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.

Understanding the ionic channel network of proton exchange membranes, which dictate fuel cell performance, is crucial when developing proton exchange membrane fuel cells. However, itis difficult to characterize due to complicated nano structure and differing changes to their structure with different amounts of water uptake. Electrostatic force microscopy (EFM) can map surface charge distribution as nano special resolution by measuring the electrostatic force between a vibrating conductive tip and a charged surface under an applied voltage, . In this study, the ionic channel network of a proton exchange membrane is analyzed using EFM. A mathematical approximation model of the ionic channel network is first derived, to explain changes in force gradient on the surface using EFM. The phase lag of dry and wet Nafion under stepwise changes to bias voltage is then measured. Based on the model, 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 connected with the ionic channel network, is calculated using the model. The results show that the difference between the mean surface charge of the dry and wet membranes is consistent with the variation in their proton conductivity.