Diffusion of Tetrafluoromethane in Single-Walled Aluminosilicate

Article pubs.acs.org/JPCC

Diffusion of Tetrafluoromethane in Single-Walled Aluminosilicate Nanotubes: Pulsed Field Gradient NMR and Molecular Dynamics Simulations Muslim Dvoyashkin,†,‡ Ji Zang,§ G. Ipek Yucelen,∥ Aakanksha Katihar,‡ Sankar Nair,§ David S. Sholl,§ Clifford R. Bowers,† and Sergey Vasenkov*,‡ †

Department of Chemistry, and ‡Department of Chemical Engineering, University of Florida, Gainesville, Florida 32611, United States § School of Chemical & Biomolecular Engineering, and ∥School of Materials Science & Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, United States

ABSTRACT: Diffusion of tetrafluoromethane (CF4) in single-walled aluminosilicate nanotubes was studied by means of pulsed field gradient (PFG) NMR and molecular dynamics (MD) simulations. The application of a high magnetic field and high magnetic field gradients allowed 13C PFG NMR measurements of diffusion to be performed under conditions of sufficiently large signal-to-noise ratios for a broad range of CF4 loadings. The PFG NMR data were analyzed to obtain the diffusivities for diffusion of CF4 inside the nanotube aggregates, in which the sorbate displacements exceeded the average length of individual nanotubes. In addition, the corresponding diffusivities under conditions of fast exchange of CF4 molecules between nanotubes or nanotube aggregates and the surrounding gas phase in a nanotube bed were also estimated. The experimental CF4 diffusivities inside the nanotube aggregates were found to be several times smaller than the corresponding diffusivities obtained by MD for diffusion inside the defect-free nanotubes. This difference points to the existence of additional transport resistances inside the nanotube aggregates under the conditions of the reported PFG NMR measurements, i.e., when the gas molecules diffuse through several nanotubes interconnected along the nanotube lengths inside the aggregates. Such additional transport resistances are likely to originate from diffusion through thin layers of microporous material, which is expected to connect the individual nanotubes in the aggregates.

1. INTRODUCTION

experimental studies and only a few simulation studies of intrachannel sorbate diffusion in aluminosilicate nanotubes have been reported in the literature.22,24 Several advanced experimental techniques have been found to be quite effective in measuring transport properties of microporous materials containing one-dimensional nanochannels. In particular, diffusion in microporous unidimentional zeolites has been successfully probed by pulsed field gradient (PFG) NMR,25−27 quasi-elastic neutron scattering (QENS),28 neutron spin−echo (NSE),29 and zero length column (ZLC) technique.30 In carbon SWNT, self-diffusion of adsorbed water was investigated using PFG NMR.31 The QENS technique was also utilized to study the loading dependence of hydrogen diffusion in

Stimulated by potential applications of systems of nonintersecting nanochannels in catalysis,1−7 gas separation,8−11 and nanofluidics,12−16 transport of molecular species in such systems has attracted strong interest in recent years. Much progress has been achieved in the synthesis, characterization, and functionalization of single-walled nanotubes (SWNTs).17−20 Fabrication of nanotubes with well-defined molecular structure and tunable dimensions is now possible. Some types of SWNTs also demonstrate potential for chemical modifications of the interior and exterior surfaces. Excellent representatives of this class of nanotubes are the aluminosilicate nanotubes,18 which consist of an aluminum(III) hydroxide sheet on the outer surface and are lined with pendant silanol groups on the inner surface. Sorption properties of this material have been studied by experiment and molecular simulation.18,21−23 Much less data are available on sorbate diffusion inside aluminosilicate nanotubes. Until now no © 2012 American Chemical Society

Received: June 2, 2012 Revised: September 4, 2012 Published: September 4, 2012 21350

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Figure 1. (A) SEM image showing freeze-dried aggregates of aluminosilicate SWNTs (scale bar is 1 μm). (B) TEM micrographs of individually dispersed as-synthesized aluminosilicate nanotubes.

Approximately 150 mg of the nanotubes were placed into a medium wall 5 mm NMR tube. The sample was made sorbatefree by evacuation under high vacuum (10−4 mbar) at 180 °C for at least 10 h. Following this activation procedure, a fixed amount of 13C-labeled CF4 was cryogenically transferred into the NMR tube containing the sample. After loading, the tube was flamesealed and separated from the vacuum system. Diffusion measurements were performed using a 17.6 T Bruker BioSpin NMR spectrometer operating at a 13C resonance frequency of 188.6 MHz. The spectrometer is equipped with a Diff60 probe and Great-60 gradient amplifier (Bruker BioSpin) capable of producing magnetic field gradients with a maximum amplitude of 30 T/m. Diffusion studies were performed using the stimulated echo sequence with longitudinal eddy current delay (PGSTE LED).34 In comparison to the PFG NMR sequences with bipolar gradients,35 this sequence has the advantage of reducing the loss of signal due to transverse (T2) NMR relaxation. Losses due to dephasing are minimized by keeping the dephasing and rephasing intervals of the sequence (i.e., the time intervals between the first and second π/2 radiofrequency pulses and between the third π/2 radiofrequency pulse and acquisition) as short as possible. The absence of disturbing magnetic susceptibility effects under our experimental conditions was confirmed by verifying that the measured diffusivity did not change upon increasing the dephasing and rephasing intervals of the PGSTE LED sequence (while keeping the effective diffusion time constant).36 Diffusion data were obtained from PFG NMR attenuation curves, i.e., the dependence of the PFG NMR signal intensity on the amplitude of the magnetic field gradient. The signal intensity was obtained by integrating the area under the single line of the 13 C NMR spectrum of CF4. In the simplest case when all probed molecules in a PFG NMR sample diffuse isotropically with the same diffusivity according to the laws of normal (i.e., Fickian) diffusion, the signal attenuation measured by the PGSTE LED sequence can be expressed as37

MIL-53(V), a metal−organic framework material where onedimensional diffusion was observed.32 In this paper we report the application of 13C PFG NMR in combination with molecular dynamics (MD) simulations to study diffusion of tetrafluoromethane (CF4) in aluminosilicate nanotubes for various CF4 loadings inside nanotubes. PFG NMR studies of CF4 selfdiffusion in aluminosilicate nanotubes have benefited from the possibility of combining the advantages of high (17.6 T) magnetic field and large (up to 30 T/m) magnetic field gradients under our measurement conditions. CF4 loadings inside nanotubes were obtained from complementary sorption studies performed by NMR and grand canonical Monte Carlo (GCMC) simulations.

2. EXPERIMENTAL SECTION Single-walled aluminosilicate nanotubes were synthesized according to the protocol given in the literature.18,20 A tetraethoxysilane and aluminum-trisec-butoxide mixture (1:2) was added dropwise to an aqueous solution of 0.05 M HClO4 at 25 °C. After 18 h of vigorous stirring, the solution was heated to 95 °C for 4 days. The nanotubes were then precipitated by addition of a 30 wt % ammonia solution. The resulting gel was centrifuged and 10 N HCl was added dropwise to redisperse the nanotubes. The nanotube dispersion was dialyzed against deionized water for 4 days using a 15 kDa membrane to obtain a pure nanotube dispersion. Nanotube powder samples were prepared by freeze-drying the pure nanotube dispersion solution at −50 °C for 5 days. The nanotubes exhibit uniform channels having an outer diameter of ∼2.8 nm and an inner diameter of ∼1.6 nm.33 Figure 1A shows an SEM image of the studied nanotube sample. The size of the nanotube aggregates ranges from half a micrometer to a few tens of micrometers. The image was recorded using a JEOL 6400 scanning electron microscope (SEM) at the UF Major Analytical Instrumentation Center. Aluminoscilicate nanotubes dispersed on a TEM grid from an aqueous suspension are shown in Figure 1B and have an average length of 400 nm. Nanotube sample volumes of 2 μL were directly taken from a batch reactor at the end of the reaction and pipetted onto thin carbon-coated 400-mesh copper grids and immediately blotted with Whatman no. 4 filter paper. Images for nanotube size analysis were recorded using a JEOL JEM-1400 transmission electron microscope (TEM) operating at 120 kV. An Orius SC1000 CCD was used to display the samples. The nanotube length distribution was determined with the help of ImageJ software. The aluminosilicate nanotube powder samples were prepared for PFG NMR measurements using the following procedure.

ψis(q , teff ) = exp( −q2teff D)

(1)

where D is the self-diffusion coefficient, q = γgδ, γ is the gyromagnetic ratio, δ denotes the duration of an applied gradient pulse with amplitude g, and teff is the effective diffusion time, which corresponds to the observation time in a PFG NMR measurement. A more complex behavior is observed when more than one type of diffusing molecule is present in a sample and/or when the diffusion process is not isotropic. For each diffusion time, the PFG NMR attenuation curves were measured by a stepwise increase of the gradient amplitude up to its maximum 21351

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the number of moles of CF4 and the NMR signal originating from these molecules to be obtained. This relationship was used to calculate the number of moles of CF4 in the nanotube bed of sample (ii). The CF4 pressure in this sample was obtained from the estimated number of moles of CF4 in the gas phase of the sample above the bed using the real gas equation of state.38 Since the volume of the nanotube bed includes the void space between the individual nanotubes and/or nanotube aggregates, determination of the loading, as shown in Figure 2, requires an estimate of the fraction of the bed volume occupied by the nanotubes and nanotube aggregates (k).

value (30 T/m), while keeping constant all other parameters of the PGSTE LED sequence. The maximum gradient duration was 1.4 ms. Carbon-13 PFG NMR was employed to take advantage of the longer 13C T2 relative to those which are typically observed for 19 F or 1H nuclei on guest molecules confined in nanopores. In particular, proton T2 relaxation times of molecules confined in nanopores tend to be very short due to intramolecular and intermolecular dipole−dipole interactions that are not completely averaged out by molecular motion and/or due to magnetic susceptibility effects.36 Such effects are reduced when using 13C NMR detection. The longitudinal (T1) and transverse (T2) NMR relaxation times were estimated using the data obtained with the PGSTE LED sequence in the absence of applied magnetic field gradients. T2 and T1 were measured by incrementing the time intervals between the first and second radiofrequency π/2 pulses or the second and third radiofrequency π/2 pulses of the PGSTE LED sequence, respectively. Under our experimental conditions, the T1 times ranged from 12 to 33 ms and the T2 times ranged from 1.5 to 2.7 ms. Measurement of adsorption isotherms by NMR is based on the proportionality between the area under the NMR line and the number of nuclei contributing to the line. The data in Figure 2

3. SIMULATION DETAILS The construction and the structural optimization of atomic models for single-walled aluminosilicate nanotubes have been described previously.22,24,39,40 Adsorption isotherms were calculated at 298 K for tetraflouromethane using GCMC as implemented in the MUSIC simulation code.41 Molecules were only inserted within the nanotube pore in these simulations. The CLAYFF42 force field for nanotubes was used, as explained in our previous work.22,24,39,40 Parameters for tetraflouromethane were taken from Heuchel et al.43 The flexibility of hydroxyl groups was included in our GCMC simulations as described previously,40 with all atoms in the nanotubes being fixed in position except for the surface hydroxyl groups. To examine the diffusion of CF4 and CF4/water mixtures in the nanotubes, we performed NVT MD simulations at 298 K using a Nosé-Hoover thermostat. The simple point charge (SPC) model was used for water. Unlike our GCMC calculations, all atoms in the nanotubes were allowed to move in the MD calculations. After equilibrating the system for 0.4 ns, MD simulations were run for 2 ns with a time step of 1 fs. The self-diffusion coefficients44 were calculated by averaging data over 10 independent trajectories for tetraflouromethane and tetraflouromethane/water mixtures with 10, 20, and 30 water molecules in simulation cell with nanotube length of 1.68 nm (saturation loading for single-component water is about 77). 4. RESULTS AND DISCUSSION Figure 2 shows the loading of CF4 in aluminosilicate NTs at 298 K as a function of the CF4 pressure in the surrounding gas phase. The adsorption isotherm data in this figure were obtained by GCMC simulations (open circles) and by NMR (filled symbols). As seen in Figure 2, satisfactory agreement between the experimental NMR data and the simulation results are obtained for k values of around 0.7 and 0.8. Such values of k are within the range that can be expected for the studied beds taking into account the planar shape of the majority of the nanotube aggregates (see Figure 1A). Figure 3 shows PFG NMR attenuation curves corresponding to CF4 diffusion in a nanotube bed for different values of the CF4 pressure in the gas phase at 298 K. These curves do not have any contributions from gas molecules that diffuse only in the gas phase of the samples. These contributions, which have been estimated in a separate experiment on an NMR tube containing only the gas at the same pressures, have been subtracted away from the attenuation curves measured for the nanotube samples. It is evident that none of the attenuation curves exhibit the monoexponential behavior defined in eq 1. This result, for the most part, is a consequence of the strongly anisotropic diffusion expected inside the nanotubes. For intrachannel diffusion within one-dimensional channels, which are randomly oriented in space,

Figure 2. Adsorption of CF4 in aluminosilicate nanotubes at 298 K. Solid symbols represent the loadings estimated from the measured NMR signal for different values of the nanotube packing factor (k), viz. the fraction of the bed volume occupied by the nanotubes and nanotube aggregates. Open circles show the data obtained by GCMC simulations.

were calculated from the intensities of the CF4 13C NMR signals acquired by application of the one pulse sequence to the following two types of samples: (i) a sealed NMR tube containing a known amount of CF4 and (ii) a sealed NMR tube containing the same amount of CF4 and a known amount of the aluminosilicate nanotube sample. The signal in sample (i) originates from the gas in the detected region of the NMR tube. The length of this region was found to be around 30 mm. The signal of sample (ii) was found to have comparable contributions from the nanotube bed, which occupied around 23 mm of the NMR tube, and from the gas phase within the detected region above the nanotube bed, around 7 mm in length. These contributions were estimated using the ratio of the signals in samples (i) and (ii), the known amount of CF4 in both samples, the length of the detected region of the NMR tube, and the total tube length. The signal measured in sample (i) and the known amount of CF4 in this sample allowed the relationship between 21352

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the attenuation function ψintra(q,teff), can be expressed in the following form:37,45 ψintra(q , teff ) = ×

1 π exp( −q2teff D⊥) 2

erf( q2teff (D − D⊥) ) q2teff (D − D⊥)

(2)

where D∥ and D⊥ are the diffusivities along the directions parallel and perpendicular to the channel axis, respectively. In addition to the sorbate molecules that diffuse inside the nanotubes and/or nanotube aggregates during the diffusion times used, we can also expect a fraction of CF4 molecules that diffuse according to the mechanism of the so-called long-range diffusion,46 i.e., diffusion leading to fast exchange between the nanotube interiors and the surrounding gas phase in-between nanotubes or nanotube aggregates. This expectation is supported by the observation of nanotubes and nanotube aggregates shorter than 1 μm (Figure 1A), which is smaller than the distances traveled by molecules during the diffusion times used. Thus, the expression for the overall PFG NMR attenuation curve is expected to contain two terms: ψtot(q , teff ) = plr exp( −q2teff D lr ) + pintra ψintra(q , teff )

(3)

with plr and pintra = (1 − plr) representing the fractions of molecules performing long-range diffusion with diffusivity Dlr and molecules performing diffusion inside nanotubes during the observation time, respectively. It is important to note that the diffusion of CF4 molecules inside nanotubes is not expected to be of a single-file type,26,27 i.e., diffusion under conditions when molecules cannot pass one another in narrow channels, because the collision diameter of CF4 (0.47 nm)47 is smaller than the reported effective radius of the aluminosilicate nanotubes (≥0.5 nm).18,20 The results in Figure 3A−C show that all PFG NMR attenuation curves can be described satisfactorily by eqs 2 and 3 (see dashed lines in the main figures). The inserts in the figures indicate that there are some deviations between the fitting curve and the experimental data in the range of large gradients. These deviations could result if the nanotube orientation distribution is not completely random, as is assumed in eq 2. The results in the figures indicate that for each CF4 pressure the same fitting curve can be used to describe the data obtained for different diffusion times in the studied range. Hence the corresponding best fit parameters are also independent of diffusion time. They are presented in Table 1. Table 2 shows the values of the root-mean-square displacements (rmsd) for diffusion inside the nanotubes and/or the nanotube aggregates as well as for the long-range diffusion. These values were obtained according to the Einstein relation

Figure 3. Normalized PFG NMR attenuation curves for diffusion of CF4 in a bed of aluminosilicate nanotubes at different effective diffusion times, which are indicated by different types of symbols. The attenuation curves were obtained for the following CF4 pressures in the gas phase of the sample: 4 bar (A), 8 bar (B), and 20 bar (C). The dashed line shows the best fit using eqs 2 and 3. The insets show selected PFG NMR attenuation curves measured in the larger gradient ranges.

Table 1. Results of Fitting the Attenuation Curves Shown in Figure 3 by eqs 2 and 3 pressure (bar) 4 8 20

plr 0.63 ± 0.08 0.62 ± 0.06 0.74 ± 0.04

Dlra (m2 s−1) −7

(6 ± 3) × 10 (7 ± 3) × 10−8 (1.4 ± 0.5) × 10−8

D∥ (m2 s−1)

D⊥ (m2 s−1)

−9

≲1 × 10−13 ≲ 1 × 10−13 ≲ 1 × 10−13

(3 ± 2) × 10 (1.3 ± 0.7) × 10−9 (5 ± 3) × 10−10

a The experimental error for the long-range diffusivity in the table does not include a possible contribution associated with the procedure of obtaining the attenuation curves in Figure 3 (i.e., subtracting away from the measured attenuation curves the contributions from diffusion in the gas phase of the samples).

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latter direction is expected to proceed at the intersections between individual nanotubes in the nanotube aggregates. Figure 4 provides a comparison of the values of D∥ measured by PFG NMR with the corresponding self-diffusion coefficients

Table 2. Values of the Root Mean Square Displacements (RMSD) Obtained by eq 4 for Different Effective Diffusion Times pressure (bar)

time (ms)

rmsd long-range (μm)

rmsd inside nanotube aggregates (μm)

4

4 8 4 8 16 4 8 16

120 ± 85 170 ± 120 41 ± 27 57 ± 38 81 ± 53 19 ± 10 26 ± 15 36 ± 22

5±4 7±5 3±2 5±3 6±5 2 ± 1.5 3±2 4±3

8

20

⟨rlr, 2⟩ = aD lr, teff

(4)

where a is equal to 6 and 2 for the long-range diffusion and diffusion along the channels, respectively. The observation that D∥ remains independent of diffusion time for the studied range of teff ≤ 16 ms and the corresponding range of rmsd ≤7 μm suggests that this diffusivity, for the most part, corresponds to diffusion inside large (∼10 μm) nanotube aggregates, where many nanotubes are loosely interconnected along the direction of the nanotube lengths. Electron micrographs shown in Figure 1B reveal the broad size distribution of as-synthesized nanotubes. Lengths of the nanotubes are ranging from ∼50 to 1000 nm. The average length of nanotubes is calculated to be around ∼400 nm based on the measurement of 100 individual nanotube lengths. Hence, D∥ for the most part corresponds to the diffusion process where sorbate molecules diffuse through several interconnected nanotubes. Possible transport resistances at the points of connections of individual nanotubes are likely to reduce the measured diffusivity in comparison to the unrestricted intrananotube diffusivity. Similar diffusivity reduction was recently reported for transport along several interconnected cylindrical mesopores of SBA-15 material.48 In that case the reduction of the diffusivity was also attributed to the existence of the additional transport resistances at the points of connections of individual channels. It is likely that the material connecting nanotubes can be described as noncrystalline microporous material allowing for the transport of sorbate molecules between adjacent nanotubes. The observed independence of the value of plr on diffusion time for the studied range of teff ≤ 16 ms can be explained by the existence of a broad distribution over nanotube bundle lengths. As a result, there is a fraction of sufficiently short nanotubes and nanotube aggregates contributing to the long-range diffusion, whereas for other (longer) nanotube aggregates the diffusion can be described as purely intra-aggregate for all diffusion times used. Finally, the observed independence of the long-range diffusivity on diffusion time suggests that the conditions of fast exchange between the short nanotubes/nanotube aggregates and the surrounding gas phase are fulfilled for all studied diffusion times. PFG NMR measurements for teff > 16 ms were prevented by insufficient PFG NMR signal-to-noise due to T1 NMR relaxation. From Table 1 it can be seen that diffusivity along the direction of the channels (D∥) is around 4 orders of magnitude larger than that in the direction perpendicular to the channels (D⊥). This result indicates that the transport resistance for diffusion of CF4 molecules along the channel axis is much smaller than that in the direction perpendicular to the channel axis. The transport in the

Figure 4. Dependence of self-diffusion coefficients of CF4 on its loading inside the nanotubes at 298 K. The data were obtained by PFG NMR for CF4 diffusion inside nanotube aggregates (solid diamonds), and by MD simulations for CF4 diffusion inside defect-free nanotubes under conditions of no water (open circles), and with ∼13%, 26%, and 39% of water loadings relative to single component water saturation loading (open triangles).

obtained from MD simulations for diffusion along defect-free nanotubes. It is seen that the diffusivities recorded by PFG NMR are around 1 order of magnitude smaller than the corresponding simulation results at zero water loading inside the nanotubes. Additional simulations were performed to evaluate a possible influence of residual amounts of water in the nanotubes on the intrachannel diffusivity. Residual water might still be present in the nanotubes even after the sample activation procedure used for preparations of the PFG NMR samples. The data in Figure 4 show that the presence of water reduces the difference between experiment and simulation. However, even with the water occupancy as large as 39%, the PFG NMR diffusivities remain significantly smaller than the corresponding values obtained by MD simulations. As discussed above, lower PFG NMR values are not unexpected because under our measurement conditions sorbate molecules travel through several interconnected nanotubes and, as a result, may experience additional transport resistances at the points of the nanotube connections. These considerations provide an explanation for the observed differences between the PFG NMR and simulation data in Figure 4.

5. CONCLUSIONS In this paper we report results of studies of tetrafluoromethane (CF4) diffusion in aluminosilicate nanotubes by PFG NMR and by MD simulations. The experimental data were obtained by high-field and high-gradient 13C PFG NMR. The PFG NMR data reveal the presence of the following two ensembles of molecules: (i) molecules diffusing under conditions of fast exchange between nanotube aggregates and the gas phase between the aggregates and (ii) molecules performing diffusion inside the nanotube aggregates. The diffusivity along the channels inside the nanotube aggregates was found to be significantly lower than the corresponding intrananotube diffusivities obtained by MD simulations. This difference was attributed to the observation that under our experimental conditions, the root MSD values of molecules diffusing along the channels inside the nanotube 21354

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(23) Zang, J.; Nair, S.; Sholl, D. S. J. Chem. Phys. 2011, 134. (24) Zang, J.; Konduri, S.; Nair, S.; Sholl, D. S. ACS Nano 2009, 3, 1548. (25) Gupta, V.; Nivarthi, S. S.; McCormick, A. V.; Davis, H. T. Chem. Phys. Lett. 1995, 247, 596. (26) Hahn, K.; Karger, J.; Kukla, V. Phys. Rev. Lett. 1996, 76, 2762. (27) Kukla, V.; Kornatowski, J.; Demuth, D.; Gimus, I.; Pfeifer, H.; Rees, L. V. C.; Schunk, S.; Unger, K. K.; Karger, J. Science 1996, 272, 702. (28) Jobic, H.; Hahn, K.; Karger, J.; Bee, M.; Tuel, A.; Noack, M.; Girnus, I.; Kearley, G. J. J. Phys. Chem. B 1997, 101, 5834. (29) Jobic, H.; Farago, B. J. Chem. Phys. 2008, 129. (30) Brandani, S.; Ruthven, D. M.; Karger, J. Microporous Mater. 1997, 8, 193. (31) Das, A.; Jayanthi, S.; Deepak, H. S. M. V.; Ramanathan, K. V.; Kumar, A.; Dasgupta, C.; Sood, A. K. ACS Nano 2010, 4, 1687. (32) Salles, F.; Jobic, H.; Maurin, G.; Koza, M. M.; Llewellyn, P. L.; Devic, T.; Serre, C.; Ferey, G. Phys. Rev. Lett. 2008, 100. (33) Yucelen, G. I.; Kang, D. Y.; Guerrero-Ferreira, R. C.; Wright, E. R.; Beckham, H. W.; Nair, S. Nano Lett. 2012, 12, 827. (34) Gibbs, S. J.; Johnson, C. S. J. Magn. Reson. 1991, 93, 395. (35) Cotts, R. M.; Hoch, M. J. R.; Sun, T.; Markert, J. T. J. Magn. Reson. 1989, 83, 252. (36) Vasenkov, S.; Galvosas, P.; Geier, O.; Nestle, N.; Stallmach, F.; Karger, J. J. Magn. Reson. 2001, 149, 228. (37) Callaghan, P. Principles of Nuclear Magnetic Resonance Microscopy, 1st ed.; Oxford University Press: New York, 1994. (38) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 4th ed.; McGraw: New York, 1987. (39) Konduri, S.; Mukherjee, S.; Nair, S. ACS Nano 2007, 1, 393. (40) Zang, J.; Chempath, S.; Konduri, S.; Nair, S.; Sholl, D. S. J. Phys. Chem. Lett. 2010, 1, 1235. (41) Gupta, A.; Chempath, S.; Sanborn, M. J.; Clark, L. A.; Snurr, R. Q. Mol. Simul. 2003, 29, 29. (42) Cygan, R. T.; Liang, J. J.; Kalinichev, A. G. J. Phys. Chem. B 2004, 108, 1255. (43) Heuchel, M.; Snurr, R. Q.; Buss, E. Langmuir 1997, 13, 6795. (44) Sholl, D. S. Acc. Chem. Res. 2006, 39, 403. (45) Naumov, S.; Valiullin, R.; Karger, J.; Pitchumani, R.; Coppens, M. O. Microporous Mesoporous Mater. 2008, 110, 37. (46) Karger, J. Ann. Phys. 1969, 24, 1. (47) delRio, F.; Ramos, J. E.; GilVillegas, A.; McLure, I. A. J. Phys. Chem. 1996, 100, 9104. (48) Menjoge, A. R.; Huang, Q. L.; Nohair, B.; Eic, M.; Shen, W.; Che, R. C.; Kaliaguine, S.; Vasenkov, S. J. Phys. Chem. C 2010, 114, 16298.

aggregates are much larger than the average nanotube length in the aggregates. Hence, these molecules are likely to experience additional transport resistances at the points of interconnections of individual nanotubes. Presence of structural defects inside nanotubes may also lead to lower diffusivities measured by PFG NMR.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +1 352 392 0315. Fax: +1 352 392 0315. E-mail: [email protected]fl.edu. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS NMR data were obtained at the Advanced Magnetic Resonance Imaging and Spectroscopy (AMRIS) facility in the McKnight Brain Institute of the University of Florida. This material is based upon work supported by the National Science Foundation under Grant No. CHE-0957641. S.N. and D.S.S. acknowledge partial support of this work from the NSF (Awards No. CBET-846586 and No. CBET −0966582). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. Helpful discussions with Prof. Haskell W. Beckham (Georgia Institute of Technology) are gratefully acknowledged.

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