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, D
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 D
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.