Simulation of electrochemical processes during oxygen evolution on $\mathrm{Pb-MnO_2}$ composite electrodes

Abstract

The geometric properties of $\mathrm{Pb-MnO_2}$ composite electrodes are studied, and a general formula is presented for the length of the triple phase boundary (TPB) on two dimensional (2D) composite electrodes using sphere packing and cutting simulations. The difference in the geometrical properties of 2D (or compact) and 3D (or porous) electrodes is discussed. It is found that the length of the TPB is the only reasonable property of a 2D electrode that follows a 1/r particle radius relationship. Subsequently, sphere packing cuts are used to derive a statistical electrode surface that is the basis for the earlier proposed simulations of different electrochemical mechanisms. It is shown that two of the proposed mechanisms (conductivity and a two-step-two-material kinetic mechanism) can explain the current increase at $\mathrm{Pb-MnO_2}$ anodes compared to standard lead anodes. The results show that although $\mathrm{MnO_2}$ has low conductivity, when combined with Pb as the metal matrix, the behaviour of the composite is not purely ohmic but is also affected by activation overpotentials, increasing the current density close to the TPB. Current density is inversely proportional to the radius of the catalyst particles, matching with earlier experimental results. A hypothetical two-step-two-material mechanism with intermediate $\mathrm{H_2O_2}$ that reacts on both the Pb matrix and $\mathrm{MnO_2}$ catalyst is studied. It was found that assuming quasi-reversible generation of $\mathrm{H_2O_2}$ followed by its chemical decomposition on $\mathrm{MnO_2}$, results are obtained that agree with the experiments. It is further emphasised that both the Pb matrix and $\mathrm{MnO_2}$ catalyst are necessary and their optimum ratio depends on the used current density. Yet, additional experimental evidence is needed to support the postulated mechanism.