Electrochemical Behavior of Nanoporous Supercapacitors with

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Electrochemical Behavior of Nanoporous Supercapacitors with Oligomeric Ionic Liquids Cheng Lian, Haiping Su, Honglai Liu, and Jianzhong Wu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b04464 • Publication Date (Web): 30 May 2018 Downloaded from http://pubs.acs.org on May 30, 2018

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The Journal of Physical Chemistry

Electrochemical Behavior of Nanoporous Supercapacitors with Oligomeric Ionic Liquids Cheng Lian1, Haiping Su1, Honglai Liu1*, and Jianzhong Wu2* 1

State Key laboratory of Chemical Engineering, and School of Chemistry and Molecular

Engineering, East China University of Science and Technology, Shanghai, 200237, China 2

Department of Chemical and Environmental Engineering, University of California, Riverside,

CA 92521, USA

Abstract According to a recent study (J. Am. Chem. Soc. 2017, 139, 16072-16075), an oligomeric ionic liquid (OIL) may exhibit a wide electrochemical window and an exceptionally high capacitance in electric double layer (EDL) transistors. However, little is known on the applicability of OILs in EDL capacitors with porous electrodes. To understand the capacitive performance of OILs, here we investigate the charging behavior, EDL structure, and the capacitance for different types of OILs using the classical density functional theory (CDFT). In contrast to their application to field-effect transistors (FET), the capacitive performance of OILs in nanoporous electrodes is sensitive to the charging potential. Whereas adoption of oligomeric cations shows little advantage for the electrical charging of a positive electrode, they enhance the energy storage density for negative electrodes.

*

Email: [email protected] or [email protected]

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■ Introduction Electric double layer capacitors (EDLCs) are commonly used for energy storage utilizing their ultra-large capacitances per unit area1. In comparison to alternative electrochemical devices such as batteries or fuel cells, EDLCs have the advantages of greater power density and more sustainable life cycles. The EDLC performance is strongly correlated with the electrical adsorption of ionic species at the inner surfaces of typically microporous electrodes2. Whereas aqueous electrolytes are often used as the charge carrier in conventional EDLCs, roomtemperature ionic liquids (RTILs) and organic electrolytes have larger electrochemical windows and better thermal stability, making them attractive for application to the next generation of supercapacitors with higher energy and power densities2-5. Ion distribution in a supercapacitor is typically more complicated than that presented in a planar EDL because it involves porous electrodes with a broad range of morphologies and poresize distributions6-9. A wide variety of carbon-based materials with tunable pore size, morphology, architecture and functionality, have been proposed to improve the capacitive performance7, 10. The effects of the pore size on the EDL structure, capacitance, and ion transport have been studied in great details both experimentally and theoretically11-23. For example, the EDLC capacitance shows an anomalous increase as the pore size becomes comparable to the dimensionality of the ionic species, suggesting that electrodes with sub-nano pores are a better choice than those with larger pores24. However, the anomalous increase in pores below 1 nm was not observed in few other experiments25-26, and some theoretical work showed the anomalous increase may diminish if the electrode has a pore-width dependent permittivity27. The supercapacitor performance depends not only on the electrode materials but also on the types of electrolytes. A recent experimental study shows that oligomeric ionic liquids (OILs)

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provide a wide electrochemical window and exhibit an exceptionally high EDL capacitance in EDL-based field effect transistors (FET)28. Inspired by the experimental work on OILs and recent theoretical studies on the charging behavior of asymmetric electrolytes29-31, it appears promising to apply OILs to EDL capacitors with porous carbon electrodes. In this work, we explore the charging and capacitive behaviors of oligomeric RTILs with polycations in nanopores based on the classical density functional theory (CDFT). Within the framework of coarse-grained models, CDFT has been successfully used in studying the EDL structure and the capacitance of ionic liquids and organic electrolyte systems13,

32-37

. While it neglects atomic

details, the coarse-grained approach is able to capture essential features underlying EDL formation and give molecular insights on the electrochemical behavior of ionic fluids under confinement. Specifically, we are interested in the dependence of the capacitance and the mechanism of EDL charging on the valence and molecular size of oligomeric RTILs. This paper is structured as follows. First, we describe our coarse-grained model for oligomeric RTILs and porous electrodes and provide a brief introduction to the CDFT method used in this work. Next, we discuss the effects of polycation chain length on the EDL charging and the capacitive performance. Finally, we summarize the main results and implications for possible future studies.

■ Models and Methods Similar to our previous work36,

38

, we use a

tangentially-connected chain model to

represent room-temperature ionic liquids (RTILs). Whereas our model is not intended to capture the chemical details of any specific RTIL system, Figure 1 shows a schematic representation of the coarse-grained model along with the chemical structures of ionic species that were used in a previous experimental investigation28. In all cases, anions are represented by charged hard

4


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spheres that intend to reproduce the electrical charge and the excluded volume of bis(trifluoromethanesulfonyl) imide (TFSI-). Oligomeric cations are represented by tangentially connected charged hard sphere chains that mimic multiple units of imidazolium ion (1-ethyl-3methylimidazolium or EMI). As typically assumed in determining the pore size distribution, the nanoporous electrode is represented by the slit-pore model. It has been shown in previous work that the coarse-grained model is able to account for electrostatic correlations and ionic excluded volume effects important for understanding the EDLC performance36, 38. The pair potential between charged beads is the same as that in the primitive model for electrolyte solutions:

∞, r < (σ i + σ j ) / 2 uij (r) =  2  Zi Z j e 4πε r ε 0r , r ≥ (σ i + σ j ) / 2

(1)

where r is the center-to-center distance, e is the elementary charge, ε 0 is the permittivity of the free space, ε r represents the residual dielectric constant (i.e., screening of electrostatic interactions due to ion polarization effects), and σ i and Zi are the diameter and the valence of particle i, respectively. Throughout this work, all segments are assumed monovalent (-1 and +1). Although all components are explicitly considered in our model, we use a residual dielectric constant ( ε r = 2 ) to account for polarizability effects. Because the residual dielectric constant is not much different from that for a carbon electrode, we assume that the electrode polarizability and the image-charge effects are relatively unimportant for determining ionic distributions. In other words, image charges become insignificant when the fictitious dielectric constant ( ε r = 2 ) matches that of the porous electrode27.

5



Figure 1. Schematic representation of oligomeric RTILs considered in this work. Because oligomeric cations consist of repeating units of imidazolium ion, they are represented by tangentially connected chains of identical charged particles. Similar to our earlier work13, the model parameters are selected such that the monomer size and charge match approximately those corresponding to 1-ethyl-3-methylimidazolium bis(trifluoromethanesulfonyl) imide (EMI-TFSI), a RTIL commonly used in electrochemical devices. Specifically, the hard-sphere diameter of the imidazolium monomer is fixed at

σ + = 0.5 nm , and that for anions (TFSI-) is also fixed at 0.5 nm. Because the electrode is 6


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modeled as a slit pore with two symmetric hard walls, the non-electrostatic component of the external potential for each charged segment is represented by

 ∞, Vi ( z ) =  0,

z
H −

2 otherwise

σi 2

(2)

where H is the surface-to-surface separation (viz., the pore width), and z is the perpendicular distance from the surface. The details of CDFT calculations have been published before.32, 35, 39-40 Briefly, we obtained the surface charge densities at various electrical potentials. Given the number densities of ionic species in the bulk, the pore size, and the surface electrical potential, we solve for the onedimensional density profiles of cations and anions across the slit pore by minimizing the grand potential

βΩ  ρ M ( R ) , { ρa ( r )} = β F  ρ M ( R ) , {ρ a ( r )} +

∫  βΨ ( R ) − βµ M

M

 ρ M ( R ) dR + ∑ ∫  βΨ a ( r ) − βµa  ρa ( r ) dr

(3)

a

where β −1 = k BT , k B is the Boltzmann constant, T = 298 K is the absolute temperature,

R ≡ (r1, r2 ,Lrm ) represents the coordinates specifying the positions of m segments in each oligomeric cation, µα is the chemical potential of anions µ M is the chemical potential of the cations Ψ a ( r ) stands for the external potential for ions, Ψ M ( R ) is the summation of the m

external potential for the oligomeric cation, i.e. Ψ M ( R ) = ∑ ϕi ( ri ) , and F is the total intrinsic i =1

Helmholtz energy. The number densities of the positive and negative segments of the oligomeric cations are calculated from

ρ m ( r ) = ∫ d Rδ ( r − rm )ρ M ( R ) 7


(4)


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where δ (r ) is the Dirac delta function. The intrinsic Helmholtz energy F includes an ideal-gas contribution and an excess contribution due to intermolecular interactions F ex

β F = ∫  ln ρ M ( R ) − 1 ρ M ( R ) d R +β ∫ Vb ( R ) ρ M ( R ) d R + ∑ ∫  ln ρ a ( r ) − 1 ρ a ( r ) dr + β F ex

(5)

a

where Vb stands for the bonding potential of oligomeric cations. The detailed expression for each contribution and numerical details for implementation of CDFT can be retrieved from Ref.35, 41 In evaluation of the Coulomb energy, we calculate the mean electrostatic potential (MEP) from the ionic density distributions using the Poisson equation

∇ 2ψ ( r ) = −

4π e

ε 0ε r

∑ Z ρ (r) . i

i

(6)

i

From the ion distributions and the electrical potential profiles, we can readily calculate the surface charge density (Q), capacitance, and other EDL properties42-43.

■ Results and Discussions In the following we consider EDL charging and capacitances of various model oligomeric ionic liquids in the potential range from -1.5V to 1.5V as typically used for commercial room temperature ionic liquids (RTIL). Our theoretical study is focused on the size and charge effects of oligomeric cations on the EDL capacitor performance. For all ionic systems, the concentration of anions is fixed at 3.8 M, which corresponds to a molar volume of 259 cm3/mol for EMIM-TFSI at 298 K and 1 bar. While our model carries no chemical identity, we refer monomeric cations and anions as EMI and TFSI for convenience of discussion; the oligomeric cations consist of multiple units of the imidazolium ion and thus are referred to as EMI2TFSI and EMI3TFSI etc. The EDL capacitance shows an anomalous increase when the pore size becomes comparable to the dimensionality of the ionic species, suggesting that electrodes

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with sub-nano pores perform better than those with larger pores29-30, 44-45. As the pore size effect has been extensively studied before, here it is fixed at H=0.8 nm. All thermodynamic conditions are selected such that the bulk ionic liquids are located within the one-phase region of the phase diagram46.

0.2

Charge density (C/m2)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


EMI1TFSI EMI2TFSI EMI3TFSI EMI4TFSI

0.1

0.0

-0.1

-0.2 -2

-1

0

1

2

Potential (V) Figure 2. Theoretical predictions of the surface charge density versus the electrical potential of the porous electrode for several model oligomeric RTILs. Figure 2 shows the surface charge density versus the surface potential for four types of oligomeric cations. Different from the monomeric case (EMI1TFSI), the ionic liquids containing oligomeric cations exhibit asymmetric charging behavior due to the differences in size, shape and charge of cations and anions. Regardless of the sign of the charging potential and cation types, the surface charge density increases monotonically with the electrode potential. When the surface potential is positive, the surface charge density is slightly dependent on the cation type 9



because ion adsorption in the pore is dominated by anions. While at a negative electrode potential, the charging curves are more distinctive for different cations. The surface charge density falls as the chain length of oligomeric cations increases, suggesting oligomeric cations are more difficult to enter the pore than monomeric cations. CDFT predicts that the surface charge density convergences as the chain length reaches 3 or 4. In other words, the surface charge density cannot be raised significantly simply by polymerization of the cations. Based on the dependence of the surface charge density on the electrode potential, we can derived the potential of zero charge, which is defined as the electrode potential when the surface charge density vanishes (not shown). We may understand the charging curves by considering the average number density of cations and anions inside the nanopores. Figure 3a shows the particle densities versus the surface electrical potential for the case with symmetric cations and anions. As the surface potential increases (on both the negative and the positive side), the charging process is dominated by coion-counterion exchanges, with almost invariance of the overall local ion concentration. When the charging potential is larger than 1 V, virtually most cations have been depleted from the pore, and the charging process is mainly determined by anion insertion inside the pore. From Figure 3b, we see that the oligomeric cations have difficulties entering the pore when the surface potential is near zero or positive, and the positive charging process for EMI2TFSI is dominated by insertion of anions. There are few anions and oligomeric cations inside the pore when the surface potential is slightly negative. As the surface potential becomes more negative (by increasing the absolute value), the charging process is characterized by a combination of polycation insertion and anion adsorption, with the oligomeric cation insertion dominating this process. Like EMI2TFSI, EIM3TFSI and EMI4TFSI show the similar charging

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behavior (Figure 3c and 3d). At the same surface potential, large cations are more difficult to enter the pore than small cations. The average number density of oligomeric cations decreases as the chain length increases. Interestingly, the average number density of anions inside the pore also decreases when the surface potential is negative. The reduction in the average anion density reflects less oligomeric cations inside the nanopore.

Figure 3. The average number densities of different oligomeric cations and monomeric anions inside a nanopore of width H=0.8 nm. Three types of mechanisms have been identified from previous investigation of EDL charging for monomeric ionic liquids40,

47-50

: (i) coion-counterion exchange, (ii) counterion

insertion, and (iii) desorption of coions. In the presence of oligomeric cations, we may identify a distinctively different charging behavior (vi) a combination of the insertion of oligomeric cations along with anion adsorption as shown in Figure 3.

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The performance of the EDLCs could be measured in terms of differential capacitance Cd , defined as a derivative of the electrode surface charge density with respect to the electrode

surface potential:

Cd =

∂Q ∂ψ

(7)

Figure 4 shows the differential capacitance changes on the surface potential ( Cd − ψ 0 curves) for different oligomeric ionic liquids. As reported in our previous work2, 38, the Cd − ψ 0 relation exhibits a “bell shape” curve for the monomeric ionic liquid. At low electrode potential (here between -0.3 V and +0.3 V), near symmetric variations of cation and anion densities suggest that the dominant charging mechanism is the exchange of co-ions (cations) in the pore with the counterions (anions) from the bulk (Figure 3a). In this case, the differential capacitance decreases sharply because ion adsorption becomes saturated at small electrical potential. At high electrode potential (above 0.3 V or below -0.3 V), co-ions are depleted from the pore as indicated by its average number density shown in Figure 3a. In the latter case, the charging process is dominated by counterion insertion, which leads to a slower decline of the differential capacitance. Unlike monomeric ionic liquids, virtually no oligomeric cations and only few anions enter the nanopore at a low charging potential. When the absolute value of the surface potential increases (for either positively or negatively charged pores), the differential capacitance rises as more counterions are transferred into the pore from the bulk. A further increase of the electrode potential leads to saturation of counterions inside the nanopore as manifested in the decline of the differential capacitance. In this case, the differential capacitance – potential ( Cd −ψ ) curves exhibit a ‘Bactrian camel shape’, which is different from the ‘bell’ shape for monomeric ionic

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liquid (IL1TFSI). A bell shape to the two-hump camel shape transition in the Cd −ψ curves varies with different oligomeric cations, indicating that the chain length of cations may lead to different charging mechanisms.


0.14

Capacitance (F/m2)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.12 0.10 0.08 0.06 0.04 -2

-1

0

1

2

Potential (V) Figure 4. Differential capacitance as a function of the applied potential shows a transition from a Bactrian camel shape to bell shape as the chain length of oligomeric cations increases. From the differential capacitance shown in Figure 4, we observe that the EDL capacitances for ionic liquids with different oligomeric cations are almost the same at the high positive potential. The invariance of the EDL capacitance with the chain length is due to the fact that the charging process at this potential range is dominated by anion insertion. In other words, only anions are adsorbed in nanopores. As shown in Figure 3, the average number densities of anions for 4 types of ionic liquids are almost the same. When the surface potential increases from the negative side, the differential capacitance for EMI2TFSI reaches the maximum before those corresponding to EMI3TFSI and EMI4TFSI. The trend is due to smaller cations could enter the

13



empty pore more easily, and could make the nanopore full of cations at a lower surface potential. From the number densities of cations and anions shown in Figure 3, we see that, when the surface potential is negative, less anions (co-ions) enter the pore as the chain length of oligomeric cations increases. The reduction in coion adsorption explains a higher capacitance for larger oligomeric cations. 1.2 1.0 0.8

Ex/E1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.6 0.4 0.2 0.0 -2

-1

0

1

2

Potential (V) Figure 5. The relative energy density as a function of the applied surface potential for ionic liquids with different oligomeric cations. The energy density in a nanopore could be obtained from ψ0

E (ψ 0 ) = ∫ CdV dV 0

(8)

where Cd is the differential capacitance as discussed above, and ψ 0 corresponds to the electrode surface potential. Figure 5 shows the relative energy densities for different types of oligomeric cations. When the charging potential is highly positive, oligomeric cations hardly enter the

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nanopore thus have negligible effects on the energy density. At low charging potentials (between -0.5 V and 0.75 V), the oligomeric cations (chain length m=2,3, and 4) reduce the energy density in comparison to that corresponding to a monomeric ionic liquid. As expected, the energy density falls as the chain length of oligomeric cations increases. However, the trend is reversed when the charging potential is highly negative. Figure 4 indicates that the peak position of the differential capacitance shifts to a higher charging potential, suggesting that we can obtain a higher differential capacitance at larger charging potentials. According to Eq. (8), charging at large capacitance and potential yield a higher energy density.

■ Conclusions In this work, we have investigated the influence of cation association (viz., oligomeric cations) on the charging mechanism and the energy density of electrical double layer capacitors (EDLCs). Using a coarse-grained model for ionic liquids and porous carbon electrodes represented by a slit pore, we demonstrate that, the cation chain length may have a significant effect on the EDL charging mechanism. As the number of monomeric charges in each cation increases, the differential capacitance-potential curve can change from the bell shape to the twohump camel shape, with the peak shifting toward a more negative potential. Whereas adoption of oligomeric cations appears insignificant for electrical charging of a positive electrode, they enhance the energy storage density for electrodes with a negative potential. When the absolute value of the surface potential is small, however, oligomeric ionic liquids can significantly reduce the energy density. From a practical prospective, the EDLC performance depends on the operation conditions. Our theoretical results indicate that in selection of ionic liquids for supercapacitor applications, special attention must be given to the nature of oligomeric cations and the applied surface

15



potential. In this work, we treat oligomeric cations as homogeneous chains of charged particles without an explicit consideration of the uncharged linkers in oligomeric EMI chains. Incorporation of neutral segments into the coarse-grained model for oligomeric cations may have significant effects on the charging behavior. Investigation of such effects is worth considering for the future work.

AUTHOR INFORMATION Corresponding Author Jianzhong Wu, Email: [email protected] Honglai Liu, Email: [email protected] ORCID Cheng Lian: orcid.org/0000-0002-9016-832X Honglai Liu: orcid.org/0000-0002-5682-2295 Jianzhong Wu: orcid.org/0000-0002-4582-5941

Acknowledgements This research was sponsored by the Fluid Interface Reactions, Structures and Transport (FIRST) Center, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences. This research was also sponsored by the financial support by the National Natural Science Foundation of China for Innovative Research Groups (No. 51621002), 111 Project of China (No. B08021), Shanghai Sailing Program (18YF1405400), Fundamental Research Funds for the Central Universities (WJ1814016), China Postdoctoral Science Foundation (2017M620137), and the National Postdoctoral Program for Innovative Talents (BX201700076).

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