J. Phys. Chem. 1981, 85,389-396
Charge-Transfer Diffusion Rates and Activity Relationships during Oxidation and Reduction of Plasma-Polymerized Vinylferrocene Films P. Daum and Royce W. Murray* Kenan Laboratories of Chemistry, University of North Carolina, Chapel Hlll, North Carollna 27514 (Recelved: June 12, 1980; In Final Form: October 24, 1980)
Ferrocene and ferrocenium sites in radiofrequency plasma polymer films on Pt electrodes can be electrochemically oxidized and re-reduced in contact with a variety of electrolyte/solvent systems. When the electrochemical reaction is conducted under near-equilibrium conditions, cyclic voltammetric and chronopotentiometric waveshapes reflect the modulation of ferrocene and ferrocenium site activities by solvent swelling of the film. In water, ferrocene sites exhibit a phase-like (constant) activity during film oxidation, but in acetonitrile ferrocene site activity is proportional to fractional film oxidation. When the film oxidation or reduction is driven by a large potential step (avoiding film ohmic resistance effects), the rate of film reaction is controlled by Fickian diffusion of electrochemical charge through the film. In water, the product of charge diffusion constant and initial concentration of electroactive sites, D1l2C,is 2 X lo4 mol/cm2 for film oxidation and 1.4 X lo4 mol/cm2 s112 for film re-reduction. The difference may be due greater film swelling in the oxidized state. The relationship of charge diffusion rates in redox polymer films on electrodes to their electrocatalytic reactions is discussed.
Modifications of the surfaces of conductor and semiconductor electrodes by thin film coatings of polymers containing pendant, electrochemically reactive sites have been described in a number of recent publications.1-8 Some of these coatings act as electron-transfer mediators in electrocatalysis h he me^.^^,^^,^^,^^,^^^,^^*^^^^^^ The coatings (1) (a) Nowak, R.; Schultz, F. A.; Umafla, M.; Abrufia, H. D.; Murray, R. W. J. Electroanal. Chem. 1978, 94, 219. (b) Nowak, R.; Schultz, F. A.; Umafia, M.; Lam, R.; Murray, R. W. Anal. Chem. 1980,52,315. (c) Daum, P.; Murray, R. W. J . Electroanal. Chem. 1979, 103, 289. (d) Murray, R. W. “Symposium on Silylated Surfaces”; Midland Macromolecular Institute, Midland, MI, May, 1978. (e) Lenhard, J. R.; Murray, R. W. J . Am. Chem. SOC.1978,100,7870. (f) Abruiia, H. D.; Meyer, T. J.; Murray, R. W. Inorg. Chem. 1979, 18, 3233. (9) Daum, P.; Lenhard, J. R.; Rolison, D.; Murray, R. W. J. Am. Chem. SOC.1980,102, 4649. (h) Abruiia, H. D.; Denisevich, P.; Umaiia, M., Meyer, T. J.; Murray, R. W. Ibid. Submitted for publication. (i) Umafia, M.; Rolison, D. R.; Nowak, R.; Daum, P.; Murray, R. W. Surf. Sci. In press. (2) Van De Mark, M. R.; Miller, L. L. J . Am. Chem. SOC.1978, 100, 3223. (b) Ken, J. B.; Miller, L. L. J . Electroanal. Chem. 1979,101,263. (c) Miller, L. L.; Van De Mark, M. R. Ibid. 1978,88,437. (d) Miller, L. 1978,100,639. (e) Kerr, J. L.; Van De Mark, M. R. J . Am. Chem. SOC. B.; Miller, L. L.; Van De Mark, M. R. Ibid. 1980, 102, 3383. (3) (a) Wrighton, M. S.; Austin, R. G.; Bocarsly, A. B.; Bolts, J. M.; Haas, 0.;Legg, K. D.; Nadjo, L.; Palazzotto, M. C. J. Electroanal. Chem. 1978, 87, 429. (b) J . Am. Chem. Soc. 1978, 100, 1602. (c) Bolts, J. M.; Wrighton, M. S. Ibid. 1978,100, 5257. (d) Bolts, J. M.; Bocarsly, A. B.; Palazzotto, M. C.; Walton, E. G.; Lewis, N. S.; Wrighton, M. S. Ibid. 1979, 101, 1378. (e) Wrighton, M. S., Palazzotto, M. C.; Bocarsly, A. B.; Bolts, J. M.; Fischer, A. B.; Nadjo, L. Ibid. 1978,100,7264. (0 Bocarsly, A. B.; Walton, E. G.; Bradley, M. G.; Wrighton, M. S. J . ElectroanaL Chem. 1979,100,283. (9) Bocarsly, A. B.; Walton, E. G.; Wrighton, M. S. J. Am. Chem. SOC.In press. (h) Bookbinder, D. C.; Wrighton, M. S., preprint; (i) Bocarsly, A. B.; Walton, E. G.; Wrighton, M. S. J. Am. Chem. SOC. 1980, 102, 3390. (4) (a) Kaufman, F. B.; Engler, E. M. J . Am. Chem. SOC.1979, 101, 547. (b) Kaufman, F. B.; Schroeder, A. H.; Engler, E. M.; Kramer, S. R.; Chambers, J. Q. Ibid. 1980, 102, 483. (5) (a) Oyama, N.; Anson, F. C. J. Am. Chem. SOC.1979,101,739. (b) Ibid. 1979, 101,3450. (c) Oyama, N.; Anson, F. C. J . Electrochem. SOC. 1980,127,247. (d) Oyama, N.; Anson, F. C. Ibid. 1980,127,247. ( e )Ibid. 1980, 127, 249. (f) Ibid. 1980, 127, 640. (6) (a) Merz, A.; Bard, A. J. J. Am. Chem. Soc. 1978, 100, 3222. (b) Itaya, K.; Bard, A. J. Anal. Chem. 1978,50, 1487. (c) Peerce, P.; Bard, A. J., preprints. (7) Laandrum,H. L.; Salmon, R. T.; Hawkridge, F. M. J . Am. Chem. SOC.1977, 99, 3154. (8) (a) Diaz, A,; Kanazawa, K. K.; Gardini, G. P. J. Chem. SOC.,Chem. Commun. 1979, 635. (b) Kanazawa, K. K.; Diaz, A. F.; Geiss, R. H.; Gill, W. D.; Kwak, J. F.; Logan, J. A.; Rabolt, J. F.; Street, G. B. J. Chem. SOC., Chem. Commun. 1979, 854. (c) Diaz, A,; Castillo, J. I.; Logan, J. A.; Lee, W.-Y., preprint. 0022-3654/81/2085-0389$01 .OO/O
are additionally interesting in that, in their electrochemical reactions, charges equivalent to oxidation or reduction of hundreds of molecular monolayers of pendant redox sites are observed. It is unlikely that all of these pendant redox sites can enjoy close contact with the underlying electrode material, since the pendant sites are affixed to the polymer film matrix, and some mechanism(s) must exist for transporting electrons through intervening redox polymer. Electron hopping between neighboring oxidized and reduced pendant site pairs has been proposed as the mechanism for this electron transport4a which is thus a selfmediated or self-exchange electron-transfer process. Since the electron transport accomplishes an overall oxidation state change during the film’s electrochemical reaction, there must be accompanying transport of charge compensating counterions from the contacting solvent into/out of the polymer film, plus associated solvent flow and polymer chain motions.1cJg~3b,4~5b,5f~6c We shall refer to the overall process as charge transport. Proposals that the rate-determining step in charge transport is ion transand polymer motion~lg,~~@ have been made but port4bt5f16c quantitative rate data are presently limited.1bJg~5f~6c Understanding of the factors controlling charge transport kinetics in redox polymers is fundamental to our understanding of their electrochemistry and of their electrocatalytic efficacies. Obviously, an ability to properly measure charge transport kinetics is vital in this context. We have described a radiofrequency plasma procedurela-cJg for coating electrodes with thin, adherant, smooth films of polymerized vinylferrocene, I. These electrodes display oxidation-reduction cyclic voltammetric waves at potentials appropriate for ferrocene + ferrocenium reactions of 1-500 X mol/cm2 of ferrocene sites in the films of I, ca. 3 X mol/cm2 corresponding to a molecular monolayer. The cyclic voltammetric waves have different shapes depending on whether the solvent used in the electrochemical experiment is acetonitrile, water, or 5050 water/ethanol.lc The solvent dependencies were qualitatively interpretedlc in terms of ferrocene activity effects modulated by solvent swelling of the polymerized vinylferrocene film, I. In nitrile solvents, where (9) Bettelheim, A.; Chan, R. J. H.; Kuwana, T., preprint.
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cyclic voltammetric waves have their simplest shapes, the kinetics of charge transport through films of I follow Fick’s diffusion law.lbJg Charge transport is very slow, in the range of D to cm2/s in low temperature butyronitrile. The purpose of this report is fourfold. First, the waveshape-olvent dependence for films of I is quantitatively examined in terms of activity relationships, using experimental conditions promoting equilibration of the entire film with the potential applied to the underlying P t electrode. Second, using potential step chronoamperometry, we have measured the rate of charge transport through I in contact with water and with water/ethanol, and will also illustrate the pitfalls of film ohmic resistance effects. Thirdly, we describe the interrelationship of solvent and charge compensating counterion effects. Lastly, we discuss some relationships between charge transport and electrocatalytic rates.
Daum and Murray
A
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Experimental Section The vinylferrocene plasma polymerization procedure used was thatlcJgJJ improving upon an earlier version,lb being quite reproducible and producing electrodes with more ideal electrochemical characteristics. Teflonshrouded Pt disk electrodes ca. 0.5 cm above a 50-mg charge of vinylferrocene in Geometry B,lb after five Ar flush-pump cycles, are exposed to a 10-W 200-pm Ar plasma for 1-15 min followed by three flush-pump cycles extending over about 30 min. These conditions promote rapid polymerization coatinglj and minimize plasma damage to ferrocene sites as indicated by a strong 708.7-eV Fe 2p3/, XPS band on the electrodes. The coated Pt disks were aged in air for several days before use, which enhances stability to electrochemical cycling. Films of conventionally prepared poly(viny1ferrocene) (AIBN) on Pt were prepared by micropipetting a few microliters of CHzC12solutions containing 1-10 mg of polymer/10 mL onto the Pt disk, and allowing the solvent to evaporate. Electrochemical experiments were performed in conventional cells (Luggin reference capillary to NaC1-saturated SCE: SSCE) with a PARC 173 potentiostat/galvanostat. Pt electrodes were mirror polished (1-pm diamond paste, Buehler) and degreased with solvents before plasma coating. Vinylferrocene (Pfaltz and Bauer), sodium tetraphenylborate, and LiC104 (G.F. Smith) were used as received. Tetraethylammonium perchlorate, Et4NC104, (Eastman) was thrice recrystallized from water and vacuum oven dried.
Is
E V S SSCE
‘A
0.5
-
I
Figure 1. (A) Cyclic voltammetry of plasma-polymerized vinylferrocene film I in 0.1 M LiClO,/acetonitrile. rT= 3 X mo1/cm2, 20 mV/s, S = 7 pA/crn2, €”& = +0.34 V vs. SSCE. (B) Chronopotentiometry of 5.9 X mol/cm2 film of I in 0.1 M Et,NClO,/acetonitrlle. i = 123 lA/cm*. Solid points represent theory (eq 1) using r = -3.1 X 10’ (anodic branch), -4.6 X 10’ (cathodic branch). = +0.36 V vs. SSCE. measured by slow potential scan cyclic voltammetry.
rr
Constant current chronopotentiometry12 has not been applied to electrodes coated with redox polymers. We have found it effective for examining Nernstian relationships between reactant/product activity and mol/cm2 ratios, and electrode potential. Very low currents can be applied to enhance (reversible) film equilibration. Figure 1B shows the potential-time response of a film of I to an anodic current step, with the current, i, being subsequently reversed a t the transition time 7 which occurs at ca. nFArT/i. The ratio of ferrocenium/ferrocene activities varies with time but not directly proportionally to their mol/cm2 coverage ratio. The chronopotentiometric potential-time shape can be accounted for by invoking the interaction parameter (r)surface activity relation advanced by Brown and Anson.13 For the chronopotentiometric technique, the interaction parameter theory gives for the case of ro = rR
Results a n d Discussion Cyclic Voltammetry and Chronopotentiometry of Films of I on Pt in Acetonitrile. Activity Relationships. Films of plasma-polymerized vinylferrocene, I, containing rT = 5 X 10-10-50 X mol/cm2 electroactive ferrocene siteslcJgJ1typically exhibit in 0.1 M LiClO,/acetonitrile, stable, symmetrically shaped cyclic voltammetry peaks (Figure 1A) at potentials characteristic of oxidation and re-reduction of ferrocene sites in the polymer film. A t low-moderate potential scan rates (1-100 mV/s), the peaks have characteristicslOJ1expected for approximate Nernstian equilibration of the ratio of ferrocenium/ferrocene sites in the overall film, at each applied value of potential.
Figure 1B shows a fit of this relation (solid points) to the experimental potential-time response; the fit is as satisfactory as analogous comparisons to cyclic voltammetric wavesleJfJ3J4and is somewhat simpler to examine. The interaction parameter ro required to fit the anodic potential-time branch in Figure 1B proves to be slightly more positive (typical result) than that which best fits the cathodic branch, indicating a small thermodynamic difference in activity coefficients of sites during oxidation and during reduction in acetonitrile. This small disequilibrium effect is in the same direction but much smaller than that observed in water and ethanol/water solvent (see below). Cyclic Voltammetry of Films of I i n Water. Kinetic Effects. At low apparent coverage, r T < 1X lo4 mol/cm2,
(10) Lane, R. F.; Hubbard, A. T. J. Phys. Chem. 1973, 77, 1407. (11)Throughout this paper, apparent coverages rT of electroactive ferrocene cited in text and figures are measured with current baseline as in Figure 1A and are invariant at low potential scan rates.
(12) Delahay, P. “New Instrumental Methods of Analysis”; Interscience: New York, 1954; p 179. (13) Brown, A. P.; Anson, F. C. Anal. Chern. 1977,49, 1589. (14) Smith, D. F.; Willman, K.; Kuo, K.; Murray, R. W. J.ElectroanuL Chem. 1979, 95, 217.
Plasma-Polymerized Vinylferrocene Films
1s
VC‘ I D 1 ;
j II I
81 I I I
I1
II
I1
I1
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The Journal of Physical Chemlstty, Vol. 85, No. 4, 198 7
?I ,/;;
.-
,E
O-0.5
0,
.’
/
-10 0.26 0.30 E VS SSCE
0.34
I1
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Flgure 2. Cyclic voltammetry of I in 0.1 M LiClO,/water. (A-D) 5, 50, 100, 200 mV/s; S = 61.7, 123,617, 617 yA/cm2,respectively. (E) plot of Evs. log ifor rising anodic current of curve A, slope = 60 mV.
Apparent coverage rT= 2.2 X lo-’ mol/cm2,curve A.
films of I on Pt in contact with 0.1 M LiC104/waterexhibit cyclic voltammograms which are broad, symmetrical, and substantially Nernstian (reversible), like those in Figure 1A. At higher apparent coverage, however, striking changedCtake place; both oxidation and reduction peaks become unsymmetrical, with currents for the oxidation peak rising sharply and falling even more sharply (Figure 2). The peak potential and peak width of the oxidation wave are also quite sensitive to potential scan rate (compare curves A-D). Potential scan rate has in contrast minimal effect on the shape of the reduction peak, and E , , varies little. Neutral site redox polymer films often4require several cyclic potential scans before a steady current-potential pattern is acquired. Such a “break-in” pattern is also observed for films of I in water. On a virgin electrode, the first oxidative potential scan produces only a smeared rise in current sometimes starting as positively as about +0.8 V vs. SSCE. The subsequent reductive potential scan shows a well-developed reduction peak like that in Figure 2. Low coverage films are at steady state on the very next cyclical potential scan, while on larger coverage films small changes are seen over several additional scans before steady-state response develops. Once an electrode has been thus broken in, however, it can be removed, stored in solvent or air, and re-used without repetition of the break-in pattern. Since oxidation and re-reduction in films of I requires movernent of large amounts of charge compensating counterion (C104-)into and out of the film, respectively, we increased the electrolyte concentration to 1 M LiClodwater. The oxidation peak retains its sharp appearance and is much less shifted by increasing potential scan rate. Otherwise, there is little change in peak shape, width, or currents. We will discuss the film break-in, and the sensitivity of the anodic wave peak potential to potential scan rate (and the effect of electrolyte concentration on this) as possible direct consequences of the ohmic resistance of the film, i.e., as uncompensated resistance phenomena. In a
39 1
three-electrode electrochemical cell as used here, the potentiostat controls the potential difference between the reference electrode Luggin capillary tip and the surface of the conducting Pt electrode. If the polymer film coating the Pt surface exhibits an ohmic resistance to charge flow, the potential actually operative at the Pt/polymer interface (the presumed site of ferrocene oxidation) is less than that applied by the product of current and the film resistance. Peak potentials in cyclic voltammetry become in this way related to potential scan rate, through the relationship of peak current to potential scan rate, and are shifted by approximatelythe amount of potential loss. The film resistance required to effect peak potential shifts of the magnitude shown in Figure 2 (e.g., ca. 150 mV) is actually quite small, only ca. 40 ohm, since the film’s currents are large (-4 mA/cm2 in curve D). The film break-in effect can be viewed as a virgin film which has low ambient internal electrolyte concentration (and thus large resistance). Oxidation of a few sites to ferrocenium draws in counterions and swelling solvent and quickly lowers the film resistance. A fully oxidized and swollen film is a concentrated ferrocenium perchlorate polyelectrolyte solution and has a much lower resistance, so that reduction peak potentials are little dependent on potential scan rate. The film becomes deswollen after reduction, so that resistance is again larger during subsequent oxidation, but apparently some electrolyte is trapped so that the film break-in does not have to be repeated. The importance of motions of the charge-compensating supporting electrolyte counterion in redox polymer film electrochemistry has been considered by a number of ~ o r k e r s . ~ Effects ~ ~ ~ observed g ~ ~in ~cyclic ~ ~voltam, ~ ~ ~ ~ ~ ~ metry have been attributed to “slow ion transport from solution into the nonpolar polymer film”.4b We stress that resistance to charge flow in a redox polymer film can have (at least) two different origins. One is associated with low ambient internal ion population and/or low ion mobility in the film which constitutes an uncompensated film ohmic resistance and which can cause loss of potential control in the electrochemical experiment. The second is associated with the rate of charge transport through the film’s internal volume which as defined in the beginning of this paper is a composite process of electron hopping and counterion, polymer chain, and solvent motions, driven by the effective electrochemical potential. Because cyclic voltammetry is so intrinsically sensitive to uncompensated resistance effects, and because the cyclic voltammetric behavior of I in water is qualitatively consistent with resistance phenomena, the above discussion of the kinetic behavior of break-in and of Figure 2 was as resistance effects, without recourse to consideration of charge transport kinetics. We in fact believe that, in part, charge transport kinetics do participate in determining peak potentials and currents in Figure 2, but quantitative interpretations (e.g., separation of charge transport kinetics) in the presence of resistance phenomena is a difficult proposition. Separation of charge transport kinetics from film ohmic resistance is more readily accomplished with techniques such as potential step chronoamperometry, with judiciously chosen potential step sizes, as we will show later. Cyclic Voltammetry and Chronopotentiometry of I i n Water. Activity Effects. If very low potential sweep rates are used in cyclic voltammetry, or very small currents in chronopotentiometry, the effects of the film resistance of I in water diminish, and the activity properties of I in contact with water can be examined under near-equilibrium conditions. Figure 3 shows the chronopotentiometric
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The Journal of Physical Chemistry, Vol. 85, No. 4, 1981 20
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80 -TIME,SEC
2
I
/
.*
t
"JC
/
t
J
t
F- I Flgure 3. (A) Chronopotentiometry of 1.7 X mollcm' film of I in 0.1 M LiClO,/water. T = 43.3 s. i = 37 pA/cm2. (B, C) Plots of log t (anodic branch) and Iog((7 - t ) / t )(cathodic branch) vs. €have slopes 56 and 60 mV, respectively. (D) Cyclic voltammetry of same electrode at 5 mV/s.
potential-time response of a 1.7 X mol/cm2 film to a small current. We have qualitatively referred to the oxidation of films of I in water as phase-like behavior of the ferrocene form of the film,lCthe essential ingredient of which would be a ferrocene activity which remains nearly constant throughout the oxidation wave. For a = 1 and aferrocenium proportional to time, model of aferrocene the chronopotentiometric anodic potential should vary with log t. Figure 3B shows that E vs. log t for the oxidation branch of the chronopotentiogram is indeed linear, with a reversible slope of 56 mV. A corollary of this activity behavior in cyclic voltammetry would be an exponential dependence of anodic current on potential in the rising portion of the sharp anodic peak (similar to a stripping peak for a thin metal film). In accord with this, a plot of E vs. log i for the oxidation branch of a 5 mV/s (slow scan) cyclic voltammogram for the same electrode as used in Figure 3 is also linear with near-reversible (76 mV) slope. A similar E vs. log i plot for the electrode of Figure 2 with reversible slope (60 mV) is shown in the inset of that figure. These results support the notion of phaselike behavior of ferrocene sites in the film during their oxidation in water. Phaselike behavior does not (necessarily) imply existence of an ordered (crystalline) structure; films of I are undoubtedly highly amorphous. Phaselike behavior does imply a low degree of intrusion by the water solvent. It is significant that the ferrocene states exhibit a phaselike property at the same time ferrocenium states being generated from them are exhibiting a time-dependent activity relation. This suggests a model of film structure in which the ferrocene and ferrocenium sites are segregated (as opposed to being uniformly co-mixed) into microscopic domains or islands, differing both in solvent content and average state of oxidation, dynamically shrinking and growing, respectively, during film oxidation. We have not observed multiple waves in our plasma-polymerized vinylferrocene films of the sort described by Peerce and BardGCfor electrochemically precipitated poly(viny1ferrocene) and ascribed to electrochemically nonequivalent sites. Our above suggestion, however, does agree with their general view that thin redox polymer films can exhibit inhomogeneities of film structure. The reverse (reductive) chronopotentiogram in Figure 3 has a completely different shape from the oxidative branch. Figure 3C shows that a plot of E vs. log [ ( T - t ) / t ] for the reduction branch is linear with slope 60 mV. This relation corresponds to eq 1with interaction parameter r = 0 and aferrocene and aferrocenium both proportional to time. Apparently, the deswelling following the reduction process is sufficiently slow that the ferrocene activity varies
s
( /
5
10 1 / n s e P
Figure 4. Potential step chronoamperometry of 4.9 X lo-' mol/cm2 fllm of I in 1 M LiClO,/water: (A) 0 to 4-0.4 V potential step: (B) 0 to +0.8 V, S = 0.77 mA/cm2; (C) plot of curve B accordins to eq 2 and 3,points are experimental currents, line Is theory for (0'' C ) , = 2.24 X lo-* mol/cm2 s"', area = 0.130 cm2.
throughout the film during reduction. In other words, while the ferrocene redox states may be at Nernstian equilibrium with electrode potential throughout the experiment, the commensurate degrees of solvent (de)swelling (and island formation?) are not. After a few minutes resting in the reduced state, deswelling has proceeded sufficiently that the result of Figure 3 can be repeated. The above results show that the thermodynamic activity properties of ferrocene and to a much lesser extent ferrocenium depend on the solvent, water differing significantly from acetonitrile. We now turn to the quantitation of the transport of charge through films of I in water. Chronoamperometry of Films of I i n Water. Charge Transport Kinetics. Because of the ohmic resistance effects on peak potential, and additionally because of the unusual peak shapes occasioned by the ferrocene phaselike property, cyclic voltammetry is poorly suited to examine charge transport through films of I in contact with water. Potential step chronoamperometry is superior because (i) an additional potential increment can be applied in the potential step to overwhelm the ohmic potential loss, (ii) no assumption about the relationship of ferrocene activity to potential need be made, and (iii) explicit theory for both semi-infinite and finite diffusion boundary conditions in chronoamperometry is known.lg The chronoamperometric technique does require an additional increment in potential step size if film resistance is to be obviated. The consequence of an oxidative potential step from 0 to +0.4 V, insufficiently positive t o overcome the f i l m resistance, is shown in Figure 4A, for mol/cm2 film in 1 M LiC104/water. The slow a5X potential scan cyclic voltammetry of Figure 2 would suggest that +0.4 V is, thermodynamically, sufficient for rapid film oxidation. Yet the current-time curve exhibiting an abnormal maximum is seen. If the potential step is repeated on the same electrode, but now from 0 to +0.8 V
The Journal of Physical Chemistry, Vol. 85, No. 4, 198 1 393
Plasma-Polymerized Vinylferrocene Films
vs. SSCE, on the other hand, a smoothly decaying current-time curve is seen (Figure 4B). The current maximum for the +0.4 V step is recognized as an artifact resulting from the film's ohmic resistance. As noted above, interpretation of the Figure 4 result requires consideration only of the film's ohmic resistance and no association of ion migration rates in the film with the overall charge transport kinetics need or should be made from such data. Charge transport through a redox polymer film via electron hopping between localized ferrocene and ferrocenium redox sites is mathematically equivalent to diffusion of such localized states (whether electron hopping per se, or an associated event such as charge compensating counterion hopping, or polymer lattice motion governing either process, is the rate-determining step). If charge transport actually follows Fick's law and is not distorted by effects such as a diffusion constant D which varies throughout the film, etc.,lg,I5the potential step currenttime response will at short time be described by the Cottrell equation16 as long as the profile of depletion of ferrocene localized states does not contact the film's outer boundary: i = nJ'AD'/2C/*1/2tl/2
(2)
In this equation C is the initial concentration of ferrocene sites in an initially reduced film, or ferrocenium sites in an oxidized film. A t longer times, where the semi-infinite boundary condition of eq 2 becomes violated, the appropriate finite diffusion relationship is1'
L
Current-time data for 0 to +0.6 V vs. SSCE oxidative and subsequentla +0.6 to 0 V reductive potential steps at a 1.6 x IO-* mol/cm2 film of I on Pt in contact with LiC104/ water are shown in Figure 5. Consider first the oxidation data, where, in 1M LiC104,i vs. t-'i2 plots are at short time mol/cm2 linear (eq 2) with slope (D1/2C)and= 2.09 X s1/2. This value can be used to calculate d2/D as (rT/ since C = rT/d, so the current-time response at longer time can be compared to eq 3. The eq 3 calculated solid curve fits the experimental data exactly (Figure 5B) showing that, just as in oxidative experiments with films of I in low temperature butyronitrile,'g the transport of charge through I in contact with 1M LiC104/water follows Fick's diffusion law as treated with a finite film thickness boundary condition. Figure 4C shows a similar comparison of current-time data ( 0 ) for the +0.8 V potential step, to eq 2 and 3. Again, the short time (D1/2C),nodresult from eq 2, when used with eq 3, provides an excellent fit to the longer time, finite diffusion part of the data. The linear i-t-'I2 region in Figure 4 is abbreviated as compared to that in Figure 5, as expected, since (according to I'T) the film of Figure 4 is three times thinner than that of Figure 5. The mol/cm2 s1/2result nonetheless (D1/'C),,d = 2.24 x ~~
~~~~
(15) If microscopic islands exist in the film structure, this sort of inhomogeneity is not detrimental to application of diffusion relations as
long as the islands have dimension
