Impedance of porous electrodes

Porous electrodes are important in practical applications of electrochemistry. Single cylindrical pore models are first presented. In the presence of dc current, dc potential and dc concentration gradients appear. These gradients are related to each other. Analytical solutions exist only in the absence of the dc potential gradient. When concentration gradient is present two semicircles appear on the complex plane plots. Solution resistivity in pores causes formation of the high frequency line at 45 o on the complex plane plots. However, the real pores are multidimensional containing macro, meso, and micro pores. Many models of inhomogeneous porosity were developed. Further models used Poisson-Nernst-Planck theory to include charge interactions. In very narrow pores double layers of the pore walls overlap. Future challenge is to obtain pore parameters from the impedance measurements of complex systems.