**Fabrication and characterization of the single CNT nanofluidic device.** We fabricate the single CNT nanofluidic device using a microfabrication process. The single CNT is confined between the SU-8 photoresist and the silicon which is covered with 300 nm-thick oxidized layer as shown in Fig. 1. Two independent microchannels for reservoirs of ionic solution are introduced, with the open-ended single CNT connecting them, forming the main part of the nanofluidic device. Polydimethylsiloxane (PDMS) is further introduced on top of the SU-8 to compose sealed microchannels. Four holes are punched on the PDMS layer as liquid inlets and outlets while the outlets are also used to insert Ag/AgCl electrodes (see Methods section for more details). Figure 1d shows the schematic of the fabricated single CNT nanofluidic device where fluid transport across the single CNT with a length of 100 µm. With both compartments filled with aqueous ionic solution using syringes, upon driven either by chemical potential or voltage drop, ion current across the reservoirs can be monitored using patch clamp amplifier (Molecular Devices, Axopatch 200B, calibrated by the original model cell).

The structure of the single CNT is characterized using a combining approach of atomic force microscope (AFM), Raman spectroscope and transmission electron microscope (TEM). The morphology of CNT (Fig. 2a) measured by AFM (Oxford MFP-3D infinity) clearly shows that the tube is straightly aligned on the silicon wafer. The outer diameter is about 6 nm (Fig. 2c) with a uniform distribution along the tube axis. TEM image (FEI Tecnai G2 20) shows the double-walled structure of the tube unambiguously (Fig. 2c), with an outer diameter of 5.3 nm and inner diameter of 4.6 nm. The resonance Raman data of individual carbon nanotube is collected using a confocal imaging microscope combined with micro-Raman spectroscopy at an excitation wavelength of 532 nm (the excitation spot size was about 1 µm in diameter, Horiba Scientific). The disappearance of the D peak and the shape of the G peak (Fig. 2d) show that the CNT is free of defects and belongs to a semiconductor tube (34, 35).

For nanofluidic device, it is critical to assess whether ionic transport occurs through the individual carbon nanotube. To address this question, we perform comparative experiments with two types of control devices, where the two reservoirs formed by SU-8 are either separated without any tube connecting them or connected with close-ended CNT. Using the same protocol for the I-V measurements with the open-ended CNT nanofluidic device, all the control devices display negligible conductance (∼1pS) being independent of the salt concentration (see SI for more details). Such small current is attributed to the intrinsic electrical conduction through the substrate and other materials constituting the microfluidic devices. These comparative experiments demonstrate the good sealing performance of the fabricated nanofluidic devices, suggest that the electrolyte ions can only flow through the single open-ended DWCNT.

**Ionic transport under salinity gradients.** With the fabricated single DWCNT nanofluidic device, we measure the osmotic energy conversion using different concentrations in the two reservoirs in the range of 1–1,000 mM for LiCl, NaCl, and KCl solutions respectively. A variety of concentration ratios, *C*max/*C*min, are used while keeping the maximum concentration *C*max at 1 M. At each concentration ratio, we extract the channel conductance, *G*, by measuring the *I* - Δ*V* curve which gives \(G=I/\varDelta V\). Following similar approach for the measurements of hBN nanotube (31, 32) and activated carbon nanoconduits (31, 32), the obtained current is corrected for the contribution that results from the Nernst potential, which originates from the difference in salt concentrations at the two electrodes, to get the osmotic current *I*osm (see SI for more details).

For the osmotic current (Fig. 3a), we observe a clear dependence of the osmotic current on the type of cation where \({I}_{osm}^{KCl}>{I}_{osm}^{NaCl}>{I}_{osm}^{LiCl}\). As *I*osm depends on the geometry of the experimental setup, it is not an intrinsic property of the channel. Therefore, we use the corresponding transport coefficient, *K*osm, to characterize the transport properties of the nanofluidic device, where \({I}_{osm}=\frac{\pi {R}^{2}}{L}{K}_{osm}\varDelta {log}\left[{C}_{s}\right]\), \(\varDelta {log}\left[{C}_{s}\right]={log}\left({C}_{max}/{C}_{min}\right)\), \(R=2.3\) nm and \(L=100\) µm are the radius and length of the tube respectively. For KCl, NaCl and LiCl solutions, the estimated values of \({K}_{osm}\) (Fig. 3b) show negligible dependence on the concentration ratio \({C}_{max}/{C}_{min}\), as *K*osm decreases only by 27.0% (K+), 21.4% (Na+), 11.2%(Li+) as \({C}_{max}/{C}_{min}\) increases from 1 to 1000. These lead to the corresponding \({K}_{osm}\) being \(11.9\pm 1.4\) A/m, \(9.4\pm 0.8\) A/m, and \(6.8\pm 0.8\) A/m respectively. It is worth noting that for KCl flowing through DWCNT, \({K}_{osm}\) is two orders higher than that of pristine graphene, and similar to that of activated carbon nanoconduits (32), showing extremely high mobility.

Such a high mobility of the particles brings hope for high power generation. We calculate the maximum power generated for single tube as \(P={I}_{osm}^{2}/4G\). The values of *P* extracted from the diffusio-osmosis experiments are displayed in Fig. 3c, where the power provided by each tube is on the order of 0.1 pW. To get a proper sense of the performance of the single DWCNT in terms of the osmotic power, we use a usual figure of merit that corresponds to the generated electrical power per unit surface of the tube. The corresponding single-pore power density (the osmotic power per unit cross-sectional area) \({P}^{*}=P/\pi {R}^{2}\) as a function of the salinity gradient is shown in Fig. 3d. Noticeably, *P** for individual DWCNT can reach up to 30 kW m−2, 20 times larger than that of pristine graphene (1.5 kW m− 2) (32), and 1–2 orders larger than other nanopores or nanotubes (31, 36). We notice that MoS2 nanopore shows a much higher *P** (106 W m− 2, 30 times larger than present) (37) and the recently reported value of activated carbon channels (100 kW m− 2) (32) is 3 times larger than ours. However, since the power density is inversely proportional to the length of the tube/channel, given that the length of MoS2 nanopore is 0.6 nm, and for activated carbon nanoconduits is 3–10 µm, the power density for DWCNT with a length of 100 µm measured here has the highest value for the power density per unit length, which could be of more practical relevance.

The ultrahigh power density and mobility of DWCNT for KCl, NaCl, and LiCl solutions are attractive, as they show great promise in extracting energy from saline water. However, the origin of such extraordinary property is intriguing, especially considering that pristine graphene channel, its allotropic substance, showing power density and mobility of 2 orders smaller. Since the power density is proportional to \({K}_{osm}^{2}\), our understanding begins with examining the factors for *K*osm.

In an attempt to rationalize our experimental findings, we analyze our results on the basis of the recently proposed theory (33) for diffusion-osmosis process as studied here: the osmotic mobility can be expressed as

$${K}_{osm}=-\frac{2{\varSigma }_{m}}{d}\frac{{k}_{B}T}{2\pi \eta {\mathcal{l}}_{B}}\left(1-\frac{{{sinh}}^{-1}\chi }{\chi }+\left(1-{\alpha }_{ion}\right)\frac{{b}_{eff}}{{\lambda }_{D}}\left(\sqrt{1+{\chi }^{2}}-1\right)\right)$$

1

where \({\varSigma }_{m}\) is the charge density due to mobile physisorbed OH− on surface, *k*B*T* is the thermal energy, a product of the Boltzmann constant and temperature, \(\eta\) is the fluid viscosity, \({\mathcal{l}}_{B}={e}^{2}/4\pi \epsilon {k}_{B}T\) is the Bjerrum length, *e* is the elementary charge, \(\epsilon\) is the dielectric permittivity, \({\lambda }_{D}={\left(8\pi {\mathcal{l}}_{B}{C}_{s}\right)}^{-1/2}\) is the Debye length, *C**s* is the concentration given as the number of ions per cubic meter, \(\chi =2\pi {\lambda }_{D}{\mathcal{l}}_{B}\frac{\left|{\varSigma }_{m}\right|}{e}={sinh}\left[\frac{-e{\varPsi }_{0}}{2{k}_{B}T}\right]\), \({b}_{eff}={b}_{0}/\left(1+{\beta }_{s}\frac{\left|{\varSigma }_{m}\right|}{e}{\mathcal{l}}_{B}^{2}\right)\) is the effective slip length, *b*0 is the slip length of the water in the absence of ions and \({\beta }_{s}=\frac{{b}_{0}}{\eta }\frac{{\lambda }_{s}{\lambda }_{w}}{{\lambda }_{s}+{\lambda }_{w}}\), where \({\lambda }_{w}\) and \({\lambda }_{s}\) are the friction coefficients of the ion with wall and water. The parameters \({\alpha }_{ion}=\frac{{\lambda }_{s}}{{\lambda }_{s}+{\lambda }_{w}}\) (\(\in \left[\text{0,1}\right]\)) is a dimensionless parameter.

From Eq. (1), it is evident that the key parameters governing the osmotic mobility are the surface charge \({\varSigma }_{m}\) and effective slip length *b*eff. For \({\varSigma }_{m}\), it was recently found in experiments with carbon nanotubes (13), graphite (38) and *ab initio* simulations (39) that the electrification of carbon nanotubes and pristine graphite are due to the physisorption of OH− groups on the carbon surface, retaining a large mobility (33). We use the values of surface charge density for pristine graphene (32), as the pH values of KCl solution are the same. For NaCl and LiCl solutions, due to the similar electronegativity of the cations and the same type of physisorbed ions on the carbon surface, it is reasonable to assume that the surface charge would remain. This consideration suggests that the different quantitative response between the different salts has to be sought elsewhere.

For the slip length *b*eff, there has been a few experimental measurements regarding the slip of water and solutions through carbon nanotube. For example, Secchi et al. reported the fabrication of nanofluidic devices comprising an individual CNT inserted into the tip of the glass capillary (1). The calculated slip length shows a negative dependence on the diameter of CNT (30–100 nm) and is 17–300 nm. Qin et al. fabricated an array of three parallel FETs along the length of a millimeter-long single-walled CNT to measure the water velocity during spontaneous internal wetting (40). The calculated slip length also negatively correlates with the diameter of CNT (0.81–1.59 nm) and falls in the range of 8–53 nm. With CNT membranes, Holt et al. estimated the slip length to be 140–1400 nm for CNTs with diameters of 1.3–2.0 nm (41), and Whitby et al. found a slip length of 35 nm for CNTs with diameter of 44 nm (42). However, for CNT with diameter in the intermediate range as studied here, i.e., from 2 to 10 nm, there is no relevant reports. To this end, we perform our own measurement to estimate the slip length.

**Ionic transport under voltage drop.** For the slip length, when the surface charge is given, theoretical study shows that it can be extrapolated by measuring the ionic transport under electric potential (33). Therefore, with the same single DWCNT nanofluidic device, we explore the ionic transport under a voltage drop. The applied voltage drop is from − 1 V to + 1 V, and the concentration of the solution is increased sequentially from 10− 3 M to 1 M. For all the 3 kinds of solutions, as shown in Fig. 4a-4c, a linear dependence of the ionic current on the voltage drop is observed, indicating a constant conductance of the single DWCNT with the applied voltage drop. The corresponding single-tube conductance (Fig. 4d) shows a strong positive correlation with the salt concentration *C*s. The single-tube conductivity, \(K=\frac{L}{\pi {R}^{2}}\frac{I}{\varDelta V}\), for all the three kinds of solution are of the same order at a given *C*s and varies from tens of S/m to few hundreds of S/m as *C*s increases from 0.001 M to 1M, with a crossover for their relative strength at a concentration around 0.02 M (Fig. 4e). At such concentration, the Debye length \({\lambda }_{D}\) is about 2.2 nm, close to the inner radius of CNT (*R*=2.3 nm). Because the Debye length is the characteristic thickness of interfacial electrical double layer, such phenomenon indicates the different effects of interfacial and bulk electrolyte solution. For \({C}_{s}<0.02\) M, \({\lambda }_{D}>R\), the flow inside CNT is dominated by interfacial electrical double layer, including the adsorbed Helmholtz layer and diffusion layer, where the ions are not hydrated. The radiuses of bare Li+, Na+, K+ ions are 0.068 nm, 0.095 nm, and 0.133 nm, respectively (43). Due to the smallest size of Li+, the number of adsorbed Li+ is the highest, corresponding to the highest conductivity. In contrast, when \({C}_{s}>0.02\) M, \({\lambda }_{D}<R\), the bulk solution can significantly affect the flow inside CNT. In bulk solution, the ions are fully hydrated, and the radiuses of hydrated Li+, Na+, K+ ions are 0.38 nm, 0.36 nm, and 0.33 nm, respectively (43). In the confined space of CNT, the hydrated K+ ions have smallest size, corresponding to the lowest friction coefficient and the highest conductivity.

For most of the ion concentration range of KCl, conductance values followed a power law dependence with the exponent very close to the value of 1/3. This apparent 1/3 power law scaling is qualitatively different from the linear conductance dependence expected for ideal channels. Our data also do not follow the *C*s1/2 scaling reported by Nuckolls and colleagues for longer CNT channels with 1.5 nm diameter (44) or the *C*s2/3 scaling measured by Noy and colleagues with 1.5 nm-diameter carbon nanotube porins (12), but is consistent with the *C*s1/3 scaling measured by Bocquet and colleagues in larger 7 − 70 nm diameter CNTs (13). For NaCl and LiCl, the exponential behavior is not the same as for KCl, presenting NaCl of 0.22 and LiCl of 0.11. Interestingly, the change of the exponential index follows the relative size of the cations.

It is worth noting that with DWCNT, for KCl, the conductivity is about 2 orders higher than that of pristine graphene and similar to that in activated carbon channels (32). Taking the bulk conductance \({K}_{b}=2\mu {e}^{2}{C}_{s}\) as reference where \(\mu =\frac{1}{2}\left({\mu }_{ca}+{\mu }_{C{l}^{-}}\right)\) and \({\mu }_{ca}\) is the mobility of K+, Na+ and Li+, all the solutions show significant enhancement in conductivity (Fig. 4f). For KCl, the enhancement \(K/{K}_{b}\) is about 2500 with *C*s = 0.001 M, and 20 at higher concentration (\({C}_{s}=1\) M). For NaCl and LiCl solutions, the enhancement coefficients show similar negative dependence on concentration, with the largest enhancement (~ 5000 times) measured for LiCl at a concentration of 0.001 M. Such high conductance and electro-osmotic mobility for all the three kinds of solution in DWCNT suggest considerable surface transport.

**Slip length estimation.** Based on the transport framework for nanofluidics (32, 33), for single DWCNT where the chemisorbed surface charge can be neglected45, the surface conductivity \({K}_{surf}=K-{K}_{b}\) can be expressed as

$${K}_{surf}=\frac{2}{R}\left[\mu e\left|{\varSigma }_{m}\right|\left(1+\delta \right)\frac{\chi }{\sqrt{1+{\chi }^{2}}+1}+\frac{{b}_{0}}{\eta \left(1+{\beta }_{s}\frac{\left|{\varSigma }_{m}\right|}{e}{\mathcal{l}}_{B}^{2}\right)}{\left(1-{\alpha }_{ion}\right)}^{2}{\varSigma }_{m}^{2}+e{\mu }_{m}\left|{\varSigma }_{m}\right|\right]$$

2

where \({\mu }_{m}\) is the surface mobility of the physisorbed hydroxide ions (45). A summary of the modelling parameters and are provided in SI. Here we consider \({\alpha }_{ion}=0.8\) which is the same as previous literatures for KCl solution sliding on pristine graphene surface (10), thus only \({b}_{0}\) and \({\beta }_{s}\) remain unknown in Eq. (2) for KCl solution. Through the measurement of *K*surf for a series salt concentration, \({b}_{0}=21\mu m\) and \({\beta }_{s}=105\) are obtained with the least square fit. With \({b}_{0}\) obtained from KCl, \(({\alpha }_{ion},{\beta }_{s})\) are fitted as (0.815, 107) and (0.833, 109) for NaCl and LiCl respectively. The details of the fitting procedure are provided in SI. Like the enhancement in conductivity, the slip length *b*eff shows a strong negative correlation with salt concentration for all the solutions (Fig. 5a) which can be expressed as \({b}_{eff}=\frac{{b}_{0}}{\left(1+{\beta }_{s}\frac{\left|{\varSigma }_{m}\right|}{e}{\mathcal{l}}_{B}^{2}\right)}\). Surprisingly, *b*eff can be up to a few micrometers at small concentration (0.001 M), and about 100 nm at large concentration (1 M). This is 2–3 orders larger than that estimated for pristine graphene and activated carbon surface. As a result, unlike the electro-osmosis measurement on pristine graphene, here we found that the slippage contribution dominates the conductivity (second term in Eq. (2)), being 1–2 orders larger than the rest, including the contribution from mobile charge (32). Using the scaling law for the slippage, the enhancement of conductivity as a function of concentration is predicted with Eq. (2), showing reasonable agreements with experimental measurements, especially in the high concentration regime (Fig. 4f). In the low concentration regime where *C*s < 0.01 M, corresponding to the transition to a Debye layer comparable to the size of the CNT, the theoretical prediction cannot fully recover the experimental results pointing out to a possible limitation of the theoretical framework for electrokinetic transport under extreme confinement with very large slippage. Consequently, the better agreement at high *C*s is understandable as it is in this range where \({\lambda }_{D}<R\) and the bulk contributions starts to play an important role.

With these values of slip length, we can now try to understand the giant power density measured during the diffusio-osmosis process, where a water flux is generated in the vicinity of a charged interface in the presence of a solute concentration gradient. In principle, the ionic diffusio-osmotic current is generated because the water flux drags the Debye layer. Using Eq. (1) with the obtained slip length, *K*osm is estimated to be of a few A/m, in agreement with the experiments (\(11.9\pm 1.4\) A/m, \(9.4\pm 0.8\) A/m, and \(6.8\pm 0.8\) A/m for KCl, NaCl and LiCl respectively). The contribution from slip (third term in Eq. (1) which includes *b*eff) to *K*osm is found to be dominant, two orders larger than the rest. This mechanism shows a distinct difference from that of activated carbon surface, where the high conductivity is attributed to an optimal combination of high surface charge and low friction (32).

The estimated slip length not only provides a fundamental understanding about the giant osmotic energy conversion, but also brings valuable information for the friction of water through CNT, a topic deeply roots in the beginning of carbon-based nanofluidics (27, 41, 47). By merging the existing slip length measured for individual CNT together with present value, a complete overview about the radius-dependent flow slippage in CNT is unfolded (Fig. 5b). Obviously, there exists a sharp increase in slip length at small radius, which can be up to 21 µm. This value is beyond the prediction based on the classical description for fluid-solid interactions (27). In fact, recent studies show that the coupling of charge fluctuations in the liquid to electronic excitations in the solid plays an important role in the radius-dependent slippage (17), which is supported by experiments measured with \(R>10\) nm (13) and \({b}_{0}<300\) nm. The present measurement for a narrow CNT (*R* = 2.3 nm) but of which the radius is still beyond the single profile range could serve as a new reference system for the nature of solid-liquid interaction.