Abstract
In the spirit of the theoretical evolution from the Helmholtz model to the Gouy–
Chapman–Stern model for electric double-layer capacitors, we explored the effect of a
diffuse layer on the capacitance of mesoporous carbon supercapacitors by solving the
Poisson–Boltzmann (PB) equation in mesopores of diameters from 2 to 20 nm. To
evaluate the effect of pore shape, both slit and cylindrical pores were considered.
We found that the diffuse layer does not affect the capacitance significantly. For slit pores,
the area-normalized capacitance is nearly independent of pore size, which is not
experimentally observed for template carbons. In comparison, for cylindrical pores,
PB simulations produce a trend of slightly increasing area-normalized capacitance with
pore size, similar to that depicted by the electric double-cylinder capacitor model
proposed earlier. These results indicate that it is appropriate to approximate the pore shape
of mesoporous carbons as being cylindrical and the electric double-cylinder capacitor
model should be used for mesoporous carbons as a replacement of the traditional
Helmholtz model.
