An Innovative Approach for Modeling Proton Conductivity of Nafion Membranes

Abstract

In this study, a hybrid mathematical model incorporating both polynomial and asymptotic terms is proposed to more accurately and comprehensively describe the relationship between membrane proton conductivity and relative humidity in PEMFCs. The proposed model covers a wide operating temperature range and is designed to better represent the physical reality of membrane water content. Furthermore, for the first time in the literature, the Particle Swarm Optimization (PSO) algorithm has been employed to determine the model parameters. The results demonstrate a high degree of agreement with experimentally validated real-world datasets. Numerical analyses reveal that the proposed model achieves a root mean square error RMSE of 0.0680, indicating an approximately 81.31% improvement in performance compared to existing models. This significant enhancement is attributed to the model’s improved representation of physical phenomena and the effectiveness of the optimization process. The proposed model provides a reliable framework for predicting the effects of relative humidity and temperature in PEMFC performance simulations, serving as a valuable reference for water management and cell design. Additionally, its validity over a broad temperature range ensures high applicability across PEMFC systems operating under diverse conditions, representing a critical advantage for the advancement and widespread adoption of fuel cell technology. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.