The Relationship of the Geometry of the Observed Steady State Chemical Conversion Rate to the Basic Surface Reaction Process in Electrochemistry

Abstract

The steady state surface reaction rate for electrochemical reactions is frequently measured by the polarization curve. In the anodic region of this curve the dynamics of the reaction process are generally described by a semiflow map. The fixed points of this map describe the steady state dynamics of the surface reactions. These generic singularities are classified according to their bifurcation structure. For the corrosion of aluminum this steady state bifurcation structure is found experimentally to be given by a butterfly catastrophy surface. Each structure has a characteristic signature which can be experimentally observed. This is most readily seen in the polarizations curves obtained in the study of surface reactions in electrochemistry and corrosion. Each characteristic signature is described by two variables: the codimension (cod) and k‐determinacy (σ). These variables are obtained directly from the polarization curve and are determined by its geometric structure. The codimension and k‐determinacy can be calculated from any detailed physical model of the surface reactions that occur. Thus the experimental results constrain the possible physical models that can be considered to describe the reaction process because the codimension and k‐determinacy values must agree for both the experiment results and the physical model. Because cod and σ are measures of the geometric shape of polarization curve what is being required is that any physical model be capable of representing the geometry of the experimental results. In the study of electrochemical corrosion reactions this analysis completely explains why the usual Tafel Law and its associated model of the surface reactions involved is entirely inadequate to describe the physics of the anodic region of the polarization curve. Results of this analysis as applied to electrochemical reaction studies of Aluminum will be described.