Activation overpotential

The cell activation overpotential is presumed to be composed of anodic and cathodic contributions: \[\eta ={{\eta }_{a}}+{{\eta }_{c}}\] Defining the electrode overpotential, \({{\eta }_{e}}={{\eta }_{a}}\) at the anode and \({{\eta }_{e}}={{\eta }_{c}}\) at the cathode. Values of \({{\eta }_{e}}\left( i \right)\) at both electrodes are obtained using a root finder based on Ridder's method coded in appSrc file, riddersRoot.C, to obtain numerical solutions of the Butler-Volmer equation \[{i}={{{i}}_{0}}\left[ \exp \left( A{{\eta }_{e}} \right)-\exp \left( B{{\eta }_{e}} \right) \right]\] where \[{A=2{{\alpha }_{e}}F}/{RT}\;\]\[{B=-2\left( 1-{{\alpha }_{e}} \right)F}/{RT}\;\] at each electrode. The exchange current densities are given by; \[{{{i}}_{0,c}}={{\gamma }_{c}}p_{{{\text{O}}_{2}}}^{m}\exp \left( -\frac{{{E}_{act,c}}}{RT} \right)\] \[{{{i}}_{0,a}}={{\gamma }_{a}}p_{{{\text{H}}_{2}}}^{a}p_{{{\text{H}}_{\text{2}}}\text{O}}^{b}\exp \left( -\frac{{{E}_{act,a}}}{RT} \right)\]

The reaction orders, a, b, m, the pre-constants \({{\gamma }_{a}}\), \({{\gamma }_{c}}\), activation energies E_act,a , E_act,c are prescribed together with the transfer coefficients, \({{\alpha }_{e}}\), \({{\alpha }_{c}}\) in the dictionary activationParameters, located in constant/electrolyte. The prescibed values are those recommended in Leonide at el. (2009). Note the partial pressures are in Atmospheres.