Abstract
The movement of small particles and molecules through nanopore membranes is widespread and has far-reaching implications. Consequently, the development of mathematical models is essential for understanding these processes on a micro level, leading to deeper insights. In this endeavor, we suggested a model based on a set of empirical equations to predict the transport of substances through a solid-state nanopore and the associated signals generated during their translocation. This model establishes analytical relationships between the ionic current and electrical double-layer potential observed during analyte translocation and their size, charge, and mobility in an electrolyte solution. This framework allows for rapid interpretation and prediction of the nanopore system's behavior and provides a means for quantitatively determining the physical properties of molecular analytes. To illustrate the analytical capability of this model, ceria nanoparticles were investigated while undergoing oxidation or reduction within an original nanopore device. The results obtained were found to be in good agreement with predictions from physicochemical methods. This developed approach and model possess transferable utility to various porous materials, thereby expediting research efforts in membrane characterization and the advancement of nano- and ultrafiltration or electrodialysis technologies.