Microelectrode Voltammetry and Electron Transport in an Undiluted

Microelectrode Voltammetry and Electron. Transport in an Undiluted Room Temperature Melt of an Oligo(ethylene glycol)-Tailed Viologen. Tsuyonobu ...
3 downloads 0 Views 280KB Size
Download PDF
Anal. Chem. 1996, 68, 597-603

Microelectrode Voltammetry and Electron Transport in an Undiluted Room Temperature Melt of an Oligo(ethylene glycol)-Tailed Viologen Tsuyonobu Hatazawa,† Roger H. Terrill, and Royce W. Murray*

Kenan Laboratories of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290

This paper describes the synthesis, characterization, and voltammetry of a oligo(ethylene glycol) trimer derivative of 4,4′-bipyridine, [N,N′-(CH3(OCH2CH2)3)2-4,4′-bipyridine][BF4]2 [V[E3M]2](BF4)2]. This “tailed” viologen is a room temperature molten salt. Its fast atom bombardment mass spectrum exhibits interesting aspects of cationation. Microelectrode voltammetry in the undiluted viologen melt shows the expected pair of reduction waves, but currents for the wave for the [V[E3M]2]2+/1+ are smaller than those for the [V[E3M]2]1+/0 couple. Analysis of the voltammetric behavior leads to the conclusion that the difference in currents arises from coupling of [V[E3M]2]1+/0 homogeneous electron exchanges to the physical diffusion of viologen species in the mixed-valent diffusion layer at the electrode interface. The physical diffusivity of the [V[E3M]2]2+ species, DPHYS, is much smaller than electron diffusivity through electron selfexchanges of the [V[E3M]2]1+/0 couple. kEX,1/0 is ∼106 M-1 s-1, or at least 10-fold larger than kEX,1/2. Viologens, or quaternized 4,4′-bipyridines, have been widely investigated owing to their versatile electrochromic,1 liquid crystalline,2 biocidal,3 and photosensitization and electron transfer properties.1,4,5 The electron transfer properties of viologens have been studied in a wide variety of electrochemical contexts, mainly as dilute solutions of the viologen1 and in a few cases as redox polymers or as counterions of ion exchange coatings on chemically modified electrodes contacted by electrolyte solutions.5 The † On leave from and supported by Sekisui Chemical Co., Ltd., Applied Electronics Laboratory, 32 Wadai Tsukuba-shi, Ibaraki, Japan 300-42. (1) (a) Bird, C. L.; Kuhn, A. T. Chem. Soc. Rev. 1981, 10, 49. (b) Sammells, A. F.; Pujare, N. V. J. Electrochem. Soc. 1986, 133, 1270. (c) Bookbinder, D. C.; Wrighton, M. S. J. Electrochem. Soc. 1983, 130, 1080. (2) (a) Tabushi, I.; Yamamura, K.; Kominami, K. J. Am. Chem. Soc. 1986, 108, 6410. (b) Yamamura, K; Okada, Y.; Ono, S.; Kominami, K.; Tabushi, I. Tetrahedron Lett. 1987, 28, 6475. (3) Summers, L. A. The Bipyridinium Herbicides; Academic Press: London, New York, 1980. (4) (a) Inoue, H.; Ichiroku, N.; Torimot, T.; Sakata, T.; Mori, H.; Yoneyama, H. Langmuir 1994, 10, 4517. (b) Ahuja, R. C.; Mo ¨bius, D. Thin Solid Films 1989, 179, 457. (c) Fujihira, M.; Sakomura, M. Thin Solid Films 1989, 179, 471. (d) Pileni, M.-P.; Braun, A. M.; Gra¨tzel M. Photochem. Photobiol. 1980, 31, 423. (e) Deronzier, A.; Essakalli, M. J. Chem. Soc., Chem. Commun. 1990, 242. (f) Bock, C. R.; Connor, J. A.; Gutierrez, A. R.; Meyer, T. J.; Whitten, D. G.; Sullivan, B. P.; Nagle, J. K. J. Am. Chem. Soc. 1979, 101, 4815. (g) Moreno-Bondi, M.; Orellana, G.; Turro, N. J.; Tomalia, D. A. Macromolecules 1990, 23, 910. (h) Fox, M. A.; Chanon, M. Photoinduced Charge Transfer; Elsevier: Amsterdam, 1988. (i) Kavarnos, G. J.; Turro, N. J. Chem. Rev. 1986, 86, 401. (j) Fendler, J. H. J. Phys. Chem. 1985, 89, 2730. (k) Meyer, T. J. Acc. Chem. Res. 1989, 22, 163. (l) Connolly, J. S. Photochemical Conversion and Storage of Solar Energy; Academic Press: New York, 1981.

0003-2700/96/0368-0597$12.00/0

© 1996 American Chemical Society

voltammetry6 of self-assembled monolayers of viologens has been described. As far as we are aware, there have been no observations of the voltammetry of a molten viologen, although the voltagedependent conductivity of a liquid crystalline viologen melt of similar structure has been reported.2 This paper describes the microelectrode voltammetry of an undiluted viologen salt that is an amorphous melt at room temperature. As part of a project examining the solid state voltammetry of various redox moieties dissolved in polyether polymer electrolytes, we observed7 several years ago that a ferrocene derivatized with a polyether chain was not only freely soluble in unlabeled polyethers but would itself act as a polyether-like solvent, dissolving LiClO4 electrolyte. It proved possible to conduct microelectrode voltammetry in this undiluted ferrocene-labeled polymer electrolyte material. Further exploring the molecular melt behavior of derivatives that combine polyethers and redox substances, we have more recently attached oligo(ethylene oxide)8,9 and oligo(propylene oxide)8 trimers to other redox moieties, including metal bipyridine complexes, tetraphenylporphyrins, and tetrathiafulvalene. Even though the polyether chains in these derivatives are quite short, they convert these normally crystalline redox compounds into highly viscous room temperature molecular melts. The melts also dissolve LiClO4 electrolyte. Microelectrodebased voltammetric observations in these materials, as undiluted melt phases, show that coupling between electron self-exchanges and physical self-diffusion can occur in the concentrated mixedvalent diffusion layers around operating electrodes.8,10 The electron exchange-diffusion coupling acts to accelerate the apparent diffusion coefficient (DAPP). In cases where coupling does not occur owing to very slow electron self-exchange, the true physical self-diffusivities of the redox centers can be exceptionally small; values less than 10-15 cm2/s have been observed.11 (5) (a) Dalton, E. F.; Murray, R. W. J. Phys. Chem. 1991, 95, 6383. (b) Downard, A. J.; Surridge, N. A.; Gould, S.; Meyer, T. J.; Deronzier, A.; Moutet, J.-C. J. Phys. Chem. 1990, 94, 6754. (c) Shu, C.-F.; Wrighton, M. S. J. Phys. Chem. 1988, 92, 5221. (d) Lewis, T. J.; White, H. S.; Wrighton, M. S. J. Am. Chem. Soc. 1984, 106, 6947. (e) Bock, C. R.; Connor, J. A.; Gutierrez, A. R.; Meyer, T. J.; Whitten, D. G.; Sullivan, B. P.; Nagle, J. K. Chem. Phys. Lett. 1979, 61, 522. (f) Oyama, N.; Ohsaka, T. In Molecular Design of Electrode Surfaces, Murray, R. W., Ed.; Wiley-Interscience: New York, 1992; Chapter 8. (6) (a) De Long, H. C.; Buttry, D. A. Langmuir 1992, 8, 2491. (b) Goss, C. A.; Miller, C. J.; Majda, M. J. Phys. Chem. 1988, 92, 1937. (7) Pinkerton, M. J.; LeMest, Y.; Zhang, H.; Watanabe, M.; Murray, R. W. J. Am. Chem. Soc. 1990, 112, 3730. (8) Velazquez, C. S.; Hutchison, J. E.; Murray, R. W. J. Am. Chem. Soc. 1993, 115, 7896. (9) Velazquez, C. S.; Murray, R. W. J. Electroanal. Chem. 1995, 396, 349. (10) Long, J.; Murray, R. W. J. Phys. Chem., in press.

Analytical Chemistry, Vol. 68, No. 4, February 15, 1996 597

Scheme 1. Material Used in This Experiment and Synthesis Pathway

In the interest of expanding the chemistry and electrochemistry of this unusual class of molecular melts, we have undertaken and describe here the synthesis of a oligo(ethylene glycol) trimer derivative of 4,4′-bipyridine, [N,N′-(CH3(OCH2CH2)3)2-4,4′-bipyridine][BF4]2 [[V[E3M]2](BF4)2], prepared as shown in Scheme 1. This material is a viscous melt at room temperature and, being ionic, is a molten salt. Its ionic conductivity is sufficient to allow microelectrode voltammetry in its undiluted state, even without adding a supporting electrolyte. The viologen centers have a 2.0 M concentration (C) and are separated by δ ) ∼9 Å [center-tocenter, based on δ ) (CNA)-1/3]. The viologen centers in the melt exhibit slow self-diffusion rates, down to 10-10 cm2/s, that are strongly plasticized by water impurity. We observe that melt currents for the V[E3M]21+/0 couple exceed those for the V[E3M]22+/1+ couple, an observation consistent with diffusional transport being more strongly accelerated by electron selfexchange reactions in the V[E3M]21+/0 couple than in the V[E3M]22+/1+ couple. It has been observed before5 that electron transfers are more facile in viologen1+/0 couples than in viologen2+/1+ couples, in a viologen polymer5a this being by a factor of ∼20fold. We have also investigated electron transport in mixed-valent forms of the [V[E3M]2](BF4)2 salt, using interdigitated array electrodes. These results, and a demonstration of making frozen concentration gradients in this material, will be reported in another paper.12 EXPERIMENTAL SECTION Preparation of Precursor Tris(ethylene glycol) Monomethyl Ether Monotosylate. Tris(ethylene glycol) monomethyl ether (1.0 mol) was slowly (4 h) dripped into a mixture of p-tosyl chloride (205 g, 1.1 mol) and pyridine (200 mL) mechanically stirred in a three-necked N2-flushed flask held at 5 °C in an ice(11) Poupart, M. W.; Velazquez, C. S.; Hassett, K.; Porat, Z.; Haas, O.; Terrill, R. H.; Murray, R. W. J. Am. Chem. Soc. 1994, 116, 1165. (12) Terrill, R. H.; Hatazawa, T.; Murray, R. W. J. Phys. Chem. 1995, 99, 16676.

598

Analytical Chemistry, Vol. 68, No. 4, February 15, 1996

water bath. The mixture was stirred for an additional 3 h, then poured into 900 mL of ice-water in a 3 L beaker, and extracted into 900 mL of CH2Cl2. The organic layer was separated, washed three times with 500 mL of ice-cold 6 M HCl, and reduced to minimum volume by evaporation in vacuo. Tosylates thus prepared were at least 90% pure and were used as obtained after drying. NMR (1H, in CDCl3): δ (ppm) 2.40 (s, 3H), 3.32 (s, 3H), 3.48 (t, 2H), 3.55 (multiplet, 6H), 3.65 (t, 2H), 4.11 (t, 2H), 7.29 (d, 2H), 7.75 (d, 2H). δ ) 3.48-4.11 ppm signals are due to the inner triethylene glycol protons. Synthesis of Tris(ethylene glycol)-Modified Viologen. A mixture of tosylated tris(ethylene glycol) monomethyl ether (0.025 mol, 7.95 g) and 4,4′-bipyridine (0.01 mol, 1.58g) was heated at 50-60 ˚C in 300 mL of N,N-dimethylformamide (DMF) in a 500 mL flask for 48 h (clear to yellow) and then stirred at room temperature for 2 weeks (yellow to brown). Unreacted 4,4′bipyridine, excess tris(ethylene glycol), and partially reacted 4,4′bipyridine were removed by extractions with diethyl ether and toluene, at least twice with each. After drying under vacuum, a yellow viscous liquid was obtained. The above product was passed through an Amberlite IRA-93 (Alfa Products) ion exchange column prepared (wet packed) with 40 mL (dry volume) of resin, eluting first with distilled water (at least 20 column volumes), then with 1.0 M aqueous fluoboric acid (until eluent pH 2), and finally with distilled water (until eluent pH 6.3). Water was removed from the eluent fractions by freezedrying. The [V[E3M]2](BF4)2 product was a slightly brown, highly viscous liquid at room temperature. NMR (1H, in D2O): δ (ppm) 3.35 (s, 6H), 4.48 (multiplet, 16H), 4.04 (t, 4H), 4.87 (t, 4H), 8.45 (d, 2H), 9.06 (d, 2H). An unassigned impurity peak appeared at 2.71 (s). After ion exchange cleanup, the [V[E3M]2](BF4)2 material was characterized by fast atom bombardment (FAB) mass spectrometry. The spectrum was consistent with the sought composition. The FAB experiments were conducted on a VG 70-SEQ mass

Figure 1. Carbon microdisk electrode assembly and vacuum cell.

spectrometer using a 3:1 dithiothreitol-dithioerythritol solution as sample matrix and 30 keV Cs ions. Elemental analysis, Found: C, 43.4; H, 6.4; N, 5.5; B, 3.2; F, 23.6;; Calcd: C, 46.2; H, 6.1; N, 4.5; B, 3.5; F, 24.4. The elemental analysis indicates the [V[E3M]2](BF4)2 sample was at least 94% pure; suggested impurities are water (the material is quite hygroscopic) and (suggested by the NMR impurity peak) dimethylamine from decomposed DMF. A density determination was converted to a 2 M concentration of [V[E3M]2](BF4)2 presuming 100% purity, so this value has a 5-10% uncertainty. Also, since the molar volume of the viologen cation should be much larger than that of the BF4- counterion, the change in molar concentration of viologen sites upon its reduction to the [V[E3M]2]+ state should be insignificant. Electrochemical. Cyclic voltammetry of N2-degassed dilute solutions of [V[E3M]2](BF4)2 in CH3CN at 25 °C was done in a conventional cell using a 5 mm diameter glassy carbon disk working electrode and a SSCE reference. Cyclic voltammetry of the undiluted [V[E3M]2](BF4)2 salt was recorded by placing a droplet of the material on the platform of the three-electrode microcell illustrated in Figure 1. The working electrode was a 40 µm diameter carbon fiber sealed collinearly with larger Ag pseudoreference and Pt auxiliary electrodes as described before.13 The microelectrode dimension was assessed by optical microscopy and by a voltammetric experiment with aqueous 0.1 M KCl/[Ru(NH3)6]2+/3+ using D ) 6.5 × 10-6 cm2/s. The electrochemical equipment was locally built and as used previously.13 RESULTS AND DISCUSSION Synthesis. The preparation of the salt [V[E3M]2](BF4)2 followed Scheme 1, in which 4,4′-bipyridine displaced the weak tosylate nucleophile from its adduct with a monomethyl-ethylene gycol trimer. The sought compound was obtained in +94% purity, by nmr and elemental analysis. The FAB mass spectrum (Figure 2) of the [V[E3M]2](BF4)2 salt displays interesting features of its gas phase cationation. Oxidative cationation of the MW ) 624.2 [V[E3M]2](BF4)2 salt is not favorable, since no peak is observed for the parent salt. A (13) Wooster, T. T.; Longmire, M. L.; Zhang, H.; Watanabe, M.; Murray, R. W. Anal. Chem. 1992, 64, 1132.

small peak appears at m/e ) 537, corresponding to loss of one BF4- counterion. The most prominent peak can be accounted for by loss of both BF4- counterions from a one-electron-reduced V[E3M]21+ cation (m/e ) 450). The large peak at m/e ) 303 is consistent with further loss of one of the E3M tails, and that at m/e ) 1161 to a dimer [V[E3M]2]2(BF4)3+ cationated by loss of one BF4-. Mass spectrometry of molecular molten salts is uncommon,14 so these results have some uniqueness. Using a modification15 of a literature preparation,16 it is also possible to prepare a polymeric version of the [V[E3M]2](BF4)2 material, by use of the tris(ethylene glycol) di-p-tosylate. This viologen, also an amorphous material, is a glass at room temperature, with much lower ionic conductivity. Experiments on its mixed-valent form will be described elsewhere.15 Voltammetry in Acetonitrile. Cyclic voltammetry of dilute (11.2 mM) acetonitrile solutions of the [V[E3M]2](BF4)2 salt (Figure 3) is ordinary in appearance. The peak currents for the [V[E3M]2]2+/1+ and [V[E3M]2]1+/0 reactions are equal, and the oxidative peak currents equal those for the reductions; i.e., the reactions are chemically reversible. There is an iRUNC contribution to the ∆EPEAK values, which was not investigated. Diffusion coefficients calculated from currents of the two waves, from

Ip ) (2.69 × 105)n3/2AD1/2ν1/2C

(1)

are D2/1 ) 5.3 × 10-6 cm2/s and D1/0 ) 5.5 × 10-6 cm2/s. In previous work,7 we examined the dilute acetonitrile solution voltammetry of a ferrrocene derivative with a 1900 MW ethyl glycol oligomer. It too, exhibited no unusual features. Voltammetry of the [V[E3M]2](BF4)2 Melt. Two series of microelectrode voltammetric experiments were performed in droplets of undiluted [V[E3M]2](BF4)2 in the cell of Figure 1. In the first experiment, the cell was evacuated first to 300 mTorr and then to 10 mTorr. Figure 4 shows voltammetry obtained under these two conditions and after 7 h further at 10 mTorr. A substantial change in the voltammetry is evident as a result of this procedure, whose most obvious effect should be drying of the [V[E3M]2](BF4)2 film. The currents become smaller (viologen self-diffusion slower), and iRUNC distortion (large ∆E) becomes obviously more severe (ionic conductivity falls), as the material is increasingly dried. The Figure 4 results indicate that the [V[E3M]2](BF4)2 sample contained volatile impurities, probably water since it is hygroscopic, water absorption plasticizing the self-diffusion of the [V[E3M]2]2+/1+/0 species. In these experiments, the various [V[E3M]2]2+/1+/0 species undergo physical diffusion through mixed-valent electrode/melt interfacial regions that, ideally, contain only those species and BF4- counterions. Clearly the presence of volatile impurities substantially elevates both the selfdiffusion of the viologen centers and the ionic mobilities in the [V[E3M]2](BF4)2 melt. Drying the film results in smaller currents and increased uncompensated resistance effects on the voltammetry. Application of eq 1 to the currents of Figure 4 shows that (14) (a) Wicelinski, S. P.; Gale, R. J.; Pamidimukkala, K. M.; Laine, R. A. Anal. Chem. 1988, 60, 2228. (b) Ackermann, B. L.; Tsarbopoulos, A.; Allison, J. Anal. Chem. 1985, 57, 1766. (c) Franzen, G.; Gilbert, B. P.; Pelzer, G.; DePauw, E. Org. Mass Spectrom. 1986, 21, 443. (15) Hutchison, J.; Terrill, R. H.; Murray, R. W. University of North Carolina, Chapel Hill, NC, unpublished results, 1994. (16) Endo, T.; Kameyama, A.; Mambu, Y.; Kashi, Y.; Okawara, M. J. Poly. Sci. Part A: Poly. Chem. 1990, 28, 2509.

Analytical Chemistry, Vol. 68, No. 4, February 15, 1996

599

Figure 2. Fast atom bombardment mass spectrum of [V(E3M)2](BF4)2.

Figure 3. Typical cyclic voltammogram of a dilute (11.2 mM) [V[E3M]2](BF4)2 solution in degassed 0.1 M Et4NBF4-CH3CN at 25 °C, at 5 mm diameter glassy carbon working electrode. Potential sweep rate 50 mV/s.

the viologen apparent self-diffusivity decreased ∼10-fold for both waves during the drying procedure. Plasticization effects on redox site diffusion in polyether polymer electrolytes have been seen previously.17 The voltammetry of Figure 4 was observed as a function of potential sweep rates; peak currents are plotted in Figure 5 according to eq 1. The plots tend to fold over at higher sweep rates, probably due to the iRUNC effects. These results and those presented below are consistent with a primarily linear diffusion (17) (a) Parcher, J. F.; Barbour, C. J.; Murray, R. W. Anal. Chem. 1989, 6, 584. (b) Barbour, C. J.; Parcher, J. F.; Murray, R. W. Anal. Chem. 1991, 63, 604.

600 Analytical Chemistry, Vol. 68, No. 4, February 15, 1996

Figure 4. Cyclic voltammetry (10 mV/s) of a film of undiluted [V[E3M]2](BF4)2 melt at 25 °C in cell of Figure 1, following evacuationdrying at 300 (top), 10 (middle), and 10 mTorr for 7 h (bottom).

geometry at the 40 µm diameter carbon microdisk electrode, although some of the data, by consideration of values of D and time scale, may have a minor amount of mixed linear-radial diffusion.18 In the second experiment, a film of [V[E3M]2](BF4)2 was more completely dried prior to initiation of the voltammetry, by 24 h (18) (a) Longmire, M. L.; Watanabe, M.; Zhang, H.; Wooster, T. T.; Murray, R. W. Anal. Chem. 1990, 62, 747. (b) For a D ) 1 × 10-8 cm2/s and 5 mV/s scan rate, the parameter log[4Dt/r2] ∼ 1 (where r is the microelectrode radius), which is ∼10% radial diffusion contribution.18a This is the worst case of radial contribution in Table 1.

Figure 5. Plots of peak currents for the [V[E3M]2]2+/1+ wave as a function of potential sweep rate, taken under the three conditions of Figure 4: b, 300 mTorr; O, 10 mTorr; 3, 10 mTorr, 7 h.

Figure 6. Cyclic voltammetry (10 mV/s) of a film of undiluted [V[E3M]2](BF4)2 melt at 25 °C in cell of Figure 1, with instrumental compensation for uncompensated resistance, following evacuationdrying at 10 mTorr for 24 h: curve A, voltammetry in the [V[E3M]2](BF4)2 melt; curve B, voltammetry after reduction of the [V[E3M]2](BF4)2 melt at -0.2 V vs E2+/1+ for 1 h; curve C, voltammetry after reoxidation of the [V[E3M]2](BF4)2 melt at +0.2 V vs E2+/1+ for 1 h; curve D, lower curve from Figure 4A, taken without instrumental feedback, for comparison to curve A. Data at different potential sweep rates as in curves A-C comprise the top, middle, and bottom data sets of Table 1, respectively.

evacuation at 10 mTorr, and in an effort to combat the meager ionic conductivity of the dried material, instrumental (positive feedback) compensation19 for uncompensated resistance was employed to improve the definition of the wave. The better defined voltammetric results in Figure 6 (compare curves A and D, with and without feedback compensation) show that this tactic was partly successful. Table 1 summarizes the results for the second experiment, showing apparent diffusion coefficients calculated from eq 1 (DAPP,2/1 and DAPP,1/0). Table 1 also examines the relative values of reduction and oxidation peak currents (ipc2/1 and ipc1/0). The ratio of these currents is consistently near 1 for the [V[E3M]2]2+/1+ (19) Bard, A. J.; Faulkner, L. R. Electrochemical Methods; John Wiley & Sons: New York, 1980.

but somewhat larger than 1 for the [V[E3M]2]1+/0 wave, consistent with some mixed linear-radial diffusion induced by the larger DAPP,1/0 for the second wave but also suggesting that the [V[E3M]2]0 species may not be completely stable. In both experiments, it is clear (Figures 4-6) that currents for the second wave are larger than those for the first, meaning that the apparent self-diffusivity DAPP,1/0 of the [V[E3M]2]1+ species exceeds that of [V[E3M]2]2+, DAPP,2/1. In the second experiment (Figure 6), the difference is a factor of 3-4-fold. The most immediate explanation for this difference is based on analogy to previous comparisons5a of the electron self-exchange dynamics of viologens embedded in polymer films. These comparisons have shown unambiguously that the rate of a viologen1+/0 self-exchange reaction exceeds that for the corresponding viologen2+/1+ reaction. The ratio is ∼20-fold.5a This suggests that in the second ([V[E3M]2]1+/0) wave, electron hopping between the [V[E3M]2]1+ and [V[E3M]2]0 states in the mixed-valent film around the electrode surface is coupled to physical diffusion, accelerating the transport of charge to/from the electrode. Analogous electron hopping-physical diffusion coupling probably also occurs in the [V[E3M]2]2+/1+ wave, but it must do so at a smaller rate, and the apparent diffusion coefficient for the former ([V[E3M]2]1+/0) wave is accordingly larger. Voltammetric measurements in undiluted redox phases, where concentrations are high and physical diffusion is slow, particularly demand consideration of charge transport contributions from electron hopping. The relevant electron hopping-diffusion coupling relations for the apparent diffusion coefficients for the two viologen couples are20,21

DAPP,2/1 ) DPHYS,2/1 + kEX,2/1δ2C/6

(2)

DAPP,1/0 ) Dphys,1/0 + kEX,1/0δ2C/6

(3)

where DPHYS and kEX are, respectively, the true physical diffusion coefficients and electron self-exchange rate constants (M-1 s-1) for the respective viologen couples, δ is the average redox site spacing (center-to-center, 0.94 nm), and C is the total viologen site concentration (2 M). These relations were first applied by Buttry and Anson22 to redox sites in Nafion films on electrodes and have been used extensively since.8,21,23 Assuming that DPHYS,2/1 and DPHYS,1/0 are little if any different, the difference of eqs 2 and 3

DAPP,1/0 - DAPP,2/1 ) (kEX,1/0 - kEX,2/1)δ2C/6

(4)

shows that the difference in diffusion currents for the two waves can be cast as a difference in their electron hopping rate constants. Equations 2-4 are, strictly speaking, applicable to transport that is observed starting from the [V[E3M]2]1+ oxidation state. (20) (a) Dahms, H. J. J. Phys. Chem. 1968, 72, 362. (b) Ruff, I.; Friedvich, V. J. J. Phys. Chem. 1971, 75, 3297. (c) Ruff, I.; Friedrich, V. J.; Demeter, K.; Csaillag, K. J. Phys. Chem. 1971, 75, 3303. (d) Ruff, I.; Korosi-Odor, I. Inorg. Chem. 1970, 9, 186. (e) Ruff, I. Electrochim. Acta 1970, 15, 1059. (f) Botar, L.; Ruff, I. Chem. Phys. Lett. 1986, 126, 348. (g) Ruff, I.; Botar, L. J. Chem. Phys. 1985, 83, 1292. (h) References f and g correct the numerical prefactor in the equation from π/4 to 1/6. (21) Majda, M. In Molecular Design of Electrode Surfaces; Murray, R. W., Ed.; Wiley Interscience: New York, 1992; Chapter 4. (22) Buttry, D. A.; Anson, F. C. J. Electroanal. Chem. 1991, 130, 333. (b) Buttry, D. A.; Anson, F. C. J. Am. Chem. Soc. 1983, 105, 685. (23) Watanabe, M.; Wooster, T. T.; Murray, R. W. J. Phys. Chem. 1991, 95, 4573.

Analytical Chemistry, Vol. 68, No. 4, February 15, 1996

601

Table 1. Diffusion Coefficients and Rate Constant Comparison scan rate, V/s

ipc 2/1/ipa 2/1a

Dapp, 2/1,b cm2/s

ipc 1/0/ipa 1/0a

Dap 1/0,b cm2/s

E°′2/1 - E°′1/0

ipc2/1/ipc 1/0c

kEX,1/0 - kEX,2/1,d 106 M-1 s-1

started from [V]2+ (Figure 6A)

5.0 × 10-3 1.0 × 10-2 2.5 × 10-2 5.0 × 10-2 1.0 × 10-1

1.3 1.1 1.3 1.2 1.2

8.1 × 10-10 6.3 × 10-10 6.2 × 10-10 5.0 × 10-10 4.8 × 10-10

1.9 2.0 1.7 1.5 2.3

9.9 × 10-9 1.0 × 10-8 9.9 × 10-9 7.7 × 10-9 7.7 × 10-9

0.44 0.45 0.43 0.43 0.44

0.29 0.25 0.25 0.26 0.25

3.1 3.2 3.2 2.4 2.4

average

Dapp, 2/1 ) 6.1 ( 0.9 × 10-10 cm2/s Dapp, 1/0 ) 9.0 ( 1.1 × 10-9 cm2/s kEX, 2/1 ≈ 2 × 105 M-1 s-1 e kEX, 1/0 - kEX,2/1 ) 2.9 × 106 M-1 s-1 d

started from [V]1+ (Figure 6B)

5.0 × 10-3 1.0 × 10-2 2.5 × 10-2 1.0 × 10-1

3.3 2.5 2.7 1.5

3.5 × 10-9 2.2 × 10-9 1.0 × 10-9 3.3 × 10-9

0.51 0.51 0.53 0.46

0.21 0.22 0.29 0.24

1.1 0.7 0.3 1.0

average

Dapp, 2/1 ) 1.3 ( 0.5 × 10-10 cm2/s Dapp, 1/0 ) 2.5 ( 1.2 × 10-9 cm2/s kEX, 2/1 ≈ 5 × 104 M-1 s-1 e kEX, 1/0 - kEX,2/1 ) 8.0 × 105 M-1 s-1 d

started from [V]2+ (Figure 6C)

5.0 × 10-3 1.0 × 10-2 2.5 × 10-2 5.0 × 10-2

3.1 3.1

5.6 × 10-9 8.9 × 10-9

0.50 0.49

0.25 0.23

1.8 2.9

2.1

2.8 × 10-9

0.49

0.27

0.9

scan conditions

average

1.5 × 10-10 1.1 × 10-10 8.2 × 10-11 1.9 × 10-10

1.1 1.1 1.1 1.1

3.5 × 10-10 4.5 × 10-10 4.4 × 10-10 2.1 × 10-10

1.0 1.3 1.1 1.4

Dapp, 2/1 ) 3.6 ( 1.1 × Dapp, 1/0 ) 5.8 ( 3.1 × 10-9 cm2/s kEX, 2/1 ≈ 1.2 × 105 M-1 s-1 e kEX, 1/0 - kEX,2/1 ) 1.9 × 106 M-1 s-1 d 10-10

cm2/s

a Ratio of reduction i b c pc and oxidation ipc peak currents for the respective waves. Calculated from ipc2/1 and ipc1/0 using eq 1. Ratio of peak currents for first and second waves. d Calculated from eq 4. e Calculated from DAPP,2/1 using eq 2 and taking DPHYS ≈ 0 in comparison to the second term.

(In potential sweep experiments started from the [V[E3M]2]2+ state, its transport rate may potentially influence that subsequently observed for the [V[E3M]2]1+/0 couple, through conproportionation24 of [V[E3M]2]2+ and [V[E3M]2]0 in the diffusion layer. Figure 6, curve A and the data in the topmost section of Table 1 were obtained from the [V[E3M]2](BF4)2 state.) In order to generate a deep layer of [V[E3M]2](BF4) around the electrode, i.e., in order to start voltammetry from the [V[E3M]2]1+ state, the carbon electrode potential was held at -0.4V vs Ag (in between the two waves) for 1 h and then potential sweeps were initiated in the negative direction (Figure 6, curve B). The data in the middle section of Table 1 were obtained in this way. We see that somewhat smaller values of both DAPP,2+/1+ and DAPP,1+/0 result, as compared to starting from the [V[E3M]2]2+ state. However, the ratio of currents ipc2/1 and ipc1/0, Table 1, remains about the same. The applied potential was then returned for a period to a more positive potential, destroying the [V[E3M]2]1+ layer, and further potential sweeps were initiated (Figure 6, curve C). The bottom section of Table 1 gives data from this part of the experiment. Comparison of the DAPP data in the top and bottom sections shows that the original values are recovered, within a factor of ∼2-fold, meaning that the [V[E3M]2]2+ composition was restored. The difference may reflect some continued drying of the film over time or perhaps some loss by chemical decay of some [V[E3M]2]0 sites. Before finishing the analysis of the results in Table 1 by eqs 2-4, we consider electrostatic migration as an alternative explanation for the differences in the [V[E3M]2]2+/1+ and [V[E3M]2]1+/0 (24) (a) Norton, J. D.; Anderson, S. A.; White, H. S. J. Phys. Chem. 1992, 96, 3. (b) Norton, J. D.; White, H. S. J. Electroanal. Chem. 1992, 325, 341.

602

Analytical Chemistry, Vol. 68, No. 4, February 15, 1996

currents. In voltammetry starting from the [V[E3M]2]1+ state (Figure 6, curve B), migration should depress currents for the [V[E3M]2]2+/1+ wave and enhance them for the [V[E3M]2]1+/0 wave, which is in the experimentally observed direction. However, according to the steady state relation25

iLIM )

iD 1 ( (z/n)tν+1

(5)

a transference number tV ) 0.6 would be required for the [V[E3M]2]1+ species in order to produce the experimentally observed current ratio ipc2/1/ipc1/0 ) 0.25. A transference number this large for [V[E3M]2]1+ is highly unlikely, since it would require that the [V[E3M]2]1+ species exhibit, in its undiluted melt, an ionic mobility twice that of the smaller BF4- counterion. Even if the two ions had the same mobility, tV would be 0.33 and the predicted ipc2/1/ipc1/0 would be 0.5, larger than that observed. It is much more likely, in fact, that the [V[E3M]2]1+ ion is much less mobile than the BF4- counterion and that the transference number of the former is quite small. This supposition is supported by other current and more detailed studies26 on analogous molecular melts having bulky redox ions and small counterions. Consequently we interpret the differences in current between the [V[E3M]2]2+/1+ and [V[E3M]2]1+/0 waves as reflecting differences more in electron transfer-diffusion coupling than a migration effect. (25) Wightman, R. M.; Wipf, D. O. In Electroanalytical Chemistry; Bard, A. J., Ed.; Marcel Dekker, Inc.: New York, 1989; Vol. 15, p 267. (26) Long, J.; Murray, R. W., University of North Carolina, Chapel Hill, NC, unpublished results.

Electrolyte was not added to the [V[E3M]2](BF4)2 melt to attempt probing or amelioration of migration effects; it is important at this point to understand the multiple consequences of adding electrolyte to polyethers. Addition of the typically used LiClO4 electrolyte to a polyether semisolid does not increase ionic conductivity and lower an ionic electrode reactant’s transference number in the straightforward manner familiar in dilute, fluid solutions. In polyethers, the strong, cross-linking ether oxygenLi+ coordination causes lowered viscosity, lowered physical diffusivities,23 possibly altered electron hopping kinetics,23 and indeed sometimes lowered ionic conductivity.26 Consequently, arguing the presence or absence of migration effects based on data with and without supporting electrolyte is far from straightforward, and such comparisons were not undertaken. An upper limit for kEX,2/1 is obtained from eq 2 by assuming that DPHYS,2/1 , DAPP,2/1. In other experiments,12 we have prepared mixed-valent [V[E3M]2]2+/1+ melts on interdigitated array electrodes, and observed the steady state current-potential behavior of this couple. Making the DPHYS,2/1 , DAPP,2/1 assumption, these experiments produce an estimate of kEX,2/1 ) 1.5 × 105 M-1 s-1 for the self-exchange rate constant for the [V[E3M]2]2+/1+ couple. This result is in good agreement with upper limit values of kEX,2/1 shown in Table 1, obtained from average DAPP,2/1 values under the same assumption. The agreement is significant in that the steady state measurements12 are not susceptible to ionic migration effects whereas ionic migration, if important in the present study, would elevate the observed DAPP,2/1 and thus kEX,2/1 values observed. (27) (a) Surridge, N. A.; Zvanut, M. A.; Keene, F. R.; Sosnoff, C. S.; Silver, M.; Murray, R. W. J. Phys. Chem. 1992, 96, 962. (b) Terrill, R. H.; Sheehan, P. E.; Long, V. C.; Washburn, S.; Murray, R. W. J. Phys. Chem. 1994, 98, 5127. (c) Sullivan, M. G.; Murray, R. W. J. Phys. Chem. 1994, 98, 4343. (d) Wooster, T. T.; Longmire, M. L.; Zhang, H.; Watanabe, M.; Murray, R. W. Anal. Chem. 1992, 64, 1132. (e) Zhang, X.; Leddy, J.; Bard, A. J. J. Am. Chem. Soc. 1985, 107, 3719. (f) Zhang, X.; Yang, H.; Bard, A. J. J. Am. Chem. Soc. 1987, 109, 1916.

We thus believe it appropriate to analyze the Table 1 data for DAPP,2/1 and DAPP,1/0 using eq 4, which leads to values of kEX,1/0 kEX,2/1 indicated in the table. By comparison to the upper limit values of kEX,2/1 calculated above from eq 2 by assuming negligible DPHYS,2./1, we see that kEX,2/1 must clearly be small in comparison to kEX,1/0. The conclusion is that the currents for the second reduction wave are dominated by electron hopping in the mixedvalent [V[E3M]2]1+/0 diffusion layer and that the rate constant kEX,1/0 for this reaction is ∼106 M-1 s-1, or at least 10-fold larger than kEX,1/2. This result is fully consistent with earlier results in viologen polymers5a where a 20-fold difference was found for a fixed-site viologen polymer. The 106 M-1 s-1 kEX,1/0 rate constant is, on the other hand, ∼100-fold smaller than that for methyl viologen dissolved in a fluid solution.5a This comparison is consistent with a growing collection of comparisons5af,8,10,22,27 in which electron self-exchange rate constants in fixed site or slowly diffusive (i.e., semisolid) phases are smaller than the corresponding ones in fluid solutions. Finally, we take note of approximations and assumptions in our analysis of the Table 1 data, which include neglect (we think correctly so) of migration effects, and the approximation of a spherically symmetric shape for the viologen (vs the cubic lattice model of eqs 2 and 3). ACKNOWLEDGMENT T.H. is on leave from and supported by Sekisui Chemical Co., Ltd. Part of this research is supported by NSF and DOE. The FAB mass spectrometry was done at the UNC facility in the Department of Environmental Science and Engineering. Received for review April 6, 1995. Accepted November 28, 1995.X AC950340G X

Abstract published in Advance ACS Abstracts, January 15, 1996.

Analytical Chemistry, Vol. 68, No. 4, February 15, 1996

603