Electrosorption of ions from aqueous solutions by carbon aerogel: An electrical double-layer model

An electrical double-layer model is developed to predict electrosorption of ions from aqueous solutions by carbon aerogel electrodes. The carbon aerogel electrodes are treated as electrical double-layer capacitors, and electrosorption is modeled using classical electrical double-layer theory. Because of the porous characteristics of the electrodes, the total capacity of the system is obtained by summing the contributions of the individual pores. The pore size distribution of the carbon aerogel is measured by the physical adsorption of N₂ and CO₂ as well as by mercury intrusion porosimetry. When a pore has a width smaller than a specific value (cutoff pore width), it does not contribute to the total capacity because of the electrical double-layer overlapping effect. This effect greatly reduces the electrosorption capacity for electrodes with significant numbers of micropores, such as carbon aerogel; thus, it is considered in the electrical double-layer model. The model in this study focuses on the electrosorption of sodium fluoride, which exhibits minimal specific adsorption. Several equilibrium electrosorption experiments are performed under various conditions of ion solution concentration and applied voltage. When the overlapping effect is considered, modeling results agree well with experimental data obtained at voltages up to 1.2 V. Without the double-layer overlapping correction, the model greatly overestimates the electrosorption capacity. The cutoff pore width is found to decrease with increasing ion solution concentration and applied voltage. An approximate modeling approach is also presented in this work, which is more efficient than the exact solution in terms of numerical computations.