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.