A universal model for nanoporous carbon supercapacitors applicable to diverse pore regimes, carbon materials, and electrolytes

Supercapacitors, commonly called electric double-layer capacitors (EDLCs), are emerging as a novel type of energy-storage device with the potential to substitute batteries in applications that require high power densities. In response to the latest experimental breakthrough in nanoporous carbon supercapacitors, we propose a heuristic theoretical model that takes pore curvature into account as a replacement for the EDLC model, which is based on a traditional parallel-plate capacitor. When the pore size is in the mesopofe regime (2-50 nm), counterions enter mesoporous carbon materials and approach the pore wall to form an electric double-cylinder capacitor (EDCC); in the micropore regime (<2 nm), solvated/desolvated counterions line up along the pore axis to form an electric wire-in-cylinder capacitor (EWCC). In the macropore regime (>50 nm) at which pores are large enough so that pore curvature is no longer significant, the EDCC model can be reduced naturally to the EDLC model. We present density functional theory calculations and detailed analyses of available experimental data in various pore regimes, which show the significant effects of pore curvature on the supercapacitor properties of nanoporous carbon materials. It is shown that the EDCC/EWCC model is universal for carbon supercapacitors with diverse carbon materials, including activated carbon materials, template carbon materials, and novel carbide-derived carbon materials, and with diverse electrolytes, including organic electrolytes, such as tetraethylammonium tetrafluoroborate (TEABF(4)) and tetraethylammonium methylsulfonate (TEAMS) in acetonitrile, aqueous H2SO4 and KOH electrolytes, and even an ionic liquid electrolyte, such as 1-ethyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide (EMI-TFSI). The EDCC/EWCC model allows the supercapacitor properties to be correlated with pore size, specific surface area, Debye length, electrolyte concentration and dielectric constant, and solute ion size It may lend support for the systematic optimization of the properties of carbon supercapacitors through experiments. On the basis of the insight obtained from the new model, we also discuss the effects of the kinetic solvation/desolvation process, multimodal (versus unimodal) pore size distribution, and exohedral (versus endohedral) capacitors on the electrochemical properties of supercapacitors.