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 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 the 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.

• Received 11 May 2019
• Revised 25 June 2019

DOI:https://doi.org/10.1103/PhysRevApplied.12.014039