  We investigate the subtle effects of diffuse charge on interfacial kinetics
by solving the governing equations for ion transport (Nernst-Planck) with
realistic boundary conditions representing reaction kinetics (Butler-Volmer)
and compact-layer capacitance (Stern) in the asymptotic limit $\epsilon =
\lambda_D/L \to 0$, where $\lambda_D$ is the Debye screening length and $L$ is
the distance between the working and counter electrodes. Using the methods of
singular perturbation theory, we derive the leading-order steady-state response
to a nonzero applied current in the case of the oxidation of a neutral species
into cations, without any supporting electrolyte. In certain parameter regimes,
the theory predicts a reaction-limited current smaller than the classical
diffusion-limited current. We also analyze the impedance of the electrochemical
cell when a small AC current modulation is added to an applied DC current. At
sufficiently high AC frequencies, the Maxwell displacement current is found to
exceed the Faradaic conduction current, and experimentally observed ``negative
impedances'' (out of phase AC voltage responses) are predicted close to the
reaction-limited current. Overall, we demonstrate that the dynamics of diffuse
charge plays a fundamental role in nonequilibrium surface reactions when the
transport of one of the reacting species is coupled to the total interfacial
reponse of the compact and diffuse layers.
