Strategies for fast ion transport in electrochemical capacitor electrolytes from diffusion coefficients, ionic conductivity, viscosity, density and interaction energies based on HSAB theory

Abstract

To elucidate factors affecting ion transport in capacitor electrolytes, five propylene carbonate (PC) electrolytes were prepared, each of which includes a salt ((C₂H₅)₄NBF₄, (C₂H₅)₄NPF₆, (C₂H₅)₄NSO₃CF₃, (C₂H₅)₃CH₃NBF₄ and LiBF₄). In addition to conventional bulk parameters such as ionic conductivity (σ), viscosity (η) and density (ρ), self-diffusion coefficients (D) of the cation, anion and PC were measured by pulsed-gradient spin-echo (PGSE) NMR. Interaction energies (ΔE) were calculated by density function theory calculations based on Hard and Soft Acids and Bases (HSAB) theory for cation–anion (salt dissociation) and solvent–cation/anion (solvation). ΔE values are related to the salt dissociation and solvation, which affect ion diffusion radii formed by solvation and/or ion pairs. The calculated solvation ΔE values were small (around 0.30 eV) and salt dissociation energies were also small. For comparison, the ΔE value for PC–Li⁺ interaction was larger than that for ammonium cations, because of strong Li⁺ Lewis acidity. Ammonium salts are highly dissociated and each ion forms a weakly solvated structure, which is quite different from Li⁺ electrolytes. Weak solvation for the cation and anion in the ammonium salts are important in enhancing fast ion transfer and electrode reactions in capacitor devices.

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Introduction

Electric double-layer capacitors (EDLCs) have received increasing attention for power supply systems, not only for small electric devices, such as smart phones and tablet computers, but also in electric vehicles. The advantages of EDLCs include their high-rate capability and semi-permanent long cycle life, which are derived from their fast charge/discharge mechanism owing to the electric double layer of activated carbon (AC) electrodes that do not undergo faradaic reactions (electrochemical redox reactions).^1–6 The cell performance of EDLCs therefore depends significantly on the electrolyte properties, i.e., the ion transport rate and electrochemical stability of the electrolytes. However, EDLC systems provide relatively small electrical capacitance because only the surfaces of the AC positive (PE) and negative (NE) electrodes are used. In recent years, due to the requirements for increased energy density of EDLCs, lithium ion capacitors (LICs), including faradaic-reaction NEs using graphite or hard carbon, have been intensively developed to overcome the low energy density limitation of EDLCs.^6–11 Many researchers have evaluated the viscosity η, ionic conductivity σ and density ρ of electrolyte solutions, together with their electrochemical stability (potential window).^12–15 Dielectric constants of solvents and degree of dissociation α of salts were also investigated to evaluate the solubility and dissociation of salts in these electrolytes.^15,16 These physical parameters are important and useful for the design of suitable electrolytes for EDLCs and LICs. Physical parameters provide understanding of the macroscopic behaviours of electrolytes; however, to design new electrolyte systems for next-generation capacitors, more direct microscopic information is necessary, such as individual transport rates of ions and solvent, and their relationships with interaction energies between the components of the capacitor electrolytes.

This study targeted four electrolytes used in EDLCs and one electrolyte comprising a lithium salt used for LICs. Fig. 1 shows the chemical structures of cations and anions in the salts used in this study. We measured individual self-diffusion coefficients D of the ions and solvent in these capacitor electrolytes by pulsed gradient spin-echo nuclear magnetic resonance (PGSE-NMR), together with conventional physical properties, i.e., ionic conductivity σ, viscosity η and density d, of the electrolytes, and discuss these with respect to ion transport behaviour. The relationships between the D values and the other conventional properties are analysed and discussed from the viewpoint of mobility and number of carrier ions in the electrolytes. To elucidate the relationship between the interactions between the chemical species and ion transport behaviour in the electrolytes, we also estimated the interaction energies between the cation–anion, propylene carbonate (PC)–cation and PC–anion by density function theory (DFT) calculation based on the Hard and Soft Acids and Bases (HSAB) theory^17–19 for each electrolyte.

Fig. 1 Chemical structures of the cations and anions used in this study, as optimized by DFT calculation using a basis set of B3LYP/6-311+G**//HF/3-21G. (a) (C₂H₅)₄N (TEA⁺), (b) (C₂H₅)₃CH₃N (TEMA⁺), (c) Li⁺, (d) BF₄⁻, (e) PF₆⁻ and (f) CF₃SO₃ (OTf⁻).

Experimental

We used five different 1.0 M (mol L⁻¹) electrolyte solutions of ammonium salts, i.e., (C₂H₅)₄NBF₄ (TEABF₄, Kishida Chemical Co., Ltd.), (C₂H₅)₄NPF₆ (TEAPF₆, Aldrich), (C₂H₅)₄NSO₃CF₃ (TEAOTf, Wako Pure Chemicals), (C₂H₅)₃CH₃NBF₄ (TEMABF₄, Tokyo Chemical Industry Co., Ltd.) and LiBF₄ (Kishida Chemical Co., Ltd.) in propylene carbonate (PC, battery grade, Wako Pure Chemicals). Prepared samples were stored in an Ar-filled dry box (VAC, NEXUS II).

Ionic conductivity σ of the electrolytes was measured in hermetically sealed cells [stainless steel (SUS)/electrolyte/SUS] and determined by complex impedance using an AC impedance analyser (Bio-Logic VSP, 200 kHz to 50 mHz; applied voltage: 10 mV) in the temperature range of 283 to 353 K. The electrolytes were thermally equilibrated at each temperature for at least 90 min prior to the measurement.

The self-diffusion coefficients of the cation (¹H or ⁷Li), anion (¹⁹F) and solvent PC (¹H) in the electrolytes were measured by PGSE-NMR using a JEOL tunable pulsed-field gradient (PFG) probe and an amplifier with a 6.4 T wide-bore superconducting magnet (¹H resonance: 270 MHz) between 353 and 253 K.^20–23 Each sample was prepared in an NMR microtube (BMS-005J, Shigemi, Tokyo) to a height less than 5 mm to prevent convection effects. The calibration of the PFG was made by H₂O (¹H resonance) and D₂O (²H resonance). Measurements were made by setting the PFG strength to 0.84 to 1.3 T m⁻¹ for ¹H and ¹⁹F and 2.5 T m⁻¹ for ⁷Li for varying duration times. The PFG interval (Δ) was set between 20 and 50 ms, depending on temperature. The confirmation of the accuracy of the diffusion constant was carried out by obtaining the same value with different Δ's.

Measurements of viscosity η and density ρ were carried out using a Stabinger-type viscometer (SVM3000G2, Anton Paar). The temperature was controlled in the range of 283 to 353 K at 10 K intervals while heating the samples.

The more quantitative cation–anion and PC–cation interactions were investigated by ab initio Hartree–Fock (HF) self-consistent field molecular orbital calculation and DFT calculation performed by Gaussian 09 software.²⁴ The geometries of the cations, anions and PC were optimized by DFT using the B3LYP form for the exchange–correlation function and the 6-311+G** basis set after HF optimization with the 3-21G basis set. From results of the total electron energy of the ions and solvent, the cation–anion, PC–cation and PC–anion interaction energies were estimated by equations based on HSAB theory.^17–19

Results

Fig. 2 shows the temperature dependences of σ for the 1.0 M PC-based electrolytes with (a) a common cation (TEA⁺) and different anions (BF₄⁻, PF₆⁻ and OTf⁻) and (b) a common anion (BF₄⁻) and different cations (TEA⁺, TEMA⁺ and Li⁺). All plots veered slightly towards higher values, but approximately followed an Arrhenius-type plot. For the common cation, the ionic conductivity decreased in order of TEABF₄ > TEAPF₆ > TEAOTf across the entire temperature range from 283 to 353 K. In contrast, for the common anion (BF₄⁻), the ionic conductivity changed in the order TEMABF₄ ≈ TEABF₄ ≫ LiBF₄. The trend in ionic conductivity for the ammonium salt-based electrolytes was in good agreement with those reported by Ue et al., for a salt concentration of 0.65 M at 298 K.¹ The LiBF₄-based electrolyte exhibited one order of magnitude lower σ than the ammonium salt-based electrolytes. This difference will be described later.

Fig. 2 Comparison of temperature dependences of ionic conductivity σ for 1.0 M PC-based electrolytes with (a) a common cation (TEA⁺) and different anions (BF₄⁻, PF₆⁻ and OTf⁻) and (b) a common anion (BF₄⁻) and different cations (TEA⁺, TEMA⁺, and Li⁺). The values for TEABF₄ and TEMABF₄ almost overlap.

The ionic conductivity of electrolytes was defined by eqn (1):

where q, μ and n are the charge, mobility and number of carrier ions per specific volume, respectively; the suffix j corresponds to the ammonium cations and anions. Ionic conductivity of electrolytes depends on (i) mobility and (ii) number of carrier ions per specific volume. Here, to consider the mobility μ of each carrier ion, we separately measured the D values of the cation, anion and PC solvent by PGSE-NMR. Typical Arrhenius-type plots for 1.0 M PC-based electrolytes containing TEABF₄ and TEAPF₆ are shown in Fig. 3. Except at high temperature, the diffusion constants of TEABF₄ are larger than those of TEAPF₆; within the same electrolyte, D_PC > D_anion > D_TEA. Summaries of the data for the other electrolytes are shown in Tables 1 (D) and 2 (η) in ESI.† For a single electrolyte, the order of the D values was PC > anion (BF₄⁻, PF₆⁻, TfO⁻) > cation (TEMA⁺, TEA⁺, Li⁺) across the entire temperature range evaluated. The temperature dependences essentially followed Arrhenius-type plots, indicating that the ions are transported by flow of the PC solvents and that the anions move more easily than the cations in these electrolytes. This trend was similar to those reported for electrolyte solutions for lithium ion batteries (LIB).²⁰ The order of magnitude of D for the four ammonium electrolytes and the lowest D for a 1.0 M LiBF₄/PC are in good agreement with the trend for σ. This indicates that σ is significantly influenced by mobility μ of the carrier ions.

Fig. 3 Typical temperature dependences of self-diffusion coefficients D for 1.0 M PC-based electrolytes containing TEABF₄ and TEAPF₆.

From the temperature dependences, the activation energies of D, i.e., E_a, were estimated from the slopes of plots for the electrolyte systems, as shown in Table 1. For all electrolytes, including LiBF₄/PC, the E_a values were around 0.20 eV. The E_a values in these capacitor electrolytes were of the same scale as those of LIB electrolytes. This means that all chemical species are transported in a similar way in these electrolytes.

Table 1 Activation energies E_a from Arrhenius-type plots of D for ions and PC solvents and transference numbers of cations t_cation at 303 K for 1.0 M PC-based electrolytes

Electrolyte solution	DPC	Dcation	Danion	tcation
	Ea/eV	Ea/eV	Ea/eV
1.0 M TEABF4/PC	0.18	0.20	0.18	0.42
1.0 M TEAPF6/PC	0.20	0.23	0.21	0.45
1.0 M TEAOTf/PC	0.21	0.22	0.21	0.45
1.0 M TEMABF4/PC	0.23	0.22	0.24	0.43
1.0 M LiBF4/PC	0.22	0.23	0.25	0.42

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From the D values of the cations and anions, the apparent transference numbers of the cations were calculated by eqn (2), as follows:

t_cation = D_cation/(D_cation + D_anion) (2)

The results at 303 K are shown in Table 1 (values for each t_cation by temperature are summarized in S1†). All t_cation values were around 0.40, which is also similar to those reported for LIB electrolytes.²⁰

In general, the σ and D values are strongly related to the viscosity of the electrolyte. The D values of electrolyte solutions are known to increase with the decrease in viscosity. Fig. 4 shows the temperature dependences of η⁻¹ for 1.0 M PC-based electrolyte solutions in (a) a common TEA⁺ cation with three anions and (b) a common BF₄⁻ anion with three cations. The η⁻¹ values for all electrolytes followed the trend of temperature dependences: TEABF₄ > TEAPF₆ > TEAOTf and TEMABF₄ ≈ TEABF₄ ≫ LiBF₄. Because we used PC as a solvent in all samples, the dominant effects on the viscosity were induced by the dissolved salt. The η⁻¹ values showed good correspondence with σ and D values.

Fig. 4 Temperature dependences for inverse of viscosity η⁻¹ values for 1.0 M PC-based electrolytes in (a) a common TEA⁺ with different anions and (b) a common BF₄⁻ with different cations.

Fig. 5 shows the density ρ of the electrolytes as a function of temperature. The ρ values linearly decreased with increase of temperature: TEABF₄ < TEAPF₆ < TEAOTf and TEMABF₄ ≈ TEABF₄ < LiBF₄. This is also in good agreement with the trend of the η values. This implies that an electrolyte with smaller ρ exhibits a lower η and higher D owing to the larger space available for the carrier ions to move in the present samples. The observed data for the LiBF₄-based electrolyte deviated considerably in σ, η⁻¹ and ρ, but not in D values. This means that the interaction in the electrolyte is quite strong for Li⁺ and there is a smaller space for the ions and PC solvent to move than that in the ammonium salt-based electrolytes.

Fig. 5 Comparison of temperature dependence of density ρ for 1.0 M PC-based electrolytes for (a) anions and (b) cations.

Discussion

To observe the effect of mobilities μ of the carrier ions on ionic conductivity σ, the σ values are plotted against the sum of D_cation + D_anion in Fig. 6 for (a) a common TEA⁺ cation with three different anions and (b) a common BF₄⁻ anion with three different cations. The σ values increased with an increase in (D_cation + D_anion) for all electrolytes. The cation and anion diffusion constants clearly influence the σ values. In the common TEA⁺ systems, the σ values depend on the counteranions in the order BF₄⁻ > PF₆⁻ > OTf⁻, although the ion diffusion constants were slightly modulated by the anions. In the common BF₄⁻ systems, the σ values are similar in the TEMA–BF₄ and TEA–BF₄ electrolytes, but the TEMA–BF₄ electrolyte exhibited larger (D_cation + D_anion). The LiBF₄ electrolyte showed exceptionally smaller σ and (D_cation + D_anion) values, suggesting different solution structures. The ammonium cations, especially TEMA⁺, therefore have an advantage from the viewpoint of mobility when compared with Li⁺.

Fig. 6 Plots of ionic conductivity σ against the sum of (D_cation + D_anion) for (a) common TEA⁺ with three different anions and (b) common BF₄⁻ with three different cations for 1.0 M PC electrolytes.

As mentioned above, ion transport in capacitor electrolytes is considered to occur via a vehicle mechanism. The relationship between D and η can therefore be defined by the Stokes–Einstein equation,¹¹ as follows:

D = kT/cπηr_ion (3)

where k is Boltzmann's constant, T is temperature (K), η is viscosity of the electrolyte (Pa s⁻¹), r_ion is the Stokes (solvated ion) radius (m) and c is a constant, which ranges between 4 and 6 for slip and stick boundary conditions, respectively.²⁵ Eqn (3) implies that an electrolyte with lower viscosity exhibits higher D value of the solvent. Fig. 7 shows the self-diffusion coefficients of PC, D_PC, plotted against η⁻¹ of the electrolytes. For all electrolytes, D_PC increased with increase of η⁻¹, according to eqn (3). At high temperatures, deviations from linear plots suggested interactions between PC and the ions.

Fig. 7 Plots of solvent self-diffusion coefficients D_PC against the inverse of viscosity η⁻¹ for 1.0 M PC electrolytes in (a) common TEA⁺ with three different anions and (b) common BF₄⁻ with three different cations.

In eqn (3), c and η are assumed to be the same for the ions and PC, so the r_ion/r_PC value is simply defined as eqn (4):²²

r_ion/r_PC = D_PC/D_ion (4)

The r_ion/r_PC value represents the effective radius of the diffusing ion in the electrolyte because the PGSE-NMR method gives average values of self-diffusion coefficients of the ions and PC. Table 2 shows the relative ion radius relative to PC (r_ion/r_PC) for the five electrolytes.

Table 2 Ionic radius relative to PC (r_ion/r_PC) in the capacitor electrolytes at 303 K, calculated using eqn (4)

Species	TEABF4	TEAPF6	TEAOTf	TEMABF4	LiBF4
Anion	1.1	1.3	1.2	1.1	1.7
Cation	1.5	1.5	1.5	1.5	2.4

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Based on their molecular structures, the ionic radii of TEA⁺, TEMA⁺, Li⁺, BF₄⁻, PF₆⁻, OTf⁻, and PC were calculated as 0.343, 0.327, 0.076, 0.229, 0.254, 0.270 and 0.276 nm, respectively.¹² In the present study, except for LiBF₄, the orders of magnitude of the r_ion/r_PC values of the cations and anions calculated from the D_ion's agreed relatively well with the estimated values from the van der waals' radii; however, all r_ion/r_PC values were slightly larger than those from the radii, implying the formation of weak solvation structures and ion pairs between the solvent and/or counterions. In contrast, the r_ion/r_PC values of Li⁺ and BF₄⁻ in the LiBF₄ electrolyte were much larger. This indicates that either Li⁺ interacts strongly with PC to form a solvated Li⁺(PC)_x species or that BF₄⁻ contributes to the formation of ion pairs. As a result, Li⁺ and BF₄⁻ in the electrolyte diffuse more slowly than the ions in the TEA and TEMA electrolytes. In addition, the r_Li/r_PC value of Li⁺ was about 2.4, implying that the number of solvated PC molecules with Li⁺ was in the range of 2 to 4. In general, it is known that Li⁺ is solvated by ca. four PC molecules.²⁶ The r_Li/r_PC value obtained by our method therefore includes exchange between molecules in the bulk PC and is in good agreement with the assumed value. In the EDLC electrolytes, the values of r_TEA/r_PC and r_TEMA/r_PC suggest that the ammonium cations interact weakly with PC and/or the counteranions to form weak solvation structures and ion pairs.

As shown by eqn (1), the ionic conductivity of solution electrolytes is also influenced by the number of carrier ions n per specific volume. To clarify the effect of the n on σ, we conducted analyses using Walden plots and the Nernst–Einstein equation.

Fig. 8 shows the Walden plots for (a) a common TEA⁺ cation and three different anions and (b) a common BF₄⁻ anion and three different cations. Here, ionic conductivity σ was converted to molar conductivity Λ_imp using the densities ρ given in Fig. 5. The Walden plots deviated downward from the ideal line. In the common TEA⁺ electrolytes (Fig. 8(a)), the deviation became little larger on changing from BF₄⁻ to PF₆⁻ to OTf⁻, following the anion size. In the common BF₄⁻ electrolytes (Fig. 8(b)), the plots of TEA⁺ and TEMA⁺ overlapped, but that for the Li electrolyte deviated considerably.

Fig. 8 Walden plots for 1.0 M PC electrolytes for (a) TEA⁺ with three different anions and (b) BF₄⁻ with three different cations.

The molar ionic conductivity Λ_NMR can be calculated from the self-diffusion coefficients (D₊, D₋) by the Nernst–Einstein equation, as follows:

Λ_NMR = Ne²(D₊ + D₋)/kT (5)

where N is the number of isolated ions per specific volume. Eqn (5) holds for electrolytes in which ions are perfectly dissociated (such as in an infinite diluted solution). From the D₊ and D₋ determined by PGSE-NMR measurements, the experimental Λ_NMR values were calculated for the five electrolytes. PGSE-NMR data provide the average D values for all ions, including isolated and paired ions. NMR measurements cannot distinguish charged (isolated) ions from paired ions, so the experimental Λ_NMR includes whole diffusion species. We have confirmed that at infinite dilution in lithium organic solutions, eqn (5) exactly holds.²¹ In practical electrolytes, the calculated experimental Λ_NMR is always larger than Λ_imp at all temperatures. The apparent degree of ion dissociation, α_app in solution electrolytes can be determined from eqn (6):^20–22

α_app = Λ_imp/Λ_NMR. (6)

Fig. 9 shows the temperature dependences of the α_app values. At 303 K, the α_app is largest for TEABF₄, followed by the order TEABF₄ > TEAPF₆ ≈ TEMABF₄ > TEAOTf ≫ LiBF₄. Generally, the α_app values are insensitive to temperature, except for the TEAPF₆ and TEMABF₄ electrolytes. At a glance, it is a little strange that the degree of ion dissociation decrease in the higher temperatures for TEAPF₆ and TEMABF₄. At the present stage, however, we cannot clearly explain the reasons why the α_app is insensitive to temperature. More studies are required to interpret the temperature dependent ion–solvent and ion–ion interactions.

Fig. 9 Plots of degree of dissociation α_app for 1.0 M PC electrolytes as a function of temperature for (a) common TEA⁺ with three different anions and (b) common BF₄⁻ with three different cations.

The Walden plots and α_app values indicate that ion dissociation is higher for TEA⁺ and TEMA⁺ ammonium salts than that for LiBF₄. The magnitude of deviation in the Walden plots agrees with the order of ion dissociation α_app: TEABF₄ > TEAPF₆ > TEAOTf and TEABF₄ ≈ TEMABF₄ ≫ LiBF₄. This trend is in good agreement with those estimated from Λ_imp and the limiting molar conductivity Λ₀ values reported by Ue et al.¹⁶ From the number of carrier ions, this order also agreed well with that of σ. Ionic conductivity of the electrolytes is, therefore also closely related to the concentration of carrier ions.

Mobility and concentration of the carrier ions are strongly related to physical parameters (η, ρ and D) and it is necessary to understand the mutual interactions between cation–anion, PC–cation and PC–anion. Here, we calculated these three interaction energies ΔE using DFT and HSAB calculations.^16–18 When an interaction occurs, for example, between M1 and M2, the change in the total energy, ΔE, and the number ΔN of electrons transferring from M1 to M2, are represented by eqn (7) and (8), as given by Pearson et al.:^27,28

ΔE = −(χ_M1 − χ_M2)²/4(η_M1 + η_M2) (7)

ΔN = (χ_M1 − χ_M2)/2(η_M1 + η_M2) (8)

where χ and η refer to the absolute electronegativity and absolute hardness of M1 and M2 without interactions, respectively. χ and η are calculated by eqn (9) and (10), respectively:

χ = (I + A)/2 (9)

η = (I − A)/2 (10)

where I and A respectively refer to the ionization potential and electron affinity between the interacting species. I and A are calculated by eqn (11) and (12), respectively:

I = E(X¹⁺) − E(X⁰) (11)

A = E(X⁰) − E(X¹⁻) (12)

where E(X⁰) refers to the total energy of the interacting species and E(X¹⁻) and E(X¹⁺) refer to ions having −1 and +1 electrons, respectively. The total energies, E(X⁰), E(X¹⁻) and E(X¹⁺), and the estimated χ and η of the cations and anions are summarized in Table 3. According to the HSAB theory, if χ is higher, the ions and solvent are stronger Lewis acids; if χ is lower, the chemical species is a stronger Lewis base. In addition, a “hard” Lewis acid prefers to interact with a “hard” Lewis base, and a “soft” Lewis acid prefers to interact with a “soft” Lewis base. As shown in Table 3, TEA⁺ and TEMA⁺ exhibited smaller χ values (8.96 and 9.00, respectively) than Li⁺ (40.8), indicating that they are weaker Lewis acids.

Table 3 Absolute electronegativity and absolute hardness of cations, anions and PC solvent

Species	E(X^1−)/au	E(X^0)/au	E(X^1+)/au	χ/eV	η/eV
TEA^+	−371.620711	−371.527501	−370.962229	8.96	6.42
TEMA^+	−332.294914	−332.201415	−331.633078	9.00	6.46
Li^+	−7.49133310	−7.28491780	−4.49025230	40.8	35.2
BF4^−	−424.480287	−424.679695	−424.410189	0.954	6.38
PF6^−	−940.707423	−940.896614	−940.597012	1.50	6.65
OTf^−	−961.555515	−961.730421	−961.537879	0.240	5.00
PC	−381.808186	−381.835289	−381.452645	4.84	5.57

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TEA⁺ and TEMA⁺ therefore weakly interact with anions as Lewis bases, compared with Li⁺, as shown in Table 4. In contrast, the hardnesses η of TEA⁺ and TEMA⁺ were smaller (6.42 and 6.46, respectively) than that of Li⁺ (35.2), so TEA⁺ and TEMA⁺ prefer to interact with the “soft” Lewis base anion OTf⁻ (5.00). The orders of magnitude for ΔE and ΔN are LiBF₄ > TEAOTf > TEMABF₄ ≈ TEABF₄ > TEAPF₆, which means that TEAPF₆ and TEABF₄ possess an advantage for the dissociation for their salts.

Table 4 Interaction energy ΔE and number of electrons transferred ΔN between cations and anions of the salts^a

Interaction	ΔE/eV	ΔN
a ΔE and ΔN correspond to changes in total energy and number of transferred electrons for each interaction, respectively. The arrows show the direction of electron transfer.
BF4^− → TEA^+	−1.25	0.313
PF6^− → TEA^+	−1.06	0.285
OTf^− → TEA^+	−1.66	0.382
BF4^− → TEMA^+	−1.26	0.314
BF4^− → Li^+	−9.56	0.479

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Considering the solvation energy of ions by PC, ΔE and ΔN for the PC–cation and PC–anion interactions are summarized in Table 5. In general, the ΔE of Li⁺–PC is quite large (−7.94 eV), which stabilizes the solvation structure. For the TEA⁺ and TEMA⁺ salts, the PC–cation ΔE is quite small (−0.35 and −0.36 eV, respectively), which is less than 1/20 of that of PC–Li⁺. ΔE of the PC–anion interaction was almost same. In addition, ΔE values for the dissociation energies of the salts were also smaller (from −1.06 for TEABF₄ to −1.66 eV for TEAOTf) than that of LiBF₄ (−9.56 eV). The ammonium salts were, therefore dissociated by interaction between the species. As a result, ammonium cations do not form strong solvation structures as do Li⁺-based electrolytes. This leads to electrolytes exhibiting higher μ and n for enhancement of ionic conductively σ: the weak Lewis acidity of TEA⁺ and TEMA⁺ provides the high α_app of these salts to increase n in the EDLC electrolytes. Consequently, the TEABF₄ salt was most highly dissociated in PC, and the TEA⁺ and BF₄⁻ ions and PC solvent were relatively freely move towards each other in the electrolytes. We therefore have to find an optimum combination of much “softer” and “weaker” Lewis acid cations and much “harder” and “weaker” Lewis base anions to improve the salt dissociation, which will lead to an increase in the number of carrier ions in the capacitor electrolytes. The ionic radii of the cation and anion are also important for capacitor electrolytes because of the relatively weak solvation by PC compared with that in Li⁺ electrolytes, such as 1.0 M LiPF₆/EC + DEC for LICs¹⁵ and LIBs.²³

Table 5 Interaction energy ΔE and number of electrons transferred ΔN between PC–cation and PC–anion^a

Interaction	ΔE/eV	ΔN
a ΔE and ΔN correspond to changes in total energy and number of electrons transferred for each interaction, respectively. The arrows show the direction of electron transfer.
PC → TEA^+	−0.354	0.172
PC → TEMA^+	−0.361	0.173
PC → Li^+	−7.94	0.441
PC → BF4^−	−0.315	0.162
PC → PF6^−	−0.227	0.136
PC → OTf^−	−0.500	0.217

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Conclusions

In this study, we discussed ion transport in 1.0 M PC capacitor electrolytes comprising of five salts, i.e., TEABF₄, TEAPF₆, TEAOTf, TEMABF₄ and LiBF₄. The mobility of individual ions and PC was determined by self-diffusion coefficients D measured by PGSE-NMR. The TEABF₄ electrolyte exhibited the highest D and σ and the lowest η, indicating highest mobility μ of the carrier ions. We also estimated the apparent salt dissociation degree, α_app by comparing Λ_imp and Λ_NMR. The TEABF₄ salt exhibited the highest α_app among these PC electrolytes in the temperature range from 283 to 353 K. Ion dissociation was shown to have close relations with the Lewis acidity of the cations and Lewis basicity of the anions, under the influence of the hardness and softness of the ions. The target samples of this study are electrolyte systems for electric double layer capacitors, and the salt concentration is relatively low. The experimental findings showed the importance of the quaternary ammonium–BF₄ electrolytes which are currently used in practical EDLC. All the data obtained in this study give sufficient consistency with ionic conductivity. The obtained physical parameters explained the mobility μ and number n of carrier ions in terms of solvation and ion pairs. Control of Lewis acidity and basicity is an important factor to design electrolytes for new-generation electrochemical capacitors. We are undertaking further investigations using new ionic species, such as cyclic cation (spiro-type) salts and low-melting-point salts (ionic liquids), and other solvents, such as acetonitrile towards better systems, based on the concepts in this study.

Acknowledgements

This work was supported by MEXT's scientific technology human resource development grant, “Program to Disseminate Tenure Tracking System,” Japan.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c7ra00455a

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