  We study the dynamics of ionic liquids in a thin slit pore geometry.
Beginning with the classical and dynamic density functional theories for
systems of charged hard spheres, an asymptotic procedure leads to a simplified
model which incorporates both the accurate resolution of the ion layering
(perpendicular to the slit pore wall) and the ion transport in the pore length.
This reduced-order model enables qualitative comparisons between different
ionic liquids and electrode pore sizes at low numerical expense. We derive
semi-analytical expressions for the impedance response of the reduced-order
model involving numerically computable sensitivities, and obtain effective
finite-space Warburg elements valid in the high and low frequency limits.
Additionally, we perform time-dependent numerical simulations to recover the
impedance response as a cross-validation step. We investigate the dependence of
the impedance response on system parameters and the choice of density
functional theory used. The inclusion of electrostatic effects beyond
mean-field qualitatively changes the dependence of the characteristic response
time on the pore width. We observe peaks in the response time as a function of
pore width, with height and location depending on the potential difference
imposed. We discuss how the calculated dynamic properties can be used together
with equilibrium results to optimise ionic liquid supercapacitors for a given
application.
