An accurate polynomial expression for the steady-state current in the case of first-order EC′ reaction is reported using scattering analogue techniques for ultramicro disk electrodes. When the reaction rate is small, seven terms of diffusion-limited current are reported, and when it is large, five terms of the same are reported. A two-point Pade ´approximant is derived for all values of reaction rates. By a proper transcription of variables, the methodology is extended to derive chronoamperometric current for diffusion-controlled processes, and excellent agreement with digital simulation data is noticed.

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The transient current-potential response of the enzyme-catalyzed oxygen reduction reaction in biofuel cells is analyzed. The onedimensional nonlinear reaction-diffusion equation is solved analytically using the homotopy method for deriving the substrate concentrations and current densities pertaining to chronoamperometric response. The time required to obtain the steady state has been obtained and the influence of film thickness, diffusion coefficients, and enzyme characteristics has been deciphered. The equations are shown to be valid for experimental data on mediated electron transfer reactions of redox polymers containing osmium complexes. The substrate concentrations and current densities for supported, gas-diffusion and flow through electrodes are also reported.