Capacitive energy storage in single-file pores: Exactly-solvable models and simulations

TL;DR

This paper introduces an exactly-solvable one-dimensional off-lattice model for charge storage in single-file pores, providing insights into capacitance behaviors and matching three-dimensional simulations, advancing understanding of electrochemical energy storage.

Contribution

It develops a new off-lattice analytical model for charging single-file pores that accurately matches 3D simulations, revealing diverse capacitance shapes and voltage dependence.

Findings

Capacitance can be bell-shaped, camel-shaped, or have four peaks.

Transformations in capacitance shape are induced by pore ionophilicity, ion size asymmetry, or solvent addition.

Capacitance decays as the inverse square of voltage at high voltages.

Abstract

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.