The Galvanostatic Method: Analysis of Error and Computation of Parameters

Galvanostatic transients arising from multi-step processes of the type: υ0O + ne = υR are treated mathematically for systems subjected to both activation and diffusion control. Analysis of error based on the error matrix is presented. The galvanostatic method is characterized by the information contents [Ī(i0) and Ī(Cdl)] for a single-estimate analysis (i.e., estimate of i0 for known Cdi or the reverse) and that for a two-estimate analysis (simultaneous determination of i0 and Cdl). The correlation between the estimates of i0 and Cdl is given as a function of the dimensionless scale T/τc. Information contents for i0 and Cdl in single and two-estimate systems are given and this permits the determination of the accuracy and the limits of the method as well as the choice of optimal experimental conditions. The optimal full time scale for estimation of i0 depends on the value of τc/td. For τc/τd between 0.5–500, T opt/τc varies from 6 to 18 (single-estimate system) and from 4 to 25 (two-estimate system). The upper limit for i0 in a single-parameter estimation is 3–12 A cm−2 (for Cd) 10–40 μF cm−2) and the upper limit for Ks(±a = ±c = 0.5) is 8 cm sec−1. This is three times greater than ks for the coulostatic method. For a given value of Ks, the accuracy of the galvanostatic method is better than that of the coulostatic for systems when τ/τa > 0.6, but is not as good when τ/τd < 0.6. The upper limit of Ks and the accuracy of the galvanostatic method for two-estimate analysis (i0 and Cdl) are considerably lower than those for single-estimate analysis. An iteration method is developed with which a large improvement is achieved. Estimation of i0 and Cdl with a computerized curvilinear regression analysis is proposed.