On the Diffusion of Ions in Membranes. II. Generalized Planckmdash;Teorell Equations

摘要

The equations given by Planck and Teorell for the fluxes of univalent ions across a uniformly charged membrane are generalized from the case of parallel plane membranes considered by the original authors to the case of membranes of arbitrary shape. It is shown that a change in membrane geometry results solely in the reciprocal membrane thickness being replaced by the vacuum membrane capacitance per unit area when the fluxes are averaged over the outer membrane surface. The generalized equations are in all other respects, in particular in their dependence on the boundary concentrations and potentials, identical with the ones for parallel plane membranes.Generalized equations for the potential and ionic concentrations within the membrane are also given. Again the functional dependence of these quantities on their boundary values is independent of the geometry.