J. Phys. Chem. 1991, 95,4573-4579
4573
Electron-Self-Exchange Reactions in Wid-State Voltammetry. The Radical Anion of 7,7,8,8-Tetracyanoqulnodlmethane In Polymer Electrolytes. 1 M. Watanabe: T. T. Wooster, and Royce W. Murray* Kenan Laboratories of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290 (Received: October 19, 1990)
Voltammetric currents for the oxidation of the lithium salt of the 7,7,8,8-tetracyanoquinodimethaneanion radical (LiTCNQ) at Pt microdisk electrodes in network poly(ethy1ene oxide) (PEO) polymer solvent are substantially larger than currents for its reduction. The difference in currents is interpreted as a combination of electron self-exchange (between TCNQ'and TCNQO) and electrostatic migration. The latter is a minor effect in the presence of LiC104 electrolyte as shown by a transference number (tma) analysis. At [LiCIO,] 5 0.4 M, the product ka#&,2 of electron-self-exchangerate constant and hopping distance (squared) for the TCNQ-IO couple is 1.0 (f0.3) X 10 cm2 M-' s-'. Assuming 61/o = 9.5 A gives kcx,l/o = 1 X lo8 M-'s-I in the polymer solvent, which is 47-fold smaller than ke,llo in acetonitrile solvent and 7-fold larger than measurable by methods subject to diffusion-controlled collision rate considerations. Physical diffusion is also slow in the polymer solvent and connections of this to kmlloare discussed, including encounter rate limitations, longer polymer solvent dipole relaxation times, and longer distance electron transfers.
This paper describes electron-self-exchange-based differences in the diffusion rates of the radical anion of 7,7,8,8-tetracyanoquinodimethane (TCNQ") in a polymer solvent, during its voltammetric oxidation and reduction at Pt microdisk electrodes. The solvent is the polymer electrolyte' "network PEO", a crosslinked polyether containing a dissolved alkali-metal salt. Polyethers readily dissolve many molecular electroactive solutes, and microelectrode voltammetry2can be used3 to measure their transport rates in the bulk polymer medium. In this study, the Li+ salt of TCNQ'- is dissolved in films of network PEO.' together with LiClO, as supporting electrolyte. The unusual observation is that the transport-limited voltammetric currents for the oxidation of TCNQ-' are larger than those for its reduction. The difference in currents depends on the concentrations of LiTCNQ and of LiC104 electrolyte. Since the diffusing species, TCNQ'-, is nominally the same in both cases, the difference in currents must arise from a special effect, shown here to be a combination of TCNQ-IO electron self-exchange (hopping) and migration transport. As compared to our previous solid-state voltammetric experiments,3c the effects of electron hopping and of migration are amplified in the present work by the relatively large concentrations of TCNQ'- employed and because the self-exchange rate constant, k, 2, for the TCNQ-I*couple is smaller than that, kex,l/o, for the TCkQ/O c o ~ p l e .O~ur analysis of the electron hopping transport reveals that kcx,llois smaller in the polymer solvent than the value reported5 in acetonitrile solvent. Physical diffusion is also slower in the polymeric solvent. The slower electron-transfer rate and physical diffusion may be mutually brought about by the slow polymer chain segmental motions. This constitutes the first detailed analysis of the dynamics of a homogeneous electron-self-exchange reaction in a polymeric solvent. The role of electron self-exchange in the transport of electrochemical charge to electrodes has been of interest since it was identified in films of electroactive polymers on electrodes6*'contacted by fluid electrolyte solutions. Electron self-exchange is the dominant transport mechanism in polymers containing electroactive sites affixed to the polymer.* It is also significant in polymers containing diffusively mobile electroactive species? where both physical diffusion and self-exchange can contribute to the transport. The (apparent) diffusion coefficient Dpppfor the electroactive species is given by the Dahms-Ruff equationlo where DphYis the physical diffusion coefficient, kexthe electron 'On leave from Deprtment of Chemistry, Sophia University, Chiyoda-ku, Tokyo I
,
,
self-exchange rate constant, 6 the center-toenter intersite distance at electron transfer, and C the total concentration of the elec(1) (a) MacCallum, J. R., Vincent, C. A., Eds. Polymer Elecrrolyre Reoiews 1; Elscvier Applied Science: London, 1987. (b) Armand, M. B. Annu. Rev. Mater. Sci. 1986,16,245. (c) Vincent, C. A. Prog. Solid Srate Chem. 1987,17,145. (d) Ratner, M. A.; Shriver, D. F. Chem. Reu. 1988,88,109. (f) Watanabe, M.; Ogata, N. Br. Polym. J. 1988,20, 181. (2)(a) Wightman, R. M. Science 1988,240, 415. (b) Ewing, A. G.; Dayton, M. A.; Wightman, R. M. Anal. Chem. 1981, 53, 1842. (c) Fleischmann, M., Pons, S.,Rolison, D. R., Schmidt, P. P., Eds. Ulrramicroelecrrodes;Datatech Systems: Morganton, NC, 1897. (d) Chidsey, C. E. D.; Murray, R. W. Science 1986,231,25. (e) Kittelsen, G. P.; White, H. S.; Wrighton, M. S. J. Am. Chem. Soc. 1985, 107, 7373 and referenccs
therein. (3) (a) Reed, R. A.; Geng, L.; Murray, R. W. J. Elecrrounal. Chem. 1986, 208,185. (b) Geng, L.; Reed, R. A.; Longmire, M.; Murray, R. W. J. Phys. Chem. 1987,91,2908.(c) Geng, L.; Reed, R. A.; Kim, M.-H.; Wooster, T. T.; Oliver, B. N.; Egekeze, J.; Kennedy, R. T.; Jorgenson, J. W.; Parcher, J. F.; Murray, R. W. J. Am. Chem. Soc. 1989, 111, 1619. (d) Geng, L.; Longmire, M. L.; Reed, R. A.; Parcher, J. F.; Barbour, C. J.; Murray, R. W. Chem. Mater. 1989,I , 58. (e) Reed, R. A.; Wooster, T. T.; Murray, R. W.; Yaniv, D. R.; Tonge, J. S.;Shriver, D. F. J. Electrochem. Soc. 1989,136, 2565. (f) Watanabe, M.; Longmire, M. L.; Murray, R. W. J. Phys. Chem. 1990,94,2614. (4)(a) Watanabe, M.; Nagano, S.;Sanui, K.; Ogata, N. Polym. J. 1986, 18,809.(b) Watanabe, M.; Itoh, M.; Sanui, K.; Ogata, N. Macromolecules 1987,20, 569. (5) (a) Haran, N.; Luz, Z.; Shporper, M. J. Am. Chem. Soc. 1974,96, 4788. (b) Komarynsky, M. A.; Wahl, A. C. J. Phys. Chem. 1975,79,695. (c) Harrer, W.; Grampp, G.; Jaenicke, W. Chem. Phys. Lett. 1984,112,263. (d) Harrer, W.; Grampp, G.; Jaenicke, W. J. Electrounal.Chem. 1986,209, 223. (e) Grampp, G.; Harrer, W.; Jaenicke, W. J. Chem. Soc., Faraday Trans. 1987,83,-161. (6)(a) Murray, R. W. Acc. Chem.Res. 1980,13,135. (b) Heller, A. Ibid. 1981.14. 154. (c) Murray. R. W. Annu. Reo. Mater. Sci. 1984. 14.145. (d) Faulkner, Chem..Eng. Nlws 1984,62,28. (e) Murray, R. W: Eiecrroailyrical Chemistry; Bard, A. J., Ed.; Marcel Dekker: New York, 1984;Vol. 13, p 191. (f) Wrighton, M. S.Science 1986,231,32. (7) (a) Kaufman, F. B.; Engler, E. M. J. Am. Chem. Soc. 1979,101,54. (b) Kaufman, F. B.; Schrocder, A. H.; Engler, E. M.; Kramer, S.R. Ibid. 1980, 102,483. (8) (a) Facci, J. S.;Schmehl, R. H.; Murray, R. W. J. Am. Chem. Soc. 1982,104,4959.(b) White, B.A.; Murray, R. W. Ibid. 1987,109,2576. (c) Dalton, E. F.; Surridge, N. A,; Jernigan, J. C.; Wilbourn, K. 0.; Facci, J. S.; Murray, R. W. Chem. Phys. 1990, 141, 143 and references therein. id) Shigehara, K.; Oyama, N.; Anson, F. C. J. Am. Chem. Soc. 1981, 103,2552. (e) Oyama, N.;Ohsaka,T.; Yamamoto. H.;Kaneko, M.J. Phys. Chem. 1986. 90,3850. (f) Ohsaka, T.; Yamamoto, H.; Oyama, N. Ibid. 1987,91,3775. (8) Morishima, Y.; Akihara, I.; Lim, H. S.;Nozakura, S. Macromolecules 1987,20,978. (h) Guadalupe, A. R.; Usifer, D. A,; Potts, K. T.; Hurrel, H. C.; Mogstad, A.-E.; Abruna, H. D. J. Am. Chem. Soc. 1988, 110,3462. (9)(a) Buttry, D. A.; Anson, F. C. J. EIecrrwnaI. Chem. 1981,130.333. (b) Buttry, D. A.; Anson, F. C. J. Am. Chem. Soc. 1983,105,685.(c) White, H. S.; Leddy, J.; Bard, A. J. Ibid. 1982, 104, 4811. (d) Martin, C. R.; Rubinstein, 1.; Bard, A. J. Ibid. 1982,104, 4817. (e) Oyama, N.; Anson. F. C. Ibid. 1979. 101.739.3450. tn Ovama. N.:Ohsaka. T.: Kaneko. M.: Sato. K.; Matsuda,'H. Ibid. i983. 105;60b3. (e) He, P.; Chen,' X . J. Eiectr&nal.' Chem. 1988,256, 353.
0 1991 American Chemical Society
4574 The Journal of Physical Chemistry, Vol. 95, No. 11, 1991 troactive species. The essence of eq 1 is that the rate of diffusional transport of electrochemical charge is noticeably enhanced by electron-self-exchangereactions within the (mixed valent) diffusion layer around the electrode, if the time scale of electron hopping between neighbor molecules separated by 6 becomes comparable to or faster than that of their physical center-to-center diffusion over the same distance. It is significant that we detect an electron transfer following a collision, which according to eq 1 produces an increase in the charge transport rate beyond a diffusional one. The consequence, as we show here, is that electron-self-exchange rate constants that are larger than those normally considered to be collision limited” can be measured. Analysis of the relation between C and Dappin eq 1 is, in polymeric phases, complicated by the general tendency for DpbP to change (typically decrease) with increasing solute concentrations. This difficulty was addressed by Buttry and Anson* with an electroactive species, [ C ~ ( b p y ) ~ ](bpy ~ ’ = 2,2’-bipyridine), electrostatically bound in the perfluorosulfonate polymer, Nafion, that could be both oxidized and reduced, and whose electrontransfer characteristics were such that only one of the two electrode reactions would be substantially affected by electron exchange. Other analogous experiments have since appeared.3c-8c.hJ2 The solid-state voltammetry of TCNQ- dissolved in network in that (i) the PEO resembles that of [ C ~ ( b p y ) ~ in ] ~Nafion, + electron-transfer dynamics for oxidation and reduction of TCNQ‘ differ, (ii) like other3*”solid-state voltammetric results, values of Dphys are small in the network PEO polymer phase, and (iii) Dphxsvaries3‘ with C. c p h y s additionally depends on the concentration of electrolyte, t e m p e r a t ~ r e , ~ ~and * ~ *the ‘ presence of plasticizers.M We have previously describedk a possible electron hopping contribution to [ C o ( b p ~ ) ~ voltammetry ]~+ in its solid solutions in high molecular weight linear PEO. The present work shows that electron hopping is an im ortant contributor to solid-state voltammetry of the TCNQ-i couple in network PEO. Migration-based transport is also detected but proves to be a relatively minor contributor to the transport. Experimental Section Electrochemical Microcell. The solid-state voltammetry cell consists of three wire tips exposed in a polished insulating plane:3 a 25-pm-diameter Pt microdisk working electrode sealed in a 1.Zmm-diameter glass capillary, and 0.35-mm-diameter Pt and Ag auxiliary and quasi-reference electrodes sealed together in a cylinder of epoxy resin (EPON 828, Miller-Stephenson Chemical). The wire tip/glass/epoxy surface was polished with successively smaller diamond and alumina pastes (Buehler) down to 0.05 Mm. The electrolyte and electroactive species were included in the network PEO polymer when it was cross-linked as a film on the microcell surface. Network PEO Polymer. Poly(ethylene oxide) triol (Daiichi Kogyo Seiyaku, M, = 3000) was dried under reduced pressure at 80 OC for 48 h. Anhydrous LiC104 (Aldrich) was stored and used in a N2-filled glovebox. Tolylene 2,4-diisocyanate (TDI, Polysciences) was purified by fractional distillation under reduced pressure and stored in the glovebox. Dibutyltin dilaurate catalyst (Aldrich) was used as received. Methyl ethyl ketone (MEK) was purified by distillation and stored over 4A molecular sieves. LiTCNQ was preparedI4from TCNQ (Aldrich) and LiI (Aldrich) (IO) (a) Dahms. H. J. Phys. Chcm. 1968,72,362. (b) Ruff, I.; Friedrich, V. J. Ibid. 1971.75,3297. (c) Ruff, I.; Friedrich, V. J.; Demctcr. K.; Csaillag, K. Ibid. 1971, 75, 3303. (d) Ruff, 1.; Korosi-Odor, 1. Inorg. Chcm. 1970, 9, 186. (e) Ruff, 1. Electrochim. Acto 1970, 15. 1059. (f) Botar. L.; Ruff, 1. Chem. Phys. Lett. 1986,126,348. (g) Ruff, I.; Botar, L. J. Chcm. Phys. 1985, 83, 1292. (h) References f-g correct the numerical prefactor in the equation from r/4 to 116. (1 1) von Smoluchowski, M.Phys. Z 1916, 17, 557, 585. (12) Surridge, N.;Jernigan, J. C.; Dalton, E. F.; Buck, R. P.; Watanabe, M.; Zhang. H.; Pinkerton,M.;Woaster, T. T.; Longmire, M. L.; Facci, J. S.; Murray, R. W. Faraduy Discuss. Chem. Soc. 1990,88, 1 . ( I 3) Longmire, M. L.; Watanak. M.;Zhang, H.; Wooster, T. T.; Murray, R. W. AMI. Chem. 1990,62,147. (14) Melby, L. R.; Harder, R. J.; Hertler, W. R.; Mahler, W.; Benson, R. E.; Mochel, W. E. J . Am. Chem. Soc. 1%2,84, 3374.
Watanabe et al. in acetonitrile (Burdick and Jackson, stored over 4A molecular sieves). Stock solutions of PEO triol in MEK containing the tin catalyst (0.1 wt 9% based on PEO triol) and LiCIO, in MEK were prepared and stored in the glovebox where network polymer electrolyte films were to be prepared. To a solution containing a known weight of LiTCNQ and a mixture of PEO and LiC10, stock solutions appropriate to the desired electrolyte concentration (expressed as the Li+/ether oxygen ratio,Li/O) was added TDI in a 3:2 molar ratio to PEO triol. This solution was thoroughly mixed and warmed at 70 OC for several minutes to initiate cross-linking as detected by an increase in its viscosity, whereupon a droplet was cast and spread on the microcell surface. The microcell was then sealed in an airtight glass container that permitted subsequent electrical connections to be made and that included an OMEGA type T or J thermocouple in the vicinity of the microcell and stopcocks for evacuation. This container was removed from the glovebox, heated at 70 OC for 1 h to complete the cross-linking reaction, and stripped of remaining MEK solvent by vacuum evaporation at room temperature for 18 h. Before making voltammetric measurements, the glass container was further purged with dry Ar gas and resealed. The resulting film of network PEO polymer solution of electrolyte and LiTCNQ was at least 0.1 mm thick, much larger than the voltammetric diffusion layer depth around the microdisk electrode. Diffusion Coefficient Measurements. Voltammetric responses were measured with a locally constructed low-current potentiostat?b a PAR Model 175 programmer for potential control, in a Faraday cage, and at temperatures controlled by an electric heater surrounding the glass microcell container. The diffusion constants were measured from potential ste chronoamperometriccurrents (times 1-100 s) plotted as i vs f ’ and extrapolated to the current (ih) at long time. This procedure, seeking a radial diffusion limited steady-statecurrent, is employed because the diffusion geometry around the microdisk electrode is mixed linear/radial for the range of Dw values involved. Details of the experimental procedure are described elsewhere.” The experimental diffusion constant Dcxpwas calculated from
P
ilim= 4nFrDapC
(2)
where C is the TCNQ‘- concentration, r is the microdisk radius (1.25 X lo-’ cm), and the notation Dolp refers to diffusion coefficients not corrected for migration effects as opposed to those which have been corrected but which still include electron hopping effects (Daw). The previous studyI3 of mixed linear/radial diffusion geometry did not involve migration effects. The data analysis here emphasizes the intercept rather than the slope of i vs r1I2 plots, since steady-state migration efffects are more readily treated (vide infra). Sometimes the i vs f1I2 plots were not linear but exhibited slopes gradually diminishing to small values, facilitating extrapolation to ilimy-intercept values. Results and Discussion Solid-state Voltammetry of LiTCNQ in Network PEO. Voltammograms for the one-electron oxidation and one-electron reduction of LiTCNQ dissolved in network PEO, Figures 1 and 2, are well-defined with no additional features. Figure 1 shows voltammogramsat several LiTCNQ concentrations, at 42 OC in network PEO/LiC104at Li/O = 0.02 (0.4 M LiC104),and Figure 2 shows voltammetry of 75 mM LiTCNQ at two different temperatures and at a series of LiClO, concentrations. Tables I and I1 give formal potentials for the two waves, measured as (Ebox + EN)/2, and for the differenceI5between them, Ei(O” - E1/2”. It is apparent from Figures 1 and 2 that the oxidation currents are larger than the reduction currents. This primary point will be addressed after we discuss the nature of the electrochemical reactions in Figures 1 and 2. (15) E O’ - El,lo’ is more reliable than the individual potentials E,,po’ and El120!’&causethe potential of the Ag wire pseudoreference shifts with changes in [ LiTCNQ] .
Radical Anion of TCNQ in Polymer Electrolytes
The Journal of Physical Chemistry, Vol. 95, No. 11, 1991 4515
TABLE I: Potential Data for Solid-state Voltammetry of LiTCNQ Dissolved in Network PE0/LiCIO4"
[LiTCNQ], M
V vs Ag 0.32 0.32
EI/0'',
0.005 0.010
L\E,lI09
0.30
0.025 0.050 0.10 0.2ob
mV
E1/2", V vs Ag
1 IO 1I5 105 145 150 180
0.27 0.23 0.24
mV
@,I/,,
Ello''
1 IO
-0.23 -0.24 -0.26 -0.30 -0.33 -0.30
- Ei/zO'rV 0.55 0.56 0.56 0.57 0.56 0.54
135 1 IO 155
135 105
" u = 20 mV/s, LiCIO, concentration of Li/O = 0.02(0.4M LiCIO,), 42 'C. These data are from Figure I . bSince some LiTCNQ precipitated
from the polymer solution, this concentration is only nominal. TABLE 11: Potential Data for Solid-state Voltammetry of 75 mhl LiTCNQ Dissolved in Network PEO/LiCIO; Li/O [LiCIO,], M T,'c @,,l/o, mV Ei/O'', V vs Ag V vs Ag AEp.112, mV 0.01 0.2 65 0.21 175 -0.35 160 0.02 0.4 65 0.30 165 -0.27 180 0.05 1 .o 125 65 0.19 -0.31 140 1.4 0.075 65 0.29 285 -0.17 150 0.10 1.9 65 0.21 205 100 -0.20 0.02 0.4 42 0.33 190 -0.25 170 0.05 1 .o 42 125 0.20 135 -0.30 0.075 1.4 42 0.30 170 -0.16 165 0.10 1.9 42 0.19 95 1IO -0.20
Elloo' - E1~20'r V 0.56 0.57 0.50 0.46 0.41 0.58 0.50 0.46 0.39
' u = 20 mV/s. Data are from Figure 2.
'/ nA
.-U
I
50mM
I0.25nA
10
05
EI Y
-05
0 VE
AQ
-10
10
05
0
-05
-10
EIVvfAg
Figure 2. Solid-state cyclic voltammetry (u = 20 mV/s) of 75 mM LiTCNQ dissolved in network PEO containing several different LiClO, supporting electrolyte concentrations, expressed as L i / O panel A, 65 'C; panel B, 42 OC. I
10
I
0 5
1
I
0 -0 5 E / V vs Ag
-1 0
Figure 1. Solid-state cyclic voltammetry (u = 20 mV/s) at 42 OC of LiTCNQ dissolved in network PEO/LiCIO, (Li/O = 0.02) at several concentrations of [LiTCNQ].
In aprotic, 02-free fluid electrolytes, TCNQO is reduced in two one-electron steps16 TCNQO + eTCNQ'-
+ e-
-
TCNQ'-
(3)
TCNQ2-
(4)
to stable" products, in acetonitrile at Elloo' = -0.1 1
V and = -0.66 V vs Ag/AgN03 (0.01 M). The difference between these potentials, Elloo' - E , 2°', is 0.55 V in the absence of ion pair formation between TC!NQ2- and cations.I6 TCNQ also forms dimers under certain circumstances. A stable dimer dianion, (TCNQ)$-, forms in aqueous solutions,18but less (16)(a) Khoo, S.B.; Foley, J. K.; Pons, S.J. Elecrroonul. Chem. 1986, 215,273. (b) Khoo, S.B.; Foley, J. F.; Korzenicwski, C.; Pons, S.;Marcott, C. Ibid. 1987, 233. 223. (17)Suchanski, M. R.;Van Duyne. R. P. J . Am. Chem. Soc. 1976,98, 250.
extensively in aprotic media. A mixed-valent dimer monoanion, (TCNQ),'-, may form during the electrochemical reduction of polymer films'g containing high concentrations (at least 1.6 MI") of TCNQ sites, which splits eq 3 into two waves with products (TCNQ),'- and 2TCNQ'-. Evidence against the involvement of either dimer, (TCNQ),Zor (TCNQ),'-, in the voltammetry of TCNQ'- in network PEO is as follows: (i) the characteristic blue color of (TCNQ)," (A= 643 nm18) was never observed in the moisture- and 02-free polymer solutions (see Experimental Section), (ii) we observe no splitting of voltammetric waves indicative of (TCNQ),', and (iii) the LiTCNQ concentration is at most 0.1 M. (The solubility limit for LiTCNQ in the polymer is around 0.1 M; attempts to prepare 0.2 M solutions leave undissolved material.) Further, at low electrolyte concentration (Li/O = 0.02, Table I), the difference in potentials Elloo' - EIj2'' of the oxidation and reduction waves does not depend on [LiTCNQ] and agrees with the difference Elloo' - E,,,'' = 0.55 V reported in fluid solution.16. Accordingly, R. H.;Phillip, W. D. J . Chem. Phys. 1965, 43,2927. (19)(a) Day, R. W.; Inzelt, G.; Kinstle, J. F.; Chambers, J. Q.J . Am. Chem. Soc. 1982, 104, 6804. (b) Inzelt, G.;Day, R. W.; Kinstle, J. F.; Chambers, J. Q.J. Phys. Chem. 1983.87,4592. (c) Inzelt, G.; Day, R.W.; Kinstle, J. F.; Chambers, J. Q.J . Electround. Chem. 1984, 161, 147. (d) Karami, H.;Chambers, J. Q.Ibid. 1987,217,313. (18) Boyd,
4576 The Journal of Physical Chemistry, Vol. 95, No. 11, 1991
0.05
0.10
[LiTCNQ] , M
Figure 3. Diffusion coefficientsfor TCNQ- as a function of [LiTCNQ] in network PEO/LiCIO, (Li/O = 0.02) at 42 "C. Solid lines are ex-
perimental diffusion coefficients (Dup uncorrected for migration effect); dashed lines are corrected D.pp values. DcxP,l/o(+); D,,,,/o (- -0--); D,,,/2 (-.-I; D.,1/2 (--.- -1; Dup,,/o - DcX*.l/2(-A+ D,,l/O - D.,1/2 (- -A--).
eqs 3 and 4 represent the TCNQ'- voltammetry, with no involvement of dimer forms. While Elloo' - El/20'seems not to change with [LiCIO,] below Li/O = 0.02 (Table 11, 65 "C), at higher Li/O Elloo' decreases with increasing LiCIO, concentration, at 65 "C from 0.57 V at Li/O = 0.02 (0.4 M)to 0.41 V at Li/O = 0.1 (1.9 M). This dependency suggests ion pairing of Li+ with T C N F and/or TCNQO-. Analogous changes in potentials in aprotic fluids containing alkali-metal salts have been attributed'6a.20 to ion pairing, in the reductions of TCNQ'- and of the radical anions of tetracyanoethylene (TCNE'),'@ benzoquinone, anthraquinone, and chloranil.zo In TCNQ' voltammetry in network PEO (Figure 2, Table II), strong ion pairing of Li+ with both TCNQ' (forming Li+TCNQ') and TCNQZ- (forming (Li+)*TCNF)should cause the potentials of both reactions to shift equally as [LP] is changed, producing no net changes in Elloo',- El/20'. On the other hand, if TCNQ'should is not significantly ion-pairedbut T C N F is, El oo' vary with log [Li+] with slope 67 mV (for {ormation of Li+TCNQ'-) and 134 mV (for formation of (Li+)zTCNQ2-),at 65 "C. The results in Table I1 indicate that Ello"' changes with log [Li+] with a varying slope rising to ca. 0.3 V at high Li/O. This is a larger [Li+] dependency than expected, but at the same time we realize that the Elloo' and EIl2O'measurements are less reliable at large [Li+], owing to the much slower diffusion rates and consequent mixed (radial/linear) diffusion situation in Figures 1 and 2. We take the strong [Li+] dependency as reflecting, at larger Li/O, the onset of strong Li+ ion pairing with TCNQ2-, probably forming (Li+)2(TCNQ)2-,but with little or no ion pairing with TCNQ'-. The lack of ion pairing of Li+ with TCNQ'- is an important point with respect to the subsequent treatment of migration effects in the network polymer. Possible Charge Transport by Electron Hopping in Network PEO. Returning to the primary observation of Figures 1 and 2, that the TCNQ' oxidation currents are larger than the reduction currents, their variations with [LiTCNQ] strongly suggest involvement of an electron-self-exchangeprocess in the transport. Table 111 and Figure 3 show the values of the experimental diffusion coefficients derived as in the Experimental Section. 0 for the TCNQ-IO oxidation modestly increases with While DcXp,' increasing (LiTCNQ], and Dcxp,l/2for the TCNQ-12- reduction decreases sharply with increasing [LiTCNQ], the difference DcXp.~/o - Dexp.l/2(Figure 3) increases linearly with [LiTCNQ], Le., behavior anticipated from eq 1. There is some considerable scatter in the plots of Dcxp,llo and Dexp,l12 but much less in their - Dcxp,l/2.The Figure 3 results are repeatable, difference, DcxRI,o especially with regard to the difference, DaRll0- D,,i12, as shown by similar experiments over a range of temperatures to be reported elsewhere. * Let us assume for the moment that the experimentally derived will change very little diffusion coefficients Dcxp,lloand Dexp,l12 (20) (21)
Paver, M. E.;Davies. J. D. 1. Elcetroanal. Chem. 1963, 6, 46. Watanabe, M.;Woostcr, T.T.; Murray, R. W. Unpublished results,
University of North Carolina, 1989.
Watanabe et al.
The Journal of Physical Chemistry, Vol. 95, No. 11, 1991 4517
Radical Anion of TCNQ in Polymer Electrolytes
r/
CL~TCNQ3. 2 5 mM h
-
%
-8
J
-9-
. 6
N
ii
I
10.1 nA
Y
OI
0 -
-10
-
-111
0
.-
'
10.25 nA
1
' I ' ' ' ' ' ' I 0.02 0.04 0.06 0 0 8 0.10
'
LIIO
Figure 4. Experimental diffusion constants D,,l,~ (0) and D,.,lp ( 0 ) of TCNQ' at 4 2 OC as a function of LiClO, supporting electrolyte concentration, Li/O, for 75 mM LiTCNQ dissolved in network PEO/ LiClO,.
upon correction (to Damll0 and Da I 2, dashed lines in Figure 3) for migration effects; this is justifdlater. Transport assisted by electron self-exchange between TCNQo and TCNQ' during TCNQ'- oxidation can be expressed as Dapp,l/O
Dphya
+ kex,l/Osl/02C/6
(5)
whereas that assisted by exchange between TCNQ' and TCNQZduring TCNQ'- reduction is Dapp,l/2
Dphya
+ kex.l/Z~1/22c/6
(6)
where C = [TCNQ"]. Taking the difference Dapp,l/o- ~ a p p , l / 2= [kex,l/osl/02/6- k e x , 1 / ~ / 1 2 ~ / (7) 6]~
shows that a D, ,I/o- Daw,,/,vs C plot (Le., Figure 3) has a slope determined by fie difference between the two self-exchange rate constants. Since the slope in Figure 3 is positive, we have kex,l/O >> k,,Ip,provided b,/o and sIl2are similar. There ISample precedent for anticipating that k,,,, >> kex,l12 for the TCNQ self-exchange reactions. ESR line-6oadening studies" show that kex,l/O for TCNQ-lO electron self-exchange in The kex,l/2for acetonitrile is very large (4.7 X lo9 M-I S-I). TCNQ-12- electron self-exchange is not available, but Chambers and co-workerslw noticed a rate difference between the two reaction steps in the electrochemistry of TCNQ polymer films on electrodes, and there are numerous data for analogous systems. Homogeneous ratesZ2for N,N,N',N'-tetramethyl- 1,Cphenylenediamine (TMPD) show that k,, for TMPDo/+ in acetonitrile is 20-fold larger than that for TMPD+l2+. The heterogeneous electron-transfer rate constants for 1,4-benzoquinone (Q) deriva t i v e ~differ ~ ~ for the Qo/- and Q-12- reactions by 1-2 orders of magnitude depending on the and results for the analogous reactions for TCNE suggest differences of between 1 and 4 orders of magnitude difference in the rate constants.IQ Also, by classical electron-transfer theory,"4an electrostatic work term should slow TCNQ-12- electron transfer relative to TCNQ-IO, and at higher Li/O where ion-paired Li2(TCNQ2-)is suggested (vide supra), the ion-paired state should offer an additional ("inner sphere") impediment to TCNQ'-/Li2(TCNQ2-) self-exchange. Finally, any change induced in TCNQ-/O electron-transfer rates by the polymer solvent dynamics (vide infra) should be mirrored by changes for TCNQ-l2-, so that solvent effects should not (22) Gramp, G.; Jaenicke, W. Ber. Bunsen-Ges. fhys. Chem. 1984, 88, 325, 335. (23) (a) ROssel, C.; Jaenicke, W. J . Elecrroanal. Chem. 1986, 200, 249. (b) Raesel, C.: Jaenicke. W. Ibid. 1986, 199, 139. (c) Riissel, C.; Jaenicke, W. Ibid. 1984, 180, 205. (24) (a) Marcus, R. A. J . fhys. Chem. 1%3,67,853. (b) Marcus, R. A. Annu. Reo. fhys. Chem. 1964, I S , 155. (c) Marcus, R. A. J . Chem. fhys. 1965,43,679. (d) Marcus, R. A.; Sutin, N. Bfochim.Biophys. Acra 1985, 811. 265.
1
I
I
1
10
05
0
-05
I
-1 0
E I V vs Ag
Figure 5. Solid-state voltammetry (v = 20 mV/s) at 4 2 "C of LiTCNQ dissolved in network PEO with no supporting electrolyte.
eliminate a difference between kcx,l12 and k,x,l/o. Our interpretation of the Dappresults is accordingly based on the assumption that kcx,l12in eq 7 is small or negligible relative so that the slope of a D, ,I/o - D,w,1/2vs C plot primarily to kWllch reflects the value of k e , , l ~ o ~ l ~ 0This 2 / ~ analysis . will be applied after correction of the DmPdata for migration effects as described next. Migration Correction. Electron self-exchange can account for the [LiTCNQ] dependency of the relative values of oxidation and reduction currents in Figure 1, but not for the changes in Figure 2 with [LiC104]. The Li/O dependency of D e x p , land / ~ Derp,l/2 shown in Figure 4 reveals that D,,l~o and Dexp,1/2 differ most at low supporting electrolyte concentration, an effect consistent with electrostatic migration. Electrolytes are added in electrochemical experiments to eliminate voltage gradients in the solvent medium and to reduce the transference numbers of ionic electrode reactants to negligible values.25 Violation of this condition produces a so-called migration effect and increases or decreases transport rates (and voltammetric currents) depending on the sign of the current and of the reactant ion charge. In TCNQ'- voltammetry, migration would increase the oxidation currents and decrease those for reduction. Since this is in the same direction as anticipated for electron-self-exchange-assisted transport, we must inquire whether migration might in fact be the main cause of the differences in currents in Figures 1 and 2. Migration has been previously observed at microelectrodes, in fluid media containing inadequate supporting electrolyte concentrations.26 The current for transport of a species toward an electrode is expressed by the Nernst-Planck equationZ5 i = zFADVC f ( z 2 p A / R T ) D C V 4
(8)
where VC and V 4 are concentration and potential gradients and A is electrode area. Under mass-transport-limited, steady-state current conditions (i-e.,ilim),V C and V 4 are constant, and upon introducing the transference number of TCNQ'-, we have2' ilim
= id/ [1
*
(n/z)tTCNQl
(9)
where at steady state the experimental diffusion constant is (25) Bard, A. J.; Faulkner, L. R. Electrochemical Methods; John Wiley & Sons: New York, 1980; Chapter 4. (26) (a) Amatore, C.; Deakin, M. R.; Wightman, R. M. J . Elecfroaml. Chem.. 1987, 220, 49. (b) Amatore, C.; Fosset, B.; Bartelt, J.; Deakin, M. R.; Wightman, R. M. Ibid. 1988. 256, 255. (27) Reference 26b points out that eq 9 is an oversimplified statement of the migration effect, because transport numbers of electroactivespbcics in the diffusion layer are not the same as thase in the bulk solution. The more correct formulation in ref 26b predicts smaller migration effects than eq 9. We have used the simpler eq 9 because, (a) unlike the assumption in ref 26b, diffusion coefficients of the different ionic constituents present in network PEO are not equal and (b) the migration correction proves to be small.
4578 The Journal of Physical Chemistry, Vol. 95, No. 11. 1991
Watanabe et al.
Thus calculated "tQ values in the solutions of all the preceding experiments are given in Table 111, as are values of Daw,l/oand DapRi/2 calculated from twNQ and DcxR1/o and DeXRII2, respectively, using eqs 10 and 1 1 . The important result seen in Table 111 is that, while tTCNQ is " 0.05 0.1 0 appreciable in network PEO solutions containing no LiC104 [LiTCNQI , M (Figures 5 and 6), tTCNQ is quite small in all the solutions containing LiCI04,so that Dap and 0, values are very similar (Table Figure 6. Ratio of experimental diffusion constants, DaRl/o/DaRl/z,. as a function of [LiTCNQ]in network PEO,in the absence of supporting 111). In other words, migration effects in Figures 1 and 2, while electrolyte: (0)4 2 OC, (0) 65 O C , ( 0 ) 101 OC. real, are quite small.32 These calculations complete the correction for the migration effect on TCNQ'- transport in network PEO, and we return to contained in ih = 4nFrD, C and the apparent diffusion constant the analysis of electron-self-exchangepicture for the TCNQ-IO in id = 4nFrDappC,and nfz = 1 for the T C N Q - reactions. It couple in network PEO. follows that Charge Transport by Electron Hopping in Network PEO. The Dcxp,1/0 Dapp,i/o/(l - ~TCNQ) (10) results were applied to migration-corrected and Dapp,1/2 eq 7 to calculate k,x,llo61102 (strictly speaking, k,,l& o2 (11) Dcxp.1/2= Dapp,1/2/(1 + ~TCNQ) kchz/i62/i2) for each experiment as shown at the right side of +able 111. Except at high electrolyte concentrations (shown in parwhich provides a way to correct DUpresults for migration provided taken at Li/O entheses, vide infra), the 10 values of kex,ilo6ilo2 the transference number tTCNQ can be found.28 5 0.02 are constant, independent of [TCNQ'] and of Li/O. The was measured from voltammetry in network PEO conconsistency with which eq 7 represents the experimental results t a z I i T C N Q b u t no LiC104, which enhances any migration is further illustrated by the linearity of the Dwil0- DamIlZ (Figure effect. Indeed, Figure 5 reveals a large difference between the 3) and Dapp,l/o/Dapp,i/2 (Figure 6) vs C plots. and TCNQ- oxidation and reduction currents, shown as De, The average value of k , x , i l o 6 1at~Li/O ~ I0.02 is 1.0 (f0.3) Dexp,l~2 results in Table 111 (bottom) at Li/O = 0. On t i e other X lod cm2 M-' s-l for the homogeneous electron-self-exchange hand, were migration to be the only operative effect (Le,, no reaction between TCNQ and TCNQ- in network PEO at 42 OC. electron self-exchange at all and Daw= Dphys),D,,,/o and DeXR1/2 This result combined with the slope of Figure 6 and eq 12 yields should according to eqs 10 and 1 1 lie in a constant ratio. a value for DphPof 9.6 X cm2 s-I for TCNQ'- in network D, i/o/D,,i/2 obviously however changes with [LiTCNQ] (Table PEO solutions containing only LiTCNQ, without any assumptions IIIE as expected for electron self-exchange occurring in addition about SI o. In the presence of high concentrations of LiC104, to migration. k,i/,&$ decreases sharply; its value at Li/O = 0.1 is ca. 103-fold The relative diffusivities of Li+ and TCNQ' are obtained from smaller than the common value at Li/O I 0.02. This change these results by using the ratio of eqs 10 and 1 1 and assuming parallels a decrease in Dphysat higher'Li/O seen in the Dapp,,/2 that kcx,l12is negligible in relation to Dphys: results in Table 111. Converting k,,ilo611~ into a self-exchange rate constant kqil0 Dexp,i/O/Dnp.i/2 = requires making some assumption about the center-to-center distance of electron transfer, b1lo. The crystallographic TCNQ + fTCNQ)/(l - tTCNQ)!(l + kex,l/06i/02C/6Dphys~(12) molecular dimensiong3is ca. 9.5 X 5.5 X 3.5 A. For the case where electron transfer occurs upon collisional contact, assuming electron A plot of D , , , I / ? / D ~ ~vs~ ,[TCNQ'] ~/~ should thus be linear with intercept containing tTCNQ. Such a plot, shown in Figure 6 for hopping distances 6i/o = 3.5 and 9.5 A, gives kcx,llo= 8 X lo8 three different temperatures,gives tmq = 0.5,which means that and 1 X lo8 M-' s-I, respectively, at low Li/O. These rate conDti/D.= 1 .O in network PEO. Previousmcomplex impedance stants (at 42 "C) are smaller by &fold and by 47-fold, respectively, and dc polarization measurements30give Dclo,/DLi = 3 for the than that observedSfor TCNQ-IO self-exchange at room temrelative diffusivity of Li+ and C104- in network PEO containing perature in acetonitrile, 4.7 X lo9 M-l s-l; Le., the electron no LiTCNQ; this result is consistent with observations in related self-exchange occurs more slowly, by a minimum (due to the polymer^.^' Combining these results gives DCIOJDTCNQ= 3. temperature difference) of 6-fold, in the polymer solvent. If Assuming that ion-pair-inducedchanges in ionic concentrations electron transfer were to occur at distances larger than the contact are negligible in polymer solutions containing mixtures of LiTCNQ distance (i.e., 6i/o > 9.5 A), the average kex,l/Oinfluencing the and LiC104, tTCNQ can now be calculated for solutions containing charge diffusion would be even smaller. both LiC104 and LiTCNQ from the relation Solute diffusion rates in network PEO solvent are also generally much smaller" than those common to fluid solvents like acetonitrile, and this is the case for TCNQ'- solute as well. The value (28) (a) We note incidentally that this analysis neglects effects associated derived above for Dphys(9.6 X lo4 cmZS-I) in the absence of with acceleration of electron hoppingnh by the small electric field in the LiC104 electrolyte is ca. (2 X lo3)-fold smaller than that in polymer solution. (b) Savant, J. M. J . Electroanal. Chem. 1986,201, 21 I . acetonitrile. That value of DPhpis nearly the same as D,pp,i/2at (c) [bid. 1988, 242, 1. (c) Andrieux, C. P.; Savant, J. M. J . Phys. Chem. low LiC104electrolyte concentrations, 9.8 X lo4 cm2s-I (average 1988,92,6761. (d) Jernigan, J. C.; Murray, R.W. [bid. 1987,91,2030. (e) Jernigan, J. C.; Surridge, N . A.; Zvanut, M. E.; Silver, M.; Murray, R. W. at Li/O I0.02, Table 111). Dapp,i,2 decreases strongly of ""'I/ [bid. 1989, 93, 4620. at hig er electrolyte concentrations. (29) Kato, Y.;Watanabe, M.; Sanui, K.; Ogata, N . Solid State tonics, submitted for publication. (30) (a) Bruce, P.;Vincent, C. A. J . Electroanal. Chem. 1987,255, 1. (b) Evans, J.; Vincent, C. A.; Bruce, P. G. Polymer 1987, 28, 2324. (c) Watanabe, M.; Nagano, s.;Sanui, K.; Ogata, N . Solid State tonics 1988,28-30, 911. (31) (a) Weston. J. E.; Steele, 9. C. H. SolidSrare tonics 1982, 7,81. (b) Bouridah, A.; Dalard, F.; Deroo, D.; Armand, M. 9. Solid State tonics 1986, 18-19,287. (C) Gorecki, W.; Andrcani, R.;Berthier. C.; Armand, M.; Mali, M.; Roos. J.; Brinkmann, D. Solid State tonics 1986, 18-19, 295. (d) Leveque. M.; LeNest, J. F.; Gandini, A.; Cheradame, H. Makromol. Chem. Rapid Commun. 1983, 4. 491.
(32) Assuming that no electron hopping occurs would force the current differences in Figures I , 2, and 5 to be accommodated by [TCNQ-]-dependent values of trCNp (Le., &CNp/DL,) and require that, in the absence of LiClO, (Figure 6), &CNQ/DU must vary from 1.25 to 3.64 over the series of LiTCNQ concentrations and in the presence of both LiTCNQ and LiClO, /4,vary from 11.7 to 3 1.4. Such large, (retaining DcQ/&, = 3) that kN variable magnitudes of the &cNQ/%Li ratio are not plausible. (33) Long, R. E.; Sparks, R.A,; Trueblood, K. N. Acta Crystallogr. 1965, 18, 932.
Radical Anion of TCNQ in Polymer Electrolytes In the polymer solvent, we thus find that both the physical rate of diffusion (Dphyr) and the rate constant k,,llo for electron self-exchange in the TCNQ-IO couple are depressed, as compared to the fluid solvent acetonitrile. Both parameters furthermore decrease together at high electrolyte concentrations. These observations are related to one another in the following three models that address possible reasons for the slowed electron-transfer dynamics: (i) Firstly, we consider whether the rate constant kWl of electron transfer might be limited by the encounter rate o/ the TCNQ and TCNQ'- reaction partners. By reaction encounter we do not necessarily mean collision contact, but rather to explicitly include Mencounters"leading to electron transfers at largerthancontact distances. One such encounter is a necessary prelude to reaction, which connects the rate constant kRll0 to Dep in that the latter will influence the encounter rate. Qualitatively, this occurs when the average time between reactant encounters becomes much longer (because Dphp becomes small) than the reaction time for electron transfer. The reaction encounter rate that is pertinent to the charge diffusion measurement (eq 1) is, contrary to previous and we now believe erroneous combinations of eqs 1 and 15,not that given by the classical collision-limited reaction rate relationI2 kd = 4rNA6(2Dphyr)/ 1O3 (14) where NAis Avogadro's number. The physical reason for this is that eq 14 gives the rate at which reactants diffuse together and collide but contains no information about the reaction's spatial displacement of charge that follows a reaction-producing collision. The electrochemical diffusion measurement, with eq 1, provides on the other hand a direct measurement of the transport of charge (toward the electrode) that occurs in the encounter pair following the collision. A result is that the analysis of electrochemical charge transport by eq 1 actually allows measurement of a rate constant larger than that given by eq 14. This is interesting since eq 14 is commonly assumed to represent the "upper measureable limit" of the reaction rate constant measurement. Thus, using DphP = 9.8 X 10" cm2 S-I gives kd = 1.4 X lo7 M-'s-l. This value is 57-fold and 7-fold smaller respectively than the kcx,lloestimate (vide supra) based on 6 = 3.5 and 9.5 A. (ii) Secondly, kcx,llocan be diminished by the effect of the relatively slow molecular dynamics of the network PEO polymer medium on the barrier-crossing rates. Recent theories35 have emphasized the importanceof reorganization of monomer solvent dipoles in electron-transfer kinetics, and there have been observations that connect monomer solvent and electron-transfer dynamics.-~)~ We hypothesize that reorganizations of solvent dipoles that are affixed to a polymer chain will necessarily depend on segmental (or subsegmental) motions of the chain and that such polymer solvent dipole relaxation times will be longer than those of monomeric solvent moieties. That is, when solvent dipole effects influence electron-transferrates, rates in polymer solvents are likely to be smaller than in monomeric solvent. Physical diffusion rates (Dphyr) of polymer solutes also reflect the rates of polymer chain segmental (or subsegmental) motions (34) We are grateful to Professor J.-M. Saveant (Comments at Paper 729, Electrochemical Society National Meting, May 1990, Montreal) for pointing out the inappropriateness of combining eqs 1 and 15 and that k,, values extracted from cq 1 could in principle exceed kd. (35) (a) Zusman. L. D. Chem. Phys. 1980,49, 295. (b) van der Zwar, G.; Hynes, J. T. J . Chem. Phys. 1982,76, 2993. (c) Calef, D.F.; Wolynes, P. G. J . Phys. Chem. 1983,87,3387. (d) Hynes, J. T. Ibid. 1986,90,3701. (e) Sumi, H.; Marcus, R. A. J . Chem. Phys. 1986,84,4894. (36) (a) Nielson, R. M.; McManis. G. E.; Golovin, M. N.; Weaver, M. J. J . Phys. Chem. 1988,92,3441. (b) McManis, 0. E.; Weaver, M. J. Chem. Phys. Left 1988,145,55. (c) Zhang. X.;Leddy, J.; Bard, A. J. J . Am. Chcm. Sor. 1985.107, 3719. (d) Zhang, X.;Yang, H.; Bard, A. J. Ibid. 1987,109, 1916. (e) Weaver, M. J.;Gennett, T. Chem. Phys. Lrtf. 1985,113,213. ( f ) Gennett, T.;Milner, D. F.; Weaver, M. J. J. Phys. Chem. 1985.89, 2787. (g) McManis, G. E.; Golovin. M. N.; Weaver, M. J. Ibid. 1986, 90, 6563. (h) Nielson, R. M.; Weaver, M. J. J . Elecfrounul. Chem. 1989,260, 15. (i) Kapturkiewicz, A,; Behr, B. Ibid. 1984, 179, 187. Kapturkiewicz, A.; Opallo, M. Ibid. 1985,185. IS. (k) Opallo. M. J . Chem. Sor., Furaduy Truns. I 1987,83, 161.
u)
The Journal of Physical Chemistry, Vol. 95, NO. 11, 1991 4519
since it is through successions of such motions that physical translations of solutes occur.3f Thus, slow physical diffusion and polymer solvent dipole reorientationantrolled electron transfers can be manifestations of a common phenomenon of slow segmental motion. In recent)' work we have observed that the cross-electrontransfer-rate constant for oxidation of an [Fe(phen),12+ complex by a poly[O~(bpy),(vpy)~]~+ surface is depressed (by 102-fold) in a polyether solvent as compared to acetonitrile and that the heterogeneous rate constant for oxidation of [ C ~ ( b p y ) ~is] ~de+ pressed in the same polymer solvent by about the same amount. The nature of both these studies excludes reaction encounter rate limitations as the source of the difference in electron-transfer rates; they are clearly solvent effects. Also, Bard et al. have in related studies heterogeneous rate constant depressions in increasingly viscous media. Given this background, it is plausible that slow polymer solvent dynamics might contributeto the slower k,,llp self-exchange rate constant for TCNQ-lO in network PEO, relative to acetonitrile. (iii) The small values of solute diffusion rates in network PEO solvent may also affect the value of kcx,llo61102 in that the rate of electron-transfer rates at distances larger than contact can become competitive with diffusion rates. This can be viewed in eq 1 as competition between the time scale tD of diffusion over the distance all0, which is expressed by [DphptD]1/2, versus the time scale ~(6) for electron transfer over the same (average) distance 6,l0 which would be expressed by the tunneling relation2" k(6) = 1 / ~ ( 6 )= k, exp[-/3(r
- ro)]
where r - ro is ca. 6 - 9.5 A. If t D >> ~ ( 6 1electron , tunneling at distances larger than that for molecular contact would surely contribute to the net charge transport, albeit with a smaller rate constant according to eq 15. By this argument, in which the average 6 becomes a function of Dphys, a correlation between physical diffusion and electron-transfer rates is expected, especially at the slowest diffusion rates. Because in this picture the average value of 6 becomes dependent on the value of Dpbyr,the separation of these quantities as given in eq 1 is no longer cleanly made, and refinement of that theory may be necessary. We note that a limiting case of the connection between physical diffusion and electron tunneling rates is already known: that of redox sites affixed to proteins?8 which are thought to be diffusively immobile relative to one another. It is difficult at this point to draw clean choices between these three models to explain the small values of kWllofor the TCNQ-IO couple in network PEO. (i) and (iii) are obviously interconnected, and we noted that the theory appropriate for a more detailed analysis is lacking. Also, it is possible that no single model applies. Thus, at high electrolyte concentration,where Dmyrbecomes very small, tunneling may be an important reaction pathway and the reaction (long-distance) encounter limited. At low electrolyte concentration and larger Dphp, the reaction may proceed in a nonencounter rate-limited manner by a largely contact pathway. We will be able to improve somewhat on distinctions between these models with temperature-dependent data to be presented in a forthcoming paper.21 Acknowledgment. This research was supported in part by grants from the National Science Foundation and from the Department of Energy (DE-FG05-87ER13675). M.W.acknowledges sabbatical leave support from Sophia University. The authors gratefully acknowledge experimental work by K. Pressprich that lead to recognition of the migration effect. See also ref 34. (37) Zhang, H.;Wooster, T. T.; Murray, R. W. 177th Meeting of the Electrochemical Society. Montreal, May 1990; Abstract 682. (38) (a) Elias, H.;Chou, M. H.; Winkler, J. R. J. Am. Chem. Soc. 1988, 110,429. (b) Winkler, J. R.; Nocera, D. G.; Yocom, K. M.; Bordignou, E.; Gray, H. B. Ibid. 1982, 104, 5798. (c) Axup, A. W.; Albin, M.; Mayo, S. L.; Crutchley, R. J.; Gray, H. B. Ibid. 1988, 110,435. (d) Karas, J. L.; Lieber, C. M.; Gray, H. B. Ibid. 1988, 110, 599.
