In the classical study of ion transport through charged membranes, Donnan potentials are used to approximate the difference between the applied electrostatic potential and the potential at the liquid/membrane interface. For very thin membranes (e.g., biological lipid bilayers), this discontinuous approximation of the potential is not sufficient. Here we derive a modification to the classic Donnan potential for ion transport through a biological ion channel embedded in a lipid bilayer. We also show how to derive the classic Donnan potential without the usual assumptions and estimate the amount of space charge at the liquid/membrane interface.
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