Insights into the influence of the pore size and surface area of activated carbons on the energy storage of electric double layer capacitors with a new potentially universally applicable capacitor model

The electric double layer formation of supercapacitors is governed by ion electrosorption at the electrode surface. Large surface areas are beneficial for the energy storage process, typically achieved by carbon electrode materials. It is a matter of debate whether pores provide the same contribution to the capacitance regardless of the size, or if subnanometer pores lead to an anomalous increase of capacitance. In our work, we developed a new model for normalized capacitance depending on pore sizes, using a combination of a sandwich type capacitor for micropores and double-cylinder capacitor model for larger pores. Modification factors for each capacitance value were calculated using the nonlinear generalized reduced gradient method to obtain a modified electric sandwich double-cylinder capacitor (ESDCC) model. The model was validated by comparing the measured capacitance values of a set of prepared activated carbons in organic electrolytes with simulated values according to the modified ESDCC model, using combined physisorption data of carbon dioxide and nitrogen. We concluded a non-constant capacitive contribution, with pores having the size of bare cations contributing to the capacitance to a larger extent and mesopores with the size of three solvated ions providing an unusual low contribution to the overall capacitance.