Quantitative Study of Charge Distribution Variations on Silica–Nafion Composite Membranes under Hydration Using an Approximation Model

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.