Abstract
The generic mechanisms of anomalous transport in porous media are investigated by computer simulations of two-dimensional model systems. In order to bridge the gap between the strongly idealized Lorentz model and realistic models of porous media, two models of increasing complexity are considered: a cherry-pit model with hard-core correlations as well as a soft-potential model. An ideal gas of tracer particles inserted into these structures is found to exhibit anomalous transport which extends up to several decades in time. Also, the self-diffusion of the tracers becomes suppressed upon increasing the density of the systems. These phenomena are attributed to an underlying percolation transition. In the soft potential model the transition is rounded, since each tracer encounters its own critical density according to its energy. Therefore, the rounding of the transition is a generic occurrence in realistic, soft systems.
Highlights
Our systems allow testing which properties of porous media are necessary for anomalous transport and a localization transition
In the cherry-pit model, the host matrix contains structural correlations which modify the structure of the void space
In the WCA model, interactions between tracer particles and the host particles are modeled with a purely repulsive and so potential. This changes the topology of the void space by introducing a potential energy landscape with nite barriers
Summary
Molecular transport in strongly heterogeneous media is fundamental for a wide range of disciplines such as molecular sieving,[1] catalysis[1,2,3,4] and ion-conductors,[5,6] and for protein motion in the interior of “crowded” cells.[7,8,9,10] Common to all of these systems is the occurrence of a quasi-immobilized host structure which restricts transport to rami ed paths through the medium. Interactions smear out the boundaries of the accessible space and change the topology of the percolation network by introducing a potential energy landscape with nite barriers between the pores. To investigate these issues, we compare simulations of two different models, which represent modi cations to the original Lorentz model. The resulting host structure is equivalent to the cherry-pit model.[31] Second, we relax the assumption of hard-core repulsion between both obstacles and tracers by introducing so interactions. We nd that an effective interaction distance can be assigned to each tracer according to its energy, thereby providing a mapping to the hard-core case
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