Finite element analysis of the Poisson–Boltzmann equation coupled with chemical equilibriums: redistribution and transport of protons in nanophase separated polymeric acid–base proton exchange membranes

Abstract

The finite element analysis is applied to the study of the redistribution and transport of protons in model nanophase separated polymeric acid–base composite membranes by the Poisson–Boltzmann equation coupled with the acid and base dissociation equilibriums for the first time. Space charge redistribution in terms of proton and hydroxide redistributions is observed at the interfaces of acidic and basic domains. The space charge redistribution causes internal electrostatic potential, and thus, promotes the macroscopic transport of protons in the acid–base composite membranes.

Keywords:

• Poisson–Boltzmann equation
• finite element analysis
• nanophase separation
• space charge distribution
• acid–base composite proton exchange membrane

Acknowledgements

They also acknowledge the High-Performance Computing Center and the Laboratory for Microstructures, Shanghai University for computing and structural characterization.