Theoretical Analysis of the Pulse-Clamp Method as Applied to Neural Stimulating Electrodes

A mathematical model was developed to simulate potential pulse clump experiments at inert-electrode/aqueous solution interfaces in the absence of dioxygen or other adventitious redox activc species. This model incorporates a potential invariant interfacial capacitor, a kinetically slow redox couple with parameters consistent with the H₂O/H₂ reaction on polyerystalline Au in acid electrolytes as the only faradaic process involved, and diffusion us the only mode of mass transport in solution phase. Numerical integration of the resulting system of differential equations was found to yield results in good agreement with experimental data reported by Mortimer and co-workers for Au in dearated sulfuric acid solutions. A detailed analysis of these cumulations identified the fast and slow recoverable charges to he capacitive and the unrecoverable charges to be faradaic. The results obtained indicated that for small overpotentials the charge is stored in the interfacial capacitor, and that significant furadaic processes occur only when the overpotential is large. Furthermore, during the delay, and despite the fact that no current flows through the external circuit, the capacitor discharges via the faradaic reaction, increasing the total amount of product generated. More importantly, under the conditions selected for the simulations, none of the faradaic charge is recovered during the potential controlled stage of the sequence. These results provide insight into the relationships between stimulus parameters and charge injected into irreversible faradaic reactions, which may generate biologically harmful .species. In general, us stimulus pulse durations increase, unrecoverable charge increases, Also, as the delay increases between the end of the primary and beginning of the secondary pulse, unrecoverable charge increases. Furthermore, based on the mathematical model used herein, the use of an electrode material with a small exchange current density would allow greater overpotentials to be reached before the onset of significant faradaic reactions, and thus greater total charge injection prior to faradaic reactions.