Understanding the Loading Dependence of Self-Diffusion in Carbon Nanotubes

Abstract

The influence of flexible walls on the self-diffusion of CH 4 in an isolated single walled carbon nanotube, as an example, is studied by molecular dynamics simulations. By simulating the carbon nanotube as a flexible framework we demonstrate that the flexibility has a crucial influence on selfdiffusion at low loadings. We show how this influence can be incorporated in a simulation of a rigid nanotube by using a Lowe-Andersen thermostat which works on interface-fluid collisions. The reproduction of the results of a flexible carbon nanotube by a rigid nanotube simulation is excellent. DOI: 10.1103/PhysRevLett.95.044501 PACS numbers: 47.55.Mh, 66.30.Pa, 83.10.Rs Carbon nanotubes (CNTs) can be aligned in a polymer film to form a well-ordered nanoporous membrane structure [1] which can be incorporated in a macroscopic structure [2] for separation devices. It is therefore of practical interest to understand the diffusive behavior of molecules adsorbed in these materials [3][4][5][6][7]. A particularly interesting observation is the remarkable increase of the diffusion coefficient of simple molecules at low densities observed by Skoulidas et al. [3]. These molecular simulations predict a diffusion coefficient higher than the corresponding gas phase value, resulting in fluxes that are orders of magnitude greater than in crystalline zeolitic membranes [3]. These results have subsequently been reproduced by other groups [8,9] and are explained in terms of the smoothness of the nanotube [3].From a computational point of view, simulations at the low density limit are surprisingly expensive; one needs an increasingly long nanotube to reach the low density limit. This poses no difficulty if one assumes a rigid substrate. However, if one has a material in which the flexibility cannot be ignored and a full atom simulation of the material is required, the calculation becomes many orders of magnitude more expensive and is completely dominated by the substrate. Therefore, most simulation studies use a rigid lattice.A novel algorithm that takes the most important aspects of flexibility into account at a fraction of the costs of a fully flexible CNT simulation is presented, resulting in effectively the same diffusivities and other effects as obtained from the flexible CNT simulations. This algorithm can be applied to other confined systems (zeolites, ion channels, membranes, etc.).Interestingly, whether or not it is reasonable to assume a rigid lattice in adsorption [10] or diffusion studies [11] is far from being understood. An obvious hypothesis would be that only in the case of narrow passages is flexibility very important, while in the case of gas molecules in carbon nanotubes, or other nanoporous materials, a rigid lattice is a very reasonable assumption. As we will show in this Letter, this assumption is the explanation of the remarkable increase of the diffusion coefficient at low loading. Molecular dynamics simulations of a fully flexible nanotube give a diffusion coefficient that is more than 1 order of magnitude lower ...

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

“…This agrees with our observations. 15 We could not observe a flexibility influence under these conditions. The influence of flexibility manifests itself in the low loading ͑high Knudsen numbers͒ regime.…”

“…Our method results in effectively the same diffusivities and other effects obtained from the flexible CNT simulations. 15 This algorithm can be applied to other confined systems ͑zeolites, ion channels, membranes, etc.͒. The central idea of this "Lowe-Andersen interface-fluid collision ͑LA-IFC͒ thermostat" is to mimic the thermal effects of a flexible framework stochastically.…”

“…In a previous Letter we reported a flexibility influence on diffusion at low loadings in CNTs. 15 The reason for the common approximation of a rigid lattice is the computationally demanding nature of simulations that treat the host matrix explicitly. A large number of intramolecular interactions must be calculated in one time step of a molecular dynamics simulation ͑large number of substrate atoms with high connectivity͒.…”

“…10 In a recent Letter we investigated the assumptions underlying these simulations. 15 In particular we focused on the differences between simulating diffusion in a nanotube in which the carbon atoms are effectively frozen ͑rigid lattice͒ and a model in which the carbon atoms undergo thermal motions. We showed that this CNT "flexibility" has a crucial influence on self-diffusion at low loadings.…”

Molecular Simulations of Zeolites: Adsorption, Diffusion, and Shape Selectivity

“…Computation studies include mixtures of (nobles) gases, 148,224,225 alkanes, 19,50,138,146,151,154,221,[226][227][228][229][230][231][232][233][234][235][236][237] or aromatics. 113,147,238,239 Detailed knowledge on the composition inside the pores of the zeolites is essential to understand mixture diffusion.…”