The Effects of Electrostatic Interaction and Chirality on the Friction

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The Effects of Electrostatic Interaction and Chirality on the Friction Coefficient of Water Flow Inside SingleWalled Carbon Nanotubes and Boron Nitride Nanotubes Xingfei Wei, and Tengfei Luo J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b11657 • Publication Date (Web): 15 Feb 2018 Downloaded from http://pubs.acs.org on February 17, 2018

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The Journal of Physical Chemistry

The Effects of Electrostatic Interaction and Chirality on the Friction Coefficient of Water Flow Inside Single-Walled Carbon Nanotubes and Boron Nitride Nanotubes Xingfei Wei† and Tengfei Luo*,†,‡ †

Department of Aerospace and Mechanical Engineering and ‡Center for Sustainable Energy at

Notre Dame (ND Energy), University of Notre Dame, Notre Dame IN 46556, United States * Corresponding author: E-mail: [email protected], (574) 631-9683.

Abstract Water transport through carbon nanotubes (CNTs) and boron nitride nanotubes (BNNTs) has attracted great scientific interest due to their potential applications in water purification and energy conversion. Recent experiments show surprising differences of the water flow friction coefficients in these two types of nanotubes with similar diameters, but the mechanism is yet to be fully understood. We use molecular dynamic (MD) simulations to model the transport process of water molecules inside CNTs and BNNTs, and the friction coefficients are calculated by the Green-Kubo formula. Our results show that at similar diameters, water molecules have smaller friction coefficients in zigzag CNTs than in zigzag BNNTs. By analyzing the potential energy landscape inside these nanotubes, we find that in CNTs the lack of partial charges, and thus the absence of electrostatic interactions with water molecules, leads to a much smoother potential energy landscape and thus smaller water friction coefficient. Although partial charges in armchair BNNTs also lead to electrostatic interactions with water, the atomic arrangement in armchair nanotubes does not create local potential energy traps, and thus the friction coefficient is smaller than the zigzag counterparts. The result helps us understand the distinct behaviors of water flowing through CNTs and BNNTs.

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Introduction Carbon nanotubes (CNTs) and Boron Nitride nanotubes (BNNTs) have promising potential applications in the nanofluidic area, 1-6 such as nano-filtration membranes, 6-8 desalination9-12 and osmotic energy conversion. 13,14 Water transport inside CNTs and BNNTs are extensively studied by both experiments and simulations. 5,6,8,15-24 It was found that the nanoscale confinement effect in these nanotubes makes the transport drastically different from those described by conventional theories, 1 and such findings inspired extensively research exploration in this field. For example, Holt et al. reported that water permeability of micro-fabricated membranes with embedded small diameter (< 2 nm) CNTs were several orders of magnitude higher than that of the commercial polycarbonate membranes. 7 Recently, Brog and Reese summarized many important studies in molecular dynamics (MD) simulations of water flow in CNTs, BNNTs and silicon carbide nanotubes (SiCNTs). It was shown that CNTs had the highest flow enhancement factor compared to the other two types at the same length. Brog and Reese also compared the flow enhancement factors calculated from MD simulations and experiments. They concluded that experimental results had large uncertainty and required many replications, while MD simulations could offer meaningful guidance. 25 Different from the above conclusion, another MD simulation of water transport across membranes made of armchair (8, 8) BNNTs and armchair (8, 8) CNTs showed that the water fluxes across them were very close to each other, 3 suggesting that they had similar friction coefficients for water transport. However, recently, Secchi et al. showed experimentally that water flow through CNTs had a surface slippage, but no such slippage was observed in BNNTs with similar diameters, meaning that water in CNTs can transport more efficiently than in BNNTs. 26 The unexpected water flow slippage differences inside CNTs and BNNTs with similar diameters were suggested to be somehow related to the link between


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hydrodynamic flow and the electronic structure of the nanotubes. 26,27 However, the fundamental differences of water transport through CNTs and BNNTs are not well clarified in the literature. Thomas et al. suggested that the rapid transport of water in CNTs and hydrophobic nanopores was due to that the electrically and mechanically smooth walls of CNT created frictionless surfaces and depletion layers near the walls. They believed that the rapid transport phenomenon was evident from simulations.28 After summarizing studies on MD simulations of water in CNTs, Kannam et al. listed a few deficiencies of the nonequilibrium MD (NEMD) simulation method, such as that the velocity gradient of water inside CNTs was too small, that the magnitude of the average velocity (10-100 m/s) was too large compared to the thermal velocity (~ 340 m/s) of water at 300 K, and the limitation of the model size. Compared to the NEMD methods, which required a very careful analysis of the velocity profile, they believed equilibrium MD (EMD) methods were more reliable. 29

In this study, we use EMD simulations with the Green-Kubo formula to calculate friction coefficients of water transport inside zigzag and armchair CNTs and BNNTs. Both single water molecule and multiple water molecules cases are simulated. The results show that for similar diameters, water molecules have smaller friction coefficients in zigzag CNTs than in zigzag BNNTs. By analyzing the potential energy landscape inside these nanotubes, we find that the lack of partial charges, and thus the absence of electrostatic interactions with water molecules, leads to a much smoother potential energy landscape and thus smaller water friction coefficient in CNTs. Meanwhile, the partial charges on BNNTs atoms induce local potential energy traps, which generate extra resistance to water transport. Interestingly, although partial charges in armchair BNNTs also lead to electrostatic interactions with water, the atomic arrangement in


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armchair nanotubes does not create local potential energy traps, and thus the friction coefficient is smaller than the zigzag counterparts. The results from this study provide important insights into the distinct behaviors of water flowing through CNTs and BNNTs.

Methods and MD Simulation Model The friction coefficient as a transport coefficient can be calculated by the following GreenKubo (GK) formula: 30,31 =

∞

〈 ( ) ∙ (0)〉

(1)

where is the force on water molecules along the axial direction of the nanotube that can be calculated during the EMD simulation, is the correlation time, is the temperature of the system at equilibrium, is the Boltzmann constant, and is the interaction area. To help achieve convergence of the friction coefficient calculated from GK, ensemble average over 1050 independent simulations is performed. In each independent MD simulation, the system is first relaxed at 300 K in the NVT (canonical) ensemble for 5-10 ns using the Nose-Hoover thermostat. After equilibration, the production run in the NVE (microcanonical) ensemble for 1 ns is carried out. The cutoff distance for the Lennard-Jones potential is 9.0 Å. The long range electrostatic interaction is calculated using the k-space particle-particle particle-mesh (PPPM) scheme with an accuracy parameter of 0.0001. The simulation time step is 1.0 fs. The autocorrelations of the instantaneous force are calculated for a duration of 500 ps. By applying ensemble average, the standard deviation (STD) of the calculated friction coefficient for each system can be deduced. We find that the STD of the friction coefficients exponentially decay with a power of ~ -0.5 with respect to the number of independent runs, which suggests a normal distribution of the friction


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coefficient data, 32 allowing us to use standard error to characterize the true uncertainty of the data. More details are shown in Sections 1-3 of the Supporting Information (SI).

The MD simulations are carried using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) package. 33 Figure 1 shows the structures of four example nanotubes: 34 (a) armchair (8, 8) CNT, (b) zigzag (14, 0) CNT, (c) armchair (8, 8) BNNT, and (d) zigzag (14, 0) BNNT. These four types of nanotubes have similar radii (~ 5.5 Å). Nanotubes of different radii with the same length of ~ 25 Å are built by changing the index of n in zigzag (n, 0) CNT and zigzag (n, 0) BNNT. During the simulations, the nanotubes are set as rigid bodies, and water molecules placed inside the nanotubes are allowed to move freely (Fig. 1). The boundary condition along the axial direction is periodic, so that the water molecules are effectively transporting inside infinitely long nanotubes. The water model used in this study is mainly TIP3P.35 We also extended our simulation with the TIP4P/2005 water model and by applying the Tersoff potential on the nanotubes. The parameters of the Lennard-Jones potential describing the carbon-oxygen interactions are the same as those used by Falk et. al. 30 with = 0.114 "#$/ &'$ and ( = 3.28 Å , where is the energy constant and ( is the distance constant. The partial charges for BNNT are 1.05 e for the boron atom and -1.05 e for the nitrogen atom, and the Lennard-Jones parameters for them are respectively = 0.0949 "#$/&'$ , ( = 3.453 Å , and . = 0.145 "#$/&'$, (. = 3.365 Å. 9,10 The cross terms are calculated using mixing rules as: = 0 ∗ , ( =

3 435 6

, . = 0. ∗ , ( =

3 435 6

.

Multiple water molecules are filled into different types of nanotubes by the Grand Canonical Monte Carlo (GCMC) simulation, which is routinely used for molecular absorption studies in


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nanotubes. The simulations are performed in LAMMPS. A total of no less than 2,000,000 MC moves for each nanotube have been carried out. The addition/deletion of water molecules is attempted every 1000 MC displacement moves using a chemical potential of -5800 cal/mol, which is used in the bulk TIP3P water simulation. 37,38 Between every 1000 MC moves, we run 1000 MD steps in the NVT ensemble to relax the system. When the nanotube is saturated with water, we stop the GCMC simulation at the steady state (fluctuation less than 2 molecules) and start MD simulations, each including a 5-ns NVT run and a 1-ns NVE run. In the end, the following numbers of water molecules are obtained: zigzag (14, 0) CNT: 41, zigzag (14, 0) BNNT: 58, armchair (8, 8) CNT: 34, armchair (8, 8) BNNT: 46, zigzag (14, 0) CNT with artificial partial charges of +/- 1.0 e: 53, and armchair (8, 8) CNT with artificial partial charges of +/- 1.0 e: 45.

Results and Discussion Partial charge effects on the friction coefficient. We first simulate one water molecule transporting inside different nanotubes and calculate the friction coefficients from our EMD simulations. The rationale of simulating a single water molecule stems from the fact that it was shown that when the slip length was much larger than the tube radius, the viscosity of the water did not affect the flow, and the liquid/solid friction coefficient was the controlling parameter for water transport. 21 Our calculation results show that water in the zigzag (14, 0) BNNT (green bar in Fig. 2) has a friction coefficient ~ 4 times of that of the zigzag (14, 0) CNT (red bar in Fig. 2), which have similar radii of ~ 5.5 Å. The same trend is found for nanotubes with larger diameters (SI, Section 4). Meanwhile, at a similar radius of ~ 5.5 Å, the friction coefficient of the water molecule in the armchair (8, 8) CNT (brown bar in Fig. 2) is close to that in the zigzag (14, 0)


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CNT (red bar in Fig. 2). These results suggest that the chirality of CNTs is not critical to the water transport in CNTs as long as the radii are the same, but the material of the nanotube (i.e., CNT vs. BNNT) can play a dominant role in water transport.

One of the major differences between the CNTs and BNNTs is the partial charge on the atoms. For CNTs, there is no charge on the carbons, but BNNTs have partial charges of +1.05 e on the boron and -1.05 e on the nitride. 9,10 In order to single out the atomic charge-induced electrostatic force effect on the water transport inside the nanotubes, we artificially assigned partial charges on the CNTs. The yellow bar in Fig. 2 shows that the zigzag (14, 0) CNT with artificial partial charges of +/- 1.0 e has a friction coefficient ~ 3 times of that of the zigzag (14, 0) CNT without charges, and this friction coefficient value is close to that of the zigzag (14, 0) BNNT. Therefore, we can attribute the difference in friction coefficients between zigzag CNTs and zigzag BNNTs to the electrostatic interactions between the nanotubes and water molecules, and this can contribute to explaining the experimentally observed phenomenon of a larger water slippage length in CNTs than in BNNTs. 26 However, for the armchair (8, 8) CNT, even when the same artificial partial charges of +/- 1.0 e are assigned, the friction coefficient does not increase (orange bar in Fig. 2) as seen for the zigzag CNTs. Our simulation result also shows that the zigzag (14, 0) CNT with artificial partial charges of +/- 0.1 e has a slightly higher friction coefficient than the pristine CNT without charges and the zigzag (14, 0) CNT with artificial partial charges of +/- 1.5 e has a friction coefficient even larger than that with artificial partial charges of +/- 1.0 e (SI, Section 5). These observations are intuitive as larger partial charges induce stronger electrostatic interactions and thus larger friction.


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Potential landscape inside the nanotubes. In order to elucidate the mechanism of the effects of electrostatic interactions on the friction coefficients, we calculate the potential energy landscape for the oxygen atom on the water molecule in the nanotubes (Figs. 3 and 4). We note that sampling the potential energy landscape using the hydrogen atoms will lead to similar observations, but we choose the oxygen atom since it dominants the mass and force of the water molecule. The potential energy experienced by the oxygen atom is calculated by summing up the van der Waals (vdW) and electrostatic potential energies of the oxygen interacting with atoms on the nanotubes with a cutoff of 12.5 Å. Figures 3a and 3b show the different views of the potential landscape inside the zigzag (14, 0) CNT, and Figs. 3c and 3d show those of the zigzag (14, 0) BNNT. For water moving through the zigzag (14, 0) CNT, it experiences a smooth potential, which will understandably lead to a small friction coefficient. On the other hand, when the water molecule moves inside the zigzag (14, 0) BNNT, it will have to overcome energy barriers ~600 cal/mol in the middle of the nanotube, which should be responsible for the much larger friction coefficient compared to the zigzag (14,0) CNT case. Figures 3e and 3f show that when the partial charges are assigned on the zigzag (14, 0) CNT atoms, the pattern of the potential energy becomes similar to that of the zigzag (14, 0) BNNT. This change in energy landscape leads to the increased friction coefficient (Fig. 2) after the artificial charges are added to the carbon atoms.

However, for the armchair (8, 8) CNT, the addition of partial charges does not lead to large potential barriers (Figs. 4a and 4b vs. Figs. 4e and 4f), and thus it does not increase the friction coefficient. The energy landscape in the armchair (8, 8) BNNT (Figs. 4c and 4d) is also relatively smooth, which explains why it has a smaller friction coefficient compared to that of the zigzag (14, 0) BNNT, despite that they are both charged and have similar radii. We should note


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that the armchair (8, 8) CNT and BNNT have almost the same radii as those of their zigzag (14, 0) counterparts (i.e., 10.8 Å and 11.2 Å), yet their potential energy landscapes are drastically different. We can thus attribute the difference in friction coefficients between these two types of nanotubes to their atomic arrangements (different chirality).

In order to map the water molecules onto the potential energy landscapes, we analyzed water trajectories during the NVE ensemble runs for different types of nanotubes filled with multiple water molecules. Figure 5a shows that the distribution of the water molecules (oxygen atoms) along the axial direction in the zigzag (14, 0) CNT is more uniform than those in the zigzag (14, 0) BNNT and the zigzag (14, 0) CNT with artificial partial charges. Figures 5b and 5d show that the distribution of the water molecules along the radial direction in the zigzag (14, 0) CNT is significantly different from that in the zigzag (14, 0) BNNT. In the zigzag (14, 0) CNT, the peak appears at 3.19 Å away from the CNT wall (2.29 Å from the center, Fig. 5b). While in the zigzag (14, 0) BNNT, the peak locates at 2.98 Å away from the BNNT wall (Fig. 5 d). In the zigzag (14, 0) CNT with artificial partial charges, the distribution of the water molecules is similar to that in the zigzag (14, 0) BNNT, where the peak appears at 2.95 Å away from the CNT wall. These observations indicate that the partial charges on the zigzag (14, 0) BNNT attract the water molecules closer to the wall, where the potential landscape is rougher (Fig. 3), and thus increase the friction force. Meanwhile, in Figs. 5d and 5f, a small peak appears near the center of the nanotubes, where the energy barrier is > 600 cal/mol (Fig. 3). The histograms in Fig. S8 (SI, Section 6) confirm that the water molecules can reach both the highest energy and the lowest energy regions at the center of the zigzag (14, 0) BNNT and the zigzag (14, 0) CNT with artificial partial charges, which means that some water molecules have to overcome a very large


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energy barrier in these nanotubes. Similar analysis is applied to armchair nanotubes, where the distance of the peaks to the walls are: 3.28 Å for the armchair (8, 8) CNT, 3.12 Å for the armchair (8, 8) BNNT, and 3.17 Å for the armchair (8, 8) CNT with partial charges (Fig. 6). The larger peak to wall distances and lack of obvious energy barrier inside nanotubes (see Fig. 4) lead to low friction coefficients inside zigzag nanotubes.

CNT and BNNT filled with multiple water molecules. Although prior studies have implied that it is the wall-water interaction instead of the water-water interaction that dominates the water transport in small nanotubes, 21 we confirm that the same trend in friction coefficients observed from single water molecule simulations can be found in nanotubes saturated with water molecules. We fill CNTs and BNNTs with water molecules using GCMC simulations. 36 The chemical potential in our GCMC simulations is set to -5800 cal/mol for the TIP3P water model, which is the same as that used in the bulk water simulation. 37,38 After water molecules are filled into the nanotubes by GCMC, we use NVT ensemble to relax the system and NVE ensemble with the GK formula to calculate the friction coefficient of water (Eq. 1). The friction coefficient curves with respect to the autocorrelation time are shown in Fig. S3 (SI, Section 2) for different systems, and the calculated friction coefficients for water in different types of nanotubes are shown in Fig. 7. The observations are similar to those in Fig. 2. The zigzag (14, 0) BNNT (green bar in Fig. 7) shows the highest friction coefficient, which is much larger than that of the zigzag (14, 0) CNT (red bar in Fig. 7). For nanotubes with larger radii, this trend is also true when the nanotubes are filled with water molecules (SI, Section 4). The armchair (8, 8) BNNT (blue bar in Fig. 7) and CNTs (red and negligible brown bars in Fig. 7) show significant lower friction coefficients compared to the zigzag (14, 0) BNNT, although they all have similar radii. When


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partial charges are artificially assigned to the CNTs, the zigzag (14, 0) CNT (yellow bar in Fig. 7) shows a significantly increased friction coefficient, while the armchair (8, 8) CNT (orange bar with black edges in Fig. 7) shows a much smaller change. However, we should point out that the magnitude of the friction coefficients in these cases are much larger than those of the single water molecule cases, indicating that the interactions among water molecules, even in such small nanotubes, can have important influence on the friction coefficients, which is on the contrary to a previous claim.

21

Nevertheless, the trend of friction coefficient with respect the type of

nanotubes (i.e., materials and chirality) from the multiple water molecules simulations is the same as that found from the single water molecule simulations.

It has been reported that different water models can lead to different water transport properties. 39,40

To ensure our observation is not water model-dependent, we use another model, the

TIP4P/2005 model,41, 42 to simulate water molecules and calculate the friction coefficient. We first use the TIP4P/2005 water model42 to run the GCMC simulations until the nanotubes are saturated with water molecules. The following numbers of TIP4P/2005 water molecules are filled into different nanotubes: zigzag (14, 0) CNT: 36, zigzag (14, 0) BNNT: 45, armchair (8, 8) CNT: 33, armchair (8, 8) BNNT: 39. The EMD method with 30 ensembles is then used to calculate the friction coefficient. While the numbers of water molecules are uniformly smaller than those obtained from the TIP3P model, Fig. 8a shows that the friction coefficients of the zigzag (14, 0) BNNT is significantly higher than the others, which is consistent with the results from the previous simulation using the TIP3P water model (Fig. 7).


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Moreover, in reality, the nanotube atoms can vibrate. To ensure that our conclusion is not influenced by the fact that the nanotube atoms are fixed in the simulations, we perform additional simulations where nanotube atoms are allowed to vibrate. This is achieved by using the Tersoff potentials on the C/B/N atoms.

43-46

The TIP3P water model is used in these simulations. The

atoms in the middle of the nanotubes are fixed to avoid the nanotubes drifting (Fig. 8b). All the friction coefficient data reported in this study is summarized in Table S1 (SI, Section 7). Two representative nanotubes, including the zigzag (14, 0) CNT and BNNT, are studied. The friction coefficients and their trends are similar to those from the simulations where nanotubes atoms are fixed (Fig. 7). In all, we believe that these provide sufficient evidence to show that the zigzag (14, 0) BNNT has much higher friction coefficient than the zigzag (14, 0) CNT, and the reason is the partial charge and the zigzag conformation.

Conclusions In this study, we use EMD simulations to study the friction coefficient of water inside CNTs and BNNTs with both zigzag and armchair configurations. We find that the friction coefficient of water transporting inside zigzag BNNTs is much larger than that in zigzag CNTs with the same diameters. We use potential energy landscape to further show that the high friction coefficient of zigzag BNNTs is due to electrostatic interactions between charged boron, nitrogen atoms and water molecules. The electrostatic potential generates deep energy traps (>600 cal/mol) along the axial direction. The armchair BNNTs show much lower friction coefficients than the zigzag BNNTs even if they have similar radii. The potential energy landscapes show that the atomic arrangement in armchair nanotubes does not generate significant energy traps. Therefore, the chirality of the nanotube plays another important role in the high friction coefficient of zigzag


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BNNTs. The results from this work will provide some insights into the observed differences in water transport behaviors in CNTs and BNNTs.

Acknowledgement The authors acknowledge the financial support from Army Office of Research (W911NF-16-10267). This computation was supported in part by the University of Notre Dame, Center for Research Computing, and NSF through XSEDE resources provided by SDSC Comet, TACC Stampede, and NICS Darter under grant number TG-CTS100078. We thank Lukas Koestler for his helpful discussion in class Molecular Level Modeling for Engineering Applications.

Supporting Information Supporting information (SI) includes the following content: standard deviation of the EMD method, raw data of the friction coefficient, convergence of the EMD method, nanotube size effect, water molecule distribution data, different artificial partial charge effect, flexible nanotube effect, all the reported friction coefficient data.

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20. Whitby, M.; Quirke, N. Fluid Flow in Carbon Nanotubes and Nanopipes. Nat. Nanotechnol. 2007, 2, 87-94. 21. Joly, L. Capillary Filling with Giant Liquid/Solid Slip: Dynamics of Water Uptake by Carbon Nanotubes. J. Chem. Phys. 2011, 135, 214705. 22. Ma, M.; Grey, F.; Shen, L.; Urbakh, M.; Wu, S.; Liu, J. Z.; Liu, Y.; Zheng, Q. Water Transport Inside Carbon Nanotubes Mediated by Phonon-Induced Oscillating Friction. J. Chem. Phys. 2015, 10, 692-695. 23. Won, C. Y.; Aluru, N. Water Permeation through a Subnanometer Boron Nitride Nanotube. J. Am. Chem. Soc. 2007, 129, 2748-2749. 24. Won, C. Y.; Aluru, N. Structure and Dynamics of Water Confined in a Boron Nitride Nanotube. J. Phys. Chem. C 2008, 112, 1812-1818. 25. Borg, M. K.; Reese, J. M. Multiscale Simulation of Enhanced Water Flow in Nanotubes. MRS Bull 2017, 42, 294-299. 26. Secchi, E.; Marbach, S.; Niguès, A.; Stein, D.; Siria, A.; Bocquet, L. Massive Radius-Dependent Flow Slippage in Carbon Nanotubes. Nature 2016, 537, 210-213. 27. Sendner, C.; Horinek, D.; Bocquet, L.; Netz, R. R. Interfacial Water at Hydrophobic and Hydrophilic Surfaces: Slip, Viscosity, and Diffusion. Langmuir 2009, 25, 10768-10781. 28. Thomas, M.; Corry, B.; Hilder, T. A. What have we Learnt about the Mechanisms of Rapid Water Transport, Ion Rejection and Selectivity in Nanopores from Molecular Simulation? Small 2014, 10, 14531465. 29. Kannam, S. K.; Daivis, P. J.; Todd, B. Modeling Slip and Flow Enhancement of Water in Carbon Nanotubes. MRS Bull 2017, 42, 283-288. 30. Falk, K.; Sedlmeier, F.; Joly, L.; Netz, R. R.; Bocquet, L. Molecular Origin of Fast Water Transport in Carbon Nanotube Membranes: Superlubricity Versus Curvature Dependent Friction. Nano Lett. 2010, 10, 4067-4073. 31. Helfand, E. Transport Coefficients from Dissipation in a Canonical Ensemble. Phys. Rev. 1960, 119, 1. 32. Wang, Z., Safarkhani, S., Lin, G., & Ruan, X. Uncertainty Quantification of Thermal Conductivities from Equilibrium Molecular Dynamics Simulations. Int. J. Heat Mass Transf. 2017, 112, 267-278. 33. Plimpton, S.; Crozier, P.; Thompson, A. LAMMPS-Large-Scale Atomic/Molecular Massively Parallel Simulator. See http://lammps.sandia.gov 2013. 34. Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual Molecular Dynamics. J. Mol. Graph. 1996, 14, 33-38. 35. Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. Comparison of Simple Potential Functions for Simulating Liquid Water. J. Chem. Phys. 1983, 79, 926-935.


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Figure 1. Example atomistic structures of one water molecule inside different types of nanotubes: (a) armchair (8, 8) CNT, (b) zigzag (14, 0) CNT, (c) armchair (8, 8) BNNT, (d) zigzag (14, 0) BNNT. The length of all the nanotubes are ~ 25 Å with periodic boundary conditions applied in the axial direction.


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Figure 2. Friction coefficients of one water molecule transport inside different types of nanotubes.


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Figure 3. The potential landscape of the oxygen atom in a water molecule experiences inside the zigzag (14, 0) CNT, zigzag (14, 0) BNNT, and zigzag (14, 0) CNT with artificial partial charges of +/- 1.0 e assigned on the carbons. Schematics on top show the views from which the potential contours are plotted. The unit of the potential bar is cal/mol. (a) The potential along the axial direction in the zigzag (14, 0) CNT. (b) The potential along the radial direction in the zigzag (14, 0) CNT. (c) The potential along the axial direction in the zigzag (14, 0) BNNT. (d) The potential along the radial direction in the zigzag (14, 0) BNNT. (e) The potential along the axial direction in the zigzag (14, 0) CNT with artificial partial charges of +/- 1.0 e. (f) The potential along the radial direction in the zigzag (14, 0) CNT with artificial partial charges of +/- 1.0 e.


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Figure 4. The potential landscape of the oxygen atom in a water molecule experiences inside the armchair (8, 8) CNT, armchair (8, 8) BNNT, and armchair (8, 8) CNT with artificial partial charges of +/- 1.0 e assigned on the carbons. The unit of the potential bar is cal/mol. (a) The potential along the axial direction in the armchair (8, 8) CNT. (b) The potential along the radial direction in the armchair (8, 8) CNT. (c) The potential along the axial direction in the armchair (8, 8) BNNT. (d) The potential along the radial direction in the armchair (8, 8) BNNT. (e) The potential along the axial direction in the armchair (8, 8) CNT with artificial partial charges of +/- 1.0 e. (f) The potential along the radial direction in the armchair (8, 8) CNT with artificial partial charges +/- 1.0 e.


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Figure 5. The normalized distribution of oxygen atoms: along the (a) axial and (b) radial directions in the zigzag (14, 0) CNT; along the (c) axial and (d) radial directions in the zigzag (14, 0) BNNT; along the (e) axial and (f) radial directions in the zigzag (14, 0) CNT with artificial partial charges of +/- 1.0 e.


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Figure 6. The normalized distribution of oxygen atoms: along the (a) axial and (b) radial directions in the armchair (8, 8) CNT; along the (c) axial and (d) radial directions in the armchair (8, 8) BNNT; along the (e) axial and (f) radial directions in the armchair (8, 8) CNT with artificial partial charges of +/- 1.0 e.


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Figure 7. Friction coefficients of multiple water molecules transporting in different types of nanotubes. The number of water molecules are determined from GCMC simulations. The zigzag (14, 0) CNT contains 41 water molecules, the zigzag (14, 0) BNNT contains 58 water molecules, the armchair (8, 8) CNT contains 34 water molecules, the armchair (8, 8) BNNT contains 46 water molecules, the zigzag (14, 0) CNT with artificial partial charges of +/- 1.0 e contains 53 water molecules, and the armchair (8, 8) CNT with artificial partial charges of +/- 1.0 e contains 45 water molecules.


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Figure 8. (a) Friction coefficients calculated from simulations using the TIP4P/2005 water model. (b) Friction coefficients from simulations where the C/B/N atoms of the nanotubes are modeled using the Tersoff potentials and allowed to vibrate. The nanotubes are filled with TIP3P water molecules and a layer of nanotube atoms are fixed to prevent nanotube drifting.


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The Effects of Electrostatic Interaction and Chirality on the Friction

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