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Behavior of Ionic Liquids Around Charged Metal Complexes: Investigation of Homogeneous Electron Transfer Reactions Between Metal Complexes in Ionic Liquids

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Abstract

The second-order electron transfer reaction between the photo-excited triplet state of [Zn(TPP)]* (TPP = 5,10,15,20-tetraphenylporphyrin) and [Co(sep)]3+ (sep = sepulchrate = 1,3,6,8,10,13,16,19-octaazabicyclo[6.6.6]eicosane) was investigated in three ionic liquids (ILs, 1-R-3-methylimidazolium bis(trifluoromethylsulfonyl)imide with R = butyl, pentyl, and hexyl) and in acetonitrile. Results of electrochemical and kinetic measurements indicated that ILs dissociate in the vicinity of charged metal complexes and at electrodes, although the dissociated anionic and cationic components of the ILs seem to exist as pairs around the metal complexes. Second-order rate constants for the electron transfer reaction are 1.88 × 109, 3.65 × 107, 2.63 × 107, and 2.01 × 107 kg·mol−1·s−1 in acetonitrile and in the butyl, pentyl and hexyl ILs, respectively, at 298 K, after correction of the contribution of diffusion. The average slope of the plot of the logarithmic second-order rate constants observed in acetonitrile and ILs against the logarithmic viscosity of each solvent was − 0.84. However, the slope of the same plot was much steeper (− 4.1) when data for only the three ILs were used. Detailed analyses of the experimental results on the basis of the Latner–Levin cross relation and the Marcus theory lead to the conclusion that the solvent properties such as the dielectric constant and refractive index around the polarized/charged transition states are different from those for the bulk ILs: observed self-exchange rate constants did not exhibit the Pekar factor dependence when dielectric constants and refractive indices for bulk ILs are used.

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Notes

  1. These reaction curves can be attributed to consecutive reactions:

    \( {\text{A}}_{1} \to {\text{A}}_{2} \to {\text{A}}_{3}.\)

    The absorbance of the reacting solution, A, can be expressed as

    \( A = P\exp({-}k_{1} t) + Q\exp({-}k_{2} t) + R \), where the terms P, Q, and R are functions of the rate constants (k1 and k2), molar absorption coefficients of each species, and the initial concentrations of A1 and A2. This expression is well documented in many textbooks for chemical kinetics such as [49].

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Acknowledgements

We wish to thank JSPS KAKENHI Grant Numbers 16K05865 and 15K05451for financial support.

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Correspondence to Masahiko Inamo or Hideo D. Takagi.

Appendices

Appendix 1

Table 6 presents the Zij values calculated by assuming a couple of plausible dielectric constants εD for ILs as solvents (see text). It is obvious that the diffusion rate constant, ZAA, is very small when cobalt complexes exist in solutions with formal charges. As the inner-sphere activation energy for the [Co(sep)]3+/2+ couple is close to 40 kJ·mol−1, the diffusion controlled rate constant has to be > 1 × 108 kg·mol−1·s−1 to reproduce the exchange rate constant of ca. 5.1 kg·mol−1·s−1. However, the ZAA values are still smaller than 107 kg·mol−1·s−1, even when the charges on the complexes are +1. Therefore, we may safely conclude that the assumption ZAB/ZAA ZBB = 1 is valid and the cobalt complexes are fully associated with the counter anions in ILs (at least the formal charges on either Co(III) or Co(II) complexes are completely cancelled). Note that the pair of a cation and an anion with the charge product of − 3 is almost fully ion paired in solvents with εD < 30 [23].

Table 6 Calculated Zij in kg·mol−1·s−1 by assuming various ionic charges for Co(III) and Zn(TPP) species in ILs and various relative dielectric constants estimated from the Born and MSA equations for different ILs

Appendix 2

Several previous articles offered new ideas concerning the modification of theoretical equations for dielectric properties of ILs on the basis of the non-linear response of solvents [64, 65]. Grampp and co-workers examined these new ideas by applying them to their experimental results for the self-exchange reaction of the TCNE0/·− couple in various ILs, and clearly concluded that none of these theories reproduced their experimental observations [17].

We attempted to re-calculate the values of the Pekar factors for BMIM and HMIM using the experimental results reported by Grampp and co-workers: the outer-sphere activation Gibbs energy for the TCNE0/·− self-exchange reaction was obtained by subtracting the estimated inner-sphere activation energy (3.25 kJ·mol−1) from each total activation energy for the reported second-order rate constants observed in BMIM and HMIM. Grampp and co-workers used an experimentally estimated value of the geometry function, that corresponds to ca. 510 pm for the radii of the TCNE and its anionic radical. As Eq. 15 and therefore the Pekar factor are very sensitive to the radii of reaction pairs, estimated Pekar factors were too large to be rationalized by any theories.

We found the experimentally obtained outer-sphere contribution to the activation Gibbs energies by Grampp and co-workers were reproduced when the radii of these species are 290–320 pm. Moreover, their experimental results are well reproduced when the Pekar factor for the reaction in HMIM is larger than that for the reaction in BMIM. This tendency is consistent with that observed in this study. Therefore, we conclude that modern theories [64, 65] cannot explain the experimental results reported by Grampp and co-workers nor the results obtained in this study. Note that our previous attempt to examine the contribution of the non-linear response of solvents to the outer-sphere electron transfer processes was not successful either, when self-exchange processes of metal complexes were examined in conventional molecular solvents [6].

We presume that the model proposed in this article, which is related to the modification of the solvent properties of ILs in the vicinity of charged precursor/successor complex because of the induced dissociation of ILs, is the most promising at this moment, at least when the classical/semi-classical treatment for the electron transfer reactions are employed [2,3,4].

In 2010 [43], Nakamura and Shikata investigated the dielectric constants of various ILs and found there are three regimes of dielectric relaxations, two of which are in the Debye regime: one corresponds to τ2 in the following equation and was attributed to the rotational relaxation of elongated IL involving free rotation of the cationic component.

$$ \varepsilon^{\prime} = \frac{{\varepsilon_{1} }}{{1 + \overline{\omega }^{2} \tau_{1}^{2} }} + \frac{{\varepsilon_{2} }}{{1 + \overline{\omega }^{2} \tau_{2}^{2} }} + \frac{{\varepsilon_{3} }}{{1 + \overline{\omega }^{2} \tau_{3}^{2} }} + \varepsilon_{\infty }$$
$$ \varepsilon^{\prime\prime} = \frac{{\overline{\omega }\tau_{1} }}{{1 + \overline{\omega }^{2} \tau_{1}^{2} }} + \frac{{\overline{\omega }\tau_{2} }}{{1 + \overline{\omega }^{2} \tau_{2}^{2} }} + \frac{({\overline{\omega }\tau_{3} })^{2-\alpha}}{{1 + \overline{\omega }^{2} \tau_{3}^{2} }} $$

where \( \varepsilon^{\prime} \) and \( \varepsilon^{\prime\prime} \) are the in-phase and the out-of-phase components of dielectric responses, and at the limit of \( \overline{\omega } = 0,\,\varepsilon_{s} = \varepsilon_{1} + \varepsilon_{2} + \varepsilon_{3} + \varepsilon_{\infty } \) (α indicates the slowest response τ3 is in the Cole–Cole regime). Nakamura and Shikata analyzed their results and concluded that (1) in the dissociated pair of ILs cationic components freely rotate and the distance between the cationic and anionic pair depended on the length of the substituents on the cationic component, (2) the dielectric constant of ILs increased with increasing the length of the substituents, and (3) the relaxation time was longer for the ILs with longer substituents on the cationic component for such dissociated pairs.

$$ \frac{1}{{\tau_{\text{av}} }} = \left( {\frac{{\varepsilon_{1} }}{{\varepsilon_{1} + \varepsilon_{2} + \varepsilon_{3} }}} \right)\frac{1}{{\tau_{1} }} + \left( {\frac{{\varepsilon_{2} }}{{\varepsilon_{1} + \varepsilon_{2} + \varepsilon_{3} }}} \right)\frac{1}{{\tau_{2} }} + \left( {\frac{{\varepsilon_{2} }}{{\varepsilon_{1} + \varepsilon_{2} + \varepsilon_{3} }}} \right)\frac{1}{{\tau_{3} }} $$

Although Nakamura and Shikata seem to believe the observed phenomena are related to the properties of the bulk ILs, it is clear that they observed properties of ILs in the vicinity of the electrodes (Israelachvili and co-workers [28] concluded that dissociation of ILs in the bulk is less than 0.1%).

In this study, we observed a similar increase of the dielectric constant in the vicinity of the transition state of homogeneous outer-sphere electron transfer reactions: the increase in the Pekar factor was in the order of the substituents on the imidazolium cation, BMIM < PMIM < HMIM. In addition, we already reported similar dependence of the activation energy on the length of substituents for the homogeneous first-order thermal isomerization reactions of substituted azobenzene with polar transition state [1].

Therefore, it is certain that the distances between the cationic and anionic components of ILs elongate because of the dissociation of ILs in the vicinity of charged/polarized species (in homogeneous solutions), and the dielectric constant of the ILs in the vicinity of charged/polarized species increases with increasing length of the substituents on the imidazolium cation of the ILs.

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Mabe, T., Doseki, F., Yagyu, T. et al. Behavior of Ionic Liquids Around Charged Metal Complexes: Investigation of Homogeneous Electron Transfer Reactions Between Metal Complexes in Ionic Liquids. J Solution Chem 47, 993–1020 (2018). https://doi.org/10.1007/s10953-018-0772-6

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