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38.For example,in the2&6co-crystal,the iodine-nitrogen
halogen bonding distance is3.07A˚,and the C–I–N angle
is174.4-.In contrast,the iodine-nitrogen distance in the
1&7co-crystal is3.21A˚,and the C–I–N angle is167.8-.
The iodine-oxygen close contact is similar,with a distance
of3.20A˚and angle of168.5-.
39.The unit cell parameters(triclinic,P¯1)are as follows:
a04.944(2)A˚,b09.142(3)A˚,c015.051(5)A˚,
a087.923(6)-,b084.590(6)-,g078.759(7)-,
V0664.1(4)A˚3,Z01.
40.We thank N.S.Sampson and H.Tang for their help in
measuring the electronic absorption spectrum of PIDA.
We are grateful to NSF(grants CHE-9984937,CHE-
0446749,and CHE-0453334)for financial support of
this research.Crystallographic details for the1&7and
2&6co-crystals are available free of charge from the
Cambridge Crystallographic Data Centre under deposition
numbers CCDC294370and CCDC294371,respectively.
Supporting Online Material
/cgi/content/full/312/5776/1030/DC1
Materials and Methods
Figs.S1to S3
Tables S1and S2
5January2006;accepted17March2006
10.1126/science.1124621
Fast Mass Transport Through
Sub–2-Nanometer Carbon Nanotubes Jason K.Holt,1*Hyung Gyu Park,1,2*Yinmin Wang,1Michael Stadermann,1
Alexander B.Artyukhin,1Costas P.Grigoropoulos,2Aleksandr Noy,1Olgica Bakajin1†
We report gas and water flow measurements through microfabricated membranes in which aligned carbon nanotubes with diameters of less than2nanometers serve as pores.The measured gas flow exceeds predictions of the Knudsen diffusion model by more than an order of magnitude. The measured water flow exceeds values calculated from continuum hydrodynamics models by more than three orders of magnitude and is comparable to flow rates extrapolated from molecular dynamics simulations.The gas and water permeabilities of these nanotube-based membranes are several orders of magnitude higher than those of commercial polycarbonate membranes, despite having pore sizes a
n order of magnitude smaller.These membranes enable fundamental studies of mass transport in confined environments,as well as more energy-efficient nanoscale filtration.
C arbon nanotubes,with diameters in the
nanometer range and atomically smooth
surfaces,offer a unique system for study-ing molecular transport and nanofluidics. Although the idea that water can occupy such con-fined hydrophobic channels is somewhat counter-intuitive,experimental evidence has confirmed that water can indeed occupy these channels (1,2).Water transport through molecular-scale hydrophobic channels is also important because of the similarity of this system to transmembrane protein pores such as aquaporins(3).In recent years,numerous simulations(4,5)of water transport through single-walled carbon nano-tubes(SWNTs)have suggested not only that water occupies these channels,but also that fast molecular transport takes place,far in excess of what continuum hydrodynamic theories would predict if applied on this length scale.Molec-ular dynamics(MD)simulations attribute this
enhancement to the atomic smoothness of the
nanotube surface and to molecular ordering
phenomena that may occur on confined length
scales in the1-to2-nm range(4,5).For similar
reasons,simulations of gas transport through
SWNTs(6)predict flux enhancements of
several orders of magnitude relative to other
similarly sized nanoporous materials.Membrane-
based gas separations,such as those using
zeolites(7),provide precise separation and size
exclusion,although often at the expense of
throughput or flux.It may be possible to use
SWNTs to create a membrane that offers both
high selectivity and high flux.
To investigate molecular transport on this
length scale,we need to fabricate a carbon
nanotube membrane that has a pore size of1to
2nm.Researchers have recently fabricated
multiwalled carbon nanotube(MWNT)mem-
branes with larger pore diameters(6to7nm)
by encapsulation of vertically aligned arrays of
MWNTs(8,9)and by templated growth within
nanochannel alumina(10).Enhanced water
transport through these larger MWNTs has
recently been reported(11).Quantifying trans-
port through an individual tube in a MWNT
membrane is difficult,however,because MWNTs
are prone to blockages,in particular by
B bamboo[structures and catalyst particles that
can migrate to and obstruct the nanotube
interior(9,12,13).The consequence of such
blockages is a marked reduction of the active
membrane pore density.In contrast,there are
few,if any,reports of B bamboo[structure
formation or catalyst migration for SWNTs or
double-walled carbon nanotubes(DWNTs).
However,it is difficult to produce verticallyreactive materials studies
aligned carbon nanotubes of this size(14,15).The
major challenges also lie in finding a conformal
deposition process to fill the gaps in this nano-
tube array,as well as in designing a selective
etching process to open up the nanotube chan-
nels without producing voids in the membrane.
1Chemistry and Materials Science Directorate,Lawrence
Livermore National Laboratory,Livermore,CA94550,USA. 2Department of Mechanical Engineering,University of
California,Berkeley,CA94720,USA.
*These authors contributed equally to this work.
†To whom correspondence should be addressed.E-mail: v Table1.Size exclusion tests on DWNT and MWNT membranes and molecular fluxes(per unit membrane area)of analytes.Values denoted by‘‘G’’were derived from the limits of detection for our concentration measurements when we did not observe any Au particles in the permeate solution.Differences of three to four orders of magnitude between this limiting value and the flux of the next smallest species indicate that the given analyte did not pass through the membrane. Analyte Analyte size
(nm)
DWNT membrane flux
(molecules cm–2s–1)
MWNT membrane flux
(molecules cm–2s–1)
Ru2þ(bipyr)
3
1.35Â10135Â1013 Colloidal Au12T0.4G2Â1091Â1011 Colloidal Au25T0.75G3Â1083Â1010 Colloidal Au310T1Not tested G4Â107
We have developed a microelectromechanical systems (MEMS)–compatible fabrication process (Fig.1A)for sub–2-nm nanotube pore membranes.The process uses catalytic chemical vapor depo-sition to grow a dense,vertically aligned array of DWNTs on the surface of a silicon chip (Fig.1B),followed by conformal encapsulation of the nano-tubes by a hard,low-pressure chemical vapor–deposited silicon nitride (Si 3N 4)matrix (Fig.1C).Scanning electron microscopy (SEM)images show that our process produces gap-free mem-branes over the length scale of the whole chip.The excess silicon nitride is removed from both sides of the membrane by ion milling,and the ends of the nanotubes are opened up with reactive ion etching.The membranes remain impermeable to both liquids and gases until the very last etching step;this is further evidence that our fabrication process produces crack-free and void-free mem-branes.Transmission electron microscopy (TEM)plan-view images (Fig.2,C to E)of a slice of the membrane also demonstrate that the silicon nitride coats the DWNTs conformally and does not leave any gaps between the outer surface of the nanotube and the silicon nitride.We also used the same nitride-encapsulation method to produce MWNT membranes (16).
To characterize the membrane pore size,we performed size exclusion measurements (Table 1)(16)and compared these results with electron microscopy (EM)data.DWNT mem-branes passed species with si
zes up to 1.3nm yet blocked 2-nm gold particles,which suggests that these membranes have pore sizes between 1.3and 2nm.Comparison of the water flow rates before and during filtration,coupled with the upper-limit estimate of the flux of 2-nm gold particles,suggests that less than 0.1%of the flux through the membrane can be attri-buted to pores larger than 2nm (16).These size exclusion measurements are further supported by the evidence obtained through EM.The dis-tribution of DWNTs,as measured by TEM,revealed an inner diameter average of 1.6nm (Fig.2B).TEM images (Fig.2C)of the mem-brane also revealed that the only holes that span the thickness of the membrane are of a size that is consistent with the inner diameter distribution of as-grown DWNTs.A MWNT membrane,
used as a reference,transported colloidal gold particles with diameters of 2and 5nm but excluded the 10-nm colloidal gold particles,in agreement with MWNT diameters of 6.5T 0.5nm estimated by TEM.This result also suggests that pore clogging by particles smaller than the average pore size is unlikely for the solution con-centrations used in these experiments.We con-clude that the transport in our samples occurs exclusively through the inner pores of the carbon nanotubes spanning the membrane.
The absolute gas flux through our mem-branes exceeded the flux predicted by the Knudsen diffusion
model.As the
dimensions
Fig.1.(A )Schematic of the fabrication process.Step 1:microscale pit formation (by KOH etching).Step 2:catalyst deposition/annealing.Step 3:nanotube growth.Step 4:gap filling with low-pressure chemical vapor–deposited Si 3N 4.Step 5:membrane area definition (by XeF 2isotropic Si etching).Step 6:silicon nitride etch to expose nanotubes and remove catalyst nanoparticles (by Ar ion milling);the membrane is still impermeable at this step.Step 7:nanotube uncapping (reactive ion etching);the membrane begins to exhibit gas permeability at this step.(B )SEM cross section of the as-grown DWNTs (CNTs).(C )SEM cross section of the membrane,illustrating the excellent gap filling by silicon nitride.(D )Photograph of the open membrane areas;inset shows a close-up of one membrane.(E )Photograph of the membrane chip that contains 89open windows;each window is 50m m in diameter.
Table 2.Comparisons of experimental air flow rates observed for several DWNT membranes with Knudsen model predictions,and of experimental water flow rates with continuum flow model predictions.The differences among the three DWNT membranes are most likely the result of different numbers of pores opened in the fabrication process.Values for a poly-carbonate membrane are provid
ed as a reference.Pore diameters were determined from size exclusion measurements,TEM measurements,and (for polycarbonate)manufacturer’s specifications.Pore density values are upper limits,as determined from TEM measurements and (for polycarbonate)manufacturer’s specifications.
Membrane Pore diameter
(nm)Pore density (cm –2)Thickness (m m)
Enhancement over Knudsen model*(minimum)
Enhancement over no-slip,hydrodynamic flow†(minimum)
Calculated minimum slip length‡(nm)DWNT 1 1.3to 2.0e 0.25Â1012 2.040to 1201500to 8400380to 1400DWNT 2 1.3to 2.0e 0.25Â1012 3.020to 80680to 3800170to 600DWNT 3
1.3to
2.0e 0.25
Â1012 2.816to 60560to 3100
140to 500
Polycarbonate
15
6
Â
108
6.0
2.1
3.7
5.1
*From (18).
†From (26).
‡From (29).
of the pore shrink,the mean free path (l )becomes larger than the channel dimensions (d )and the transport enters the molecular flow regime.In such situations,where particle-surface collisions dominate over particle-particle collisions,the Knudsen diffusion model (17)is frequently applied.Indeed,our pore geom-etries are characterized by Knudsen num-bers (l /d )of 10to 70,which places them well into the free molecular transport regime.However,the flux measured through our mem-branes exceeded the flux predicted by the Knudsen model (18)by at least one to two orders of magnitude (Table 2).By compari-son,a polycarbonate membrane (Nucleopore,Osmonics Inc.)revealed just a slight enhance-ment in flux.The single largest uncertainty in quantifying the flux through our membrane pores lies in determination of the active pore density (i.e.,those nanotubes that are open and spanning the membrane).A pore density esti-mate of 2.5Â1011cm j 2was derived from the plan-view TEM images of the DWNT mem-brane (Fig.2,C to E),and the enhancement factors that we report represent lower bound-ary estimates (19).The observed flow enhance-ment is most likely caused by the intrinsic smoothness of the nanotube surface,as predicted by MD simulations of gas flow through SWNTs (6,20–22).In atomically smooth pores,the nature of gas-wall collisions can change from purely
diffuse (as in the Knudsen model)to a combination of specular and diffuse collisions (23),thus leading to observed faster transport.We found that single-component selectivity for most of the gases exhibited the expected inverse-square-root scaling of molecular mass (Fig.3,inset)with the exception of hydro-carbons,whose selectivities were higher.This result is not surprising for a molecular diffusion process because it reflects the mass dependence of molecular velocity (note that the nature of wall collisions would not affect the mass scaling).Of all the measured gases,only the hydrocarbons deviated from this pattern,exhib-iting a higher selectivity (Fig.3)in both
DWNT
Fig.2.(A )TEM images of as-grown nanotubes,prepared by removing them from the silicon substrate and dispersing them in dimethyl-formamide.The majority of the carbon nanotubes are double-walled,as identified in the high-resolution inset.(B )Pore size distribution,derived from TEM measurements of the inner diameter of 391individual carbon nanotubes,reveals an average pore size of 1.6nm.The average outer diameter of these DWNTs is estimated to be 2.3nm.(C to E )Plan-view TEM images of carbon nanotube membrane taken with the beam parallel to the nanotube axis.In (C),the nanotube membrane shows continuous nitride coating on the scales examined in this image (È0.2m m by 0.2m m).No microcracks or microvoids can be seen.The bright white spots (circled in yellow)are carbon nanotube pores,which can be identified by the surrounding ring-shaped coating of silicon nitride.For clarity,not all visible nanotubes were circled.The density of carbon nanotubes is measured to be È2.5Â1011cm –2from several similar TEM images.In (D)and (E),high-resolution TEM images of selected areas from (C)show conformal coating of silicon nitride.The bright white spots in the images have the same inner diameter as the carbon nanotubes.
Fig.3.Gas selectivity (defined as permeability relative to He)data for sub–2-nm DWNT (triangles)and MWNT (circles)membranes.Open symbols denote nonhydro-carbon gases (H 2,He,Ne,N 2,O 2,Ar,CO
2,Xe);solid symbols denote hydrocarbon gases (CH 4,C 2H 6,C 3H 6,C 4H 6,C 4H 8).The solid line is a power-law fit of the non-hydrocarbon gas selectivity data,showing a scaling predicted by the Knudsen diffusion model (ex-ponent of –0.49T 0.01).The dashed line is a power-law fit of the hydrocarbon gas data,show-ing a deviation from the Knudsen model (exponent of –0.37T 0.02).The inset shows the full mass range of the nonhydrocarbon gas data,again illustrating agreement with the Knudsen model
scaling.Fig.4.Air (red)and water (blue)permeabil-ity as measured for three DWNT membranes (DW#1,2,and 3)and a polycarbonate membrane (PC).Despite considerably smaller pore sizes,the permeabilities for all DWNT membranes greatly exceed those of the polycarbonate
membrane.
and MWNT membranes.Interestingly,a refer-ence polycarbonate membrane with a pore size of 15nm did not show this deviation.We attribute the deviation to the preferential interaction of hydro-carbons with the carbon nanotube sidewalls.The hydrocarbon transport enhancement most likely results from surface diffusion or possibly a solubility/diffusion mechanism (24).Pulse mass analysis of various organic compounds has shown strong adsorption of hydrocarbon molecules (e.g.,hexane)on SWNTs relative to more polar molecules (e.g.,ethanol)(25).It is noteworthy that the hydrocarbon selectivity we observe in these single-component experiments may be more pronounced for practical gas separation problems where mixtures are involved (20).
Our membranes also transported water across the carbon nanotube channels at rates that can-not be accounted for by continuum flow mod-els.The measured water flow rates reveal a flow enhancement (Table 2)that is more than three orders of magnitude faster than the no-slip,hydrodynamic flow as calculated from the Hagen-Poiseuille equation (26).Breakdown of this continuum model is not surprising for chan-nels 1to 2nm in size.If we take the formalism used for gases and define a mean free path in liquids as the molecular diameter (e.g.,È0.3nm for H 2O),the Knudsen number for a 1-to 2-nm pore is 0.15to 0.3.These values lie on the border between B slip flow [and B transitional flow.[In this size regime,where the pore is only È7water molecules in diameter,contin-uum theory concepts such as a velocity profile may be difficult to define.For this reason,MD simulations are often used for the prediction of water flows through carbon nanotube pores with diameters on the order of 1nm (4,5).However,the computational expense of MD simulations,as well as observations of a finite fluid B slipping velocity [at hydrophobic inter-faces (27),have motivated attempts to use meso-and macroscopic flow models to simu-late flow through SWNTs (28).These simu-lations calculated a corresponding B slip length [that describes the noncontinuum behavior of a liquid near the pore walls.If we apply a similar formalism for the flow through our sub–2-nm nanotube membranes,we calculate (29)slip lengths as large as 1400nm (Table 2).These values are almost three orders of magnitude larger than the pore size and are on the order of the overall size of the system (pore length).In contrast,
the polycarbonate membrane with a pore size of 15nm reveals a much smaller slip length of just 5nm.This comparison suggests that slip-flow for-malism may not be applicable to water flow through sub–2-nm carbon nanotubes,possibly because of length scale confinement (30)or partial wetting of the carbon nanotube surface (31).Our observed water flux compares well with that predicted by the MD simulations (5).The simulations predict a flux of 12water molecules through 1nm 2of the nanotube cross-sectional area in 1ns;our measured flux,extrapolated to
the simulation pressure drop,corresponds to 10to 40water molecules nm –2ns –1(32).The MD simulations attributed the observed high water flow rates to the formation of water B wires [in the confined space inside the nanotube.The strong dependence of the structure of the water in the nanotube on diameter (33)indicates that small differences in nanotube diameter can have large effects on transport.Therefore,it is unclear whether the mechanism proposed by MD is responsible for the high water flow rates observed with the larger nanotubes used in our experiments,or whether the flow enhancement can be attributed simply to the presence of a nearly frictionless surface.
Membrane permeability provides a figure of merit for membrane performance for practical applications.Despite having an order of mag-nitude smaller pore size,the enhanced flow rate per pore and the higher pore density render the sub–2-nm membranes superior to conventional polycarbonate
membranes in both air and water permeability (34)(Fig.4).
References and Notes
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17.A.F.Mills,Mass Transfer (Prentice-Hall,Upper Saddle
River,NJ,2001),pp.68–69.
18.For gas flow in the Knudsen regime,the overall
membrane flow rate can be determined from
Q gas 0
23ffiffiffiffiffiffiffiffiffi8p MRT r ðd =2Þ3V m D p
L s A where M is molecular weight,R is the universal gas
constant,T is absolute temperature,d is pore diameter,V m is the molar volume,D p is the pressure drop,L is the thickness of the membrane,s is the areal pore density,and A 089I p (25m m)20175,000m m 2is the total area of the membrane.
19.This density is only a factor of 4smaller than the catalyst
density on the substrate (È1012cm –2),also determined by TEM.This areal density is comparable to the measured areal density of SWNTs/DWNTs produced using a catalyst recipe similar to the one we used (12).The estimate from the TEM images still represents the upper bound for the density
because it assumes that every DWNT that spans the section imaged in the TEM (thickness 50nm)also spans the entire membrane thickness.
20.
H.B.Chen,D.S.Sholl,J.Membr.Sci.269,152(2006).21.D.M.Ackerman,A.I.Skoulidas,D.S.Sholl,J.K.Johnson,Mol.Sim.29,677(2003).
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26.
The Hagen-Poiseuille equation is
Q HP 0
p ðd =2Þ4D p
where Q HP is the volumetric flow rate,D p is the pressure drop,d is the pore diameter,m is the water viscosity,and L is the membrane thickness.
27.J.Baudry,E.Charlaix,A.Tonck,D.Mazuyer,Langmuir
17,5232(2001).
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Multiphase Flow 30,995(2004).
29.With the inclusion of a slip-flow correction,the Hagen-Poiseuille equation becomes
Q SLIP 0
p ðd =2Þ4þ4ðd =2Þ3L s h i D p
where L s is defined as the slip length,
L s 0
U wall
dU =dr
where U wall is the axial velocity at the wall,and dU/dr is the radial velocity gradient at the wall (or shear rate).30.C.Cottin-Bizonne et al.,Eur.Phys.J.E 9,47(2002).31.V.S.J.Craig,C.Neto,D.R.M.Williams,Phys.Rev.Lett.87,054504(2001).
32.
The simulation considered water transport across the carbon nanotubes driven by an osmotic pressure of about 100atm.Our experiments used pressure drops of 1atm.We have also observed linear dependence between the applied pressure drop and the flow rate across the membranes.As an approximation,we therefore used a linear extrapolation to compare our measured flows to the simulation results.We note two key differences between our experiments and the simulations:(i)The simulations used nanotubes 0.8nm in diameter,whereas our samples were 1.6nm in diameter on avera
ge;and (ii)the pressure drops were È100atm in the simulations versus 1atm in our experiments,and it is unclear whether our linear extrapolation in flow rate versus pressure drop is valid over this range.
33.K.Koga,G.T.Gao,H.Tanaka,X.C.Zeng,Nature 412,802(2001).
34.Permeability is defined as the volumetric flux,normalized by the pressure drop.
35.
We thank J.Muyco for help with Raman spectroscopy,R.Friddle for assistance with atomic force microscopy measurements,W.J.Moberlychan for his assistance on FIB and TEM experiments,and D.Eaglesham for early contributions to the project and lively discussions.This work was performed under the auspices of the U.S.Department of Energy by University of California
Lawrence Livermore National Laboratory under contract W-7405-Eng-48with funding from the Laboratory
Directed Research and Development Program.H.G.P.and A.B.A.were supported by a Student Employee Graduate Research Fellowship.
Supporting Online Material
/cgi/content/full/312/5776/1034/DC1Materials and Methods Fig.S1
15February 2006;accepted 15March 200610.1126/science.1126298
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