Analysis of Ionic Domains on a Proton Exchange Membrane Using a Numerical Approximation Model Based on Electrostatic Force Microscopy

Understanding the ionic channel network of proton exchange membranes that dictate fuel cell performance is crucial when developing proton exchange membrane fuel cells. However, it is difficult to characterize this network because of the complicated nanostructure and structure changes that depend on water uptake. Electrostatic force microscopy (EFM) can map surface charge distribution with nano-spatial resolution by measuring the electrostatic force between a vibrating conductive tip and a charged surface under an applied voltage. Herein, the ionic channel network of a proton exchange membrane is analyzed using EFM. A mathematical approximation model of the ionic channel network is derived from the principle of EFM. This model focusses on free charge movement on the membrane based on the force gradient variation between the tip and the membrane surface. To verify the numerical approximation model, the phase lag of dry and wet Nafion is measured with stepwise changes to the bias voltage. Based on the model, the variations in the ionic channel network of Nafion with different amounts of water uptake are analyzed numerically. The mean surface charge density of both membranes, which is related to the ionic channel network, is calculated using the model. The difference between the mean surface charge of the dry and wet membranes is consistent with the variation in their proton conductivity.