  Capacitive mixing (CAPMIX) and capacitive deionization (CDI) are promising
candidates for harvesting clean, renewable energy and for the energy efficient
production of potable water, respectively. Both CAPMIX and CDI involve
water-immersed porous carbon (supercapacitors) electrodes at voltages of the
order of hundreds of millivolts, such that counter-ionic packing is important
for the electric double layer (EDL) which forms near the surface of these
porous materials. Thus, we propose a density functional theory (DFT) to model
the EDL, where the White-Bear mark II fundamental measure theory functional is
combined with a mean-field Coulombic and a mean spherical approximation-type
correction to describe the interplay between dense packing and electrostatics,
in good agreement with molecular dynamics simulations. We discuss the
concentration-dependent potential rise due to changes in the chemical potential
in capacitors in the context of an over-ideal theoretical description and its
impact on energy harvesting and water desalination. Compared to less elaborate
mean-field models our DFT calculations reveal a higher work output for
blue-energy cycles and a higher energy demand for desalination cycles.
