Experiments Based on One-Dimensional Diffusion Modeling to Determine Critical Factors in Pitting
Authors: Srinivasan Jayendran , Kelly Robert G. 
Published: February 2020

Critical conditions for stable pitting were first formulated by Galvele1, considering mass transport in a one-dimensional pit, with the parameter (i*x) (pit stability product2) describing steady-state kinetics. Beck3, Alkire and coworkers4, and Newman and coworkers5,6 established artificial pits as the experimental tool to examine these kinetics. An associated descriptor of critical conditions is the critical potential1,7–9. Given the quasi-steady state obtained under a salt film6,10,11 for a corroding pit, this potential was taken as the potential at which this film was first stable, the transition potential ET
6. However, pitting was observed to proceed stably at potentials below ET
12–14, calling into question its validity as the critical potential as well as the salt film as a critical surface condition.

Long-term experiments oriented towards establishing a potential lower bound for propagating pits showed that the repassivation potential Erp
15–18 below which no new pits nucleate and any existing pits repassivate, could be a critical potential. Erp would describe the same conditions as the critical pit stability product (i*x)crit, a fraction of (i*x) measured under a salt film. Studies to date have focused on determining either the critical potential15,18–20 or the critical pit stability product2,13,21,22, and have not provided a definitive quantitative connection between the two and to other associated critical factors like surface concentration (CS
12) and pH.  This work presents a combined experimental and modeling framework that relates these factors. Artificial pit experiments were performed using 316L stainless steel wires in sodium chloride solution. Experimental estimates related to the critical factors include (i*x)saltfilm and Erp. Experimental results were fed into a one-dimensional diffusion model. A graphical method for determining CS at the transition between pitting stability and repassivation was developed, comparing a) Δt, the difference between tact (time taken to scan to Erp from ET) and tf (time taken for the CS to dilute to different fractions of saturation), and b) Erp (Fig. 1).

Experiments were also designed to obtain anodic kinetics at different CS. The time required for a corroding surface under a salt film to dilute to various CS values was calculated from the mass transport model developed. Pits were grown under a salt film to predetermined depths and then allowed to dilute under open circuit to various CS. Rapid scanning to anodic potentials was subsequently carried out once each CS was achieved, so that the anodic kinetics at that particular CS could be determined, removing the need for separate experiments in simulated pit chemistries. Results showed that there was a change in type of behavior and not merely in degree for CS < 50% of saturation (Fig. 2), indicating that the critical CS is lower than previously considered estimates, which has implications on damage estimation models based on anodic stability. Estimates of the critical pH associated with this transition was also obtained based on the influence of local cathodic reactions23,24. A single quantitative framework was therefore developed relating key parameters describing pitting stability and repassivation. 

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Figure 1