  We present a modified Poisson-Boltzmann model that adds steric repulsion of
ions, providing an approximation to ion-ion correlations. Controlled by
specific ion sizes, this steric contribution provides a concentration cap.
Importantly, the steric contribution to the total free energy is comparable in
size to the electrostatic contribution and exceeds the classical energy
$1/2CV^2$. Capacitance varies non-monotonically with voltage, with a maximum
near 0.2-0.3V depending on the ion size. An analytic expression for the total
free energy is derived in terms of the size of the counterion, surface
potential, and charge density at each electrode.
