^{1}, J. Adler

^{1,a)}and M. Sheintuch

^{2}

### Abstract

The transport of gas mixtures through molecular-sieve membranes such as narrow nanotubes has many potential applications, but there remain open questions and a paucity of quantitative predictions. Our model, based on extensive molecular dynamics simulations, proposes that ballisticmotion, hindered by counter diffusion, is the dominant mechanism. Our simulations of transport of mixtures of molecules between control volumes at both ends of nanotubes give quantitative support to the model's predictions. The combination of simulation and model enable extrapolation to longer tubes and pore networks.

We acknowledge the HPC-EUROPA project for support of this work under Grants No. RII3-CT-2003-506079. T.M. acknowledges support from the Leonard and Diane Sherman Foundation.

I. INTRODUCTION

II. DETAILS OF OUR SYSTEM AND SIMULATION APPROACH

III. THE SINGLE-FILE TRANSPORTMODEL

IV. SINGLE SPECIES MODEL VALIDATION

V. EXTENSION TO MULTISPECIES TRANSPORT

VI. DISCUSSION AND CONCLUSION

### Key Topics

- Carbon nanotubes
- 36.0
- Diffusion
- 20.0
- Ballistic transport
- 11.0
- Trajectory models
- 9.0
- Carbon
- 7.0

## Figures

Simulation system with white/black (yellow/blue online) molecules moving from CV1/CV2 through a nanotube of length *L*.

Simulation system with white/black (yellow/blue online) molecules moving from CV1/CV2 through a nanotube of length *L*.

Testing directional symmetry of single species transport with varying tube length. Transport probability of from CV1 (CV2) to CV2 (CV1) vs counter diffusion of through a (6,6) SWNT of *L* = 30, 50, and 70 Å and bars (red diamonds). Eight more simulations of through a (6,6) SWNT (*L* = 100Å) are shown. Pressure values of = 10, 19, 23, 32, 37, 56, 74, 93 bars were given to both CVs and the results shown with black circular symbols with increasing pressures left to right on the figure. Error bars are shown on selected symbols. The solid curve represents the transport probability obtained from the single-file transport theory. This curve represents transport probability of molecules from CV1 to CV2 vs counter diffusion of molecules transporting from CV2 to CV1 for the case where *i* = 1, *j* = 2 and in the opposite direction for *i* = 2, *j* = 1.

Testing directional symmetry of single species transport with varying tube length. Transport probability of from CV1 (CV2) to CV2 (CV1) vs counter diffusion of through a (6,6) SWNT of *L* = 30, 50, and 70 Å and bars (red diamonds). Eight more simulations of through a (6,6) SWNT (*L* = 100Å) are shown. Pressure values of = 10, 19, 23, 32, 37, 56, 74, 93 bars were given to both CVs and the results shown with black circular symbols with increasing pressures left to right on the figure. Error bars are shown on selected symbols. The solid curve represents the transport probability obtained from the single-file transport theory. This curve represents transport probability of molecules from CV1 to CV2 vs counter diffusion of molecules transporting from CV2 to CV1 for the case where *i* = 1, *j* = 2 and in the opposite direction for *i* = 2, *j* = 1.

Varying pressure: transport probability of through a (6,6) SWNT (*L* = 100 Å) from CV1(CV2) to CV2(CV1) vs counter diffusion of under pressure gradients (open symbols). Transport probabilities of with =10, 19, 23, 32, 37, 56, 74, 93 bars (were also shown in Fig. 2 are added for comparison (filled circles). The solid curve represents the transport probability obtained from the single-file transport theory.

Varying pressure: transport probability of through a (6,6) SWNT (*L* = 100 Å) from CV1(CV2) to CV2(CV1) vs counter diffusion of under pressure gradients (open symbols). Transport probabilities of with =10, 19, 23, 32, 37, 56, 74, 93 bars (were also shown in Fig. 2 are added for comparison (filled circles). The solid curve represents the transport probability obtained from the single-file transport theory.

Transport probability of from CV1 to CV2 vs counter-diffusion parameter in a single-component system (*k* = ) (•), in a bicomponent mixture (*k*= , ) (□), and in a triple-component mixture (*k* = , , ) (♦). The pressure values are: = = 10, 19, 37, 56, 74, 93 bars. The partial fixed pressures are: = = 37 bars (in the binary and ternary cases) and = = 19 bars (in the ternary case). The solid curve represents the transport probability obtained from the single-file transport theory.

Transport probability of from CV1 to CV2 vs counter-diffusion parameter in a single-component system (*k* = ) (•), in a bicomponent mixture (*k*= , ) (□), and in a triple-component mixture (*k* = , , ) (♦). The pressure values are: = = 10, 19, 37, 56, 74, 93 bars. The partial fixed pressures are: = = 37 bars (in the binary and ternary cases) and = = 19 bars (in the ternary case). The solid curve represents the transport probability obtained from the single-file transport theory.

Transport probability of *q*= from CV1 to CV2 vs counter-diffusion parameter, in a single-component system (*k*=)□, in a bicomponent mixture (*k*= , ) (•), and in a triple-component mixture (*k*= , , ) (♦). The pressure values are: = =10, 19, 37, 56, 74, 93 bars, partial pressures are: = = 19 bars, and = = 37 bars. The transport probability of *q* = in a single-component system (*k*= ) (▵), in a binary mixture (*k* = , ) (▪), and in a triple molecular mixture (*k*= , , ) (○) are also shown. The pressure values are: = = 10, 19, 37, 56, 74, 93 bars, fixed partial pressures are: = = 19 bars and = = 37 bars. The solid curve represents the transport probability obtained from the single-file transport theory.

Transport probability of *q*= from CV1 to CV2 vs counter-diffusion parameter, in a single-component system (*k*=)□, in a bicomponent mixture (*k*= , ) (•), and in a triple-component mixture (*k*= , , ) (♦). The pressure values are: = =10, 19, 37, 56, 74, 93 bars, partial pressures are: = = 19 bars, and = = 37 bars. The transport probability of *q* = in a single-component system (*k*= ) (▵), in a binary mixture (*k* = , ) (▪), and in a triple molecular mixture (*k*= , , ) (○) are also shown. The pressure values are: = = 10, 19, 37, 56, 74, 93 bars, fixed partial pressures are: = = 19 bars and = = 37 bars. The solid curve represents the transport probability obtained from the single-file transport theory.

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