Van 't Hoff Institute for Molecular Sciences
University of Amsterdam
The Netherlands
beerdsen@science.uva.nl
Can we predict the diffusion behaviour of molecules in confinement by looking at the match between the molecule and the structure of the confinement? This question has proven difficult to answer for many decades. As a case study, we use methane and a simple model of ellipsoids to arrive at a molecular picture that allows us to make a classification of pore topologies and to explain their diffusion behaviour as a function of loading. Our model is surprisingly simple: regarding a structure as consisting of interconnected ellipsoids is enough to understand the full loading dependence.
We combine molecular-dynamics simulations with calculations using the new dcTST
method[1] to gain insight in the diffusion of twelve different types of zeolites
spanning the range of different pore topologies: LTA, CHA, ERI, FAU, SAS, LTL, MTW,
AFI, MFI, BOG, BEC, and ISV. We calculate self and corrected diffusivities as a
function of loading and find an explanation of their diffusion behaviour by studying
the free-energy changes as the loading is increased.
We can divide the twelve zeolites in three different groups, each having their own
diffusion behaviour: cage-type zeolites, channel-type zeolites, and
intersecting-channel-type zeolites.[2]
In cage-type zeolites both the self and the corrected diffusion go through a maximum
in the diffusion when the loading is increased. This is due to an increased free
energy in the cage regions at the addition of particles at low loadings. The free
energy in the windows separating the cages remains approx. constant, resulting in an
effective decrease of the free-energy barrier. The loading at which the maximum is
observed is dependent on the cage size. The value of the maximum depends mainly on
the diameter of the window.
In channel-type zeolites the diffusion generally decreases as a function of loading
in smooth channel-type zeolites. The steepness of the curve depends on the
'cagelikeness' of the zeolite structure: the ratio between the window and the cage
diameters. The decrease in the diffusion is caused by a collective effect of
increasing free-energy barriers and increased interparticle-collision frequency.
As far as the self diffusion is considered, the class of intersecting-channel-type
zeolites resembles the class of channel-type zeolites. The corrected diffusion,
however, has its own distinct behaviour: initially it remains more or less constant
as a function of loading; at high loadings it becomes a rapidly decreasing function
of loading. The exact behaviour is a complex interplay between the main and
intersecting channels, and can be explained by studying the free-energy profiles as
a function of loading.[3]