Supplementary Information
Methods:
S1.1
Estimating the permeable pore density from KCl diffusion measurements.
The pore density of the membranes was estimated using KCl diffusion through the membrane. The feed
solution was 7.5 cc of 669 ppm of KCl (standard solution). The volume in the permeate is 1.5 cc. The
maximum concentration measured is 25 ppm. Thus, the total mass of KCl in the feed solution is about 2
orders of magnitude greater than that in the permeate, eliminating depletion effects. Both the feed and the
permeate cells were stirred with a magnetic stirrer. The conductivity of the permeate was monitored by a
conductivity electrode (Microelectrodes Inc.), connected to a conductivity meter (Orion 150 A+
conductivity meter) and the data was collected in a spread sheet using Balance Talk SL (Labtronics) every
15 min. The conductivity meter was calibrated using 66.9 ppm standard solution before the start of any
experiment. The conductivity data was converted into flux data using an appropriate calibration curve of
ppm of KCl vs. conductivity. The permeable pore area (Ap) can be estimated from the equation:
Ap=D*c/J*l
Where D is the bulk diffusivity of KCl at 210C ( ~ 1.96*10-5 cm2/s), c is the concentration of the feed
(8.97*10-3 M ), l is the membrane thickness (from SEM cross sectional pictures), and J is the
experimental steady state flux of KCl (moles/s). A representative example of ionic flux data is shown in
Figure S1. The permeable pore density can be calculated from:
Permeable pore density (#/cm2) = (Ap/Am)/(πd2/4)
Where, d is the pore diameter (7 nm), and Am is the membrane area exposed in the diffusion experiment
(0.19 cm2). Salt rejection of the CNT membranes was determined by analyzing the permeate during
pressure flow of 1.7*10-2 (M) KCl. Minimal (~ 4%) salt rejection was observed. Thus, there is not a
significant underestimation of Ap from surface charge repulsion.
To further test the basic assumption of bulk diffusivity of KCl inside CNT cores, we performed diffusion
experiments on a wide variety of ions. Figure S2 shows diffusional flux through CNT membrane
normalized to that of KCl versus the reduced pore diameter of a variety of ions. Shown with
experimental data are the two possible extremes of bulk diffusivity and hindered diffusion (strong
interaction with the CNT core). Experimentally observed values fall between the two extremes. In the
case of small positive ions (methyl viologen, Ru-bipyr) the values are within a few percents of bulk
expectation. Negatively charged larger molecules have slightly reduced diffusivity, consistent with a
charge repulsion with carboxylate groups at the entrance to the CNT cores. The available pore density
(Table S1) is significantly less than the microscopically determined density due to Fe blockage from the
CVD growth process.
nanomoles transported
160
140
120
100
80
y = 19.584x
R2 = 1
60
40
20
0
0
2
4
6
8
Time (hours)
Fig. S.1. Representative plot of KCl diffusion, as measured by the conductivity of the permeate solution
as a function of time.
Diffusion Flux normalized to KCl
1
0.9
Experimental
0.8
Hindered Diffusion
0.7
Bulk Diffusion
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Reduced Pore Diameter
Fig S.2 Diffusional flux through the CNT membrane normalized to that of KCl versus reduced pore
diameter (Stoke’s diameter/pore diameter) of a variety of ions (data clusters from left to right are: KCl,
Methyl viologen+2, naphthalenedisulfonic-2 acid, Ru(bipyridine)3+2, Rhodamine, fast dye-2). Bulk diffusion
values were taken from available literature except for fast dye which was calculated from the Wilkie
Chang equation.1 Hindered diffusion points are calculated using reduced pore diameter and the Renkin
equation.1 Experimentally observed values lie between the two extremes.
S1.2
Flow cell experiment.
Fig. S.3 Schematic of flow cell set up for determining the permeability of the CNT membrane.
Fig. S.4 Photograph of pressure flow cell. The aligned CNT membrane is supported on porous metal
disk (right) and the top seal is made by a vitron o-ring.
Figure S.3 shows a diagram of the pressure-flow experimental apparatus and Figure S.4 shows a
photograph of the pressure cell. All associative liquids (water, isopropal alchohol (IPA), ethanol (EtOH))
are boiled in a vacuum oven for a period of 12-24 hours and allowed to cool in vacuum. For
measurements of different liquids on the same membrane, it is dried in air for 12 hours and then soaked in
the solvent for 1-2 hours prior to the experiment. The syringe is then filled with the liquid and the pipe
line is purged with the liquid at 2.5 ml/min flow rate, keeping the valve completely open so that any air in
the pipes is driven away. Thereafter, the valve is gradually closed manually to increase pressure inside the
flow cell. Once a drop of liquid is seen coming out of the nipple, the data acquisition in the computer is
started. Time dependent pressure data is also collected manually.
The zero time for the flow experiments is the time we notice the first drop of liquid coming out of the
nipple. So, there is a systematic error (due to the hold-up volume) in determining the initial permeability.
This is significant for the associative liquids, where the flow rate declines with time. Therefore, an
estimate of the hold-up volume was also made. The weight of the bottom plate with a small piece of
paraffin was first measured. In place of the CNT membrane, a PAN membrane was used and the pressure
flow experiment was conducted. The pump was then stopped and the last drop was allowed to fall out of
the nipple. The piece of paraffin was used to close the opening of the nipple and then the flow cell was
disassembled. The water poured from the top cell and the water from the bottom cell was dried with
Kimwipes and weighed. The difference between the initial and final weights gives the hold-up volume
and was found to be ~ 0.5cc.
In general, flow of liquids (J) through porous membranes can be predicted using the Haagen-Poiseuille
equation2 given by:
J=(εr2ΔP)/(8μτL)
Where ε is relative porosity, r is pore radius (7nm for our system), P pressure applied, μ dynamic
viscosity, τ tortuosity (1.1) and L length of pore. The basic assumptions of this equation are laminar flow
and ‘no-slip’ at the boundary layer, i.e. the velocity of the fluid at the CNT wall is zero. The slip lengths
for the solvents on the CNTs can be calculated from the equation:3
V(λ)/Vns = 1 + 4 λ/r;
Where, V(λ)is the experimentally observed flow velocity (cm/s), Vns is the flow velocity calculated from
the Haagen-Poiseuille Equation, λ is the slip length and r is the radius of the nanotube. Higher slip lengths
were observed for the polar molecules.
S1.3 Flow measurements through commercial membranes to verify lack of fouling or air bubble
formation in experimental setup.
To calibrate the pressure induced flow system, commercial porous alumina and polymer membranes were
incorporated into the experimental apparatus. Of particular concern was to test whether fouling or air
bubble formation would slow observed flow rates for porous membranes of similar pore size. This was
not observed in either case (Fig S.5), indicating that the experimental method eliminates fouling particles
and absorbed air.
4
2
3.5
Permeability
(cc/min-cm2-bar)
2.5
1.2
2
0.8
1.5
1
Flow (cc/min-cm2-bar)
Pressure (bar)
0.5
0.4
0
0
0
(a)
5
Time (mins)
10
15
Pressure (bar)
1.6
3
2.5
0.8
1.5
Flow (cc/cm2-min-bar)
pressure(psi)
1
0.4
0.5
0
Pressure (bar)
Permeability
(cc/min-cm2-bar)
2
0
0
5
10
15
20
25
30
Time (mins)
(b)
Fig. S.5 Water Flow Measurements using vacuum boiled DI water in the flow set-up through two
commercial membranes (a) Anodised alumina oxide membrane (with 20 nm top pores and 200 nm
bottom pores) and (b) PAN membrane (24,000 molecular weight cutoff) showed a constant permeability
and stable pressure with time. The water permeabilities are close to the specifications provided by the
manufacturers.
S1.4 Nanocrystalline Au (10nm) diffusion experiment to rule-out presence of micro-cracks
4
Absorbance
3.5
Feed (0.005 w t % 10 nm
Au colloids)
Permeate after1 hour
3
2.5
Permeate after 3 hours
2
Permeate after 25 hours
1.5
1
0.5
0
200
300
400
500
600
700
800
Wave length (nm)
Fig. S.6. UV-vis absorption monitoring of nc-Au (10nm diameter) diffusion across aligned CNT
membrane after 25 hours.
Several control experiments were performed to ensure that the observed fluid flow is through the core of
CNTs and not through cracks, macro-voids, or mesoporosity in the matrix polymer. A diffusion
experiment with a feed solution of 10nm diameter Au nanocrystals (Ted Pella Inc., 10 nm) showed no
detectable visible absorption from nc-Au in the permeate solution while the small-molecule citrate (UV
active) was visible (Figure S.6). This indicated a nanoporous membrane without cracks/pores larger than
10nm. Chemical modification of the CNT entrances4 resulted in a change in the selectivity of different
sized permeates by hindered diffusion which would not be possible in pores/cracks larger than 10nm. A
similar experiment using the pressure cell was performed with nc-Au in the feed solution. Rapid fouling
occurred and no detectable nc-Au was present in the effluent. However a control experiment showed that
the porous metal support disk absorbed nc-Au, making this pressure flow experiment inconclusive.
Membranes made from blocked MWCNTs (grown in a region of the furnace with high iron content) of
the same thickness and polymer processing, showed no detectable ionic diffusion or pressure flow for all
solvents. Hence the polystyrene matrix was not rendered mesoporous during plasma oxidation nor is
there any transport through polymer/CNT interface. The integrity of the o-ring seals was also confirmed
by the lack of flow through impermeable films and repeatable observations.
S1.5 Experimental data of fluid flow through aligned CNT membrane summarized in Table 1
Figure S.7 shows the raw data collected for Table 1 in the main text. Table S.1 is an expansion of Table 1
of the main text, showing other pertinent data for analysis.
20
1.7E-02(M)KCl
Water
Hexane
EtOH
IPA
Decane
18
Vol (cc) of solvent
/cm2 of membrane
16
14
12
10
8
6
4
2
0
0
5
10
15
20
Time (mins)
Fig. S.7 Cumulative volume of different solvents collected over a balance per unit area (cm3/cm2) of the
membrane flowing through the CNT membrane as a function of time at (0.7-1bar applied pressure).
Water flow data shown here has been normalized by permeable pore density. Detailed parameters are
shown in Table S.1. Reduction in the flow of associate liquids (water and alcohols) with time can be
attributed to flow induced solvent ordering or formation of bubbles. This mechanism is currently under
investigation.
Liquid
Hexane
Decane
Water
0.017(M)
KCl
EtOH
IPA
Permeable
pore density
Membrane
thickness
Initial
permeability
(# per cm2)
(micron)
(cm3/cm2-min-bar)
9
3.4*10
3.4*109
1*109
126
126
34
3.4*109
3.4*109
3.4*109
3.4*109
Flow velocity
normalized
at 1 bar
(cm/s)
Viscosity
(cP)
Calculated
Newtonian
flow velocity
at 1 bar (cm/s)
-4
Slip length
(micron)
5.6
0.67
25
43.9
9.5
19.6
0.3
0.9
1.0
126
126
0.44
0.053
0.58
1.01
0.72
1.25
5.16*10
1.72*10-4
5.7*10-4
5.7*10-4
1.5*10-4
1.5*10-4
9.5
3.4
54
68
39
108
126
126
0.35
0.088
4.5
1.12
1.1
2
1.4*10-4
7.7*10-4
28
13
Table S1. Expanded table summary of observed pressure driven flow through aligned MWCNT membrane.
1
Welty, J.R.; Wicks, C.E.; Wilson, R.E.; Rorrer, G. Fundamentals of Momentum, Heat and Mass Transfer 439-446
(John Wiley & Sons, New York, NY, 2000)
2
Mulder, M. Basic Principles of Membrane Technology (Kluwer Acad. Publ., Boston, 1991)
3
Lauga,E;Brenner, M.P.;Stone, H.A.; “Microfluidics No-Slip Boundary Condition” to appear in Handbook of
Experimental Fluid Dynamics, (Springer, New York, 2005)
4
Majumder, M.; Chopra, N.; Hinds, B. J. “Effect of Tip Functionalization on Transport through Vertically Oriented
Carbon Nanotube Membranes” J. Amer. Chem. Soc. 127, 9062 (2005)