The Characteristics of Component Transfer
through Barrier Membrane Layers

S. F. Timashev

Karpov Research Institute of Physical Chemistry, ul. Vorontsovo pole 10, Moscow, 105064 Russia

e-mail: serget@mail.ru

Received January 31, 2008

Abstract—A uniform matrix with randomly distributed impurity centers, which create an effective field repuls-
ing particles that diffuse in the membrane and prevent the formation of “percolation” paths in “thick” mem-
branes, is considered as a barrier layer model. Two repulsive potential types were analyzed, one decreasing
according to a power law depending on the distance between the localization center of an impurity and the dif-
fusing particle and the other decreasing exponentially as a function of this distance. An exponential dependence
of the permeability constants of the desired components on the membrane layer thickness was predicted.
According to this dependence, the components to be separated effectively pass through membrane layers only
in local regions, where the force field that retards particles is weakened because of a fluctuation decrease in the
concentration of centers repulsing the diffusing particles. The process is then characterized by nonequilibrium
transmembrane transfer conditions, under which particles have time to be effectively “sorbed” only in regions
of increased membrane permeability. Under these conditions, the selectivity of membrane separation can be
influenced by the state of the surface of membranes. For this reason, the modification of the surface of barrier
structures can be used to control their selective permeability to the desired products. Equations for the rate of
component transfer through barrier membrane layers under the most general boundary conditions were
obtained. These equations can be used to analyze separation on membranes with barrier structures subjected to
surface modification.

DOI: 10.1134/S0036024408100099

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