The unprecedented anomalous increase in capacitance of nanoporous carbon supercapacitors at pore sizes smaller than 1 nm [Science 2006, 313, 1760.] challenges the long-held presumption that pores smaller than the size of solvated electrolyte ions do not contribute to energy storage. We propose a heuristic model to replace the commonly used model for an electric double-layer capacitor (EDLC) on the basis of an electric double-cylinder capacitor (EDCC) for mesopores (2 {50 nm pore size), which becomes an electric wire-in-cylinder capacitor (EWCC) for micropores (< 2 nm pore size). Our analysis of the available experimental data in the micropore regime is confirmed by 1st principles density functional theory calculations and reveals significant curvature effects for carbon capacitance. The EDCC (and/or 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. The new model not only explains the experimental data, but also offers a practical direction for the optimization of the properties of carbon supercapacitors through experiments.

Theoretical Model for Nanoporous Carbon Supercapacitors

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 mesopore 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 ( 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 H(2)SO(4) 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.

A Universal Model for Nanoporous Carbon Supercapacitors Applicable to Diverse Pore Regimes, Carbon Materials, and Electrolytes

The effect of porous structures on the electrocatalytic activity of N-doped carbon is studied by using electrochemical analysis techniques and the result is applied to synthesize highly active and stable Fe–N–C catalyst for oxygen reduction reaction (ORR). We developed synthetic procedures to prepare three types of N-doped carbon model catalysts that are designed for systematic comparison of the porous structures. The difference in their catalytic activity is investigated in relation to the surface area and the electrochemical parameters. We found that macro- and mesoporous structures contribute to different stages of the reaction kinetics. The catalytic activity is further enhanced by loading the optimized amount of Fe to prepare Fe–N–C catalyst. In both N-doped carbon and Fe–N–C catalysts, the hierarchical porous structure improved electrocatalytic performance in acidic and alkaline media. The optimized catalyst exhibits one of the best ORR performance in alkaline medium with excellent long-term stabili...

Design Principle of Fe-N-C Electrocatalysts: How to Optimize Multimodal Porous Structures?

Potentiostatically deposited nanostructured α-Co(OH)2: A high performance electrode material for redox-capacitors

To understand the relationship between the specific energy and power of lithium (Li)-ion batteries, the dependence of the internal resistance of porous electrodes with high loading weight on thickness was systematically investigated. The ionic resistance in pores (Rion) and charge-transfer resistance for Li intercalation (Rct) normalized per unit electrode geometric area were assessed using a combination of electrochemical impedance spectroscopy with symmetric cells and the transmission line model for cylindrical pores. The changes of Rion and Rct and their magnitude show opposite trends with respect to electrode thickness. For thin electrodes, Rion is lower than Rct. The specific power decreases slightly as the electrodes become thicker because the total internal resistance is predominantly affected by the charge-transfer resistance, and there is no delay of the response in the depth direction. In contrast, for thick electrodes, Rion is higher than or approximately equal to Rct, so there is a delay of th...

Impedance Spectroscopy Characterization of Porous Electrodes under Different Electrode Thickness Using a Symmetric Cell for High-Performance Lithium-Ion Batteries

Hiroshi Nakazawa

Papers

Impedance analysis on electric double layer capacitor with transmission line model