Effect of Ion Binding on the Structure and Capacitance of EDLs

For different types of impurity molecules, the impurity can attach not only to the surface

but also to the cations or anions in the ionic liquid. As an illustrative example, here we consider

an ionic liquid containing impurity that strongly binds with the ionic species. The computational

procedure is the same as before. For simplicity, we fixed the intermolecular attraction between

the impurity and cations or anion as _{0, / } = 40 k T_B while the surface energy acting on the impurity is



_w =0. The reduced bulk density of the impurity is  _{0 0}3 = 2.9 × 10−5. We investigate the dependence of capacitance on the pore size and the structure of EDLs in RTIL on a single

cathode where the surface voltage is fixed at



_s = 1.5V.

Figure 4.7 The integral capacitance versus the pore size in the presence of an impurity. Here, the voltage is

fixed at _s= 1.5 V. The impurity binds strongly with the cation (dashed line) or anions (dash-dotted line). The different lines represent the pure RTIL and mixture, respectively.

Figure 4.7 shows how the capacitance changes with the pore size. The dependence of the

capacitance on the pore size of a pure ionic liquid is also shown in this figure as a reference. We

find that the magnitude of the capacitance oscillation is enhanced for the two hybrid RTILs and

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RTIL, the integral capacitance does not simply increase or decrease when the impurity molecules

strongly bind to the ions. The integral capacitance shows a complex pattern in the pore size range

of 1–5 times the ion diameter. In a 0.55 nm pore, the pore size is close to the ion diameter, the

capacitance increases only when the impurities are strongly affixed to the counterions. For a pore

narrower than 1.4 nm, the integral capacitance of the RTIL with counterion bound impurity

shows an increase while that of the RTIL with co-ion bound impurity is reduced. Further

increasing the pore size to 1.8 nm, both hybrid RTILs show an increase in the capacitance. When

the pore width is larger than 1.8 nm, the size dependence becomes even more complicated.

To understand the change in the C_I H curve, we present in Figure 4.8 the ionic distributions inside different nanopores. As we discussed before, the constructive or destructive

interference between the EDLs stemming from the changes in the layering structure of the ionic

liquid, leading to a peak or trough in the capacitance. [47] Both confinement and impurity

contribute to the EDL interference. To better illustrate this enhanced oscillation, we have

analyzed the EDL structure in the slit pore with various widths. Figure 4.8(a) shows the reduced

density profiles of a pure ionic liquid across a 2.5 nm slit pore. We can see the ions form

alternating layers inside the pore. The EDL at the interfacial is dominated by counterions. For the

RTIL containing counterion-bounded impurity (Figure 4.8(b)), the impurity molecules and the

ionic species form more ordered alternating layers compared to that for the pure ionic liquid. In

this case, the layering structures become more distinctive. The intensity of the first layer is higher

than that of the pure ionic liquid. The strong electrostatic coupling between counter- and co-ions

is destroyed by the impurity molecules that distribute around the counterions. For the RTIL

containing coion-bounded impurity (Figure 4.8(c)), the impurity has little impact on the EDL

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sizes of slit pores, the strongly coupled impurity also shows a significant impact on the ionic

distributions (Figure 4.9).

Figure 4.8The reduced density profiles of the impurity and ions across a 2.5 nm slit pores at _s= 1.5 V (a)

a pure RTIL, (b) the RTIL containing an counterion bounded impurity and (c) the ionic liquid containing an co-ion bounded impurity, respectively.

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Figure 4.9 The reduced density profiles of the impurity and ions across slit pores with various widths at the

positive electrode: (a) a pure RTIL, (b) the RTIL containing counterion bounded impurity and (c) the RTIL containing a co-ion bounded impurity, respectively. The surface electrical potential is fixed at 1.5 V.

It should be noted that strong coupling of the impurity and ionic species results in the

formation of clusters rather than dimers. To see the difference between an ionic liquid with strong

affinity to impurities and that of an ionic liquid with a neutral segment tethered to ionic species,

we investigate a binary ionic liquid in which the coion is the same as that in the above example

while each counterion is composed of a monovalent spherical particle. The dumbbell-shaped

dimer consists of two tangential tethered hard spheres, one is negative charged and the other is

neutral. From the density profiles (Figure 4.10), we found that the ionic distributions for this

binary ionic liquid is almost the same as those corresponding to a monomeric ionic liquid with the

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difference in the ionic density profiles suggests that the cooperative coupling is responsible for

changing the ionic distributions even at a very low bulk concentration. Such cooperative binding

impacts ion packing in the slit pore.

Figure 4.10 The reduced density profiles for a binary mixture of ionic liquids across slit pores with various

widths. From the top to bottom, the pore size is 0.55, 1.6 and 2.5 nm respectively. The ratio of the dimer to the monomer co-ion in the ionic mixture is 10-4_{. The surface voltage is fixed at 1.5 V.}

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In Figure 4.11, we compare the average ionic density inside the pore for the pure RTIL

and for those containing impurities that bind with one of the ionic species. In all cases, the overall

number density of the ions in the bulk is 2.32 nm−3. The average number density _iave inside the pore is defined as 0 1 ( ) . H ave i i z dz H  



 (4.7)

We see that the average number density of ions in the hybrid RTIL is higher than that in

the pure RTIL. In other words, the impurity would enable a denser packing ionic species in slit

pores.

Figure 4.11 The average number density of the impurity and ions inside a 2.5 nm slit pore at _s= 1.5 V.

In document Density Functional Theory for Confined Electrolytes: Phase Behavior, Interfacial Phenomena and Application to Capacitive Energy Storage (Page 112-117)