The complete optimization of fuel cell´s performance involves the prediction of its operation conditions and electrochemical characteristics for short and long-time periods. One of the topics not studied in detail is the change in the surface morphology of metallic catalytic layers as a time-dependent function of the fuel cell working conditions. For single platinum catalysts a columnar growth is demonstrated after 1 month of hydrogen/oxygen continuous operation at the plateau, where electrochemical distributions of smooth surfaces are not operative. Since they act as a completely dynamic system, numerical solutions are not useful as they permanently need parametric profile optimizations. The employ of exact analytical functions instead, reduces large computational times and assures this information only knowing the final structure morphology. In this sense we encouraged current, concentration and potential shapes for these columnar electrodes adapting mass balance differential equations with a parametric profile to model these columns (trochoid curvilinear contours). The analytical solutions were compared with those of a smooth surface (early uses of the fuel cell) and with experimental values obtained using a home-made hydrogen/oxygen polymeric membrane cell.