1. Introduction
Growing energy demand and environmental protection inspire the exploit of renewable energy such as solar energy, wind energy and ocean energy. Its intermittence necessitates the development of high-performance storage devices to achieve excellent energy storage and thus stabilize the large-scale practical supplies in the form of electrochemical energy.1Supercapacitors (also called ultracapacitors) and batteries are important candidates for electrochemical energy storages,2 and have been extensively studied by experiments and theoretical methods.3-5The physical adsorption and diffusion of electrolytes in supercapacitor ensure its high power density6-7 and outstanding cycling performance.8 However, the energy storage density is much lower compared to the chemical storage batteries.9
In recent years, the microporous materials involving liquid electrolytes have exhibited tremendous potential for promoting the energy density of supercapacitor. Gogotsi and his co-workers et al.10-11manufactured a microporous TiC carbide-derived carbon (TiC-CDC) electrode, and this electrode displays outstanding performance in energy storage capacity. For example, by tuning the average pore size of the microporous electrode to 1.0 nm, Chmiola et al.12 found that the capacitance anomalously increases for the supercapacitor involving acetonitrile-based liquid electrolyte. Further decreasing the pore size down to about one ion size, the anomalously promoted capacitance is observed.13These results are soon confirmed by different theoretical studies such as Monte Carlo simulations,14 molecular dynamics (MD) simulations,15-16 atomistic MD simulations,17-18and theoretical methods.19-20
The mechanism for the abnormally increased capacitance can be generally attributed to two aspects: the confinement effect (i.e., the steric effect of ions and the overlapping effect of electrostatic potentials) and the ion desolvation.21-22Specifically, for the confinement effect in nanoscale pores, both the overlapped electrostatic potential23 and the convex inner surfaces of electrodes24-25 contribute to the high-performance of supercapacitors. The ion desolvation is closely associated with the ion adsorption amount.26-27By integrating the ion desolvation with hierarchical nanopores, the microporous electrodes have attracted considerable interests to achieve excellent charge storage efficiency in recent years.28-29However, because the ion desolvation, usually occurred in confined space, causes the rearrangement of microscopic solvent structure surrounding the ion, leading to the variations of solvent local density and ion solvation diameter,30-31 the relation between the solvation diameter of ion in nanopore with the pore size is highly desirable yet lacking, and this causes a significant bottleneck for properly understanding the contribution of ion desolvation to the capacitance of microporous electrodes. Compromisingly, unified ion size is employed in most coarse-grained studies on electrochemical properties of confined electrolytes disregarding the variation of pore size.20, 32
Theoretical methods and computer simulations are employed to investigate the ion solvation in bulk solutions and interfacial systems on molecular level.33-35Recently we proposed a model to examine the ion desolvation in confined water by incorporating the molecular density functional theory (MDFT) with an proposed desolvation model,36 and successfully demonstrated the disturbed hydration shell and the decreased hydration numbers of ions in nanoslits. MDFT is a molecular version of the classical density functional theory (CDFT), which additionally involves the molecular orientation as variables in local density distribution.37Herein, we integrate a similar desolvation model with coarse-grained description of solvated ions in nanopores to investigate the ion desolvation effect on capacitance. Particularly, we evaluate the capacitance by adopting the simple version of CDFT, in which the ionic components are described with coarse-grained spherical particles. Historically this version is simply called as CDFT. CDFT has been applied to predict the capacitances by accurately accounting for the excluded volume effect and electrostatic correlation in confined simple electrolytes.38-40
By combining the MDFT and CDFT, the ion desolvation and its contribution to the capacitance of the microporous electrodes are investigated. We show that this combination can unravel the ion desolvation effect to electrochemical properties, and give satisfactory predictions on the capacitances of practical microporous electrodes with liquid electrolytes as long as the pore size distribution (PSD) is provided.
The remainder of this work is organized as follows. In Section 2, the ion desolvation in the microporous electrode is introduced and the essential equations of MDFT and CDFT are provided. In Section 3, the solvation diameters of ions in different nanoslits under ambient condition are evaluated by using the MDFT, and thereafter the capacitances of the nanoslits with different pore sizes are predicted by using CDFT. Next, integrating the pore-size dependent capacitances with the PSD, we study the ion desolvation contribution to the overall capacitance of the microporous electrodes in comparison with experimental measurements. Finally, a brief summary is given in Section 4.