Cyclic Voltammetric Study of Heterogeneous Electron

Z. Phys. Chem. / DOI 10.1524/zpch.2012.0217 © by Oldenbourg Wissenschaftsverlag, München

Cyclic Voltammetric Study of Heterogeneous Electron Transfer Rate Constants of Various Organic Compounds in Ionic liquids: Measurements at Room Temperature By Noureen Siraj1 , ∗, Günter Grampp2 , Stephan Landgraf2 , and Kraiwan Punyain2 1 2

Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana, USA Institute of Physical and Theoretical Chemistry, Graz University of Technology, Graz, Austria

(Received January 30, 2012; accepted July 21, 2012) (Published online September 24, 2012)

Ionic Liquids / Diffusion Coefficients / Electrochemical Kinetics / Medium Effects / Viscosity Room temperature ionic liquids (RTILs) are of growing interest due to their outstanding solvent properties. The high conductivity and large electrochemical window of RTILs have enabled their use in electrochemistry without adding supporting electrolyte. Heterogeneous electron transfer rate constants (khet ) and diffusion coefficients (D) of ferrocene, 2,6-dimethylbenzoquinone, bromanil, tetracyanoethylene, tetrathiofulvalene, methylviologen, and ethylviologen were determined in several RTILs such as [emim][BF4 ], [bmim][OTf], [bmim][BF4 ] and [bmim][PF6] using cyclic voltammetry. The results obtained for khet and D, range from 0.25–29.6 × 10−4 cm s−1 and 1.27–25.5 × 10−8 cm2 s−1 respectively. Both were significantly lower than those found in organic solvents like acetonitrile (MeCN), dimethylformamide (DMF), etc. It was found that khet and D were two to three orders of magnitude lower in more viscous RTILs. Diffusion coefficients were inversely proportional to the viscosity of the RTILs for all substances under investigation. Marcus theory was applied to compare the khet . The main problem arising is to understand the role of solvent reorganization energy (λo ). Whereas Marcus theory describes λo in two parts of polarization, a fast electronic and a slower orientational contribution both expressed by the Pekar factor γ = (1/n 2 − 1/εs ), the solvent is treated as a continuum having a dielectric constant (εs ) and a refractive index (n). Such a concept seems to be not applicable to ionic liquids.

1. Introduction Room temperature ionic liquids (RTILs) are of growing interest due to their outstanding solvent properties. RTILs are liquids that consist of ions, like molten salts, with freezing points below room temperature and negligible vapour pressures [1]. RTILs are composed of two oppositely charged ions and, in principle, unlimited combinations of cations and anions are possible. Due to the option of varying cations and anions, RTILs * Corresponding author. E-mail: [email protected]

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can be designed to exhibit desired physicochemical properties. RTILs are very promising in the field of electrochemistry because of their unusual properties such as high conductivity, which eliminates the need of supporting electrolyte in electrochemistry. They have excellent chemical and thermal stability as well as wide electrochemical window. Due to these properties, RTILs can act as solvent and conductive media in electrochemical measurements. RTILs are also very popular as alternatives to conventional organic solvents. In the past decades, heterogeneous electrochemical redox reactions of simple inorganic ions [2,3], organic compounds [4,5] and transition metal complexes [6] have been studied in conventional organic solvents. The effect of the solvent on kinetics of heterogeneous electron transfer rate constants (khet ) has received considerable attention for many years [7–11]. In recent years, the number of reports documented on electron transfer reactions in RTILs has increased [12–19]. In this work, four different RTILs: [emim][BF4 ], [bmim][OTf], [bmim][BF4 ] and [bmim][PF6 ], were used to investigate the effect of these media on the heterogeneous electron transfer reactions. These RTILs were selected to observe their change in physicochemical properties by varying the anions, while keeping cations constant or vice versa. This work was conducted to further understand the solvent reorganization energy in ionic liquids. The heterogeneous electron transfer reaction of different organic compounds was studied in the four different RTILs by cyclic voltammetry. Various redox couples, acting either as acceptor (A) or donor (D) systems were examined. The results obtained for heterogeneous electron transfer rate constants in RTILs have been compared with those found in classical organic solvents, like acetonitrile (MeCN), dimethylformamide (DMF) and hexamethylphosphoramide (HMPT). Additionally, the diffusion coefficients were measured in the ionic liquids and also compared with those found in organic solvents. The four ILs of different viscosities were also used to investigate the effect of viscosity on the electrochemical reaction of each compound.

1.1 Heterogeneous electrochemical rate constants According to Marcus, the rate constant for heterogeneous electron transfer, khet , may be written as, −ΔG ∗ khet = κel Z het exp (1) RT where κel is the transmission coefficient (≈ 1 for adiabatic reaction), ΔG ∗ represents the activation energy required for the electron transfer and Z het is the pre-exponential factor.

1.2 The collision model Different models have been described in the literature for the pre-exponential factor (Z het ) of the rate expression [20]. The simple collision model of reactant molecules upon the electrode surface, which is often estimated by kinetic molecular theory, gives: 1/ kB T 2 Z het = (2) 2πm where kB is the Boltzmann constant and m is the reduced mass of the reactant.

Electrochemical Kinetics in RTILs

1.3 The pre-equilibrium model Weaver et al. [20] proposed a pre-equilibrium model for Z het . The pre-equilibrium constant is simply given by the electrode reaction zone thickness, δr (δr is normally assumed as 0.8 Å) that encompasses those molecules that are sufficiently close to the electrode surface and therefore contribute importantly to the observed rate constants. Z het = δrκel νn

(3)

The weighted mean characteristic frequency, νn , is also involved (νn ≈ 5 × 1013 s−1 for organic systems).

1.4 Reorganization energies The free energy of activation, ΔG ∗ , is related to the reorganization parameters λi and λo , neglecting the small resonance energy gap ΔG ∗ =

λi + λo 4

(4)

where λi is the inner sphere reorganization energy and λo is the outer sphere reorganization energy. λi depends upon the bond length changes and the corresponding force constants of the reactants and products. The inner sphere reorganization energy for the totally excited vibrations, λ∞ i , is explained from the classical expression λ∞ i =

f j · f j∗ (Δq j )2 ∗ f + f j j j

(5)

where f j and f j∗ are the force constants of the j-th normal vibration of the neutral molecule and the radical anion respectively. Δq j is the change in bond lengths of bond j, which accompanies the electron transfer reaction. λ∞ i can been determined by a method of quantum chemical calculations which was first introduced by Nelsen et al. [21]. According to this, λ∞ i can be obtained from the relative energies for the conformations of oxidized and reduced species with or without relaxation. The Holstein equation [22] was employed to obtain the corrected value of λi at room temperature. hν j ∞ 4RT λi (T) = λi tanh (6) hν j 4RT The outer sphere reorganization energy, λo , depends upon the solvent properties. If a continuum model for the solvent is used, λo is a function of the dielectric properties of the medium, the distance between the reactant and the electrode surface, and the shape of the reactant. The value of λo may also be estimated on the basis of a dielectric polarization model. For one electron electrode process, λo is given by the well-known Marcus relation, e2o · NL 1 1 λo = ·γ (7) − 8 · π · εo r dhet

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where eo is the elementary charge, N L is Avogadro’s constant and εo is the absolute dielectric constant. The radius of the molecule is denoted by r and dhet is the reaction distance to the electrode surface, which is assumed by Marcus to be 2r based on the classical electro-dynamical picture of a reactant-electrode image interaction. In contrast to this, Hush [23] argues that dhet is larger than 2r since the molecules react in the outer Helmholtz plane. This idea is expressed by dhet → ∞. The Pekar factor, γ , includes the solvent properties and is given by γ=

1 1 − n 2 εs

(8)

where n is the refractive index and εs is the static dielectric constant of the solvent. The main challenge is to understand the role of the solvent reorganization energy, λo , in RTILs because Marcus theory uses a dielectric polarization model based on the dielectric constant and the refractive index of the solvent. Such a polarization concept based on solvent dipoles is not applicable to the charged ions of RTILs acting as solvents. It is not surprising that a theory based on the reorganization of solvent dipoles does not apply to solvents consisting entirely of charged ions. Additionally, the static dielectric constants of RTILs are not measurable by conventional methods because the samples are largely short-circuited by their intrinsic electrical conductance [24,25]. Microwave dielectric relaxation spectroscopy is used to deduce εs values for RTILs. Reported εs values are between 10.0 and 13.2 for various RTILs [24]. Similar results questioning the Marcusian concept of λo are found from ESR-spectroscopic measurements of the homogeneous electron-self exchange rate constants of the MV++ /MV+. redox couple in RTILs [26]. To understand the solvent contribution arising from RTILs, λo is estimated from the current data. However, to determine the correct value of λo , temperature dependent measurements are necessary to obtain values of the different activation energies, ΔG ∗ . Provided the inner sphere reorganization energies, λi , are independent from the solvent, which is normally the case, the solvent contribution can be obtained from these measurements [27]. Such temperature dependent measurements are under investigation in our laboratory.

2. Experimental methods 2.1 Ionic liquids and reagents 1-ethyl-3-methylimidazolium tetrafluoroborate ([emim][BF4 ], 98%), 1-butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF4 ], 99%) and 1-butyl-3-methylimidazolium hexafluorophosphate ([bmim][PF6 ], 99%) were purchased from Io-li-tec (Germany) and 1-butyl-3-methylimidazolium trifluoromethanesulfonate ([bmim][CF3 SO3 ] or [bmim][OTf], 99%) were acquired from Solvent Innovation, Cologne (Germany). The structures of the ionic liquids are given in Fig. 1. The physical properties of RTILs were greatly affected by the presence of even small amounts of moisture [28,29]. Therefore, before using the RTILs, the water content was removed by placing them under high vacuum (5 × 10−5 Torr) for one day at a constant temperature of 60 ◦ C and thereafter kept in a desiccator containing P4 O10 .


Fig. 1. Structures of the RTILs, where R is ethyl in [emim] and butyl in [bmim].

Fig. 2. NIR spectra for [bmim][OTf] with an optical path length of 1 mm. The dotted grey line represents undried and the black solid line is for dried IL.

The water content in the RTILs was assessed by NIR-spectrometry. Water strongly absorbs in the region of 1428 nm and 1920 nm [30]. The recorded spectra for the undried and dried ionic liquids are shown in Fig. 2. Comparing the two spectra, it was clearly realized that after applying high vacuum for one day, water impurity was almost completely removed from the RTILs. The heterogeneous electron transfer reactions of the following compounds were investigated in RTILs. Ferrocene (Fc) (Fluka, 98%), 2,6-dimethylbenzoquinone (2,6DMBQ) (Aldrich, 98%), bromanil (TBBQ) (Merck, 96%), tetracyanoethylene (TCNE) (Aldrich, 98%) and tetrathiofulvalene (TTF) (Fluka, 97%), were purified by vacuum sublimation. Methylviologen (MV2+ ) and ethylviologen (EV2+ ) were recrystallized from ethanol. Methylviologen hexafluorophosphate was prepared from methylviologen dichloride (Fluka, 98%) and sodium hexafluorophosphate in water, to increase the solubility of methylviologen in ionic liquids. A similar procedure was applied for ethylviologen. To avoid moisture uptake, all solutions were prepared under dry argon in dried RTILs using the Schlenck-technique. All experiments were conducted at room temperature of 298 ± 1 K.

2.2 Apparatus Cyclic voltammetric experiments were carried out using a homemade electrochemical cell, depicted in Fig. 3, which was designed for investigations of micro-volume samples

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Fig. 3. Cell design for electrochemical measurements in RTILs at room temperature.

of ionic liquids under argon. This cell was similar to that first described by Compton et al. [31]. All experiments were performed with a three electrode arrangement in one drop of ionic liquid solution. Ag/AgCl or tungsten wire was used as a reference electrode. A glassy carbon rod of 2 mm diameter functioned as a working electrode while a Pt-wire served as a counter electrode. A drop of ionic liquid solution was placed into the cell at the surface of the working electrode, which was surrounded by the Ptwire counter electrode. The reference electrode was in contact with the solution from the upper side of the cell. The measurements were performed using an Autolab/EAs 2 computer-controlled electrochemical system equipped with a potentiostat (model PGSTAT 302N). The software GPES (version 4.9.007) was used for the electrochemical measurements.

2.3 Computational methods The Molden software [32] was utilized for the visualization of the reactant and product structures. The bond angles and bond lengths were measured for the reactant first, and then the changes in bond lengths and bond angles were observed after the electron transfer reaction. The ORCA program [33] was employed for computation. All compounds were optimized to obtain energy values using ORCA program. The single point energy calculation was also done with the same program.


Fig. 4. Bode plot of the uncompensated resistance of the cell arrangement using [bmim][BF4 ], Ru = 160 Ω.

3. Results and discussion 3.1 Cyclic voltammograms Before conducting cyclic voltammetric experiments, iR-drop was estimated in a custom made cell. Several methods were applied to determine the uncompensated resistance, Ru , in this cell arrangement. First, the peak separation potentials, ΔE p , of the ferrocene/ferrocenium couple were measured as a function of the ferrocene concentration within a range of 5.0 × 10−2 M to 5.5 × 10−3 M. The corresponding ΔE p values were constant within 66 to 68 mV. Second, a simple calculation of the resistance, R, based on the geometry of the cell was conducted according to Oelssner [34]: R = [arctan(d/r)]/(2πκr) where r is the radius of the circular working electrode (1 mm), d is the distance between the working electrode and the reference electrode (0.5 mm) and κ is the specific conductivity of the electrolyte solution. For [bmim][BF4 ] (κ = 3.5 mS cm−1 ) [17], the value of R was determined to be 210 Ω. Finally, we estimated the resistance of the cell arrangement experimentally using Bode-plot measurements. The Ru was measured within a frequency range up to 100 kHz. Above 10 kHz, Ru was constant around 160 Ω as observed in Fig. 4. The recorded experimental Ru value was close to the calculated one. Cyclic voltammetric experiments were performed at various scan rates from 0.02 to 0.5 V s−1 . In this work, only the first electrochemical electron transfer step was taken into account, where more than one electron transfer reactions were possible (e.g. MV2+ and EV2+ ), Fig. 5. Experimental cyclic voltammograms were corrected with the computer software GPES (Autolab) using the experimental Ru values. All of the compounds exhibited reversible behaviour in the four different RTILs.

3.2 Formal potentials The formal potentials, E o , were calculated using the average of the cathodic and anodic peak potentials. The E 1/2 is equal to E o when the ratio of diffusion coefficients of the

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Fig. 5. Cyclic voltammograms of (a) EV2+ in [emim][BF4 ] (b) TTF in [bmim][OTf] (c) TCNE in [bmim][PF6 ] and (d) Fc in [bmim][BF4 ] at scan rates of 0.1 Vs−1 at 298 K.

Table 1. Formal potentials in RTILs vs. Ag/AgCl (V). Compounds

[emim][BF4 ]

[bmim][OTf]

[bmim][BF4 ]

[bmim][PF6 ]

Fc TBBQ 2,6-DMBQ TTF MV2+ EV2+ TCNE

0.310 −0.017 −0.561 0.280 −0.516 −0.474 0.235

0.270 – −0.568 0.222 −0.547 −0.539 –

0.313 −0.028 −0.563 – −0.563 −0.557 0.118

0.248 −0.032 – 0.131 −0.597 −0.560 0.109

reduced (DR ) and oxidized (DO ) species is 1. Formal potentials for all compounds are reported in Table 1. Here all values are reported against Ag/AgCl. Recently, Hapiot et al. [35] pointed out that the DR was not equal to DO in ILs for the charge localized radical anions of aromatic nitro compounds, in contrast to charge delocalized radical anions where DR /DO were close to unity. A ratio of DR /DO for the charge delocalized redox couple TMPPD/TMPPD+ (N,N,N ,N tetramethylparaphenylenediamine) was found to be 1.47 in 1-decyl-3-methylimidazoloium bis(trifluoromethylsulfonyl)imide by Compton et al. [36] which led to only a 0.92 fold change in khet based on the root dependence of khet on D. Whereas, a strong inequality by a factor of 30 for the diffusion coefficients was reported by Compton et al. [37] for the O2 /O−2 couple in hexyltriethylammonium bis(trifluoromethylsulfonyl)imide. In view of the literature, there is a possibility of different hydrodynamic radii of oxidized and reduced states of some materials in RTILs which consequently caused the dra-


Fig. 6. TBBQ in [bmim][PF6 ] at different scan rates recorded at 298 K.

matic change in diffusion coefficients. In the current measurements of mainly charge delocalized compounds, minimal differences were observed between the DR and DO . Therefore, it was assumed with a good approximation that the diffusion coefficients of the reduced and the oxidized species were equal, since the radii did not change much upon electron transfer.

3.3 Diffusion coefficients Diffusion coefficients were calculated using the Randles-Sevcik equation. 1/ nF 2 1 1 Ip = 0.4463n F AD /2 Cυ /2 RT

(9)

Here, Ip is the peak current (A), A is the area of the electrode (cm2 ), D is the analyte diffusion coefficient (cm2 s−1 ), C is the analyte concentration (mol cm−3 ) and υ is the scan rate (V s−1 ). Equation (9) is valid if the system is in the planar diffusion regime [38]. Straight lines were obtained by plotting peak currents vs. square root of scan rates, presented in Fig. 6. From the slope of these plots, values of diffusion coefficients were determined. The linearity also confirmed that the heterogeneous electron transfer was reversible and the overall reaction was diffusion controlled in all four investigated RTILs. Additionally, the electron transfer processes were not coupled to any other reactions on this time scale. Recently, Speiser et al. [39] published detailed measurements on the diffusion coefficients of ferrocene showing the consistency of NMR and electrochemical results, in which the utilization of Eq. (9) was explained in detail. The values of the diffusion coefficient obtained in RTILs were two to three orders of magnitude smaller than in conventional organic solvents (e.g. MeCN), as presented in Table 2. This behaviour was similar to other redox couples studied in ionic liquids [12,14,17], which was attributed to the high viscosity of ionic liquids. Viscosity values, η, were reported as 43 cP [44], 64 cP [45], 104 cP [46] and 312 cP [47] for [emim][BF4 ], [bmim][OTf], [bmim][BF4 ] and [bmim][PF6 ], respectively. Unfortunately, various η values were reported for the same ionic liquids [28,45,48,49]. The η values were selected where detailed experimental conditions about the purity of the corresponding ionic liquid were examined. A graph was plotted to confirm the relation

N. Siraj et al. Table 2. Diffusion coefficient (cm2 s−1 ) in RTILs, compared with classical organic solvents at 298 K. Compounds

[emim][BF4 ] D/10−8

[bmim][OTf] D/10−8

[bmim][BF4 ] D/10−8

[bmim][PF6 ] D/10−8

Solvent D/10−5

Fc

25.5

10.7

8.96

2.90

2.37 (MeCN) [4] 1.07 (DMF) [39]

TBBQ

17.9

9.08

6.78

2.04

1.25 (MeCN) [40]

2,6-DMBQ

19.6

8.26

6.89

2.23

2.14 (MeCN) [41] 0.16 (HMPT) [42]

TTF

7.96

17.8

5.22

2.58

2.7 (MeCN) [5] 0.46 (HMPT) [5]

MV2+

4.89

–

2.96

1.27

1.0 (DMF) [43]

2+

EV

15.0

10.8

9.17

2.51

TCNE

7.81

–

–

2.53

Fig. 7. Plot of the diffusion coefficients vs. the inverse viscosity for four different RTILs: (•) TBBQ, () MV2+ , () EV2+ .

between the diffusion coefficients and viscosity, displayed in Fig. 7. This showed the linearity between the diffusion coefficients, D, and inverse viscosity, η.

3.4 Heterogeneous electron transfer rate constants The well-known Nicholson method [50] was applied to calculate the heterogeneous electron transfer rate constants. 1

α

khet = ψ (πn FυD/RT ) /2 (DR /DO ) /2

(10)

Here, n is the number of electrons transferred in the electrode reaction, υ is the scan rate, α is the transfer coefficient (0.5) and ψ is a dimensionless charge transfer parameter related to ΔE p . ψ values for various ΔE p at 25 ◦ C were tabulated by Nicholson [50].

Electrochemical Kinetics in RTILs Table 3. Measured heterogeneous electron transfer rate constants (cm s−1 ) in RTILs in comparison with classical organic solvents. Compounds

[emim][BF4 ] khet /10−4

[bmim][OTf] khet /10−4

[bmim][BF4 ] khet /10−4

[bmim][PF6 ] khet /10−4

Solvent khet

Fc

1.45

2.83

2.67

0.25

2.6 (MeCN) [56]a 0.40(DMF) [56]

TBBQ

13.3

2.80

1.82

1.34

0.3 (MeCN) [40]

2,6-DMBQ

9.48

2.84

8.63

2.15

0.31 (HMPT) [42]

TTF

29.6

8.65

3.47

1.91

2.2 (MeCN) [5] 0.031 (HMPT) [5]

MV2+

6.82

–

2.32

1.66

0.004 (DMF) [57]

EV

9.21

3.18

2.24

1.82

TCNE

7.56

–

–

3.87

2+

a

> 1 (MeCN) [58]

for a critical review of the different published rate constants, see Ref. [11].

However, the application of the original dataset was quite limited and resulted in large ψ values when ΔE p was close to 59 mV. An improvement of this dataset was reported by Heinze [51] using computer calculations of khet , which needed an analytical function: ΔE p = f(ψ). Further attempts of that improvement were published by Parker et al. [52], but with a limited range of application. A much better approximation was reported by Swaddle [53]: ln ψ = 3.69 − 1.16 ln(ΔE p − 59). A detailed analysis [54] of the published datasets [50,51] led to the following equation: ΔE p = A +

B D C + 1 + 1 / Ψ Ψ 2 Ψ /3

(11)

where, A, B, C and D are 81.34 mV, − 3.06 mV, 149 mV and − 145.5 mV at 298 K, respectively. Over a wide range of ΔE p (61 mV ≤ ΔE p ≤ 212 mV), the error in Eq. (11) was less than 0.9 mV, which was comparable with the accuracy of the electrochemical measurements. An error of only 1.58 mV was observed when ΔE p was 60 mV. A similar but mathematically more complex method using hyperplanes was reported by Speiser et al. [55]. It should be taken into account that ΔE p measurements were useful only over a certain range. For ΔE p of 150 mV or more, the cyclic voltammetric peaks became broad and difficult to measure accurately, since the baseline was often sloped. Also, at high scan rates, corrections for double-layer charging currents became necessary [53]. In this paper, Eq. (11) was used. The values obtained for the heterogeneous electron transfer rate constants of the different compounds, Table 3, clearly displayed variations with the viscosity of ILs and were two to three orders of magnitude smaller than conventional organic solvents. Similar results were reported for N,N,N ,N -tetramethylparaphenylenediamine [18] and 2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO) [59]. Hapiot et al. studied several nitro compounds [14], as well as 1,2-dimethoxybenzene and methylated benzenes [60],

N. Siraj et al. Table 4. Calculated inner sphere reorganization energies at 298 K. Compounds

λi /kJ mol−1

Fc0/+ TBBQ0/− 2-6DMBQ0/− TTF0/+ MV2+/+ EV2+/+ TCNE0/−

0.60 11.7 12.7 6.3 13.1 13.6 6.4

which also showed reduced rate constants as compared to classical organic solvents. Various arenes and substituted anthracenes exhibited the same behaviour [13].

3.5 Quantum chemical calculations of the inner sphere reorganization energies The inner sphere reorganization energies, λi , were determined by quantum mechanical calculations. According to the Nelsen method [21], λi is the difference of vertical ionization potential and the electron affinity. The evaluation of geometries and energies through DFT computations were performed by employing the molecular modeling software ORCA [33] with the inclusion of optimization. The DFT method, B3LYP, was used for the calculations of λi . Relative energies for the conformations of oxidized and reduced species with and without relaxation were determined with the basis set TZVPP. These calculated inner sphere reorganization energies represent λ∞ i values. The temperature corrected values, according to Eq. (6) are listed in Table 4. The Molden software [32] was used for the structural visualization of the reactant and product species. 3.6 Discussion Using Eqs. (1), (2) and (4), the outer sphere reorganization energies, λo , can be calculated from the experimental heterogeneous electron transfer rate constants, khet . As an example: for the TBBQo/− couple, the Z het value was obtained as 3 × 103 cm s−1 from Eq. (2) and λi (TBBQo/− ) was calculated as 11.7 kJ/mol, Table 4. The use of Eq. (1) led to an unrealistic λo value of 133 kJ mol−1 , whereas the Marcus relation, equation 7, produced only 38.3 kJ mol−1 . Please note it is well-known that Eq. (7) overestimates λo . The value obtained from the Marcus relation was achieved on the basis of the dielectric polarization model with a deduced dielectric constant of 11.7 [61] and a refractive index of 1.4218 [62] for [bmim][BF4 ]. These results indicated that the classical Marcus relation for λo is not applicable for ILs as solvents due to the use of the Pekar factor. Of course, dielectric constants can be obtained from broadband dielectric spectroscopy, as pointed out in detail by Buchner et al. [63,64]. However, the physical basis using the Pekar factor and the polarization concept expressed by Eq. (7) is questionable if applied to ionic liquids.


It seems that the dielectric polarization method can not be transcribed to ionic liquids. A dipole moment of an ion is an ill-defined quantity [24,65]. The ion charges of the ILs screen the dipole-dipole interactions and can induce charge-ordered structures, leading to a different dielectric environment of the precursor-complex compared to classical organic solvents. All these results indicate that the classical Marcus continuum description for λo is not applicable to ionic liquids as solvents. Of course, the smaller rate constants measured in ILs can also be caused by smaller pre-exponential factors, Z het . Solvent dynamical effects can also lower the khet values [51,63]. In fact, Buchner et al. reported average solvent relaxation times larger than those measured for classical organic solvents [64]. In a series of significant papers, Kobrak et al. [66,67] pointed out that it was dangerous to use classical dipole and dielectric descriptions for ILs. They demonstrated that the use of dipolar description on an ionic charge distribution or the use of the dielectric continuum model for the medium was problematic for fundamental physical reasons [68]. This was in contrast to recent theoretical calculations by R. M. LyndenBell [69,70], which indicated that the outer sphere reorganization energies of ILs should be similar to those calculated from Eq. (7) The obtained λo values from room temperature measurements were not in agreement with the calculated values using the Marcus equation, which suggested that statements by Kobrak about the dielectric constants were appropriate. Activation energies determined from temperature dependent measurements can better explain the λo applicability for ILs acting as solvents. To clarify these findings in a more appropriate manner, temperature dependent measurements of the heterogeneous electron transfer rate constants are under investigation.

4. Conclusions The diffusion coefficients measured in various RTILs were significantly smaller than those obtained in classical organic solvents due to the higher viscosity of ILs. This behaviour was found for both donor and acceptor redox couples. The heterogeneous rate constants of different organic donor and acceptor redox couples were three orders of magnitude smaller in ionic liquids as compared to common organic solvents. The classical Marcus concept of dielectric polarization for the outer sphere reorganization energy based on a continuum approximation was not applicable to the heterogeneous electron transfer reactions in ILs. The classical Pekar factor can not be used for the calculation of the outer sphere reorganization energies in ILs.

Acknowledgement N. S. would like to thank Higher Education Commission (Pakistan) for financial support and A. M. Kelterer for the help in computational work. Financial support from the Austrian-Hungarian Project 76öu2 (Federal Ministry of Education, Science and Culture Vienna, Austria) is also acknowledged.

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