4. Electrolyte effect on the capacitive performance

#### 4.1. Solvent effect

Commercial EDLC devices mainly use the organic electrolyte in which a salt such as tetraethylammonium tetrafluoroborate is dissolved in an organic solvent such as acetonitrile (ACN) or propylene carbonate. It is very intriguing to unravel the role of the solvent during EDL charging inside small pores. By introducing a molecular dipole into our electrolyte, CDFT also allows us to examine the capacitance of an organic EDLC for different pore sizes and solvent polarity.

Our previous work illustrates the dependence of the capacitance on the pore size for the electrolyte/electrode models [45, 53]. For an ionic liquid EDLC, the capacitance oscillates with the pore size with a dampened magnitude around an average value of about 7.5 μF/cm2 . The maximum capacitance occurs when the pore size is about the same as the ion diameter, which coincides with the anomalous increase of capacitance observed by Largeot et al. [17] Whereas a similar peak appears for the organic electrolyte, there is no significant oscillation as the pore size increases, and the capacitance at the first peak is less dramatic in comparison with the asymptotic value. The theoretical results thus offer a reconciliatory picture of the capacitance dependence on the pore size for ionic liquid and organic electrolyte EDLCs. In the previous section, we discussed the capacitance dependence on pore size for an organic electrolyte with a moderate-polarity solvent (with a dipole moment of 3.4 Debye). But how would the solvent polarity affect the pore-size dependence of capacitance in a wide range of organic electrolyte EDLC?

Our CDFT calculations provide valuable insights into the effects of the dipole moment of the solvent in an organic electrolyte [43]. We found an optimal dipole moment that yields a maximum in the large-pore capacitance. These theoretical results further illustrate the rich behavior of the organic electrolytes inside porous electrodes. Moreover, it provides new considerations that can be taken into account when designing new experiments to select organic electrolytes for EDLCs.

## 4.2. Impurity or additive

ionopobilic pore), while a positive δE means an ionophobic pore. For simplicity, we assume that δE is independent of the ion valence, the pore size, and the surface electrical potential.

In an ionopobic pore with a large ion resolvation energy, both counterions and coions are nearly excluded from the nanopore at low surface electrical potential. In this case, counterions are inserted into the empty pore only when the electrical potential is sufficiently large to overcome the surface repulsion. The differential capacitance increases with the surface potential until it reaches a maximum. A further increase of the surface electrical potential leads to saturation of counter ions inside the pore and thus a decline of the capacitance. In both ionopobic cases shown in Figure 2(b), the capacitance versus potential curve has a two-hump camel shape, and the capacitance value at the minimum is close to zero, in stark contrast to the maximum for an ionophilic pore. Figure 2(b) indicates that the peak capacitance shifts to a higher potential as the ionophobicity increases. In other words, we may find a bell shape to the two-hump camel shape transition in the capacitance-electrical potential curves by changing the surface ionophobicity. Figure 2(d) shows that, at low electrical potential, the energy density

<sup>0</sup> CDð Þx xdx) for an ionophilic pore is higher than that of an ionophobic pore, while

the trend is opposite at high potentials. Because the peak of the camel shape differential capacitance shifts to higher potential, a more ionophobic pore offers higher storage energy. On the other hand, increasing ionophobicity prohibits counter ions from entering the pore, thus reduces the energy density at low potential. From the discussions above, we find that an ionophobic nanopore prevents counterion insertion and shifts the saturation point to a higher voltage. The energy stored in the EDLC can be promoted by the ionophobicity only when the

Commercial EDLC devices mainly use the organic electrolyte in which a salt such as tetraethylammonium tetrafluoroborate is dissolved in an organic solvent such as acetonitrile (ACN) or propylene carbonate. It is very intriguing to unravel the role of the solvent during EDL charging inside small pores. By introducing a molecular dipole into our electrolyte, CDFT also allows us to examine the capacitance of an organic EDLC for different pore sizes and solvent

Our previous work illustrates the dependence of the capacitance on the pore size for the electrolyte/electrode models [45, 53]. For an ionic liquid EDLC, the capacitance oscillates with the pore size with a dampened magnitude around an average value of about 7.5 μF/cm2

maximum capacitance occurs when the pore size is about the same as the ion diameter, which coincides with the anomalous increase of capacitance observed by Largeot et al. [17] Whereas a similar peak appears for the organic electrolyte, there is no significant oscillation as the pore size increases, and the capacitance at the first peak is less dramatic in comparison with the asymptotic value. The theoretical results thus offer a reconciliatory picture of the capacitance

. The

(Eð Þ¼ <sup>ψ</sup> <sup>Ð</sup> <sup>ψ</sup>

4.1. Solvent effect

polarity.

electrode voltage is larger than a critical value [54].

144 Supercapacitors - Theoretical and Practical Solutions

4. Electrolyte effect on the capacitive performance

RTIL has been used as electrolytes widely to increase the capacitive performance of electrochemical capacitors [82]. However, there are always some small amounts of impurity (e.g., water, alkali salts, and organic solvents) in RTIL, which may affect the electrochemical behavior of electrochemical devices. To understand the impurity effect, the RTIL with different impurities in the porous carbon electrodes is studied via CDFT. With a different type of binding energy with the surface or ionic species, the impurity shows a different influence on the EDL microstructures and contributes differently to the integral capacitance. It is noted that the impurity can be considered as either a contaminant or an additive to the ionic liquid, all depending on the interaction between the impurity and the electrode or ions [79, 80]. Meanwhile, the capacitance strongly oscillates with the variation of the pore size similar to that for the pure ionic liquid electrolyte. With strong binding of impurity to the ionic species, the RTIL/ impurity mixture may lead to an enhanced capacitance oscillation. In certain pores, a significant increase in the capacitance can be obtained. The theoretical results provide insights for further investigation of supercapacitors aiming at rational design of porous electrode materials and charge carriers.

We also demonstrate that, under conditions favoring impurity accumulation in the nanopores of the electrode, impurity can change the EDL charging mechanism even at low bulk densities, shown in Figure 3. As the adhesion energy of impurity molecules with the electrode surface increases, the capacitance-potential curves can change from the bell shape to the two-hump camel shape, with the peak shifting toward a higher charging potential. Qualitatively the impurity effect on the charging behavior is similar to the solvent effect as studied by Rochester and coworkers [81]. Whereas the amount of impurity and solvent in the bulk is considerably different, the concentration effect can be compensated by the change in the transfer energy to yield a same charging behavior. As an ionophobic pore could be beneficiary for improving charge storage and charging dynamics, introduction of impurity molecules inside the pore makes it essentially more ionophobic thus enhances the energy storage. Our theoretical results suggest that special attention should be given to the nature of impurity and operation voltages when the surface properties nanoporous electrodes are modified to enhance the performance of EDLCs. It is worth noting that association between ions and impurity molecules, which

might happen for impurity molecules with large polarity, may give rise to different pictures of the charging behavior. For impurity molecules without affinity to ionic species, their accumulation inside the pore will increase the charge storage and capacitance, regardless of the polarity. The effects of ion binding with impurity molecules on the charging mechanism and energy density will be investigated in the future work. From a practical prospective, the impurity can be considered as either a contaminant (undesirable) or an additive (desirable) to room-temperature ionic liquids. Based on this study and our previous work [80], we suggest new experimental strategies to introduce additives into ionic liquids with specific surface binding affinity to the porous electrodes (e.g., by surface modifications). While significant efforts have been devoted to formulation of ionic liquid mixtures and selection of solvents [47], much less is known on how supercapacitor performance may be influenced by potent

Formulating RTIL mixed electrolytes was recently proposed as an effective and convenient strategy to increase the capacitive performance of electrochemical capacitors [82]. However, little is known about how the properties of EDLCs containing RTIL mixtures would be affected by the electrolyte composition [83–86]. Here, we investigate the EDL structure and the capacitance of two RTILs, 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (EMI-TFSI and 1-ethyl-3-methylimidazolium tetrafluoroborate (EMI-BF4, and their mixtures with onion-like carbon electrodes using experiment and the CDFT. The principal difference between

EMI<sup>+</sup> cation in Figure 4. We find that the capacitance versus the composition of the RTIL mixture exhibits a volcano-shaped trend; in other words, there exists a composition of the ionic mixture that yields a maximal integral capacitance [47]. The mixture effect, which makes more counterions pack on and more co-ions leave from the electrode surface, leads to an

Figure 4. (a) Calculated integral capacitance for the positive, negative and total electrodes when the operating potential window (OPW) is fixed as 3.0 V. (b) Experimental results for a symmetric supercapacitor operating at 3.0 V. The electrode capacitance is shown as a function of the concentration of the RTIL mixture for different scan rates. Reproduced from

� anion relative to the TFSI� anion and the

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147

additives at a low concentration.

these ionic liquids is the smaller diameter of the BF4

Ref. [82] with permission. Copyright 2016 American Chemical Society.

4.3. Ionic liquid mixture

Figure 3. The number densities of ions and impurity molecules inside a nanopore of width H = 0.6 nm with different surface adhesion energies for the impurity molecules: (a) ω ¼ �10kBT; (b) ω ¼ �5kBT; (c) ω ¼ 0:0kBT.

might happen for impurity molecules with large polarity, may give rise to different pictures of the charging behavior. For impurity molecules without affinity to ionic species, their accumulation inside the pore will increase the charge storage and capacitance, regardless of the polarity. The effects of ion binding with impurity molecules on the charging mechanism and energy density will be investigated in the future work. From a practical prospective, the impurity can be considered as either a contaminant (undesirable) or an additive (desirable) to room-temperature ionic liquids. Based on this study and our previous work [80], we suggest new experimental strategies to introduce additives into ionic liquids with specific surface binding affinity to the porous electrodes (e.g., by surface modifications). While significant efforts have been devoted to formulation of ionic liquid mixtures and selection of solvents [47], much less is known on how supercapacitor performance may be influenced by potent additives at a low concentration.

#### 4.3. Ionic liquid mixture

Figure 3. The number densities of ions and impurity molecules inside a nanopore of width H = 0.6 nm with different

surface adhesion energies for the impurity molecules: (a) ω ¼ �10kBT; (b) ω ¼ �5kBT; (c) ω ¼ 0:0kBT.

146 Supercapacitors - Theoretical and Practical Solutions

Formulating RTIL mixed electrolytes was recently proposed as an effective and convenient strategy to increase the capacitive performance of electrochemical capacitors [82]. However, little is known about how the properties of EDLCs containing RTIL mixtures would be affected by the electrolyte composition [83–86]. Here, we investigate the EDL structure and the capacitance of two RTILs, 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (EMI-TFSI and 1-ethyl-3-methylimidazolium tetrafluoroborate (EMI-BF4, and their mixtures with onion-like carbon electrodes using experiment and the CDFT. The principal difference between these ionic liquids is the smaller diameter of the BF4 � anion relative to the TFSI� anion and the EMI<sup>+</sup> cation in Figure 4. We find that the capacitance versus the composition of the RTIL mixture exhibits a volcano-shaped trend; in other words, there exists a composition of the ionic mixture that yields a maximal integral capacitance [47]. The mixture effect, which makes more counterions pack on and more co-ions leave from the electrode surface, leads to an

Figure 4. (a) Calculated integral capacitance for the positive, negative and total electrodes when the operating potential window (OPW) is fixed as 3.0 V. (b) Experimental results for a symmetric supercapacitor operating at 3.0 V. The electrode capacitance is shown as a function of the concentration of the RTIL mixture for different scan rates. Reproduced from Ref. [82] with permission. Copyright 2016 American Chemical Society.

increase of the counterion density within the EDL and thus a larger capacitance. These theoretical predictions are in good agreement with our experimental observations and offer guidance for designing RTIL mixtures for EDL supercapacitors with optimal performance [47].

#### 4.4. Ion-ion interaction on the transport in nanopore

The charging kinetics of EDLs has a pivotal role in the performance of a wide variety of nanostructured devices. Despite the prevalent use of ionic liquids as the electrolyte, relatively little is known on the charging behavior from a microscopic perspective [33, 75, 77, 87–90]. Here, we study the charging kinetics of ionic liquid EDLs using the TDDFT that captures the molecular excluded volume effects and electrostatic correlations [39]. We found that the thermodynamic non-ideality plays a pivotal role in electrodiffusion and such effect cannot be captured by the lattice-gas model for the excluded volume effects. In particular, TDDFT predicts "wave-like" variation of the ionic density profiles that has not been identified in previous investigations [34]. This unusual charging behavior can be explained in terms of the oscillatory structure of ionic liquids near the electrodes. For ion transport in narrow pores with a high gating voltage, in Figure 5, the conductivity shows an oscillatory dependence on the pore size owing to the strong overlap of electric double layers [91].

Besides, our new TDDFT is able to account for the molecular excluded volume effects, electrostatic correlations, and the dispersion interactions. Our results show that the dispersion interaction between ions makes the surface charge be a non-monotonic function of time shown in Figure 6. However, the dispersion interaction between the electrode and ionic-liquid does not

change the monotonic evolution of surface charge density [92]. Both the ion-ion and the electrode-ion dispersion interactions increase the duration of the EDL charging process [92]. We also identified significant influence of the gating potential on the scaling behavior of the conductance with changes of pore size and the salt concentration. For ion transport in narrow pores with a high gating voltage, the conductivity shows an oscillatory dependence on the pore size owing to the strong overlap of electric double layers [91]. We hope these theoretical work enables a way to tune the charging behavior of electric double layer capacitors (EDLCs)

Figure 6. Evolution of surface charge density for different strengths of dispersion forces. (Inset) The time toward equilibrium as a function of the dispersion energy parameter ε. Reproduced from Ref. [92] with permission. Copyright

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In our recent works, the CDFT was developed and applied by us to study the electrode/ electrolyte interface behaviors, to understand capacitive energy storage. As a statistical mechanical tool and an alternative to molecular dynamics or Monte Carlo simulation methods, CDFT offers a powerful and efficient mathematical framework to describe the equilibrium and dynamic properties of many-body systems in terms of the one-body density profiles. It allows one to precisely tune the parameters such as ion diameter, solvent dipole, and pore size over a large range and to focus on the most important physical problems to be addressed, using a computationally efficient coarse-grained approach to model real fluids. Through CDFT, we have found novel behaviors of electrolytes inside nanopores, such as capacitance oscillation, optimal dipole moment, and wave-like charging. Further development of CDFT for complex pore structures and charging kinetics would allow us to directly predict power density and

by an appropriate choice of electrodes and ionic liquids.

5. Conclusion and perspective

2016 American Physical Society.

energy density for supercapacitors.

Figure 5. The conductivity shows an oscillatory dependence on the pore size [91]. Copyright 2017 Royal Society of Chemistry.

Figure 6. Evolution of surface charge density for different strengths of dispersion forces. (Inset) The time toward equilibrium as a function of the dispersion energy parameter ε. Reproduced from Ref. [92] with permission. Copyright 2016 American Physical Society.

change the monotonic evolution of surface charge density [92]. Both the ion-ion and the electrode-ion dispersion interactions increase the duration of the EDL charging process [92]. We also identified significant influence of the gating potential on the scaling behavior of the conductance with changes of pore size and the salt concentration. For ion transport in narrow pores with a high gating voltage, the conductivity shows an oscillatory dependence on the pore size owing to the strong overlap of electric double layers [91]. We hope these theoretical work enables a way to tune the charging behavior of electric double layer capacitors (EDLCs) by an appropriate choice of electrodes and ionic liquids.
