Electron Transport and Counterion Relaxation ... - ACS Publications

J. Phys. Chem. C 2008, 112, 18207–18216

18207

Electron Transport and Counterion Relaxation Dynamics in Neat Ferrocenated Imidazolium Ionic Liquids Wei Wang,† Ramjee Balasubramanian,‡ and Royce W. Murray* Kenan Laboratories of Chemistry, UniVersity of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-3290 ReceiVed: July 11, 2008; ReVised Manuscript ReceiVed: September 3, 2008

The electron transport properties of 12 imidazolium ionic liquids (ILs) in which ferrocene groups have been attached to the imidazolium center by different linkers have been investigated. Cobalticenium is alternatively attached in another ionic liquid. The electron transport is measured in the neat (undiluted) ILs, which are very concentrated and viscous, so that electron transport (“electron diffusion”, DE) occurs by electron selfexchange (hopping) reactions of the Fc+/0 couple. The ionic conductivities are also measured and converted into counterion diffusion coefficients DION assuming that the small counterions (PF6- or BF4-) carry most of the ionic current. Converting the electron diffusion rate into an electron exchange rate constant, kEX gives only an apparent rate constant value, and electron transport is instead demonstrably controlled by the values of DION, as expected from a previously introduced transport model called ion atmosphere relaxation. The fluctuational rate of counterion motions around a donor-acceptor pair governs formation of a precursor complex within which electron transfer takes place. In keeping with the model, values of kEX and DION vary in a parallel fashion, and indeed DE and DION are nearly numerically equal. Activation barriers for ionic conductivity and electron transport are also equal. Log-log plots of kEX vs DION are linear with slopes of one, and all of the imidazolium transport data fall onto a common correlation line. The generality of the ion atmosphere relaxation explanation for electron transport control is shown by a log-log coplot of the imidazolium IL data with previous data for PEG-based ILs, where the results also all fall onto a common correlation line. Introduction Moisture-stable molten salts based on N,N′-dialkylimidazoliums (room-temperature ionic liquids, abbrev. ILs)1,2 offer attractive physical and chemical properties,2 including good stability, negligible vapor pressure, and solubility of a wide range of organic and inorganic compounds. They are experiencing investigation for uses as solvent media in organic synthesis,3 catalysis,4 separations,5 photochemistry,6 and electrochemistry.7-11 In electrochemistry, they offer intrinsic ionic conductivity and a spacious potential window (∼4 V) and have been studied, for example, in the contexts of electrodeposition,8 solar cells,9 and electrical devices.10 A recent review11 on electrochemistry cites 276 publications. Most electrochemical investigations7-11 of ILs have used them as solvents for dilute solutions of redox species, and some have used ILs as electrolyte media covering a film of redox material on a solid electrode surface.7 There also exist ILs that are intrinsically electroactive, where the redox species may be a counterion of the imidazolium cation (notably iodide)12 or a pendant group on an N-alkylimidazolium side chain.13 It is possible to study the IL electroactivity in the undiluted (neat) molten salt form. This paper follows our recent preliminary description13 of the latter experiment with a fuller description of electron transport dynamics and related properties of imidazolium ionic liquids containing pendant ferrocene (and in one case, cobalticenium) redox entities. The three sets of synthesized13 ferrocenated imidazolium ILs (and one containing * Corresponding author. E-mail: [email protected]. † Present address: Total Petrochemicals, La Porte, Texas 77571. ‡ Present address: Departments of Chemistry and Biochemistry, Old Dominion University, Norfolk, Virginia 23529.

cobalticenium) listed in Table 1 include ILs with alkylester, alkyl, and ethylene oxide linkers (IL #1-3, respectively) between ferrocene and the imidazolium cation, either methyl or butyl as the other imidazolium substituent, and either BF4or PF6- counterions. IL #4 is the same as IL #1 except that it contains cobalticenium instead of ferrocene. The redox site concentrations in the ferrocenated imidazolium ILs are large (2∼3 M), and their densities are higher and fluidities and ionic conductivities much lower, as compared to analogous nonredox ILs (such as 1-butyl-3-methyl imidazolium hexafluorophosphate, [BMI][PF6] salt). We have a long-standing interest in molecular design and properties of such redox semisolids and in study of the hopping-based electron transport dynamics within them.14-19 We have shown that redox melts based on synthetic combinations of a redox moiety14-17 with short poly(ethylene) glycol (PEG) chains are, without exception, viscous, amorphous room-temperature melts. The redox structures include metal polypyridine complexes,14 cobalticenium,17 Au nanoparticles,18 and a liquid form of DNA.15 The large concentrations of redox sites and the low fluidities of these ionically conductive materials favor electron transport mainly by electron hopping reactions, as opposed to simple physical diffusion (DPHYS) of the redox site. The rates of electron hopping can be determined as “electron diffusion coefficients” (DE) by chronoamperometry at microelectrodes placed in the undiluted redox IL. We have established that the DE values parallel those of the diffusion coefficients of the melt counterions (DION), over orders of magnitude of variation of each caused by manipulation of temperature or plasticization. We have formulated a model, termed counterion relaxation dynamics, in which the rate of electron transport is controlled by the physical rate of fluctua-

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TABLE 1: Structure and Physical Properties of Ferrocene and Cobalticenium Imidazolium ILs

IL no. #1, Fc

linkera

side chain

-CO2-C3-

-Me

-CO2-C6-

-Me

-CO2-C11-

-Me

-CO2-C3-

-Bu

-CO2-C6-

-Bu

-CO2-C11-

-Bu

-C4-

-Me

-C4-

-Bu

-C6-

-Bu

#3, Fc

-CO2-C2OC2-

#4, CoCp2

-CO2-C3-CO2-C6-CO2-C6-

-Me -Bu -C2OMe

#2, Fc

a

-Bu

MW

D

Cb

Vmc

anion, X-

g · mol-1

g · cm-3 (25 °C)

M

cm3 · mol-1

[PF6] [BF4] [PF6] [BF4] [PF6] [BF4] [PF6] [BF4] [PF6] [BF4] [PF6] [BF4] [PF6] [BF4] [PF6] [BF4] [PF6] [BF4] [PF6] [PF6] [PF6] [PF6] 2[PF6]

498 440 540 482 610 552 540 482 582 524 652 594 468 410 510 452 538 480 528 570 542 584 730

1.49 1.37 1.47 1.36 1.29 1.23 1.44 1.34 1.39 1.39 1.28 1.18 1.45 1.36 1.36 1.29 1.32 1.26 1.47 1.43 1.45 1.35 1.43

2.93 3.11 2.71 2.83 2.12 2.23 2.67 2.79 2.39 2.65 1.97 1.99 3.10 3.31 2.67 2.86 2.46 2.62 2.78 2.51 2.68 2.31 1.96

342 322 369 353 472 448 375 358 418 377 508 503 322 302 375 350 407 382 360 398 373 433 510

CO2 ) ester; Cx ) alkyl chain; C2O ) CH2CH2O. b Molar concentration calculated from density. c Molecular volume.

tional counterion diffusion.18,19 While this model explains the electron transport rates in PEG-based redox ILs, a crucial test of its generality is to observe it in electron transport in chemically disparate materials, such as imidazolium redox ILs. The present work successfully applies the counterion relaxation dynamics model to the ferrocenated imidazolium ILs of Table 1 and offers a more detailed analysis of charge transport in such redox ILs than in the previous work.12,13 The ferrocenated imidazolium ILs are well suited to the counterion relaxation model by having, like the PEG-based redox melts, high redox concentrations (which favors electron hopping, a bimolecular event in the mixed valent layer electrogenerated at the electrode interphase), low fluidities (which depresses values of DPHYS), and low ionic conductivities. The latter attribute at the same time of course makes voltammetry in the neat redox IL more demanding. The rates of electron transport (i.e., DE) and counterion diffusion (i.e., DION) in the ferrocenated ILs are varied over a ∼103-fold range by alterations in the IL structure and counterion (Table 1), by manipulating the melt temperature and by sorption of CO2 gas as a plasticizer. Rates of physical diffusion (DPHYS) are shown to be small, in comparison to electron diffusion, by use of a dilute solution of the cobalticenium IL #4, as a mimic diffusant, in a ferrocenated IL. We find that, throughout, measured values of DE and DION, and their thermal activation barrier energies, lie near one another for both the ferrocene and the cobalticenium imidazolium ILs, as predicted18,19 by the counterion relaxation model. As a consequence, values of electron exchange rate constants for the ferrocene1+/0 reaction which can be calculated from DE are only apparent rates and do not reflect the intrinsic electron transfer dynamics of the ferrocene itself. These apparent values of kEX parallel those of the counterions DION, irrespective of variations in IL linker and side-chain structure (Table 1), counterion, temperature, and plasticizer, and in fact, we show that they

correlate very well with analogous results obtained in PEGbased redox melts, over a range of different redox centers. We also describe density and viscosity properties of the redox IL that in turn influence values of DION and thus charge transport rates. Experimental Chemical and Reagents. All chemicals and solvents were used as received. Synthesis. Synthesis and characterization of the ferrocenated dialkylimidazolium ILs was reported earlier13 (see also Supporting Information in ref 13). Details on the synthesis and characterization of [Cp2Co-CO2-C6-Im-Bu][PF6]2 are found in the Supporting Information of this paper. The cyclic voltammetry of the redox groups was clean and without extraneous electrochemical features (see later Figure 1). UV-Vis Spectra. UV-vis spectra of dilute CH2Cl2 solution of ferrocenated ILs were obtained with a Shimadzu UV-1601 spectrometer with reference to the blank solvent. These spectra display absorbance features at ca. 440 and 320 nm, characteristic of ferrocene. Absorbance at ca. 620 nm, symptomatic of its oxidation, was absent in the synthetic products. Data on absorbance coefficients (at ca. 440 nm) are found in the Supporting Information (Table S-1). Densities. Room-temperature densities were obtained by syringing (using a syringe fitted with an adapter) known volumes of the viscous sample redox ILs (with warming as necessary) into preweighed 1 µL capillaries (Drummond MicroCaps). Viscosities. Viscosities of selected ILs were measured using a cone-plate rheometer (Brookfield digital viscometer, model DV3, CP52 cone), at varied temperatures (RTE-140 NesLab circulator) allowing at least one hour for thermal equilibration at each temperature. Viscosity at each temperature was measured at a series of spin rates (shear rate).

Electron Transport in Ferrocenated Imidazolium ILs

J. Phys. Chem. C, Vol. 112, No. 46, 2008 18209 s) of undiluted [Fc-CO2-C6-Im-C2OMe][PF6] at 75 °C was done by comparison to simulated voltammograms (DigiElch2 (http://www.digielch.de, copyright by M. Rudolph). The results show that the experimental peak separation is dominated by iRUNC distortion as opposed to heterogeneous rate constant effects. Results and Discussion The essential feature of electrochemically measuring electron hopping transport rates is the determination of an apparent diffusion coefficient (DAPP) for electron transport to the working electrodesthrough the electrogenerated mixed valent working electrode’s interphasesunder circumstances in which DAPP is influenced more by the rate of electron hopping (e.g., DE) than by actual reactant physical diffusion (DPHYS). The relevant equation is20

Figure 1. Cyclic voltammetry (50 mV/s) of ferrocenated imidazoliums and (for comparison) ferrocene (black) in dilute methylene chloride solutions and of cobalticenium imidazolium in dilute acetone solution, using 0.2 M Bu4NClO4 as supporting electrolyte. The molar concentrations are 1.6, 1.2, 0.9, and 0.7 mM for [Fc-CO2-C6-Im-Me][PF6] (red), [Fc-CO2-C2OC2-Im-Me][PF6] (green), [Fc-C6-Im-Me][PF6] (blue), and [Co(Cp)2-CO2-C6-Im-Bu][PF6]2 (pink), respectively.

Voltammetry in Dilute Solutions. Cyclic voltammetry was performed in degassed CH2Cl2/0.2 M Bu4NClO4 (Fluka) using 1.6 mm diameter Pt disk working, Pt coil counter and aqueous Ag/AgCl/0.1 M NaCl reference electrodes, and a CH Instruments Electrochemical Workstation. Electrochemistry in Undiluted Ionic Liquids. Cyclic voltammetry and chronoamperometry in undiluted ILs was done as previously described for redox polyether hybrids.19 Briefly, ca. 10 mg of IL is drop-cast onto a small, polished insulating platform in which the tips of wire electrodes are exposed: a 25 µm diameter Pt microdisk working electrode, a Ag wire for quasi-reference electrode (Ag QRE), and two 0.4 mm diameter Pt disk electrodes (one serves as the counter electrode in voltammetry; the pair is used in measuring ionic conductivity). The cylindrical electrode assembly is potted (epoxy resin) into a short length of 1/4 in. stainless steel tube. Each redox IL sample was dried at 75 °C in vacuum for at least 12 h prior to voltammetry, which was typically performed in active vacuum. For voltammetry at differing temperatures, the IL droplet and entire cell enclosure are equilibrated at each temperature for at least 2 h. The electrochemical cell is in a Faraday cage. Ionic conductivities were measured by AC impedance (0.1 Hz to 100 kHz, 0 V dc bias, 50 mV amplitude) using the abovementioned pair of 0.4 mm diameter Pt disk electrodes. Melt resistance was taken from the low-frequency real-axis intercept of the complex impedance semicircle in Nyquist plots, with IL ionic conductivities calculated using a geometric cell constant determined with standard solutions. Measurements on redox ILs under CO2 pressure were taken in a homemade cylindrical stainless steel pressure cell (the electrode assembly faces up) with two sapphire windows. The CO2 gas was introduced using a syringe pump (model 260 D, Isco) monitoring the pressure with a pressure transducer (model TJE AP121DV, Sensotec) and controlling the temperature of the pressure cell with a water jacket connected to a Neslab RTE110 circulator. Temperature within the pressure cell is monitored with a thermocouple, and ILs are equilibrated for at least 2 h prior at each CO2 pressure and temperature. Digital Simulations. Analysis of iRUNC effects (RUNC ) uncompensated resistance) on cyclic voltammograms (10 mV/

kEXδ2C DAPP ) DPHYS + DE ) DPHYS + 6

(1)

where δ is the average equilibrium center-to-center distance between neighboring redox sites and C is the total concentration of redox sites. DPHYS is assessed using a diffusant mimic (cobalticenium) of the ferrocene imidazolium IL reactant, as discussed later and in the Supporting Information. Our interpretation of values of DE as being controlled by counterion relaxation dynamics means that values of counterion diffusion coefficients, DION, must also be measured in the redox IL for comparison to DE. Measurements of DION are discussed next. Ionic Conductivity. Ionic conductivities (σION) of the ferrocenated imidazolium ILs, measured by ac impedance from 25 to 75 °C, are listed for 75 °C in Table 2. As in previous work in PEG-based melts, the DION coefficients were calculated from σION using the Nernst-Einstein equation14b,21

σION )

F2 2 F2ZC 2 DIONCION] ) [zIMDIMCIM + zION [DIM + RT RT DION] (2)

where z, D, and C are charge, physical diffusion coefficient, and concentration of the indicated species (IM ) the ferrocenated imidazolium ion). Assuming14b,c that ionic conductivities are dominated by mobilities of the smaller counterions (i.e., DIM , DION) produces results for DION as listed in Table 2. The temperature dependencies of DION values yield linear Arrhenius plots (Figure S-1, see Supporting Information), the slopes of which give activation barrier energies for counterion diffusion as shown in Table 2. These barrier energies are rather large but, as seen below, largely match those found for electron hopping. The relation of the DION data to IL viscosity is discussed later. Dilute Solution Voltammetry of Redox ILs. Examples of dilute solution CVs of the ferrocenated and cobalticenium imidazolium ILs, and that of ferrocene itself, are shown in Figure 1. These CVs serve to demonstrate electrochemical purity of the synthesized ILs and are otherwise unremarkable, showing single, well-defined Fc+1/0 and Co(Cp)2+1/0 redox waves. The formal potentials for the ferrocenes with alkyl linkages are ca. -0.05 V relative to ferrocene, and those with ester linkages are ca. +0.2 V relative to ferrocene, typical of ferrocene bearing these substituents. The CV ∆EPEAK values exceed the ideal 59 mV, demonstrably because of iRUNC effects (see Supporting Information, Figure S-2). Voltammetry in Undiluted Redox Ionic Liquids. The σION ionic conductivities of the redox ILs (Table 2) are small, so it

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TABLE 2: Physical Transport and Electron-Transfer Results (75°C) for Various Ferrocene and Cobalticenium Imidazolium Ionic Liquids σ 10 S · cm (75 °C) -6

no. 1

cation [Fc-CO2-C3-Im-Me] [Fc-CO2-C6-Im-Me] [Fc-CO2-C11-Im-Me] [Fc-CO2-C3-Im-Bu] [Fc-CO2-C6-Im-Bu] [Fc-CO2-C11-Im-Bu]

2

[Fc-C4-Im-Me] [Fc-C4-Im-Bu] [Fc-C6-Im-Bu]

3

[Fc-CO2-C2OC2-Im-Me] [Fc-CO2-C2OC2-Im-Bu] [Fc-CO2-C3-Im-C2OMe] [Fc-CO2-C6-Im-C2OMe] [Co(Cp)2-CO2-C6-Im-Bu]

4 a

anion [PF6] [BF4] [PF6] [BF4] [PF6] [BF4] [PF6] [BF4] [PF6] [BF4] [PF6] [BF4] [PF6] [BF4] [PF6] [BF4] [PF6] [BF4] [PF6] [PF6] [PF6] [PF6] 2[PF6]

0.49 0.25 1.7 0.41 14 7.3 0.13 0.036 5.1 3.3 13 12 9.9 28 17 24 39 18 8.7 11 1.3 4.6 2.7

DION -1

10 cm · s (75 °C) -9

2

0.052 0.024 0.19 0.047 2.0 1.0 0.015 0.0040 0.66 0.38 2.1 1.8 0.99 2.7 1.9 2.6 5.0 2.1 0.97 1.4 0.15 0.62 0.22

EA,ION -1

kJ · mol-1 109 121 100 105 70 67 115 122 75 80 60 60 65 61 53 63 58 52 98 83 115 81 81

DAPP cm · s (75 °C)

10-8

2

EA,EX -1

kJ · mol-1

iRa iR iR iR 1.5 n/a iR iR 0.63 0.61 1.7 1.0 8.5 10 5.4 13 25 4.3 iR 2.7 iR 1.7 2.2

------------67 n/a ------76 80 68 75 58 44 51 56 56 43 ---75 ---73 70

kEX 106

-1 -1

M s (75 °C) ------------4.9 n/a ------2.0 1.9 5.7 3.3 25 30 17 39 79 13 ---8.5 ---5.6 7.4

DE,CORR 10 cm · s (75 °C) -8

2

------------0.89 n/a ------0.34 0.23 0.97 0.64 0.81 2.0 1.4 2.0 3.5 1.4 ---0.92 ---0.42 0.23

EA,EX,CORR

kEX,CORR

kJ · mol-1

106M-1s-1 (75 °C)

------------68 n/a ------75 80 65 72 64 60 53 63 58 50 ---82 ---80 81

------------3.0 n/a ------1.1 0.71 3.3 2.2 2.4 5.6 4.2 6.0 11 4.2 ---2.9 ---1.4 0.77

-1

Chronoamperometric measurements not available due to the severe iRUNC distortion.

Figure 3. Microelectrode cyclic voltammetry (12.5 µm Pt disk electrode, in vacuum, 10 mV/s) of undiluted ferrocenated imidazolium ionic liquids: [Fc-CO2-C6-Im-Bu] (blue), [Fc-C6-Im-Bu] (red), [FcCO2-C2OC2-Im-Bu] (green), and [Co(Cp)2-CO2-C6-Im-Bu][PF6]2 (black, 5 mV/s), all at 75 °C.

Figure 2. Microelectrode cyclic voltammetry (12.5 µm Pt disk electrode, in vacuum) of undiluted ferrocenated imidazolium, [Fc-CO2C6-Im-C2OMe][PF6], at (a) varied temperatures (10 mV/s) and (b) different scan rates (75 °C).

is unsurprising that the Fc+1/0 CV waves seen in undiluted ferrocenated imidazolium ionic liquids (Figure 2) are substantially distorted (large ∆EPEAK) by uncompensated resistance effects. Figure 2 shows examples at varied potential scan rates

and temperatures for [Fc-CO2-C6-Im-C2OMe][PF6], and Figure 3 shows further CV examples of undiluted ferrocenated and cobalticenium imidazolium ILs. The three ferrocenated imidazolium IL CVs shown represent behavior typical of the three IL structure designs (Table 1). As expected, the degrees of iRUNC distortion scale with the σION results of Table 2. Several criteria were brought to bear to show that ∆EPEAK separations in Figures 2 and 3 result from iRUNC as opposed to a slow heterogeneous electron transfer rate constant kS for the Fc1+/0 reaction. First, comparison of experimental and simulated ∆EPEAK separations (Figure S-3, see Supporting Information) shows that the ∆EPEAK distortions are fully accountable by uncompensated resistance effects and are not simulated even by adjusting kS to unrealistically small values. Second, σION ) 4.6 × 10-6 S · cm-1 (75 °C) measured for the ferrocenated IL in Figure 2a gives RUNC ) 1.4 × 107 Ω and thereby a simulated ∆EPEAK ≈ 424 mV22c that differs from the experimental 498 mV result (Figure 2a) by 74 mV. The Nernstian expectation

Electron Transport in Ferrocenated Imidazolium ILs

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TABLE 3: Physical transport and electron-transfer results (25°C) for selected ferrocenated imidazolium ionic liquids: [Fc-CO2-C6-Im-Bu][PF6], [Fc-C6-Im-Bu][PF6], and [Fc-CO2-C2OC2-Im-Bu][PF6] ionic liquid DION (25 °C)/cm · s EA,ION/kJ · mol-1 DAPP (25 °C)/cm2 · s-1 kEX (25 °C)/M-1s-1 EA,EX/kJ · mol-1 DE,CORR (25 °C)/cm2 · s-1 kEX,CORR (25 °C)/M-1s-1 EA,EX,CORR/kJ · mol-1 2

-1

[Fc-CO2-C6-Im-Bu]

[Fc-C6-Im-Bu]

[Fc-CO2-C2OC2-Im-Bu]

8.4 × 75 7.5 × 10-11 2.4 × 104 76 4.2 × 10-11 1.3 × 104 75

1.7 × 58 1.0 × 10-8 3.2 × 106 56 1.2 × 10-9 3.7 × 105 58

9.9 × 10-12 83 3.6 × 10-10 1.2 × 105 75 7.4 × 10-11 2.3 × 104 82

10-12

(at 75 °C) for a reversible one electron electrochemical reaction is a very similar 69 mV.22a Previous charge transport studies in PEG-based ILs have shown that chronoamperometric19 DAPP measurements with microelectrodes can ameliorate effects of large RUNC values (even up to Gohms14e) because the diffusion time constants are even larger than the cell charging time constants. As previously, potential steps are made from a non-Faradaic region more negative than the ferrocene wave to somewhat beyond what is needed to attain the diffusion-limited region of the redox wave, and currents are recorded for 300-500 s. The slopes of current vs 1/t1/2 Cottrell plots22a (examples in Supporting Information, Figure S-4) gave DAPP values as listed in Tables 2 and 3 for, respectively, experiments at 75 and 25 °C. Their temperature dependences gave linear Arrhenius plots (Figure S-1, see Supporting Information) and activation barrier energies EA,EX as given in Tables 2 and 3. The above procedure yields, according to eq 1, an overall charge transport coefficient DAPP that contains contributions from both the rates of electron hopping (self-exchange, DE) in the redox IL couple and from its own physical diffusion (DPHYS). In previous work in PEG-based redox ILs, we have employed14 an isostructural version of the IL with a redox couple whose electron transfers are kinetically very slow in comparison to the studied redox couple (such as a CoIII/II polypyridine couple, relative to a CoII/I one). A second approach was used here, namely to dissolve a low concentration of an IL isostructural with the ferrocenated imidazolium IL (i.e., cobalticenium imidazolium IL# 4, [Cp2Co-CO2-C6-Im-Bu][PF6]2), in the ferrocenated imidazolium IL. The cobalticenium imidazolium IL concentration (10 mol %) is well below any reasonable percolation threshold (50% for a rigid matrix), so that electron transport by Cp2Co1+/0 electron hopping should not be significant. The results show by comparison of Cp2Co1+/0 and Fc1+/0 currents (see Supporting Information, Figure S-5, and associated discussion of Cobalticenium Surrogate Experiments) that the concentration normalized ratio DPHYS/DAPP is, at most, ∼ 0.1. The ferrocenated imidazolium IL chosen for this comparison was, according to its DAPP, DION, and activation barrier energy parameters, more or less typical of those in Table 2. On the basis of the above, we assume in eq 1 that DAPP ≈ DE generally and neglect DPHYS when calculating the electron diffusion coefficient and kEX results given in Tables 2 and 3. That is, DAPP in Tables 2 and 3 equals DE. A further factor to consider when extracting electron hopping rate constants from DAPP and DE measurements is electronic migration, an effect that is present since the initially measured DE electron diffusion coefficients are larger than, or comparable to, the counterion diffusion coefficients (DION). According to the theory,23 when the ratio DION/DE e 1, electroneutrality coupling occurs between electron hopping between localized redox sites and (slower) displacements of electroinactive counterions and induces a “migration” enhancement of the charge

10-10

transport (i.e., current). The sluggish counterion mobility yields an electric field gradient in the sample that assists the rate of electron hopping, producing an overestimation of the true value of DE. This correction has been applied previously in PEGbased ILs14-17 and was discussed in refs 14c and d. Correcting for electronic migration23 decreases the Table 2 and 3 electron diffusion coefficients by ca. 2- to 10-fold; these and the corresponding electron hopping rate constants are listed as DE,CORR and kEX,CORR values. Applying this correction to varied temperature data causes only minor changes in the thermal activation energy barrier values (see EA,EX,CORR). Table 3 shows that kEX,CORR values at 25 °C in ferrocenated imidazolium ILs are in the range of 104 to 105 M-1s-1. For comparison, the ferrocene+1/0 self-exchange rate constant in dilute acetonitrile solution is much faster: kEX ∼ 107 M-1s-1.24 In contrast, kEX,CORR in the Fc imidazolium ILs resembles those observed in dry, mixed valent poly(vinylferrocene) films (in N2 atmosphere), which range from 6 × 104 to 4 × 105 M-1s-1.25 The smaller electron hopping rate constants in Fc imidazolium ILs also reflect their relatively large thermal activation energy barriers. Like PEGbased ILs, electron hopping rate constants in the semisolid ILs are consistently smaller than those for the analogous, freely diffusing donor/acceptor pairs in dilute solutions. Ion Atmosphere Relaxation-Controlled Electron Transport. Previous electron transport studies in various redox semisolids, from PEG-based metal complex melts19 to PEGbased Au nanoparticle melts,18 have led to a model for control of electron transfer rates called “ion atmosphere relaxation”. In this model, the effective electron transport rate (detectable by electrode current flow) is controlled by the diffusive relaxation, or reorganization, of counterions around the electron donoracceptor pair. The essential ideas of this model come from an analysis of the effects of ion pairing on electron transfer rates.26 Inasmuch as highly concentrated redox ILs (containing no “solvent”) are intrinsically “ion paired”, we adopted the following scheme, which can be written (case I of ref 26) in the context of the Fc+1/0 reaction as k1

k2

X-Fc+1Fc0 y\z X-Fc0Fc+1 98 Fc0Fc+1X-

(3)

k-1

where the forward electron transfer reaction (k1) is followed by the relaxation of counterions (k2), which occurs in competition with the back electron transfer (k-1). In this representation, the effective oVerall rate constant (kEX), assuming a steady-state condition, is given by

kEX )

k1k2 k2 + k-1

(4)

The reorganization of counterions (k2) can be represented as diffusion over a distance “a” to relieve a Coulombic imbalance induced by the electron transfer26

18212 J. Phys. Chem. C, Vol. 112, No. 46, 2008

( 2aπ )

k2 ) DION

2

Wang et al.

(5)

These relations indicate that if counterion diffusion is much faster than the electron transfer reaction (k-1 , k2), kEX should reflect the intrinsic electron transfer dynamics (k1), but if k1 . k2, then kEX becomes controlled by the rearrangements of counterions and reflects the dynamics of their diffusion and not that intrinsic for the electron transfer reactions. Another, probably more realistic, view of the ion atmosphere relaxation process is that it is not a two-step process as in eq 3 but is instead a fluctuational counterion reorganization (Case III of ref 26).

X-Fc1+Fc0 f

〈[

] [

Fc1+Fc0 Fc0Fc1+ S XX-

]〉

#

fFc0Fc1+X-

(6) in which the rate of diffusive fluctuations of counterion positions over an activation distance of x+ govern formation of a precursor complex () within which electron transfer takes place, followed by diffusive reorganization of the Xatmosphere to a Coulombically more favorable environment. The fluctuational view transforms the counterion motion into the actual reaction coordinate. It is difficult, we think, to defend the two- vs one-step models based on the experimental evidenceseither yields a scenario of overall rate control by counterion diffusion ratessbut the fluctuational view (eq 6) is more akin to basic concepts of activation in electron transfer chemistry. In either case, the value of kEX reflects the dynamics of counterion motion and of electron transport, not that of the intrinsic electron transfer (self-exchange) dynamics. The experimental predictions of the above dynamics model are that: (a) values of the electron hopping diffusion coefficient DE,CORR and counterion diffusion coefficient DION should be numerically equalsproducing a log-log plot with slope of unity, (b) similarly, values of the activation barrier energies for electron hopping EA,CORR and counterion diffusion EION should be numerically equal, and (c) all redox couples whose electron transport rates are controlled by counterion diffusion should lie on a common log-log plot line, with unity slope. These predictions assume that measurements of values of DION based on bulk, macroscopic transport counterion motions (as in ac impedance experiments) faithfully represent the counterion dynamics over more microscopic distances as in the fluctuational model of eq 6. The results of Tables 2 and 3, over a variety of ferrocenated imidazolium IL structures, are in strong agreement with the preceding predictions. The diffusion coefficient DE,CORR and counterion diffusion coefficient DION data in Table 2 (75 °C) differ numerically by less than a factor of 2-fold, for the 13 ferrocenated imidazolium ILs (with one exceptionsfactor of 3-fold) and one cobalticenium imidazolium ILs. The numerical agreement in Table 3 (at 25 °C, a more demanding experimental domain) is not as good, a ∼7-fold numerical offset appears. Also in Table 2, the activation barrier energies EA,CORR and EION for all (except one) of the redox ILs lie within 2 kJ/mol of one another. Further from Table 2, the Figure 4a log-log plots of kEX,CORR (derived from DE,CORR) vs DION for all of the ferrocenated and cobalticenium imidazolium ILs fall very nearly on the same line, and for 10 of the 12 data sets, the kEX,CORR vs DION correlation (in terms of r2) is within 3% of a unity log-log slope (see figure legend). In these plots, the changes in kEX,CORR and DION for each specific IL are caused by changes in the IL temperature.

Figure 4. (a) Linear log-log relationship between DION and kEX for Fc+1/0 electron transport in undiluted ferrocenated imidazolium ionic liquids and Co(Cp)20/-1 electron transfer reaction in undiluted cobalticenium imidazolium ionic liquid over a range of temperatures in vacuum. The ionic liquids include [Fc-CO2-C11-Im-Me][PF6] (pink b), [Fc-CO2-C6-Im-Bu][PF6] (pink 9), [Fc-CO2-C6-Im-Bu][BF4] (pink 2), [Fc-CO2-C11-Im-Bu][PF6] (pink 1), [Fc-CO2-C11-Im-Bu][BF4] (pink (), [Fc-C4-Im-Me][PF6] (red b), [Fc-C4-Im-Me][BF4] (red 9), [Fc-C4-Im-Bu][PF6] (red 2), [Fc-C4-Im-Bu][BF4] (red 1), [Fc-C6-ImBu][PF6] (red (), [Fc-C6-Im-Bu][BF4] (red b), [Fc-CO2-C2OC2-ImBu][PF6] (green b), [Fc-CO2-C6-Im-C2OMe][PF6] (green 9), and [Co(Cp)2-CO2-C6-Im-Bu][PF6]2 (blue 2). The slopes of linear correlation in the plot are 0.97, 1.01, 1.03, 1.08, 1.27, 0.99, 0.97, 0.99, 0.99, 1.01, 0.96, 0.98, 0.98, and 0.97, respectively. (b) The data in (a) coplotted with literature data from CO2 plasticized melts, [Co(phen)3](MePEG350SO3)219b (3) and [Co(bpy(CO2MePEG350)2)3](ClO4)219a (1), MePEG350 plasticized melt [Co(phen)3](MePEG350SO3)219c in mole a ratio of 6:1 (O), 3:1 (0), and 2:1 (4), and [Co(bpy(CO2MePEG350)2)3](ClO4)2 + xLiClO414b (9) (x ) 0∼1.31), [Ru(bpy(CH2MePEG350)2)2](CN)2 plasticized with CO2 (over a range of temperatures)19d (b), [Ru(bpy(CO2MePEG350)2)3][X]2, where X- ) ClO4- or a mixture of ClO4- and I-(+),19e [Cp2Co](MePEG350SO3) melt (neat, MePEG350 plasticized or mixed with [FcTMA]+)41,36 (2), and Au25 nanoparticle polyether molten salts (().18 The overall slope for the linear correlation is 1.0.

The results for the Figure 4a imidazolium-based redox ILs are not unique, and analogous agreement has been seen with the counterion relaxation model for redox polyether ILs.18,19 Figure 4b shows the present data coplotted with previous results for 10 different PEG-based ILs (which we have also called hybrid redox polyether melts), where transport rates were varied by both temperature changes and small molecule plasticization. The 22 sets of data, taken by multiple laboratory members over a period of years, distribute around a common fitting line with a slope of 1.0. The earlier data include redox couples of ferrocene, cobalticenium, Ru(III/II), and Co(II/I)

Electron Transport in Ferrocenated Imidazolium ILs

J. Phys. Chem. C, Vol. 112, No. 46, 2008 18213 TABLE 4: Physical Transport and Electron-Transfer Results for [Fc-CO2-C3-Im-Me][PF6] Ionic Liquid in High-Pressure CO2

Figure 5. Microelectrode cyclic voltammogram (10 mV/s) of undiluted ferrocenated imidazolium ionic liquids, [Fc-CO2-C3-Im-Me][PF6], at 65 °C on a 12.5 µm Pt disk electrode in vacuum and different CO2 pressure.

polypyridine complexes and a Au250/1- nanoparticle. The selfexchange rate constants for these redox couples in dilute fluid solution widely differ one from another and exceed the values of kEX,CORR in Table 3, reflective of the common, leveling control of reaction rate by counterion fluctuational reorganization as in eq 6. In regard to the intercepts in Figure 4b, assuming that KEQ ) k1/k-1 ) 1, the common intercept seen for most of the redox systems (having different dimensions and concentrations), suggests that the reorganizational diffusive length x+ (or “a”) is not very sensitive to the average redox center-to-center (for ferrocene, 8∼9 Å; for metal complex polyethers, 15∼17 Å20) distance (δ).27 From Figure 4b, x+ (which we approximate as “a” of eq 5) is much smaller, namely, in the ca. 2∼3 Å range for the ferrocenated ILs and 5.1 Å for the common correlation line in Figure 4b. The principal outlier in Figure 4b is the PEGbased [Ru(bpy(CH2MePEG350)2)2](CN)2 melt, which unlike all the other redox centers, has an asymmetric structure. A discussion of this case has been presented elsewhere.19d Again, the significance of Figure 4b is that the ionic relaxation model of control of electron transport, which contains no assumption regarding the particular nature of redox sites, is quite general for different redox semisolid systems, from metal complexes19 to molecule-like Au nanocrystals18 to redox imidazoliums. The relaxation model seems to fulfill the test of chemical generality, which is a criterion for a successful general model for electron transport in a mixed valent semisolid medium in which counterion diffusion is very slow. Plasticization by CO2 Sorption at High Pressure. Electron transport rates in Figure 4 were caused to vary by melt temperature. Ferrocenated imidazolium ILs with short alkyl chains and ester linkages (Table 2) proved to exhibit ionic conductivities too low for reliable electron hopping transport measurements by chronoamperometry, even at elevated temperatures. To obtain transport results for them, we used a previously used plasticization (e.g., diffusion-enhancement) tactic18,19a,b based on the proclivity of CO2 at high pressure to dissolve into organic phases.28 Thus, experiments like those in Figure 2 were carried out on the ferrocenated IL [Fc-CO2-C3Im-Me][PF6], with voltammetric results as illustrated in Figure 5. We interpret the CO2 pressure-dependent diminution of iRUNC ohmic distortion as sorption of CO2 lowering the IL viscosity and enhancing the diffusivity of its counterions. The resulting quantitative measurements of electron (DAPP, taken as ) DE),

measured parameter/CO2 pressure (psi)

200

400

600

800

1000

σ/10-6S · cm-1 DION (65 °C)/10-10 cm2 · s-1 EA,ION/kJ · mol-1 DE,APP (65 °C)/10-9cm2 · s-1 EA,EX/kJ · mol-1 kEX (65 °C)/105M-1s-1 DE,CORR (65 °C)/10-9cm2 · s-1 EA,EX,CORR/kJ · mol-1 kEX,CORR (65 °C)/105M-1s-1

0.31 0.3 92 0.8 109 2.3 0.25 94 0.75

1.1 1.2 82 1.4 82 4.2 0.64 79 1.9

2.8 2.9 58 2.5 71 7.3 1.4 66 4.3

5.4 5.5 38 3.2 56 9.6 2.1 52 6.3

9.2 9.5 34 4.2 53 12 3.0 50 8.8

counterion (DION) mass transport, and activation barriers for the [Fc-CO2-C3-Im-Me][PF6] IL are reported in Table 4 and in Figure 6 as a function of CO2 pressure and in Figure S-6 as a function of temperature (see Supporting Information). Figure 6 shows that the plasticization effects of increasing CO2 pressure, while strong at first, elevating counterion, and electron-hopping diffusivities tend to level off at the highest pressures (probably reflecting saturation of the extent of CO2 sorption19a). Increase of CO2 pressure into the supercritical (T > 31 °C)29 or liquid state (T < 31 °C) had no further effect.30 The increases of DAPP and DION are accompanied by a lowering of activation barriers by 2- to 3-fold at higher CO2 pressure (Table 4). The CO2 plasticized results are further examined in Figure 7, a log-log plot between kEX and DION at different CO2 pressures. The plots exhibit linear correlations (slope 1) at lower CO2 pressures, but at higher pressures, kEX increases at a faster pace (slope > 1) than DION. The data at lower CO2 pressures (which were unavailable without CO2 plasticization) are consistent with the ion atmosphere relaxation model discussed above. We will not speculate on the reason(s) that data at higher CO2 pressure depart from model: possibilities are greatly increased ion-pairing that degrades the calculation of DION, microphase segregation of the IL, and increase of DPHYS of the redox site. Physical Properties of Ferrocenated Ionic Liquids. Density measurements were necessary to establish ferrocene concentrations in the ILs. Here, in the interest of completeness, we present a further analysis of the IL densities and viscosities. Such data have not previously been assessed for imidazolium-based ILs with covalently linked redox functions, although data are

Figure 6. Apparent electron diffusion coefficients (b) and physical diffusion coefficients of counterions (red 9) of [Fc-CO2-C3-ImMe][PF6] in varied CO2 pressure at 65 °C.

18214 J. Phys. Chem. C, Vol. 112, No. 46, 2008

Wang et al. Following a related explanation by Huddleston et al.,32 lower overall densities and ferrocene concentrations result from longer alkyl chain segments, consistent with higher proportions of low density -CH2- units and correspondingly lowered proportions of high density Fc and imidazolium rings. The densities, presented as molar volumes (Vm ) nVCH2 + V0 where V0 is the molar volume occupied by the groups other than -CH2-; see Supporting Information, Figure S-7), are in fact linearly correlated with the numbers (n) of -CH2- groups. Slopes of plots in Figure S-7 give molar volume values for -CH2- groups (VCH2) of 16.0 to 17.1 cm3/mol, consistent with reported literature values.33 Comparing densities of ILs with BF4- vs PF6- counterions reveals a possible influence of electrostatic interactions32b on IL densities. Table 1 shows that all ILs with PF6- counterions have larger densities and molar volumes. Vm values for the PF6salts are an average 21.7 cm3/mol larger, a value much larger than the reported34 difference in BF4- vs PF6- van der Waals volumes (12.0 cm3/mol). This counterion volume discrepancy suggests stronger electrostatic interactions of the small BF4anion with imidazolium cations. Changes in molar volumes due to groups other than the alkyl segments and counterions can be estimated by comparing V0 values from ILs that are structurally different but have the same counterion. Thus, comparing V0 for the series of PF6- ILs having ester linkages with those lacking them (see Figure S-7, Supporting Information) and for those having ether units with those lacking them gives, respectively, 24 and 5 cm3/mol for the ester group and ether oxygen molar volumes. These values reasonably agree with those (15.5∼23.9 cm3/mol for ester and 5.5∼6.7 cm3/ mol for ether) obtained from polymers.33b Fluidity. Viscosities of five ILs, selected for different structural combinations of ester linkage, alkyl chain length, and ethylene oxide group, were measured as a function of temperature and shear rate. The room-temperature viscosities (Table 5) are both large and varied (103 ∼ 107 cP). The most viscous IL has an ester linkage and short alkyl chain; viscosity lessens in structures free of ester linkages and with longer alkyl chains. Viscosities of dialkylimidazolium ILs (without the ferrocene substituents) are known to vary with specific structural details and counterion over tens to hundreds of centipoises at room temperature.7a,b Viscosities of ferrocenated imidazolium ILs especially those with ester linkages are much larger; these groups clearly greatly diminish the structural flexibilities important in fluidic translation. Ferrocenated IL viscosities decrease with increasing alkyl chain lengths, a trend opposite to that seen for dialkylimidazolium ILs (viscosities increase with longer alkyl chains presumably due to enhanced van der Waals interactions7,8j,35) but parallel to that seen for hybrid redox polyether molten salts which become14c,36 less viscous with an increase in the numbers of ethylene oxide repeat units (at least for relatively short chain lengths). Those results were interpreted as introducing greater numbers of structurally flexible components that countered the

Figure 7. (a) Linear log-log relationship between DION and kEX for Fc+1/0 electron transport in [Fc-CO2-C3-Im-Me][PF6] ionic liquid at different CO2 pressure: 200 psi (teal b), 400 psi (teal 9), 600 psi (teal 2), 800 psi (teal 1), and 1000 psi (teal (). The slopes of linear correlation in the plot are 1.0, 1.1, 1.4, and 1.5 for 400 psi, 600 psi, 800 psi, and 1000 psi, respectively. (b) The data in (a) coplotted with data from ionic liquids in vacuum include [Fc-CO2-C11-Im-Me][PF6] (pink b), [Fc-CO2-C6-Im-Bu][PF6] (pink 9), [Fc-CO2-C6-Im-Bu][BF4] (pink 2), [Fc-CO2-C11-Im-Bu][PF6] (pink 1), [Fc-CO2-C11-ImBu][BF4] (pink (), [Fc-C4-Im-Me][PF6] (red b), [Fc-C4-Im-Me][BF4] (red 9), [Fc-C4-Im-Bu][PF6] (red 2), [Fc-C4-Im-Bu][BF4] (red 1), [FcC6-Im-Bu][PF6] (red (), [Fc-C6-Im-Bu][BF4] (red b), [Fc-CO2C2OC2-Im-Bu][PF6] (green b), [Fc-CO2-C6-Im-C2OMe][PF6] (green 9), and [Co(Cp)2-CO2-C6-Im-Bu][PF6]2 (blue 2).

available31 for ILs with redox counterions. The ferrocenated ILs are, in general, denser and much more viscous than nonferrocenated imidazoliums. Except for [Fc-C6-Im-Me][PF6] (mp ca. 102 °C), all of the Table 1 ferrocenated imidazolium ILs are amorphous phases at room temperature. Density and Molar Volume. IL densities and corresponding molar concentrations (C) and volumes (VM) are listed in Table 1. The ferrocene concentrations are large (>2 M), and density clearly is influenced by the particular molecular structure.

TABLE 5: Structure and Physical Properties of Selected Ferrocenated Imidazolium Ionic Liquids: Viscosity and Ionic Diffusion Coefficients DION no. 1

cation

2

[Fc-CO2-C3-Im-Bu] [Fc-CO2-C6-Im-Bu] [Fc-CO2-C11-Im-Bu] [Fc-C6-Im-Bu]

3

[Fc-CO2-C2OC2-Im-Bu]

/s (25 °C)

anion

cm2

[PF6] [PF6] [PF6] [PF6] [BF4] [PF6]

1.0 × 10 8.4 × 10-12 6.3 × 10v11 1.7 × 10-10 1.0 × 10-10 9.9 × 10-12 -14

EA,ION

η

kJ/mol

cP (25 °C)

kJ/mol

115 75 60 58 52 83

1.4 × 5.8 × 105 1.6 × 105 8.5 × 103 1.4 × 104 5.4 × 105

97∼155 83∼106 77∼87 68 72 90∼123

EA,η 107

Electron Transport in Ferrocenated Imidazolium ILs

J. Phys. Chem. C, Vol. 112, No. 46, 2008 18215

typical stiffening effect of the inflexible redox unit and were analyzed using free volume theory assuming a fractional free volume (FFV) content proportional to the numbers of ethylene oxide segments.37a We inspected a parallel explanation for the alkyl chain length effects seen in Table 5: diluting the concentration of the rigid ferrocene structure with longer alkyl segments diminishes, in a relative way, its stiffening influence on physical viscosity. The free volume theory predicts37b,c exponential changes in both viscosity and ionic diffusivity with FFV-1, which is defined as

FFV )

VCH2 · nCH2 Vm

(7)

Figure S-8 (see Supporting Information) shows plots of ln[viscosity] and of ln[DION] against FFV-1. The former gives a linear relation (but for limited data), and for the latter, the trend is in the expected direction but is not linear. Viscosity measurements of the ferrocenated ILs at varied shear rates produced linear changes of shear stress with shear rate (Figure S-9, see Supporting Information) that at constant shear rates were invariant with time.38 Isotropic Newtonian behavior of ILs has been reported previously by Seddon et al.38 for 1-alkyl-3-methylimidazolium with short alkyl chains (n ) 2∼11); Figure S-9 shows that Newtonian behavior is retained after incorporation of ferrocene substituents. Viscosities measured at different temperatures (25∼75 °C) give slightly curved Arrhenius plots (Figure S-10, see Supporting Information), which is also seen for dialkylimidazolium ionic liquids35 and for metal complex polyether molten salts.14,36 A classical explanation for such behavior would involve coupling of chain motions (alkyl and polyether) with the physical transport process.39 The viscosity thermal energy barriers were taken from Figure S-10 (Supporting Information) plots as averages over a range of apparent activation barrier energies, which are listed in Table 5. The energy barriers to viscous flow of the ferrocenated ILs are much larger than those of dialkylimidazoliums, where reports range from 2135 to 38 kJ/mol.40 The energy barriers are, as expected, larger for the ferrocenated IL structures with larger viscosities. Finally, we see (Table 5) substantial differences between activation energy barriers for ionic conductivity and viscous flow, the former being smaller. This is expected since ionic conductivities of ferrocenated ILs are expected to be dominated by motions of the small counterions ions (BF4- and PF6-), the bulky redox imidazolium being relatively less mobile. Viscous flow, on the other hand, entails significant, enforced motions of both the bulky imidazolium cation and its counterion, producing a larger activation energy barrier and probably the Arrhenius curvature mentioned above. Arrhenius plots (not shown) of ionic conductivity are linear, in contrast, indicating an absence of strong coupling to motions of alkyl chain segments. Acknowledgment. This research was supported in part by grants from the NSF and DOE Basic Chemical Sciences. The authors thank Daniel Buttry for important suggestions regarding the ion atmosphere relaxation model. Supporting Information: Cobalticenium IL surrogate experiments and synthesis, activation plots, UV-vis, electrochemical, and viscosity data, and molar and free volume plots. This material is available free of charge via the Internet at http:// pubs.acs.org.

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