Free energy barriers for TMEA+, TMA+, and [formula omitted] ion diffusion through nanoporous carbon electrodes

The energy storage of supercapacitors can be enhanced by utilizing porous carbon electrodes with nanometer or even sub-nanometer sized pores that exhibit close match of the pore and ion size. In these highly confined regimes, ion diffusion barriers may be substantial, leading to a tradeoff between power output and energy storage. In this work, we utilize molecular dynamics simulations to quantify free energy barriers for ion diffusion through nanometer and sub-nanometer sized pores in carbon electrodes. We focus on prototypical electrolytes composed of trimethylethylammonium (TMEA⁺) and tetramethylammonium (TMA⁺) cations, and tetrafluoroborate (BF4-) anions, with both acetonitrile and 1,2-dichloroethane solvents. We quantify the dependence of diffusion barriers on nanopore width and pore length as a function of solvent and ion type. Our overarching conclusion is that sub-nanometer sized pores of 7.5–10 A diameter, as previously demonstrated to be optimal for energy storage, lie exactly at the limit of diffusion accessibility at low voltage. We show that nanopore accessibility depends sensitively on the solvent dielectric strength, and that for low dielectric solvents, barriers are dictated by diffusion of ion pairs rather than single ions.