Transport into Nanosheets: Diffusion Equations Put to Test

Ultrathin porous materials, such as zeolite nanosheets, are prominent candidates for performing catalysis, drug supply, and separation processes in a highly efficient manner due to exceptionally short transport paths. Predictive design of such processes requires the application of diffusion equations that were derived for macroscopic, homogeneous surroundings to nanoscale, nanostructured host systems. Therefore, we tested different analytical solutions of Fick’s diffusion equations for their applicability to methane transport into two different zeolite nanosheets (AFI, LTA) under instationary conditions. Transient molecular dynamics simulations provided hereby concentration profiles and uptake curves to which the different solutions were fitted. Two central conclusions were deduced by comparing the fitted transport coefficients. First, the transport can be described correctly only if concentration profiles are used and the transport through the solid–gas interface is explicitly accounted for by the surface permeability. Second and most importantly, we have unraveled a size limitation to applying the diffusion equations to nanoscale objects. This is because transport-diffusion coefficients, <i>D</i>_T, and surface permeabilities, α, of methane in AFI become dependent on nanosheet thickness. Deviations can amount to factors of 2.9 and 1.4 for <i>D</i>_T and α, respectively, when, in the worst case, results from the thinnest AFI nanosheet are compared with data from the thickest sheet. We present a molecular explanation of the size limitation that is based on memory effects of entering molecules and therefore only observable for smooth pores such as AFI and carbon nanotubes. Hence, our work provides important tools to accurately predict and intuitively understand transport of guest molecules into porous host structures, a fact that will become the more valuable the more tiny nanotechnological objects get