It is important to characterize the proton transport mechanisms of proton exchange membranes (PEMs). Electrostatic force microscopy (EFM) is used to characterize the ionic structures of membranes. In this study, we attempted to quantitatively analyze the proton conductivity enhancement of Nafion-sulfonated silica (SSA) composite membranes with variations in the ionic channel distribution. This study involved several steps. The morphology and surface charge distribution of both membranes were measured using EFM. The measured data were analyzed using a numerical approximation model (NAM) that was capable of providing the magnitude and classification of the surface charges. There were several findings of ionic channel distribution variations in Nafion-SSA. First, the mean local ionic channel density of Nafion-SSA was twice as large as that of the pristine Nafion. The local ionic channel density was non-uniform and the distribution of the ionic channel density of Nafion-SSA was 23.5 times larger than that of pristine Nafion. Second, local agglomerations due to SSA were presumed by using the NAM, appearing in approximately 10% of the scanned area. These findings are meaningful in characterizing the proton conductivity of PEMs and imply that the NAM is a suitable tool for the quantitative assessment of PEMs.

Understanding the ionic structure and charge transport on proton exchange membranes (PEMs) is crucial for their characterization and development. Electrostatic force microscopy (EFM) is one of the best tools for studying the ionic structure and charge transport on PEMs. In using EFM to study PEMs, an analytical approximation model is required for the interoperation of the EFM signal. In this study, we quantitatively analyzed recast Nafion and silica–Nafion composite membranes using the derived mathematical approximation model. The study was conducted in several steps. In the first step, the mathematical approximation model was derived using the principles of electromagnetism and EFM and the chemical structure of PEM. In the second step, the phase map and charge distribution map on the PEM were simultaneously derived using atomic force microscopy. In the final step, the charge distribution maps of the membranes were characterized using the model. There are several remarkable results in this study. First, the model was accurately derived as two independent terms. Each term shows the electrostatic force due to the induced charge of the dielectric surface and the free charge on the surface. Second, the local dielectric property and surface charge are numerically calculated on the membranes, and the calculation results are approximately valid compared with those in other studies.