Kinetic restriction of simple gases in porous carbons: transition-state theory study

Abstract

The separation of simple gases such as N₂, Ar, CO₂, and CH₄ is an industrially important problem, particularly for the mitigation of greenhouse emissions. Furthermore, these gases are widely accepted as standard probing gases for the characterization of the microstructure of porous solids. However, a consistent set of microstructural parameters of a microporous solid determined from the use of adsorption measurements of these different gases is not always achieved because of differences in their pore accessibility. This is a long-standing and poorly understood problem. Here, we present the calculated results of the crossing time of N₂, Ar, CO₂, and CH₄ between two neighboring cages through a constricted window in a realistic structural model of saccharose char, generated from hybrid reverse Monte Carlo (HRMC) simulation (Nguyen, T. X.; Bhatia, S. K.; Jain, S. K.; Gubbins, K. E. Mol. Simul. 2006, 32, 567-577) using transition state theory (TST), as described in our recent work (Nguyen, T. X.; Bhatia, S. K. J. Phys. Chem. 2007, 111, 2212-2222). The striking feature in these results is that whereas very fast diffusion of carbon dioxide within the temperature range of 273-343 K, with crossing time on the molecular dynamics scale (10⁻⁴-10⁻⁶ s), leads to instantaneous equilibrium and no hysteresis on the experimental time scale, slower diffusion of Ar and N₂ at the low temperature of analysis indicates an accessibility problem. These results rationalize the experimental results of hysteresis for N₂ at 77 K and Ar at 87 K but not for CO₂ at 273 K in Takeda 3 Å carbon molecular sieves. Furthermore, it is shown that CH₄ diffusion through narrow pore mouths can be hindered even at ambient temperature. Finally, we show that the use of pore size and wall thickness distributions extracted from the adsorption of Ar at 87 K using the finite wall thickness (FWT) model (Nguyen, T. X.; Bhatia, S. K. Langmuir 2004, 20, 3532-3535 and Nguyen, T. X.; Bhatia, S. K. J. Phys. Chem. B 2004, 108, 14032-14042) provides the correct prediction of experimental CO₂ adsorption in BPL and PCB carbons whereas that from N₂ at 77 K gives a significant underprediction for both CO₂ and CH₄ in the BPL carbon. These trends are in excellent agreement with those predicted using the calculated crossing times.