Relation between Charging Times and Storage Properties of Nanoporous Supercapacitors

Abstract

An optimal combination of power and energy characteristics is beneficial for the further progress of supercapacitors-based technologies. We develop a nanoscale dynamic electrolyte model, which describes both static capacitance and the time-dependent charging process, including the initial square-root dependency and two subsequent exponential trends. The observed charging time corresponds to one of the relaxation times of the exponential regimes and significantly depends on the pore size. Additionally, we find analytical expressions providing relations of the time scales to the electrode’s parameters, applied potential, and the final state of the confined electrolyte. Our numerical results for the charging regimes agree with published computer simulations, and estimations of the charging times coincide with the experimental values.

Understanding the Electric Double-Layer Structure, Capacitance, and Charging Dynamics

“…C. Contributions of cations and anions to the total charge pore charge. Reproduced from ref . CC BY: Creative Commons Attribution.…”

“…Because of the crowding effects, counterion adsorption and co-ion release are strongly correlated. , While such correlation plays an important role for EDL charging in concentrated electrolytes, it is relatively insignificant for dilute solutions as described by the TL model. Based on the numerical results from the TDDFT calculations over a broad range of conditions, Aslyamov et al found that the two relaxation time scales can be estimated from where d and L are the pore width and length, respectively, ρ s ∞ is the total ion density inside the pore at equilibrium, ρ s ∞ (σ/2) is the total contact density, and φ s is the reduced surface potential. For charging a large pore at low electrolyte concentration, τ 1 becomes identical to τ TL .…”

“…TDDFT was used, probably for the first time, by Aslyamov and co-workers to investigate the charging dynamics of porous electrodes in organic electrolyte solutions . As shown in Figure , the model system consists of a slit pore in contact with an electrolyte solution represented by the restricted primitive model (RPM).…”

“…TDDFT was used, probably for the first time, by Aslyamov and co-workers to investigate the charging dynamics of porous electrodes in organic electrolyte solutions. 289 As shown in Figure 21, the model system consists of a slit pore in contact with an electrolyte solution represented by the restricted primitive model (RPM). The parameters were selected to mimic those corresponding to a nanoporous electrode such as graphene or MXenes in an organic electrolyte, and the excess chemical potential was derived from one of the most accurate versions cDFT to describe excluded-volume effects and electrostatic correlations.…”

Direct numerical simulations of the modified Poisson-Nernst-Planck equations for the charging dynamics of cylindrical electrolyte-filled pores

“…Accordingly, Niya and Andrews studied the charging of porous conductive carbon materials [35] through the modified Poisson-Nernst-Planck (MPNP) equations [36]. Aslyamov, Sinkov, and Akhatov [37] used classical density functional theory to study slit pore charging. They unified all three known charging regimes: the pore's charge first increases as if it were semi-infinite (Q ∝ √ t), then slows down and approaches its equilibrium value exponentially with an RC time, and then slows down even further and equilibrates exponentially with the salt diffusion timescale [37].…”