  Investigating the correlations between dynamic and static storage properties
of nanoporous electrodes is beneficial for further progress of
supercapacitors-based technologies. While the dependence of the capacitance on
the pores' sizes is well described by classical Density Functional Theory
(c-DFT), the lack of dynamic c-DFT extension capable for correct estimation of
the charging time has been noted in the literature. Here, we develop a dynamic
model of the electrolyte inside nanopores based on c-DFT and realistically
describing both the time-dependent charging process and maximum static
capacitance. Our calculations show that the charging starts with a square-root
dependency of the total charge on time and then follows two subsequent
exponential trends with significantly different time scales that agree with
published simulations. We demonstrate that the full charging time corresponds
to the timescale of either the first or the second exponential trend depending
on the pores' size. Also, we find analytical expressions to fit the timescales
for a wide range of parameters. Derived correlations provide the relation of
charging time to pores' size, applied voltage, and final ions' densities inside
the pore, making these expressions useful to design supercapacitors with an
optimal combination of power and energy characteristics.

Statistical Mechanics;Mesoscale and Nanoscale Physics