A macrohomogeneous model is presented for a porous electrode that includes coupled potential and concentration gradients with linear kinetics. The equations are solved to obtain an analytical expression for the impedance of a porous electrode. Complex plane plots are presented that illustrate two well-defined arcs: a kinetic arc and a diffusion arc with their time constants far apart. The effects of parameters such as exchange current density, porosity, diffusion coefficient, thickness, and interfacial area on the impedance spectra are presented. The usefulness of the analytical solution in investigating the effect of solution phase diffusion is also presented.

An analytical expression is presented for the voltage response including the transient voltage for a simple ͑i.e., no concentration gradients͒ porous electrode model subject to a sinusoidal input current density. The transient voltage response as a function of the frequency, exchange current density, and double layer capacitance is studied independent of the periodic ͑steady state͒ voltage response. The change in the voltage response in the transient region is compared to that of the periodic voltage response with respect to the parameters. The physical properties of the porous electrode can be estimated using the voltage response in the transient region is presented. The methodology for doing this is described.

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A short-time transient analysis is presented for a sinusoidal input potential for a spherical particle. The objective of this work was to extract accurate values of the parameters associated with an intercalation into a spherical particle. These parameters are exchange current density, double-layer capacitance, and diffusion coefficient. The effects of these parameters on the response were examined using a sensitivity analysis, which indicated that optimum frequency values of the input perturbation exist for estimation of these parameters. A procedure is presented to obtain all these parameters using the short-time response. The results show that the short-time analysis is a useful method for estimating rapidly the values of these parameters of a system.