  In this work, we develop an extended uniform potential (UP) model for a
membrane nanopore by including two different charging mechanisms of the pore
walls, namely by electronic charge and by chemical charge. These two charging
mechanisms will generally occur in polymeric membranes with conducting agents,
or membranes made of conducting materials like carbon nanotubes with surface
ionizable groups. The electronic charge redistributes along the pore in
response to the gradient of electric potential in the pore, while the chemical
charge depends on the local pH via a Langmuir-type isotherm. The extended UP
model shows good agreement with experimental data for membrane potential
measured at zero current condition. When both types of charge are present, the
ratio of the electronic charge to the chemical charge can be characterized by
the dimensionless number of surface groups and the dimensionless capacitance of
the dielectric Stern layer. The performance of the membrane pore in converting
osmotic energy from a salt concentration difference into electrical power can
be improved by tuning the electronic charge.
