The geometric area of an electrode can be far less than the actual surface area. Using the actual surface area of an electrode is important when calculating values like current density (current per unit area of electrode surface) and area specific capacitance. The Butler-Volmer equation relates the overpotential (difference between the applied potential and the rest potential) to the current density, and the calculation of an accurate current density requires an accurate electrode surface area.
A Tafel plot can be used to determine the anodic and cathodic transfer coefficient and also the exchange current density for a given electrode/electrolyte system, but, as with the Butler-Volmer equation, an accurate electrode surface area is necessary in order to calculate an accurate electrode current density for use in the plot.
The area specific capacitance of an electrode surface is an important parameter for determining the suitability of an electrode material for use in a capacitor. An accurate area specific capacitance requires an accurate electrode surface area. Porous electrodes have specific surface areas (SSA) much greater than their geometric area. Mass specific surface areas (surface area per gram) can vary from 1 m2/gram to over 2000 m2/gram. One should note that SSA values determined from gas adsorption are most appropriate for determining the effective surface area of catalysts as used in plug flow reactors. The surface area of an electrode is best represented as an effective electrochemical surface area which may be less than the SSA determined by gas adsorption owing to current shielding. The effective electrochemical surface area and the SSA determined by gas adsorption will converge at low current density. Current shielding increases with increasing current density. New high SSA electrodes are important in the development of new supercapacitors. Some recent developments in the area of supercapacitors are given below.
Porous electrode with specific surface area of 2248 m2/g & 341 F/g: “High Specific Capacitance Electrode Material for Supercapacitors Based on Resin-Derived Nitrogen-Doped Porous Carbons” Jing Yu; Ning Fu; Jing Zhao; Rui Liu; Feng Li; Yuchuan Du; Zhenglong Yang*; ACS Omega 2019, 4, 14, 15904–15911. Publication Date: September 19, 2019
New porous silver electrode with mass specific capacitance of 412 F/g: “New 3D Porous Silver Nanopolycluster as a Highly Effective Supercapacitor Electrode: Synthesis and Study of the Optical and Electrochemical Properties” Qing-Shi Wu; Fahime Bigdeli; Farzaneh Rouhani; Xue-Mei Gao; Hamed Kaviani; Hong-Jing Li; Wei Wang; Kuan-Guan Liu*; Mao-Lin Hu; Xiao-Qing Cai*; Ali Morsali*; Inorg. Chem. 2021, 60, 3, 1523–1532. Publication Date: January 20, 2021
The area specific capacitance of these supercapacitor electrodes can be calculated from the mass specific capacitance and the mass specific surface area.
Note that this value of area specific capacitance is consistent with values measured by voltage step and voltage ramp experiments. See the paper linked below for a complete derivation of the current-time transient in a perturbed RC circuit and the use of said i/t transient to determine the capacitance at an electrode's surface.
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