J. Phys. Chem. 1983, 87, 640-647
640
periments and INDO calculations clearly suggest that upon warming to temperatures where reorientation is possible internal H bonding becomes strongly favored over such matrix interactions. Acknowledgment. We thank the Office of Health and
Environmental Research of the U.S. Department of Energy for support of this research. Registry No. I, 84130-15-4; 11,84130-14-3;111,84130-13-2;IV, 84109-22-8;V, 84109-23-9;VI, 84130-18-7;VII, 84130-17-6;VIII, 84109-24-0; IX, 84130-16-5.
Diffusional Pathways for Multiply Charged Ions Incorporated in Polyelectrolyte Coatings on Graphite Electrodes. C O ( C , O ~ ) ~in ~ -Coatings of Protonated Polylysine Fred C. Anson,’ Takeo Ohsaka, Arthur Amos Noyes Laboratories. California Institute of Technoiogy, Division of Chemistry and C h e m h l Engineering, Pasadena, California 9 I 125
and Jean-Michel Saveant Laboratoire d’Nectrochimie, Universite de Paris 7, 75221 Paris, Cedox 05,France (Received: March 15, 1982; I n Final Form: September 30, 1982)
Two independent pathways are identified for the diffusional motion of C O ( C ~ O ~anions ) ~ * incorporated within cationic films of protonated polylysine (PLL) coated on graphite electrodes. The coatings are regarded as consisting of two phases both of which contain the incorporated reactant and provide parallel diffusional pathways. Because the reduced reactant rapidly decomposes, neither pathway is assisted by in-phase or cross-phase electron-exchangereactions between pairs of the oxidized and reduced reactant. One pathway is followed by ions confined to the “Donnan domains” within the coatings by electrostatic forces while the second pathway is traversed by the ions present in the solution that occupies the space between the polyelectrolyte chains in the highly swollen coatings. Rotating-disk-electrodeexperimentsare combined with short-time chronocoulometric data to estimate the apparent diffusion coefficients governing each of the diffusional pathways.
The mechanisms of charge transport within polyelectrolyte coatings have received considerable recent scrutiny as the number of cases in which such coatings are used to bind multiply charged, electroactive counterions to electrode surfaces has increased.1-20 Previous studies have concentrated on the incorporation of stable redox couples in polyelectrolyte coatings so that reversible electrochemical responses could be observed. In such cases the reduction (or oxidation) of the incorporated ions may occur either after they diffuse within the polyelectrolyte to reach the electrode surface or by a series of electron hops between adjacent pairs of oxidized and reduced reactant21 that serves to shuttle electrons from the underlying electrode to reactant that is located away from the electrode surface. In either case (or with combinations of the two) the response obtained can be described in terms of apparent diffusional m o t i ~ n . ~In~most * ~ ~previous studies the contributions from each of these dual pathways for charge transport have not been separated so that only overall, apparent diffusion coefficients for the incorporated reactants have been reported. The separation of contributions from both pathways wm reported in ref 20. In the present study we incorporated into a polycationic coating under conan anionic cobalt(II1) reactant, c0(c204)33-, ditions where it was stable only in the 3+ oxidation state so that electrons could not be transported within the coating by self-exchange between pairs of cobalt(I1) and cobalt(II1) complexes. The (totally irreversible) electrochemical response obtained from electrodes coated with a polycationic film in which CO(C~O,),~anions were incorporated was therefore attributable entirely to the Contribution No. 6620.
0022-3654/83/2087-0640$0 1.50/0
physical motion (diffusion) of the anions through the coating to the electrode surface where they could be di(1) N. Oyama and F. C. Anson, J . Electrochem. SOC.,127,247 (1980). (2) N. Oyama, T. Shimomura, K. Shigehara, and F. C. Anson, J . Electroanal. Chem., 112, 271 (1980). (3) N. Oyama and F. C. Anson, Anal. Chem., 52, 1192 (1980). (4) K. Shigehara, N. Oyama, and F. C. Anson, Inorg. Chem., 20,518 (1981). (5) N. Oyama, K. Sato, and H. Matsuda, J . Electroanal. Chem., 115, 149 (1980). ( 6 ) I. Rubinstein and A. J. Bard, J. Am. Chem. Soc., 102,6641 (1980); 103, 5007 (1981). (7) D. C. Bookbinder, J. A. Bruce, R. N. Dominey, N. S. Lewis, and M. S. Wriehton. Proc. Natl. Acad. Sci. U.S.A.. 77. 6280 (1980). (8) K.-R. Kuo and R. W. Murray, J . ElectroanaL Chem., 131, 37 (1982). (9) J. A. Bruce and M. S. Wrighton, J.Am. Chem. Soc., 104,74 (1982). (10) J. Facci and R. W. Murray, J. Electroanal. Chem., 124, 339 (1981). (11) J. Facci and R. W. Murray, J. Phys. Chem., 85, 2870 (1981). (12) D. A. Buttry and F. C. Anson, J . Electroanal. Chem., 130, 333 (1981). (13) R. J. Mortimer and F. C. Anson, J. Electroanal. Chem., 138,325 (1982). (14) N. Oyama, S. Yamaguchi, Y. Nishiki, K. Tokuda, H. Matsuda, and F. C. Anson, J. Electroanal. Chem., 139, 371 (1982). (15) H. S. White, J. Leddy, and A. J. Bard, J . Am. Chem. Soc., 104, 4811 (1982). (16) C. R. Martin, I. Rubinstein, and A. J. Bard, J . Am. Chem. SOC., 104, 4817 (1982). (17) D. A. Buttry and F. C. Anson, J . Am. Chem. Soc., in press. (18) M. Majda and L. R. Faulkner, J. Electroanal. Chem., 137, 149 (1982). (19) F. C. Anson, J. M. Saveant, and K. Shigehara, J . Phys. Chem., in press. (20) F.C. Anson, J. M. Saveant, and K. Shigehara, J.Am. Chem. SOC., in press. (21) F. B. Kaufman and E. M. Engler, J . Am. Chem. SOC.,101, 547 (1979). (22) C. P. Andrieux and J. M. Saveant, J . ElectroanaL Chem., 11,377 (1980).
@ 1983 American Chemical Society
CO(C~O,)~~in Coatings of Protonated Polylysine
rectly reduced. The magnitude of the reduction currents observed corresponded to diffusion coefficients almost as large as that in homogeneous solution despite the absence of a diffusional pathway involving electron self-exchange. The highly swollen protonated polylysine coatings employed in this study apparently allow relatively facile movement of the c O ( c ~ 0 4 ) anions. 3~ A recently proposed model involving two distinguishable domains in the interior of swollen polyelectrolyte coating^'^^^ is utilized to account for the magnitudes and the rotation rate dependence of the limiting currents obtained at polylysine-coatedrotating disk electrodes in solutions of C O ( C ~ O ~ ) ~ ~ - .
Experimental Section Materials. K3Co(C204)3.3H20and K3Cr(C204).3H20 were synthesized by standard proceduresu and were stored in the dark. Fresh solutions of the salts were prepared just before use to avoid photodecomposition. Poly(L-lysine hydrobromide) was available from a sample in this laboratory. It had been prepared by the ring-opening polymerization of N-carbobenzoxy-L-lysine initiated by ethylamine in dry, deaerated dimethylformamide.26 The carbobenzoxy group was removed from the polymer by hydrolysis with 20% hydrobromic acid in acetic acid to yield fCHCONWrl I
(yHd4 NH,+Br-
The degree of polymerization, n, was estimated as 2 x IO3 from vapor-pressure osmometry of dimethylformamide solutions of the poly(N-carbobenzoxy-L-lysine)prior to its hydrolysis. All other chemicals were reagent grade and were used as received. Supporting electrolytes were prepared from appropriate mixtures of trifluoroacetic acid and sodium hydroxide. Laboratory distilled water was further purified by passage through a purification train (Barnsted Nanopure). Pyrolytic graphite electrodes with 0.17 cm2of the basal plane of the graphite exposed were prepared and mounted as previously d e ~ c r i b e d . ~ Apparatus and Procedures. Cyclic and rotating-disk voltammograms were obtained with standard, previously described procedures and a p p a r a t ~ s .Rotating-disk ~ current-potential curves were recorded by scanning the electrode potential at 5-10 mV s-l. Even at these low scan rates current peaks preceding the flat current plateau were usually observed with coated electrodes. The peaks resulted from the reaction of the reactant incorporated in the electrode coatings. However, as expected, the steady-state plateau currents were independent of the rate of potential scan. The quantities of anionic reactants incorporated in the polylysine coatings were determined by coulometric assay. After incorporation of the reactant the electrodes were washed and transferred to solutions containing only supporting electrolyte (CF3COONa+ CF3COOH)where the electrode potential was scanned from a value ahead of the reduction wave for the incorporated reactant to a value well beyond the peak potential where it was maintained until the current fell to background levels (20-120 8). The quantity of incorporated reactant was calculated from the integral of the current after correction for background contributions. Chronocoulometric charge-time data were (23) E. Laviron, J.Electroanal. Chem., 112, 1 (1980). (24) J. C. Bailar and E. M. Jones, Inorg. Synth., 1, 37 (1939). (25) P. Doty, J.Am. Chem. SOC.,79,396 (1957); Y. Iwakura, K. Uno, and M. Oya, J.Polym. Sci., Part A, 6,2867 (1967); M. Oya, T. Takahashi, and R. Katakai, J. Polym. Sci., Polym. Chem. Ed., 14, 2065 (1976).
The Journal of Physical Chemistry, Vol. 87, No. 4, 1983 641
obtained and analyzed with the aid of a computer-controlled apparatus previously described.26 Positive feedback circuitry was employed to provide as much compensation as possible of the resistances associated with the polylysine coatings. The resistance of the coatings was not excessive (- 10-20 Q) but the large reactant concentrations at the electrode surface resulting from the electrostatic attraction of the coatings caused unusually large initial currents to flow that amplified the effects of the coating resistance. Adherent coatings of polylysine were produced by transferring aliquots of a 0.5 wt % aqueous solution of the polymer to the surface of a freshly cleaved graphite electrode. (The solution of PLL was prepared about 6 months before it was used to prepare coatings. Fresh solutions of the polymer yielded coatings that were less stable. The reasons for this apparent age dependence are under current investigation.) The solvent was allowed to evaporate at room temperature (ca. 5-10 min). The resulting, slightly moist film was then heated with a heat gun to ca. 80 "C for 30 s. This final step produced more stable films thought to contain chains that are partially cross-linked by hydrogen bonding. In solutions the configuration of polylysine can be converted from a random coil to an a helix to a p sheet by control of pH, temperature, and the concentration of the p ~ l y m e r ? ~ ~The ' - ~ coatings resulting from this procedure appeared to remain insoluble at all pH values and electrolyte compositions and we believe that the coatings of polylysine may assume the @-sheetstructure when they are heated to 80 "C during their preparation. Estimates of the thickness of wet, swollen films of polylysine were obtained by the following procedure: A thin (- 1 mm), cylindrical, edge-plane pyrolytic graphite electrode was hand-polished on both top and bottom faces with moist silicon carbide. A coating was then applied to one of the polished faces by the procedure described above. The coating was equilibrated with each solution of interest until all swelling appeared to be complete. The electrode was then removed from the solution and the droplet of solution adhering to the coating was carefully removed by the wicking action of a small piece of filter paper. The total thickness of the electrode and its coating was then carefully measured with a micrometer while the interface between the coating and the micrometer head was observed under a magnifying glass to avoid crushing the coating. The difference in this micrometer reading and that obtained with the original uncoated electrode was taken to be the thickness of the swollen film. This procedure proved reliable with films having thicknesses of several hundred microns or more. For thinner films the thickness was assumed to be proportional to the quantity of polylysine used to prepare the coating. Solutions were deaerated with prepurified argon and measurements were conducted at the laboratory temperature (22 f 2 "C). Potentials were measured and are quoted with respect to a sodium chloride saturated calomel electrode (SSCE).
Results Electrochemical Behavior of c0(c@4),3- at Bare Graphite Electrodes. Although the literature contains an early study in which a reversible potentiometric response was (26) G. Lauer, R. Abel, and F. C. Anson, Anal. Chem., 39,765 (1967). (27) U. Sameli and W. Taub, J. Mol. Biol., 12, 205 (1965), and references therein. (28) B. Davidson and G. D. Fasman, Biochemistry, 6,1616 (1967), and references therein. (29) F. J. Padden, Jr., H. D. Keith, and G. Giannoni, Biopolymers, 7, 793 (1969).
642
The Journal of Physical Chemistry, Vol. 87, No. 4, 1983
Anson et al.
k L LL
ct
a
c
I
I
1
c.4
E
I
0 -0.4 vs S S C E , volt
I
I
I
-0.8
Flgure 1. Cyclic voltammograms for CO(C~O~),~-: (A) 10 mM Co(CO , &”, at a bare graphite electrode. (e) Same electrode coated with 2.8 X lo-’ mol cm-2 of IJUafter the electrode was soaked for 30 min in a 1 mM solution of cO(c204)33-, washed, and transferred to pure supporting electrolyte which was 0.2 M CF,COONa -I-CF,COOH (pH 1.5) in both cases. Scan rate for both curves: 200 mV s-‘.
claimed for mixtures of C O ( C ~ O ~and ) ~ ~Co2+ - in the presence of excess C2042-and HC204- anions,30we found no conditions where the oxidation of a cobalt(I1)-oxalate complex could be observed at graphite, platinum, or mercury electrodes. A typical cyclic voltammogram for C0(C204)$-at an uncoated graphite electrode is shown in Figure 1A. No anodic wave was observed before the oxidation of oxalic acid at scan rates up to 100 V s-l as would be expected in acidic supporting electrolytes where the labile CO(C~O,),~complex rapidly decomposes to Co(OH2)? and oxalic acid. Response of C O ( C ~ O ~ )at, ~ Electrodes Coated with Polylysine. The pendant amino groups in poly(L-lysine), PLL, are protonated at pH values below 11 (pK, for the protonated amine is 10.727*2s) so that coatings of PLL are polycationic over a wide pH range. Such coatings spontaneously incorporate multiply charged anions such as C O ( C ~ O ~ )A~ large ~ - . portion of the incorporated anions are lost from the coatings only slowly when they are transferred to supporting electrolyte solutions containing no C0(C204)$-so that the electroreduction of the anions retained by the coating can be observed. Figure 1B shows an example of such an experiment. The c0(c204)s3-anions were incorporated in a PLL coating by soaking a coated electrode for 30 min in a 1.0 mM solution of the complex. (The results were unchanged for soaking periods of 5-60 min.) After the electrode was washed with a supporting electrolyte solution at pH 1.5, it was transferred to a cell containing the same solution and the voltammogram recorded. The reduction peak current is about 10 times larger than would have been measured at a bare electrode ) ~ ~ - solution because the in the 1.0 mM C O ( C ~ O ~loading concentration of the complex within the PLL coating is much greater than its concentration in the loading solution. Figure 1B shows that the reduced complex is not reoxidized at the electrode so that only a single voltammogram is obtained for each loading of the PLL coating with Co(C204),,-. To repeat the experiment the coated electrode had to be transferred again to the loading solution and reequilibrated. Repetitive experiments with the same (30) L. Hin-Fat and W. C.E. Higginson, J. Chem. SOC.A , 298 (1967).
I
1
0.8
0.6
,W 0.4
E vs
I
I
0.2
0
I
-0.2
-0.4
SSCE,volt
Flgure 2. Cyclic voltammetry of Fe(CN):incorporated in a coating of PLL (2.7 X lo-’ mol cm-’) on a graphite electrode. The electrode was soaked for 30 min in a 1 mM solution of Fe(CNIe3-in 1 M CF,C0.1 M CF,COOH, washed, and transferred to the same pure OONa isupporting electrolyte. Scan rate: 200 mV s-‘. The outer curve is the first scan; the Inner curve is the second and subsequent scans.
“ L ?? w
= Y
o
4
f
L
Flgure 3. Variation of the thickness of a PLL coating (5.6 X 10“ mol cm-*) on a graphite electrode with the concentration of C O ( C ~ O ~ ) ~ ~ in the solution to which the coating was exposed. Supporting elecCF,COOH (pH 1.5). trolyte: 0.2 M CF,COONa
+
electrode coating produced peak currents that were reproducible to about f15%. The behavior of CO(C~O,),~in PLL coatings contrasts with that observed when reversible redox couples are incorporated in the coatings. Figure 2 shows the response obtained when Fe(CN)63- was incorporated in a PLL coating. Successive cycling of the electrode potential in pure supporting electrolyte solutions yielded a stable voltammogram in which the incorporated redox couple could be cycled continuously between its two oxidation states. Swelling of PLL Coatings. The thicknesses of swollen coatings of PLL on polished graphite electrodes were measured micrometrically under magnification as described in the Experimental Section. In pure supporting electrolytes the swelling was quite extensive with measured film thicknesses almost 100 times greater than those corresponding to the dry density of the polyelectrolyte.
Co(C,O,):-
in Coatings of Protonated Polylysine
The Journal of Physical Chemistty, Vol. 87, No. 4. 1983 643
-~ -~
Figwe 4. Schematic model for a portion of a swollen poiycationic film on an electrode surface. In this example, the film has been equilibrated with a solutlon containing an electrolnactive supporting electrolyte composed of C’X- and the oxidized half of an electroactive couple, Z-/Zz-. The electrode potential is adjusted to the limiting cwrent plateau for the reduction of Z-to Zz-both of which are stable species (unlike the CO(C~O,):-’~ couple). Solid lines represent the polyelectrolyte chains. The dashed lines indicate the regions of extension of the “Donnan domains” containing the electrostatic fields generated by the fixed cationic sites on the chains. The remaining, empty space is filled by the supporting electrolyte solution that permeates the coating.
However, the films swelled less extensively in solutions containing multiply charged anions that were incorporated in the film and presumably acted as electrostatic crosslinking agents within the Figure 3 shows how the thickness of the swollen film decreased in the presence of C O ( C ~ O ~anions. )~~The swollen PLL coatings constitute a barrier layer that CO(C,O,)~~anions must traverse in order to reach the electrode surface where they can be reduced. The rates at which the anions diffuse within PLL coatings were evaluated both by transient potential-step experiments and by measurements of limiting reduction currents at rotating disk electrodes. Two-Phase Model of PLL Coatings. Recently we s h o ~ e d ’that ~ * ~coatings ~ of swollen polyelectrolytes such as PLL can be regarded as consisting of two phases as depicted in Figure 4: One phase, termed the “Donnan domains”, represents the immediate neighborhood of the fixed charge groups where counterions are held by electrostatic forces. The second phase, comprising the remainder of the volume occupied by the coating, is filled by the electrolyte solution with which the coating is equilibrated. Reactant ions can be present in both of the phases and the rate of supply of reactants to the electrode surface is determined by the sum of the reactant transpoit rates in the two phase^.'^^^^ With complexes such as Fe(CN)63-and Fe(CN)64-that are stable in both oxidation states the transport processes may include electron-exchange reactions between pairs of oxidized and reduced reactants. As a result, electrons can be shuttled to oxidized reactants at some distance from the electrode so that they can be reduced without having to reach the electrode surface.21 In addition, the transport in both phases can be coupled if oxidized and reduced reactant pairs exchange electrons or places across the “boundary” separating the two phase^.'^^^^ These interesting but complicating features are not encountered with the Co(C2O4)33-system because the reduced form of the complex does not survive long enough to participate in such electron- or place-exchange reactions. That is the primary reason that this complex was selected for the present study.
I!
IO0
0
I i
I
i
I
I
I
I
I
I
I
I
+0.8 +0.6 +0.4 +0.2 0 -0.2 -0.4 -0.6 -0.8 E vs SSCE, volt
Figure 5. Current-potential curves for the reduction of 0.5 mM Co(C,0,)g3- at a rotated pyrolytlc graphite disk electrode coated with 2.8 x IO- mol cm-2 of PLL. Supporting electrolyte as in Figure 1. Scan rate: 7 mV s-‘. Rotation rate, w , is indicated on each curve.
Rotating-Disk Voltammetry at PLL-Coated Electrodes. Figure 5 shows a set of current-potential curves for the reduction of c0(c204)33-at a rotating disk electrode coated with PLL. The “hump” in the curves arises from the reduction of the complex that is electrostatically attracted into the film before the curve is recorded. The hump is absent in steady-state curves recorded at zero scan rate. The limiting currents of the curves in Figure 5 provide measures of the rate at which C O ( C ~ O ~anions ) ~ ~ - move through the coating to reach the underlying electrode. Figure 6 shows Levich plots31 for the reduction of Co(C204)33-at both bare and PLL-coated rotating disk electrodes. The deviations of the limiting currents from the straight line obtained with the bare electrode increase with coating thickness as expected for a reactant that must penetrate the coating to reach the electrode surface.32 Figure 7 shows the corresponding plots of the reciprocal plateau currents (i1J1 vs. u-1/2where w is the electrode rotation rate. The linearity of these plots with slopes that match that at a bare electrode shows that they obey the Koutecky-Levich equation33 1/ilim
= l/iA
+ l/iF
(1)
where i A is the Levich current,31proportional to that would be observed at a bare electrode and iF is the “film current” representing the intercepts of the plots in Figure 7. The slope of the lines in Figure 7 can be used to calculate a diffusion coefficient for c0(c20&3in the solution of 6.6 X lo+ cm2 s-l. Once the steady state is attained, currents at polyelectrolyte-coated rotating disk electrodes will be influenced only by the transport of reactant across the coating in regions outside of the Donnan domains (Figure 4) unless a mechanism exists for the spent reactant inside the Donnan domains to be regenerated.19gm (It is assumed that (31)V. G.Levich, “Physicochemical Hydrodynamics”,Prentice-Hall, Englewood Cliffs, NJ, 1962. (32)D. A. Gough and J. K. Leypoldt, Anal. Chem., 51, 439 (1979). (33)J. Koutecky and V. G. Levich, Zh.Fiz. Khim., 32, 1565 (1956).
644
The Journal of Physical Chemistty, Vol. 87, No. 4, 1983
Anson et 81.
Oao9I
Q
E -I
I
H
0.5
I
L
I
C - c.5 E vs SSCE ,volt
-I.(
Figure 8. Current-potential curves for the reduction of 0.5 mM Co(C,O,)qs at a rotated pyrolytic graphite disk electrode coated wlth 5.6 X 10- mol cm-' of PLL. Supporting electrolytes: (A) 0.2 M CF3COONa CF,COOH (pH 1.5); (B) the same 5 mM Cr(C20,)2-. Rotation rate: 3600 rpm. Scan rate: 10 mV s-'.
+
0
20
40
w
60
+
80
112
, (rpm)'"
Figure 6. Levich plots of limitin current vs. (rotation rate)''2 for the reduction of 0.5 mM Co(C,O,)jat rotating pyrolytic graphite disk electrodes coated with PLL. The coatings contalned (A) 0, (B) 2.8 X (C) 5.6 X lo-', and (D)1.1 X 10" mol cm-2 of PLL. Supporting electrolyte as in Figure 1.
w " ~(rpm)-'l2 , Figure 9. Koutecky-Levich plots for the reductioti of Co(C204),3-at a rotating disk electrode coated wlth 5.6 X mol cm-' of PLL. The sdutlons contained (A) 0.5, (C) 1.0, (D)2.0, and (E)4.0 mM co(C204h3-. Line B is for a solution containing 0.5 mM C O ( C ~ O ~ and ) ~ ~ -5 mM Cr(C204)2-. Supporting electrolyte as in Figure 8.
the Donnan domains to diffuse across the coating. It was possible to demonstrate the absence of such cross-phase ion exchange as follows: Film currents (obtained from the intercepts of plots such as those in Figure 7) measured in 0.5 mM solutions of C O ( C ~ O ~were )~~compared with those obtained in solutions containing 0.5 mM C O ( C ~ O ~and ) ~ 5~ mM - Cr(C204),3-. The latter com0.05 0.I plex is structurally identical with C0(C204)2- and is -1/2 w , (rpm)-'I2 strongly incorporated by the PLL coatings but it is not reducible in the potential range of interest. The idea was Figure 7. Koutecky-Levich plots of (llmmng current)-' vs. (rotatlon to greatly decrease the incorporation of C O ( C ~ Owithin ~)~~ for the data of Figure 6. the Donnan domains by forcing it to compete with Crdirect entry of the Donnan domains by reactant from the (C204)33for binding sites without affecting the concenbulk of the solution is unimportant because over 98% of tration of C0(C2O,),3- present in the solution outside of the interface between the Donnan domains and the soluthe Donnan domains. Figure 8 compares the reduction of tion phase lies inside the highly swollen coatings.) With C O ( C ~ O ~at) ~the ~ -coated rotating disk electrode in the reactants like Fe(CN)63-such regeneration is possible by presence and absence of Cr(C204)33-.The only effect of means of cross-phase (i.e., across the Donnan domain-sothe Cr(C204)33-is a marked decrease in the peak at the lution interface) electron exchange but with C O ( C ~ O ~ ) ~ ~beginning of the wave reflecting the smaller concentration ) ~ ~ -the Donnan domains. Kouteckythe only possible mechanism for resupplying CO(C~O,)~~- of C O ( C ~ O ~within Levich plots for the same pair of solutions are shown in to the Donnan domains is for cross-phase anion exchange to occur during the time required for the reactant outside Figure 9 (lines A and B). Note that the addition of the
co(C20,):-
The Journal of Physical Chemlstty, Vol. 87, No. 4, 1983 645
in Coatings of Protonated Polylysine
TABLE I: Film Currents for Reduction of Co(C,O,),3- at PLLCoated Electrodesa
2.8 5.6 10.2 5.6 5.6 5.6 5.6
0.5 0.5 0.5 1 2 4
0.5f
2.3
1.1 0.61
3.0 7.8 17.8 0.92
4.8 2.3 1.3 3.1 4.0 4.6 1.9
0.8 1.6 3.2 1.4 1.2 0.96 0.9
3.8 3.6 4.0 4.3 4.8 4.4
1.7
Total quantity of PLL in electrode coating. Supporting electrolyte: 0.2 M CF,COONa + CF,COOH (pH 1.5). Evaluated from eq 2. e CoatFilm current determined from the intercept of Koutecky-Levich lots (Figures 7 and 9). ing thickness measured as described in the Experimental Section. ?Solution also contained 5 mM Cr(C,0,),3-. a
10-fold excess of Cr(C204)33-produces a very small change in the film current. Coulometric assay of the coatings showed that the addition of 5 mM Cr(C2O4)?-decreased the quantity of C O ( C ~ O ~in)the ~ ~ Donnan domains in the film from 4.9 X to 0.9 X lo-* mol cm-2. Despite this large difference in the quantity of the reactant initially present in the Donnan domains, the film current at the rotating disk showed no corresponding change. The film thickness is smaller in the presence of the irreducible surrogate reactant and this is expected to produce an increase in the film current. The small decrease in film current that is actually observed (Figure 9) presumably results because of a decrease in the effective diffusion coefficient of c0(c204)33- within coatings in which there is extensive electrostatic cr~ss-linkin$~by Cr(C204)3s. In any case, the absence of a large decrease in the film current in the presence of excess C I ( C ~ O , )constitutes ~~ very clear evidence that the Donnan domains play no important role in the transport of C O ( C ~ O ~to) ~the ~ -electrode surface under steady-state conditions at the coated rotating disk electrode. On the basis of this result the film currents evaluated from the intercepts of the Koutecky-Levich plots in Figures 7 and 9 were identified with the current, is, that measures the rate of permeation of the coating by the reactant:19 where Ds is the diffusion coefficent of Co-
lution phase inside the PLL coatings, we transferred the coated electrodes to a pure supporting electrolyte solution after they had been equilibrated with solutions of Co(c204)3? Chronocoulometric charge-(time)1/2plotsu were measured when the electrode potential was stepped to -0.8 V where the reduction of C0(C204)2-proceeded at a diffusion-controlled rate. Diffusion coefficients were evaluated from eq 3, where DD is the diffusion coefficient of the DD1/2 = ?r'/2S/(2FC~)
(3)
C O ( C ~ O ~within ) ~ " the Donnan domains, S is the slope of the charge-(time)1/2 plot, and CDis the concentration of the complex within the Donnan domains. The use of eq 3 to evaluate DD depends upon the retention of the Co(C204)33-anions within the Donnan domains when the electrode is transferred to pure supporting electrolyte and the rapid departure from the coating of the C O ( C ~ O ~ ) ~ ~ anions that were present outside of the Donnan domains. The retention of the electrostatically bound C0(C204)2was demonstrated by increasing the time that elapsed between the transfer of the coated electrode from the loading solution to the pure supporting electrolyte and the coulometric assay of the quantity of C O ( C ~ O ~in) the ~~coating. The assays were independent of the elapsed time for periods of at least 30 min. The rapid loss of the Co(C204)33-outside of the Donnan domains was confirmed by showing that the quantity of C O ( C ~ O , )found ~ ~ - by is = FDs~Cb/@ (2) coulometric assays in pure supporting electrolyte of PLL (c204)3*in the regions of the PLL coating outside the films that had been equilibrated with concentrated soluDonnan domains, K is the partition coefficient giving the tions of the complex never exceeded one-third of the amratio of the equilibrium concentration of C O ( C ~ Oin~the ) ~ ~ monium groups in the PLL coatings. If the C O ( C ~ O , ) ~ ~ bulk of the solution, Cb,to that in the solution phase within dissolved in the solution within the coating did not diffuse the coating, and @ is the thickness of the coating. The rapidly out of the coating when it was transferred to sovalues of is and eq 2 provide a measure of the combination lutions containing no complex, the quantity of cO(Cz04)3* aslipas summarized in the fourth column of Table I. found within the coating could exceed this value. For Using the film thicknesges determined by the procedure example, PLL coatings equilibrated with 0.1 M solutions described in the Experimental Section, we calculated the of C0(C204)2-will incorporate comparable quantities of values of asin the last column in Table I. The film the complex inside and outside of the Donnan domains. thicknesses listed in Table I correspond to films equiliHowever, when such a coating was transferred to pure brated with supporting electrolyte solutions containing supporting electrolyte and assayed for C0(C204)2- as c0(c204)33-because experiments indicated that reductive rapidly as possible (-90 s), the value obtained correremoval of these anions during the recording of the cursponded close to one C O ( C ~ O , )anion ~ ~ - for every three rent-potential curves does not result in rapid changes in NH3+groups in the coating. film thickness. For example, the steady-state disk currents The value of CD required to evaluate DD by means of obtained by stepping the electrode potential from a value eq 3 was assumed to be equal to reo/@, where rc0is the ahead of the reduction wave onto the current plateau were total quantity of C O ( C ~ O ~retained )~* by the PLL coating independent of time for at least 5 min. when it was transferred to the pure supporting electrolyte. The values of KDSlisted in Table I are larger than the Thus, the value of CDemployed is a fictitious concentration diffusion coefficient of CO(c@4)3* in aqueous solution, D representing an average over the entire volume of the = 6.6 X lo4 cm2 s-l, which points to a value of K significoating of the higher concentration of complex within the cantly greater than unity. Donnan domains. The latter could be written as I'co/@y Evaluation of the Diffusion Coefficient of CO(c204)3* where y is the fraction of the total volume of the coating within the Donnan Domains. To measure the rate of ) ~ ~ - the Donnan domains diffusion of C O ( C ~ O ~within without interference from C O ( C ~ O present ~ ) ~ ~ - in the so(34)N. Oyama and F.C. Anson, J . Electrochem. Soc., 127,640 (1980).
646
Anson et ai.
The Journal of Physical Chemistty, Vol. 87, No. 4, 1983
TABLE 11: Diffusion Coefficients for Co(C,04),3- inside the Donnan Domains within Coatings of PLL'
10;. electrode no. 1
2 3
S, C [CO(C,O,),'-],~ ~ C O ( C , O , ) , ~ -em-' ~~ mM mol cm-, s-"' 109.
0.5 1.0 2.0
4.7 5.7 7.1
3.4 3.7 4.0
10'. lo4, DD, Cmz cm s-l
8
2.8
7 6.5
1.7 1.1
The coatings consisted of 2.8 X 10.' mol cm-' of PLL. Concentration of Co(C,O,),3- in the solution with which the coating was equilibrated before transfer. The solution also contained 0.2 M CF,COONa + CF,COOH (pH 1.5). Quantity of Co(C,O,),J- retained by the coating after transfer. Measured by coulometric assay. Slope of the chronocoulometric charge-( time)", curve evaluated at times between 5 and 50 ms after the potential step was applied. e Coating thickness; measured as described in the Experimental Section.
occupied by the Donnan domains. Table I1 contains typical values of DD obtained from eq 3 by this chronocoulometric procedure. Both DD and CP appear to depend on rc0but the most striking feature is the large magnitude of the values of DD that result from eq 3 when the large measured values of CP are used to evaluate CD. The resulting values of DD are not much smaller than the value measured in homogeneous solution (6.6 X lo4 cm2 s-l). Thus, if the values of @ are correct, the diffusion-like motion of the C0(C204),3-anions confined within the Donnan domains appears to proceed remarkably rapidly considering that the pathways open to the moving anions must be severely restricted by the electrostatic forces that constrain them to remain within the Donnan domains. The apparent concentration dependence of DD might reflect steric crowding within the Donnan domains leading to a single-file diffusional mode that is intrinsically concentration dependent." Estimation of Ds. If the chronocoulometric experiment used to evaluate DD is repeated without transferring the electrode from the loading solution, the linear charge(time)'i2 plots have a larger slope because of the additional contribution to the current from the C O ( C ~ O ~present )~~in the volume of the film outside of the Donnan domains. The difference, AS, in chronocoulometric slopes recorded before and after transfer of the electrode is given by eq 4, which shows that the product K D S ~can / ~ be evaluated A s = ~F@KDS'/~/T~/~ (4) from the measurement of A S without the need to know the film thickness. Some values of KOs1J2obtained in this way are listed in the sixth column of Table 111. The values are 5-10 times larger than D1J2for the diffusion of Co( C 2 0 4 ) 2 -in homogeneous solution, D1J2= 2.5 X cm s-lJ2,which supports the earlier conclusion, based on rotating-disk film currents (Table I), that K is significantly larger than unity. Moreover, these chronocoulometric data TABLE 111: Estimates of D S and
K
lead to this conclusion independent of any uncertainties in the estimates of the film thickness. The combination of measured values of AS with the film currents obtained when the same electrode is used as a rotating disk allows estimates of both Ds and K to be obtained if CP is known. Equations 5 and 6 give the relevant
DS1l2= 2CPis/(~1/2AS)
(5)
= rAS2/(4FCbCPis)
(6)
K
relationships. The precision in measurements of A S was poor at concentrations of Co(C204),3-above 1mM so eq 5 and 6 were applied to 0.5 and 1.0 mM solutions to obtain the results summarized in Table 111. The values of DS and K seem reasonably constant considering the experimental uncertainties involved in their estimation. The average values are Ds = 2.3 X lo4 cm2s-l and K = 15. The value of Ds is somewhat smaller than the value measured in homogeneous solution (6.6 X lo4 cm2 s-l) as might be expected for diffusion within a polyelectrolyte film. The relatively large value of K indicates substantial partitioning of C0(C204)2-(along with three unipositive cations) into the solution phase within the PLL coatings. Test of Self-Consistency. It is possible to test the values of K and Ds that we obtained from the combination of steady-state rotating-disk film currents and transient chronocoulometric charge-(time)'J2 plots for self-consistency. When the chronocoulometric measurements are extended to longer times so that the diffusion layer thickness becomes comparable to the film thickness, the difference, AS, in chronocoulometric slopes before and after transfer of the electrode from a solution containing the reactant is given by eq 7 , instead of eq 4, where ASo
is given by eq 4 and D is the diffusion coefficient of Co(Cz04)33-in homogeneous solution. Values of KDS'~'are available from ASo, i.e., from the values of AS recorded at short times (Table 111)and values of CPDS-lJ2are available from the ratio of A 9 to is, A s o f i s = 2 9 / ( 7 ~ D ~ ) lThus, / ~ . eq 7 can be used to plot A S vs. time without having to know the film thickness. The solid curve in Figure 10 was calculated from eq 7 in this way. The plotted points in Figure 7 are experimental values of A S determined at various measurement times. The reasonable agreement between the calculated line and the experimental points shows that the three experimental measurements involved (rotating-disk film currents, short- and
for Co(C,O,),9- in Coatings of PLL"
lo8, [co(czo~),'-], mM
rc0(czo4),:-> mol cm-
103(AS), C
lo3@,'cm
i s , d mA cm-Z
cm-, s - " ~
~ O ' ( K D _ S ~ ~ 106Ds,f ),~ cm s c m 2s-'
2.6 1.7 1.0 1.4 9.4 1.6 2.8 3.9 11.4 1.4 3.0 2.4 0.83 1.7 1.2 0.88 0.92 0.92 Quantity of Co(C,O,),'- retained by the coating after transfer. The coatings contained 5.6 X 10.' mol cm-' of PLL. Permeation Measured by coulometric assay. Coating thickness; measured as described in the Experimental Section. Evaluated from eq 5. Evaluated from eq 4. current obtained from the film currents, iF, in Table I; see text. Partition coefficient evaluated from eq 6. Solution also contained 5 mM Cr(C204):-, 0.5 1.0 0.5h
CO(C,O,),”
0
The Journal of Physical Chembtry, Vol. 87, No. 4, 1983 647
in Coatings of Protonated Poiyiysine
0
1
2
3
4
5
TIME, SEC.
Flgure 10. Comparison of differences in chronocouiometric slopes, AS,calculated from eq 7 (solld line) with experimental values (plotted points). The electrode was coated with 5.6 X lo-’ mol cm-, of PLL. The test solution contained 0.5 mM C O ( C ~ O , )in~ 0.2 ~ M CF,COONa CF,COOH @H 1.5). The chronocoukmetrlc data were recorded over a total time of 5 s and anatyred in lO-ms segments by least-squares fMng to obtain the slope of a charge-(time)” plot for each segment. The range of AS values measured at each time is indicatd by the vertical line passing through each point.
+
long-time chronocoulometric slopes) yield self-consistent values of Dsand K. It is unfortunate that the three experiments do not provide three independent relationships among K , Ds,and CP so that these three parameters could be evaluated directly from the electrochemical measurements. The absolute values of K and Ds obtained are dependent on the accuracy of the measured film thickness, b,but the internal consistency in the values of K and Ds would remain the same even if there was a large error in CP. However, the surprisingly large value of K that we obtined would be even larger if the films were less thick than our measurements indicated (eq 6) and we are confident that we have not underestimated the thicknesses. Thus, the surprisingly large value of K seems to reflect a real affinity of the C O ( C ~ O ,complex )~~ for the uncharged portions of the interior of the coating. The origin of this affinity is not immediately evident but its reality seems inescapable. We are continuing to investigate this interesting observation.
Discussion Swollen coatings of polyelectrolytes such as PLL can be modeled as an intimate mixture of two phases, the Donnan domains where counterions are bound electrostatically and the remainder of the coating volume that is occupied by supporting electrolyte (Figure 4).19t20 By incorporating in PLL coatings a counterion reactant (CO(C~O,)~~-) with chemical properties that prevent its participation in electron- or place-exchange reactions either within or across the two phases in the coating, it has been possible to assess the rate at which the reactant diffuses across the coating to reach the electrode surface where it can be reduced. The two-phase model for the interior of the coating (Figure 4) leads to two diffusional pathways for the C O ( C ~ O ~The )~~. first involves those reactant anions that remain under the influence of the fixed cationic charges as they move through the polyelectrolyte coating so that they follow pathways lying close to the fixed cationic sites. The diffusion coefficient for this pathway lies in the range of 1 X 10-7-2 X cm-2 s-l depending on the quantity of C0(C204)2-that is incorporated (Table 11). The second diffusional pathway is utilized by those additional reactant anions that are dissolved in the solution between the polymer chains inside of the swollen coating.
It was not surprising to find that the diffusion coeffient for these anions, 2 X lo4 cm2b’, is not much smaller than the corresponding value in bulk solutions of the anion, 6.6 X lo* cm2 s-l. The apparent preferential extraction of C O ( C ? O ~by) ~the ~ solution within the coating was a more surprising result. It is interesting to note that, although the diffusion coefficient for the anions that diffuse inside the Donnan domains is ca. 10 times smaller than that for the remaining anions in the coating, their concentration is so much greater that they carry about 75% of the current through the coating during transient potential-step experiments with a 0.5 mM solution of C O ( C ~ O ~ ) With ~ ~ - . a 2 mM solution this fraction drops to just under 50%. The successful evaluation of the two diffusion coefficients depended upon the very slow rate at which electrostatically bound anions departed from the PLL coatings when they were transferred to solutions containing none of the anion. Without this kinetic feature it would have been much more difficult to evaluate the two components of the transient diffusion currenh flowing across the coatings. The value of DD obtained in this study is much larger than most values that have been reported in previous studies for electrostatically bound ions in polyelectrolyte coatings6~8J*18 despite the lack of acceleration of the diffusive motion by electron-exchange reactions. However, similarly large diffusion coefficients were also observed recently for the diffusion of EDTA (ethylenediamminetetraacetate) complexes of Fe(I1) and Fe(II1) within the Donnan domains in PLL coatings under conditions where possible contributions to the diffusion rate by electronexchange reactions could be ruled out.20 We believe that these large diffusion coefficients are the result of the extensive swelling of PLL coatings which may result in a less tortuous diffusional pathway for the incorporated ions. In addition, most previous studies have used the dry densities of polymers to estimate coating thicknesses. Since the diffusion-limited currents measured experimentally depend inversely on the square of the coating thickness, even modest swelling of the coatings would result in calculated diffusion coefficients that appear smaller than their true values. In any case, a much wider range of ionic diffusion coefficients is to be expected when the ions are diffusing in various polyelectrolyte coatings than when they are diffusing in much less disparate homogeneous solutions. When the ions incorporated in polyelectrolyte coatings form reversible redox couples (e.g., Fe(CN):-/“, IrC&*/2-), there are at least two differences to be considered: The diffusion of the ions can be facilitated by electron exchange between pairs of oxidized and reduced readants within the Donnan domains.12 In addition, the ions dissolved in the solution phase within the coating may rapidly exchange electrons (but usually not places) with their redox counterparts in the Donnan domains to provide a coupling between the diffusional pathways available in the two phases that is absent with irreversible systems such as C O ( C ~ O ~The ) ~ consequences ~. of this type of coupling by electron-exchange reactions have been discussed elsewheres17Jgv20
Acknowledgment. Dr Kiyotaka Shigehara provided much invaluable assistance in the preparation and utilization of electrode coatings. This work was supported by the National Science Foundation and the U.S.Army Research Office. A NATO Travel Grant is also gratefully acknowledged. Registry NO. CO(C&)&~*, 15053-34-6;Fe(CN)6“, 13408-62-3; Fe(cN),&, 13408-63-4;CF3COONa,2923-18-4; CF&OOH, 76-05-1; poly(L-lysine)hydrobromide,51728-67-7; graphite, 7782-42-5.
