Atomistic modeling and/or experimental methods were conducted to study transport processes in the porous electrodes of polymer electrolyte fuel cells (PEFCs) and of mediator enhanced polymer electrolyte supercapacitors (MEPESCs). The simulations show that vibrations of the Pt nanocrystallines on rhe carbon supports significantly impacts diffusion in the Nafion electrolyte clusters between the carbon supports and enhances the diffusivity of hydrogen, oxygen, methanol, water, and hydronium up to 8 times the nominal value Charging the carbon support alters the diffusivities. It was visualized that charging of Pt nanocrystallines resulted in disintegration of the Pt catalysts leading to a reduction in catalytic activity of the catalyst layer. Re-precipitation and re- crystallization of the Pt under a full discharging condition can also be visualized using the molecular dynamics (MD) modeling method. MD simulations also indicate that the mobility of the iodine mediators is at least 10 times greater than other small ions in the Nafion electrolyte. The degradation of the MEPESC is dominated by the crossover of I ions but not I2 in Nafion.