This work aims to study the scattering dynamics of electron–H₂⁺ molecules under the influence of self-generated laser and thermal fields in a Proton Exchange Membrane Fuel Cell (PEMFC). The system is modeled considering that one electron of the hydrogen molecule participates in an exothermic reaction that is catalyzed by platinum, while the other electron remains non-reactive, forming –H₂⁺ . The reaction generates localized temperature rise and motion of charged particles, which produce a spectrum of electromagnetic wavelengths, contributing to a laser-like field within the PEMFC. To analyze this system, thermal Volkov wavefunctions and the hydrogen ion potential were employed to calculate the scattering and transition matrices, which were then used to determine the differential cross-section (DCS) of electron–H₂⁺ interactions near the PEMFC electrode. This approach is significant, because although numerous studies focus on material selection, design, and simulations, few address the microscopic scattering processes affecting PEMFC performance. The computed results reveal that the DCS decreases with increasing incident electron energy [1], increases with thermal conductivity, and rises with temperature, showing oscillatory sinusoidal behavior. As the DCS is directly related to the temperature, and the temperature is inversely related to the cell voltage, an increase in temperature leads to a decrease in voltage and overall performance of the PEMFC. Therefore, understanding electron–H₂⁺ scattering dynamics is essential for improving PEMFC efficiency and thermal management. These findings highlight the importance of incorporating microscopic scattering analysis alongside conventional approaches for optimizing fuel cell operation .

[1] Dhobi, S. H., Gupta, S. P., Yadav, K., & Jha, A. K. (2025). Scattering Dynamics in Thermal Environments Around PEMFC Electrode. International Energy Journal, 25(1A).