Osmotic Transport across Surface Functionalized Carbon Nanotube

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Osmotic Transport across Surface Functionalized Carbon Nanotube Membrane Mahesh Lokesh, Seul Ki Youn, and Hyung Gyu Park Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b01891 • Publication Date (Web): 12 Oct 2018 Downloaded from http://pubs.acs.org on October 12, 2018

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Osmotic Transport across Surface Functionalized Carbon Nanotube Membrane Mahesh Lokesh†‡, Seul Ki Youn†§, Hyung Gyu Park†π*

†Department

of Mechanical and Process Engineering

Eidgenössische Technische Hochschule (ETH) Zürich Tannenstrasse 3, Zurich, CH-8092, Switzerland π

Mechanical Engineering

Pohang University of Science and Technology (POSTECH) 77 Cheongam-ro, Nam-gu, Pohang, Gyeongbuk, Republic of Korea

‡

Current Address: Department of Materials

Eidgenössische Technische Hochschule (ETH) Zürich Vladimir-Prelog-Weg 5, CH-8093, Switzerland

§

Current Address: ABB Semiconductors

Fabrikstrasse 3, Lenzburg, CH-5600, Switzerland

*Corresponding author: [email protected]

ABSTRACT Osmosis plays a central role in many chemical separation processes. Among various biological and artificial channels, carbon nanotubes (CNTs) stand out due to their exceptional water transport efficiency and variability of pore-size, down to molecular dimensions, thereby approaching ideal semipermeability. We report osmotically driven water and salt transport across

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a membrane of vertically aligned CNTs in a titania matrix whose surface is functionalized with a self-assembled monolayer of octadecylphosphonic acid. The increased steric hindrance and hydrophobicity at the pore entrance of CNTs improved salt rejection while maintaining enhanced osmotic water transport, thanks to atomically smooth surface of the nanotubes. In addition to the experimental demonstration of osmosis, we observed a net negative osmotic water flow at lower salt concentration gradient and non-Fickian behavior of the reverse salt flux. This observation is attributable to the interface driven fluidic phenomenon known as diffusio-osmosis that drives water flow in the direction opposite to osmotic flow. The ion-CNT interactions are responsible for the simultaneous occurrence of the two osmotic transport mechanisms and the salt specific osmotic transport characteristics. KEYWORDS Carbon Nanotubes, Membrane, Osmosis, Diffusio-osmosis, Desalination MAIN TEXT Global water shortage and rising concerns for the pollution of aquatic environment pose a threat to sustainable development, with increased demands for less energy and resource- intensive separation processes1, 2. The current membrane-based desalination technologies suffer from an inherent permeability-selectivity trade-off and severe fouling propensity3, 4. New membrane materials with finely tailored pores in their dimension, morphology and surface chemistry such as carbon nanotube (CNT)5, porous graphene6 and graphene oxide7 have great potential to overcome these issues. In particular, molecular dynamics simulations8-10 and experimental studies11-13 of water transport through CNTs have reported flow enhancement many orders higher than predicted by the classical Hagen-Poiseuille formalism. Membranes incorporating sufficiently narrow CNTs can thus achieve a high degree of separation in membrane processes with water flow rates far in excess of conventional polymeric membranes14. Despite recent advances and efforts in realizing CNT membranes15-17, researchers have yet to achieve complete salt rejection comparable to aquaporins, water channels present in cell membranes, reporting very limited 2 ACS Paragon Plus Environment

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rejection that even deteriorates at high salt concentrations and low pH18. Salt rejection of the reported CNT membranes is largely governed by size exclusion and charge (Donnan) exclusion. These effects can be reinforced by the physiochemical and structural modification of the nanotube entrance with functional molecules of desired bulkiness and charges that impose additional resistances to ions and molecules via steric and Coulombic repulsion19-22. Molecular dynamics simulation of osmosis across 0.81 nm wide CNT indicated an osmotic water flow of 5.8 × 109 H2O molecules/s, under a large osmotic gradient of 5.8 M NaCl23. A recent experimental study13 across short segment CNT porins in a bio-mimetic platform of lipid vesicles has indicated osmotic permeabilities of CNT porins exceeding values obtained with aquaporin water channels. However, there is still a lack of understanding of osmotic transport in CNTs and across a range of osmolyte concentration and using different inorganic salts. In our study, we measure simultaneous water and salt transport through the CNTs, so as to give a better understanding of the transport process. For the case of nanopore or nanochannel membranes, osmotic transport is significantly influenced by the interactions between the osmolyte and the membrane pore channel. For this reason, osmosis across nanochannel membranes such as CNT differs from osmosis across polymer membranes. Here, we investigate the potential of vertically aligned CNTs (VA-CNTs) in a titania matrix whose surface is functionalized with a hydrophobic self-assembled monolayer of octadecylphosphonic acid (ODPA) in improving salt rejection along with enhanced water flux in an osmotically driven membrane process. Along with the characterization of osmotic water flux and reverse salt flux through VA-CNTs, a hitherto unseen nanofluidic phenomenon in carbon nanotubes, so-called diffusio-osmosis or capillary osmosis is observed. Osmosis across a membrane drives the solvent transport from a region of lower solute concentration to higher solute concentration, whereas, interface driven diffusio-osmosis drives the solvent from a region of higher solute concentration to lower solute concentration, along the solute gradient that builds up within the diffuse ion-layer 3 ACS Paragon Plus Environment

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at the solution-wall interface24, 25. The ODPA modified VA-CNT/titania membrane shows unique osmotic transport dependency on concentration and salt type, attributable to the interplay between osmosis and diffusio-osmosis inside the nanotubes. Figure 1a illustrates the key steps of our VA-CNT membrane fabrication26, which begins with the catalytic chemical vapor deposition of VA-CNTs atop alumina supported iron catalyst on a microfabricated silicon chip, followed by pinhole-free encapsulation of individual CNTs and subsequently inter-CNT-TiO2 nanotubes with titanium dioxide using atomic layer deposition (ALD). Optimization of the ALD process27 onto the given VA-CNTs structure28 (i.e., height shorter than 20 m and areal density around 1011 cm-2) is essential for the conformal deposition and gapfilling of such high-aspect-ratio structures. A cross-sectional SEM image of the membrane (Figure 1b) confirms the integrity of the membrane, and indicates that a gap-free membrane is obtained over the length scale of the entire chip. The resultant membrane thicknesses are between 2 and 3 m (Figure 1b). Argon ion-beam-milling was then used in steps to etch away excess ALD deposited titania from either sides of the membrane and the catalyst particles and alumina support layer from the backside of the membrane (Figure 1c). In between the Ar ion-beam-milling etch steps, nitrogen gas permeance was measured, and the Ar ion-beam-milling etching was stopped once the nitrogen gas permeance reached a constant value (confirmation of complete opening of all the CNT pores in the membrane matrix). This method also provided a foolproof method to detect surface cracks or broken windows by discrepancies in nitrogen gas flow. TEM analysis shows that all nanotubes are single-walled with diameters in the range of 1-3.5 nm (daverage = 2.2 nm) (Figure 1d). The Raman spectrum corroborates the presence of small-diameter CNTs by the multiple radial breathing modes in the range of 100-300 cm−1 and the Raman G-band/D-band intensity ratio is around 3 (Figure 1e). The areal density of VA-CNTs, quantified from the steadystate NaCl diffusion experiment29 is ~ 0.35 × 1011 cm-2, (see Supporting Information). Both sides of the open CNT membrane were chemically modified with ODPA by immersing the membrane


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in a 1.3 mM ODPA/Toluene solution overnight, followed by multiple rinsing in toluene, and later by isopropanol30. The contact angle of water on CNT-titania surface changed from 78.3° to 103.3° upon ODPA functionalization (Figure 1f).

Figure 1. Fabrication procedure and characteristics of the VA-CNTs/titania membranes: (a) Schematic description of the key steps of membrane fabrication and surface modification with ODPA, SEM images of (b) FIB-microtomed cross-section and (c) top and bottom surfaces of the membrane after CNT-pore opening (d) CNT diameter distribution measured from high-resolution TEM images (inset), (e) Raman spectrum of the VA-CNTs, (f) contact angle measurement of the VA-CNT-titania surface before and after ODPA functionalization.

We first investigated water and salt transport across both ODPA-functionalized and nonfunctionalized membranes in forward osmosis (FO) type process using a homemade diffusion cell setup (Figure 2a). Macroscopic measurement of water permeance and salt diffusion across the membrane containing a large number of VA-CNTs across an impermeable matrix can provide on average the osmotic water flux and the reverse salt flux per CNT channel. Sodium chloride (NaCl) with its high solubility in water and negligible change of viscosity with concentration is our primary solute of choice for preparing the draw solutions for the FO-type characterization. The diffusion cell setup also allows for the simultaneous measurement of electrical conductivity of feed water via a dip-in conductivity probe (ET-915, eDAQ instruments, Australia). Osmotic water flux across 5 ACS Paragon Plus Environment

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the VA-CNT membrane increased almost linearly with the salt concentration gradient (osmotic pressure), which even exceeds the water fluxes of the commercial thin-film-composite (TFC) FO membrane (Porifera, Hayward, USA) at higher salinity gradients (Figure 2b). A self-limiting behavior of water flux due to severe internal concentration polarization (ICP) at high salt concentrations within the porous support has been one of the major limiting issues in the use of polymer based membranes for osmotically driven membrane processes31. It is also important to note that the linear dependence of the osmotic water flux on the draw solution concentration is maintained for both the functionalized and non-functionalized VA-CNT membrane, thus indicating that surface modification with ODPA does not introduce additional concentration polarization effects. From the linear fitting of the osmotic flux over the concentration gradient, an osmotic permeability of 4.7 × 10-13 cm3/s per CNT was obtained for the non-functionalized membrane, with the permeability improving to 12.1 × 10-13 cm3/s per CNT for the ODPA functionalized membrane (Figure 2b). This increased water permeation is caused by the net decrease in the salt passage as an outcome of ODPA surface functionalization. The order of magnitude is similar to the previously measured osmotic permeabilities of even narrower CNT porins13 and definitely higher than Aquaporins32. Interestingly, at draw solution concentrations lower than 0.2 M NaCl, a net negative (reverse) flow of water was observed for the ODPA-functionalized membrane. This reverse flow hints at a non-negligible contribution of diffusio-osmosis inside the nanotubes that may even outweigh that of osmotic water flow. During the FO operation, electrical conductivity of the feed solution increased linearly over time caused by the salt passage from draw to feed solutions. The reverse salt (NaCl) flux across the ODPA-modified VA-CNT membrane is on the same order of magnitude as that of a commercial FO membrane, yet exhibits a weak concentration dependence (Figure 2c). Noticeably, VA-CNT membrane showed a moderate decrease of osmotic water flux but a significant reduction of reverse salt flux upon surface functionalization with ODPA (Figure 2d). A monolayer of ODPA on the surface appears to impose additional steric hindrance near the CNT-titania pore entrance, thereby impeding the salt 6 ACS Paragon Plus Environment

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passage, without much affecting the water flow enhancement from the CNT interior. For a better comparison of membrane performance, we plotted the reverse salt flux relative to the osmotic water flux (Figure 2e). ODPA modified VA-CNT membrane showed lower salt leakage per produced water at higher salinities, unlike the commercial FO membrane showing nearly constant ratio of reverse salt flux to water flux over the osmotic gradient. The osmotic process across both ODPA-functionalized and non-functionalized VA-CNT membranes stopped after sometime, and the times scales for stoppage of osmosis depends on the concentration of draw solution (for NaCl) and type of salt (LiCl, KCl and NaCl). Increasing the concentration of draw solutions lead to osmosis stopping sooner, and between Li+, K+ and Na+, we observe that the time scales of stoppage are related to the strength of the cation-pi interactions33 of the hydrated ions in the CNT interior (see Supporting Information). A similar observation has previously been seen across nanoporous graphene membranes34, although exact mechanism has not been reported. For CNT channels, using MD and DFT based methods, Liu et al.35 have once argued that ion interactions with aromatic rings of CNTs can lead to blockage of water flow in a reverse osmosis process.

Figure 2. Osmotic water and salt transport across VA-CNT/titania membranes in forward osmosis (FO) setup: (a) Schematic of the homemade diffusion cell, equipped with magnetic stirring and chiller to reduce the concentration polarization and temperature fluctuation, a dip-in conductivity electrode in the feed reservoir to monitor salt transport and meniscus capillaries to monitor osmotic water transfer across the


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membrane, (b) Osmotic water flux and (c) Reverse salt flux through the VA-CNT membranes (■,▲) over the solute concentration gradient compared to commercial TFC FO membrane (●), (d) bar charts of water and reverse salt flux of the VA-CNT membrane before and after surface modification with ODPA at 0.3 M NaCl concentration gradient and (e) a comparison of membrane performance expressed by reverse salt flux relative to osmotic water flux; the vertical line indicates typical salinity range of seawater.

Similar to previously reported result on nanochannels such as boron nitride nanotubes36, CNTs are believed to possess a negative charge. The physical basis for the induced negative charge at the CNT interior is yet to be ascertained, but there have been studies attributing it to the presence of  electrons37 or hydroxide ion adsorption on the hydrophobic surface38. The  electrons of CNT surface could lead to charge close to the wall through cation- interactions33, 35. The negative surface charge on the hydrophobic CNT interior induced by the OH− adsorption can also lead potentially to cation localization close to the wall surface38. As described in Figure 3a, under concentration gradient across a channel, the solute diffuses inside the channel following Fick’s law, and the solute can be accumulated or depleted near the surface by attractive or repulsive electrostatic interactions with the surface, leading to a diffuse layer of counter-ions. The interaction energy of the solute with the surface, together with the bulk solution concentrations at each end of the channel determine the magnitude of solute gradient within the diffuse layer as well as the thickness of the diffuse layer. A radially decaying concentration of the solute away from the CNT wall sets up an osmotic pressure in the radial direction. Due to the solute gradient along the channel, the osmotic pressure, too, varies along the channel, thus leading to an osmotic pressure gradient that eventually drives the flow of solution towards the region of low solute concentration in the case of attractive solute-channel interactions. To investigate this hypothesis, we employed inorganic salts with different mass diffusivities to verify the effect of induced electric field diffusio-osmotic flow in addition to the concentration gradient induced diffusio-osmotic flow. In principle, interfacially driven diffusio-osmosis will occur whenever the membrane deviates from ideal semi-permeability, which is the major difference from osmosis.


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To ascertain the diffusio-osmotic contribution in the net osmotic transport across VA-CNTs, we normalize the reverse salt flux at steady state with the draw solution concentration. The normalized flux should be constant in the case of simple Fickian diffusion of salt. Instead, we observe an enhancement of the reverse salt flux at low draw solution concentrations, which can be rationalized by the occurrence of diffusio-osmosis (Figure 3b). The salt flux through the CNT is influenced by three principal factors – a) Fickian diffusion, b) osmotic water transport and c) diffusio-osmotic water transport. The first two factors are bulk phenomena, and hence present at all concentrations, whereas diffusio-osmotic water transport, a surface phenomenon, would dominate at low concentrations where surface interactions are maximum. At draw solution concentrations higher than 0.5 M NaCl, normalized reverse salt fluxes are nearly constant, indicating a major subsiding of surface interactions between solute and CNT interior, leading to lower contribution of diffusio-osmosis to total transport. Besides ionic strength of draw solution, the cation type and ion valence of solute can also influence the relative magnitude of diffusio-osmotic transport due to the difference in interaction energies with CNT interior surface and ionic mobilities39. To capture the salt-specificity of diffusioosmosis inside nanotubes, we further characterized the osmotic transport under a concentration gradient of 300 mM but using different, 1:1 and 2:2 symmetric salts – LiCl, NaCl, KCl and MgSO4. By using multivalent salts, we are able to ascertain the role of cation charges in accounting for the diffusio-osmotic transport, thereby comparing our experimental results with theory40. We chose the concentration of 300 mM, because of the observation of stronger diffusio-osmotic transport at this concentration (as seen from data presented in Figure 3b). Figure 3c shows that the net osmotic water permeance, defined as the measured water flux normalized by actual

 

kT



 2 B2 2 ln(1   )  , osmolality of salt solutions, scales linearly with diffusio-osmotic factor  Ze Z e   2

(refer to Supporting Information), which represents the propensity of the salt to induce diffusio-


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osmotic water flow. Here,  

 D  D   D  D 

quantifies the difference between cation and anion

 Ze   and kB T Z, e and  denote Boltzmann constant, solution  4 k BT 

diffusivities of the salt,   tanh 

temperature, ion valence number, elementary charge of electron and surface zeta potential, respectively. This linear scaling behavior is consistent with the analytical model prediction40 (see Supporting Information). While estimating the value of the diffusio-osmotic factors for the various salts, we had assumed the same value of zeta potential and viscosity for the different salts. The net osmotic water permeance decreases as KCl > NaCl > LiCl, which is not surprising given that the values of the diffusio-osmotic factors of the three chloride salts increases in the opposite order, majorly influenced by the difference in  values: LiCl (-0.327) < NaCl (-0.208) < KCl (-0.017), and agrees well with previous report on diffusiophoretic motion of colloidal particles driven by the diffusio-osmotic flows using the same salts41, 42. It is worthwhile to note that the estimated values of Debye length at 300 mM for univalent salts (KCl, NaCl and LiCl) and the symmetric divalent salt (MgSO4) are λD,1:1 = 0.56 nm and λD,2:2 = 0.28 nm, respectively. Although Debye layer thickness can capture the ion-wall interactions and transport in microchannels and large nanochannels, Debye layer alone cannot explain the differences in the observed transport for different univalent salts, as their Debye lengths are nearly identical. In case of divalent symmetric salt such as MgSO4, the thickness of diffuse layer at a certain solution concentration is thinner than those of monovalent salts43 while the  value is -0.146, which is smaller than  (KCl) but larger than  (NaCl). The net osmotic water permeance of MgSO4 positioned between those of KCl and NaCl is due to the effect of both diffuse layer thickness and salt-specific  value on diffusio-osmosis.


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Figure 3. Interplay between osmosis and diffusio-osmosis through CNTs: (a) A schematic description of diffusio-osmotic flow induced by the concentration gradient of ionic solution across a charged CNT channel, (b) the concentration dependence of the normalized reverse salt flux by draw solution concentration (fitting line is for visual guidance) and (c) net osmotic water permeance under the same concentration gradient (300 mM) generated by four different symmetric salts over salt-specific diffusio-osmotic factor: details of diffusio-osmotic factors for various salts used in these experiments are provided in the Supporting Information.

In practical applications of water purification and desalination, water permeance and salt rejection provide a figure of merit for membrane performance. Water permeance is defined as the measured osmotic water flux divided by the exposed membrane area and actual osmolality of draw salt solution, and salt rejection is calculated from reverse salt flux relative to osmotic water flux. These quantities are compared for CNT membranes and commercial TFC FO membrane (Figure 4a). The ODPA-modified CNT membrane clearly exhibits enhanced water permeance along with higher salt rejection at high salinity conditions comparable to seawater. Inverse relationship between permeance44 and rejection originating from inherent limitations of dense polymeric materials4 and severe concentration polarization with high salinity feed waters have been the major issues in membrane based desalination and power generation processes, as seen for the TFC membrane in Figure 4a. In the same plot, we see that salt rejection and osmotic water permeance improve simultaneously for ODPA-functionalized CNT membrane. In Figure 4b, we 11 ACS Paragon Plus Environment

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compare the osmotic permeabilities per CNT channel to other nanopores23, 32, 45 and CNT porins13. The permeabilities from our work even exceed those of Aquaporin (dpore ~ 0.3 nm). For osmotic transport across non-ideal channels (i.e., permeable to solute), one can also estimate the reflection coefficient46 (σ) to better understand the transport properties of the channel using different osmolytes. To estimate the experimental reflection coefficient of our CNT channels before ODPA functionalization, we measured the hydraulic permeabilities (lp) independently using hydrostatic-pressure-driven water transport across our non-functionalized CNT membrane and obtained an experimental reflection coefficient, σexp = 0.4061 (see Supporting Information). This value of σexp compares well with the theoretical prediction of σtheor,1D = 0.5231 and σtheor,3D = 0.2736 for a 1-dimensional or 3-dimensional conduit transport, given the geometrical sizes of our channel and ions. Our current approach of modifying the surface near CNT tips to gain sufficient rejection property while preserving the low-friction graphitic channel for enhanced water transport is not only effective but may enable more widespread and faster deployment of CNT-based membrane technology than the efforts to reduce the nanotube diameters of the membrane down to the level comparable to hydrated solute sizes.

Figure 4. Comparison of VA-CNT membranes: (a) Water permeance and salt rejection properties of ODPAmodified VA-CNT/titania membrane (■) in osmotically driven membrane processes in comparison to commercial thin film composite FO membrane (●): the larger the symbol size, the larger the concentration gradient imposed across the membrane in FO experiments. (b) Per-pore osmotic permeability of our CNT


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channels in comparison to permeabilities obtained from experiments and simulation of other nanochannels and CNTs13, 23, 32, 45.

We demonstrated a post modification approach in using wider diameter CNT (average: 2.2 nm) membrane to improve the salt rejection while maintaining enhanced water transport by the selfassembly of octadecylphosphonic acid (ODPA) on the CNT-titania membrane surface. ODPAfunctionalized CNT membrane showed significant reduction of salt passage with sustained osmotic water flux. Moreover, severe concentration polarization and saturation of osmotic water flux with increasing salinity conditions due to concentration polarization was not observed in the freestanding VA-CNT membranes. In particular, applications with highly concentrated streams can benefit from CNT membranes in improving water recovery and operational efficiency, as the rejection increases at higher concentrations. The CNT membrane also provided a platform to study the interplay between osmosis and diffusio-osmosis, where ion-specific interactions were shown to affect osmotic transport. Knowledge about ion-specific interactions inside CNTs is important for applications in nanofluidics, drug delivery, energy storage and sensing. The current insight into diffusio-osmosis across CNT channels could also help decrease the power requirements for electrophoretic drug delivery using CNT patches29, and thus providing other avenues of commercialization for CNT nanofluidic devices. Harnessing large currents in osmotic power generation applications47, involves the ability to generate a convective flow of ions through diffusio-osmosis across a charged nanochannel membrane36. CNT membranes with their ability to generate diffusio-osmotic flows could therefore become a viable candidate for osmotic power generation vis-à-vis 1-D boron nitride (BN) nanotubes47 and nanoporous 2-D molybdenum disulfide (MoS2) based membranes48. Further study on ion-CNT interactions is underway with the aim of understanding the kinetics of osmotic processes; which is important in the design of efficient and practical membrane systems for osmotic separation processes. AUTHOR CONTRIBUTIONS:


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ML, SKY and HGP conceived the experimental study. ML fabricated the CNT membranes. ML and SKY performed experiments and material characterizations. All the authors contributed in writing the manuscript. ASSOCIATED CONTENT Supporting Information: Characterization of CNT membrane (gas permeation, estimation of CNT areal density from salt permeation); Salt transport measurements; Estimation of osmotic and hydraulic permeabilities, Estimation of experimental and theoretical reflection coefficients; Correlation between diffusio-osmosis and osmotic water permeance. ACKNOWLEDGEMENTS: All authors thank the support received from the Binnig and Rohrer Nanotechnology Center (BRNC) of ETH Zurich and IBM Zurich. ML thanks Prof. Jan Vermant for his comments and discussion on the manuscript. ML also appreciates Prof. Chih-Jen Shih for discussions on the zeta potential and surface charge of graphitic surfaces. REFERENCES 1. Shannon, M. A.; Bohn, P. W.; Elimelech, M.; Georgiadis, J. G.; Mariñas, B. J.; Mayes, A. M. Nature 2008, 452, 301-310. 2. Elimelech, M.; Phillip, W. A. Science 2011, 333, 712-717. 3. Park, H. B.; Kamcev, J.; Robeson, L. M.; Elimelech, M.; Freeman, B. D. Science 2017, 356, eaab0530. 4. Werber, J. R.; Osuji, C. O.; Elimelech, M. Nat. Rev. Mater. 2016, 1, 16018. 5. Thomas, M.; Corry, B. Philos. Trans. R. Soc. A 2016, 374, 20150020. 6. Celebi, K.; Buchheim, J.; Wyss, R. M.; Droudian, A.; Gasser, P.; Shorubalko, I.; Kye, J.-I.; Lee, C.; Park, H. G. Science 2014, 344, 289-292. 7. Abraham, J.; Vasu, K. S.; Williams, C. D.; Gopinadhan, K.; Su, Y.; Cherian, C. T.; Dix, J.; Prestat, E.; Haigh, S. J.; Grigorieva, I. V.; Carbone, P.; Geim, A. K.; Nair, R. R. Nat. Nanotechnol. 2017, 12, 546-550. 8. Hummer, G.; Rasaiah, J. C.; Noworyta, J. P. Nature 2001, 414, 188-190. 9. Joseph, S.; Aluru, N. R. Nano Lett. 2008, 8, 452-458. 10. Falk, K.; Sedlmeier, F.; Joly, L.; Netz, R. R.; Bocquet, L. Nano Lett. 2010, 10, 4067-4073. 11. Hinds, B. J.; Chopra, N.; Rantell, T.; Andrews, R.; Gavalas, V.; Bachas, L. G. Science 2004, 303, 6265.


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Osmotic Transport across Surface Functionalized Carbon Nanotube

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