Figure 7 . (a) Predicted
solvation diameter of BF4- varying
with the pore width of nanoslit. (b)
Capacitance
with and without ion desolvation effect varying with the pore size of
nanoslit. The blue dotted line is drawn to guide the eye.
Overall, the predicted capacitance in terms of pore width displays an
oscillating feature, and besides, the capacitances in both cases become
almost identical as the pore width exceeds 2.0 nm. This is because the
solvation diameter of BF4- gradually
recovers to its bulk value when increasing the pore width. Nevertheless,
two important different features can be found between the capacitances
considering ion-desolvation effect and that without ion-desolvation
effect. Firstly, owing to the pore size limit, the capacitance with
uniform ion size vanishes when the pore width is less than 0.73 nm;
while for the case considering ion-desolvation, as the ion size can
decrease down to 0.33 nm, the capacitance sharply increases when the
pore width decreases from 0.73 to 0.33 nm, generally according with the
experimental observation.12 Secondly, an
obvious deviation in the capacitance can be observed when the pore width
varies from 1.0 nm to 2.0 nm. This is likely due to the mismatch between
and resulting from the oscillation of solvation diameter in confined
MeCN.
The
overall capacitance, , is calculated with the help of eq.(10) and the
PSD extracted from the measurement
of
TiC-CDC microporous material.56Two
types of overall capacitances are calculated, i.e ., the ones with
and without ion desolvation. The calculated overall capacitances versus
the average pore size are plotted in Figure 8 in comparison
with the experimental measurement from Chmiola et
al.12The
predicted overall capacitance involving ion desolvation effect nicely
agrees well with the experimental observation in both the magnitude and
the variation trend along with the average pore size.
Particularly,
the sharp increase of capacitance is well captured as decreasing the
average pore size. However, the overall capacitances without ion
desolvation are overall much smaller than the experimental values, and
in addition, the sharp increase of
capacitance in nanopore is not captured. These differences highlight the
importance of ion-desolvation effect in determining the capacitance of
microporous electrode. Furthermore, the agreement between our
predictions and experimental measurements shows that the capacitances of
practical microporous electrodes involving liquid electrolytes can be
quantitatively predicted by the proposed multiscale molecular approach.