  A major challenge in the molecular simulation of electric double layer
capacitors (EDLCs) is the choice of an appropriate model for the electrode.
Typically, in such simulations the electrode surface is modeled using a uniform
fixed charge on each of the electrode atoms, which ignores the electrode
response to local charge fluctuations induced by charge fluctuations in the
electrolyte. In this work, we evaluate and compare this Fixed Charge Method
(FCM) with the more realistic Constant Potential Method (CPM), [Reed, et al.,
J. Chem. Phys., 126, 084704 (2007)], in which the electrode charges fluctuate
in order to maintain constant electric potential in each electrode. For this
comparison, we utilize a simplified LiClO$_4$-acetonitrile/graphite EDLC. At
low potential difference ($\Delta\Psi\le 2V$), the two methods yield
essentially identical results for ion and solvent density profiles; however,
significant differences appear at higher $\Delta\Psi$. At $\Delta\Psi\ge 4V$,
the CPM ion density profiles show significant enhancement (over FCM) of
"partially electrode solvated" Li$^+$ ions very close to the electrode surface.
The ability of the CPM electrode to respond to local charge fluctuations in the
electrolyte is seen to significantly lower the energy (and barrier) for the
approach of Li$^+$ ions to the electrode surface.
