Adsorption and Diffusion of Fluids in Defective Carbon Nanotubes

Sep 15, 2017 - Single-walled carbon nanotubes (SWNTs) have been shown from both simulations and experiments to have remarkably low resistance to gas a...
0 downloads 11 Views 2MB Size
Download PDF
Article Cite This: Langmuir 2017, 33, 11834-11844

pubs.acs.org/Langmuir

Adsorption and Diffusion of Fluids in Defective Carbon Nanotubes: Insights from Molecular Simulations Benjamin J. Bucior,†,‡ German V. Kolmakov,†,§ JoAnna M. Male,† Jinchen Liu,† De-Li Chen,†,∥ Prashant Kumar,† and J. Karl Johnson*,† †

Department of Chemical & Petroleum Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, United States Chemical & Biological Engineering, Northwestern University, Evanston, Illinois 60208, United States § Physics Department, NYC College of Technology, the City University of New York, Brooklyn, New York 11201, United States ∥ Institute of Physical Chemistry, Zhejiang Normal University, Jinhua 321004, China ‡

ABSTRACT: Single-walled carbon nanotubes (SWNTs) have been shown from both simulations and experiments to have remarkably low resistance to gas and liquid transport. This has been attributed to the remarkably smooth interior surface of pristine SWNTs. However, real SWNTs are known to have various defects that depend on the synthesis method and procedure used to activate the SWNTs. In this paper, we study adsorption and transport properties of atomic and molecular fluids in SWNTs having vacancy point defects. We construct models of defective nanotubes that have either unrelaxed defects, where the overall structure of the SWNT is not changed, or reconstructed defects, where the bonding topology and therefore the shape of the SWNT is allowed to change. Furthermore, we include partial atomic charges on the SWNT carbon atoms due to the reconstructed defects. We consider adsorption and diffusion of Ar atoms and CO2 and H2O molecules as examples of a noble gas, a linear quadrupolar fluid, and a polar fluid. Adsorption isotherms were found to be fairly insensitive to the defects, even for the case of water in the charged, reconstructed SWNT. We have computed both the selfdiffusivities and corrected diffusivities (which are directly related to the transport diffusivities) for each of these fluids. In general, we found that at zero loading that defects can dramatically reduce the self- and corrected diffusivities. However, at high, liquidlike loadings, the self-diffusion coefficients for pristine and defective nanotubes are very similar, indicating that fluid−fluid collisions dominate the dynamics over the fluid−SWNT collisions. In contrast, the corrected diffusion coefficients can be more than an order of magnitude lower for water in defective SWNTs. This dramatic decrease in the transport diffusion is due to the formation of an ordered structure of water, which forms around a local defect site. It is therefore important to properly characterize the level and types of defects when accurate transport diffusivities are needed.

■

INTRODUCTION

rise to strikingly high diffusivities of gases and liquids in comparison to porous materials having similar size pores.14−22 Most molecular modeling studies on adsorption and diffusion in CNTs assume perfect, defect-free CNTs in order to simplify calculations. However, real CNTs contain some level of defects that depend on the synthesis method and postsynthesis purification. Experimental studies indicate that high-quality single-walled carbon nanotubes (SWNTs) may have defect densities as low as one defect per 4 μm,23,24 corresponding to about 1 defect in 1012 carbon atoms in the SWNT. Defects in SWNTs are thought to be mainly point defects, with single and divacancies being most common.25

Molecular diffusion through nanoporous materials plays a key role in many industrial applications for gas separations and catalytic processes.1−3 Polymeric membranes are widely used for gas separation applications, but their performance is limited by a universal compromise between permeability and selectivity.4−6 Mixed matrix membranes (MMM) are hybrid materials consisting of a polymer and a dispersed filler; these are promising materials that have the potential to outperform polymer membranes,transcending their limits of performance, while still retaining many of their advantages.7−9 Materials used for the dispersed phase in MMM include porous materials such as zeolites, metal organic frameworks, carbon molecular sieves, and so forth. Carbon nanotubes (CNTs), in both their multiand single-walled forms, have also been used as fillers in MMM to enhance fluid transport for both gases and liquids.10−13 The advantage of using CNTs over other filler materials is that the internal pores of CNTs can be atomically smooth, which gives © 2017 American Chemical Society

Special Issue: Tribute to Keith Gubbins, Pioneer in the Theory of Liquids Received: August 16, 2017 Revised: September 15, 2017 Published: September 15, 2017 11834

DOI: 10.1021/acs.langmuir.7b02841 Langmuir 2017, 33, 11834−11844

Article

Langmuir

correction factor and can be calculated from the equilibrium adsorption isotherm. The corrected diffusivity can be computed from the equilibrium molecular dynamics (EMD) simulations14,36,37 as

The aim of this study is to quantify the impact of realistic types and densities of defects on adsorption and molecular diffusion in SWNTs. We consider three classes of adsorbates: spherical (argon), linear quadrupolar (CO2), and nonlinear dipolar (H2O). We study vacancy defects over a range of concentrations, from 0.75% to 2.75% of missing carbon atoms. While this density of defects is much higher than the estimated values for high-quality SWNTs,23,24 they are probably in a reasonable range for SWNT samples that have had their caps removed by etching and subsequent annealing.26,27 We consider the effect of defect reconstruction and the resulting atomic partial charges due to defects. We also account for the impact of nanotube flexibility on diffusion of Ar through pristine and defective SWNTs. Carbon nanotubes were first discovered by Iijima as multiwalled structures consisting of concentric shells.28 Single-walled carbon nanotubes (SWNTs) were found later by both Iijima and Ichihashi29 and Bethune et al.30 The diameter, helicity and electronic properties of SWNTs are defined by the nanotube indices, (n, m), where n and m are integers.31 These indices define how the SWNT may be formed by mapping a graphene sheet to the surface of a cylinder. In this work, we consider nanotubes defined by the indices (10, 10), having a diameter of 1.356 nm. We chose this size because it is consistent with the diameters most commonly observed in experimentally produced SWNT samples.32−34 Two different diffusivities are of interest in both experiments and simulations. These are self- and transport diffusivity. Selfdiffusivity characterizes the diffusion of a single tagged molecule through a fluid. The self-diffusion coefficient, Ds, can be measured experimentally through incoherent quasi-elastic neutron scattering (QENS) and pulsed field gradient NMR.1,35 Molecular simulations can be used to measure the self-diffusion coefficient through the Einstein relation, Ds(c) = lim

t →∞

1 2dt

1 N

N

D0(c) =

N

(1)

where c is the concentration or density, t is the time, N is the number of molecules in the system, d is the dimensionality (which for SWNTs is 1), and ri is the vector position of molecule i. Transport diffusivity relates the macroscopic flux of molecules in a system to a driving force in the concentration. It is defined by Fick’s law of diffusion, J = −Dt (c)∇c

(2)

where J is the flux, Dt is the transport diffusion coefficient, and ∇c is the gradient of the concentration. Dt is also known as the Fickian diffusion coefficient. The self- and transport-diffusion coefficients depend on concentration in different ways in microporous solids and have different values except at zero concentration where they are equal.1 In contrast to selfdiffusivity, the transport diffusivity is a collective property, depending on the motion of the entire fluid. The transport diffusivity can be defined in terms of the corrected diffusivity, D0, as ⎛ ∂ln f ⎞ ⎟ Dt (c) = D0(c)⎜ ⎝ ∂ln c ⎠T

(4)

where ⟨...⟩ denotes an average over multiple independent EMD trajectories, each of which contain N mobile molecules. As follows from eq 4, the corrected diffusivity is related to the diffusive motion of the center of mass of the mobile molecules in the simulation volume. In this paper, we compute both Ds and D0, for Ar, CO2, and H2O in pristine and defective SWNTs. We do not compute Dt because we find that defects have very little impact on the adsorption isotherms. Moreover, computation of Dt from D0 requires numerically fitting of the adsorption isotherms and taking derivatives of the fitted data, as seen in eq 3. This process introduces numerical uncertainty, making examination of D0 the most direct method of assessing the impact of defects on transport diffusivity. There are many simulation studies reported in the literature that consider the impact of defects or point charges or modifications of the solid−fluid potentials on adsorption and mobility of molecules in CNTs and related materials. However, to the best of our knowledge, none of these studies consider the impact of defects on transport diffusivities. Moreover, the models used to represent defects in SWNTs are typically not realistic in light of what is known about the defect levels and types of defects in high-quality SWNT samples. Our study addresses both of these deficiencies: we compute both self- and corrected diffusion coefficients and we consider concentrations and types of defects that might be found in high-quality heattreated SWNT samples. We here review previous work on defective SWNTs and related systems. Several groups have studied the impact of defects on the adsorption of molecular hydrogen in CNTs. Most studies consider physisorption on Stone−Wales-like defects using classical potential models.38−42 Hydrogen diffusion into SWNTs through vacancy defects and binding to the defects has been studied using density functional theory (DFT) electronic structure methods.43,44 They found enhanced binding of H2 at defect sites. However, none of these studies reported diffusion coefficients. Lithium interaction with pristine and defective SWNTs has been studied by Nishidate and Hasegawa45 using DFT. They studied the energy barriers and diffusion dynamics for Li migrating through defects in the SWNT sidewall from the outside to the inside of the nanotube. Xenon adsorption in defective and pristine (10,10) SWNTs was studied by MD simulations using classical two-body and many-body potentials.46 The defective SWNTs had multiple Stone−Wales defects. The adsorption isotherms and isosteric heats in the pristine and defective SWNTs were found to be qualitatively similar. Kuznetsova et al.47 studied the impact of the degree etching of SWNTs with ozone on the adsorption kinetics and amount of Xe adsorbed at low temperatures using both experiments and simulations. They found that the adsorption rate is maximized for defects of about 0.5−0.7 nm in radius, with both the rate of adsorption and the surface area decreasing upon further etching. They also noted that polar functional groups at the perimeter of the defect sites cause a

∑ |ri(t ) − ri(0)|2 i=i

1 1 lim ⟨|∑ ri(t ) − ri(0)|2 ⟩ 2dN t →∞ t i = i

(3)

Here, f is the fugacity of the bulk fluid in equilibrium with the adsorbed phase at the given concentration c at temperature T. The derivative term is referred to as the thermodynamic 11835

DOI: 10.1021/acs.langmuir.7b02841 Langmuir 2017, 33, 11834−11844

Article

Langmuir

create hydrophilic tubes, and transport of water/methanol mixtures was measured through functionalized and unfunctionalized SWNTs.56 A constant chemical potential gradient across the nanotube was maintained though the dual-control-volume grand canonical molecular dynamics formalism.60 They found that the overall flux of the mixture through the nanotubes was faster for the hydrophilic than the unfunctionalized hydrophobic SWNT of similar effective diameter. However, the increase in flux was due to entrance effects. The hydrophilic SWNTs filled more rapidly than hydrophobic, but once molecules were in the nanotubes the mobility of molecules was faster for the unfunctionalized hydrophobic SWNTs.56 Huang et al.57 studied the impact of carboxylic acid groups attached to the entrance of narrow (6,6) and (10,0) SWNTs. They found that the functional groups blocked entry of water for the (10,0) case but allowed entry for the (6,6) case.57 A similar study examined functionalization of (6,6), (7,7), (10,0), and (12,0) SWNTs with carboxylic and methyl moieties on one or both ends.58 Structural properties of the water in the nanotubes was analyzed for the functionalized and unfunctionalized pristine SWNTs. The methyl functional groups had no impact on the structure of the water in the SWNTs, whereas the carboxylic acid groups impacted the density of water molecules at the ends of the nanotubes, with results depending on the diameter and helicity of the SWNT.58 Other researchers have also studied placement of functional groups at the ends of SWNTs and their impact on water transport. Chan et al.13 found that zwitterions attached to the ends of SWNTs decreased water flux but increased salt rejection for desalination. These effects were found to be dominated by steric hindrance due to the zwitterion functional groups, rather than due mainly to charge interactions. In contrast, fluorine atoms at the ends of SWNTs were found to increase water flux compared to unfunctionalized nanotubes.61 Self-diffusion coefficients for water passing through a model SWNT membrane were found to be slightly larger when the nanotubes were functionalized with fluorine atoms at each end.61 The effect of partial charges at the ends of finite-length (6,6) SWNTs on the self-diffusion of water has been studied by Sahu and Ali.62 They computed partial charges at the ends of SWNT terminated with H atoms to saturate the dangling bonds and computed flux of water through nanotubes with and without charges. They found that the charges modestly increased the entry rate of water into the nanotube and hence the diffusivity of water through the SWNT having charges at the ends. A similar study by Won et al.63 examined the effects of partial charges on transport of water through finite sized (6,6) and (10,0) SWNTs, where the terminal carbon atoms were not saturated (i.e., had dangling bonds). The charge profiles are substantially different on the (6,6) and (10,0) SWNTs, although they have very similar diameters. The charges at the ends of (10,0) SWNTs are close to a factor of 5 larger in magnitude than the charges on the ends of the (6,6) SWNTs. They found that charges increased the self-diffusion coefficients by around 20% relative to uncharged nanotubes. Surprisingly, the larger charges on the (10,0) SWNT did not result in a larger increase in the diffusivity compared with the (6,6) SWNT. The slower self-diffusion in the charged (10,0) compared with the charged (6,6) SWNT was attributed to a more corrugated potential of mean force inside the charged (10,0) SWNT.63 The transport properties of single-file water through a (6,6) SWNT having external point charges have been studied as a

reduction in the rate of adsorption. Diffusivities were not computed. The transport of water through SWNTs has been studied more comprehensively than any other fluid, from both experiments and simulations (see Holt,20 Hassan et al.,48 and references therein). We here summarize results from several groups who have studied water interacting with defective or functionalized SWNTs, and closely related systems. Vijayaraghavan and Wong studied pressure-driven flow of water through SWNTs of various diameters with and without vacancy defects.49 They studied a range of defect densities and two different defect sizes. They observed a decrease in the number of water molecules transported through the defective SWNTs due to loss of molecules from the defects to the outside of the SWNT, because the defects were large enough to allow water to cross through the nanotube wall. No diffusion coefficients were computed. Li et al.50 studied water permeation through nitrogen-doped double-walled carbon nanotubes. They used narrow diameter inner tubes, such that only a single-file of water molecules is possible. They found that there is a threshold of interaction energy of about −34 kJ/mol between the defect and the water molecule, below which the flow was not affected. Carbonyl groups bound to the inside of SWNTs have been used as a way of modeling chemical heterogeneity on SWNTs.51−54 We note that binding chemical moieties to the inside of SWNTs is generally not energetically favorable because of the high degree of curvature, making the formation of chemical bonds to the carbons inside SWNTs improbable. Indeed, ozone attack of SWNTs is known to produce oxygen containing functional groups on the outside wall of the nanotube, pointing outward rather than into the nanotube.55 Nevertheless, binding functional groups to the interior of SWNTs provides an extreme example of defects. Zhu et al.53 considered the effect of carbonyl groups anchored to the inner wall of (8,8) and (10,10) SWNTs on the hydration of cations inside the modified SWNTs. The carbonyl groups were observed to modify the structure of water in the first hydration shells of the ions. Dynamics were not considered. In similar work, Wu et al.54 studied how internally bound carbonyl groups and electric fields impact the density profiles, orientational, and hydrogen bonding properties of water confined in functionalized (8,8) SWNTs. They found that three rings of carbonyl groups (24 CO moieties) in the SWNT had a larger impact on the structure of H2O than the strongest electric field of 1.0 V/ nm.54 Striolo and co-workers studied the impact of carbonyl groups on the adsorption of water and found that these polar groups can dramatically impact the adsorption at low pressures because of strong hydrogen bonds between the carbonyl groups and the adsorbing water molecules.51 Striolo also studied the impact of a single ring of carbonyl groups inside a narrow (8,8) SWNT on the mobility of water inside the functionalized SWNT.52 As could be expected, the ring of inward pointing carbonyl groups presents a significant barrier to diffusion, resulting in low mobility at low water concentrations, increasing mobility at intermediate loading, and again slower mobility when the SWNT is filled with water. Diffusion coefficients were not reported; results were based on comparison of mean square displacement plots.52 Several studies have investigated the effect of carboxylic acid groups bound to the inside or ends of SWNTs.56−59 The insides of SWNTs of various diameters were functionalized with a high density of carboxylic acid groups, 1.59/nm2, to 11836

DOI: 10.1021/acs.langmuir.7b02841 Langmuir 2017, 33, 11834−11844

Article

Langmuir

Figure 1. From left to right, structures of (a) (10,10) SWNT with no defects, (b) defective, nonreconstructed SWNT with 2.75% defects, generated by randomly removing carbon atoms without relaxation or reconstruction of the structure, and (c) defective, reconstructed SWNT with 0.83% defects, periodically repeated every three unit cells of the pristine SWNT.

Figure 2. Distribution of charges in a defective, reconstructed single-walled nanotube with 0.83% defects. (a) Histogram showing the distribution of carbon atomic charges on a defective SWNT. The charges were calculated by fitting the DFT electrostatic potential.76 The atomic charges are distributed in the range from 0.84 to −0.91e, where e is the elementary charge. (b) Representation of charges on the SWNT. The carbon atoms are positioned at each vertex; the links between the vertices represent the carbon−carbon chemical bonds and the color maps to the charge on each carbon.

relative contributions of the number of defect sites, flexibility, charges, and hydrogen bonding, on transport in models of SWNTs.

model of water transport through biological channels.64 The number of water molecules as a function of time passing through the SWNT was observed and free energy profiles were calculated. Charges produce a more corrugated free energy profile, but do not induce directional flow. Joseph and Aluru examined the velocity and concentration profiles for water in four different model nanotubes. They compared larger diameter (16,16) SWNTs with similar sized boron nitride nanotubes, a nanotube having the same geometry as the (16,16) SWNT but having much stronger van der Waals interactions with water, as modeled by using Lennard-Jones parameters for silicon, and a rough nanotube composed of three rings of a (16,16) SWNT followed by three rings of a (18,18) SWNT, periodically repeated.65 They demonstrated that the structure and velocity profiles are sensitive to the potentials and structures of the nanotubes. Others have noted that, in some cases, small changes to the selected force field parameters for H2O-SWNT interactions can lead to large changes in water occupancy in SWNTs and the formation of ice-like structures.66,67 The velocity profiles in the rough nanotubes are dramatically smaller than those in the pristine SWNTs. Moreover, the value of the solid−fluid potential also adversely affects the velocity profiles.65 Note that the extreme roughness they considered is not a realistic model of any of the expected defects in high quality SWNT samples. In this work, we focus on diffusion of argon, carbon dioxide, and water in SWNTs for both defect-free (pristine) and defective cases. The pristine nanotubes are atomically smooth, with no asperities on the inside of the nanotube. This smoothness of the nanotube walls results in very long slip lengths,68,69 which corresponds to high values of the corrected diffusivity of the fluid. In contrast, in defective nanotubes the scattering of the molecules on the walls could be relatively strong and could lead to much lower corrected diffusivities, depending on the density of defects.70 This work will assess the

■

METHODS

We studied three primary configurations of single-walled nanotubes (SWNTs) in this work, illustrated in Figure 1. The pristine SWNT is the base approximation commonly used in molecular simulations. The coordinates for this defect-free SWNT were generated from geometric parameters for an ideal (10,10) SWNT. For comparison, we generated simple models of nanotubes containing structural defects. To introduce these defect sites, we removed random individual carbon atoms from the nanotube walls. Furthermore, we considered two distinct cases of defective structure. In the first, we randomly eliminated carbon atoms from the walls and fixed the structure in place (Figure 1b). In the second, we remove one carbon atom from a supercell constructed from three primitive cells of the SWNT (each primitive cell contains 40 carbon atoms or 0.83% defects), followed by a finite temperature ab initio molecular dynamics simulation to allow for reconstruction of the carbon−carbon bonds and shape of the nanotube. The final reconstructed defective nanotube is shown in Figure 1c. In order to capture the effects of the charge distribution created by the defects, we considered both neutral and charged models for a defective, reconstructed SWNT. The defective carbon nanotube was built based on (10, 10) armchair nanotube with three unit cells, and a large supercell with dimension of 2.5 × 2.5 × 0.738 nm was used in our DFT calculations. The structure was optimized using the PW91 functional71 within the Vienna ab initio simulation package (VASP),72−75 using Γ-point sampling of the Brillouin zone. A kinetic energy cutoff of 500 eV was used for all of the calculations. The atomic charges for the defective, reconstructed nanotube were fitted to the periodic electron densities from our DFT calculations by employing the electrostatic fitting algorithm of Chen et al.76 These charges were then used in our classical simulations to account for the electrostatic interactions between polar molecules and the defective nanotube. The distribution of the charges in a defective single-walled nanotube near a defect site are presented in Figure 2a. It is seen that the atomic charges 11837

DOI: 10.1021/acs.langmuir.7b02841 Langmuir 2017, 33, 11834−11844

Article

Langmuir are distributed in the range from 0.84 to −0.91e, where e is the elementary charge. The charges on each of the atoms are presented as a color map in Figure 2b. Unsurprisingly, partial charges are concentrated near the defect site. We used grand canonical Monte Carlo (GCMC) techniques77 to compute the adsorption isotherms for Ar, CO2, and H2O. We studied adsorption for Ar in pristine SWNTs and defective, nonreconstructed SWNTs at multiple levels of defects. We studied the adsorption of CO2 and H2O in pristine SWNTs and defective, reconstructed SWNTs with and without charges on the sidewall. In most of our simulations, we used a rigid SWNT model, holding the carbon atoms of the SWNT stationary at their original coordinates. In a few of the Ar simulations, denoted “flexible,” we replaced the rigid SWNT backbone with an explicitly flexible SWNT, which modeled carbon−carbon interactions with the second-generation Reactive Empirical Bond Order (REBO) potential,78 a force field that has been used in several studies for modeling flexible CNTs.49,79−81 To prevent rotation or translation of the CNT, three of the atoms along the CNT were held at their original positions using Hookean springs.80 In order to study transport properties, we used classical molecular dynamics simulations using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) software package82 and visualized the trajectories with Visual Molecular Dynamics (VMD).83 We performed classical simulations of pure light gases in pristine and defective nanotubes to compute self-diffusivities and corrected diffusivities. The fluid components, namely, argon, carbon dioxide, and water, were simulated with appropriate charges, harmonic bonds, and Lennard−Jones pairwise potentials, and utilized the PPPM (particle−particle particle-mesh) technique84 for electrostatic calculations. Cross interaction terms were calculated using Lorentz− Berthelot combining rules. As in a previous study of diffusion in nanotubes,15 interaction parameters for carbon atoms in the SWNT were taken from Steele.85 Lennard−Jones parameters for argon were taken from Skoulidas and Sholl,86 and the TraPPE potential was used for carbon dioxide.87 Water was modeled with TIP3P parameters modified for long-range Coulombic interactions.88 The bulk selfdiffusivity of this TIP3P water model at ambient conditions was reported to be 4.0 × 10−5 cm2/s.88 This value is somewhat larger than the experimentally reported value of 2.57 × 10−5 cm2/s.89 We simulated diffusion in the zero density limit by disabling the interactions between gas molecules, such that mobile species interact exclusively with the atoms of the SWNT.90 The loading of fluid molecules in the SWNTs was accomplished with GCMC simulations at various bulk phase gas fugacities (related to pressures through the thermodynamic activity and converted to pressures through an equation of state for plotting in Figures 3 and 4).

Before collecting the MD trajectories for diffusion calculations, the system underwent a short equilibration for 1 ns under NVT conditions at 298 K. After equilibration, the linear momentum of the system was zeroed. We calculated 25 ns trajectories of Ar and CO2 and 100 ns simulations of H2O using a Nosé−Hoover thermostat at 298 K.91,92 We considered only “infinitely long” SWNTs (via periodic boundary conditions) in our simulations. Hence, we are only probing the intrinsic diffusivity, rather than the overall diffusivity measured when entrance and exit effects are included. We calculated the diffusion coefficients from the equilibrium molecular dynamics trajectories according to eqs 1 and 4. Multiple time origins were used to average the diffusivities over independent trajectories to improve the statistics.93 Each diffusivity calculation comprised 30−100 independent equilibrium molecular dynamics simulations. The center of mass trajectory and mean square displacement of the mobile atoms were averaged in groups of 10 independent runs. We calculated the mean and standard deviation of the self- and corrected diffusion coefficients for each group of 10 runs.

■

RESULTS AND DISCUSSION Below we present the results of the simulations of Ar, CO2, and H2O in various nanotube models, first discussing adsorption isotherms and then considering the diffusivity calculations. Adsorption Isotherms. We performed GCMC simulations to compare adsorption of Ar gas in pristine and unreconstructed, defective SWNT models without charges. The adsorption isotherms for Ar are shown in Figure 3. The isotherms are similar for all defect levels, indicating that the presence of defects has a minimal impact on the equilibrium adsorption. The adsorption isotherms for CO2 and H2O are shown in Figure 4. As in the case of argon, there is close agreement between the adsorption isotherms for the pristine and defective nanotubes. Since the CO2 and H2O potentials include electrostatic interactions, we have repeated the adsorption calculations for defective nanotube models with and without charges. Electrostatic interactions, which are strongest at the defect sites, have a small impact on the amount of fluid adsorbed. This is a very surprising result, especially for water, and is apparently in disagreement with previous results showing uptake of water at much lower pressure in SWNTs having the internal surface of the SWNT decorated with carbonyl groups than for pristine SWNTs.94 The reason for the small effect of the charges on adsorption isotherms of both CO2 and H2O is that the charge distribution, shown in Figure 2, is very compact, with negative charges surrounded by counterbalancing positive charges, and vice versa (red and blue surround each other in Figure 2b). Moreover, the one carbon atom that is not bonded to three other atoms is pointing out of the nanotube, which is opposite to the case modeled by Striolo and co-workers, where the charged group is pointing to the center of the nanotube from the inside wall.94 Hence, in our case, the H2O molecule interacts with a close and compact arrangement of counterbalancing charges. Therefore, the effect of the charge centers on the atoms of the nanotube is screened by the surrounding charges, at least for this type of defect (missing atoms). The result of this screening is that the charge distribution due to carbon atom vacancies does not have a significant impact on the adsorption isotherms for CO2 and H2O. This result is not expected to hold when defects involve incorporation of heteroatoms, such as oxygen. We note that adsorption isotherms of water can be very difficult to converge, especially near the transition region. We therefore caution the reader that the location of the jump in the isotherms from low to high

Figure 3. Adsorption isotherms for Ar atoms in pristine and defective (10,10) single-wall nanotubes. Defective nanotubes were generated by randomly removing atoms from a supercell containing 20 unit cells. In the simulations, atom positions were not allowed to relax or reconstruct. Temperature was set to T = 298 K. 11838

DOI: 10.1021/acs.langmuir.7b02841 Langmuir 2017, 33, 11834−11844

Article

Langmuir

Figure 4. Adsorption isotherms for (a) CO2 and (b) H2O at 298 K in pristine and defective nanotubes.

Figure 5. (a) Self-diffusion and (b) corrected diffusion coefficients for argon in the SWNT as a function of loading. Diffusion through pristine nanotubes is denoted as blue triangles, defective nonreconstructed with 2.75% defects with green squares, and defective reconstructed with 0.83% defects with red circles. Purple stars represent diffusion through a flexible pristine nanotube and cyan pentagons through a flexible defective, nonreconstructed CNT.

decrease modestly, but remain within an order of magnitude of their values at zero loading. As noted previously, most simulations of fluids in SWNTs assume perfect, defect-free structures. We here examine the validity of that assumption. Based on Figure 5, we observe that the presence of nanotube defects has a large effect on the corrected diffusivity of Ar. At most loadings, the corrected diffusivity is up to an order of magnitude slower through the defective, nonreconstructed SWNTs than the idealized pristine case. The transport becomes even slower in a model where the defect sites have been allowed to reconstruct, even though the concentration of defects in the reconstructed nanotube is much lower (0.83% compared with 2.75%). Thus, the presence and structure of rough defect sites can adversely impact transport properties by disrupting the long slip length across an otherwise smooth carbon surface. However, the distinction between SWNT models virtually disappears at nonzero loading for selfdiffusion; this is because argon−argon interactions dominate argon-nanotube collisions, even for the reconstructed nanotube. The differences between Ds and D0 at high loadings for pristine and defective SWNTs can be traced back to eqs 1 and 4. The self-diffusivity is a single-molecule property and hence is sensitive to both fluid−fluid and solid−fluid collisions, whereas D0 is a function of the center of mass motion of the fluid molecules, hence averaging out fluid−fluid collisions. Therefore, SWNT defects reduce the transport diffusion (through the corrected diffusivity) at high loadings, whereas the reduction in Ds due to fluid−fluid collisions is orders of magnitude greater than the effect of solid−fluid collisions.

coverage cannot be reliably determined from our simulations. The adsorption isotherms for water in the pristine (10,10) SWNT are consistent with previously reported values in the literature.94 Transport of Argon. The dependence of the self-diffusivity and the corrected diffusivity on the loading of argon atoms in five different SWNT models is plotted in Figure 5. The models of SWNTs are (1) pristine, rigid; (2) pristine, flexible; (3) defective, nonreconstructed, rigid; (4) defective, reconstructed, rigid; and (5) defective, nonreconstructed, flexible. The pristine rigid model is the most commonly used in the literature. The other four models provide a check of the accuracy of this idealized model, by introducing defects and nanotube flexibility. As expected, the self- and corrected diffusion coefficients for each system match at zero loading. We see from Figure 5a that for each of the models that the self-diffusivities drop by 2−3 orders of magnitude from their zero loading values to the values at the highest loadings. This behavior for pristine SWNTs has been previously noted and ascribed to the dominance of fluid− fluid scattering events relative to solid−fluid scattering, because of the smoothness of the SWNTs.14,15 However, it has also been observed that the decrease in Ds with increased loading is relatively modest for diffusion in zeolites, because the scattering from solid−fluid collisions in the zeolites dominates, due to the roughness of the surface potentials for zeolites.14,15 The fact that the defective and flexible SWNT models follow the trends for the pristine SWNTs means that defects and flexibility do not induce solid−fluid collisions that dominate over fluid−fluid collisions. In contrast to Ds, the corrected diffusion coefficients 11839

DOI: 10.1021/acs.langmuir.7b02841 Langmuir 2017, 33, 11834−11844

Article

Langmuir

Figure 6. (a) Self-diffusion and (b) corrected diffusion coefficients for CO2 through single-walled nanotubes. Blue triangles represent pristine nanotubes, green squares denote simulations with uncharged, defective nanotubes, and red diamonds show charged, defective nanotubes.

Table 1. Self-diffusion and Corrected Diffusion Coefficients (cm2/s) for H2O through Various Models of SWNTsa zero loading diffusion coefficient D0

Ds

a

SWNT model pristine defective, defective, pristine defective, defective,

uncharged charged uncharged charged

mean 1.99 1.34 6.00 9.96 4.98 3.07

× × × × × ×

high loading

standard deviation

10−1 10−1 10−2 10−2 10−2 10−2

9.27 7.72 2.14 2.54 9.69 8.70

× × × × × ×

10−2 10−2 10−2 10−3 10−4 10−4

mean 1.09 7.68 1.26 1.56 1.36 1.23

× × × × × ×

10−1 10−3 10−3 10−5 10−5 10−5

standard deviation 1.67 4.51 6.00 2.09 1.82 8.98

× × × × × ×

10−2 10−3 10−4 10−7 10−7 10−8

The defective nanotube models correspond to the reconstructed model of Figure 1.

simple (spherical) molecules, including self- and corrected diffusivities, except at very low loading. Transport of Molecular Fluids. The transport properties of CO2 and H2O in SWNTs were examined to identify the impact of nanotube defects and charges on the diffusivities for linear quadrupolar and nonlinear dipolar (hydrogen bonding) molecules. We considered the cases of the pristine nanotube and reconstructed defective nanotubes with and without charges. Results for simulations of CO2 through the SWNT are shown in Figure 6. At zero loading, the presence of defects (without charges) reduces D0 and Ds by approximately a factor of 2 below the values for the pristine SWNT. Including electrostatics further reduces the diffusivities, but only slightly. As the loading increases from 0 to 0.5 molecules (corresponding roughly to a pressure of 0.2 bar from Figure 4) per unit cell, Ds decreases by more than an order of magnitude in the three SWNT models. At sufficiently high loading, the diffusivities in the three different SWNT models converge to the same values, which is similar to the behavior observed for argon. In contrast, the corrected diffusivities are consistently lower for the defective SWNTs at all loadings, with the difference increasing with increased loading. The largest deviation in D0 occurs for a loading of 2 molecules per unit cell (roughly a pressure of 2 bar, see Figure 4) where the values are 0.085 and 3.79 × 10−3 cm2/s for D0 in pristine and defective, charged SWNTs, respectively, corresponding to a factor of about 22 decrease in the diffusivity. We calculated diffusion coefficients for H2O at zero loading and at a dense liquidlike loading, having roughly the number of molecules per unit cell corresponding to an external pressure of 1 bar, as show in Figure 4. The results are listed in Table 1. At zero loading, we see that the transport of H2O in the defective nanotubes is only about a factor of 2−4 slower than in the pristine SWNT. In each of the three SWNTs studied, we note

Another common modeling simplification is to hold the atoms of the SWNT rigidly fixed. To test this approximation on Ds and D0, we compared transport of fluids through the rigid, pristine model against a flexible, pristine SWNT. At zero loading, the diffusivities of argon in flexible SWNTs are about a factor of 3 lower than those in rigid SWNTs. At a higher loading of 2.0 atoms per unit cell (corresponding roughly to a pressure of 40 bar as seen from Figure 3), the values of D0 and Ds for the two nanotube models are very similar, with Ds = 2.4 × 10−4 and 2.2 × 10−4 cm2/s, for the rigid and flexible SWNTs, respectively and D0 = 0.24 and 0.17 cm2/s, for the rigid and flexible SWNTs, respectively. Overall, these trends are consistent with the relative contributions of argon−argon and argon−nanotube interactions noted for defects. The flexible SWNT forms a rougher surface for argon diffusion than the rigid, pristine SWNT, hence resulting in lower diffusion coefficients at zero loading. However, at higher loading, fluid−fluid collisions dominate and the flexibility of the SWNT does not have a substantial impact on the transport. A comparison of rigid and flexible defective SWNT models yields similar conclusions, as seen by comparing the pentagons and squares in Figure 5. Our results are corroborated by molecular dynamics simulation studies of flexible CNT models in the literature, which implemented flexibility using a modified thermostat instead of an explicit atom model. Jakobtorweihen et al. found that the self-diffusivities of methane in rigid and flexible CNTs are in excellent agreement at high loading, but that at very low loadings Ds in flexible CNTs can be much lower than that in rigid nanotubes.95 Chen et al. extended this analysis to Dt and to the limit of zero loading, where they found up to an order of magnitude difference in methane transport, but less than a factor of 2 difference at high loadings.90 Together, these results indicate that a rigid nanotube model is generally appropriate for simulation of transport properties of 11840

DOI: 10.1021/acs.langmuir.7b02841 Langmuir 2017, 33, 11834−11844

Article

Langmuir Table 2. Probability Density of Water with Respect to Positiona

a

Snapshots were taken down the axis of the SWNT. Carbon atoms of the SWNT are denoted as black dots. Darker blue color indicates a higher concentration of water oxygen atoms.

using a combination of neutron diffraction and molecular dynamics studies.96 They noted that water first adsorbs on the interior nanotube wall, which lowers the energy barrier for occupation of the center of the SWNT, consistent with our analysis. Wang et al. studied confinement effects of water in nanotubes of various diameters.67 They showed that a (5,5) SWNT is ideal for accommodating one water layer and (10,10) for two. Byl et al. identified ring structures in SWNTs at low temperatures from spectroscopy and simulations.97 Transport simulations by Ye et al. indicate that diffusion of confined water is dependent on both surface effects and size effects.98 For SWNTs with diameter smaller than 1.492 nm ((11,11) SWNTs), nanoconfinement constrains motions of water molecules through the SWNT, reducing transport. They find that (10,10) is a transition point from confinement effects to a more bulklike diffusion. Larger nanotubes benefit from enhanced transport, because the surface of SWNT walls is smoother than bulk water molecules. We see from Table 2 that at zero loading for the defective SWNTs there is a high probability density for water to be located near the walls of the SWNTs, similar to the pristine SWNT. However, with the difference that the highest probability region is located near the defect sites. Note that the probability density is highest at the defect sites for the charged case, as one would expect, indicative of attractive charge-dipole interactions. The defective cases at high loading exhibit a more complex structure than the pristine case. Like the zero loading cases, the highest probability region is again located near the defect sites, but now probability bands appear along the wall of the nanotube, producing a striped pattern, alternating between areas of high and low probability. This indicates the presence of

that the self-diffusion coefficients at high loading are fairly insensitive to the selected SWNT model (pristine, defective uncharged, and defective charged). However, the corrected diffusivities at high loading are dramatically lower for the defective SWNTs than for the pristine case, dropping by as much as a factor of about 86. Note that, compared with CO2, the corrected diffusivity of H2O has a more pronounced decrease from zero loading to high loading for defective SWNTs. We also note a discrepancy between the self-diffusion and corrected diffusion coefficients for water in all SWNT models at zero loading. The error bars for the self- and corrected diffusivities do not quite overlap, likely due to underestimating the errors for the corrected diffusivities. Structure of Water Diffusing through the SWNT. To better understand water transport through the SWNT, we studied the structure of water molecules in the three SWNT models. Plots of the probability density of water oxygen atoms in the SWNTs are given in Table 2. These heat maps are plotted along a cross section of the nanotube, summing all oxygen atoms (at all time steps) in the axial direction. Starting with the pristine SWNT model, we see that at zero loading the probability of finding an H2O molecule is highest near the walls of the nanotube, with lower, but nonzero probability near the center of the nanotube, indicating reasonably high mobility of H2O in the radial direction. At high loadings of water there is a ring of high probability next to the SWNT wall due to the formation of a ring of hydrogen bonded water molecules, and also a high-probability region at the center of the SWNT corresponding to an axial phase. Similar shell and axial water structures in SWNTs have been previously reported in the literature. Kolesnikov et al. identified ice-shell plus water-chain structures in similar sized SWNTs 11841

DOI: 10.1021/acs.langmuir.7b02841 Langmuir 2017, 33, 11834−11844

Langmuir an ordered hydrogen-bonded network of water molecules, the structure of which is determined by the defect site. We deduce that this ordered structure significantly reduces the value of the corrected diffusivity at high density relative to the pristine case, as seen in Table 1. Unexpectedly, the striped pattern is just as apparent in the uncharged, defective SWNT. Heat maps for the charged and uncharged SWNT models at high loading are visually almost identical. Therefore, the presence of defects alone, even without charges, is responsible for creating the unusual striped structure seen in Table 2. We note, however, that the corrected diffusivities at high loading reported in Table 1 are about a factor of 6 lower in the charged defective SWNT compared with the uncharged defective SWNT. This indicates that while the structure of the water in both cases is similar, charges act to pin the structures more effectively than the defects alone.

■

ACKNOWLEDGMENTS

■

REFERENCES

B.J.B. was supported through an NSF REU site grant, EEC1005048. Simulations were performed at the University of Pittsburgh’s Center for Research Computing.

(1) Kärger, J.; Ruthven, D. M. Diffusion in Zeolites and Other Microporous Solids; John Wiley and Sons: New York, 1992. (2) Yang, R. Gas Separation by Adsorption Processes; Butterworth Publishers: Stoneham, MA, 1987. (3) Buonomenna, M. G. Membrane processes for a sustainable industrial growth. RSC Adv. 2013, 3, 5694−5740. (4) Robeson, L. M. Correlation of separations factor versus permeability for polymeric membranes. J. Membr. Sci. 1991, 62, 165−185. (5) Freeman, B. D. Basis of permeability/selectivity tradeoff relations in polymeric gas separation membranes. Macromolecules 1999, 32, 375−380. (6) Robeson, L. M. The upper bound revisited. J. Membr. Sci. 2008, 320, 390−400. (7) Bastani, D.; Esmaeili, N.; Asadollahi, M. Polymeric mixed matrix membranes containing zeolites as a filler for gas separation applications: A review. J. Ind. Eng. Chem. 2013, 19, 375−393. (8) Nasir, R.; Mukhtar, H.; Man, Z.; Mohshim, D. F. Material Advancements in Fabrication of Mixed-Matrix Membranes. Chem. Eng. Technol. 2013, 36, 717−727. (9) Goh, P. S.; Ismail, A. F.; Sanip, S. M.; Ng, B. C.; Aziz, M. Recent advances of inorganic fillers in mixed matrix membrane for gas separation. Sep. Purif. Technol. 2011, 81, 243−264. (10) Zhao, Y.; Jung, B. T.; Ansaloni, L.; Ho, W. S. W. Multiwalled carbon nanotube mixed matrix membranes containing amines for high pressure CO2/H2 separation. J. Membr. Sci. 2014, 459, 233−243. (11) Favvas, E. P.; Nitodas, S. F.; Stefopoulos, A. A.; Papageorgiou, S. K.; Stefanopoulos, K. L.; Mitropoulos, A. C. High purity multi-walled carbon nanotubes: Preparation, characterization and performance as filler materials in co-polyimide hollow fiber membranes. Sep. Purif. Technol. 2014, 122, 262−269. (12) Kim, S.; Chen, L.; Johnson, J. K.; Marand, E. Polysulfone and functionalized carbon nanotube mixed matrix membranes for gas separation: Theory and experiment. J. Membr. Sci. 2007, 294, 147− 158. (13) Chan, W.-F.; Chen, H.-y.; Surapathi, A.; Taylor, M. G.; Shao, X.; Marand, E.; Johnson, J. K. Zwitterion functionalized carbon nanotube/ polyamide nanocomposite membranes for water desalination. ACS Nano 2013, 7, 5308−5319. (14) Skoulidas, A. I.; Ackerman, D. M.; Johnson, J. K.; Sholl, D. S. Rapid transport of gases in carbon nanotubes. Phys. Rev. Lett. 2002, 89, 185901. (15) Ackerman, D. M.; Skoulidas, A. I.; Sholl, D. S.; Johnson, J. K. Diffusivities of Ar and Ne in carbon nanotubes. Mol. Simul. 2003, 29, 677−684. (16) Kondratyuk, P.; Wang, Y.; Liu, J.; Johnson, J. K.; Yates, J. T., Jr. Inter- and intratube self-diffusion in n-heptane adsorbed on carbon nanotubes. J. Phys. Chem. C 2007, 111, 4578−4584. (17) Hinds, B. Dramatic transport properties of carbon nanotube membranes for a robust protein channel mimetic platform. Curr. Opin. Solid State Mater. Sci. 2012, 16, 1−9. (18) Majumder, M.; Chopra, N.; Andrews, R.; Hinds, B. Nanoscale hydrodynamics - Enhanced flow in carbon nanotubes. Nature 2005, 438, 44. (19) Hinds, B.; Chopra, N.; Rantell, T.; Andrews, R.; Gavalas, V.; Bachas, L. Aligned multiwalled carbon nanotube membranes. Science 2004, 303, 62−65. (20) Holt, J. K. Carbon Nanotubes and Nanofluidic Transport. Adv. Mater. 2009, 21, 3542−3550. (21) Fornasiero, F.; Park, H. G.; Holt, J. K.; Stadermann, M.; Grigoropoulos, C. P.; Noy, A.; Bakajin, O. Ion exclusion by sub-2-nm

■

CONCLUSIONS We have examined the sensitivity of transport of fluids in defective SWNTs to the level of defects, geometric effects from reconstruction, and partial charges. Surprisingly, adsorption isotherms for Ar, CO2, and H2O in SWNTs from GCMC simulations were fairly insensitive to the level of defects and electrostatics. At high loadings, the self-diffusivities are insensitive to defects, because scattering from fluid−fluid collisions dominate over the fluid−SWNT collisions. We have found that nanotube flexibility only significantly decreases diffusivity at low loadings, both for Ds and D0, and can therefore be safely neglected in most cases. Reconstruction of the nanotube due to missing carbon atoms decreases D0 values by introducing geometric asperities in the SWNT surface. These reconstructed defects have a bigger impact on diffusivities compared with point vacancy defects where the structure was not allowed to relax or reconstruct, even when the density of defects was much higher than the reconstructed case. Charges on the carbon atoms due to defects can reduce diffusivities of molecules having quadrupole moments, like CO2. The behavior of water in defective SWNTs is more complicated than that of Ar or CO2. The defects, with and without charges, impact the structure of H2O at high loadings fairly dramatically by creating ordered structures near the defect sites, as seen in the density heat maps at high loading in Table 2. This ordered structure reduces the corrected diffusivities for both charged and uncharged defects. Although the water structure is similar in both cases, charges decrease D 0 significantly. We have shown that defects can reduce transport diffusivities of fluids in SWNTs and this is especially true for polar fluids like water. However, even the lowest defect level studied here, with 0.83% of carbon atoms missing, is much higher than estimates of defects in high-quality SWNTs, having only about one defect per 1012 carbon atoms.23,24 It is therefore feasible that diffusion in carefully prepared SWNT samples will not be significantly impacted by the presence of defects.

■

Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

J. Karl Johnson: 0000-0002-3608-8003 Notes

The authors declare no competing financial interest. 11842

DOI: 10.1021/acs.langmuir.7b02841 Langmuir 2017, 33, 11834−11844

Article

Langmuir carbon nanotube pores. Proc. Natl. Acad. Sci. U. S. A. 2008, 105, 17250−17255. (22) Holt, J.; Park, H.; Wang, Y.; Stadermann, M.; Artyukhin, A.; Grigoropoulos, C.; Noy, A.; Bakajin, O. Fast mass transport through sub-2-nanometer carbon nanotubes. Science 2006, 312, 1034−1037. (23) Mann, D.; Javey, A.; Kong, J.; Wang, Q.; Dai, H. Ballistic transport in metallic nanotubes with reliable Pd ohmic contacts. Nano Lett. 2003, 3, 1541−1544. (24) Fan, Y.; Goldsmith, B.; Collins, P. Identifying and counting point defects in carbon nanotubes. Nat. Mater. 2005, 4, 906−911. (25) Rao, R.; Islam, A. E.; Pierce, N.; Nikolaev, P.; Maruyama, B. Chiral angle-dependent defect evolution in CVD-grown single-walled carbon nanotubes. Carbon 2015, 95, 287−291. (26) Byl, O.; Liu, J.; Yates, J. T., Jr. Etching of carbon nanotubes by ozone-A surface area study. Langmuir 2005, 21, 4200−4204. (27) Geng, H.; Zhang, X.; Mao, S.; Kleinhammes, A.; Shimoda, H.; Wu, Y.; Zhou, O. Opening and closing of single-wall carbon nanotubes. Chem. Phys. Lett. 2004, 399, 109−113. (28) Iijima, S. Helical microtubules of graphitic carbon. Nature 1991, 354, 56−58. (29) Iijima, S.; Ichihashi, T. Single-shell carbon nanotubes of 1-nm diameter. Nature 1993, 363, 603−605. (30) Bethune, D.; Kiang, C.; de Vries, M.; Gorman, G.; Savoy, R.; Vazquez, J.; Beyers, R. Cobalt-catalized growth of carbon nanotubes with single-atiomic-layer walls. Nature 1993, 363, 605−607. (31) White, C.; Robertson, D.; Mintmire, J. Helical and rotational simmetries of nanoscale praphitic tubules. Phys. Rev. B: Condens. Matter Mater. Phys. 1993, 47, 5485−5488. (32) Zou, Y.; Li, Q.; Liu, J.; Jin, Y.; Liu, Y.; Qian, Q.; Jiang, K.; Fan, S. Diameter distribution control of single-walled carbon nanotubes by etching ferritin nanoparticles. Appl. Phys. Express 2014, 7, 055102. (33) Chen, G.; Seki, Y.; Kimura, H.; Sakurai, S.; Yumura, M.; Hata, K.; Futaba, D. N. Diameter control of single-walled carbon nanotube forests from 1.3−3.0 nm by arc plasma deposition. Sci. Rep. 2015, 4, 3804. (34) Toni, F.; Xing, H.; Walter, J.; Strauss, V.; Nacken, T. J.; Damm, C.; Wirth, K.-E.; Guldi, D.; Peukert, W. Production of well dispersible single walled carbon nanotubes via a floating catalyst-method. Chem. Eng. Sci. 2015, 138, 385−395. (35) Springer, T. Quasielastic Neutron Scattering for the investigation of Diffusive Motion in Solids and Liquids; Springer Tracts in Modern Physics; Springer: Berlin, 1972; Vol. 64. (36) Maginn, E.; Bell, A.; Theodorou, D. Transport diffusivity of methane in silicalite from equilibrium and nonequilibrium simulations. J. Phys. Chem. 1993, 97, 4173−4181. (37) Skoulidas, A. I.; Sholl, D. S. Direct tests of the Darkin approximation for molecular diffusion in zeolites using equilibrium molecular dynamics. J. Phys. Chem. B 2001, 105, 3151−3154. (38) Ghosh, S.; Padmanabhan, V. Hydrogen storage capacity of bundles of single-walled carbon nanotubes with defects. Int. J. Energy Res. 2017, 41, 1108−1117. (39) Ghosh, S.; Padmanabhan, V. Adsorption of hydrogen on singlewalled carbon nanotubes with defects. Diamond Relat. Mater. 2015, 59, 47−53. (40) Sun, G.; Tangpanitanon, J.; Shen, H.; Wen, B.; Xue, J.; Wang, E.; Xu, L. Physisorption of molecular hydrogen on carbon nanotube with vacant defects. J. Chem. Phys. 2014, 140, 204712. (41) Zolfaghari, A.; Pourhossein, P.; Jooya, H. Z. The effect of temperature and topological defects on H2 adsorption on carbon nanotubes. Int. J. Hydrogen Energy 2011, 36, 13250−13254. (42) Okati, A.; Zolfaghari, A.; Hashemi, F. S.; Anousheh, N.; Jooya, H. Z. Hydrogen Physisorption on Stone-Wales Defect-embedded Single-walled Carbon Nanotubes. Fullerenes, Nanotubes, Carbon Nanostruct. 2009, 17, 324−335. (43) Orellana, W. Reaction and incorporation of H2 molecules inside single-wall carbon nanotubes through multivacancy defects. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 80, 075421. (44) Xia, Y.; Zhu, J.; Zhao, M.; Li, F.; Huang, B.; Ji, Y.; Liu, X.; Tan, Z.; Song, C.; Yin, Y. Enhancement of hydrogen physisorption on

single-walled carbon nanotubes resulting from defects created by carbon bombardment. Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 71, 075412. (45) Nishidate, K.; Hasegawa, M. Energetics of lithium ion adsorption on defective carbon nanotubes. Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 71, 245418. (46) Jalili, S.; Vaez, A. Xenon adsorption on defected single-walled carbon nanotubes. Chem. Phys. Lett. 2007, 437, 233−237. (47) Kuznetsova, A.; Yates, J. T., Jr.; Simonyan, V. V.; Johnson, J. K.; Huffman, C. B.; Smalley, R. E. Optimization of Xe adsorption kinetics in single walled carbon nanotubes. J. Chem. Phys. 2001, 115, 6691− 6698. (48) Hassan, J.; Diamantopoulos, G.; Homouz, D.; Papavassiliou, G. Water inside carbon nanotubes: structure and dynamics. Nanotechnol. Rev. 2016, 5, 341−354. (49) Vijayaraghavan, V.; Wong, C. H. Transport characteristics of water molecules in carbon nanotubes investigated by using molecular dynamics simulation. Comput. Mater. Sci. 2014, 89, 36−44. (50) Li, X.; Shi, Y.; Yang, Y.; Du, H.; Zhou, R.; Zhao, Y. How does water-nanotube interaction infiuence water flow through the nanochannel. J. Chem. Phys. 2012, 136, 175101. (51) Striolo, A.; Chialvo, A. A.; Cummings, P. T.; Gubbins, K. E. Simulated water adsorption in chemically heterogeneous carbon nanotubes. J. Chem. Phys. 2006, 124, 074710. (52) Striolo, A. Water self-diffusion through narrow oxygenated carbon nanotubes. Nanotechnology 2007, 18, 475704. (53) Zhu, Y.; Guo, X.; Shao, Q.; Wei, M.; Wu, X.; Lu, L.; Lu, X. Molecular simulation study of the effect of inner wall modified groups on ionic hydration confined in carbon nanotube. Fluid Phase Equilib. 2010, 297, 215−220. (54) Wu, X.; Lu, L.; Zhu, Y.; Wei, M.; Guo, X.; Lu, X. Changes in CNT-conflned water structural properties induced by the variation in water molecule orientation. Mol. Simul. 2012, 38, 1094−1102. (55) Yim, W.-L.; Johnson, J. K. Ozone oxidation of single walled carbon nanotubes from density functional theory. J. Phys. Chem. C 2009, 113, 17636−17642. (56) Zheng, J.; Lennon, E. M.; Tsao, H.-K.; Sheng, Y.-J.; Jiang, S. Transport of a liquid water and methanol mixture through carbon nanotubes under a chemical potential gradient. J. Chem. Phys. 2005, 122, 214702. (57) Huang, L.-L.; Shao, Q.; Lu, L.-H.; Lu, X.-H.; Zhang, L.-Z.; Wang, J.; Jiang, S.-y. Helicity and temperature effects on static properties of water molecules confined in modified carbon nanotubes. Phys. Chem. Chem. Phys. 2006, 8, 3836−3844. (58) Huang, L.-L.; Zhang, L.-Z.; Shao, Q.; Wang, J.; Lu, L.-H.; Lu, X.H.; Jiang, S.-Y.; Shen, W.-F. Molecular dynamics simulation study of the structural characteristics of water molecules confined in functionalized carbon nanotubes. J. Phys. Chem. B 2006, 110, 25761−25768. (59) Zhu, Y.; Wei, M.; Shao, Q.; Lu, L.; Lu, X.; Shen, W. Molecular Dynamics Study of Pore Inner Wall Modification Effect in Structure of Water Molecules Confined in Single-Walled Carbon Nanotubes. J. Phys. Chem. C 2009, 113, 882−889. (60) Heffelfinger, G. S.; van Swol, F. Diffusion in Lennard-Jones fluids using dual control volume grand canonical molecular dynamics simulation (DCV-GCMD). J. Chem. Phys. 1994, 100, 7548−7552. (61) Panahi, A.; Sabour, M. H. Electrokinetics desalination of water using fluorinated carbon nanotubes embedded in silicon membrane: Insights from molecular dynamics simulation. Chem. Eng. Sci. 2017, 173, 60−73. (62) Sahu, P.; Ali, S. M. The entropic forces and dynamic integrity of single file water in hydrophobic nanotube confinements. J. Chem. Phys. 2015, 143, 184503. (63) Won, C. Y.; Joseph, S.; Aluru, N. R. Effect of quantum partial charges on the structure and dynamics of water in single-walled carbon nanotubes. J. Chem. Phys. 2006, 125, 114701. (64) Zuo, G.; Shen, R.; Ma, S.; Guo, W. Transport Properties of Single-FileWater Molecules inside a Carbon Nanotube Biomimicking Water Channel. ACS Nano 2010, 4, 205−210. 11843

DOI: 10.1021/acs.langmuir.7b02841 Langmuir 2017, 33, 11834−11844

Article

Langmuir (65) Joseph, S.; Aluru, N. R. Why are carbon nanotubes fast transporters of water? Nano Lett. 2008, 8, 452−458. (66) Hummer, G.; Rasaiah, J. C.; Noworyta, J. P. Water conduction through the hydrophobic channel of a carbon nanotube. Nature 2001, 414, 188−190. (67) Wang, J.; Zhu, Y.; Zhou, J.; Lu, X.-H. Diameter and helicity effects on static properties of water molecules confined in carbon nanotubes. Phys. Chem. Chem. Phys. 2004, 6, 829−835. (68) Sokhan, V.; Nicholson, D.; Quirke, N. Fluid flow in nanopores: An examination of hydrodynamic boundary conditions. J. Chem. Phys. 2001, 115, 3878−3887. (69) Sokhan, V.; Nicholson, D.; Quirke, N. Fluid flow in nanopores: accurate boundary conditions for carbon nanotubes. J. Chem. Phys. 2002, 117, 8531−8539. (70) Noy, A. Kinetic model of gas transport in carbon nanotube channels. J. Phys. Chem. C 2013, 117, 7656−7660. (71) Perdew, J. P.; Wang, Y. Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Rev. B: Condens. Matter Mater. Phys. 1992, 45, 13244−13249. (72) Kresse, G.; Hafner, J. Ab Initio molecular dynamics for liquid metals. Phys. Rev. B: Condens. Matter Mater. Phys. 1993, 47, 558−561. (73) Kresse, G.; Hafner, J. Ab Initio molecular-dynamics simulation of the liquid-metal-amorphous-semiconductor transition in germanium. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 49, 14251−14269. (74) Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 11169−11186. (75) Kresse, G.; Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 1996, 6, 15−50. (76) Chen, D.-L.; Stern, A. C.; Space, B.; Johnson, J. K. Atomic Charges Derived from Electrostatic Potentials for Molecular and Periodic Systems. J. Phys. Chem. A 2010, 114, 10225−10233. (77) Simonyan, V. V.; Johnson, J. K.; Kuznetsova, A.; Yates, J. T., Jr. Molecular simulation of xenon adsorption on single-walled carbon nanotubes. J. Chem. Phys. 2001, 114, 4180−4185. (78) Brenner, D. W.; Shenderova, O. A.; Harrison, J. A.; Stuart, S.; Ni, B.; Sinnott, S. B. A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J. Phys.: Condens. Matter 2002, 14, 783−802. (79) Lee, K. H.; Sinnott, S. B. Computational studies of nonequilibrium molecular transport through carbon nanotubes. J. Phys. Chem. B 2004, 108, 9861−9870. (80) Bucior, B. J.; Chen, D.-L.; Liu, J.; Johnson, J. K. Porous carbon nanotube membranes for separation of H2/CH4 and CO2/CH4 mixtures. J. Phys. Chem. C 2012, 116, 25904−25910. (81) Bartuś, K.; Bródka, A. Methane behavior in carbon nanotube as a function of pore filling and temperature studied by molecular dynamics simulations. J. Phys. Chem. C 2017, 121, 4066−4073. (82) Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys. 1995, 117, 1−19. (83) Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual molecular dynamics. J. Mol. Graphics 1996, 14, 33−38. (84) Hockney, R.; Eastwood, J. Computer Simulation Using Particles; Adam Hilger: New York, 1989. (85) Steele, W. A. The Interaction of Gases With Solid Surfaces; Permagon Press: Oxford, 1974. (86) Skoulidas, A. I.; Sholl, D. S. Transport diffusivities of CH4, CF4, He, Ne, Ar, Xe, and SF6 in silicalite from atomistic simulations. J. Phys. Chem. B 2002, 106, 5058−5067. (87) Potoff, J. J.; Siepmann, J. I. Vapor-liquid equilibria of mixtures containing alkanes, carbon dioxide, and nitrogen. AIChE J. 2001, 47, 1676−1682. (88) Price, D. J.; Brooks, C. L. A modified TIP3P water potential for simulation with Ewald summation. J. Chem. Phys. 2004, 121, 10096− 10103. (89) Wang, J. H. Self-diffusion coefficients of water. J. Phys. Chem. 1965, 69, 4412−4412.

(90) Chen, H.; Johnson, J. K.; Sholl, D. S. Transport diffusion of gases is rapid in flexible carbon nanotubes. J. Phys. Chem. B 2006, 110, 1971−1975. (91) Martyna, G. J.; Klein, M. L.; Tuckerman, M. Nose-Hoover chains - The canonical ensemble via continuous dynamics. J. Chem. Phys. 1992, 97, 2635−2643. (92) Kamberaj, H.; Low, R. J.; Neal, M. P. Time reversible and symplectic integrators for molecular dynamics simulations of rigid molecules. J. Chem. Phys. 2005, 122, 224114. (93) Rowley, R. L.; Painter, M. M. Diffusion and viscosity equations of state for a Lennard-Jones fluid obtained from molecular dynamics simulations. Int. J. Thermophys. 1997, 18, 1109−1121. (94) Striolo, A.; Chialvo, A. A.; Gubbins, K. E.; Cummings, P. T. Water in carbon nanotubes: Adsorption isotherms and thermodynamic properties from molecular simulation. J. Chem. Phys. 2005, 122, 234712. (95) Jakobtorweihen, S.; Verbeek, M. G.; Lowe, C. P.; Keil, F. J.; Smit, B. Understanding the loading dependence of self-diffusion in carbon nanotubes. Phys. Rev. Lett. 2005, 95, 044501. (96) Kolesnikov, A. I.; Zanotti, J.-M.; Loong, C.-K.; Thiyagarajan, P.; Moravsky, A. P.; Loutfy, R. O.; Burnham, C. J. Anomalously soft dynamics of water in a nanotube: A revelation of nanoscale confinement. Phys. Rev. Lett. 2004, 93, 035503. (97) Byl, O.; Liu, J.-C.; Wang, Y.; Yim, W.-L.; Johnson, J. K.; Yates, J. T., Jr. Unusual hydrogen bonding in water-filled carbon nanotubes. J. Am. Chem. Soc. 2006, 128, 12090−12097. (98) Ye, H.; Zhang, H.; Zheng, Y.; Zhang, Z. Nanoconfinement induced anomalous water diffusion inside carbon nanotubes. Microfluid. Nanofluid. 2011, 10, 1359−1364.

11844

DOI: 10.1021/acs.langmuir.7b02841 Langmuir 2017, 33, 11834−11844