Electrochemical Kinetics of Ferrocene-Based Redox-ILs Investigated

Article pubs.acs.org/JPCC

Cite This: J. Phys. Chem. C XXXX, XXX, XXX-XXX

Electrochemical Kinetics of Ferrocene-Based Redox-ILs Investigated by Multi-Spectrum Impedance Fitting J. Wallauer,* K. Jaḧ me, A. Venker, P. Kübler, J. Sundermeyer, and B. Roling* Department of Chemistry, University of Marburg, Hans-Meerwein-Strasse 4, D-35032 Marburg, Germany ABSTRACT: Redox-active ionic liquids are of interest for various applications in electrochemistry, for example, as electrochemically active anions and cations in supercapacitors, as redox mediators in dye-sensistized solar cells and for overcharge protection in batteries. Due to the chemical variability of redox-active ionic liquids, their electrochemical properties can be easily tuned. Here, we investigate the electrochemical kinetic properties of four ionic liquids containing sulfonium and phosphonium cations, with ferrocenyl substituents directly attached to the onium center. The redox-active ionic liquids are dissolved in the electrochemically innocent ionic liquid [EMIm]TFSI. The results are compared to the electrochemical kinetic properties of free ferrocene standard. We obtain precise values for the heterogeneous rate constant k0 by means of a multispectrum fit of impedance spectra measured at different overpotentials. Diffusion coefficients are derived from a convolution analysis of cylic voltammograms. The redox active cations exhibit lower k0 values and lower diffusion coefficients than ferrocene, but the k0 values are only weakly dependent on the chemical structure of the cations. Furthermore, we observe no correlation between k0 and the hydrodynamic radius of the redox active cations. We offer an explanation for these observations based on kinetic barriers caused by the structure of the electrochemical double layer.

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INTRODUCTION AND MOTIVATION Understanding the kinetics of electrochemical reactions in room-temperature ionic liquids (RTILs) has attracted great interest in recent years due to various challenges in mobile and stationary energy storage. RTILs are being used, for example, as electrolytes in batteries,1,2 for metal deposition,3−5 for supercapacitors,6,7 and as electrolytes in dye-sensitized solar cells.8,9 Pioneering studies on the kinetics of electrochemical reactions in ionic liquids were carried out during the mid-2000s.10 The heterogeneous rate constant k0 is of particular interest, as it gives direct information about the rate of charge transfer reactions.11,12 In classical electrolytes with a redox species dissolved in an organic solvent/inert salt mixture, the heterogeneous charge transfer kinetics was found to be in agreement with the predictions of the Marcus theory, as was summarized by Miller in ref 13. Clegg et al.14 showed that the heterogeneous rate constants k0 of various anthracene derivatives dissolved in an acetonitrile-based electrolyte exhibit a pronounced maximum when plotted versus the hydrodynamic radii r of the derivatives, as predicted by the Marcus theory. Furthermore, it was demonstrated in various works that k0 is greatly affected by the double-layer structure. Petersen et al.15 showed that electrolytes containing tetraalkylammonium cations form a strongly bound cation monolayer on the electrode surface with a thickness depending on the length of the alkyl chains attached to the ammonium center. In this case, k0 decreases with increasing side chain length, since the tunneling probability of the electron through the monolayer decreases with increasing thickness. © XXXX American Chemical Society

The same effect could also be observed for self-assembled monolayers.16−18 Since the electrochemical double layers at ionic liquid/electrode interfaces exhibit a complex multilayer structure, as observed in AFM and STM studies19,20 as well as in MD simulations, 21,22 it can be expected that the heterogeneous rate constants of redox molecules in ILs are lower than in classical organic electrolytes. Furthermore, the solvation shell of redox-active molecules in a double layer may differ from that in the bulk, which can lead to an additional reorganization energy increasing the activation energy of the charge transfer.23 Slower charge transfer reactions in ILs as compared to classical electrolytes were confirmed experimentally by Lagrost et al.,10 who measured k0 and the diffusion coefficient of ferrocene in imidazolium- and tetraalkylammonium-based ILs. Both quantities were found to be 1−2 orders of magnitude lower than in an acetone/Bu4NPF6 electrolyte. The decrease in the rate constant was especially profound for outer sphere redox species, like ferrocene. Fietkau and Compton24 supported these measurements and studied furthermore the relation between k0 and the hydrodynamic radius of the redox species, which was found to be at variance with the Marcus theory. This was later controversially discussed by various authors on the basis of both experimental results25,26 and simulations.27 Received: September 29, 2017 Revised: November 4, 2017

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DOI: 10.1021/acs.jpcc.7b09693 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

compare the kinetic electrochemical properties of these cations with those of ferrocene.

Unfortunately, the reported experimental values for the kinetic parameters, even of the same system, are quite diverse. In the extensively studied case of ferrocene in the ionic liquid 1ethyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imid ([EMIm]TFSI), the reported values span several orders of magnitude, as was recently pointed out by Bentley et al.25 One reason for these discrepancies may be that electrochemical methods, which were established for classical electrolytes with low viscosities, were used for IL systems without careful analysis of approximations being made for their applicability. This is especially true for easily accessible methods, such as cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS). In the analysis of cyclic voltammogramms, complications introduced by slow electron transfer kinetics need to be taken into account. For instance, the often used Randles-Sevcik analysis for obtaining diffusion coefficients, requires corrections with regard to low Matsuda numbers.11,28 The determination of the heterogeneous rate constant k0 by EIS is sometimes based on taking only a single impedance spectrum at the open-circuit potential,29 which may not be identical to the equilibrium or half-wave potential. This procedure cannot be expected to lead to precise k0 values. Therefore, other sophisticated methods were used for kinetic studies, such as high speed channel electrode,24 scanning electrochemical microscopy,30 or high amplitude ac voltammetry.25 However, these methods are not available in all electrochemical laboratories. In this paper, we describe a method for obtaining precise electrochemical kinetic parameters from EIS and CV measurements. The method is based on a simultaneous fit of impedance spectra obtained at different overpotentials in combination with a convolution analysis of cyclic voltammograms. The method is, first of all, used for obtaining kinetic parameters of a model system, namely, ferrocene in the ionic liquid [EMIm]TFSI. We compare our results to previous studies. Then we apply the method to four redox-active ionic liquids dissolved in the ionic liquid [EMIm]TFSI. The chemical structures of these redoxactive ILs are illustrated in Figure 1. The cations consist of a

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MULTI-SPECTRUM FIT: IMPEDANCE MODEL A simple one-electron charge transfer reaction at the liquid electrolyte/electrode interface is characterized by two rate constants kox and kred: k red

Ox n + + ne− HooI Red kox

These rate constants are potential-dependent as described by kinetic theories, like the Butler−Volmer theory and the Marcus theory.12 In the case of the Butler−Volmer theory, the rate constants are given by ⎛ αF(E − Eeq ) ⎞ ⎟⎟ kox = k 0 exp⎜⎜ RT ⎝ ⎠

(1)

⎛ (1 − α)F(E − Eeq ) ⎞ ⎟⎟ k red = k 0 exp⎜⎜ − RT ⎝ ⎠

(2)

Here F is the Faraday constant, E is the electrode potential, Eeq is the equilibrium potential, R is the gas constant, T is the temperature, α is the transfer coefficient, and k0 is the heterogeneous rate constant. The impedance of the charge transfer reaction can be described by a Randles-type equivalent circuit as shown in Figure 2,33,34

Figure 2. Randles equivalent circuit, including an electrolyte resistance, the Faradaic impedance composed of the charge transfer resistance and the Warburg diffusion element, and a parallel doublelayer capacitor (or constant phase element).

The double-layer capacitance of ionic liquids depends only weakly on the electrode potential.35 The electrolyte resistance as a bulk property is independent of potential. The Faradaic impedance, which is composed of the charge transfer resistance and the Warburg diffusion element, is, however, strongly potential-dependent. Lasia expressed the charge transfer resistance Rct and the Warburg coefficient σ as follows:34 R ct = Figure 1. Four redox-ILs used in this study. The cations consist of a phosphonium or sulfonium unit with alkyl, phenyl, and ferrocenyl substituents directly bound at the onium center.

σ=

RT 1 2 F αkoxcred,0 + (1 − α)k redcox,0

⎛ k RT 1 ⎜⎜ ox + F 2 αkoxcred,0 + (1 − α)k redcox,0 ⎝ 2Dred

(3)

k red ⎞ ⎟⎟ 2Dox ⎠ (4)

phosphonium or sulfonium unit with alkyl and phenyl substituents and with one additional ferrocenyl substituent directly bound to the onium center. This direct link of the electron-withdrawing cationic center to the electron-rich ferrocene unit has a strong impact on the redox potentials. The redox-active cations undergo a one-electron oxidation with the standard reduction potential Cat2+/Cat+ depending on the substituents at the phosphonium/sulfonium unit.31,32 We

Here, cred,0 and cox,0 denote concentrations of the reduced and the oxidized species, respectively, at the electrode surface. No approximations were made in the derivation of these expressions. Typically, approximate relations for the surface concentrations are introduced at this point.34 However, since the denominators in eqs 3 and 4 are identical, we can alternatively define a new quantity Φf as the ratio of σ to Rct: B


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Figure 3. (a) Experimental Φf values from fitting a Randles equivalent circuit to the individual impedance spectra, (b) comparison of simulated CVs, based on kinetic parameters from (a) and from Butler−Volmer with experimental data.

Φf ≡

σ = R ct

kox + 2Dred

k red 2Dox

(5)

Z(̂ ω , Ei) =

R el, i

⏟

Φf is independent of the surface concentrations. After inserting expressions for kox and kred, for example, from the Butler− Volmer theory (eqs 1 and 2), Φf can be directly compared to experimental data. In the following we denote eq 5 with inserted Butler−Volmer expressions as Φf,BV. If σ and Rct can be measured accurately as a function of overpotential, Φf,BV can be directly fitted to the experimental data to give the kinetic parameters. It should be noted, however, that not all parameters can be used as free fit parameters due to interdependencies in the model. Free parameters can be, for instance, k0, α, and Eeq with fixed diffusion coefficients, or k0, α, and Dox with fixed Eeq and Dred. In practice, it is advisible to determine, for example, Eeq independently (see Experimental Section) and to fix it. If the charge transfer semicircle and the Warburg impedance at low frequencies overlap significantly, the other nonidealities in the spectra, like nonideal capacitive behavior of the double layer, described by a constant-phase element, can lead to significant cross-influencing of the parameters. While σ can usually be determined quite reliably, the overlap of charge transfer resistance and Warburg impedance at high overpotentials often leads to an overestimation of Rct. Figure 3 a) shows the Φf values for 5 mM solution of ferrocene in [EMIm]TFSI as obtained from a Randles circuit fit of individual impedance spectra taken at different electrode potentials. Instead of the parabola-like dependence expected for Butler−Volmer kinetics, we find a camel-shaped curve. The kinetic data derived from Figure 3a were then used to simulate a cyclic voltammogram via finite-element simulations. In Figure 3b, we compare the simulated CV to the experimentally obtained one. Due to the camel-shape dependence of Φf on the electrode potential, the current drop in the simulated CV above the peak potential is determined by charge-transfer limitations, in contrast to the typical diffusion limitations in the experimental CV. This shows clearly that the camel shape of Φf is caused by an overestimation of Rct in the Randles circuit fits at high overpotentials. Based on these findings, we developed an impedance fitting approach based on Φf,BV, which allows us to fit multiple electrode-potential-dependent impedance spectra as a combined data set. The model equations are given by

electrolyte resistance

⎛ ⎜ ⎜ 1 +⎜ + Zf (ω , Ei) ⎜      ⎜ ⎝ Faradaic impedance

⎞−1 ⎟ ⎟ βi (iω) Q i ⎟  ⎟ CPE double‐layer capacitance⎟ ⎠

with Zf̂ (ω , Ei) =

σi σi σ́ + +i i ω ω Φf,BV (Ei , k 0 , α , E0)     charge‐transfer resistance

Warburg impedance

(6)

All spectra were fitted with the same values for the parameters k0, α, Eeq, Dred, and Dox, with the diffusion coefficients and Eeq as fixed values. Furthermore, the model contains the individual parameters σi (Warburg coefficients) Rel (electrolyte resistance), Qi, and βi for each spectrum taken at electrode potential Ei. Qi and βi are constant-phase-element parameters describing nonideal double-layer charging. A fit of, for example, 10 spectra therefore typically contains 43 parameters. While this seems overwhelming, it must be kept in mind that all 10 individual parameter sets are perfectly independent of each other, which allows the fit to succeed reliably. Here it is worth noting that the idea of using combined fitting of multiple spectra is currently becoming more popular, as shown, for example, by Landesfeind et al., who fitted spectra of a lithium battery recorded at different states of charge with several shared and some individual parameters.36 Further details about the chosen potential regions are given in the Experimental Section. We note that in the case of the redox-ILs, one further assumption was made: The diffusion coefficient of the oxidized species could not be measured directly, since their bulk concentration was zero. Therefore, we assumed that the diffusion coefficient of the oxidized species is by a factor of 2 lower than that of the reduced species, as was found for the ferrocene/ferrocenium redox couple.

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EXPERIMENTAL SECTION Electrochemical measurements were carried out using a threeelectrode measurement cell for liquid samples (TSC 1600, rhd instruments) mounted on a microcell HC cell stand (rhd instruments). The temperature in all experiments was 19.7 ± 0.1 °C. The working electrode consisted of a glassy carbon (GC) rod, press-fitted into a PEEK mantle with an exposed flat surface area of 7.07 mm2. A silver wire with 315 μm diameter (Scientific Wire Company) was used as a quasi-reference electrode. A platinum crucible acted as the sample container C


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The Journal of Physical Chemistry C and counter electrode. The cell was connected to a Zahner Zennium potentiostat (Zahner-elektrik) for EIS measurements or to a Bio-Logic SP-150 (Bio-Logic Science Instruments SAS). Impedance spectra were evaluated using the software RelaxIS 3 (rhd instruments). The multispectrum fit procedure was also implemented in RelaxIS 3 via a plugin. Cyclic voltammograms were evaluated by means of a self-written software, which employs the Math.NET Numerics package37 for numeric integration in the calculation of convolution voltammograms. Ferrocene was purchased from Acros Organics (98%), ferrocenium-hexafluorophosphate from Sigma-Aldrich (98%) and ethyl-methyl imidazolium bis-trifluoromethyl sulfonylimide (EMImTFSI) from Iolitec (>99%). The ionic liquid was stored over active charcoal for 24 h, before filtering and drying at 10−6 mbar for 48 h, resulting in a completely colorless liquid. The ionic liquid was then stored in an argon glovebox (MBRAUN). The redox-active ILs were prepared based on previously published work,31,32 dried at a pressure of 10−6 mbar for 48 h and then stored in sealed Schlenk ampules inside the glovebox. Solutions of ferrocene and of the redox-ILs in [EMIm]TFSI were prepared with a concentration of ∼5 mM and likewise stored in the glovebox. Prior to each use, the working and counter electrodes were polished subsequently with 3 and 1 μm diamond paste (Kemet) and thoroughly cleaned with deionized water and HPLC grade acetone (Sigma-Aldrich). The silver wire reference electrode was also cleaned with acetone and mounted in the cell close to the working electrode. After drying at reduced pressure for 5− 10 min to remove volatile solvents, the cell parts were immediately transferred into the glovebox. After cell assembly, a cyclic voltammogram well inside the electrochemical window of [EMIm]TFSI was recorded with a scan rate of 100 mV/s to determine the half-wave potential, E1/2, of the redox process. Subsequently, impedance spectra in a range of ±150 mV around E1/2 were recorded in steps of 10 mV in a frequency range of 100 kHz to 1 Hz using an rms ac voltage of 10 mV. Afterward, another cyclic voltammogram was measured to determine the reference electrode drift. The procedure was repeated multiple times with fresh samples in order to assess the statistical uncertainty of the data. Results are given with the standard error in the following. Diffusion coefficients were obtained from the cyclic voltammograms by a mathematical convolution of the timedependent current density with 1/√t.38 This convolution leads to current density plateaus at high overpotentials with the plateau values being proportional to the bulk concentration of the active species and to the square root of the diffusion coefficient of the active species. For instance, the current density in the anodic regime is given by Jc,max = nFcred Dred

Figure 4. Convolution CVs of ferrocene and ferrocenium, and a mixture of both, indicating the reliable values for Dred and Dox can even be found from a single measurement of a mixture of both species.

was then calculated from E1/2 using the ratio of diffusion coefficients and fixed in the fits. Spectra in a potential region of ±50 mV around the equilibrium potential were chosen for the fits with Eeq and diffusion coefficients as fixed values.

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RESULTS AND DISCUSSION Diffusion Coefficients. The diffusion coefficients of all species are summarized in Table 1. Two trends can be

Table 1. Diffusion Coefficients for All Measures Species in This Studya species ferrocene ferrocenium FcPPh2Me+ FcPBu2Me+ FcSMe2+ FcSBuMe+

D (m2/s·1011) 5.2 2.9 1.9 1.6 2.9 2.5

± ± ± ± ± ±

0.13 0.4 0.02 0.019 0.015 0.048

charge

rhydr (pm)

±0 +1 +1 +1 +1 +1

160 287 439 521 287 333

a

The value for ferrocenium was measured from two convoluted CVs (one of Fc+ alone, one of a mixture, see Figure 4). Hydrodynamic radii are estimated from the Stokes-Einstein-relation with ηIL = 38.6 mPas.39.

observed: (i) The diffusion coefficient of the uncharged ferrocene molecules is about two times larger than the diffusion coefficient of the ferrocenium cations. (ii) The diffusion coefficients of all charged species are similar. The ferrocene and ferrocenium diffusion coefficients are in good agreement with previously reported values for the same system,10 or slightly higher.24 Since ferrocene, as an outer sphere redox species, does not change its chemical structure during the oxidation, the lower diffusion coefficient of the charged oxidized species is most likely related to the interactions with the other ions in the ionic liquid. These interactions may lead to a slower self-diffusion of ferrocenium as compared to ferrocene. However, by means of cyclic voltammetry, we measure the chemical diffusion coefficient of the species in Nernst diffusion layers. The chemical diffusion of a charged species, like ferrocenium, is always coupled to the diffusion of other ions in order to ensure electroneutrality of the diffusion layer. This may lead to chemical diffusion coefficients, which are smaller than selfdiffusion coefficients. From these considerations, it is understandable that the charge of an ion plays a more important role for the chemical diffusion coefficient than its size.

(7)

with cred denoting the bulk concentration of the reduced species.Jc,max is independent of k0 and of any uncompensated resistance during the measurement, which offers advantages over the standard Randles-Sevcik analysis. For ferrocene, the convolution approach was carried out for solutions containing either the reduced or the oxidized species, see Figure 4. From the current density plateaus, we obtained reliable values for both Dred and Dox. To perform the multispectrum fit, the spectra were first fitted individually to the Randles-circuit in Figure 2. E1/2 was taken as the potential at the minimum of the Warburg coefficient.34 Eeq D


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the data: (i) The k0 values of the redox-active cations are 4−5× lower than the k0 value of ferrocene. (ii) The k0 values of all the redox-active cations are similar. We note that similar reduction in k0 due to the introduction of a charged side chain was found by Fontaine et al.,29 who compared the kinetics of ferrocene with [FcEMIm]TFSI dissolved in [EMIm]TFSI and found a reduction of k0,app (obtained from a CV) by a factor of 4. The Sumi and Marcus kinetic theory14,44 predicts the following relation between the heterogeneous rate constant k0 and the radius of the redox molecule, r:

When calculating the hydrodynamic radii of the ions from the Stokes−Einstein relation for perfect slip behavior:

rhydro =

kBT 4πηD

(8)

there is no clear correlation between the size of the cations and the hydrodynamics radius. For instance, FcSMe2+ is larger than Fc+, but both ions exhibit the same hydrodynamic radius. Deviations between van der Waals radii and hydrodynamic radii have also been observed for other ionic liquids40−42 and are expected due to the complex molecular interactions in ionic liquids. Heterogeneous Rate Constants. An example for a multispectrum fit is illustrated in Figure 5. The Nyquist plots

k0 = Q

ψ 4π

⎡ ⎛ ψ ⎞⎤ 1 exp⎢ −⎜Br + ⎟⎥ ⎝ ⎣ r r ⎠⎦

(9)

with Q=

K pκel0 exp[−B(δ − σ )]

and

τl ψ=

NAe 2 ⎛ 1 1⎞ ⎜⎜ − ⎟⎟ 32πε0RT ⎝ εop εs ⎠

(10)

Here, Kp denotes the equilibrium constant for the formation of a precursor complex between redox molecule and electrode surface. κ0el is the standard electronic transmission coefficient, δ is the difference between the molecule-electrode separation and the molecule radius, σ is the distance of closest approach of molecule and electrode, τl is the longitudinal relaxation time of the electrolyte, εop and εs are the optical and static permittivity, respectively, of the electrolyte, and B is a constant. Equations 9 and 10 predict a pronounced maximum when k0 is plotted versus r. As already mentioned, Clegg et al. found such a maximum for the redox kinetics of anthracene derivatives in acetonitrilebased electrolytes, when the radius of the redox molecule was approximated by the hydrodynamic radius.14 In later work of the same group, the same relation was found to be invalid when k0 and r were measured in ionic liquids.45,46 Both studies investigated uncharged reduced species and found that k0 did not change significantly with r. In Figure 6, we plot k0 versus r for all redox species investigated in this study. While k0 depends strongly on the charge state of the reduced species, an influence of the hydrodynamic radius on k0 is not detected. The lower k0 values of the redox-active cations suggest that the barrier for the

Figure 5. (a) Nyquist plot of impedance data of the ferrocene redox systems at different overpotentials (symbols) and best fit lines for several spectra obtained from the multispectrum fit. (b) Comparison of the results for Φf between fitting each spectrum individually (symbols) and the multispectrum fit (line).

of the impedance in a potential region of ±100 mV around the equilibrium potential are shown together with the best fits. It is obvious that the shared kinetic parameters in combination with the individual Warburg and double-layer elements can describe all spectra in this large range reasonably well. Figure 5b shows electrode-potential-dependent Φf values obtained by the multispectrum Butler−Volmer-based fit in comparison to the individual fit results without assuming Butler−Volmer kinetics. The results for Φf are similar for low overpotentials, but due to the overestimation of Rct in the individual fits, there are huge differences at high overpotentials. The results from the multispectrum fits are summarized in Table 2. The k0 value obtained for ferrocene is in good agreement with previously reported values,29,43 but is about 1 order of magnitude lower than values from high speed channel electrode measurements.24 Two trends can be deduced from Table 2. Heterogeneous Rate Constants, Transfer Coefficients, and Half-Wave Potentials versus E1/2,Fc for All Measured Reactions in This Study species

k0 (m/s·105)

ferrocene FcPPh2Me+ FcPBu2Me+ FcSMe2+ FcSBuMe+

24.6 ± 0.33 5.6 ± 0.73 5.0 ± 1.55 4.9 ± 0.83 3.9 ± 1.18

α 0.60 0.54 0.58 0.50 0.55

± ± ± ± ±

E1/2 vs E1/2,Fc (V) 0.035 0.038 0.049 0.10 0.070

0.0 0.50431 0.45431 0.527 0.527

Figure 6. Plot of the rate constants k0 vs the estimated hydrodynamic radii for perfect-slip behavior (Stokes−Einstein parameter P = 4). The labels designate the reduced forms of the reacting species. E


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interface than for neutral probe particles. Our experimental results are well in line with these simulation results.

charge transfer reaction is higher as compared to the neutral ferrocene molecules. We propose that this difference in the k0 values is related to the structure of the double layer at the IL/electrode interface. The double layer is typically composed of several ionic layers causing oscillation in the charge density, in particular at potentials close to the potential of zero charge (PZC). In molecular dynamics simulations of an imidazolium-based ionic liquid in contact to a graphene sheet electrode, Lynden-Bell et al. found that at for low charges of the graphene sheet (i.e., for potentials close to PZC), the free energy barrier for a positively charge probe particle is higher than for a neutral probe particle.47 This was explained by the structure of the double layer close to the PZC. Since the imidazolium rings orient parallel to the electrode surface, the imidazolium cations approach the electrode surface more closely than the anions. The resulting dipole moment and the Poisson potential drop between the center of cationic charge and the center of anionic charge leads to an additional electrostatic contribution of the free energy barrier for positively charge probe particles. To the best of our knowledge, exact values for the PZC of the [EMIm]TFSI/glassy carbon interface were not reported. However, typical values for the potential of zero charge of IL/ electrode interfaces were found to be in the range of +200 mV versus ferrocene.48,49 This implies that the typical half-wave potential of ferrocene in ILs is around −0.2 V versus PZC and that the half-wave potentials of our redox ILs are around +0.3 V versus PZC (see also Table 2). Together with a typical double layer capacitance of 8 μF/cm2 found for IL/electrode interfaces, this results in electrode charges in the range from −1.6 μC/cm2 = −0.1 e/nm2 to 2.4 μC/cm2 = 0.15 e/nm2. This is well within the range of electrode charges, in which the free energy barrier for positive probe particles was found to be higher than for a neutral probe particle.47 This gives strong indication that the higher k0 values found for the redox-active cations are indeed caused by an additional electrostatic barrier related to the structure of the double layer.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: roling@staff.uni-marburg.de. ORCID

J. Wallauer: 0000-0003-4378-2535 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge financial support of this work by the German Science Foundation (DFG) and by the Hessian Graduate School Program for Basic Science and Technology of Electric Mobility.

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REFERENCES

(1) Menne, S.; Pires, J.; Anouti, M.; Balducci, A. Protic Ionic Liquids as Electrolytes for Lithium-Ion Batteries. Electrochem. Commun. 2013, 31, 39−41. (2) Huber, B.; Rossrucker, L.; Sundermeyer, J.; Roling, B. Ion Transport Properties of Ionic Liquid-based Polyelectrolytes. Solid State Ionics 2013, 247−248, 15−21. (3) Abbott, A. P.; Frisch, G.; Ryder, K. S. Electroplating Using Ionic Liquids. Annu. Rev. Mater. Res. 2013, 43, 335−358. (4) Liu, Z.; Elbasiony, A. M.; Zein El Abedin, S.; Endres, F. Electrodeposition of Zinc-Copper and Zinc-Tin Films and FreeStanding Nanowire Arrays from Ionic Liquids. ChemElectroChem 2015, 2, 389−395. (5) Shapouri Ghazvini, M.; Pulletikurthi, G.; Liu, Z.; Prowald, A.; Zein El Abedin, S.; Endres, F. Electrodeposition and Stripping Behavior of a Zinc/Polystyrene Composite Electrode in an Ionic Liquid. J. Solid State Electrochem. 2015, 19, 1453−1461. (6) Balducci, A.; Dugas, R.; Taberna, P. L.; Simon, P.; Plée, D.; Mastragostino, M.; Passerini, S. High Temperature Carbon−Carbon Supercapacitor Using Ionic Liquid as Electrolyte. J. Power Sources 2007, 165, 922−927. (7) Chen, Y.; Zhang, X.; Zhang, D.; Yu, P.; Ma, Y. High Performance Supercapacitors Based on Reduced Graphene Oxide in Aqueous and Ionic Liquid Electrolytes. Carbon 2011, 49, 573−580. (8) Lau, G. P. S.; Tsao, H. N.; Zakeeruddin, S. M.; Grätzel, M.; Dyson, P. J. Highly Stable Dye-Sensitized Solar Cells Based on Novel 1,2,3-triazolium Ionic Liquids. ACS Appl. Mater. Interfaces 2014, 6, 13571−13577. (9) Wang, P.; Zakeeruddin, S. M.; Humphry-Baker, R.; Grätzel, M. A Binary Ionic Liquid Electrolyte to Achieve ≥ 7% Power Conversion Efficiencies in Dye-Sensitized Solar Cells. Chem. Mater. 2004, 16, 2694−2696. (10) Lagrost, C.; Carrié, D.; Vaultier, M.; Hapiot, P. Reactivities of Some Electrogenerated Organic Cation Radicals in Room-Temperature Ionic Liquids: Toward an Alternative to Volatile Organic Solvents? J. Phys. Chem. A 2003, 107, 745−752. (11) Hamann, C. H.; Hamnett, A.; Vielstich, W. Electrochemistry, 2nd ed.; Wiley-VCH: Weinheim, 2007. (12) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications, 2nd ed.; Wiley: New York, 2001. (13) Physical Electrochemistry: Principles, Methods, and Applications; Rubinstein, I., Ed.; Monographs in Electroanalytical Chemistry and Electrochemistry; Dekker: New York, NY, 1995. (14) Clegg, A. D.; Rees, N. V.; Klymenko, O. V.; Coles, B. A.; Compton, R. G. Marcus Theory of Outer-sphere Heterogeneous Electron Transfer Reactions: Dependence of the Standard Electrochemical Rate Constant on the Hydrodynamic Radius from High Precision Measurements of the Oxidation of Anthracene and Its

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SUMMARY AND CONCLUSIONS We have measured the heterogeneous rate constant k0 and the diffusion coefficients of four redox-active ionic liquids dissolved in the ionic liquid [EMIm]TFSI. The redox-ILs are based on sulfonium and phosphonium cations, with ferrocenyl substituents directly attached to the onium center. In order to obtain precise values for both heterogeneous rate constant and diffusion coefficient, we have combined multispectrum fitting of impedance spectra obtained at various overpotentials with a convolution analysis of cyclic voltammograms. The diffusion coefficients of the redox cations are by a factor of about 2 lower than the diffusion coefficient of ferrocene in [EMIm]TFSI, while the heterogeneous rate constants k0 are by a factor of about 5 lower. k0 shows no significant dependence on the hydrodynamic radius of the redox cations, which is at variance with the predictions of the Marcus theory. We explain the lower k0 values of the redox cations by the structure of the electrochemical double layer close to the potential of zero charge (PZC). In MD simulations of imidazolium-based ionic liquids at charged interfaces, the double layer structure close to the PZC is characterized by a smaller distance of the parallel oriented imidazolium rings to the interface as compared to the anions. The resulting dipole moment causes a higher free energy barrier for positive probe particles approaching the F


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The Journal of Physical Chemistry C Derivatives in Nonaqueous Solvents Using the High-speed Channel Electrode. J. Am. Chem. Soc. 2004, 126, 6185−6192. (15) Petersen, R. A.; Evans, D. H. Heterogeneous Electron Transfer Kinetics for a Variety of Organic Electrode Reactions at the MercuryAcetonitrile Interface Using either Tetraethylammonium Perchlorate or Tetraheptylammonium Perchlorate Electrolyte. J. Electroanal. Chem. Interfacial Electrochem. 1987, 222, 129−150. (16) Miller, C.; Cuendet, P.; Grätzel, M. Adsorbed Omega-Hydroxy Thiol Monolayers on Gold Electrodes: Evidence for Electron Tunneling to Redox Species in Solution. J. Phys. Chem. 1991, 95, 877−886. (17) Miller, C.; Grätzel, M. Electrochemistry at Omega-Hydroxythiol Coated Electrodes. 2. Measurement of the Density of Electronic States Distributions for Several Outer-Sphere Redox Couples. J. Phys. Chem. 1991, 95, 5225−5233. (18) Smalley, J. F.; Feldberg, S. W.; Chidsey, C. E. D.; Linford, M. R.; Newton, M. D.; Liu, Y.-P. The Kinetics of Electron Transfer Through Ferrocene-Terminated Alkanethiol Monolayers on Gold. J. Phys. Chem. 1995, 99, 13141−13149. (19) Atkin, R.; Borisenko, N.; Druschler, M.; el-Abedin, S. Z.; Endres, F.; Hayes, R.; Huber, B.; Roling, B. An in situ STM/AFM and Impedance Spectroscopy Study of the Extremely Pure 1-butyl-1methylpyrrolidinium tris(pentafluoroethyl)trifluorophosphate/ Au(111) Interface: Potential Dependent Solvation Layers and the Herringbone Reconstruction. Phys. Chem. Chem. Phys. 2011, 13, 6849−6857. (20) Atkin, R.; El Abedin, S. Z.; Hayes, R.; Gasparotto, L. H. S.; Borisenko, N.; Endres, F. AFM and STM Studies on the Surface Interaction of [BMP]TFSA and [EMIm]TFSA Ionic Liquids with Au(111). J. Phys. Chem. C 2009, 113, 13266−13272. (21) Vatamanu, J.; Borodin, O.; Smith, G. D. Molecular Simulations of the Electric Double Layer Structure, Differential Capacitance, and Charging Kinetics for N-Methyl-N-Propylpyrrolidinium Bis(Fluorosulfonyl)Imide at Graphite Electrodes. J. Phys. Chem. B 2011, 115, 3073−3084. (22) Kirchner, K.; Kirchner, T.; Ivaništšev, V.; Fedorov, M. V. Electrical Double Layer in Ionic Liquids: Structural Transitions from Multilayer to Monolayer Structure at the Interface. Electrochim. Acta 2013, 110, 762−771. (23) Li, Z.; Jeanmairet, G.; Méndez-Morales, T.; Burbano, M.; Haefele, M.; Salanne, M. Confinement Effects on an Electron Transfer Reaction in Nanoporous Carbon Electrodes. J. Phys. Chem. Lett. 2017, 8, 1925−1931. (24) Fietkau, N.; Clegg, A. D.; Evans, R. G.; Villagran, C.; Hardacre, C.; Compton, R. G. Electrochemical Rate Constants in Room Temperature Ionic Liquids: The Oxidation of a Series of Ferrocene Derivatives. ChemPhysChem 2006, 7, 1041−1045. (25) Bentley, C. L.; Li, J.; Bond, A. M.; Zhang, J. Mass-Transport and Heterogeneous Electron-Transfer Kinetics Associated with the Ferrocene/Ferrocenium Process in Ionic Liquids. J. Phys. Chem. C 2016, 120, 16516−16525. (26) Kim, D. Y.; Yang, J. C.; Kim, H. W.; Swain, G. M. Heterogeneous Electron-transfer Rate Constants for Ferrocene and Ferrocene Carboxylic Acid at Boron-doped Diamond Electrodes in a Room Temperature Ionic Liquid. Electrochim. Acta 2013, 94, 49−56. (27) Lynden-Bell, R. M. Can Marcus Theory Be Applied to Redox Processes in Ionic Liquids? A Comparative Simulation Study of Dimethylimidazolium Liquids and Acetonitrile. J. Phys. Chem. B 2007, 111, 10800−10806. (28) Matsuda, H.; Ayabe, Y. Zur Theorie der Randles-Sevčikschen Kathodenstrahl-Polarographie. Z. Elektrochem. 1955, 59, 494−503. (29) Fontaine, O.; Lagrost, C.; Ghilane, J.; Martin, P.; Trippé, G.; Fave, C.; Lacroix, J.-C.; Hapiot, P.; Randriamahazaka, H. N. Mass Transport and Heterogeneous Electron Transfer of a Ferrocene Derivative in a Room-temperature Ionic Liquid. J. Electroanal. Chem. 2009, 632, 88−96. (30) Taylor, A. W.; Qiu, F.; Hu, J.; Licence, P.; Walsh, D. A. Heterogeneous Electron Transfer Kinetics at the Ionic Liquid/Metal

Interface Studied Using Cyclic Voltammetry and Scanning Electrochemical Microscopy. J. Phys. Chem. B 2008, 112, 13292−13299. (31) Kübler, P.; Sundermeyer, J. Ferrocenyl-phosphonium Ionic Liquids - Synthesis, Characterisation and Electrochemistry. Dalton T. 2014, 43, 3750−3766. (32) Venker, A.; Vollgraff, T.; Sundermeyer, J. Ferrocenyl Sulfonium Ionic Liquids - Synthesis, Characterization and Electrochemistry. Dalton Trans. 2017, submitted for publication. (33) Randles, J. E. B. Kinetics of Rapid Electrode Reactions. Discuss. Faraday Soc. 1947, 1, 11. (34) Lasia, A. Electrochemical Impedance Spectroscopy and its Applications. In Modern Aspects of Electrochemistry; Conway, B. E., Bockris, J. O., White, R. E., Eds.; Modern Aspects of Electrochemistry; Kluwer Academic Publishers: Boston, 2002; pp 143−248. (35) Wallauer, J.; Drüschler, M.; Huber, B.; Roling, B. The Differential Capacitance of Ionic Liquid/Metal Electrode Interfaces − A Critical Comparison of Experimental Results with Theoretical Predictions. Z. Naturforsch., B: J. Chem. Sci. 2013, 68, 1143−1153. (36) Landesfeind, J.; Pritzl, D.; Gasteiger, H. A. An Analysis Protocol for Three-Electrode Li-Ion Battery Impedance Spectra: Part I. Analysis of a High-Voltage Positive Electrode. J. Electrochem. Soc. 2017, 164, A1773−A1783. (37) Math.NET Numerics, version 3.12.0.0; Math.NET Project, http://numerics.mathdotnet.com, 2016. (38) Imbeaux, J. C.; Savéant, J. M. Convolutive Potential Sweep Voltammetry. J. Electroanal. Chem. Interfacial Electrochem. 1973, 44, 169−187. (39) Fröba, A. P.; Kremer, H.; Leipertz, A. Density, Refractive Index, Interfacial Tension, and Viscosity of Ionic Liquids EMIMEtSO4, EMIMNTf2, EMIMN(CN)2, and OMANTf2 in Dependence on Temperature at Atmospheric Pressure. J. Phys. Chem. B 2008, 112, 12420−12430. (40) Araque, J. C.; Yadav, S. K.; Shadeck, M.; Maroncelli, M.; Margulis, C. J. How Is Diffusion of Neutral and Charged Tracers Related to the Structure and Dynamics of a Room-Temperature Ionic Liquid? Large Deviations from Stokes-Einstein Behavior Explained. J. Phys. Chem. B 2015, 119, 7015−7029. (41) Herold, E.; Strauch, M.; Michalik, D.; Appelhagen, A.; Ludwig, R. Dynamics of Methanol in Ionic Liquids: Validity of the StokesEinstein and Stokes-Einstein-Debye Relations. ChemPhysChem 2014, 15, 3040−3048. (42) Kaintz, A.; Baker, G.; Benesi, A.; Maroncelli, M. Solute Diffusion in Ionic Liquids, NMR Measurements and Comparisons to Conventional Solvents. J. Phys. Chem. B 2013, 117, 11697−11708. (43) Tachikawa, N.; Katayama, Y.; Miura, T. Electrode Kinetics of Ferrocenium/Ferrocene in Room-Temperature Ionic Liquids. In 214th ECS Meeting, Honolulu, Hawaii, Oct 12−17, 2008, ECS, 2008; pp 589−595. (44) Sumi, H.; Marcus, R. A. Dynamical Effects in Electron Transfer Reactions. J. Chem. Phys. 1986, 84, 4894−4914. (45) Belding, S. R.; Rees, N. V.; Aldous, L.; Hardacre, C.; Compton, R. G. Behavior of the Heterogeneous Electron-Transfer Rate Constants of Arenes and Substituted Anthracenes in Room-Temperature Ionic Liquids. J. Phys. Chem. C 2008, 112, 1650−1657. (46) Long, J. S.; Silvester, D. S.; Barnes, A. S.; Rees, N. V.; Aldous, L.; Hardacre, C.; Compton, R. G. Oxidation of Several p-Phenylenediamines in Room Temperature Ionic Liquids: Estimation of Transport and Electrode Kinetic Parameters. J. Phys. Chem. C 2008, 112, 6993− 7000. (47) Lynden-Bell, R. M.; Frolov, A. I.; Fedorov, M. V. Electrode Screening by Ionic Liquids. Phys. Chem. Chem. Phys. 2012, 14, 2693− 2701. (48) Müller, C.; Vesztergom, S.; Pajkossy, T.; Jacob, T. Immersion Measurements of Potential of Zero Total Charge (pztc) of Au(100) in an Ionic Liquid. Electrochim. Acta 2016, 188, 512−515. (49) Lockett, V.; Sedev, R.; Ralston, J.; Horne, M.; Rodopoulos, T. Differential Capacitance of the Electrical Double Layer in Imidazolium-Based Ionic Liquids: Influence of Potential, Cation Size, and Temperature. J. Phys. Chem. C 2008, 112, 7486−7495. G


Electrochemical Kinetics of Ferrocene-Based Redox-ILs Investigated

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