Coupling between ion transport and electronic properties in individual carbon nanotubes

Abstract

Carbon nanomaterials exhibit unique electrokinetic phenomena due to rapid ion transport within the Debye layer, which have been exploited for energy conversion, membrane technology, and liquid lubrication. The electronic properties of solids have been found to influence water permeation and proton transport; however, their effect on ion transport has not been observed. Here, we present an experimental investigation of ion transport in individual double-walled carbon nanotubes (CNTs) of both semiconducting and metallic nature. Systematic measurements show that conductance, streaming current, and osmotic current are larger in semiconducting tubes than in metallic ones. Together with a complete theoretical framework, we found that such behavior is caused by the smaller liquid-solid friction with the same surface charge density for the semiconducting system. As fast ion transport is the key element for efficient energy conversion, in CNTs, the thermoelectric conversion efficiency with ions is two orders of magnitude larger than with electrons, showing the supremacy of ions to recover the waste heat.

Semiconducting CNTs lead the charge, surpassing metallic tubes in ion transport and thermoelectric performance.

INTRODUCTION

Ions inside the Debye layer dominated the electrokinetic phenomena through nanochannels because of the similar characteristic length of the nanochannel and the Debye length. Understanding the friction between the salt solution and the solid wall at nanoscale has a profound impact on energy conversion (1, 2), membrane technology (3, 4), and liquid lubrication (5–7). The classical description of liquid-solid friction is based on the picture of the solid as a static periodic potential, with friction between the solid and liquid resulting from the collisions of the fluid molecules on the surface roughness, as flows induced on the roughness scale dissipate mechanical energy (8). This classical theoretical framework has been constantly challenged by recent developments in measurements of the ion and mass transport in carbon nanomaterials such as carbon nanotubes (CNTs) and graphene nanochannels (9, 10), which leads to a theory of quantum friction originating from the couplings between water fluctuations and the electronic degrees of freedom inside the confining walls (11). Recently, enhanced permeation of water molecules and proton through metallic CNTs (with a diameter of 0.76 nm) compared to semiconducting CNTs (with a diameter smaller than 0.81 nm), both 10 nm in length, was found due to the weaker water-CNT polarization interactions (12). However, the influence of the electronic properties of solid on the ion transport has not been observed.

Investigating the electronic liquid-solid friction to tune ion transport inside the Debye layer requires nanochannels with atomically flat surfaces, to minimize classical dissipation, and with varying electronic properties of solid. CNTs are the perfect candidates, which feature an atomically smooth surface that is either metallic or semiconducting along the axial direction tuned by chirality without changing solid materials (13). Previous studies (14–17) mostly focused on the ion transport through CNT under external driving force; however, the systematic measurements of electrokinetic phenomena with well-controlled electronic properties of CNTs are still lacking. Here, the electrokinetic phenomena across individual double-walled CNT (DWCNT) of both semiconducting and metallic nature with a length of 100 μm and an inner diameter ranging from 2.6 to 5.4 nm are reported. Ultralow friction at the liquid-CNT interface is found based on a comprehensive theoretical framework of ion transporting through slippery surfaces. Ion transport is faster in the semiconducting tubes than in metallic ones, resulting in high efficiency in converting mechanical and chemical energy with semiconducting nanotubes.

RESULTS

Fabrication and characterization of the individual DWCNT nanofluidic device

The individual CNT nanofluidic device was fabricated using a microfabrication process as detailed in our previous work (18). As shown in Fig. 1A, the individual CNT is confined between the silicon and the SU-8 photoresist with polydimethylsiloxane covering the top of the SU-8. Ag/AgCl electrodes are used to impose a voltage forcing and monitor ion current across the individual CNT that connects two reservoirs of the KCl aqueous solution using a patch-clamp amplifier (Molecular Devices, Axopatch 200B; calibrated by the original model cell). CNT is the only channel for fluid transport, proven by negligible conductance, for measurements with two reservoirs that are either separated without a tube connecting them or connected with a close-ended CNT.

Fig. 1. CNT nanofluidic device and measurement setup.

(A) Schematic of individual CNT nanofluidic device. (B) TEM image shows that the single CNT is a double-walled tube with an inner radius of 2.1 nm. (C and D) The Raman spectra of metallic (C) and semiconducting (D) DWCNT. The excitation energy is shown on the left side of each panel. au, arbitrary unit. (E and F) Voltage-induced current for metallic and semiconducting CNT at different concentrations.

The properties of the individual CNT are characterized using transmission electron microscopy (TEM) and Raman spectroscopy. In this study, 10 devices with different radii belonging to the metallic and semiconducting families are fabricated. The TEM image (FEI Tecnai G2 20) shows the double-walled structure of the nanotube unambiguously (Fig. 1B). The inner radius ranging from 1.3 to 2.7 nm and the interlayer distance d of ~0.36 nm are obtained from TEM images of nanotubes (see details in Materials and Methods and see Supplementary Text S2: TEM and SEM characterization). The disappearance of the D peak indicates that the DWCNTs are free of defects. The shape of the G peak in the Raman spectra (Fig. 1, C and D) indicates that the DWCNTs belong to either semiconducting or metallic tube (19, 20). Following the protocol introduced by Levshov et al. (21), the shift of the G⁺ and G⁻ peaks allows us to complete the assignment of G components observed in our resonance Raman spectra to either the inner or outer walls and to assess the metallicity of the inner and outer walls of the DWCNT (see Supplementary Text S3: Raman characterization). Here, a DWCNT is considered as semiconducting only if both walls are semiconducting and as metallic if at least the inner wall is metallic. The Raman characterizations of 10 nanotubes are provided in Supplementary Text S3: Raman characterization.

Ion transport under external forcings

Electrokinetic phenomena and ionic current induced by an external forcing allow us to understand the interfacial properties at nanoscale, since surface ions and slippage dominated ion transport at such scale. First, we applied a voltage drop V between −1 and +1 V, while the concentration C_s of the KCl aqueous solution is increased sequentially from 10⁻³ to 1 M. For all the CNTs investigated, a linear dependence of the ionic current I on the voltage drop is observed, indicating a constant conductance within the ranges of applied voltage drop (see Fig. 1, E and F, and fig. S7). From the experimental results, the ionic current through the semiconducting CNT (29.9 pA with a radius of 1.5 nm at 1 V) for C_s of 1 M is about 1.8 times larger than that of the metallic CNT (17.2 pA with a radius of 1.3 nm at 1 V) with a similar radius. The conductivity measurements are also carried out through two nanochannels using the same individual CNT, to exclude the extrinsic variations between different CNTs and verify the reproducibility of the device fabrication and measurements (see details in Supplementary Text S5: Ion transport under voltage drop). The corresponding conductance $G=I/V$ displays a typical nonlinear correlation with the salt concentration C_s (see fig. S8). Such behavior is well known in nanofluidics and attributed to ions on solid surfaces, as G is dominated by the transport of surface ions at low concentration (22). As shown in Fig. 2 (A and B), the conductivity, $K=\frac{L}{\mathrm{\pi }{R}^2}G$ , can be obtained to eliminate the geometry effect, where R and L (100 μm) are the inner radius and length of the CNTs, respectively. The conductivity K varies from tens to few hundreds siemens per meter as C_s increases from 10⁻³ to 1 M. At low salt concentrations, K nearly saturates to the value of ~10 to 40 S/m for all nanotubes, with C_s of less than 10⁻² M, and then starts to deviate from the saturations and increase rapidly for larger C_s. A direct comparison of K between semiconducting and metallic CNTs is presented in Fig. 2 (C and D) for different C_s and R. For both large and small C_s (1 M and 0.01 M), the K of semiconducting tubes has a systematically upward shift with respect to that of metallic tubes, with R ranging from 1.3 to 2.7 nm.

Fig. 2. Ion transport under voltage and pressure drop through 10 individual DWCNT devices.

(A and B) Ionic conductivity K as a function of concentration for all (A) metallic and (B) semiconducting nanotubes investigated. (C and D) Conductivity as a function of the radius at (C) large and (D) low salt concentration. The dashed lines in [(C) and (D)] are used to guide the eyes. The error bar for ionic conductivity is ~1.3 S/m, which is too small to be shown in the figures. (E and F) Streaming current I_s as a function of pressure drop for all (E) metallic and (F) semiconducting nanotubes investigated. The error bar for I_s is smaller than 0.03 pA, which is too small to be shown in the figures. (G and H) Zeta potential as a function of the radius at (G) large and (H) low salt concentration.

In addition, streaming current I_stream driven by pressure drop was measured (Keithley 6430 with an accuracy of 0.03 pA) for all tubes, and the details of the measurements are provided in Supplementary Text S6: Streaming current driven by pressure drop. We present in Fig. 2 (E and F) the measured streaming current as a function of the external applied pressure. Analogous to voltage-induced current, a larger I_stream for semiconducting tubes compared to metallic ones is obtained. The streaming currents reflect electroosmotic mobility ${\mathrm{\mu }}_{\text{EO}}$ of ions through DWCNT with $I_{\text{stream}}=\frac{\mathrm{\Delta P}\mathrm{\pi }{R}^2}{L}{\mathrm{\mu }}_{\text{EO}}$ , where ΔP is the pressure drop between the two sides of the nanotube. The downstream convection of ions via pressure-driven flow induces a streaming potential, which, for steady incompressible and laminar flow, can be related to the apparent zeta potential ${\mathrm{\zeta }}_{\text{app}}$ via ${\mathrm{\mu }}_{\text{EO}}=-\frac{\mathrm{\epsilon }{\mathrm{\zeta }}_{\text{app}}}{\mathrm{\eta }}$ with ε as the dielectric permittivity and $\mathrm{\eta }$ as the viscosity of liquid. As shown in Fig. 2 (G and H), the zeta potential with a magnitude of tens of volts is plotted versus the radius. Such large ${\mathrm{\zeta }}_{\text{app}}$ was also found in the previous two-dimensional nanochannel (22), ascribed to a relatively large surface charge density and enhanced by the low friction at the liquid-solid interface (23). The apparent zeta potential ${\mathrm{\zeta }}_{\text{app}}$ is the characterization of streaming mobility for ions driven under pressure, rather than the intrinsic zeta potential (ζ). Detailed descriptions of the difference between ${\mathrm{\zeta }}_{\text{app}}$ and $\mathrm{\zeta }$ are provided in Supplementary Text S6: Streaming current driven by pressure drop.

Last, the osmotic current induced by a salinity gradient between the two extremities of the CNT further confirms that ion transport in semiconducting nanotubes is enhanced compared to metallic ones (see Supplementary Text S7: Osmotic current driven by concentration gradient). The systematic enhancement of electrokinetic phenomena through semiconducting CNT compared with metallic ones demonstrates the existence of coupling between ion transport and electronic properties of the solid wall.

Surface charge density and effective slip length

To decouple the influence of surface charge density and friction on the ion transport through the nanochannel, a theoretical framework with fixed surface charge was derived (8) based on nonlinear Poisson-Boltzmann (PB) electrostatics. The application of PB theory is an assumption for high concentration due to the mean-field and point-charge approximation. The examinations of these assumptions are given in Supplementary Text S8: Theoretical analysis of ion transport. Although such assumption may cause a quantitative difference on the results of slip length and surface charge density, it does not diminish the observed differences between metallic and semiconducting CNTs. With the conductivity K measured, an enhancement factor K/K_b, where K_b = 2μeC_s is the bulk conductivity of KCl aqueous solution, spreading from about 6 to 2670, is found for all C_s and R. Such a large enhancement reveals the synergetic role of surface charge and low friction at the liquid-solid interface.

At high concentrations ( $\ge 100\text{mM}$ ), where the thin Debye layer assumption is valid, the surface conductivity K_surf = K − K_b can be expressed as $K_{\text{surf}}=\frac{2}{R}[\mathrm{\mu }e\mid \mathrm{\Sigma }\mid (1+\mathrm{\delta })\times \frac{\mathrm{\chi }}{\sqrt{1+{\mathrm{\chi }}^2}+1}+\frac{b_{\text{eff}}}{\mathrm{\eta }}{\mathrm{\Sigma }}^2]$ , where μ is the mobility of KCl salt ions, e is the elementary charge, $\mathrm{\eta }$ is the viscosity, $\mathrm{\delta }=\frac{1}{2\mathrm{\pi }{l}_{\mathrm{B}}\mathrm{\mu \eta }}$ with the Bjerrum length $l_{\mathrm{B}}=\frac{e^2}{4\mathrm{\pi \epsilon }{k}_{\mathrm{B}}T}$ , and $\mathrm{\chi }=\frac{2\mathrm{\pi }{\mathrm{\lambda }}_{\mathrm{D}}{l}_{\mathrm{B}}\mid \mathrm{\Sigma }\mid }{e}$ where ${\mathrm{\lambda }}_{\mathrm{D}}=\frac{1}{\sqrt{8\mathrm{\pi }{l}_{\mathrm{B}}{C}_{\mathrm{s}}}}$ is the Debye length. The b_eff is the effective slip length for salt solution at the CNT interface, accounting for both water-CNT and ion-CNT interaction, and $\mathrm{\Sigma }$ is the surface charge density. A summary of the modeling quantities is provided in table S3 in Supplementary Text S8: Theoretical analysis of ion transport. The electroosmotic mobility takes the expression ${\mathrm{\mu }}_{\text{EO}}=-\frac{\mathrm{\epsilon }{\mathrm{\psi }}_0}{\mathrm{\eta }}-\frac{b_{\text{eff}}}{\mathrm{\eta }}\mathrm{\Sigma }$ , with ψ₀ as the surface potential (24). By combining the two expressions of surface conductivity and electroosmotic mobility

$$\begin{array}{c}{K}_{\text{surf}}=\frac{2}{R}[\mathrm{\mu }e\mid \mathrm{\Sigma }\mid (1+\mathrm{\delta })\times \frac{\mathrm{\chi }}{\sqrt{1+{\mathrm{\chi }}^2}+1}-({\mathrm{\mu }}_{\text{EO}}+\frac{\mathrm{\epsilon }{\mathrm{\psi }}_0}{\mathrm{\eta }})\times \mathrm{\Sigma }],\\ b_{\text{eff}}=-({\mathrm{\mu }}_{\text{EO}}+\frac{\mathrm{\epsilon }{\mathrm{\psi }}_0}{\mathrm{\eta }})\times \frac{\mathrm{\eta }}{\mathrm{\Sigma }}\end{array}$$ (1)

According to the Grahame equation (25), surface potential ${\mathrm{\psi }}_0=\frac{2k_{\mathrm{B}}T}{e}{\text{sinh}}^{-1}\left(\frac{\mathrm{\Sigma }}{\sqrt{8\mathrm{\epsilon }{k}_{\mathrm{B}}T{C}_{\mathrm{s}}}}\right)$ . For $\mid \mathrm{\Sigma }\mid <$ 0.1 C/m², the linear approximation ${\mathrm{\psi }}_0=\frac{3}{4}\frac{{\mathrm{\lambda }}_{\mathrm{D}}\mathrm{\Sigma }}{\mathrm{\epsilon }}$ is used. The validations of such linear approximation are provided in Supplementary Text S8: Theoretical analysis of ion transport.

At low concentrations ( $\le 10\text{mM}$ ), the thick Debye layer assumption is valid. The surface conductivity $K_{\text{surf}}$ and electroosmotic mobility ${\mathrm{\mu }}_{\text{EO}}$ can be derived (26) as

$$\begin{array}{c}K=\frac{2}{R}\mathrm{\mu }e\sqrt{{\left(C_{\mathrm{s}}R\right)}^2+{\left(\frac{\mathrm{\Sigma }}{e}\right)}^2}+\frac{{\mathrm{\Sigma }}^2}{3\mathrm{\eta }}+\frac{2b_{\text{eff}}{\mathrm{\Sigma }}^2}{R\mathrm{\eta }},\\ b_{\text{eff}}=-\frac{{\mathrm{\mu }}_{\text{EO}}\mathrm{\eta }}{\mathrm{\Sigma }}+\frac{R}{4}\end{array}$$ (2)

Then, the effective slip length b_eff and surface charge density $\mathrm{\Sigma }$ can be calculated using Eqs. 1 and 2 for different salt concentrations from systematic measurements of electrokinetic transport (K_surf and μ_EO) considering the homogeneous dielectric.

For all tubes investigated, b_eff decreases from 2.67 to 0.36 μm, with the radius increasing from 1.3 to 2.7 nm (Fig. 3A). At first analysis, there is no substantial difference of b_eff between the two kinds of system, with C_s ranging from 10 mM to 1 M. The surface charge density $\mathrm{\Sigma }$ , presented in Fig. 3B, ranges from −0.025 to −0.01 C/m² for 1 M and from −0.01 to −0.005 C/m² for 10 mM, in agreement with the surface charge density (from −0.054 to −0.0016 C/m²) for pristine graphene nanochannel (23). Combining experimental conductivity and streaming current, we can now disentangle the role of total liquid-solid friction (b_eff) and surface charge density ( $\mathrm{\Sigma }$ ), and, as a result, the very low liquid-solid friction and moderate surface charge density at the CNT-water interface boost the ion transport in CNT.

Fig. 3. Electrokinetic properties of individual DWCNT.

(A) Effective slip length as a function of CNT radius. Red (black) semiconducting (metallic) CNT measured at C_s = 1 M (solid) and C_s = 10 mM (hollow). (B) Surface charge density as function of CNT radius. An error of ~20 nm for slip length and an error of ~0.0005 C/m² for surface charge are obtained by considering the transfer of error on K_surf (~1.3 S/m) and μ_EO (~1.4 × 10⁻⁷ As² kg⁻¹). (C) Liquid-solid friction coefficient as a function of surface charge density. Solid and dashed lines are theoretical results of Eq. 3 for semiconducting and metallic CNTs, respectively. The parameter $\mathrm{\gamma }$ in Eq. 3 versus Debye length is shown in the inset.

Liquid-solid friction

To show the dependency of the ion transport on the electronic properties of solid, the relation between liquid-solid friction coefficient ${\mathrm{\lambda }}_{\text{eff}}$ and surface charge density $\mathrm{\Sigma }$ for both semiconducting and metallic systems at different concentrations is plotted in Fig. 3C. The ${\mathrm{\lambda }}_{\text{eff}}$ can be calculated as λ_eff = η/b_eff. For all radii investigated, the λ_eff of semiconducting CNT is smaller than that of metallic ones at the same $\mathrm{\Sigma }$ . Although the geometry chirality angle of CNTs can affect flow rates by stretching the classical potential energy landscape of the inner surface, it can be ignored here since substantial shift is obtained with random chirality index of nanotubes, which further demonstrates that the electronic properties of the solid surface play a key role in ion transport.

As shown in Fig. 3C, the ${\mathrm{\lambda }}_{\text{eff}}$ follows a square dependency on $\mid \mathrm{\Sigma }\mid$ for ion transport through both semiconducting and metallic CNTs. Such phenomena recall the theoretical framework according to the Green-Kubo relation proposed by Joly et al. (27, 28), where friction is related to the square of surface charge density by assuming a uniformly distributed surface charge

$${\mathrm{\lambda }}_{\text{eff}}={\mathrm{\lambda }}_0+\mathrm{\gamma }\frac{\mathrm{\eta }{\mathrm{\sigma }}^2{\mathrm{\Sigma }}^2}{4\mathrm{\pi \epsilon }{k}_{\mathrm{B}}T}$$ (3)

where ${\mathrm{\lambda }}_0$ is the friction coefficient when $\mathrm{\Sigma }=0$ , $\mathrm{\eta }$ is the viscosity, σ is the length scale characterizing the roughness of the solid surface, $\mathrm{\epsilon }$ is the permittivity, and $\mathrm{\gamma }$ is the numerical factor. Despite the inherent limitation of this model in describing the response of the complex liquid-CNT interface, it can be applied to our experimental results and rationalize the dependency on the CNT metallicity. Equation 3 is applied to fit the relation between ${\mathrm{\lambda }}_{\text{eff}}$ and $\mathrm{\Sigma }$ with ${\mathrm{\lambda }}_0$ and $\mathrm{\gamma }$ as two parameters. The ${\mathrm{\lambda }}_0$ is below 164 N·s·m⁻³ for all CNTs investigated in this work. As shown in the inset of Fig. 3C, the factor $\mathrm{\gamma }$ for semiconducting CNTs is smaller than that for the metallic system, which indicates that the coupling for ions and electrons inside the metallic tube is stronger. The $\mathrm{\gamma }$ increases with the thickness of the Debye layer, showing that the strength of such coupling also relates to the distribution of ions.

Ionic Seebeck coefficient and waste-heat recovery

The enhancement of ion transport in CNT can be harnessed for efficient conversion of thermal energy and waste heat. Waste heat, a byproduct of industrial processes and power generation, represents a loss of energy that could otherwise be used. Recovering this heat faces challenges such as varying temperatures, high initial costs, and integration difficulties within existing systems (29). Addressing these issues is essential to improve energy efficiency, reduce emissions, and achieve economic benefits. State-of-the-art devices exploit the Seebeck effect to convert a temperature difference in electrical current because the heat causes charge carriers in the materials to diffuse from the hot side to the cold side, creating a potential difference. The Seebeck effect is the foundational principle behind thermoelectric generators, which can convert waste heat into electrical energy. While electrons in solid materials are usually exploited in current applications, we show here that exalted ion transport in CNT can boost the recovery of waste heat using ions as charge carriers. The experimental setup is shown in Fig. 4A, where the ionic current is induced by a temperature difference between the two reservoirs. More details of experimental set and examination are provided in Supplementary Text S10: Thermoelectric current driven by temperature gradient. After correction of the electrodes’ response (see Supplementary Text S10: Thermoelectric current driven by temperature gradient), for both semiconducting and metallic nanotubes, we measured a large ionic current in the order of tens of picoamperes when a temperature difference of 50 K is imposed, as shown in Fig. 4 (B and C). Such current is generated by a difference in the electrochemical potential between the two extremities of the nanotube.

Fig. 4. Ionic thermoelectric conversion through individual DWCNT.

(A) Schematic of the experimental setup to measure thermoelectric current I_T. (B and C) The I_T as a function of temperature drop for all (B) metallic and (C) semiconducting nanotubes is investigated. The error bar of I_T is ~0.7 pA, which is too small to be shown in the figures. (D) Seebeck coefficient obtained from I_T. (E) The ratio of figure of merit between ions (ZT_ion) and electrons (ZT_E).

From the value of the ionic thermoelectric current, we can now obtain the value of Seebeck coefficient $S_{\mathrm{e}}=\frac{I_{\mathrm{T}}}{G_{\text{ion}}\mathrm{\Delta T}}$ . In Fig. 4D, we plot the Seebeck coefficient for all the tubes investigated, showing an ionic Seebeck coefficient in the order of 10 mV/K, three orders of magnitude larger than the electronic Seebeck coefficient measured in individual single-walled CNT (~0.040 mV/K) (30). The efficiency in ionic thermoelectric generators at slippery charged interface has been theoretically and experimentally detailed in (31). Similarly to voltage and pressure-driven transport, ionic thermoelectric current is exalted by the surface conductivity of the mobile charges with the ionic Seebeck coefficient $S_{\mathrm{e}}\propto ({\mathrm{\psi }}_0+\frac{\mathrm{\Sigma }{b}_{\text{eff}}}{\mathrm{\epsilon }})$.

To evaluate the efficiency of ions compared to electrons in recovering waste heat, we calculated the figure of merit $\mathit{ZT}=\frac{S_{\mathrm{e}}^2{K}_{\text{ions}/\text{electrons}}}{{\mathrm{\lambda }}_{\mathrm{T}}}$ with the ionic/electronic conductivity $K_{\text{ions}/\text{electron}}$ and the thermal conductivity λ_T of the nanofluidic device used in this study. Ionic conductivity at 1 M has been obtained from Fig. 2 (A and B), while the electronic conductivity has been measured to be $K_{\text{electrons}}$ of $\approx 1\times {10}^5$ S/m (32). With the same device, the ratio of ZT between ionic and electronic, $\frac{Z{T}_{\text{ion}}}{Z{T}_{\mathrm{E}}}=\frac{{\left(S_{\mathrm{e}}^{\text{ion}}\right)}^2{K}_{\text{ion}}}{{\left(S_{\mathrm{e}}^{\text{electron}}\right)}^2{K}_{\text{electron}}}$ , is plotted in Fig. 4E, showing that the ionic ZT is two orders of magnitude larger than the electronic counterpart. The very low liquid-solid friction coupled to the relatively large surface charge is the key for the efficient conversion, demonstrating the supremacy of ions for waste heat and thermal energy conversion.

DISCUSSION

In conclusion, our experimental investigations of electrokinetic transport in individual DWCNTs demonstrate that the electronic properties of solid can be exploited to fine tune and enhance ion transport. Altogether, our experimental results point out a large effective slippage at interface, leading to a very large ion transport and zeta potential, which depends on the electronic properties in the solid material. Such influence is not observed in the CNT porin system (12), which may be due to the strong entrance effect considering the small diameter and length of the nanotubes in their systems (12).

Our study offers insights into the complex interplay between fluid transport and electronic properties of the confining materials, bridging the gap between soft and hard condensed matter. It paves the way for the field of quantum electrokinetics where active control and manipulation of fluids and ions can be achieved by tuning the quantum properties of the liquid-solid interface. Last, we demonstrate that the very low liquid-solid friction coefficient in DWCNT can be harnessed for efficient conversion of thermal energy, paving the way to the quantum engineered material for waste-heat recovery.

MATERIALS AND METHODS

TEM characterization

TEM characterization was used to determine the number of wall layer and inner diameters of the CNT. The cellulose acetate film, which can be dissoluble in acetone, was used to transfer the CNT from the SiO₂ substrate to the TEM grid. First, acetone liquid was dropped onto the SiO₂ surface to immerse the selected CNT. A cellulose acetate film with thickness of 60 μm was used to cover the CNT before the vaporization of acetone. The film was pressed tightly on the CNT and SiO₂ substrate in a slow manner from one side to the other side to ensure that no air bubble was produced. Then, the film was peeled off the substrate, with CNT pasted on the film. Same options were used to press the film on the TEM grid tightly in acetone liquid. The whole TEM grid with film on it was soaked in 100 ml of acetone for half an hour to wash out the cellulose acetate film before it was taken off the acetone solution slowly and placed horizontally on a clean glass substrate. Next, 50 ml of acetone was spouted on the TEM grid three times to ensure the clearance of cellulose acetate. Last, CNT on TEM grid without residuals was prepared to conduct characterization. More details are provided in see Supplementary Text S2: TEM and SEM characterization.

Raman characterization

The resonance Raman data of individual CNT inner walls are collected using a confocal imaging microscope combined with micro-Raman spectroscopy (Horiba Scientific). We performed detailed Raman measurements across a wide energy range from 2.33 eV (532 nm) to 1.58 eV (785 nm) using a tunable dye laser system (Quantel PMBX0103) pumped by our 532-nm laser. Three measurements are conducted at different locations of every individual CNT to verify consistent properties of the whole CNT. More details are provided in Supplementary Text S3: Raman characterization.

Measurements of streaming current driven by pressure drop

As shown in Fig. 1A, individual CNT connects two reservoirs with two holes on each. Pressure is applied to one reservoir, keeping the pressure of other reservoirs as atmospheric pressure. For the reservoir pressure applied, one hole is connected to a voltage-controlled pressure regulator with the other hole sealed. The pressure regulator is connected to an air compressor via air filters to ensure good quality of air and control the pressure applied. The streaming current I_stream is measured by Ag/AgCl electrodes with zero voltage drop, when the pressure drop is applied. More details are provided in Supplementary Text S6: Streaming current driven by pressure drop.

Supplementary Materials

This PDF file includes:

Supplementary Text

Figs. S1 to S18

Tables S1 to S13

References