Measurement of the rate of water translocation through
Supporting information for
Measurement of the rate of water translocation through carbon nanotubes Xingcai Qin, Quanzi Yuan, Yapu Zhao, Shubao Xie and Zhongfan Liu*
Center for Nanochemistry, Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China.
State Key Laboratory of Nonlinear Mechanics, Chinese Academy of Sciences,
Beijing 100190, China *Corresponding author: [email protected]
S1 Growth of ultralong individual CNTs and fabrication of CNT-FETs At first, platinum (Pt) was sputtered and patterned as electrodes on SiO2/Si substrate by standard technique of photolithography and magnetron sputtering. The photoresist was removed by hot acetone, followed by ultrasonic cleaning using acetone and ultrapure water. Before CNTs growth, the Pt-patterned substrates were boiled in a solution of H2SO4 and H2O2 (volume ratio 3: 1) for 5 min, rinsed in water extensively, and finally dried by flow of N2. Ultralong CNTs were synthesized by catalytic chemical vapor deposition (CVD) with low feeding gas rate and Fe catalyst1-3. Catalysts pattern was made on the substrate surface using PDMS stamp from the ethanol solution of 0.01 mol/L FeCl3. The typical growth conditions are 930-950°C, 3 sccm CH4 and 5 sccm H2. CNTs thus grown are mostly single-walled carbon nanotubes (SWNTs) and lying parallel with each other on substrate. The tube lengths are up to centimeters long and the diameters are smaller than 2 nm. Atomic 1
force microscopy (AFM) and multi-wavelength Raman spectroscopy (632.8 nm, 514.5 nm, 488 nm) were employed to distinguish individual CNTs from bundles and to determine the exact tube structures together with measurements of electrical resistance and saturation current of CNTs4,5. Figure S1 exhibits the characterization results of a typical individual CNT with FET configuration. The packing density of aligned CNTs was controlled so as to make the FET device with one single tube.
Figure S1. Characterization of the CNT-FETs. (a), Raman RBM spectrum of the CNT (excited at 514.5 nm; 303 cm-1 was from substrate Si). The diameter calculated from the RBM peak, 155.6 cm-1 was 1.59 nm (diameter = 248/ωRBM). (b), AFM image of the CNT (1 µm × 1 µm). Together with the resistance and saturation current measurements, this specific CNT was confirmed to be a single-walled tube.
2
S2 Molecular dynamics simulations of water-CNT system
Figure S2. Radial density profiles of water in (a) (7,7), (b) (8,8), (c) (10,10) and (d) (11,11) SWNTs.
S3 Calculation of enhancement factor and slip length Velocity from Hagen-Poiseuille (H-P) equation is
ν=
r 2 ∆P ⋅ 8ξ L
(1)
where r is the radius of a nanopore, ξ the viscosity of water, and ∆P/L the pressure gradient along nanotube. Set a = (r2·∆P)/8ξ, then
ν=
dL a = dt L
(2)
and
L2 = 2at 3
(3)
Hence the average velocity of water flow from FET2 to FET3 is
ν av =
Lm Lm a = = Lm t 2 − t1 ( Lm + Ld ) 2 L2d ( + Ld ) − 2 2 a 2 a
(4)
which means that the average velocity is equivalent to a velocity at the length of Lm/2+Ld. For a typical damping length of 280 µm and measure length of 1050 µm, the
equivalent length is 805 µm. In Table S1 are listed the expected flow velocities calculated from Hagen-Poiseuille equation. Enhancement factor is defined as the ratio of observed velocity to that predicted from Hagen-Poiseuille equation. By taking slip flow into consideration, we can also obtain the slip length (Ls) from the following equation
ν slip
r 2 + 4rLs ∆P = ⋅ 8ξ L
(5)
Chemical potential difference of tube-trapped water with bulk water got from MD simulations can be used to give an estimate of the pressure that drives the water through the tube by ∆P = -∆µ/V
(6)
where V is the molar volume of water. For all calculations, the viscosity of water was taken as 10-3Pa·s. The enhancement factors and slip lengths for different CNTs are given in Table S1.
4
Table S1. Nanofluidic parameters obtained from individual CNTs CNT diameter
Observed velocity
Pressure
H-P velocity
(nm)
(µm/s)
(100MPa）
(µm/s)
factor
(nm)
CNT1
0.81
928±107
1.1760
1.0512
882
53.0
CNT2
0.87
671±40
0.8957
1.014
662
44.6
CNT3
0.98
312±8
0.5209
0.8810
354
29.3
CNT4
1.10
366±10
0.3137
0.6310
580
56.6
CNT5
1.42
73±1
0.1621
0.7121
103
13.5
CNT6
1.52
49±1
0.1543
0.8364
59
8.4
CNT7
1.59
46±1
0.1509
0.9024
51
7.9
Sample
Enhancement Slip length
Enhancement factors were calculated by comparison of experimental velocity with Hagen-Poiseuille prediction. Slip lengths were calculated from Hagen-Poiseuille equation with a slip-flow correction. Pore radius got from r = (d-0.33)/2, where 0.33 was van der Waals diameter of carbon atom or the thickness of a single carbon wall of CNT, and d the diameter of CNT .
S4 Pore diameter and viscosity
It is noted that there exists a slight difference of pore diameter and viscosity values from different authors to calculate the expected velocity from Hagen-Poiseuille equation and the slip length from slip-flow corrected Hagen-Poiseuille equation. All the calculations in Table S1 were based on bulk viscosity (1 mPa·s) and r = (d-0.33)/2 nm (inner pore diameter), where 0.33 nm was twice the van der Waals radius of carbon atom or the thickness of single wall of CNT. Considering that some previous works employed full diameter as the pore size and modified viscosity, we performed similar calculations using r = d/2 (Fig. S3c) and effective viscosity (Fig. S3d) got from reference6 (Fig. S3a). Thus-obtained enhancement factors and slip lengths are only a little bit smaller than those in Table S1, and it is clearly that all the calculations gave the similar tendency. 5
Figure S3. Dependences of enhancement factors (red) and slip lengths (blue) on CNT
diameters. (a), Correlation of effective water viscosity with CNT diameter got from reference6. (b), Full diameter and effective viscosity were used for calculations. (c), Full diameter and viscosity of 1 mPa·s were used for calculations. (d), Pore diameter and effective viscosity were used for calculations.
References (1)
Yao, Y. G.; Li, Q. W.; Zhang, J.; Liu, R.; Jiao, L. Y.; Zhu, Y. T.; Liu, Z. F. Nature Materials 2007, 6,
283-286. (2)
Zheng, L. X.; O'Connell, M. J.; Doorn, S. K.; Liao, X. Z.; Zhao, Y. H.; Akhadov, E. A.; Hoffbauer, M.
A.; Roop, B. J.; Jia, Q. X.; Dye, R. C.; Peterson, D. E.; Huang, S. M.; Liu, J.; Zhu, Y. T. Nature Materials 2004, 3, 673-676. (3)
Jin, Z.; Chu, H. B.; Wang, J. Y.; Hong, J. X.; Tan, W. C.; Li, Y. Nano Letters 2007, 7, 2073-2079.
(4)
Dresselhaus, M. S.; Dresselhaus, G.; Saito, R.; Jorio, A. Physics Reports-Review Section of
Physics Letters 2005, 409, 47-99. (5)
Villalpando-Paez, F.; Son, H.; Nezich, D.; Hsieh, Y. P.; Kong, J.; Kim, Y. A.; Shimamoto, D.;
Muramatsu, H.; Hayashi, T.; Endo, M.; Terrones, M.; Dresselhaus, M. S. Nano Letters 2008, 8, 3879-3886. (6)
Thomas, J. A.; McGaughey, A. J. H. Nano Letters 2008, 8, 2788-2793.
6
Measurement of the rate of water translocation through carbon nanotubes Xingcai Qin, Quanzi Yuan, Yapu Zhao, Shubao Xie and Zhongfan Liu*
Center for Nanochemistry, Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China.
State Key Laboratory of Nonlinear Mechanics, Chinese Academy of Sciences,
Beijing 100190, China *Corresponding author: [email protected]
S1 Growth of ultralong individual CNTs and fabrication of CNT-FETs At first, platinum (Pt) was sputtered and patterned as electrodes on SiO2/Si substrate by standard technique of photolithography and magnetron sputtering. The photoresist was removed by hot acetone, followed by ultrasonic cleaning using acetone and ultrapure water. Before CNTs growth, the Pt-patterned substrates were boiled in a solution of H2SO4 and H2O2 (volume ratio 3: 1) for 5 min, rinsed in water extensively, and finally dried by flow of N2. Ultralong CNTs were synthesized by catalytic chemical vapor deposition (CVD) with low feeding gas rate and Fe catalyst1-3. Catalysts pattern was made on the substrate surface using PDMS stamp from the ethanol solution of 0.01 mol/L FeCl3. The typical growth conditions are 930-950°C, 3 sccm CH4 and 5 sccm H2. CNTs thus grown are mostly single-walled carbon nanotubes (SWNTs) and lying parallel with each other on substrate. The tube lengths are up to centimeters long and the diameters are smaller than 2 nm. Atomic 1
force microscopy (AFM) and multi-wavelength Raman spectroscopy (632.8 nm, 514.5 nm, 488 nm) were employed to distinguish individual CNTs from bundles and to determine the exact tube structures together with measurements of electrical resistance and saturation current of CNTs4,5. Figure S1 exhibits the characterization results of a typical individual CNT with FET configuration. The packing density of aligned CNTs was controlled so as to make the FET device with one single tube.
Figure S1. Characterization of the CNT-FETs. (a), Raman RBM spectrum of the CNT (excited at 514.5 nm; 303 cm-1 was from substrate Si). The diameter calculated from the RBM peak, 155.6 cm-1 was 1.59 nm (diameter = 248/ωRBM). (b), AFM image of the CNT (1 µm × 1 µm). Together with the resistance and saturation current measurements, this specific CNT was confirmed to be a single-walled tube.
2
S2 Molecular dynamics simulations of water-CNT system
Figure S2. Radial density profiles of water in (a) (7,7), (b) (8,8), (c) (10,10) and (d) (11,11) SWNTs.
S3 Calculation of enhancement factor and slip length Velocity from Hagen-Poiseuille (H-P) equation is
ν=
r 2 ∆P ⋅ 8ξ L
(1)
where r is the radius of a nanopore, ξ the viscosity of water, and ∆P/L the pressure gradient along nanotube. Set a = (r2·∆P)/8ξ, then
ν=
dL a = dt L
(2)
and
L2 = 2at 3
(3)
Hence the average velocity of water flow from FET2 to FET3 is
ν av =
Lm Lm a = = Lm t 2 − t1 ( Lm + Ld ) 2 L2d ( + Ld ) − 2 2 a 2 a
(4)
which means that the average velocity is equivalent to a velocity at the length of Lm/2+Ld. For a typical damping length of 280 µm and measure length of 1050 µm, the
equivalent length is 805 µm. In Table S1 are listed the expected flow velocities calculated from Hagen-Poiseuille equation. Enhancement factor is defined as the ratio of observed velocity to that predicted from Hagen-Poiseuille equation. By taking slip flow into consideration, we can also obtain the slip length (Ls) from the following equation
ν slip
r 2 + 4rLs ∆P = ⋅ 8ξ L
(5)
Chemical potential difference of tube-trapped water with bulk water got from MD simulations can be used to give an estimate of the pressure that drives the water through the tube by ∆P = -∆µ/V
(6)
where V is the molar volume of water. For all calculations, the viscosity of water was taken as 10-3Pa·s. The enhancement factors and slip lengths for different CNTs are given in Table S1.
4
Table S1. Nanofluidic parameters obtained from individual CNTs CNT diameter
Observed velocity
Pressure
H-P velocity
(nm)
(µm/s)
(100MPa）
(µm/s)
factor
(nm)
CNT1
0.81
928±107
1.1760
1.0512
882
53.0
CNT2
0.87
671±40
0.8957
1.014
662
44.6
CNT3
0.98
312±8
0.5209
0.8810
354
29.3
CNT4
1.10
366±10
0.3137
0.6310
580
56.6
CNT5
1.42
73±1
0.1621
0.7121
103
13.5
CNT6
1.52
49±1
0.1543
0.8364
59
8.4
CNT7
1.59
46±1
0.1509
0.9024
51
7.9
Sample
Enhancement Slip length
Enhancement factors were calculated by comparison of experimental velocity with Hagen-Poiseuille prediction. Slip lengths were calculated from Hagen-Poiseuille equation with a slip-flow correction. Pore radius got from r = (d-0.33)/2, where 0.33 was van der Waals diameter of carbon atom or the thickness of a single carbon wall of CNT, and d the diameter of CNT .
S4 Pore diameter and viscosity
It is noted that there exists a slight difference of pore diameter and viscosity values from different authors to calculate the expected velocity from Hagen-Poiseuille equation and the slip length from slip-flow corrected Hagen-Poiseuille equation. All the calculations in Table S1 were based on bulk viscosity (1 mPa·s) and r = (d-0.33)/2 nm (inner pore diameter), where 0.33 nm was twice the van der Waals radius of carbon atom or the thickness of single wall of CNT. Considering that some previous works employed full diameter as the pore size and modified viscosity, we performed similar calculations using r = d/2 (Fig. S3c) and effective viscosity (Fig. S3d) got from reference6 (Fig. S3a). Thus-obtained enhancement factors and slip lengths are only a little bit smaller than those in Table S1, and it is clearly that all the calculations gave the similar tendency. 5
Figure S3. Dependences of enhancement factors (red) and slip lengths (blue) on CNT
diameters. (a), Correlation of effective water viscosity with CNT diameter got from reference6. (b), Full diameter and effective viscosity were used for calculations. (c), Full diameter and viscosity of 1 mPa·s were used for calculations. (d), Pore diameter and effective viscosity were used for calculations.
References (1)
Yao, Y. G.; Li, Q. W.; Zhang, J.; Liu, R.; Jiao, L. Y.; Zhu, Y. T.; Liu, Z. F. Nature Materials 2007, 6,
283-286. (2)
Zheng, L. X.; O'Connell, M. J.; Doorn, S. K.; Liao, X. Z.; Zhao, Y. H.; Akhadov, E. A.; Hoffbauer, M.
A.; Roop, B. J.; Jia, Q. X.; Dye, R. C.; Peterson, D. E.; Huang, S. M.; Liu, J.; Zhu, Y. T. Nature Materials 2004, 3, 673-676. (3)
Jin, Z.; Chu, H. B.; Wang, J. Y.; Hong, J. X.; Tan, W. C.; Li, Y. Nano Letters 2007, 7, 2073-2079.
(4)
Dresselhaus, M. S.; Dresselhaus, G.; Saito, R.; Jorio, A. Physics Reports-Review Section of
Physics Letters 2005, 409, 47-99. (5)
Villalpando-Paez, F.; Son, H.; Nezich, D.; Hsieh, Y. P.; Kong, J.; Kim, Y. A.; Shimamoto, D.;
Muramatsu, H.; Hayashi, T.; Endo, M.; Terrones, M.; Dresselhaus, M. S. Nano Letters 2008, 8, 3879-3886. (6)
Thomas, J. A.; McGaughey, A. J. H. Nano Letters 2008, 8, 2788-2793.
6
