Computational Studies of Non-Equilibrium Molecular Transport through Carbon Nanotubes

Adsorption and Diffusion of Fluids in Defective Carbon Nanotubes: Insights from Molecular Simulations

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 self-diffusivities 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.

Dependence of single-walled carbon nanotube adsorption kinetics on temperature and binding energy

We present results for the isothermal adsorption kinetics of methane, hydrogen, and tetrafluoromethane on closed-ended single-walled carbon nanotubes. In these experiments, we monitor the pressure decrease as a function of time as equilibrium is approached, after a dose of gas is added to the cell containing the nanotubes. The measurements were performed at different fractional coverages limited to the first layer. The results indicate that, for a given coverage and temperature, the equilibration time is an increasing function of E/(k(B)T), where E is the binding energy of the adsorbate and k(B)T is the thermal energy. These findings are consistent with recent theoretical predictions and computer simulations results that we use to interpret the experimental measurements.

Oscillation of gas molecules in carbon nanotubes

The dynamics of N(2) molecules blocked in open single-walled carbon nanotubes is investigated using molecular dynamics simulations. It is found that periodic axial and radial oscillations with extremely high frequency exist widely among these molecules. Between the two nanotube ends, N(2) molecules oscillate along or parallel to the nanotube axis, and their frequencies show an inverse length dependence in the range of 22 to 64 GHz. Accompanying the axial oscillation, the molecules oscillate radially with small amplitudes in the lateral potential well. The corresponding frequencies have a magnitude of several hundred gigahertz, and the maximum exceeds 1800 GHz. These periodic oscillations contribute to the molecular blockage in nanotubes.

Kinetics of molecular transport in a nanoporous crystal studied by confocal Raman microspectrometry: single-file diffusion in a densely filled tunnel

Confocal Raman microspectrometry has been used as an in situ probe of the transport of guest molecules along the one-dimensional tunnels in a crystalline urea inclusion compound, under conditions of guest exchange in which "new" guest molecules (pentadecane) are introduced at one end of the tunnel and displace the "original" guest molecules (1,8-dibromooctane). The Raman spectra, recorded as a function of position along the tunnel direction and as a function of time, have been used to establish details of the kinetics of the guest transport process. In particular, the transport of the new pentadecane guest molecules along the tunnel is found to exhibit a linear dependence on time, with the rate of the process in the region of 70-100 nm s-1. Mechanistic aspects relating to the guest transport process are discussed.

Interfacial interactions of glutamate, water and ions with carbon nanopore evaluated by molecular dynamics simulations

Molecular dynamics simulations were used to assess the transport of glutamate, water and ions (Na(+) and Cl(-)) in a single wall carbon nanopore. The spatial profiles of Na(+) and Cl(-) ions are largely determined by the pore wall charges. Co-ions are repelled whereas the counter-ions are attracted by the pore charges, but this 'rule' breaks down when the water concentration is set to a level significantly below that in the physiological bulk solution. In such cases water is less able to counteract the ion-wall interactions (electrostatic or non-electrostatic), co-ions are layered near the counter-ions attracted by the wall charges and are thus layered as counter-ions. Glutamate is concentrated near the pore wall even at physiological water concentration, and irrespective of whether the pore wall is neutral or charged (positively or negatively), and its peak levels are up to 40 times above mean values. The glutamate is thus always layered as a counter-ion. Layering of water near the wall is independent of charges on the pore wall, but its peak levels near the wall are 'only' 6-8 times above the pore mean values. However, if the mean concentration of water is significantly below the level in the physiological bulk solution, its layering is enhanced, whereas its concentration in the pore center diminishes to very low levels. Reasons for such a 'paradoxical' behavior of molecules (glutamate and water) are that the non-electrostatic interactions are (except at very short distances) attractive, and electrostatic interactions (between the charged atoms of the glutamate or water and the pore wall) are also attractive overall. Repulsive interactions (between equally charged atoms) exist, and they order the molecules near the wall, whereas in the pore center the glutamate (and water) angles are largely randomly distributed, except in the presence of an external electric field. Diffusion of molecules and ions is complex. The translational diffusion is in general both inhomogeneous and anisotropic. Non-electrostatic interactions (ion-wall, glutamate-wall or water-wall) powerfully influence diffusion. In the neutral nanopore the effective axial diffusion constants of glutamate, water and Na(+) and Cl(-) ions are all <10% of their values in the bulk, and the electrostatic interactions can reduce them further. Diffusion of molecules and ions is further reduced if the water concentration in the pore is low. Glutamate(-) is slowed more than water, and ions are reduced the most especially co-ions. In conclusion the interfacial interactions influence the spatial distribution of glutamate, water and ions, and regulate powerfully, in a complex manner and over a very wide range their transport through nanosize pores.

Significant conformational changes associated with molecular transport in a crystalline solid

Confocal Raman microspectrometry has been applied as an in situ probe of the transport of guest molecules along the one-dimensional tunnels in a crystalline urea inclusion compound, under conditions of guest exchange in which "new" guest molecules (pentadecane) are introduced at one end of the tunnel and displace the "original" guest molecules (1,8-dibromooctane). The Raman spectra, recorded as a function of position along the tunnel direction and as a function of time, demonstrate that the transport process is associated with a significant change in the conformational properties of the original (1,8-dibromooctane) guest molecules. In particular, in the boundary region between the original and new guest molecules, there is a substantial increase in the proportion of 1,8-dibromooctane guest molecules that have the gauche end-group conformation. The wider implications of this observation are discussed in relation to fundamental aspects of the molecular transport process in this material.

Diffusion of chain molecules and mixtures in carbon nanotubes: The effect of host lattice flexibility and theory of diffusion in the Knudsen regime

A novel algorithm for modeling the influence of the host lattice flexibility in molecular dynamics simulations is extended to chain-like molecules and mixtures. This technique, based on a Lowe-Andersen thermostat, maintains the advantages of both simplicity and efficiency. The same diffusivities and other properties of the flexible framework system are reproduced. Advantageously, the computationally demanding flexible host lattice simulations can be avoided. Using this methodology we study the influence of flexibility on diffusion of n-alkanes inside single-walled carbon nanotubes. Furthermore, results are shown for diffusion of two mixtures (methane-helium and ethane-butane). Using these results we investigate the accuracy of theories describing diffusion in the Knudsen regime. For the dynamics in carbon nanotubes the Knudsen diffusivities are much too low. The Smoluchowski model gives better results. Interestingly, the extended Smoluchowski model can reproduce our simulation results obtained with a rigid host lattice. We modify this model to also treat collisions with a flexible interface correctly. As the tangential momentum accommodation coefficient is needed for the theoretical models, we introduce a simple concept to calculate it.

Strong correlations and Fickian water diffusion in narrow carbon nanotubes

The authors have used atomistic molecular dynamics (MD) simulations to study the structure and dynamics of water molecules inside an open ended carbon nanotube placed in a bath of water molecules. The size of the nanotube allows only a single file of water molecules inside the nanotube. The water molecules inside the nanotube show solidlike ordering at room temperature, which they quantify by calculating the pair correlation function. It is shown that even for the longest observation times, the mode of diffusion of the water molecules inside the nanotube is Fickian and not subdiffusive. They also propose a one-dimensional random walk model for the diffusion of the water molecules inside the nanotube. They find good agreement between the mean-square displacements calculated from the random walk model and from MD simulations, thereby confirming that the water molecules undergo normal mode diffusion inside the nanotube. They attribute this behavior to strong positional correlations that cause all the water molecules inside the nanotube to move collectively as a single object. The average residence time of the water molecules inside the nanotube is shown to scale quadratically with the nanotube length.

A novel algorithm to model the influence of host lattice flexibility in molecular dynamics simulations: Loading dependence of self-diffusion in carbon nanotubes

We describe a novel algorithm that includes the effect of host lattice flexibility into molecular dynamics simulations that use rigid lattices. It uses a Lowe-Andersen thermostat for interface-fluid collisions to take the most important aspects of flexibility into account. The same diffusivities and other properties of the flexible framework system are reproduced at a small fraction of the computational cost of an explicit simulation. We study the influence of flexibility on the self-diffusion of simple gases inside single walled carbon nanotubes. Results are shown for different guest molecules (methane, helium, and sulfur hexafluoride), temperatures, and types of carbon nanotubes. We show, surprisingly, that at low loadings flexibility is always relevant. Notably, it has a crucial influence on the diffusive dynamics of the guest molecules.

Flow structure of water in carbon nanotubes: Poiseuille type or plug-like?

We have conducted molecular dynamics simulations of water flow in carbon nanotubes (CNTs) for (6,6) to (20,20) CNTs at a streaming velocity of 100 ms. The fluidized piston model (FPM) and the ice piston model (IPM) are employed to drive flow through the CNTs. The results show that the single-file water flow inside (6,6) CNT has a convex upward streaming velocity profile, whereas the velocity profiles in (10,10) to (20,20) CNTs are flat except near the tube wall. The flow structure of cylindrical water in the (8,8) CNT is intermediate between that for the (6,6) CNT and the larger CNTs. The flow parameters are found not to exhibit any dependence on streaming velocity at up to 300 ms in the (12,12) CNT. The hydrogen bond lifetimes of water flowing in CNTs tend to be longer than for the corresponding equilibrium states, and nonzero flow does not reduce the microscopic structure or structural robustness (hydrogen bond lifetime). Although the atomic density profile varies with tube diameter, reflecting the change in static microscopic structure of flow from single file to cylindrical, tube diameter does not induce a clear transition in streaming velocity, temperature, or hydrogen bond lifetime over this diameter range. The results suggest that water flow in CNTs of this size is more pluglike than Poiseuille type, although the flow structure does not strictly accord with either definition.