  Understanding charge storage in low-dimensional electrodes is crucial for
developing novel ecologically friendly devices for capacitive energy storage
and conversion, water desalination, etc. Exactly-solvable models allow in-depth
analyses and essential physical insights into the charging mechanisms. So far,
however, such analytical approaches have been mainly limited to lattice models.
Herein, we develop a versatile, exactly-solvable, one-dimensional off-lattice
model for charging single-file pores. Unlike the lattice model, this model
shows an excellent quantitative agreement with three-dimensional Monte Carlo
simulations. With analytical calculations and simulations, we show that the
differential capacitance can be bell-shaped (one peak), camel-shaped (two
peaks), or have four peaks. Transformations between these capacitance shapes
can be induced by changing pore ionophilicity, cation-anion size asymmetry, or
by adding solvent. We find that the camel-shaped capacitance, characteristic of
dilute electrolytes, appears for strongly ionophilic pores with high ion
densities, which we relate to charging mechanisms specific to narrow pores. We
also derive a large-voltage asymptotic expression for the capacitance, showing
that the capacitance decays to zero as the inverse square of the voltage, $C
\sim u^{-2}$. This dependence follows from hard-core interactions and is not
captured by the lattice model.
