Attractive forces in microporous carbon electrodes for capacitive deionization

The recently developed modified Donnan (mD) model provides a simple and useful description of the electrical double layer in microporous carbon electrodes, suitable for incorporation in porous electrode theory. By postulating an attractive excess chemical potential for each ion in the micropores that is inversely proportional to the total ion concentration, we show that experimental data for capacitive deionization (CDI) can be accurately predicted over a wide range of applied voltages and salt concentrations. Since the ion spacing and Bjerrum length are each comparable to the micropore size (few nanometers), we postulate that the attraction results from fluctuating bare Coulomb interactions between individual ions and the metallic pore surfaces (image forces) that are not captured by mean-field theories, such as the Poisson-Boltzmann-Stern model or its mathematical limit for overlapping double layers, the Donnan model. Using reasonable estimates of the micropore permittivity and mean size (and no other fitting parameters), we propose a simple theory that predicts the attractive chemical potential inferred from experiments. As additional evidence for attractive forces, we present data for salt adsorption in uncharged microporous carbons, also predicted by the theory.