Butler-Volmer equation/expression/relation

Figure 5. Measurement and analysis of steady-state i— V characteristics, (a) Following subtraction of ohmic losses (determined from impedance or current-interrupt measurements), the electrode overpotential rj is plotted vs ln(i). For systems governed by classic electrochemical kinetics, the slope at high overpotential yields anodic and cathodic transfer coefficients (Ua and aj while the intercept yields the exchange current density (i o). These parameters can be used in an empirical rate expression for the kinetics (Butler—Volmer equation) or related to more specific parameters associated with individual reaction steps.(b) Example of Mn(IV) reduction to Mn(III) at a Pt electrode in 7.5 M H2SO4 solution at 25 Below limiting current the system obeys Tafel kinetics with Ua 1/4. Data are from ref 363. (Reprinted with permission from ref 362. Copyright 2001 John Wiley Sons.)...

The activation polarization region is observed at low current densities. In this region, the voltage losses are associated with the activation energy barrier that must be overcome in the cathode and anode electrodes. The current density dependency on parameters related to overcoming the activation energy barrier is expressed in the Butler-Volmer equation [31]. Thus, activation losses are function of electrode properties, temperature, and pressure conditions. The performance of an HT-PEMFC is represented by (17.1). 

The first equation expresses the decay of ionic current with x at a Butler-Volmer rate (the right-hand side of this equation) [6]. The second is Ohm s law relating the ionic current to the overpotentiai gradient. The third indicates that the local difiusion flux of feed molecules is equal to the molar flux of electrons to be converted into ions. 

Figure 3a is an illustration of the effect of surface overpotential on the limiting-current plateau, in the case of copper deposition from an acidified solution at a rotating-disk electrode. The solid curves are calculated limiting currents for various values of the exchange current density, expressed as ratios to the limiting-current density. Here the surface overpotential is related to the current density by the Erdey Gruz-Volmer-Butler equation (V4) ... 

---