3086
J. Phys. Chem. 1984, 88, 3086-3091
Enhancement of Charge-Transport Rates by Redox Cross-Reactions between Reactants Incorporated in Nafion Coatingst Daniel A. Buttry,$ J. M. Saveant,$and Fred C. Anson* Arthur Amos Noyes Laboratories, Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91 125, and Universite de Paris VU, Laboratoire d'Electrochimie, Tour 44-45, 75221 Paris, Cedex 05, France (Received: September 16, 1983)
The rate of charge transport within Nafion coatings by Co(typ)?' (tpy = 2,2',2"-terpyridine) is enhanced when it is measured in the presence of Ru(NH3);+ with which it undergoes a rapid electron-transfer cross-reaction. Similarly, the presence of Cp,FeN(CH&,+ (Cp = cyclopentadienide) enhances the propagation rate of Co(tpy)z2+. Cyclic voltammetry was used to demonstrate the effect qualitatively and chronocoulometryto document it quantitatively. The enhancement results because electron transfer between the more slowly diffusing complex (C0(tpy)2~+or Co(tpy),*+) and the more rapidly diffusing Ru(NH&~' or CpzFeN(CH3)32+complexes allows the latter to carry charge between the electrode surface and the slower moving complex. A formula for the extent of the enhancement is derived for the case of potential step chronocoulometry or chronoamperometryand used to compare calculated enhancements with those measured experimentally. Some implications of electron-transfer enhancement of charge propagation rates for electrocatalytic applications with polymer-coated electrodes are pointed out.
Redox couples incorporated in polymer and polyelectrolyte coatings on electrodes exhibit a much wider range of effective diffusion coefficients than they do when dissolved in fluid solutions.'+ One result of this fact is that electron exchange between pairs of the oxidized and reduced form of a redox couple can contribute significantly to, or even become the predominant mode of, diffusion of redox species in the coating^.^^^^^ A second interesting phenomenon can be encountered in cases where two redox couples having disparate diffusion coefficients and formal potentials are both incorporated in an electrode coating. If the more rapidly diffusing reactant is reduced (or oxidized) at more negative (or positive) potentials than the more slowly diffusing reactant, the rate at which the latter is reduced (or oxidized) can be enhanced by the faster moving reactant's shuttling electrons between the electrode surface and the more slowly moving reactant at positions in the interior of the coating. So long as the rate of the electron-transfer cross-reaction between the two complexes is sufficiently high, the result is a net current that can be considerably greater than the sum of the currents delivered by the two reactants when examined separately. The effect becomes greater as the equilibrium constant for the electron transfer between the oxidized and reduced halves of the two redox couples and the ratio of their individual diffusion coefficients become larger. The lack of large differences in the diffusion coefficients of redox reagents prevents comparably large enhancements of diffusional rates in fluid solutions. However, the phenomenon is essentially the same as that first reported by Miller and Orelmann in the case of dc polarographyiOand subsequently examined by several groups in studies of the ac polarography of mixtures of redox reagents."-I5 Enhanced currents at electrodes coated with a quinoid polymer were reported recently by Miller and co-workersI6when a rapidly diffusing redox mediator was added to the solution in which the coating was being reduced. They clearly identified the crossreaction between the mediator and the essentially immobile quinoid groups as the source of the current enhancement. Facci and Murray also obtained qualitative evidence of mediated charge transport in an electrode coating containing two redox couples3 but the difference in diffusion coefficients of the two couples in their system was too small to produce large current enhancements. In this study we have examined two pairs of redox couples that have quite disparate diffusion coefficients when incorporated in +Contributionno. 6872 of the Arthur Amos Noyes Laboratories. *Present address: IBM Research Center, San Jose, CA 95193. Universite de Paris VII. *Address correspondence to this author at the Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA 91125.
*
0022-3654/84/2088-3086$01SO/O
Nafion coatings as the countercations of the fixed anionic sulfonate groups. Binary mixtures of the redox couples exhibit large enhancements of the diffusion-controlled reduction currents. Comparison of the current enhancements with those calculated on the basis of a simple model results in moderately good agreement. The phenomenon seems likely to be a commonly encountered feature for electrodes coated with polymers in which mixtures of redox couples are incorporated.
Experimental Section Materials. Nafion coatings were prepared from a 5.2 wt % solution of the polymer (970 equivalent weight) supplied by E. I. du Pont de Nemours Co. a number of years ago. (Solutions of soluble Nafion are now commercially available from C. G. Processing, Inc., Box 133, Rockland, DE 19732.) A stock coating solution was prepared by diluting this solution 10-fold with 2propanol. Co(tpy),C12 (tpy = 2,2',2"-terpyridine) was prepared by the procedure given in ref 17. Co(tpy)?+ was prepared by electrolytic oxidation of Co(tpy)22ein 0.5 M Na2S04. Ferrocenyltrimethylammonium perchlorate (Cp2FeTMA+C10~)was obtained by metathesis from Cp,FeTMA+Br- (Research Or-
(1) Daum, P.; Lenhard, J. R.; Rolison, D.; Murray, R. W. J . Am. Chem. SOC.1980,102,4649.
(2) Daum, P.; Murray, R. W. J . Phys. Chem. 1981,85,389. (3) Facci, J.; Murray, R. W. J . Phys. Chem. 1981,85, 2870; J . Electroanal. Chem. 1981,124,339. (4) Facci, J.; Schmel, R. H.; Murray, R. W. J. Am. Chem. SOC.1982,104, 4959. (5) Kuo, K.; Murray, R. W. J . Electroanal. Chem. 1982,131,37. ( 6 ) White, H. S.; Leddy, J.; Bard, A. J. J . Am. Chem. SOC.1982,104, 4811. (7) Martin, C. R.; Rubinstein, I.; Bard, A. J. J. Am. Chem. SOC.1982,104, 4817. (8) Shigehara, K.;Oyama, N.; Anson, F. C. J . Am. Chem. SOC.1981,103, 2552.
6)
(a) Buttry, D. A.; Anson, F. C. J . Electroanal. Chem. 1981,130,333; (b) J . Am. Chem. SOC.1983,105,685. (10)Miller, S.L.;Orlemann, E. F. J. Am. Chem. SOC.1953, 75, 2001. (11)Yamoaka, H.J . Elecrroanal. Chem. 1972,36, 457. (12)Ruzic, I.; Smith, D. E.; Feldberg, S.W. J. Electroanal. Chem. 1974, -5-7 , 157 - - .. (13) Schwall, R. J.; Ruzic, I.; Smith, D. E. J . Electroanal. Chem. 1975, 60,117. (14)Schwall, R. J.; Smith, D. E. J . Electroanal. Chem. 1978,94, 227. (IS)Matusinovic, T.;Smith, D. E. J . Elecrroanal. Chem. 1979,98, 133. (16) Fukui, M.; Kitani, A,; Degrand, C.; Miller, L. L. J . Am. Chem. SOC. 1982,104, 28. (17)Musumeci, S.;Rizzarelli, E.; Sammartano, S.;Bonoma, R. P. J . Electroanal. Chem. 1973,46, 109. ~
0 1984 American Chemical Society
Enhancement of Charge-Transport Rates ganic/Inorganic Corp.) and recrystallized from water. Ru(NH3)6C13was obtained from Matthey Bishop, Inc. Solutions were prepared from distilled water that was further treated by passage through a purification train (Barnstead Nanopure). Pyrolytic graphite electrodes (Union Carbide Co.) were cut and mounted as previously describedls to expose 0.17 cm2 of the basal plane of the graphite. Potentials were measured and are quoted with respect to a calomel reference electrode saturated with sodium chloride (SSCE). Procedures. Cyclic voltammetry and coulometry were carried out with appropriate combinations of PAR instruments (EG&G, Inc.). Chronocoulometry was conducted with a computer-controlled apparatus similar to one previously d e ~ c r i b e d . ' ~ Nafion coatings were prepared by evaporation of 8-pL aliquots of the 0.52% coating solution on the surface of the graphite electrodes. To prepare the resulting coatings for measurements they were cycled a few times over the potential range of interest in solutions of the complexes to be examined and then allowed to equilibrate with the solution until there was no further change in the magnitude of the voltammetric peak currents that were dominated by the cationic complexes incorporated in the polyanionic coatings because of ion-exchange interactions. Low concentrations of the complexes were employed (1-40 pM) and the period required for equilibration varied from ca. 20 min for R u ( N H ~ ) ~to~90 + min for Cp2FeTMA+to 6-7 h for Co(tpy)?+ or C ~ ( t y p ) , ~ +Once . equi!ibrated, the films were quite stable in the dilute solutions of the complexes although loss of the complexes occurred if the electrodes were transferred to pure supporting electrolyte solutions (0.5 M Na2S04). For this reason all subsequent measurements were performed in the presence of the incorporating cation. Their presence produced negligible effects in cyclic voltammetric and chronocoulometric measurements because of the low concentrations of the complexes present in the solution. The coulometric assays of the extent of the incorporation (described below) were somewhat affected by the need to conduct the measurements in the presence of the reactants. However, we believe that the assays are accurate to at least 10% with the systematic error being in the direction of an overestimate of the quantity of incorporated complex. Coulometric assays of the quantity of R u ( N H ~ ) present ~ ~ + in an equilibrated coating were obtained by measuring the areas under the cyclic voltammetric peaks recorded at a scan rate low enough (5 mV s-l) to ensure that all of the complex in the coating had reacted. To assay for incorporated C ~ ( t p y ) ~and ~+ Cp2FeTMA+ when both were present in the coating a potential step procedure was employed. The potential was first stepped over both of the oxidation waves (from -0.2 to 0.5 V) and the resulting charge flow was measured until the current decreased to background levels. The total charge was taken as a measure of the sum of the incorporated C ~ ( t p y ) ~and ~ +Cp,FeTMA+. The potential was then held at 0.2 V until all of the resulting Cp2FeTMA2+was re-reduced to Cp,FeTMA+ without reducing the C ~ ( t p y ) , ~ +The . amount of Cp,FeTMA+ in the coating was then determined without interference from the cobalt complex by stepping the potential again to 0.5 V and measuring the resulting charge flow. This procedure involves the assumption that the quantity of Cp2FeTMA+incorporated by the coating is independent of the oxidation state of the coincorporated cobalt terpyridine complex. A similar procedure was employed to determine the quantity of and Co(tpy)?+ coincorporated in Nafion coatings. However, the proximity of the reduction waves for the two complexes in the measurement required a modification in the procedure. The sum of the two complexes present was determined from exhaustive reduction at -0.4 V. The potential was then adjusted to -0.15 V where the stable form of the ruthenium complex is R u ( N H ~ ) and ~ ~ +a portion of the cobalt complex is converted to C ~ ( t p y ) ~ ~A+cyclic . voltammogram was then recorded at a low scan rate (5 mV s-l) commencing at -0.15 V and (18) Oyama, N.; Anson, F. C. J. Am. Chem. SOC.1979, 101, 3450. (19) Lauer, G.; Abel, R.; Anson, F. C. Anal. Chem. 1967, 39, 765.
The Journal of Physical Chemistry, Vol. 88, No. 14, 1984 3087
-02
02
00
04
06
E, volts vs SSCE
Figure 1. Cyclic voltammograms for a mixture of Co(tpy)?+ and Cp2FeTMA+C104-incorporated in a Nafion coating: (A) potential scan restricted to -0.2 to +0.2 V; (B) potential scan restricted to 0.2-0.6 V; (C) potential scanned over both waves. Supporting electrolyte 0.5 M Na2S04also containing 8 X IO-' M C ~ ( t p y ) and ~ ~ ' 1.6 X 10" M Ru(NH3)2+.Scan rate: 50 mV s-I. Anodic currents are plotted upward.
scanning to -0.4 V. The irregularly shaped cathodic peak was ignored but the area under the subsequent, well-shaped anodic peak showed no evidence of any contribution from Co(tpy)?+ and in the coating. was used to estimate the quantify of All solutions were bubbled with prepurified argon for 45 min to ensure the absence of dioxygen which otherwise interfered in the coulometric assays at negative potentials because of the long integration times involved.
Results Mixtures of C ~ ( t p y ) , ~and + Cp2FeTMA+ in Nafon. The diffusion coefficient of Co(tpy)z2+in Nafion coatings is much smaller than that of Cp2FeTMA+. This is made clear by the cyclic voltammograms for the two couples shown in Figure 1. The coating contains 3.5 times more Co(tpy)?+ than Cp,FeTMA+, but almost equal (anodic and cathodic) peak currents are obtained for both couples when the potential scan is limited to a range where the response from each couple is not influenced by the presence of the other (waves A and B in Figure 1). However, when the potential scan encompasses both waves, the composite response exhibits distinctly different features (wave C): The oxidation peak appearing at the potential corresponding to the Cp,FeTMA+ couple is much larger and the corresponding cathodic peak much smaller than when the same couple is examined in isolation (wave B). In addition, the cathodic peak for the reduction of C ~ ( t p y ) , ~ + is considerably larger than that obtained for the same process in wave A. These differences are the result of reaction 1 occurring
-
Cp2FeTMAZ++ Co(tpy)22+
Cp2FeTMA+
+ C~(tpy)*~+ (1)
in the coating. The equilibrium constant for this reaction, calculated from the difference in the formal potentials of the two couples, is 1.2 X IO5 so that the cross-reaction is highly favored in the direction written. As a result of this reaction the more rapidly diffusing Cp2FeTMA2+ and Cp2FeTMA+ ions carry electrons between the electrode surface and the more slowly diffusing C ~ ( t p y ) , ~ions + so that these ions are oxidized within a layer next to the electrode that is much thicker than the diffusion layer corresponding to the small diffusion coefficient of Co(tpy),2+.
3088 The Journal of Physical Chemistry, Vol. 88, No. 14, 1984
Buttry et al.
TABLE I: Chronocoulometric Slopes for the Reduction of Mixtures of Ru(NH3)6)' and Co(tpy)?' in Nafion Coatings" 109rRU:
io8rCo,b
mol cm-2
pC cm-2 S - I / ~
0.35 1.4 2.0 2.1 4.4
1.9 1.o
2.1 7.9 11 15 28
1.6 3.2 3.0
SCo!
SRure
mol cm-2
pc
cm-'
30 40 44 89 94
1O-'(sRu
+ SCo),
pc
s-I12
0.32 0.48 0.55 1.o 1.1
1O-'SRutCo,e
& cm-'
1.1
1.6 2.1 2.1 3.5
"All coatings contained 2.4 X lo-' mol cm-2 of Nafion. bTotal quantity of Ru(NH&'+ or Co(tpy)?' in the coating. cChronocoulometricslope for the reduction of Ru(NH3)2' (calculated from measurements with separate films) that would have resulted for the same value of r R u in the absence of Co(tpy),". "Measured chronocoulometric slope for the reduction of Co(tpy),'+ when the potential was stepped from 0.25 to -0.125 V. e Measured chronocoulometric slope for the reduction of both Co(tpy)?' and Ru(NH3)6,' when the potential was stepped from 0.25 to -0.4V. The Cp2FeTMA2+ions that chemically oxidize the C ~ ( t p y ) , ~ + complexes are unavailable for re-reduction during the return potential scan and that is the reason for the smaller cathodic peak current at 0.32 V. The large cathodic peak current a t 0 V corresponding to the (unmediated) reduction of Co(tpy)?+ has a different origin. It arises because the diffusion coefficient of Co(tpy)?+ in Nafion is about 3 times larger than that of Co(tpy)?+. This does not produce unequal peak currents in ordinary cyclic voltammetry of this (or any other) couple examined in isolation (wave A) but in the presence of Cp2FeTMAt the effective diffusion layer of the Co(tpy)?+ extends much further from the electrode surface. The cathodic response therefore reflects the diffusion coefficient of Co(tpy)?+ rather than that of C ~ ( t p y ) ~ ~ + just as would be true if the voltammogram were recorded by adjusting the initial potential to a value where C ~ ( t p y ) were ~~+ the stable species at the electrode surface and the potential was scanned in the negative direction. The important point made clear by the voltammograms in Figure 1 is that reaction 1 serves to couple the diffusion of the two complexes in the coating, the more rapidly diffusing component accelerating the effective diffusion rate of its slower partner. If the two components had equal or very similar diffusion coefficients (the usual case at uncoated electrodes in fluid solutions), - 0.4 -0.2 0.o 0.2 0.4 the enhancement in the peak current for the faster moving species would be absent or too small to measure reliably. E, volts vs SSCE Mixtures ofCo(fpy)?+ and h ( N f f 3 ) 6 3 + .The R u ( N H ~ ) ~ ~ + Figure 2. Cyclic voltammogram for a mixture of Co(tpy)?+ and Rucomplex also diffuses much more rapidly than the Co(tpy)?+/2+ (NHJ)2+incorporated in a Nafion coating. Supporting electrlyte: 0.5 complexes in Nafion and is reduced at potentials negative of those M Na2S04also containing 8 X lo-' M Co(tpy)?+ and 8 X 10" M where Co(tpy)l+ is reduced. The cyclic voltammogram in Figure R u ( N H ~ ) ~ Scan ~ + . rate: 50 mV s-l. Anodic currents are plotted up2 is for a mixture of R U ( N H ~ ) ~and , ~ +3 times as much Co(tpy)?+ ward. in a Nafion coating. As with the Cp2FeTMA+-Co(tpy)22+ mixture, the more rapidly diffusing mediator couple (Rugreater and provide quantitative evidence of the magnitude of the (NH3)63+/2+)allows more of the slowly diffusing reactant (Coeffect that the coupling phenomenon can produce. (tpy)?+) to be consumed during the recording of the voltamThe ratios Sco/rcoand S R u / r R u in Table 1 are not independent mogram and this is reflected in an enhanced peak current for the of the values of r as they would be if the diffusion coefficients reduction of R u ( " ~ ) ~ ~ + a t -0.26 V and a depression of the of the two complexes in the Nafion coating were independent of corresponding peak for the oxidation of Ru(NH3):+. The cathodic r. Such dependence of effective diffusion coefficients on the peak for the direct reduction of C ~ ( t p y ) , ~is+ larger than the concentration of the diffusion species in Nafion coatings was also corresponding anodic peak on the return scan as expected on the observed in a previous studyS9It can arise from changes in the basis of the arguments presented above to account for the inecoating thickness, single-file diffusion, electron hopping, et^.^ quality of the two waves in the case of Cp2FeTMA'-Co(tpy)?+ It proved possible to derive an expression for for the case mixtures. where the electron-transfer cross-reaction (eg., reaction 2) is fast To obtain more quantitative data on the effects of electronand irreversible. (The derivation is outlined in the Appendix. A transfer coupling of the diffusion of R u ( N H ~ ) and ~ ~ +C ~ ( t p y ) ~ ' + more detailed derivation and discussion of the assumptions involved in Nafion coatings the slopes of chronocoulometric chargefor the present as well as related cases will be presented else(time)'/* plots were recorded when the electrode potential was where.20) The result is stepped from 0.25 to -0.125 V, i.e., across the first cathodic in Figure 2, and when the step was from 0.25 to -0.4 V, Le., across S R u + C o = Scoyd1i2/erf p = SRu/erf p (2) both waves. Similar experiments were also conducted with where d = DRu/Dc,, y = r R u / r C oerf , denotes the error function, coatings containing only Ru(",),~+ to determine the chronoand erf p is given implicitly by coulometric slope for this ion in the absence of electron-transfer coupling. The results are summarized in Table I with the third erf /3 = yd1/2exp[(d - l)p2] erfc (d1/2p) (3) and fourth columns listing the chronocoulometric slopes for each complex when evaluated in the absence of the second complex. To apply eq 2 to the data of Table I it is necessary to know the The sum of these two slopes, listed in the fifth column, is the diffusion coefficient ratio, d . Unfortunately the diffusion coefexpected slope for mixtures of the two complexes in the absence of electron-transfer coupling of their diffusion rates or of other influences of the second complex on the diffusion rate of the first.3 (20) Andrieux, C. P.; Hapiot, A,; Saveant, J. M. J. Electroanal. Chem., The experimentally observed slopes in the final column are much in press.
The Journal of Physical Chemistry, Vol. 88, No. 14, 1984 3089
Enhancement of Charge-Transport Rates
TABLE II: Comparison of Observed and Calculated Chronocoulometric Slopes for the Reduction of Mixtures of R u ( N H ~ ) and ~ ~ +C ~ ( t p y ) ~in~ ' Nafion Coatings
0.018 0.07 0.084 0.125 0.147
0.30 0.40 0.89 0.44 0.94
I .07 1.24 1.28 1.40 1.46
2.47 4.53 4.96 6.09 6.62
0.32 0.49 1.1 0.62 1.4
0.74 1.8 4.4 2.7 6.2
1.1 1.6 2.7 2.1 3.5
"y = FRu/rCo. bFrom Table I. 'Evaluated from eq 3 for d = 3.9 "Evaluated from eq 3 for d = 167. eCalculated from eq 2 for d = 3.9. /Calculated from eq 2 for d = 167.
ficients for both Co(tpy)?+ and Ru(NH,),,+ in Nafion as measured by chronocoulometry or chronoamperometry exhibit large variations with the coating thickness.21 The average values of Sco/rco and S R u / r R u in Table I correspond to values of apparent diffusion coefficients for these ions that are much smdller than those that are measured with thicker coatings where a dependence on thickness is no longer present. Thus, with the thin Nafion cm2 s-l and DRu 7 X coatings of Table I, Dco 2 X cm2 s-l, while the corresponding values in coatings that are 10-20 times thicker are Dco 1.2 X IO-" cm2 s-l and D R u 2 X lo4 cm2 We believe the apparent dependence of D on the coating thickness results from difficulties in obtaining uniform coatings cm). Nonas thin as those employed in Table I (-4.8 X uniformity in thin coatings can cause the thinner portions to become depleted of reactant during chronocoulometric measurements leading to decreased slopes and calculated diffusion coefficients. This problem is much less serious with thicker coatings because the chronocoulometric measurements of diffusion coefficients can be completed before significant depletion occurs in any portion of the coating. In applying eq 2 to the data of Table I we used two limiting values of d. In the first case an average value of d was calculated from the parameters in Table I according to eq 4. The resulting
-
-
-
-
Discussion The cyclic voltammograms in Figures 1 and 2 and the data in Table I clearly demonstrate the phenomenon of electron-transfer enhancement of effective diffusion rates. For the particular pair of redox couples and experimental conditions utilized to obtain the data in Table I the coupling produces an enhancement in the current (as reflected in the chronocoulometric slope) of over threefold compared to that which would be obtained in the absence of coupling. The equation derived to account for the enhancement (eq 2) allows a general expression for the ratio of the currents (or chronocoulometric slopes) in the presence and absence of coupling to be written: yd1I2
scoup -icoup - --juncoup
Sun~~up
(1
+ y d 1 I 2 )erf (3
(5)
This function will, in general, have a maximum at the values of y and d that produce the largest net rate of reduction (or oxidation) of the two reactants. Thus, for a given value of d, the concentration ratio, y, can be chosen to optimize the current flow. Such considerations can be important in electrocatalytic applications of polymer-coated electrodes in which the catalyst and charge propagation roles are played by different species that may have quite disparate diffusion coefficients.22 (4) The enhancement of effective diffusion rates by electron transfer between slow and rapidly diffusing species also occurs in the average value of d was 3.9. This value of d is almost certainly homogeneous fluid solutions most often employed in electromuch smaller than is appropriate for the actual experiment because chemical measurement^.'"'^ However, the much smaller range the cross-reaction between R U ( N H , ) ~ and ~ + C ~ ( t p y ) , ~will + act to diminish the extent of the diffusion layer for the R u ( N H ~ ) ~ + / ~ + of diffusion coefficients typically encountered in such media compared to polymeric coatings makes the effect of coupling less couple, thus partially avoiding the depletion that produced the dramatic but by no means negligible. For example, in a normal in Table I. Nevertheless, this misleadingly small values of SRu pulse polarogram23of a solution containing equal concentrations value of d should represent a lower limit. In the second case d (y = 1) of two reactants whose diffusion coefficients differed by was calculated from the diffusion coefficients of the two complexes a factor of 2 ( d = 2), electron-transfer coupling of their diffusion measured independently in thicker films.9b The value of d in the would cause the second wave to be larger than the first by a factor second case was assumed to be constant and equal to 167. This of 1.6 instead of the factor of 1.4 that would be observed in the value of d is probably too large because there may be some deabsence of coupling. If d were as great as 5 , the two factors would pletion of the reactants during the actual experiment. It should, be 2.9 vs. 2.2, respectively. Thus, the consequences of electronhowever, provide an upper limit on d . transfer coupling as expressed in eq 2 may be important in The results obtained when these two values of d are used to electrochemical measurements on mixtures of redox couples both evaluate erf (3 by means of eq 3 are summarized in Table 11. in homogeneous solutions as well as within polymeric electrode Except for the first entry (for which Scois anomalously low) the coatings. observed slopes are bracketed by those calculated with the two In their recent study White et a1.6 prepared Nafion coatings limiting values of d. Considering the limitations imposed by the in which both Ru(bpy),Z+ and Os(bpy)?+ (bpy = 2,2'-bipyridine) experimental system, we regard this as reasonable evidence that were incorporated. They reported a diffusion coefficient within eq 2 is able to account for the large experimental slopes obtained Nafion for the O ~ ( b p y ) , ~complex + that was about one-sixth as in the presence of electron-transfer coupling of the diffusion of large as that for R ~ ( b p y ) , ~but + the apparent absence of electhe two complexes. Both the uncertainties in the correct value tron-transfer enhancement of the peak current for oxidation of of d and likely overestimates in the values of r R u obtained in Ru(bpy)?+ (Ep 1.0 V) in the presence of a comparable quantity coulometric assays conducted with the higher concentrations of of O~(bpy),~+ (Ep 0.6 V). This result conflicts with what would RU("~)~'+ required to obtain larger values of r R u (see Experbe expected on the basis of eq 2 (as applied to the Ruimental Section) doubtless contributed to the differences between (bpy)32+-Os(bpy)32+system). We have also measured the difthe observed and calculated slopes. We anticipate that a better fusion coefficient for Os(bpy)?+ in Nafion coatings and obtained test of eq 3 will become possible with an alternative experimental values ((5-7) X cm2 s-1)24 that are larger than those reported system in which the reactants are retained by the coating even when they are exposed to pure supporting electrolyte solutions for periods long enough to conduct the chronocoulometric mea(22) Buttry, D. A.; Anson, F. C. J . Am. Chem. Soc. 1984, 106, 59. surements. (23) Bard, A. J.; Faulkner, L. R. "Electrochemical Methods";Wiley: New
--
(21) Buttry, D. A.; Anson, F. C., unpublished experiments.
York, 1980; p 186 ff. (24) Anson, F. C.; Saveant, J. M., Tsou, Y.-M., submitted to J . Electroanal. Chem.
3090
The Journal of Physical Chemistry, Vol. 88, No. 14, 1984
Buttry et al. P / Q and A/B waves. Writing Fick's law in terms of the dimensionless parameters Oo,y=o
Y
e=-
is assumed to be irreversible and to proceed at a high rate. The initial conditions are ?
b=O
erf
(-)
('412)
2(d7) '/'
At y = 0, p = 0 so (A131
With these values of C, C',D, and D', eq A7 can be used to derive an expression that determines 1.1:
When fl is defined as p / [ 2 ( d ~ ) ' / ~ eq ] , A14 becomes eq 3. fl is a function that is independent of 7 and can be numerically calculated for any value of y and d from eq 3. The formula 1.1 = 2fl(d7)'/* defines the way in which the point labeled 1.1 in Figure 3 moves away from the electrode surface with time.
3091
J. Phys. Chem. 1984,88, 3091-3095 The dimensionless current, $, can be calculated from eq A15
or A16.
SP+A = (1 /erf @SA
(A19)
Equation A19 corresponds to eq 2 in the text. The concentration profiles depicted in Figure 3 can be calculated from eq A20 and A21.
The total current, i = J . ( i C o t t ) P d / 2 , is then
erfc p = l -
Recasting eq A18 in terms of the chronocoulometric slopes instead of Cottrell currents
(&)
erfc (d1I2p)
(A2 1)
Registry No. Co(tpy)z, 18308-16-2;C~(tpy),~',19137-07-6; Cp,FeTMAtC104-, 90149-69-2;CpzFeTMA2', 51 150-33-5;Ru(NH3)63', 18943-33-4; Nafion, 39464-59-0; graphite, 7782-42-5.
Photoionization of Aromatic Diamines in Electron-Accepting Solvents: Formation of Short-Lived Ion Pairs Yoshinori Hirata* and Noboru Mataga* Department of Chemistry, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka 560, Japan (Received: September 26, 1983)
The photoionization of N,N,N',N'-tetramethyl-p-phenylenediamine (TMPD), 2,7-bis(dimethylamino)-4,5,9,lO-tetrahydropyrene, and N,N,N'fl-tetramethylbenzidine has been studied by using transient absorption and transient photoconductivity measurements with the picosecond laser photolysis method. Benzonitrile and pyridine, which act as electron acceptor, were used as solvents. In these solute-solvent systems, the formation of a short-lived ion pair which consists of the amine cation and solvent anion has been demonstrated directly and the importance of the solvent-solute exciplex interaction for the photoionization of these systems has been confirmed. The dissociatiofl yield of the ion pair was rather small in all amine-solvent systems examined here and showed dependence upon the nature of amine and solvent. The yield was smaller for the stronger electron-accepting solvent. In order to elucidate the relation between the exciplex and the ion pair, we studied several fluorescent exciplex systems such as TMPD-benzonitrile and TMPD-pyridine in isooctane.
where E,+ and E; represent the solvent polarization energy and EA and Ec are the trap electron affinity and the Coulomb energy due to the interaction between charged species, respectively. The magnitude of AZ should depend on the nature of the system, especially the solvent. EA is usually almost zero for a system which does not contain an electron acceptor and Ec is also nearly zero because of the large separation between positive and negative charges. This is actually the case for photoionization in alkane solvents and, for example, AI is about 0.9 eV in a 3-methylpentane matrix.2 In a polar solvent, the polarization energies have large values and EA may have a nonzero value, which results in a large AI
value. In electron acceptors as halomethanes, EA and probably also Ec have large values and monophotonic ionization by near-ultraviolet excitation can be observed in both the liquid and solid (low temperature) phases. AI = 1.90 eV2 has been obtained for the photoionization of N,N,N',N'-tetramethyl-p-phenylenediamine (TMPD) in methanol a t 77 K, while the threshold for photoionization does not exist a t room temperature3 because of the quite large AI value. For systems such as pyrene-N,N-dimethylaniline which forms exciplex, ionic photodissociation occurs in polar solvents and produces a pair of cation and anion radicals: This is another case which does not have a photoionization threshold. In a nonpolar solvent which does not contain an electron acceptor the photoionization mechanism may be rather similar to that in gas phase and appears to be well understood. On the contrary, the photoionization mechanism in a polar solvents still remains obscure. An intermediate state such as the semionized state has been proposed by several researcher^,^ but until quite recently such a state is not observed directly and is not well documented. In previous papers we have demonstrated that the solventsolute exciplex interactions play an important role in the photoionization
(1) Lesclaux, R.; Joussot-Dubien, J. 'Organic Molecule Photophysics"; Birks, J. B., Ed.; Wiley-Interscience: London, 1973; Vol. 1, pp 457-587. (2) Bernas, A.; Gauthier, M.; Grand, D.; Parlant, G. Chem. Phys. Lett. 1972, 17, 439.
(3) Hirata, Y.;Mataga, N. J. Phys. Chem. 1983, 87, 3190. Kanda, Y.; Mataga, N. J . Phys. Chem. 1983,87, 1659, and (4) Hirata, Y.; papers cited therein. (5) Ottolenghi, M. Chem. Phys. Lett. 1971, 12, 339.
Introduction Since 1942 the photoionization of aromatic compounds in condensed media has been extensively studied by many researchers.' The energy required for the photoionization of a solute molecule in a liquid or solid solutibn is lower than that in the gas phase and the amount of the energy lowering, AI, is expected to be
0022-3654/84/2088-3091$01.50/0
0 1984 American Chemical Society
