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The theory of the feedback mode of scanning electrochemical microscopy is extended for probing heterogeneous electron transfer at an unbiased conductor. A steady-state SECM diffusion problem with a pair of disk ultramicroelectrodes as a tip and a substrate is solved numerically. The potential of the unbiased substrate is such that the net current flow across the substrate/solution interface is zero. For a reversible substrate reaction, the potential and the corresponding tip current depend on SECM geometries with respective to the tip radius including not only the tip-substrate distance and the substrate radius but also the thickness of the insulating sheath surrounding the tip. A larger feedback current is obtained using a probe with a thinner insulating sheath, enabling identification of a smaller unbiased substrate with a radius that is approximately as small as the tip radius. An intrinsically slow reaction at an unbiased substrate as driven by a SECM probe can be quasi-reversible. The standard rate constant of the substrate reaction can be determined from the feedback tip current when the SECM geometries are known. The numerical simulations are extended to an SECM line scan above an unbiased substrate to demonstrate a "dip" in the steady-state tip current above the substrate center. The theoretical predictions are confirmed experimentally for reversible and quasi-reversible reactions at an unbiased disk substrate using disk probes with different tip radii and outer radii.

Probing Heterogeneous Electron Transfer at an Unbiased Conductor by Scanning Electrochemical Microscopy in the Feedback Mode