003c/sup\u003e and super-lubricity\u003csup\u003e38\u003c/sup\u003e, are still unexpectedly valid at the macroscopic length scales. Now, we are focusing on the super-transport of fluids in ultralong CNTs, which is closely related to the frictionless solid-liquid interfaces. In this work, a MS system is used to precisely measure small quantity changes of molecules passing through a single ultralong CNT. The transport time of water or heavy water (deuteroxide, D\u003csub\u003e2\u003c/sub\u003eO) in CNT can be obtained from the responses of ion current curves to estimate the velocities. A series of velocity data help us investigate the effects of surface energy, entrance/exit losses and interface slippage on the super-transport property of water through the CNT, as well as its temperature independence. In the centimeter-length CNT, we get the lowest friction coefficient \u003cem\u003eλ\u003c/em\u003e and the highest enhancement ratio \u003cem\u003eε\u003c/em\u003e with two orders of magnitude of improvements, which can be predicted by the modified model and the previous data in references.\u003c/p\u003e \u003cp\u003eThe ultralong CNT was synthesized on a Si/SiO\u003csub\u003e2\u003c/sub\u003e substrate (see Materials and Methods) as shown in Supplementary Discussion 1, which can reach a centimeter length and have been proven to be perfectly constructed and defect-free\u003csup\u003e33\u0026ndash;38\u003c/sup\u003e (Supplementary Discussion 2). Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea shows an atomic force microscopic (AFM) image of the single ultralong CNT that we studied in this work. The profile analysis of this AFM image (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb) was used to measure the diameter of this CNT. Consistent with previous studies\u003csup\u003e33\u0026ndash;38\u003c/sup\u003e, the CNTs synthesized by this method are mainly double walled, further demonstrated by the transmission electron microscopy results in Supplementary Discussion 3. Electron diffraction analysis and resonant Raman-Rayleigh spectroscopy accurately identified the ultralong CNT indexed by (16,2)@(17,12). It indicates an inner radius of the CNT, \u003cem\u003eR\u003c/em\u003e\u0026thinsp;\u0026asymp;\u0026thinsp;0.67 nm, besides a similar outer radius of 0.99 nm to that measured by AFM. Figures\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec, d are the true-color Rayleigh image and the Raman spectrum of this CNT, showing a consistent chirality and continuous defect-free structure (no visible D band indicating defects can be detected). The length of CNT was controlled by cutting it with a metal probe. Examples of the cutting process are given in Supplementary Discussion 4, where the cutting can also create an open end of CNT for water transport. Then the water transport properties of this CNT at a length of 1.6, 2.2 and 2.4 cm were studied by using a MS system to precisely detect the change of a micro amount of water passing through a single CNT.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ee shows the schematic set-up of the MS system for measuring water transport. The substrate with a CNT was sealed at the entrance of this MS system making the outside atmosphere and vacuum chamber only connected by the CNT (Supplementary Discussion 5). During the measurements, the D\u003csub\u003e2\u003c/sub\u003eO was used as probe molecules and injected into the chamber by a driving force of 1-atm pressure drop, in order to avoid the interference of H\u003csub\u003e2\u003c/sub\u003eO signals in the air (Supplementary Discussion 6). With the D\u003csub\u003e2\u003c/sub\u003eO feeding (defined as time zero) in the 1.6-cm CNT (Supplementary Table), Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea shows the changing ion currents (corresponding to the quantity of each component detected in chamber) for N\u003csub\u003e2\u003c/sub\u003e (blue line), O\u003csub\u003e2\u003c/sub\u003e (red line) and D\u003csub\u003e2\u003c/sub\u003eO (black line), respectively. After a time interval (\u003cem\u003e∆t\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;81.8 s, Supplementary Discussion 7), the ion currents for three components changed synchronously. The decreasing N\u003csub\u003e2\u003c/sub\u003e, O\u003csub\u003e2\u003c/sub\u003e and the increasing D\u003csub\u003e2\u003c/sub\u003eO indicate that the D\u003csub\u003e2\u003c/sub\u003eO molecules were squeezed through the CNT by internal-external pressure difference \u003cem\u003e∆P\u003c/em\u003e, and then the N\u003csub\u003e2\u003c/sub\u003e and O\u003csub\u003e2\u003c/sub\u003e molecules in the CNT were discharged, which is defined as the filling process. As a benchmark, the results of the unopened CNT in Supplementary Discussion 8 show no component change after the D\u003csub\u003e2\u003c/sub\u003eO feeding and prove the air tightness of this system. Then, at \u003cem\u003et\u003c/em\u003e\u0026thinsp;=\u0026thinsp;850 s, the D\u003csub\u003e2\u003c/sub\u003eO was switched to H\u003csub\u003e2\u003c/sub\u003eO. After another time interval (\u003cem\u003e∆t\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;13.8 s), only the ion current for D\u003csub\u003e2\u003c/sub\u003eO decreased. This reflects that the H\u003csub\u003e2\u003c/sub\u003eO passed through the CNT and extruded the D\u003csub\u003e2\u003c/sub\u003eO from the CNT, which is defined as the transport process. Meanwhile, there was no gas (air) leak during this water switching and transport process, indicating that the water keeps filling the CNT.\u003c/p\u003e \u003cp\u003eIt should be noticed that there is an obvious difference between \u003cem\u003eΔt\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e and \u003cem\u003eΔt\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e when the CNTs are encapsulated by air and water, that is, the filling and transport processes. In Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb, we summarized the MS responses of the filling and transport processes in this CNT at different lengths, and the change of the time delay in MS response with the CNT length is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec. Then, two sets of data points were fitted together with the origin, respectively. It can be seen that linear fitting is more reasonable compared with quadratic fitting, showing two different velocities of 2.24\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e and 1.43\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e m/s (calculated by the slopes of linear fitting). These results can be explained by the comparison among the Hagen-Poiseuille (HP) model, slippage HP (SHP) model and modified SHP (MSHP) model (considering both slippage and entrance/exit effect). Based on the HP model and SHP model, the velocities can be predicted as:\u003c/p\u003e\u003cp\u003e\u003cimg 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\"\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eΔP\u003c/em\u003e is the driving pressure of water transport, \u003cem\u003eR\u003c/em\u003e and \u003cem\u003eL\u003c/em\u003e are the radius and length of tube, and \u003cem\u003eL\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e can also be expressed as a ratio of viscosity \u003cem\u003e\u0026micro;\u003c/em\u003e and friction coefficient \u003cem\u003eλ\u003c/em\u003e (\u003cem\u003eL\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003e\u0026micro;\u003c/em\u003e/\u003cem\u003eλ\u003c/em\u003e) considering the slippage on water-carbon interface. It is obvious that the \u003cem\u003eΔt\u003c/em\u003e is proportional to the quadratic power of \u003cem\u003eL\u003c/em\u003e in these two models. However, in the MSHP model that involves the losses at entrance/exit\u003csup\u003e39\u003c/sup\u003e, the total pressure drop can be divided into two parts (Supplementary Discussion 9). One is subject to the slippage and deduced from Eq.\u0026nbsp;\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. Another is contributed by the entrance/exit effect and estimated as \u003cem\u003eπ\u0026micro;Cv/R\u003c/em\u003e, where the coefficient \u003cem\u003eC\u003c/em\u003e represents the losses at entrance/exit\u003csup\u003e39,40\u003c/sup\u003e. Therefore, the relation between \u003cem\u003eΔt\u003c/em\u003e and \u003cem\u003eL\u003c/em\u003e in the MSHP model should be expressed as:\u003c/p\u003e\u003cp\u003e\u003cimg 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\"\u003e\u003c/p\u003e \u003cp\u003ewhere the first and second terms are linear and quadratic terms of \u003cem\u003eL\u003c/em\u003e, respectively. According to the linear fitting in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec, it is worth noting that even in such an ultralong CNT, the entrance/exit effect on the velocity of water passing through CNT (expressed by the linear term in Eq.\u0026nbsp;\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) is still dominant, which explains why the velocities of filling and transport processes will not change significantly as the \u003cem\u003eL\u003c/em\u003e changes.\u003c/p\u003e \u003cp\u003eMeanwhile, there is at least an order of magnitude difference between the velocities in the filling and transport processes. An essential difference between these two processes is that both the solid-liquid and solid-vapor interfaces exist in the filling process, while only a solid-liquid interface exist in the transport process. Therefore, the slowing filling process is attributed to the change in driving pressure \u003cem\u003eΔP\u003c/em\u003e caused by surface energies, which can be expressed as:\u003c/p\u003e\u003cp\u003e\u003cimg src=\"data:image/png;base64,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\"\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eP\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e is the atmosphere (1.01\u0026times;10\u003csup\u003e5\u003c/sup\u003e Pa), \u003cem\u003eγ\u003c/em\u003e\u003csub\u003eSV\u003c/sub\u003e and \u003cem\u003eγ\u003c/em\u003e\u003csub\u003eSL\u003c/sub\u003e are the surface energies for solid-vapor and solid-liquid interfaces, respectively, and \u003cem\u003eγ\u003c/em\u003e\u003csub\u003eSV\u003c/sub\u003e-\u003cem\u003eγ\u003c/em\u003e\u003csub\u003eSL\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;σcosθ in the Young-Laplace equation (σ is the water surface tension and θ is the contact angle for water on CNT surface). In the transport process, the second term in Eq.\u0026nbsp;\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e does not exist. Because \u003cem\u003eΔP\u003c/em\u003e is directly proportional to \u003cem\u003ev\u003c/em\u003e in all models, we can estimate the contribution of surface energies (the second term in Eq.\u0026nbsp;\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) according to two velocities measured in the filling and transport processes:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\frac{{v}_{filling}}{{v}_{transport}}=\\frac{{P}_{0}+\\frac{2\\left({\\gamma }_{SV}-{\\gamma }_{SL}\\right)}{R}}{{P}_{0}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e,\u003c/p\u003e \u003cp\u003ewhere the calculated \u003cem\u003eγ\u003c/em\u003e\u003csub\u003eSV\u003c/sub\u003e-\u003cem\u003eγ\u003c/em\u003e\u003csub\u003eSL\u003c/sub\u003e=-2.85\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;5\u003c/sup\u003e J/m\u003csup\u003e2\u003c/sup\u003e, corresponding to a nearly vertical contact angle of 90.02\u0026deg;. This slightly hydrophobic CNT inner surface agrees with the molecular mechanism of water super-transport in narrow-diameter CNTs, since it has been widely reported that the water molecules can be linked in single file with dynamic hydrogen bonding during the filling process\u003csup\u003e41\u0026ndash;43\u003c/sup\u003e. These results not only explain the slowdown of the filling process, but also help us to reveal the nano-scale capillarity with surface energies, while previous methods cannot provide this part of information.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFurthermore, we studied whether such water super-transport in CNT was affected by temperature. After the room-temperature (R.T.) measurement of the 1.6-cm sample, we further tried to carry out the water transport experiments at different temperatures (40 and 60\u0026deg;C) for this sample. Although water evaporation and tightness decrease in this system prevent it from operating stably at higher temperatures, the temperature range from R.T. to 60 ℃ is enough to judge the temperature effect and meets most application conditions. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea shows the MS responses of the filling and transport processes in this CNT at R.T., 40 and 60\u0026deg;C, respectively. We found that in such a temperature range, the time intervals of water filling and transport did not change dramatically. Converting them into the data of average velocities in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb, we noticed that in both the filling and transport processes, there is only a difference of average velocity up to 7.5%, which should be ignored under such a huge enhancement of super-transport. On the one hand, these results confirmed the repeatability of our experiments, and on the other hand, they also revealed the temperature independence of water transport in a certain range. The strong confinement of a 1.34-nm-diameter CNT on water molecules greatly limits their thermal motion within the temperature range as we studied in this work\u003csup\u003e7\u003c/sup\u003e so that the ordered structures and corresponding high transport velocity will be maintained.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo describe the enhancement of water transport in this CNT, we review the models in Eqs.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. In following discussions, we only used the data for the transport process that exclude the pressure change caused by the surface energies. The water viscosity \u003cem\u003e\u0026micro;\u003c/em\u003e will not change by orders of magnitude and has little effect on the enhancement ratio \u003cem\u003eε\u003c/em\u003e (Supplementary Discussion 10). Therefore, \u003cem\u003eΔP\u003c/em\u003e and \u003cem\u003e\u0026micro;\u003c/em\u003e can be fixed as 1.01\u0026times;10\u003csup\u003e5\u003c/sup\u003e Pa and 0.9\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e Pa\u0026middot;s, respectively. Putting the measured \u003cem\u003eR\u003c/em\u003e and \u003cem\u003eL\u003c/em\u003e of our CNT into Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, the theoretical \u003cem\u003ev\u003c/em\u003e\u003csub\u003eHP\u003c/sub\u003e is only 3.19\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;10\u003c/sup\u003e m/s. Therefore, the enhancement ratio \u003cem\u003eε\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003ev/v\u003c/em\u003e\u003csub\u003eHP\u003c/sub\u003e is up to 4.48\u0026times;10\u003csup\u003e6\u003c/sup\u003e in this work, nearly two orders of magnitude higher than the previous results\u003csup\u003e8\u0026ndash;16\u003c/sup\u003e. Here we summarized the enhancement ratios \u003cem\u003eε\u003c/em\u003e versus the aspect ratios \u003cem\u003eL/R\u003c/em\u003e of CNTs in these results (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea). Based on the MSHP model in Eq.\u0026nbsp;\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, the \u003cem\u003eε\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003ev/v\u003c/em\u003e\u003csub\u003eHP\u003c/sub\u003e can be expressed as:\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\frac{1}{\\epsilon }=\\frac{1}{1+\\frac{4\\mu }{R\\lambda }}+\\frac{C\\pi }{8}\\bullet \\left(\\frac{R}{L}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e,\u003c/p\u003e \u003cp\u003ewhere two terms represent the contributions of slippage (first) and entrance/exit effect (second), respectively. The first term is independent of CNT length, while the second term reduces with CNT length, which means that the slippage will gradually dominate the \u003cem\u003eε\u003c/em\u003e in longer CNTs. As we have discussed that the second term is much larger than the first one even in our ultralong CNT (according to the linear fitting in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec), the \u003cem\u003eε\u003c/em\u003e should show a positive correlation with \u003cem\u003eL/R\u003c/em\u003e as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea. After ignoring the first term, a linear fitting gives a \u003cem\u003eC\u003c/em\u003e value of 3.82 indicating the limited values of \u003cem\u003eε\u003c/em\u003e by the entrance/exit effect (the dash line in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea). The deviation of data points from linearity is mainly due to the difference in \u003cem\u003eC\u003c/em\u003e value, which is caused by the different entrance/exit structures in these CNTs. Then, the dot lines show the slippage limit to the \u003cem\u003eε\u003c/em\u003e calculated by the first term, where \u003cem\u003eR\u003c/em\u003e was fixed as 0.67 nm, and \u003cem\u003eλ\u003c/em\u003e was set as 0.1, 1 and 10 Pa\u0026middot;s\u0026middot;m\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, respectively. These results provide a unified description of the historical data and the measurements in this work and explain why we can get the highest \u003cem\u003eε\u003c/em\u003e with two orders of magnitude of improvements in the CNT with a macroscopic length. Since increasing the CNT length will reduce the second term in Eq.\u0026nbsp;\u003cspan refid=\"Equ6\" class=\"InternalRef\"\u003e6\u003c/span\u003e to make the slippage play a more important role in water transport, using longer CNTs for measurements may allow us to approach the slippage limit of \u003cem\u003eε\u003c/em\u003e and find the real \u003cem\u003eλ\u003c/em\u003e (an intrinsic property of water-carbon interface) that gradually excludes the entrance/exit effect.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFor example, in the previous calculations of apparent \u003cem\u003eλ\u003c/em\u003e values (using the SHP model in Eq.\u0026nbsp;\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e), the entrance/exit losses were usually not considered, as we summarized in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb. Putting our measured velocity into Eq.\u0026nbsp;\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, the slip length \u003cem\u003eL\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e is only 7.56\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e m, corresponding to an ultra-low \u003cem\u003eλ\u003c/em\u003e of 1.19 Pa\u0026middot;s\u0026middot;m\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e (the lowest value reported). Overall, the apparent \u003cem\u003eλ\u003c/em\u003e value shows a downward trend with the increase of CNT length \u003cem\u003eL\u003c/em\u003e, and a linear relation between the logarithms of \u003cem\u003eλ\u003c/em\u003e and \u003cem\u003eL\u003c/em\u003e (log\u003csub\u003e10\u003c/sub\u003e\u003cem\u003eλ\u003c/em\u003e and log\u003csub\u003e10\u003c/sub\u003e\u003cem\u003eL\u003c/em\u003e) was found in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb, indicating an inversely proportional relation between \u003cem\u003eλ\u003c/em\u003e and \u003cem\u003eL\u003c/em\u003e. The \u003cem\u003eλ\u003c/em\u003e is only related to the water-carbon interface and cannot change by over six orders of magnitude. Thus, the decrease in \u003cem\u003eλ\u003c/em\u003e with \u003cem\u003eL\u003c/em\u003e is due to the weakening of entrance/exit effect relative to the slippage in ultralong tubes, as we have discussed on the \u003cem\u003eε\u003c/em\u003e in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea. If we attribute the resistance entirely to the entrance/exit losses and combine Eqs.\u0026nbsp;\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and \u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e (see details in Supplementary Discussion 9), the apparent \u003cem\u003eλ\u003c/em\u003e can be simplified as \u003cem\u003eλ\u0026thinsp;\u0026asymp;\u0026thinsp;π\u0026micro;C\u003c/em\u003e/(2\u003cem\u003eL\u003c/em\u003e), which is consistent with the dash line in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb.\u003c/p\u003e \u003cp\u003eIt is worth noting that our estimation of \u003cem\u003eλ\u003c/em\u003e value (1.19 Pa\u0026middot;s\u0026middot;m\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) is only an upper limit of its real value, because we have noticed that the entrance/exit effect is also dominant that still cannot be ignored in such centimeter-long CNTs. The measurement in a longer CNT, although it brings more difficulties in the synthesis and fabrication of samples, can further magnify the contribution of slippage to the overall losses to obtain a lower \u003cem\u003eλ\u003c/em\u003e approaching the intrinsic water-carbon interface property, which is important for us to truly reveal the confined water structures, the friction between water and carbon, and the principles of nanofluidics. Meanwhile, these results also confirm that some quantum behaviors, such as the super-transport phenomenon in nanotube, may still exist when a certain dimension of the system reaches the macroscopic length scale. It motivates our further studies on other quantum behaviors using even longer CNTs, since the stronger quantum effects may be detected in such macroscopic materials when it is possible to ignore the interference of aperiodic local structures, such as terminations and defects.\u003c/p\u003e"},{"header":"Materials and Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eSynthesis of ultralong CNTs\u003c/h2\u003e \u003cp\u003eThe ultralong CNTs were prepared on a Si/SiO\u003csub\u003e2\u003c/sub\u003e substrate in a tube reactor using the CVD method. FeCl\u003csub\u003e3\u003c/sub\u003e\u0026middot;nH\u003csub\u003e2\u003c/sub\u003eO powder (0.5 g) was preloaded on the substrate as the precursor for Fe particle catalysts. The precursor was reduced under the flow of Ar/H\u003csub\u003e2\u003c/sub\u003e (V\u003csub\u003eAr\u003c/sub\u003e:V\u003csub\u003eH2\u003c/sub\u003e =1:2; F\u003csub\u003etotal\u003c/sub\u003e=100\u0026ndash;200 sccm) to form Fe particles after heating up to 910\u0026deg;C. Then, the temperature was slowly increased to 1020\u0026deg;C and maintained for 20 min under H\u003csub\u003e2\u003c/sub\u003e/Ar protection. The CH\u003csub\u003e4\u003c/sub\u003e as carbon source was supplied with H\u003csub\u003e2\u003c/sub\u003e and H\u003csub\u003e2\u003c/sub\u003eO (V\u003csub\u003eCH4\u003c/sub\u003e:V\u003csub\u003eH2\u003c/sub\u003e=1:2.2; F\u003csub\u003etotal\u003c/sub\u003e=75 sccm, with 0.5% H\u003csub\u003e2\u003c/sub\u003eO). After 120 min, the CNTs propagated to the enough lengths and were cooled down to be carefully kept for further transport measurements.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003eCharacterizations of ultralong CNTs\u003c/h2\u003e \u003cp\u003eThe TEM images were obtained using a transmission electron microscope (JEM 2010, JEOL) operated at 120 kV. The SEM images were obtained using a high-resolution scanning electron microscope (JSM-7401, JEOL) at 1 kV. The Raman spectroscopy (HR 800, Horiba) was used to characterize and confirm the CNT structure. Combining it with the analysis in previous works\u003csup\u003e33\u0026ndash;38\u003c/sup\u003e, the structural integrity of ultralong CNTs can be confirmed. The AFM image was obtained by the Dimension Icon (Bruker). These results provide an important basis for our research of water super-transport.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003eMeasurements of water transport\u003c/h2\u003e \u003cp\u003eThe measurement set-up was established by assembling the transport system with the detection system (MS system). In the transport system, the substrate with single CNT was carefully attached to an O-shape ring by the sealant for high vacuum applications (Torr Seal, Agilent) and fixed in a specific flange. The air tightness of the total set-up was tested by the uncut samples as shown in Supplementary Fig.\u0026nbsp;13. The detection system consists of a vacuum chamber, a gas analyzer (GSD 320 Gas Analysis System, Pfeiffer Vacuum) and a pump. The gas analyzer provides the real-time ion currents of the target gas components with a minimum time interval of about 1.5 s between each detection.\u003c/p\u003e"},{"header":"Declarations","content":" \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003eData availability:\u003c/h2\u003e \u003cp\u003eThe data supporting the findings of this study are available from the corresponding authors upon request.\u003c/p\u003e \u003c/div\u003e\u003cp\u003e \u003ch2\u003eCompeting interests:\u003c/h2\u003e \u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor contributions:\u003c/h2\u003e \u003cp\u003eB.S., Z.Z. and F.W. conceived the project. S.S., Z.Z. and B.S. performed the experiments and data analysis. J.G. and Z.Z helped in the synthesis and characterizations of the samples. B.S. and Z.Z. wrote the manuscript with the contributions from all authors.\u003c/p\u003e\u003ch2\u003eAcknowledgments:\u003c/h2\u003e \u003cp\u003eThis work was supported by the Ministry of Science and Technology of China (2022YFA1203301) and the National Natural Science Foundation of China (grant 22108155 and 22275133). B.S. thanks the support from Suzhou Key Laboratory of Functional Nano \u0026amp; Soft Materials, Collaborative Innovation Center of Suzhou Nano Science \u0026amp; Technology, the 111 Project, Joint International Research Laboratory of Carbon-Based Functional Materials and Devices.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eBocquet, L. \u0026amp; Charlaix, E. Nanofluidics, from bulk to interfaces. Chem. Soc. Rev. 39, 1073\u0026ndash;1095 (2010).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBocquet, L. Nanofluidics coming of age. Nat. 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U.S.A.\u003c/em\u003e 119, e2211348119 (2022).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Tsinghua University","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"carbon nanotubes, macro length, water super-transport, nanofluidics, frictionless","lastPublishedDoi":"10.21203/rs.3.rs-3267193/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3267193/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe emergent nanofluidics promotes the exploration of the special hydrodynamics of fluid transport in a nano-sized flow domain\u003csup\u003e1\u0026ndash;3\u003c/sup\u003e. Water, the most common fluid in the nature and human society, will form the ordered structures\u003csup\u003e4\u0026ndash;7\u003c/sup\u003e by reducing the hydrogen bonding and transport ultra-fast in carbon nanotubes\u003csup\u003e8\u0026ndash;16\u003c/sup\u003e. However, such behaviors have only been reported in the tubes with nano- or micro-meter lengths far away from what can be considered as the macroscopic scales. Here we establish a mass spectroscopy system to detect the super-transport of water and heavy water in individual ultralong carbon nanotubes with an enhancement ratio \u003cem\u003eε\u003c/em\u003e over 10\u003csup\u003e6\u003c/sup\u003e, two orders of magnitude higher than previous results. It indicates that the physics behind water super-transport is still efficient in a macroscopic length scale, where the effects of entrance/exit losses, surface energies, and temperature on the water super-transport can also be evaluated. Such a long transport system will reduce the contribution of entrance/exit effect to the total pressure drop to approach the intrinsic slippage resistance. This work not only extends the super-transport property of nanofluidics into macroscopic length scale, but also provide new hope to detect the intrinsic ultra-low friction on solid-liquid interface for a lossless mass transport in macroscopic applications.\u003c/p\u003e","manuscriptTitle":"Macroscopic Length Scale of Water Super-Transport in Single Ultralong Carbon Nanotube","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2023-08-18 23:51:49","doi":"10.21203/rs.3.rs-3267193/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"8b9a03a8-da98-4246-99ea-9e90eaabeb37","owner":[],"postedDate":"August 18th, 2023","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":24066060,"name":"Nanoscience"}],"tags":[],"updatedAt":"2023-08-18T23:51:49+00:00","versionOfRecord":[],"versionCreatedAt":"2023-08-18 23:51:49","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3267193","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3267193","identity":"rs-3267193","version":["v1"]},"buildId":"FbvkV6FR0MCFSLy54lSbu","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}