  Porous carbon is well known as a good candidate for the development of
electrochemical double-layer capacitors. Predominantly, many conventional
carbons are microporous and often well described by the assumption of slit pore
geometry. However, there is a class of carbons that is significantly different
from the others, namely templated mesoporous carbons. In this work, we study
electrosorption-induced deformation in CMK-3-like mesopores having nonconvex
geometry applying a mean-field approach. The model is based on the modified
Poisson-Boltzmann equation taking into account the excluded volume of the ions
within the hard-sphere model in the Percus-Yevick approximation. We assume that
the deformation is caused by two effects: ion osmotic pressure and
electrostatic interactions of the electric double layers on charged rods. The
latter were calculated via the Maxwell stress tensor agreeing with the modified
Poisson-Boltzmann equation. We estimated the pore-load modulus of the
CMK-3-like material and found an agreement with the previously obtained values
by small-angle neutron scattering (SANS). Additionally, we studied the
differential capacitance in the non-convex pore geometry and found that the
behavior of the differential capacitance profiles was similar to that of the
profiles obtained for flat electric double layers. Namely, we obtained the
crowding regime at rather high voltages and more pronounced profile asymmetry
with increasing differences in the ionic sizes.
