Scaling the Mass Transport Enhancement through Carbon Nanotube Membranes Seul Youn, Jakob Buchheim, Mahesh Lokesh, Hyung Park
To cite this version:
Seul Youn, Jakob Buchheim, Mahesh Lokesh, Hyung Park. Scaling the Mass Transport Enhancement through Carbon Nanotube Membranes. 2018. hal-01890716
HAL Id: hal-01890716 https://hal.archives-ouvertes.fr/hal-01890716 Preprint submitted on 8 Oct 2018
HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Scaling the Mass Transport Enhancement through Carbon Nanotube Membranes
Seul Ki Youn, Jakob Buchheim, Mahesh Lokesh, Hyung Gyu Park*
Nanoscience for Energy Technology and Sustainability, Department of Mechanical and Process Engineering, Swiss Federal Institute of Technology (ETH) Zurich, Tannenstrasse 3, Zurich CH-8092, Switzerland *Corresponding author: [email protected]
ABSTRACT
Measuring and controlling enhanced mass transport in carbon nanotube (CNT) and membranes thereof have been of great interest and importance in fundamental studies of nanofluidics as well as practical applications including desalination and gas separation. Experiments and simulations have claimed nearly frictionless transport and attributed it to tight graphitic confinement. Nevertheless, rare and scattered experimental data are obscuring the transport efficiency limit and the mechanistic understanding of fluid transport through
CNTs. Here we present a new fabrication process for a manifold membrane of reinforced CNTs, a method applicable to any type of CNT including single-walled CNTs (SWCNTs) and extendable to various end- use-oriented matrix materials. Reaffirming the remarkable water and gas flow enhancement, we observe their strong correlation with the aspect ratio and the qualityof SWCNTs, leading to a new scaling for proper assessment of the enhanced mass transport through CNT membranes. As the result, we recognize the conceptual equivalence between the nearly frictionless CNT channel and the channel of infinitesimal length, an orifice. It is hoped that our work could correct the misleading message about the theoretical limit of flow enhancement to the readership, hence providing a valuable source of reference on designing and analyzing high-performance CNT membranes.
KEYWORDS: Enhanced Mass Transport, Carbon Nanotube, Reinforced CNT, Aspect Ratio and Quality
Scaling, High-Performance CNT Membrane
1 INTRODUCTION Transport of confined fluids in artificial nanoconduits have attracted significant interest in last decade due to its great potential for a variety of applications1 including sensing2, separation3, energy storage4 and conversion5, and water desalination6. Examples include silicon-based nanopores7, carbon nanotubes, boron nitride nanotubes8, porous graphene9, and lamellar graphene oxides10. In particular, a membrane that the carbon nanotube (CNT) interior serves as pores can achieve facile permeation by the atomically smooth11, hydrophobic graphitic conduit12-13 and selectivity by well-defined diameter14 and charged nanotube mouth15, thereby making a promising candidate for nanofluidic studies and membrane technology applications. A large number of theoretical studies have unveiled interesting mechanistic features of confined fluids in CNTs such as spontaneous filling of water16-17, curvature- dependent interfacial friction11, existence of multiple phases of water at nanotube interface18, specular gas- nanotube collisions19-20 and gas adsorption on the nanotube wall21-22. Simultaneously, rapid advancements in nanofabrication and nanotechnology have been enabling their experimental verification, starting from
Hinds et al.’s23 reports using vertically aligned (VA-) multiwalled CNTs to recent reports using a single-
CNT24-28 or several CNTs29-30-based fluidic devices. Although the latter may ease the quantitative analysis of structure-induced transport dynamics, a wider and more rapid deployment of CNTs in practical applications in separation industries demands a macroscopic membrane platform having a myriad of CNTs
31 and the rational interpretation of the ensemble-averaged data collected from such membranes.
Pressure-driven water and gas flows have been investigated using various types of CNT membranes (Table
S1). Although a fast flow rate has been confirmed by experiments, and also by molecular dynamics (MD) simulations32, there is still little consensus on how fast a fluid flows through CNT membranes in practice.
What is also surprising is that large degrees of flow enhancements appear incoherent beyond the structural variations among these CNT membranes33. So far reported CNT membranes differ greatly not only in the intrinsic characteristics of nanotubes – diameter (d), length (L), quality and wall number – but also in the traits of the membrane composite – entrance geometry and surface property near the CNT mouths, which are incidental to the very different fabrication methods and the choice of matrix materials (Figure 1a). In an ideal case of subnanometer-wide and almost defect-free CNTs, a combination of unique molecular
2 ordering, reduced interfacial friction34-36 and a depletion region at the liquid-solid interface16, 18 leads to large flow enhancement. Precise control of the structural variety of CNT membranes is, however, still challenging and such non-idealities in practice greatly disrupt the nearly frictionless mass transport. Above all, narrowing CNT diameter (d) which determines the degree of molecular confinement 37-38 and the molecular friction at the graphitic interface11 has been considered critical to larger flow enhancement38. For instance, membranes of a sub-2-nm-wide CNT manifold reported by Holt et al. have demonstrated many order-of-magnitude flow enhancement for both gas and water.39 On the other hand, CNT length (L) may not be a key factor as long as the nanotube is straight and defect-free and causes negligible friction inside the channel. In this case, the total flow is mainly governed by the resistance at the CNT entrance40, while the channel flow characteristics such as length dependency41 would intervene if the structural non-idealities of CNT channel signifies. In particular, surface defects on the CNT interior such as doping sites, vacancies and chemical functional groups can increase the channel resistance to a great extent42-44. The number and types of defects are practically challenging to control and characterize precisely45-46, and there has been no experimental work on the effect of surface defects on the transport efficiency of CNT membrane. On the other hand, the local defects at the entrance of the nanotubes such as carboxylic groups on the CNT rim have an impact on entrance resistance by imposing steric hindrance or additional energy barrier of water- ion interactions. According to recent MD simulations47-49, the resistance at the CNT mouths can also be reduced by adding a conical entrance, mimicking the hourglass shape of aquaporins. In this work, we report a new fabrication method of CNT membrane that incorporates reinforced VA-CNTs in various types of matrices reliably, with which to obtain correlation between structural attributes and flow enhancement of
CNTs. In particular, we report the effect of nanotube quality as critical as nanotube diameter on the flow enhancement. While revisiting the question on “how fast does fluid flow through CNTs?”, we consider a scaling of aspect ratio (AR) for assessing the enhanced mass transport through CNTs, which allows us to explain the flow dynamics in the framework of entrance and channel resistances with the upper bound of transport efficiency that follows the scaling of the orifice model: e.g., Sampson’s formula for liquids and effusion dynamics for gases.
3 Fabrication of vertically aligned single-walled carbon nanotube membranes
Figure 1. Fabrication of vertically aligned single-walled carbon nanotube (VA-SWCNT) membranes: (a) a schematic of a CNT channel with the structural factors affecting transport properties; (b) schematic illustration of the new approach of mechanical reinforcement for the membrane fabrication using VA- SWCNTs of small diameters; and SEM images of the cross-section of (c) pristine VA-SWCNTs, (d) mechanically reinforced with ~20-nm-thick ALD coating, (e) gap-filled with polyethylene and titanium oxide, (f) SEM images of the etched surface of the reinforced VA-SWCNT/polyethylene and VA- SWCNT/titania membranes; and (g) AFM images (3D height and peak force error) of VA-SWCNT/titania membrane surface, showing pothole-like features and the conically shaped entrance region of open CNT tips (indicated by blue arrows).
We have successfully demonstrated a membrane fabrication method for vertically aligned single-walled
CNTs (VA-SWCNTs). SWCNTs are highly preferred because of their structural uniformity, relative ease of tailoring and defining the structural properties,50-51 and little pore blockage by metal catalyst in
4 comparison to multiwalled CNTs (MWCNTs). However, SWCNTs are prone to collapse, disintegration and void formation when infiltrated by matrix material52, be it liquid or vapor due to their low bending stiffness and high areal density. Beyond the mechanical robustness of the membrane, it is of utmost importance to preserve innate surface quality and alignment of the as-grown VACNTs during the fabrication process. Our strategy to meet this need is to strengthen the mechanical stiffness of pristine CNTs with a thin conformal coatings of metal oxides via atomic layer deposition (ALD) prior to filling the inter- nanotube gaps with matrix materials (Figure 1b). The precisely controllable deposition rate and the layer- by-layer nature of ALD technique facilitate the delicate modification of VA-SWCNTs without causing deformation53 (Figure 1d). At this step, ALD reactants do not penetrate in the interiors of VA-SWCNTs having intact caps and bases anchored on metal catalysts.54 This fabrication approach using reinforced
CNTs will help us broaden the end-use-oriented choice of matrix materials, combined with other existing gap-filling processes for versatile applications of CNT membranes including pharmaceutical separations, sensors, and instant or portable filtrations. Despite the chemical inertness of basal graphitic surface, surface defects and the local bundling of SWCNTs55 facilitate the adsorption of ALD precursors and the subsequent nucleation and layer growth56-57. No change in the Raman spectrum of VA-SWCNTs before ALD and after removal of the ALD coating attests the intactness of the CNT surface property during ALD process (Figure
S1). After the reinforcement step, VA-SWCNTs obtain structural continuity and resilience to both lateral and vertical compressive stresses, yet still maintain the interstitial space of a few tens of nanometers between CNTs to provide the matrix material with infiltration paths. The remaining interstices were filled with either polymers such as polyethylene (PE) and epoxy or metal oxides (alumina and titania) via direct infiltration of a polymer melt or dry ALD using ozone for an oxygen source, respectively, to yield an impermeable composite film (Figure 1e). Subsequent plasma etching and ion beam milling turn this hermetic freestanding film into a gas permeable membrane. When the membrane permeance stops increasing with further etching (Figure S2), we regard that most CNTs spanning across the impermeable matrix are open. As shown in Figure 1f, after the complete etching we could detect the ALD-reinforced
VA-SWCNTs exposed on the etched surface of the polymer or titania matrix with their caps being etched
5 away. We further analyzed the open membrane surface using high resolution, peak-force tapping-mode
AFM. The 4–5-nm-wide pothole-like features appearing all over the matrix surface in the AFM image
(Figure 1g) can be related to the near-surface CNTs seen in the top-view SEM images. We believe that the open CNT tips are slightly embedded in the matrix or located at the matrix surface, rather than protruding as reported in a previous study23. We note that surface topography at the open CNT (entrance region) show a conical shape, likely due to the difference of etching rate between CNT and titania matrix.
We verified the integrity of the fabricated membranes as follows. The constant gas permeances independent of pressure indirectly evidence absence of relatively large cracks in the membranes. Figure 2a,b confirms the good impregnation of CNT structure in the matrix with no voids that span through the membrane thickness. Note that nanometer-sized voids were sometimes detectable in the membrane cross section, but they are found discrete with never spanning the entire membrane thickness; thus, it would be reasonable to neglect their contribution to the membrane transport properties. Also, our membranes with sub-5-nm-wide
VA-SWCNT pores completely rejected the 5-nm-large gold nanoparticles (Figure S10). In addition, the activation energies (Ea), calculated from the temperature dependence of water transport rates can provide an additional clue whether the transport across CNT membranes is diffusion-driven or CNT-facilitated.
Here, the activation energy can be defined as the minimum energy required for water molecules to overcome its intermolecular interactions, which is for bulk fluid dominated by the interaction among liquid molecules. For nanoconfined fluid, on the other hand, the activation energy is predicted to decrease with stronger confinement (i.e., in narrower CNTs) and to be smaller than that for the viscous flow of water,58 ascribed to the reduction in the number of neighboring molecules and the weak water-CNT interaction. We obtained the apparent Ea values of 3.75 and 4.13 kcal/mol from two different membranes, generally not
59 higher than the apparent Ea value of the viscous water flow (4.136 kcal/mol) in the measured temperature
o range of 10-35 C (Figure 2c). Indicating the ease of water transport through CNTs, these lower Ea values strongly evidence the CNT-facilitated water transport. Similarly, previous studies on the biomimetic membranes embedded with aquaporins, allowing channel-facilitated transport, have reported the Ea values
6 60-62 as low as 3.4 kcal/mol . It is noticeable that Ea value of 3.75 kcal/mol is obtained from the membrane sample that contains narrower, less defective CNTs (d=2.11 nm, I(G)/I(D)=5.2), while the Ea value of wider, highly defective CNTs (d=4.69 nm, I(G)/I(D)=1.3 nm) is found close to that of viscous flow of water or of the track-etched polycarbonate membrane with 50-nm-wide pores (4.27 kcal/mol). All these observations support that water transport occurs through the membrane-spanning VA-SWCNTs, not through any nanovoids or large pinholes.
Figure 2. SEM and TEM images of the cross sections and the FIB-cut lamellae of (a) a VA- SWCNT/polyethylene membrane (left) and (b) a VA-SWCNT/titania membrane (right), confirming the absence of microcracks spanning across the membrane thickness; and (c) apparent activation energy (Ea) of water transport through VA-SWCNT/titania membranes with average diameters of 2.11 nm (red square) and 4.69 nm (blue triangle) as well as a 50-nm-diameter track-etched polycarbonate (PC) membrane (black circle) with an inset of the corresponding Arrhenius plots. Ea values for water transport through Aquaporin Z-incorporated biomimetic membranes are taken from the literature60-61 and plotted for comparison
Effect of tube diameter and quality on the mass transport through CNT membranes
If the curvature-dependent atomic smoothness in the potential energy landscape is one of the attributes of
CNT responsible for the fast mass transport11, surface defects on the nanotubes would also act as a critical source of frictional 12, 19. In that case, transport properties through CNTs should reveal correlations with all these structural parameters of the nanotubes such as diameter and quality, which could not have yet been
7 sufficiently investigated due to the technical difficulties in the sample preparation as well as in the material and dynamic characterizations at the nanometer scale. To address this question, we fabricated several- micrometer-thick CNT membranes with various nanotube diameters and qualities, as summarized in Table
1 and characterized their pressure driven flow rates of nitrogen gas and water.
Table 1. Comparisons of experimental gas flow rates (Qexp) of VA-SWCNT membranes with Knudsen (QKn) and Sampson (Qs) predictions, and of experimental water flow rates with Hagen-Poiseuille flow (QHP) and effusion (Qeff) model predictions. Membrane fabrication is demonstrated with various matrix materials such as alumina (AlOx), polyethylene (PE) and titania (TiOx). CNT diameters (d) and membrane thickness (L) were determined from TEM and SEM measurements respectively and CNT qualities were described by the distinct features of Raman spectra. Due to the long-term chemical instability of alumina in water, VA- SWCNT/alumina membranes are excluded from water permeation tests. Other details are provided in SI.
CNT quality Water flow Gas flow enhancement Matrix L D band enhancement d (nm) material (µm) I(G)/I(D) Qexp/Qs Qexp / Qeff ω FWHM Qexp/QHP Qexp / QKn D (%) (%) 1.93 2.74 16.2 1290.8 34.5 ̶ ̶ 34 ̶ 71 21 ̶ 26
AlOx 2.15 6.28 10.6 1289.0 52.6 ̶ ̶ 14 ̶ 34 5 ̶ 8 2.39 6.34 6.4 1290.0 53.6 ̶ ̶ 12 ̶ 39 2.4 ̶ 8
AlOx 3.62 2.14 4.7 1290.9 50.8 19 ̶ 42 2 ̶ 4 7 ̶ 15 6 ̶ 13 /PE 4.15 4.49 2.1 1297.1 62.9 25 ̶ 69 1 ̶ 4 6 ̶ 16 4 ̶ 8 2.10 4.58 - 1288.0 36.2 92 – 199 2 – 5 5 – 10 1 – 2.5 AlOx /Epoxy 3.34 18.70 3.4 1309.1 91.3 1383 – 3074 13 – 30 26 – 58 2.5 – 5.5 2.11 8.26 5.2 1290.0 43.5 1695 ̶ 3389 26 ̶ 51 36 ̶ 87 5 ̶ 12 2.23 2.68 3.2 1291.3 72.7 125 ̶ 658 6 ̶ 32 2 ̶ 11 1 ̶ 5 TiOx 2.31 1.27 0.6 1323.8 91.6 23 ̶ 116 3 ̶ 12 4 ̶ 17 4 ̶ 16 3.53 1.22 1.4 1307.7 91.5 5 ̶ 13 1 ̶ 2 14 ̶ 34 0.5 ̶ 1 4.69 7.61 1.3 1301.4 87.9 20 ̶ 60 1 ̶ 2 8 ̶ 12 2 ̶ 4
We note that CNTs with larger diameters tend to possess a relatively higher density of structural defects and it is still challenging to tune the diameter and quality of the nanotube individually. Nevertheless, comparing the following two sets of our data reveals the dependences of water and nitrogen permeances
(per CNT) on the diameter and I(G)/I(D) of the CNTs – (i) CNT membranes with I(G)/I(D) > 2 and various
8 diameters and (ii) sub-2.5-nm CNT membranes with various I(G)/I(D) values (Figure 3). Several MD simulations20, 37 have predicted that large flow enhancement in a strong confinement regime can lead to inverse correlation of gas and water permeances with the nanotube diameter. Our data indeed confirms the higher permeances for small diameter CNTs and more importantly reveals that such a diameter dependence cannot be achieved when CNTs are considerably defective. In other words, the flow enhancement effect caused by CNT diameter can be nullified to a great extent by surface defects present on the nanotube wall.
To our knowledge, there has been no empirical research addressing the strong interplay between these structural parameters and the fluid flow behaviors of CNT membranes.
Figure 3. Per-CNT permeances of (a) water and (b) nitrogen gas through the VA-SWCNT membranes with respect to nanotube diameter (d), nanotube quality (I(G)/I(D)) and membrane thickness (L) (titania: squares, polyethylene: triangles, alumina: circles and alumina/epoxy: diamonds); black symbols denote the data from the CNTs with I(G)/I(D) > 2 in permeance-d diagrams, and those with d < 2.5 nm in permeance- I(G)/I(D) diagrams, respectively.
In general, enhanced mass transport has been quantified by so-called an enhancement factor (EF) defined as a ratio of the measured flow rate to the predicted channel flow: no-slip Hagen-Poiseuille flow model for
9 water (QHP) and Knudsen diffusion model (QKn) for gas. Calculated EFs of our membranes shows more than one-order-of-magnitude enhancement for gas flow and one-to-three order-of-magnitude enhancement for water flow (Table 1). EF is useful for evaluating the transport efficiency of CNT channels relative to other similarly sized nanoporous materials, yet, can be misleading when scaled by the individual structural factors of the membrane in order to find their correlation with flow enhancement. Figure 4 displays the plots of all the EF values available in this work and literature with respect to tube diameter (d), membrane thickness (L) and tube quality (I(G)/I(D)). EFs show an increasing tendency with the membrane thickness
(L). However, we notice that the membranes, which have a common structural feature of being far thicker than a few micrometers do not follow the diameter dependence (marked by dotted circles). Also, no conclusive correlation could be found between the EFs and the CNT quality, I(G)/I(D).
Figure 4. Dependence of the enhancement factors of (a) water and (b) nitrogen flows through CNTs on the nanotube length (membrane thickness, L), the nanotube diameter (d) and the nanotube quality (I(G)/I(D)): red filled and black empty symbols correspond to the experimental data plotted in Figure 3 and in literature39, 63-72, respectively.
10 Aspect ratio scaling for mass transport enhancement through CNT membranes
Water transport Previously, to express the flow rate of water through nanochannels, Sisan et al. introduced an analytical model, considering the resistance at the aperture (Sampson’s formula)73 and resistance inside the channel (Hagen-Poiseuille formalism with a slip boundary condition)74 and reported a theoretical continuum limit to the flow rates through nanochannels.40 Here, to include the effects of entrance shape47-48 and phonon-induced channel oscillation75 on the transport properties, we further modified the model using α and β factors:
−1 ∆P 1 3µµ 18L 1 QP= =∆+ , (1) water T 34 RRentrance++ channel αr βπ r 1 4/ br where µ is the dynamic viscosity of water, r is the CNT radius, and L is the CNT length, respectively. The slip length, b, quantifies the slippery drift of liquid along the nanotube and depends on diameter11, 37 and quality42-44, 76 of CNT. If we adopt the formalism used for gases and define a mean free path of liquids as the molecular diameter (e.g., ~0.24 nm for H2O), the Knudsen number (Kn) for a 1 – 2-nm-wide CNT will be in the range of 0.12 to 0.24. This range lies at the borderline between “slip flow” and “transitional flow”.
Thus, it is important to bear in mind that the continuum theory, such as Sampson’s flow across an orifice and Hagen-Poiseuille flow through a channel, would be valid only for the fluid flow through nanochannels or nanopores with lateral dimensions equal to or larger than ~2 nm, as in the cases of our VA-SWCNT membranes. We note that rentrance may differ from rchannel in case that open CNTs are not protruding and rather positioned below the membrane surface. A detailed and statistical analysis of the geometry and the exposed matrix material properties near open CNT entrances, however, is beyond the scope of this paper and its possible effect has been incorporated by factor α in Eq. (1). α accommodates the effect of geometry and chemical groups at the CNT mouth on the entrance resistance47, 77-79 (e.g., α >1 for hourglass-shaped entry as found in aquaporins or α <1 for the additional energy barrier present at the entrance), and β harbors the effect of the phonon-induced oscillation on the channel resistance75 (e.g., β >1 for MWCNTs
11 where the phonon vibration modes are shielded by multiple outer shells not in direct contact with the matrix). Eq. (1) can be rearranged for the flow rate in a slippery channel (b >> r) as follows:
−−11 13µµ 12 LL α2 =∆+ =⋅+α QP33 Qsampson 1 , (2) water αr βπ rb βπ3 b where α·Qsampson is the theoretical maximum corresponding to a flow in a nearly frictionless channel such as a perfect (or defect free) CNT or atomically thin porous graphene.9 Eq. (2) indicates that for short CNTs
(L << b) or nearly frictionless CNTs (b→∞), the entrance resistance becomes the limiting factor to the total flow rate. Otherwise, both resistances need be taken into account, and the diameter, length and quality of the CNT come into play in the transport mechanism. Interestingly, the ratio of the measured flow rate through our CNT membranes to the theoretical maximum, Qexp / α·Qsampson, is less than unity (Table 1). It points to the significant contribution of the channel resistance in the realistic cases of large L and smaller
I(G)/I(D). We conceive that once a CNT diameter determines a theoretical maximum flow rate, it appears to be the length and imperfect quality of the nanotube that decline the actual flow rate. From eq. (1), we deduce an expression for the enhancement factor, EF = Qexp / QHP, as a function of dimension (L and d) and slip length (b) of CNT as follows:
13QHP π d 1 = = + , (3) EF Qexp 16αβ L( 1+ 8 b / d ) where the first and second terms on the right hand side correspond to the entrance and channel resistances,
4 respectively, both normalized by the channel resistance of the no-slip Hagen-Poiseuille flow (128μL/πd ).
The inverse of the first term is the ratio of the Sampsonian flow prediction to Poiseuillian formalism whereas that of the second term the effect of the slippery channel. Eq. (3) shows that for cases of short or nearly frictionless CNTs (L << b or b→∞), EF reaches its theoretical maximum solely determined by the entrance resistance with the α factor: EF ≤ (16α/3π)·(L/d) (Sampsonian upper bound, marked by gray lines in Figure 5). Note that the validity of the upper bound set by the Sampson’s formula may weaken in a sub-
12 continuum regime, as implied in recent reports using nanopores on graphene80-81. In the sub-continuum regime, three- to one-dimensional transition of water hydrogen bonding network would take crucial part in the entrance resistance82. In order to overcome aforementioned limitations of using individual structural factors of the CNT membrane as a scale and to reveal the detailed transport characteristics such as transition from Sampsonian to Poiseuillian flows as predicted by eq. (3), we plot the EFs as a function of the aspect ratio (AR, or L/d) in Figure 5. This AR scaling not only reveals clearly the increasing trend of EF values but also provides an enriched representation of the flow enhancement factor, from which to obtain the following findings. First, the increasing tendency of EF with AR indicates that the water flow in CNT does not entirely scale with the length (L) in a Poiseuillian way but has the characteristics of 2D orifice flows.
Second, neither narrow but highly defective CNTs nor high-quality but wide CNTs could lead to the large
Figure 5. Scaling behavior of the enhancement factors (EF) for water transport through CNT membranes with respect to the aspect ratios (AR, L/d) of CNTs: VA-CNTs with titania, polyethylene and alumina/epoxy matrix (red filled squares triangles and diamonds), previous experimental (black filled symbols)28, 39, 64-66, 68, 70, 83 and simulation reports (black empty symbols)37-38, 84 in comparison to the Sampsonian upper bound (solid gray line). Inset shows the correlation between the deviation of EFs from Sampsonian flow and CNT quality featured by I(G)/I(D) found among sub-2.5-nm CNT membranes. The vertical and horizontal error bars, when present, indicate range of the density and diameters of nanotubes in the experiments, respectively.
13 flow enhancements. The largest EF value is obtained from the smallest CNTs with the highest I(G)/I(D) value (b>>d). It implies the collective importance of diameter (nano-confinement) and quality (surface hydrophobicity) of CNTs for flow enhancement.
Third, the membrane made out of more defective CNTs shows EF values that deviate more from
Sampsonian upper bound. It can be seen by comparing the three CNT/titania membranes having similar diameters around 2 nm, similar thicknesses within an order of magnitude, but different I(G)/I(D) values
(red highlighted area in Figure 5). The inset of Figure 5 displays the stronger deviation of EF from
Sampsonian upper bound with decreasing I(G)/I(D) ratio of the nanotubes. Eq. (3) predicts that even at the same L/d condition, lower EF will be obtained when the CNTs are very defective (b→d and/or β < 1).
Thanks to the use of SWCNTs, we could for the first time prove the correlation of flow enhancement with
I(G)/I(D) ratio. Note that Mattia et al.’s highly defective carbon nanopipes based membranes (d=15-60 nm) showed so far the most deviating EF values (Figure 5 black line symbols) from the Sampsonian upper bound 83, while EFs of Secchi et al.’s less defective CNTs having similar diameters are found close to the
Sampsonian upper bound (black filled triangles)28. Lastly, while all our EF values remain below the
Sampsonian prediction, some of the reported EF values in the literature are found above it. Even though one cannot fully rule out experimental uncertainties or unknown parameters, this overshoot can be explained by the larger α and β values, ascribed to the additional flow enhancement mechanisms such as the effects of the geometry and chemical groups at the CNT mouth (Figure S8) and of the coupling of water molecules with the low frequency phonon modes of CNT channels. Especially, the latter effect might be manifested for DW- or MWCNT membranes rather than SWCNT membranes. An interesting observation is that the large EF values beyond the Sampsonian upper bound are all reported from DW- or MWCNT membranes, while SWCNT membranes showed at least an order of magnitude lower EF values compared to the Sampsonian flow. Earlier, Walter et al. have claimed that EFs are length dependent for short CNTs
(≤ 300 nm) due to entrance and exit losses84, whereas for longer CNTs EF asymptote to 2 orders of magnitude over the continuum predictions, governed solely by the slip length. Eq. (3) also predicts the
14 asymptotic EF value of β·(1+8b/d) for long CNTs (L/d →∞), thus influenced by not only the slip length
(b), but also β factor. We believe, it would be rash to draw an absolute value of the theoretical limit due to the current limitations in defining slip length (b) and β factor.
Gas transport Dynamics of the gas transport can be understood in the framework of entrance and channel resistances. First, the resistance to the gas permeation at the pore opening can be described by the effusion mechanism as long as Kn=λ/d ≥1, placing the transport in the transition or free molecular regime.
The potential effect of the direct interaction between gas molecules and membrane surface22, 85, for instance via adsorption on the membrane exterior can be accommodated by the prefactor, α′. On the other hand, the channel resistance arises from the tight confinement and the surface adsorption of gases along the CNT.
The former is often described by Knudsen diffusion model86, which however assumes the nature of the collisions to be solely diffuse. Ideal defect-free CNTs can allow almost elastic specular collisions so that molecules retain the velocity component tangential to the surface and impose no resistance to the transport.
The Knudsen-Smoluchowski model87 counts such influences of specular reflections by the use of tangential momentum accommodation coefficient (TMAC, σv) as a measure of a portion of diffuse reflections, so as to correct the simple Knudsen diffusion by (2-σv)/σv. Estimated TMAC values of the CNT membranes in this work are 0.03-0.35, meaning that statistically 3-35 % of gas molecules randomize their reflection velocities upon collisions with the nanotube wall. The Knudsen-Smoluchowski model is to gas transport what the slip-modified Hagen-Poiseuille flow model is to water transport. There is, however, a major difference that the gas molecules can adsorb on the interior surface of CNT and diffuse along the generated concentration gradient even at an ambient pressure, according to Skoulidas et al.’s MD simulation20. The smaller the CNT diameter, the more the surface diffusion can contribute to the total transport, and the gas transport rates can be related to the CNT diameter in this way. Despite some pioneering efforts19, mechanistic details of the ballistic transport and surface diffusion in the CNT channel remain to be further unveiled. Here, we lump the Knudsen-Smoluchowski correction and the influence of surface diffusion to a
15 factor, γ. Accordingly, we express the total gas flow rate through a CNT, considering both entrance resistance (effusion) and channel resistance (modified Knudsen model counting coexisting mechanisms of specular transport and surface diffusion), as follows:
−1 −1 1 13Lπα MRT ′ 3L Q=∆+ Vππ r2 P21 MRT =+α′Q , (4) gas m effusion αγ′ 28rrγ8 where M is the molar weight, R is the universal gas constant, T is the absolute temperature, and Vm is the molar volume. While the mean free path, λ, equals to CNT diameter (d) for the Knudsen diffusion, it may correspond to the distance between surface scattering sites (in relation to the defect indicator of I(G)/I(D)) for defective CNTs and that it could approach the entire length of the nanotube for the ideal nearly frictionless CNT. Based on this total gas flow prediction, we express the enhancement factor, EF = Qexp /
QKn as a function of CNT dimensions (L and d) and γ as follows:
1Qd 41 =Kn = + , (5) EF Qexp 3αγ′ L where the first and second terms on the right hand side correspond to the entrance and channel resistances,
1/2 3 respectively, both normalized by the Knudsen diffusion resistance (3L(2πMRT) /πd Vm). The inverse of the first term is the ratio of the effusion rate to Knudsenian formalism whereas that of the second term is the effect of the channel smoothness. Gas flow enhancement approaches the maximum when the channel resistance part (γ) becomes negligible: EF ≤ (3α′/4)·(L/d). The prefactor α′ is supposedly close to unity for
Kn>1, while owing to molecular interaction with pore mouths, α′ could deviate from unity when d gets comparable to the molecular dimension85.
Similar to the case of water flow enhancement, we plot the EF values against the aspect ratio (AR, or L/d) to reveal the detailed transport characteristics such as transition from effusion-like to Knudsen-like flows as predicted by Eq. (5). Figure 6 shows the increasing tendency of EF with AR, revealing the characteristics of effusion invariant to the channel length or membrane thickness (L). Eq. (5) predicts that even at the same
L/d condition membranes with smaller α′ or γ lead to lower EF values, more strongly deviating from
16 effusion upper bound. Indeed, we observe the largest EF value is obtained from the smallest CNTs with the highest I(G)/I(D) value, that is, having the largest γ factor among our membranes and all the EF values in this study as well as in previous works are found far below the effusion upper bound. It is noticeable in the inset of Figure 6 that the I(G)/I(D) dependence of gas flow enhancement appear to be weaker than that of water flow enhancement. Also, EFs obtained from large diameter MWCNT membranes are found to deviate the most from effusion scaling. Although the nanotube quality of these membranes are unknown, this strong deviation shall be attributed to low γ (effect of molecular interaction with the defective CNT channel) as well as low α′(effect of molecular interaction at the CNT mouth.
Figure 6. Scaling behavior of the enhancement factors (EF) for gas transport through CNT membranes with respect to the aspect ratios (AR, L/d) of CNTs: VA-SWCNTs with titania, polyethylene and alumina matrices (red filled squares, triangles and circles) and previous experimental reports (black symbols)39, 64, 67-69, 71-72 in comparison to effusion model prediction (solid gray line). Inset shows the deviation of EFs from effusion flow for sub-2.5-nm CNT membranes with respect to CNT quality featured by I(G)/I(D). The vertical and horizontal error bars, when present, indicate range of the density and diameters of nanotubes in the experiments, respectively.
17 CONCLUSION Since the emergence of CNT nanofluidics, many uncertainties have sprung around the characteristics of the fast mass transport in CNTs. On one hand, it is because of the discrepancy between previous experiments and simulations performed in periodic boundary conditions, for relatively short times and with very simplified pore configuration. On the other hand, it is due to the insufficient experimental data obtained from well-controlled CNT membranes, hence the lack of a comprehensive understanding of the nanofluidic transport dynamics, to which conventional continuum flow theories cannot be blindly applicable. Devising the mechanical reinforcement step for preserving the delicate structure and the surface property of pristine VA-SWCNTs, we successfully fabricated a number of VA-SWCNT membranes with the coherent and reliable platforms and collect a valuable dataset of mass transport through SWCNTs to unveil the correlation of flow enhancement with the structural parameters of the membranes. In particular, the first experimental support for the effect of nanotube quality on enhanced mass transport is demonstrated.
It is hard to overstate the collective importance of diameter (nano-confinement effect) and quality (surface hydrophobicity and lubricity) of nanotubes for flow enhancement. Our observation that the conventional notion of enhancement factor (EF) do not scale well with the individual structural factors of the membrane led us to a new scaling of aspect ratio, with which we recognize the conceptual equivalence between the nearly frictionless CNT channel and the channel of zero thickness, an orifice. It engender us to explain the flow dynamics inside CNTs in the framework of entrance and channel resistances with the upper bound of transport efficiency that follows the scaling of the orifice model: e.g., Sampson’s formula for liquids and effusion dynamics for gases. For water transport in particular, the validity of this new scaling is further supported by the fact that most of the previous experimental and simulation data fall close to or below the
Sampsonian upper bound. In practice, the EF could deviate from the orifice scaling only in a negative direction, depending on the nanotube quality and other energy dissipation mechanism associated with the transport. We believe that considering the current limitations in defining slip length and additional flow enhancement or hindrance factors, it would be premature to draw an absolute value for the theoretical limit of flow enhancement. We expect further studies on the molecular origin of the AR scaling of the enhanced transport through CNT membranes and the decoupled manipulation of CNT structural parameters in CVD
18 synthesis. Comparative study with other 2D membranes sharing similar pore sizes, yet, atomically thin would be useful for understanding the structure-induced dynamics embracing the transition between the orifice and channel flow regimes under the graphitic confinement.
ACKNOWLEDGMENTS
We appreciate the support from the ETH Zurich microfabrication center (FIRST), ETH Zurich Scientific
Center for Optical and Electron Microscopy (SCOPE-M) and Binnig and Rohrer Nanotechnology Center
(BRNC) of ETH Zurich and IBM Zurich. J.B. and S.K.Y. thank the Swiss National Science Foundation for financial supports (200021-137964 and 200021-146856). M.L. appreciates partial financial support from
Saudi Arabia Basic Industry Corporation (SABIC). This work was also partly supported by LG Electronics
Advanced Research Institute, for which H.G.P is grateful. Three-dimensional AFM scan images of our
CNT membrane samples were obtained in courtesy of Bruker AG (Dr. Samuel Lesko).
AUTHOR CONTRIBUTIONS
H.G.P. and S.K.Y. conceived and designed the project. S.K.Y. and J.B. established the microfabrication process for the CNT membrane manufacturing. S.K.Y. and M.L. fabricated the membranes. S.K.Y and J.B. performed material analysis and mass transport experiments. S.K.Y. performed temperature-dependent measurements. S.K.Y. and H.G.P. analyzed the data for physical interpretation and wrote the manuscript.
19 REFERENCES
1. Park, H. G.; Jung, Y., Carbon nanofluidics of rapid water transport for energy applications. Chemical Society Reviews 2014, 43 (2), 565-576. 2. Farimani, A. B.; Heiranian, M.; Aluru, N. R., Electromechanical Signatures for DNA Sequencing through a Mechanosensitive Nanopore. The Journal of Physical Chemistry Letters 2015, 6 (4), 650-657. 3. Fornasiero, F.; Park, H. G.; Holt, J. K.; Stadermann, M.; Grigoropoulos, C. P.; Noy, A.; Bakajin, O., Ion exclusion by sub-2-nm carbon nanotube pores. Proceedings of the National Academy of Sciences 2008, 105 (45), 17250-17255. 4. Liu, C.; Gillette, E. I.; Chen, X.; Pearse, A. J.; Kozen, A. C.; Schroeder, M. A.; Gregorczyk, K. E.; Lee, S. B.; Rubloff, G. W., An all-in-one nanopore battery array. Nat Nano 2014, 9 (12), 1031-1039. 5. Wang, Q. H.; Bellisario, D. O.; Drahushuk, L. W.; Jain, R. M.; Kruss, S.; Landry, M. P.; Mahajan, S. G.; Shimizu, S. F. E.; Ulissi, Z. W.; Strano, M. S., Low Dimensional Carbon Materials for Applications in Mass and Energy Transport. Chemistry of Materials 2014, 26 (1), 172-183. 6. Shannon, M. A.; Bohn, P. W.; Elimelech, M.; Georgiadis, J. G.; Marinas, B. J.; Mayes, A. M., Science and technology for water purification in the coming decades. Nature 2008, 452 (7185), 301-310. 7. Plesa, C.; Verschueren, D.; Pud, S.; van der Torre, J.; Ruitenberg, J. W.; Witteveen, M. J.; Jonsson, M. P.; Grosberg, A. Y.; Rabin, Y.; Dekker, C., Direct observation of DNA knots using a solid-state nanopore. Nat Nano 2016, 11 (12), 1093-1097. 8. Siria, A.; Poncharal, P.; Biance, A.-L.; Fulcrand, R.; Blase, X.; Purcell, S. T.; Bocquet, L., Giant osmotic energy conversion measured in a single transmembrane boron nitride nanotube. Nature 2013, 494 (7438), 455-458. 9. Celebi, K.; Buchheim, J.; Wyss, R. M.; Droudian, A.; Gasser, P.; Shorubalko, I.; Kye, J.- I.; Lee, C.; Park, H. G., Ultimate Permeation Across Atomically Thin Porous Graphene. Science 2014, 344 (6181), 289-292. 10. Nair, R. R.; Wu, H. A.; Jayaram, P. N.; Grigorieva, I. V.; Geim, A. K., Unimpeded Permeation of Water Through Helium-Leak–Tight Graphene-Based Membranes. Science 2012, 335 (6067), 442-444. 11. Falk, K.; Sedlmeier, F.; Joly, L.; Netz, R. R.; Bocquet, L., Molecular Origin of Fast Water Transport in Carbon Nanotube Membranes: Superlubricity versus Curvature Dependent Friction. Nano Letters 2010, 10 (10), 4067-4073. 12. Joseph, S.; Aluru, N. R., Why Are Carbon Nanotubes Fast Transporters of Water? Nano Letters 2008, 8 (2), 452-458. 13. Ritos, K.; Mattia, D.; Calabrò, F.; Reese, J. M., Flow enhancement in nanotubes of different materials and lengths. The Journal of Chemical Physics 2014, 140 (1), 014702. 14. Thomas, M.; Corry, B., A computational assessment of the permeability and salt rejection of carbon nanotube membranes and their application to water desalination. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 2016, 374 (2060). 15. Secchi, E.; Niguès, A.; Jubin, L.; Siria, A.; Bocquet, L., Scaling Behavior for Ionic Transport and its Fluctuations in Individual Carbon Nanotubes. Physical Review Letters 2016, 116 (15), 154501. 16. Hummer, G.; Rasaiah, J. C.; Noworyta, J. P., Water conduction through the hydrophobic channel of a carbon nanotube. Nature 2001, 414 (6860), 188-190.
20 17. Pascal, T. A.; Goddard, W. A.; Jung, Y., Entropy and the driving force for the filling of carbon nanotubes with water. Proceedings of the National Academy of Sciences 2011, 108 (29), 11794-11798. 18. Barati Farimani, A.; Aluru, N. R., Existence of Multiple Phases of Water at Nanotube Interfaces. The Journal of Physical Chemistry C 2016, 120 (41), 23763-23771. 19. Noy, A., Kinetic Model of Gas Transport in Carbon Nanotube Channels. The Journal of Physical Chemistry C 2013, 117 (15), 7656-7660. 20. Skoulidas, A. I.; Sholl, D. S.; Johnson, J. K., Adsorption and diffusion of carbon dioxide and nitrogen through single-walled carbon nanotube membranes. The Journal of Chemical Physics 2006, 124 (5), 054708. 21. Cooper, S. M.; Cruden, B. A.; Meyyappan, M.; Raju, R.; Roy, S., Gas Transport Characteristics through a Carbon Nanotubule. Nano Letters 2004, 4 (2), 377-381. 22. Newsome, D. A.; Sholl, D. S., Influences of Interfacial Resistances on Gas Transport through Carbon Nanotube Membranes. Nano Letters 2006, 6 (9), 2150-2153. 23. Hinds, B. J.; Chopra, N.; Rantell, T.; Andrews, R.; Gavalas, V.; Bachas, L. G., Aligned Multiwalled Carbon Nanotube Membranes. Science 2004, 303 (5654), 62-65. 24. Liu, H.; He, J.; Tang, J.; Liu, H.; Pang, P.; Cao, D.; Krstic, P.; Joseph, S.; Lindsay, S.; Nuckolls, C., Translocation of Single-Stranded DNA Through Single-Walled Carbon Nanotubes. Science 2010, 327 (5961), 64-67. 25. Pang, P.; He, J.; Park, J. H.; Krstić, P. S.; Lindsay, S., Origin of Giant Ionic Currents in Carbon Nanotube Channels. ACS Nano 2011, 5 (9), 7277-7283. 26. Choi, W.; Ulissi, Z. W.; Shimizu, S. F. E.; Bellisario, D. O.; Ellison, M. D.; Strano, M. S., Diameter-dependent ion transport through the interior of isolated single-walled carbon nanotubes. Nat Commun 2013, 4. 27. Liu, L.; Yang, C.; Zhao, K.; Li, J.; Wu, H.-C., Ultrashort single-walled carbon nanotubes in a lipid bilayer as a new nanopore sensor. Nature Communications 2013, 4, 2989. 28. Secchi, E.; Marbach, S.; Niguès, A.; Stein, D.; Siria, A.; Bocquet, L., Massive radius- dependent flow slippage in carbon nanotubes. Nature 2016, 537 (7619), 210-213. 29. Geng, J.; Kim, K.; Zhang, J.; Escalada, A.; Tunuguntla, R.; Comolli, L. R.; Allen, F. I.; Shnyrova, A. V.; Cho, K. R.; Munoz, D.; Wang, Y. M.; Grigoropoulos, C. P.; Ajo-Franklin, C. M.; Frolov, V. A.; Noy, A., Stochastic transport through carbon nanotubes in lipid bilayers and live cell membranes. Nature 2014, 514 (7524), 612-615. 30. Kim, K.; Geng, J.; Tunuguntla, R.; Comolli, L. R.; Grigoropoulos, C. P.; Ajo-Franklin, C. M.; Noy, A., Osmotically-Driven Transport in Carbon Nanotube Porins. Nano Letters 2014, 14 (12), 7051-7056. 31. Ahn, C. H.; Baek, Y.; Lee, C.; Kim, S. O.; Kim, S.; Lee, S.; Kim, S.-H.; Bae, S. S.; Park, J.; Yoon, J., Carbon nanotube-based membranes: Fabrication and application to desalination. Journal of Industrial and Engineering Chemistry 2012, 18 (5), 1551-1559. 32. Kannam, S. K.; Todd, B. D.; Hansen, J. S.; Daivis, P. J., How fast does water flow in carbon nanotubes? The Journal of Chemical Physics 2013, 138 (9), 094701. 33. Guo, S.; Meshot, E. R.; Kuykendall, T.; Cabrini, S.; Fornasiero, F., Nanofluidic Transport through Isolated Carbon Nanotube Channels: Advances, Controversies, and Challenges. Advanced Materials 2015, 27 (38), 5726-5737. 34. Sokhan, V. P.; Nicholson, D.; Quirke, N., Fluid flow in nanopores: Accurate boundary conditions for carbon nanotubes. The Journal of Chemical Physics 2002, 117 (18), 8531-8539.
21 35. Cottin-Bizonne, C.; Cross, B.; Steinberger, A.; Charlaix, E., Boundary Slip on Smooth Hydrophobic Surfaces: Intrinsic Effects and Possible Artifacts. Physical Review Letters 2005, 94 (5), 056102. 36. Xu, B.; Li, Y.; Park, T.; Chen, X., Effect of wall roughness on fluid transport resistance in nanopores. The Journal of Chemical Physics 2011, 135 (14), 144703. 37. Thomas, J. A.; McGaughey, A. J. H., Water Flow in Carbon Nanotubes: Transition to Subcontinuum Transport. Physical Review Letters 2009, 102 (18), 184502. 38. Thomas, J. A.; McGaughey, A. J. H., Reassessing Fast Water Transport Through Carbon Nanotubes. Nano Letters 2008, 8 (9), 2788-2793. 39. Holt, J. K.; Park, H. G.; Wang, Y.; Stadermann, M.; Artyukhin, A. B.; Grigoropoulos, C. P.; Noy, A.; Bakajin, O., Fast Mass Transport Through Sub-2-Nanometer Carbon Nanotubes. Science 2006, 312 (5776), 1034-1037. 40. Sisan, T. B.; Lichter, S., The end of nanochannels. Microfluidics and Nanofluidics 2011, 11 (6), 787-791. 41. Nicholls, W. D.; Borg, M. K.; Lockerby, D. A.; Reese, J. M., Water transport through (7,7) carbon nanotubes of different lengths using molecular dynamics. Microfluidics and Nanofluidics 2012, 12 (1), 257-264. 42. Joly, L.; Tocci, G.; Merabia, S.; Michaelides, A., Strong Coupling between Nanofluidic Transport and Interfacial Chemistry: How Defect Reactivity Controls Liquid–Solid Friction through Hydrogen Bonding. The Journal of Physical Chemistry Letters 2016, 7 (7), 1381-1386. 43. Nicholls, W. D.; Borg, M. K.; Lockerby, D. A.; Reese, J. M., Water transport through carbon nanotubes with defects. Molecular Simulation 2012, 38 (10), 781-785. 44. Songyan, L.; Peng, X.; Hangjun, L.; Xiaojing, G.; Kefei, W.; Rongzheng, W.; Haiping, F., Water permeation across nanochannels with defects. Nanotechnology 2008, 19 (10), 105711. 45. Picher, M.; Navas, H.; Arenal, R.; Quesnel, E.; Anglaret, E.; Jourdain, V., Influence of the growth conditions on the defect density of single-walled carbon nanotubes. Carbon 2012, 50 (7), 2407-2416. 46. Vinten, P.; Marshall, P.; Lefebvre, J.; Finnie, P., Thermodynamic and Energetic Effects on the Diameter and Defect Density in Single-Walled Carbon Nanotube Synthesis. The Journal of Physical Chemistry C 2013, 117 (7), 3527-3536. 47. Gravelle, S.; Joly, L.; Ybert, C.; Bocquet, L., Large permeabilities of hourglass nanopores: From hydrodynamics to single file transport. The Journal of Chemical Physics 2014, 141 (18), 18C526. 48. Gravelle, S.; Joly, L.; Detcheverry, F.; Ybert, C.; Cottin-Bizonne, C.; Bocquet, L., Optimizing water permeability through the hourglass shape of aquaporins. Proceedings of the National Academy of Sciences 2013, 110 (41), 16367-16372. 49. Belin, C.; Joly, L.; Detcheverry, F., Optimal shape of entrances for a frictionless nanochannel. Physical Review Fluids 2016, 1 (5), 054103. 50. Youn, S. K.; Park, H. G., Morphological Evolution of Fe–Mo Bimetallic Catalysts for Diameter and Density Modulation of Vertically Aligned Carbon Nanotubes. The Journal of Physical Chemistry C 2013, 117 (36), 18657-18665. 51. Youn, S. K.; Yazdani, N.; Patscheider, J.; Park, H. G., Facile diameter control of vertically aligned, narrow single-walled carbon nanotubes. RSC Advances 2013, 3 (5), 1434-1441. 52. Buchheim, J.; Park, H. G., Failure Mechanism of the Polymer Infiltration of Carbon Nanotube Forests. 2016, 27 (46), 464002.
22 53. Tawfick, S.; Zhao, Z.; Maschmann, M.; Brieland-Shoultz, A.; De Volder, M.; Baur, J. W.; Lu, W.; Hart, A. J., Mechanics of Capillary Forming of Aligned Carbon Nanotube Assemblies. Langmuir 2013, 29 (17), 5190-5198. 54. Zhang, Y.; Guerra-Nuñez, C.; Li, M.; Michler, J.; Park, H. G.; Rossell, M. D.; Erni, R.; Utke, I., High Conformity and Large Domain Monocrystalline Anatase on Multiwall Carbon Nanotube Core–Shell Nanostructure: Synthesis, Structure, and Interface. Chemistry of Materials 2016, 28 (10), 3488-3496. 55. Einarsson, E.; Shiozawa, H.; Kramberger, C.; Rümmeli, M. H.; Grüneis, A.; Pichler, T.; Maruyama, S., Revealing the Small-Bundle Internal Structure of Vertically Aligned Single-Walled Carbon Nanotube Films. The Journal of Physical Chemistry C 2007, 111 (48), 17861-17864. 56. Yazdani, N.; Chawla, V.; Edwards, E.; Wood, V.; Park, H. G.; Utke, I., Modeling and optimization of atomic layer deposition processes on vertically aligned carbon nanotubes. Beilstein Journal of Nanotechnology 2014, 5, 234-244. 57. Guerra-Nunez, C.; Zhang, Y.; Li, M.; Chawla, V.; Erni, R.; Michler, J.; Park, H. G.; Utke, I., Morphology and crystallinity control of ultrathin TiO2 layers deposited on carbon nanotubes by temperature-step atomic layer deposition. Nanoscale 2015, 7 (24), 10622-10633. 58. Babu, J. S.; Sathian, S. P., The role of activation energy and reduced viscosity on the enhancement of water flow through carbon nanotubes. The Journal of Chemical Physics 2011, 134 (19), 194509. 59. Korson, L.; Drost-Hansen, W.; Millero, F. J., Viscosity of water at various temperatures. The Journal of Physical Chemistry 1969, 73 (1), 34-39. 60. Wang, H.; Chung, T.-S.; Tong, Y. W.; Jeyaseelan, K.; Armugam, A.; Chen, Z.; Hong, M.; Meier, W., Highly Permeable and Selective Pore-Spanning Biomimetic Membrane Embedded with Aquaporin Z. Small 2012, 8 (8), 1185-1190. 61. Kumar, M.; Grzelakowski, M.; Zilles, J.; Clark, M.; Meier, W., Highly permeable polymeric membranes based on the incorporation of the functional water channel protein Aquaporin Z. Proceedings of the National Academy of Sciences 2007, 104 (52), 20719-20724. 62. Zeidel, M. L.; Ambudkar, S. V.; Smith, B. L.; Agre, P., Reconstitution of functional water channels in liposomes containing purified red cell CHIP28 protein. Biochemistry 1992, 31 (33), 7436-7440. 63. Majumder, M.; Chopra, N.; Andrews, R.; Hinds, B. J., Nanoscale hydrodynamics: Enhanced flow in carbon nanotubes. Nature 2005, 438 (7064), 44-44. 64. Majumder, M.; Chopra, N.; Hinds, B. J., Mass Transport through Carbon Nanotube Membranes in Three Different Regimes: Ionic Diffusion and Gas and Liquid Flow. ACS Nano 2011, 5 (5), 3867-3877. 65. Du, F.; Qu, L.; Xia, Z.; Feng, L.; Dai, L., Membranes of Vertically Aligned Superlong Carbon Nanotubes. Langmuir 2011, 27 (13), 8437-8443. 66. Baek, Y.; Kim, C.; Seo, D. K.; Kim, T.; Lee, J. S.; Kim, Y. H.; Ahn, K. H.; Bae, S. S.; Lee, S. C.; Lim, J.; Lee, K.; Yoon, J., High performance and antifouling vertically aligned carbon nanotube membrane for water purification. Journal of Membrane Science 2014, 460, 171-177. 67. Ge, L.; Wang, L.; Du, A.; Hou, M.; Rudolph, V.; Zhu, Z., Vertically-aligned carbon nanotube membranes for hydrogen separation. RSC Advances 2012, 2 (12), 5329-5336. 68. Kim, S.; Fornasiero, F.; Park, H. G.; In, J. B.; Meshot, E.; Giraldo, G.; Stadermann, M.; Fireman, M.; Shan, J.; Grigoropoulos, C. P.; Bakajin, O., Fabrication of flexible, aligned carbon nanotube/polymer composite membranes by in-situ polymerization. Journal of Membrane Science 2014, 460, 91-98.
23 69. Zhang, L.; Zhao, B.; Wang, X.; Liang, Y.; Qiu, H.; Zheng, G.; Yang, J., Gas transport in vertically-aligned carbon nanotube/parylene composite membranes. Carbon 2014, 66, 11-17. 70. Lee, K.-J.; Park, H.-D., The most densified vertically-aligned carbon nanotube membranes and their normalized water permeability and high pressure durability. Journal of Membrane Science 2016, 501, 144-151. 71. Bui, N.; Meshot, E. R.; Kim, S.; Peña, J.; Gibson, P. W.; Wu, K. J.; Fornasiero, F., Ultrabreathable and Protective Membranes with Sub-5 nm Carbon Nanotube Pores. Advanced Materials 2016, 28 (28), 5871-5877. 72. Park, H. G. Mass Transport through Carbon Nanotubes. Dissertation, University of California, Berkeley, 2007. 73. Sampson, R. A., On Stokes's Current Function. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 1891, 182, 449-518. 74. Happel, J., Brenner, H., Low Reynolds number hydrodynamics. Springer Netherlands: 1983; Vol. 1. 75. Ma, M.; Grey, F.; Shen, L.; Urbakh, M.; Wu, S.; Liu, J. Z.; Liu, Y.; Zheng, Q., Water transport inside carbon nanotubes mediated by phonon-induced oscillating friction. Nat Nano 2015, 10 (8), 692-695. 76. Lee, K. P.; Leese, H.; Mattia, D., Water flow enhancement in hydrophilic nanochannels. Nanoscale 2012, 4 (8), 2621-2627. 77. Song, Z.; Xu, Z., Ultimate Osmosis Engineered by the Pore Geometry and Functionalization of Carbon Nanostructures. Scientific Reports 2015, 5, 10597. 78. Heiranian, M.; Farimani, A. B.; Aluru, N. R., Water desalination with a single-layer MoS2 nanopore. Nat Commun 2015, 6. 79. Majumder, M.; Chopra, N.; Hinds, B. J., Effect of Tip Functionalization on Transport through Vertically Oriented Carbon Nanotube Membranes. Journal of the American Chemical Society 2005, 127 (25), 9062-9070. 80. Suk, M. E.; Aluru, N. R., Molecular and continuum hydrodynamics in graphene nanopores. RSC Advances 2013, 3 (24), 9365-9372. 81. O’Hern, S. C.; Jang, D.; Bose, S.; Idrobo, J.-C.; Song, Y.; Laoui, T.; Kong, J.; Karnik, R., Nanofiltration across Defect-Sealed Nanoporous Monolayer Graphene. Nano Letters 2015, 15 (5), 3254-3260. 82. Kalra, A.; Garde, S.; Hummer, G., Osmotic water transport through carbon nanotube membranes. Proceedings of the National Academy of Sciences 2003, 100 (18), 10175-10180. 83. Mattia, D.; Leese, H.; Lee, K. P., Carbon nanotube membranes: From flow enhancement to permeability. Journal of Membrane Science 2015, 475, 266-272. 84. Walther, J. H.; Ritos, K.; Cruz-Chu, E. R.; Megaridis, C. M.; Koumoutsakos, P., Barriers to Superfast Water Transport in Carbon Nanotube Membranes. Nano Letters 2013, 13 (5), 1910- 1914. 85. Drahushuk, L. W.; Strano, M. S., Mechanisms of Gas Permeation through Single Layer Graphene Membranes. Langmuir 2012, 28 (48), 16671-16678. 86. Steckelmacher, W., Knudsen flow 75 years on: the current state of the art for flow of rarefied gases in tubes and systems. Reports on Progress in Physics 1986, 49 (10), 1083. 87. v. Smoluchowski, M., Zur kinetischen Theorie der Transpiration und Diffusion verdünnter Gase. Annalen der Physik 1910, 338 (16), 1559-1570.
24
Supplementary Information
Scaling the Mass Transport Enhancement through Carbon Nanotube Membranes
Seul Ki Youn, Jakob Buchheim, Mahesh Lokesh, Hyung Gyu Park*
Nanoscience for Energy Technology and Sustainability, Department of Mechanical and Process Engineering, Swiss Federal Institute of Technology (ETH) Zurich, Tannenstrasse 3, Zurich CH-8092, Switzerland *Corresponding author: [email protected]
Contents I. Structural and flow enhancement properties of the previously reported CNT membranes II. Fabrication and characterization of CNT membranes A. CVD Synthesis of VA-SWCNTs B. Fabrication of VA-SWCNT membrane via mechanical reinforcement C. Opening the CNT Membrane via surface etching process D. Characterization of pristine VA-SWCNTs and permeable CNT Membranes III. Mass transport measurement across CNT membranes A. Nitrogen gas measurement B. Water flow measurement C. Temperature dependent water flow measurement
IV. Effect of additional flow enhancement or hindrance factor, α and β on the scaling behavior of water flow enhancement factors with the aspect ratios (AR, L/d) of CNTs
1 I. Structural and flow enhancement properties of the previously reported CNT membranes
Table S1. Summary of the basic properties of CNT membranes and enhancement factors defined by the ratio of experimentally obtained flux (Q) to the corresponding channel-flow-model prediction: Knudsen diffusion (Kn) for gas and Hagen-Poiseuille flow (HP) for water (SW, DW, FW and MW stand for single- walled, double-walled, few-walled and multi-walled, respectively.)
Gas flow Water flow CNT CNT Membrane CNT enhancement enhancement Ref. Matrix diameter density thickness type factor factor (nm) (1010/cm2) (μm) (Qexp / QKn) (Qexp / QHP) 1-2 Polystyrene MW 6-7 6 34-126 28-32 44,000-76,000 3 SiNx(<4/3) DW 1.3-2.0 25 2.0 16-120 560-8,400 4 Epoxy DW 10 2.4 ≤ 4,000 ̶ 388,709 MW 5.1 0.5-0.8 105 30-80 ̶ 5 Epoxy 7.7 0.9-1.3 110 30-60 ̶ 6 Epoxy - 4.8 6.8 200 ̶ 70,000 7 Polystyrene SW/DW 3.3 20 20-50 118 366 8 Parylene-C FW 7-8 0.17 10 34.9-39.0 ̶ 9 Polyurethane FW 4.1 300 1000 ̶ 155,043 10 Parylene-N SW 3.3 50-65 23 50 87-326
II. Fabrication and characterization of CNT membranes
A. CVD Synthesis of VA-SWCNTs: 4″ Si wafer ((100), 525 µm thick) coated with low stress SiNx is photolithographically patterned using photoresist (PR) AZ4515. PR pattern is transferred to 150 nm thick
SiNx, forming a hard mask through reactive ion etching with CHF3/O2 plasma. Etching for 30 hr in 44%
KOH solution at 60°C forms 89 micropits, at the bottom of which have ~20 um thick freestanding Si layer.
Remaining SiNx is removed by the RIE process mentioned above and the wafer is finally cleaned in buffered
HF solution for 8 min. As catalysts for growing VACNTs, AlOx (20 nm) and Fe (0.1-0.4 nm) films are sequentially deposited on membrane frame by ALD and e-beam evaporation. Catalytic CVD is performed in a cold-wall, vertical CVD reactor (6 inch Black Magic, Aixtron) (Table S2). First, the membrane frame is introduced into a low pressure CVD chamber at 300 oC. Then, the chamber temperature is raised to a
o target value at a fast ramp rate of 300 C/min in Ar or H2 condition (total pressure of 200 mbar) and kept for 0.5-5 minutes for catalyst activation. For CNT growth, H2 flow is replaced by Ar flow or mixed with
Ar flow and C2H2 (>99.6%, PanGas) is supplied for 20-60 sec.
2 Table S2. Summary of CVD parameters for controlled growth of VA-SWCNTs CNT Growth Fe catalyst Pre-annealing Growth Partial pressure diameter temperature condition duration of acetylene (nm) o (nm) ( C) (H2%, min) (H2%, sec) (mbar) 1.93 0.1 700 0, 0.5 0, 20 0.03 2.10 0.2 720 70, 2 70, 130 0.03 2.15 0.15 700 0, 1 0, 30 0.03 2.39 0.2 720 0, 2.5 0, 40 0.03 3.62 0.3 720 0, 5 0, 30 0.1 4.15 0.4 750 0, 5 0, 30 0.1 2.11 0.1 720 0, 5 0, 60 0.03 2.23 0.2 720 20, 3 20, 60 0.1 2.31 0.1 720 0, 5 0, 60 0.1 3.34 0.8 750 55, 2 55, 180 0.05 3.53 0.2 740 40, 3 0, 30 0.1 4.69 0.3 740 40, 3 0, 30 0.1
B. Fabrication of VA-SWCNT membrane via mechanical reinforcement Conformal coating of
VA-SWCNTs is conducted in an ALD reactor (Picosun Sunale) at 150-200 oC. Each ALD cycle consists of 3 pulses (0.5-1 sec) of TMA (trimethyl-aluminum) or TIP (titanium isopropoxide) and 3 pulses (0.5-1 sec) of water vapor with 10 sec N2 purges in between the pulses. AlOx and TiOx growth-per-cycle rate on a flat Si substrate at the given ALD condition is 0.1 nm/cycle and 0.03 nm/cycle. We run about 100-150 ALD cycles to produce mechanically reinforced VA-SWCNTs with sufficiently large inter-bundle spacing. As shown in Figure S1, this mechanical reinforcement step help the pristine VA-SWCNTs preserving their initial alignment and morphology without affecting the surface property of the nanotube interiors. For the complete infiltration of impermeable matrix materials, we either (i) fill the gap with polymers via thin polymer film melts and in-situ polymerization or (ii) keep depositing the metal oxides via ALD (ii). For the gap filling by polymer melts, we prepare a thin film of thermoplastic polyethylene (Mw ~35,000, Aldrich) with the thickness corresponding to the height of target VA-SWCNTs using microtoming and place it on top of VA-SWCNTs covering the surface evenly. When heated to the Tm of PE under vacuum, the PE melts gradually penetrates into the structure, fills up the rest of the spaces within 5-6 hours. The PE melt with low surface energy favors to wet high energy ALD coated surface11 and is known to spread in complete wetting
12 mode thanks to its low viscosity in molten state . When heated at Tm that is below its Ts, the PE chains flow not like a liquid but only creep flowing down along the ALD coated surface without forming a
3 microscopic meniscus across the gap13-14. For the gap filling via in-situ polymerization of VACNTs/epoxy, we prepare a homogeneous mixture of 10 mL RIM-235 and 4 mL RIM-238 (Hexion Chemicals). 100 uL of the epoxy mixture was pipetted over the top surface of VACNTs structure placed in a vacuum desiccator.
After pulling a vacuum for 2 minutes to promote the infiltration, the sample was taken out and spun for 1 minute at 400 rpm in order to remove the excess polymer on top of the VACNTs structure. After repeating this process of epoxy infiltration and excess removal three times, the membrane was cured in an oven at 50 oC for 2 days. For approach (ii), we conduct continuous “dry” ALD process of metal oxide in a plasma enhanced ALD system (Oxford instrument) using tetrakis-dimethyl-amido titanium (TDMAT) and ozone at 120 oC. Each ALD cycle consists of a pulse (1.5 sec) of TDMAT and a pulse of ozone (10 sec) with 8 sec N2 purges in between the pulses. TiOx growth-per-cycle rate on a flat Si substrate at the given ALD condition is 0.03-0.05 nm/cycle. We run 1200-1600 ALD cycles to fill up the remaining gaps completely.
Figure S1. Effect of ALD process on the interior surface property of VA-SWCNTs; (a) change of Raman G-to-D ratios with respect to the number of ALD cycles, (b) Raman spectra (λ = 785 nm) of as-grown, ALD coated and regenerated VA-SWCNTs; no change observed in the Raman spectrum after the removal of ALD coating attests the intactness of CNT surface by ALD process; It indicates that the interiors of CNTs are not exposed to the gas phase reactants of ALD process, (c) SEM image of the cross-section of ALD-coated SWCNT bunch for mechanical reinforcement, (d) TEM image of the ALD-coated SWCNTs that are mechanically detached from catalyst substrate and dispersed by sonication and (e) cross-sectional TEM image of the VA-SWCNTs/titania membrane taken with the beam perpendicular to the nanotube axis.
C. Opening the CNT Membrane via surface etching process For membrane opening, first the excess polyethylene (PE) layer on the top of the membrane is removed by gentle O2 ion milling till the ALD coated surface appears. Ion milling using 20 sccm O2 at a beam current of 250 mA, 600V beam energy and
70° incident angle selectively etches the PE at 70 nm/min but does not remove the PE from the gaps. In
4 case of VACNTs/AlOx-epoxy membrane, the top surface was opened by 5 to 10 minutes of reactive ion etching (RIE) with a mixture of Ar and O2 gases at the RF power of 150 W and the chamber pressure of 20 mTorr, followed by 35 minutes of Ar ion beam milling. The remaining freestanding Si layer of micropits on the backside of the membrane is removed by XeF2 etching to expose the catalyst layer, which is subsequently removed by Ar ion milling using a 250 mA, 600V ion beam at 70° incident angle. After exposing the CNT on the back side, CNT tips on the top side of the membrane are exposed and uncapped from polymer and ALD coating by the sequential Ar ion beam milling with an etch rate of 10-20 nm/min.
We thoroughly monitor the nitrogen permeance of the membrane and continue to etch until it reaches the maximum to make sure all the CNT channels across the membrane become open (Figure S2).
Figure S2. Nitrogen gas permeance with ion milling etching time; the more the CNTs are open by etching, the more permeable the membrane becomes and the permeance reaches a plateau/maximum when all CNTs are open. Black circles and blue squares correspond to VA-SWCNT membranes with d=3.62 nm and d=2.11 nm, respectively. The remaining Si and exposed iron-alumina catalyst layer on the bottom side of the membrane were completely removed by XeF2 and Ar ion milling prior to the CNT tip opening on the top side of the membrane. Depending on the thickness of the excess layer on the top side of membrane, 10 to 30 minutes of initial etching is required for initiating the CNT opening.
5 D. Characterization of pristine VA-SWCNTs and permeable CNT Membranes
Figure S3. TEM diameter histogram of pristine VA-SWCNTs used for membrane fabrication
6 The diameter distributions of nanotubes were obtained by TEM (Philips CM12, 100 keV) imaging of pristine VA-SWCNTs dispersed in ethanol by sonication (Figure S3). For CNT number density, the upper limits were estimated based on the AFM images of catalyst nanoparticles formed at CVD condition
(Asylum Research MFP-3DTM) and the lower limits were derived from the SEM images of open membrane surface or the TEM image of the FIB-cut membrane cross-section or from KCl diffusion experiments as used in the previous literature15 (Figure S4, Table S3). TEM specimen (dimension: 12 × 3 × 5 µm) was cut using dual beam FIB (FEI Helios 450), either vertically or laterally from membrane surface using Ga ions at 30 kV and 9.4 nA current and glued on a TEM grid to further thin down to 120 nm using a Ga beam at
30kV and 0.77pA. The sample was then gently cleaned and further thinned to 50 nm using 5kV and 120 nA.
Figure S4. Determination of CNT areal densities based on the number of nanotubes counted from (a) AFM image of catalyst particles formed at CVD condition (~2.0 × 1015 m-2), (b) SEM image of open membrane surface (~6.11 × 1014 m-2) and (c) TEM images of FIB-cut membrane cross-section (~5.58 × 1014 m-2).
7 Table S3. Effective membrane areas and CNT densities of VACNT membranes fabricated in this work.
CNT diameter CNT density Membrane CNT diameter CNT density Membrane (d, nm) (1010/cm2) area (cm2) (d, nm) (1010/cm2) area (cm2) -2 -2 1.93 (0.75 ̶ 2.95) 10 ̶ 20 1.3 × 10 2.11 (1.21 ̶ 3.12) 25 ̶ 50 2.4 × 10 -3 -3 2.15 (1.15 ̶ 3.05) 8 ̶ 20 4.1 × 10 2.23 (1.05 ̶ 3.60) 3.7 ̶ 20 0.7 × 10 -3 -2 2.39 (1.40 ̶ 3.95) 6 ̶ 20 9.4 × 10 2.31 (1.35 ̶ 3.70) 10 ̶ 50 2.3 × 10 -2 -2 3.62 (2.25 ̶ 4.73) 9 ̶ 20 1.3 × 10 3.53 (2.03 ̶ 5.22) 6 ̶ 20 0.8 × 10 -3 -2 4.15 (2.35-5.40) 5.5 ̶ 15 0.8 × 10 4.69 (2.55 ̶ 5.90) 5 ̶ 15 1.7 × 10 -2 -2 2.10 (0.79 – 4.48) 9.3 – 20 1.3 × 10 3.34 (2.08 ̶ 4.52) 2.3 – 5 1.7 × 10
The quality of VA-SWCNTs was analyzed by and Raman spectroscopy (Renishaw RM 1000, 785 nm excitation) (Figure S5). Whereas the nanotube diameters are directly measured by TEM, CNT crystallinity can only be deduced from disorder-induced peak (D band) frequencies and intensities in the Raman spectra of the bulk CNTs sample16. The intensity ratio of the G band to the D band, I(G)/I(D) is indicative of the surface defect density of the CNT sample. In this work, CNT samples were so thick that the underlying Si substrate was not visible in the Raman spectrum. Because the laser spot size and penetration depth remain constant, the total volume of the VA-SWCNT sample contributing to the Raman signal remains constant, and thus the I(G)/I(D) ratio can provide a meaningful measure of the density of defects. Also, the linewidth
17 broadening of D band indicates the high density of structural defects (Ds) and/or the presence of defective
18 carbonaceous impurities (Di) that lead to multiple peaks at lower frequencies. We observed a single D band peak and used the D and G+ band peaks for calculating the I(G)/I(D).
8 Figure S5. Raman Spectrum of as grown VA-SWCNTs used for membrane fabrication commonly contains the two dominant Raman features at around 1350 cm-1 and 1580 cm-1, the disorder-induced D band and the tangential (G band) band.19 Other weak features appearing at higher frequencies are the M band (an overtone mode, ~1740 cm-1) and the iTOLA band (a combination of optical and acoustic modes, ~1950 cm-1, known 20-21 to depend on the tube diameter and chirality, and the energy of van Hove singularity relative to Elaser.
During membrane opening process, the etched surface of the CNT membrane was continuously analyzed using SEM to detect the open CNT tips (Figure S6). Once the etching process is completed, the effective
9 membrane area determined by imaging the areas of micropits one-by-one using SEM (Table 3, Figure 7).
Membrane thickness was determined by SEM imaging (Zeiss ULTRA 55) of the FIB-cut cross section of
CNT membrane after complete etching (Figure S8). Also, the surface morphology of open VA-SWCNT membranes was analyzed in air or water using AFM (Bruker Dimension ICON microscope) using peak force tapping mode with a single super-sharp probe (0.2 N/m) (Figure S9). In order to check the absence of large pinholes or cracks, size exclusion tests with 5-nm gold nanoparticle solution were performed by mounting the membrane in an O-ring sealed, dead-end flow cell (Figure S10). Approximately 3 mL of analyte solution was placed into the top side of the membrane through transparent tubing, with the bottom side kept dry. The top side was pressurized to ~300 mbar and the liquid emerging from the bottom side of the membrane was collected into a reservoir. The presence of gold nanoparticle in the permeate solution and the remaining gold nanoparticles on the membrane surface on the feed side were checked by UV-
Visible spectroscopy and SEM imaging, respectively.
10 Figure S6. Top-view SEM images of the (etched) surface of the VA-SWCNT membrane as etching proceeds using reactive ion etching (RIE) and ion beam milling. Both RIE and ion beam milling techniques are used for the membranes (a) with a polymer matrix, while only the Ar ion beam milling is used for the membrane (b) with an inorganic matrix such as alumina.
Figure S7. Top-view SEM image of open VACNT membrane freestanding (indicated by dashed line) on the micro-patterned Si chip (shown in low magnification as an inset) after the completion of Si and catalyst underlayer to determine effective membrane area, also summarized in Table S3
11 Figure S8. Cross-sectional SEM images of VA-SWCNTs membrane (a) before and (b) after etching process;
Figure S9. Additional AFM images (3D height and peak force error) of the maximally permeable VA- SWCNT/titania membrane surface immersed (a) in air and (b) in water; it shows pothole-like features all over the surface area and the conical shaped entrance region of open CNT tips.
Figure S10. Filtration of 5-nm-large colloidal gold nanoparticles through the VA- SWCNT/titania membranes; all the nanoparticles remained on the feed side surface of the membrane (evidenced by the photograph and the EDX spectrum on the right hand side), and the permeate liquid remained free of particles (according to the photograph and a UV-Vis spectrum (not shown here)).
12 III. Mass transport measurement across CNT membranes
A. Nitrogen gas flow measurement CNT membranes were mounted in an O-ring (FPM) sealed polycarbonate flow cell. The integrity of the O-ring seal was checked through leak rate tests using gas impermeable Si chip. The membrane fixture was connected to a homemade setup assembled using standard stainless steel ¼ inch tubings and a high precision pressure regulator (SMC IR1000N01BG), which allows to apply pressure up to 1.5 bar on the feed side of CNT membrane. Feed pressure was read on the handheld manometer (Omega HHP91) and permeate flow rate was measured by a high precision flow meter (MKS
Instruments MF1 calibrated for N2) placed downstream of the membrane (Figure S11a).
Figure S11. Schematics of (a) gas and (b) water flow measurement setups
B. Water flow measurement The two reservoirs of membrane fixture and the feed line tubings were carefully filled with the Milli-Q water, which was then pressurized up to 1 bar using compressed air adjusted by the high precision pressure regulator (Figure S11b). The water flow rate was calculated by recording the meniscus movement of feed water every 20-30 s and processing the images of meniscus change with
MATLAB. Note that due to the poor chemical stability of alumina matrix in water, the VA-
SWCNT/alumina membranes were excluded from water flow measurements.
13 C. Temperature dependent water flow measurement The entire measurement set-up including the feed line tubing was dipped in a temperature controlled chiller and pre-conditioned for 30 min-1 hr prior to the measurement. For a comparative study, VA-SWCNT membranes with average tube diameters of 2.11 nm and 4.69 nm and track-etched polycarbonate membrane with average tube diameters of 50 nm were chosen and the water flow rates were measured at constant pressure of 200 mbar and different temperatures in the range of 10-35 oC. The apparent activation energies for water transport rates are calculated from the slopes of exponentially increasing water transport rate plotted against the inverse of temperature, as described in the inset of Figure 2c and Table S4.
Table S4. Arrhenius plot parameters from the temperature dependent water transport experiments of CNT membranes with average channel diameters of 2.11 nm and 4.69 nm and track-etched polymer membranes with channel diameters of 50 nm.
3 Slope (-Ea/R) Intercept (ln P [m /Pa/s]) Ea (kcal/mol) Polycarbonate (50 nm) -2146.9 -24.759 4.266 SWCNT/Titania (2.11 nm) -1993.2 -16.061 3.961 -1896.4 -16.494 3.768 SWCNT/Titania (4.69 nm) -2080.3 -16.699 4.134 -2098.0 -17.099 4.169
14 IV. Effect of additional flow enhancement or hindrance factor, α and β on the scaling behavior of water flow enhancement factors with the aspect ratios (AR, L/d) of CNTs
Figure S12. Scaling behavior of the enhancement factors (EF) for water transport through CNT membrane with the aspect ratios (AR, L/d) of CNTs that are experimentally obtained in this work (red symbols) and previously reported in literatures (black symbols) with the guidelines of Sampson-like flows upon the changes of additional flow enhancement or hindrance factor α and β.
15 REFERENCE
1. Majumder, M.; Chopra, N.; Hinds, B. J., Mass Transport through Carbon Nanotube Membranes in Three Different Regimes: Ionic Diffusion and Gas and Liquid Flow. ACS Nano 2011, 5 (5), 3867-3877. 2. Majumder, M.; Chopra, N.; Andrews, R.; Hinds, B. J., Nanoscale hydrodynamics: Enhanced flow in carbon nanotubes. Nature 2005, 438 (7064), 44-44. 3. Holt, J. K.; Park, H. G.; Wang, Y.; Stadermann, M.; Artyukhin, A. B.; Grigoropoulos, C. P.; Noy, A.; Bakajin, O., Fast Mass Transport Through Sub-2-Nanometer Carbon Nanotubes. Science 2006, 312 (5776), 1034-1037. 4. Du, F.; Qu, L.; Xia, Z.; Feng, L.; Dai, L., Membranes of Vertically Aligned Superlong Carbon Nanotubes. Langmuir 2011, 27 (13), 8437-8443. 5. Ge, L.; Wang, L.; Du, A.; Hou, M.; Rudolph, V.; Zhu, Z., Vertically-aligned carbon nanotube membranes for hydrogen separation. RSC Advances 2012, 2 (12), 5329-5336. 6. Baek, Y.; Kim, C.; Seo, D. K.; Kim, T.; Lee, J. S.; Kim, Y. H.; Ahn, K. H.; Bae, S. S.; Lee, S. C.; Lim, J.; Lee, K.; Yoon, J., High performance and antifouling vertically aligned carbon nanotube membrane for water purification. Journal of Membrane Science 2014, 460, 171-177. 7. Kim, S.; Fornasiero, F.; Park, H. G.; In, J. B.; Meshot, E.; Giraldo, G.; Stadermann, M.; Fireman, M.; Shan, J.; Grigoropoulos, C. P.; Bakajin, O., Fabrication of flexible, aligned carbon nanotube/polymer composite membranes by in-situ polymerization. Journal of Membrane Science 2014, 460, 91-98. 8. Zhang, L.; Zhao, B.; Wang, X.; Liang, Y.; Qiu, H.; Zheng, G.; Yang, J., Gas transport in vertically-aligned carbon nanotube/parylene composite membranes. Carbon 2014, 66, 11-17. 9. Lee, K.-J.; Park, H.-D., The most densified vertically-aligned carbon nanotube membranes and their normalized water permeability and high pressure durability. Journal of Membrane Science 2016, 501, 144-151. 10. Bui, N.; Meshot, E. R.; Kim, S.; Peña, J.; Gibson, P. W.; Wu, K. J.; Fornasiero, F., Ultrabreathable and Protective Membranes with Sub-5 nm Carbon Nanotube Pores. Advanced Materials 2016, 28 (28), 5871-5877. 11. Yung, K.-L.; Kong, J.; Xu, Y., Studies on flow behaviors of polymer melts in nanochannels by wetting actions. Polymer 2007, 48 (26), 7645-7652. 12. de Gennes, P. G., Wetting: statics and dynamics. Reviews of Modern Physics 1985, 57 (3), 827-863. 13. Dommanget, C.; Boisson, C.; Charleux, B.; D’Agosto, F.; Monteil, V.; Boisson, F.; Junkers, T.; Barner-Kowollik, C.; Guillaneuf, Y.; Gigmes, D., Enhanced Spin Capturing Polymerization of Ethylene. Macromolecules 2013, 46 (1), 29-36. 14. Petermann, J.; Gleiter, H., Observation of interface melting in polyethylene. Journal of Polymer Science: Polymer Physics Edition 1976, 14 (3), 555-558. 15. Wu, J.; Gerstandt, K.; Zhang, H.; Liu, J.; Hinds, B. J., Electrophoretically induced aqueous flow through single-walled carbon nanotube membranes. Nat Nano 2012, 7 (2), 133- 139. 16. Vinten, P.; Marshall, P.; Lefebvre, J.; Finnie, P., Thermodynamic and Energetic Effects on the Diameter and Defect Density in Single-Walled Carbon Nanotube Synthesis. The Journal of Physical Chemistry C 2013, 117 (7), 3527-3536.
16 17. Ferrari, A. C.; Robertson, J., Raman spectroscopy of amorphous, nanostructured, diamond–like carbon, and nanodiamond. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 2004, 362 (1824), 2477-2512. 18. Picher, M.; Navas, H.; Arenal, R.; Quesnel, E.; Anglaret, E.; Jourdain, V., Influence of the growth conditions on the defect density of single-walled carbon nanotubes. Carbon 2012, 50 (7), 2407-2416. 19. Dresselhaus, M. S.; Dresselhaus, G.; Saito, R.; Jorio, A., Raman spectroscopy of carbon nanotubes. Physics Reports 2005, 409 (2), 47-99. 20. Zhang, L.; Huang, L.; Lind, M.; Liao, V.; O’Brien, S.; Yu, Z., Excitation, Temperature, and Structural Dependence of Second-Order Raman Modes in Single-Wall Carbon Nanotubes. The Journal of Physical Chemistry C 2009, 113 (37), 16432-16438. 21. Brar, V. W.; Samsonidze, G. G.; Dresselhaus, M. S.; Dresselhaus, G.; Saito, R.; Swan, A. K.; Ünlü, M. S.; Goldberg, B. B.; Souza Filho, A. G.; Jorio, A., Second-order harmonic and combination modes in graphite, single-wall carbon nanotube bundles, and isolated single-wall carbon nanotubes. Physical Review B 2002, 66 (15), 155418.
17