586
J. Phys. Chem. 1987, 91, 586-593
time scale and evenly spread over 20 ns. The true k(MV2+) is therefore accordingly higher, or k(MVZ+)r 1.1 X IO9 s-I. This value agrees well with the estimate of =IO9 s-l derived from picosecond laser techniques.26 The rate constant k(Rho) can then be estimated as ca. 2 X 1OIo s-I. To the best of our knowledge, no estimation of this rate constant has been previously reported in CdS colloid systems. The concentrations of CdS-adsorbed MVZf,MV" and Rho in eq 5 and I were expressed over the whole sample volume, while these species were confined on the colloid surface. Due to large uncertainties in actual surface area, no surface concentration has been used. Nevertheless, the first-order rate constant (s-l) are unaffected since the analytical concentrations used are proportional to the true surface concentrations. Considering the approximations made in deriving these rate constants, their absolute magnitude has to be taken with caution. However, they provide a basis of comparison with values reported for other colloidal semiconductor systems. For instance, diffusion-limited values in T i 0 2 colloids were found25to be ca. IO7 s-l for electron transfer to MV2+. As reactive species in CdS colloids are adsorbed, the observed electron-transfer rates are not limited by diffusion, but by the adsorption density at close packing. The rhodium efficiency to scavenge e- in the presence of MV2+ can be compared to the activity of Pt deposits on HMP-stabilized CdS colloids.23 These authors reported the effect of a single Pt concentration of "8% Pt loading", for which the observed ratio [MV'+]o/[MV'+]R was 1.5, under conditions of MV2+saturation of the colloid surface. From Figure 4, we obtain the same ratio M Rho, which was 9% of CdS concentration. We at 2.6 X conclude, then, that Pt and Rh had similar activities in their respective systems. No quantitative comparison can be made, however, since no Pt-concentration dependence was reported. Finally, it should be mentioned that no MVZ+transmembrane diffusion occurred in our vesicle preparations, unlike what was reported to happen under photoexcitation of sensitizer Ru(bpy), in the same D H P vesicles.44 Slight MV2+ transmembrane dif(44) Lee, L. Y.-C.; Hurst, J. K.; Politi, M.; Kurihara, K.; Fendler, J . H. J . A m . Chem. SOC.1983, 105, 370.
fusion was observed only when the samples were heated above 60 "C for periods of hours, in agreement with earlier premeability studies.45 However, as was suggested graphically in Figure 3, reduced MV2+(MV") was found to diffuse rapidly through DHP membranes and, once formed at the CdS surface, could escape into both the water and hydrocarbon phases. A detailed study of this phenomenon will be reported elsewhere.43
Summary and Conclusion This work has provided a detailed picture of the electron-transfer process in the photoredox system formed by methylviologen, colloidal CdS, and benzyl alcohol at the DHP vesicle surface. In our application of laser flash photolysis techniques, we have ( I ) determined reactant concentration and pH effects and indirectly estimated the amount of CdS-adsorbed methylviologen; (2) measured the hydrogen production activity of CdS-deposited rhodium catalyst by its effect on reduced methylviologen formation, over a range of rhodium concentrations; (3) derived the individual electron-transfer rate constants and, from their magnitude, demonstrated the high activity of the CdS catalyst; (4) illustrated the unique vesicle structure by its effect on the electron donor efficiency in asymmetrically organized samples. We believe these results will be of great help in designing more complex vesicular or other surface-confined photoredox chemical devices. Acknowledgment. The authors are much indebted to the United States Department of Energy for their generous support. We thank Ms. Asa Emeren for some initial measurements, and Dr. Subhash Baral for helpful discussions. Registry NO.DHP,2197-63-9; M P , 4685-14-7;MV", 25239-55-8; CdS, 1306-23-6;Rh, 7440-16-6;H 2 0 , 7732-18-5; benzyl alcohol, 10051-6.
(45) Tricot, Y.-M.; 37. 703.
Furlong, D. N.; Sasse, W. H. F. Aust. J . Chem. 1984,
Mechanisms of Charge Transfer at the Chemically Derivatlzed Interface: The Ni/[Ni11(CN)Fe11"11(CN)5]2-I'System as an Electrocatalyst Brian D. Humphrey, Sujit Sinha, and Andrew B. Bocarsly* Department of Chemistry, Princeton University, Princeton, New Jersey 08544 (Received: April 7 , 1986; In Final Form: July 1I , 1986) The [Ni(NC)Fe(CN)S]2-/1-derivatized nickel electrode represents an electrocatalytic surface for a variety of oxidations and reductions. This surface exhibits a unique dependence of redox potential on supporting electrolyte cation, which allows for a direct analysis of the effect of surface redox potential on the electrocatalytic rate constant. Two electrocatalytic systems have been evaluated with respect to surface redox potential: the one-electron reduction of Fe3+(aq) and the two-electron (two-proton) oxidation of ascorbic acid. Mediated charge transfer is found to be an operational electron-transfer mechanism in both cases, with the bimolecular surface species to solution species charge transfer being rate limiting. In the case of Fe3+(aq) reduction Marcus theory is found to yield a good description of the relationship between surface redox potential and the electrocatalyticrate constant. Pseudo-first-order rate constants as large as 0.1 5 cm/s (in LiN03 supporting electrolyte) have been observed for this reaction. The ascorbic acid oxidation rate constant is found to be cm/s. This rate constant is independent of surface redox potential, suggesting that the transfer of the second electron is rate limiting.
-
Introduction Research in this laboratory has shown that the surface of anodically unstable electrode materials such as nickel can be chemically derivatized with a variety of [M(CN),L,]" comp l e ~ e s . l - ~In the case of nickel' the surface derivative consists ( I ) Sinha, S.; Humphrey, B. D.; Bocarsly, A. B. Znorg. Chem. 1984, 23, 203-21 1. (2) Sinha, S.; Humphrey, B. D.; Fu, E.; Bocarsly, A. B. J . Elecrroanal Chem. 1984, 162, 351-357.
0022-365418712091-0586$01.50/0
of an extended [Ni"(NC)M"/"' (CN),-,L,]" lattice, as characterized by a variety of electrochemical and spectroscopic means.'.5 It has been demonstrated that such surfaces protect against anodic (3) Rubin, H. D.; Arent, D. J.; Bocarsly, A. B. Nature (London) 1984, 308, 339-341, (4) Rubin, H. D.; Arent, D. J.; Bocarsly, A. B. J . Electrochem. SOC.1985, 132, 523-524. (5) Humphrey, B. D.; Sinha, S.; Bocarsly, A. B. J . Phys. Chem. 1984, 88, 736-143.
0 1987 American Chemical Society
Charge Transfer at Derivatized Interface
The Journal of Physical Chemistry, Vol. 91, No. 3, 1987
581
a series of substrates.1°J2 In these cases, in order to make the decomposition and passivation of the nickel surface and thus allow necessary perturbation in the system free energy, either the surface one to study a variety of redox reactions that are not possible at layer or the solution species must be changed. Unfortunately, the nonderivatized surface. For example, we have previously noted varying the chemical nature of the system often induces changes the facile oxidation of ferrocene at the Fe(CN)64-/3-derivatized besides free energy. For example, self-exchange rates and steric nickel interface, though it occurs only slowly at the untreated surface.' Such surfaces also exhibit an electrocatalytic capability, factors also change. In order to minimize the complications associated with changing the chemical nature of one of the redox allowing the reduction (or oxidation) of certain solution species partners, previous electron-transfer studies have consisted solely at potentials significantly less than needed at the nonderivatized of very facile reactions between transition-metal complexes, nickel surface, as demonstrated herein. thereby limiting the kinetic information to thermodynamically A distinction must be drawn here between the chemical nature unfavorable processes. In the current system the ability to vary of the surface of present interest and the Fe(CN)64-/3- redox system. A primary difference between these two systems is the surface redox potential, without inducing major chemical or structural changes in the redox partners, allows for the first time solid-state nature of the [NiFe(CN),I2-i1- surface which, for the direct verification of Marcus theory at a derivatized electrode. example, removes the possibility of contact ion pairing processes This flexibility allows a choice of solution substrates having associated with solution Fe(CN)64-/3- electron transfer.'9296 moderate self-exchange rates, thus making possible the study of Further, the crystalline, zeolitic nature of this system might be both thermodynamically favorable and unfavorable reactions. We expected to have a major impact on a variety of charge-transfer = +0.51 V vs. SCE) couple events including rates of electron transfer, ability of solution have chosen the Fe2+/3+(aq)(Eredox as a substrate because it fits the criteria of slow reaction kinetics substrate to enter (or exit) the derivatizing layer, and restrictions and falls in the region of the redox potential shift such that the associated with the migration or diffusion of supporting electrolyte into and out of the surface layer as needed for electrone~trality.~~~ cross-reaction with ferrocyanide (reaction 1) can be either thermodynamically favorable or unfavorable depending on the supOne of the more unique aspects associated with the solid-state porting electrolyte.8c nature of these surfaces is that the surface-confined iron center displays an E l / 2value which is quite sensitive to the supporting kiz electrolyte cations present.''' Thus, by simply varying the alkali [NiFe(CN),]'-(surf) + Fe(OH)2'(aq) metal ions present in the supporting electrolyte, one can shift the [NiFe(CN),]-(surf) Fe2+(aq) OH-(aq) (1) surface E I j 2value over a -400-mV window. The nature of this On the other hand, the oxidation of ascorbic acid represents effect has been previously discussed;I it is important to note that a significantly more complicated system involving the removal this phenomenon is not obtained with other "Prussian Blue" of two electrons and two protons. Solution-mediated charge surfaces.* In the present context we have exploited this effect to transfer between Fe(CN)63-(aq) and this species has previously quantitatively probe the relationship between the surface's redox been describedl43l5 as occurring via two one-electron reduction potential and its ability to act as an electrocatalyst. processes involving the formation of a free radical intermediate, In order to consider in detail the mechanisms by which elecas shown by the reactions trocatalysis occurs at the [NiFe(CN)6]2-I'- derivatized nickel interface, a variety of solution couples have been i n v e ~ t i g a t e d . ~ ~ . ~ ki M + AH2 M- AH' H+ (2) Of the couples investigated, two are discussed here as representative of electrocatalytic redox mechanisms occurring at the nickel ferricyanide derivatized interface; the reduction of M M - + A H+ (3) Fe3+(aq)7dand the oxidation of ascorbic acid. Both these couples where M is a charge-transfer mediator. It has also been noted yield slow charge-transfer rates at nickel electrodes in the absence that, depending on solution pH, reaction 2 may occur with the of a catalyst. On thermodynamic grounds these couples may AH- species replacing AH2.I4 The complexity of this reaction undergo surface-mediated charge transfer at the [NiFe(CN)6]2-/1precludes an analysis based on simple one-electron charge-transfer derivatized surface. That is, charge transfer to the solution species theories. Yet, a knowledge of the relationship between reaction may proceed via a pathway in which the surface-bound iron rate and reaction free energy is of utility in further defining the complex is oxidized (or reduced) by the electrode surface in a reaction mechanism. heterogeneous process followed by a bimolecular charge-transfer reaction between surface-bound iron and the solution species. Experimental Section Several investigator^^^'^ have previously suggested that meElectrode Preparation. Working electrodes for cyclic voltamdiated charge transfer at the derivatized electrode interface often metric studies consisted of 0.63-mm-diameter nickel wire (Alfa). involves an outer-sphere mechanism and that a linear free energy Rotating disk electrodes were fashioned from a nickel rod (Alfa, relationship such as provided by Marcus theory yields a suitable 6.35" diameter) which was cut into disks (3.4 mm thick) and description of this process. However, to date the ability to test polished to a mirror finish to remove impurities associated with whether or not Marcus electron-transfer theory is an appropriate cutting and provide for laminar flow conditions. Electrodes were model to employ has been limited, since experimental results are lightly abraded with 150-J metalite cloth and washed with distilled only available for polymer-coated electrodes (with constant water before derivatization. After derivatization, they were wiped standard redox potential) reacting with a solution substrate or with a Kimwipe and washed with distilled water to remove loosely adhering substances. Typically, surface derivatization was ac(6) Bocarsly, A. B.; Sinha, S. J. Elecrroanab Chem. 1982, 137, 157-162. complished by potentiostating the Ni electrodes at 1.O V vs. SCE (7) (a) Bocarsly, A. B.; Sinha, S. J. Elecrroanal. Chem. 1982, 140, 167-172. (b) Humphrey, B. D. Ph.D. Thesis, Princeton University, 1984. (c) for 50 s in an electrolyte containing 0.1 M N a N 0 3 and 0.005 M Sinha, S. Ph.D. Thesis, Princeton University, 1984. (d) Fe'+(aq) is used to [Fe(CN),13-. By appropriate variation of potentiostating voltage, represent Fe3+in aqueous solution at its natural pH. Due to hydrolysis, the time, and concentration of [Fe(CN),13-, different electrode covactual species present is Fe"'(OH), where x varies from 1 to 3. erages were obtained, as previously described. (8) Itaya, K.; Uehida, I.; Toshiona, S. J . Phys. Chem. 1983, 87, 105-1 12. Electrochemistry. Cyclic voltammetry was carried out using (9) Laviron, E. J . Electroanal. Chem. 1982, 131, 61-75. (10) (a) Lewis, N. S.; Bocarsly, A. B.; Wrighton, M. S. J. Phys. Chem. a PAR 174A polarographic analyzer controlled by a PAR 175 1980,84,2033-2043. (b) Lewis, N. S.;Wrighton, M. S. J . Phys. Chem. 1984, universal programmer. Data were output to a Houston Instru88, 2009-2017. ments 2000 X-Y recorder. Rotating disk experiments were ac(11) (a) Anson, F. C. J . Phys. Chem. 1980,84, 3336-3338. (b) Shigera, complished with a Pine RDE-4 potentiostat and Pine ASR 2 K.; Oyama, N.; Anson, F. C. J. Phys. Chem. 1981, 20, 518-522.
+
-
+ AH*^
(12) (a) Ikeda, T.; Leidner, C. R.; Murray, R. W. J. Am. Chem. SOC. 1981,103,7422-7425. (b) Kuo, K. N.; Murray, R. W. J. Electroanal. Chem. 1982, 131, 37-60. (c) Leidner, C. R.; Murray, R. W. J . Am. Chem. SOC. 1984, 106, 1606-1614. (13) Andrieux, C. P.; Dumas-Bouchiat, J. M.; Saveant, J. M. J. Electroanal. Chem. 1982, 131, 1-35.
+
-+
+ +
(14) Khan, M. M. T.; Martell, A. E. J. Am. Chem. SOC.1967, 89, 4 176-4 185 . (15) Winograd, N.; Blount, H. N.; Kuwana, T. J . Phys. Chem. 1969, 73, 3456-3462.
588
The Journal of Physical Chemistry, Vol. 91, No. 3, 1987
I
I M NaN03
t
Humphrey et al.
50 mM Fe(NO&
b'
00 Polential,
1
I
0
0.4
I
Potential, V vs. S C E
I
0.8
Figure 1. (a) Cyclic voltammogram of a [NiFe(CN)6]2-/1-derivatized
nickel electrode in 1 M NaNO,(aq) supporting electrolyteat a scan rate of 100 mV/s. (b) Linear scan voltammograms initialized at +1.0 V vs. SCE in an electrolyte containing 50 mM Fe3+(aq). A scan rate of 100 mV/s was employed. The dashed line represents a nonderivatized electrode, while the solid line is the electrode used in part a. The data in parts a and b were obtained by using the same current scale. variable-speed rotator. The electrochemical cell consisted of a derivatized nickel work electrode, a Pt counter electrode, and a S C E as a reference electrode, all mounted in a Pyrex cell. Preliminary characterization of all derivatized electrodes was carried out by cyclic voltammetry. Electrode coverages were established by integration of the anodic cyclic voltammetric wave area with respect to time.' All chemicals were reagent grade and used as received. The reduction of Fe3+(aq)was carried out at the system's natural pH. The iron concentrations were selected such that solution pH was 2.5-4, since surface degradation was observed under more acidic conditions. Ascorbic acid experiments were carried out at pH 4 using either phosphate buffer, Tris buffer, or ascorbate buffering. All three buffers yielded identical results. Results and Discussion Fe3+(aq)Reduction. The linear sweep voltammetric response of a nonderivatized nickel electrode in a relatively concentrated Fe3+(aq) solution is shown by the dashed curve in Figure lb. Although the redox potential for the Fe2+/3+(aq)couple is +0.51 V vs. SCE, no current associated with the formation of Fe2+(aq) is observed even at potentials as negative as 0 V vs. SCE, indicating that the activation energy for heterogeneous charge transfer in this system is greater than 10 kcal/mol. If this same electrode is derivatized with nickel ferrocyanide (surface coverage I? = 9 X lo-* mol/cm2) and placed into the same Fe3+(aq)-containing electrochemical cell, the solid line in Figure 1b is observed in response to a linear sweep of the electrode potential. This response is identical with that of a platinum electrode in the same solution (no effort has been made to rigorously exclude halide ions which electrocatalyze this process at platinum)16 and indicates the facile generation of Fe2+(aq) at all potential negative of +0.50 V vs. (16) Johnson, D. C.; Resnick, E. W. Anal. Chem. 1977, 49, 1918-1924. (17) Schneemeyer, L. F.; Spengler, S.E.; Murphy, D. W. Inorg. Chem. 1985, 24, 3044.
04 V vs S C E
08
Figure 2. Linear sweep voltammograms of Fe"(aq) in various alkali metal cation containing supporting electrolytes at a derivatized nickel electrode. All scans were initiated at +1.0 V vs. SCE. The ionic strength of the electrolyte was held constant. A scan rate of 100 mV/s was employed.
SCE. That the current observed is associated with Fe3+(aq) reduction and not the reduction of surfaceattached [NiFe(CN)J is demonstrated by comparing the currents in part b of Figure 1 with part a of Figure 1 which shows the cyclic voltammetric behavior of the derivatized electrode in an electrolyte (1 M NaN03(aq)) containing no purposely added electroactive species. Note that the cathodic current associated with the surface-attached material is significantly less than that obtained in the solution containing Fe3+(aq). The observation of a reducing current which initiates -0.5 V more positive than that observed at the nonderivatized electrode leads to the conclusion either that the surface-attached material is an electrocatalyst for the Fe3+(aq) species or that the surface layer is acting to inhibit the formation of a passivating surface oxide. Although it has previously been illustrated that the derivatizing layer suppresses oxide passivation of the nickel surface,' it can be shown by considering the effect of surface redox potential, ERS, on the Fe3+(aq) reduction that surface-mediated charge transfer leads to electrocatalysis in the present case. Since mediated charge transfer is a bimolecular process between the surface-attached and solution species, a strong dependence on ERSis expected. On the other hand, if the charge-transfer mechanism involves heterogeneous charge transfer between the solutions species and the solid electrode directly, it should not be influenced by the redox potential of the surface-attached material. Further, since varying the supporting electrolyte has no effect on the surface oxide inhibition properties of the derivatizing layer, if removal of a surface oxide were responsible for the observed catalysis, there should be no observable cation effect on the voltammetric properties of the system. However, as can be seen in Figure 2, there exists a strong cation effect on the reduction of Fe3+(aq) to Fe2+(aq). If, for example, the supporting electrolyte is composed of CsN03, the redox potential of the surface-attached material lies 100 mV positive of the redox potential of the solution couple (+0.61 V vs. SCE) and very little current is observed, most of which can be attributed to the reduction of the surface-attached material. This is as expected for mediated charge transfer since the reverse reaction is thermodynamically favored in this case. Shifting the redox potential of the surface-attached material negative to a position 40 mV positive of the solution species (RbN03 supporting electrolyte) induces a larger current, indicating the reduction of more solution Fe3+; however, the rate is slow since AG is still slightly positive. Employment of a potassium-containing electrolyte moves the redox poential of the surface-attached material negative
The Journal of Physical Chemistry, Vol. 91, No. 3, 1987 589
Charge Transfer at Derivatized Interface
1
TABLE I: Typical Koutecky-Levich Intercepts as a Function of Electrode Coverage for the Reduction of Fe3+
electrolyteb LiNO,
1.30 1.45 1.37 1.02 1.15 1.01 1.49
9.2 X 6.6 X lo-" 4.0 X
3.0 x 2.0 x 10-8 2.7 x 10-7 8.5 X 6.2 X 6.9 X 5.58 X 1.9 x 10-7 5.9 x 10-8
KNO,
RbNO3
.-V
U
0
f0
1.38
V
1.17 2.0 2.1 14.3 14.7
3600 rpm I
0 .o
-I < 0.3 E
; 1
.
:
2
.
:
3
I
3
V
Y
:
1
I
c
0.4t
4
I
I
E L
cyclic voltammetric response of the electrodes. *All supporting electrolytes are at 0.1 M concentrations. The Fe3+concentration is 5 mM in all cases. cAn error of 115% is associated with these values.
0
I
I
c
'Coverages are obtained by integration with respect to time of the
0
I
Koutecky-Levich intercept: mA-'
coverage,' mol/cm2 1.3 x 10-7
NaN0,
I
C
.
CONCENTRATION
:
4
:
:
5
:
I
6
(mM)
Figure 3. Relationship between the inverse of the Koutecky-Levich intercept and the Fe3+concentration in a 0.1 M KN03 supporting elec-
trolyte. of that of the solution species (by 65 mV) with a concomitant large increase in the observed electrocatalytic current, consistent with a favorable value of AG for the reaction. Further shifts negative cause an increase in the current associated with the reduction of Fe3+(aq). By comparison of Figure 2 with Figure l b it can be seen that, even at the most negative ERSvalues employed (LiNO, supporting electrolyte, hE = -180 mV), the peak electrocatalytic current falls in a potential region where no current is observed at the nonderivatized electrode. Thus, it is fairly certain that none of the Fe3+(aq) is reduced directly at the electrode surface; only mediated charge transfer can be occurring. In order to quantitatively separate out the current associated with Fe3+(aq) reduction from the current associated with the surface-attached material, rotating disk electrode experiments were carried To ascertain the spatial region in which the charge transfer to solution species takes place, the reduction of Fe3+(aq) was observed as a function of the amount of surface-attached material. These studies resulted in the observation of a mediated current which was independent of surface coverage (for a given supporting electrolyte) for electrodes containing in excess of 10 monolayers (see Table I), as ascertained by the Koutecky-Levich experiments described below. Thus, once a fairly homogeneous distribution of surface-attached species is present, the reaction apparently involves only the outer layers of surface-attached material. Further evidence for this type of reaction zone is found in considering the dependence of the limiting hydrodynamic current on concentration of solution Fe3+(aq). As can be seen in Figure 3, up to at least 5 mM there exists a linear correlation between the inverse Koutecky-Levich intercept and the Fe3+(aq) concentration. Within the framework of Saveant's rotating disk analysis,13this is expected for an outer layer reaction zone. It is possible that the Fe3+(aq) species has access to the electrode surface via cracks and pinholes
I
0.8
0.4
Potential ( V v s . S C E ) Figure 4. Typical rotating disk voltammogram as a function of rotation
rate (rpm) for the reduction of Fe3+(aq)at a derivatized nickel electrode in LiNO, supporting electrolyte. Scans were initiated at +1.0 V vs. SCE using a 20 mV/s scan rate. in the derivatizing layer; this would lead to an effective roughness factor associated with the reaction zone area. Such defects do not yield access to the interior of the surface-attached layer. It should be noted that the present data cannot rule out a slight amount of penetration by the solution species. In fact, the coverage studies, though of very low resolution, suggest a reaction zone as thick as 50-100 %, may be involved. The key point is that for electrodes containing a 200-1 000-%,thickness of surface-confined material the reactivity can be considered constrained to an outer layer of the derivative. All experiments reported herein have been carried out with surface coverages between 20 and 100 monolayers and Fe3+(aq) concentrations no greater than 1 mM to guarantee that the reaction zone is defined as described above. Experiments have been carried out for a series of solution concentrations and surface coverages within these established ranges and yield a consistent set of results. For reasons of clarity and brevity only representative experimental results are reported. Typical rotating disk voltammetric data are demonstrated in Figure 4 for the reduction of Fe3+(aq) in the presence of LiNO, at an electrode having J? = 4.7 X mol/cm2. Note that, in the presence of LiNO,, ERSis shifted to its most negative value, yielding the fastest electrocatalyst for the Fe3+(aq) reduction. In this electrolyte the plateau current, iL,is established at a potential of -+0.2 V vs. SCE. In this case ERS = +0.32 V vs. SCE; thus, the limiting current is reached within 100 mV of the surface redox potential. Figure 5a illustrates that for the data in Figure 4 the value of iL does not vary linearly with the square root of the rotation rate (Levich plot). Further, iLis always found to be less than calculated by using the Levich equation (4) which describes a purely mass
-
ileV= 0.620nFAD2/3w112v-'16C*
(4)
transport limited process,'* where D and C* are the diffusion coefficient and bulk concentration of the solution species (mol/ cm3), respectively, w is the rotation rate, and v is the kinetic viscosity of the aqueous electrolyte. On the other hand, the data are well described by the Koutecky-Levich equation ( 5 ) , as il-1= - +1 - 1 i~ ilcv lact lustrated in Figure 5b,19 where i,, is an activation energy associated current component having no rotation rate dependence. There exist a variety of chemical processes which might be held responsible for the activation energy observed. For example, diffusion of the Fe3+(aq) species into the surface layer represents (1 8) Levich, V. G.Physicochemical Hydrodynamics; Prentice-Hall: Englewood Cliffs, NJ, 1962. (19) Koutecky, J.; Levich, V. G. Zh. Fir. Khim. 1956, 32, 1565.
590
The Journal of Physical Chemistry, Vol. 91, No. 3, 1987
Humphrey et al.
TABLE II: Reduction of Fe3+(aq) at the Derivatized Interfaceo
range of k12rs: cm/s
kl2rsr)
cation
AEI~',V
Li+ Na"
+0.180 +0.140
K+
+0.065
Rb+ cs+
-0.040 -0.100
cm/s
Kl2
1.1 2.3 1.2 2.1 2.0
x 103 X lo2
x 10' x lo-' x 10-2
3.2 X 1.3 X 4.0 x 10-3 7.9 x 10-4 2.0 x 10-4
1.5 3.2 1.6 2.0 2.7
X 10-'-1.1 X X 10-2-6.5 X X 10-2-3.2 X X 10-3-7.1 X
x 10-4-1.8 x 10-4
kl2,d M-l s-l
3.2 x 1.3 x 4.0 x 7.9 x 2.0 x
105 105 104 103 103
1% f 1.7 X 10-I 1.0 x 10-1 2.2 x 10-2 8.3 x 10-3 5.2 X
"All measurements by RDE in 0.1 M supporting electrolyte at the systems natural pH. bThese are typical values. cEach value represents a series of experiments carried out on five electrodes. More than 40 measurements were carried out for each cation at a variety of Fe3+(aq)concentrations (0.1-5 mM). The range was established by T-testing to 85% confidence. dAssuming rs= mol/cm2.
E w.12
Y
s
0
20
0
40
60
w l / * (rpmj"
(reaction 1) and rsis the coverage of surface-bound iron centers actually involved in the reaction (Le., accessible to solution species and in the correct oxidation state). The product k I 2 r srepresents a pseudo-first-order rate constant having standard heterogeneous units of cm/s. Using a maximum value for C* of 1 mM, it can be seen that the surface charge diffusion flux (eq 7 ) will support at most a pseudo-first-order electron-transfer rate constant of 0.1 cm/s. In evaluating this number, it should be realized that it is a conservative estimate since the smallest possible values have been employed in eq 6 to obtainfcT. As can be seen from the experimental values of k 1 2 r S(Table 11), only in the presence of LiN0, supporting electrolyte will fEX approach f C T . However, the value of k12and thus kI2rfor the LiNO, system is totally consistent with the values obtained for the other four supporting electrolytes where the surface derivative to solution species electron-transfer rate is clearly the rate-limiting step. Thus, we observe no evidence for a mechanism switch rate limiting vs. fEX rate limiting) in the Li+ supporting electrolyte. The data in Figure 3 provide a second line of evidence indicating that the rate-limiting process is bimolecular exchange. Although data are only provided here for the K+ case, it is found that a linear relationship exists between the concentration of Fe3+i2+(aq)and the extrapolated zero rotation rate current (inverse KouteckyLevich intercept) for all supporting electrolytes. Comparing eq 6 and 7, it can be seen that this is only expected if the mechanism described by eq 7 is limiting. It is therefore concluded that, in all cases investigated, the activation barrier is the cross electron exchange as given by reaction 1. The Koutecky-Levich equation (5) then becomes
vcT
0.01
0.02
0.03
0.04
0.06
CROTATION RATE]-"*(rpm-w)
Figure 5. (a) Levich plot (points) for data in Figure 4 (Fe3+(aq)re-
duction). The dashed line is the expected mass transport limited current as given by eq 4. (b) Koutecky-Levich plot for data in Figure 4. See eq 5.
a process which is independent of the dynamic flow conditions of the rotating disk. This process has already been ruled out by the data provided above, delineating the outer surface reaction zone. However, the diffusion of charge (or electrobalancing cations) through the derivatizing layer might be the rate-limiting process. Alternately, the energy barrier associated with the bimolecular charge transfer from the surface-attached nickel ferrocyanide to the solution Fe3+(aq)could provide the rate-limiting process. In order to examine the possibility of charge diffusion through the derivatizing layer as the rate-limiting step, a flux can be carried out. The charge-transfer flux, fCT, through the derivatizing layer is given by1, fCT
=
DCTr/d2
where d is the layer thickness (cm) and DCT is the apparent charge-transfer diffusion coefficient. Chronocoulometric techn i q u e ~can ~ be employed to directly measure the value of Om/&. This has previously been accomplished by using electrodes of composition and coverage similar to those employed in the present s t ~ d y . From ~ . ~ ~these data a value of fcT = 1.0 X lo-' mol/(cm2 s) is obtained as a worst case value. Therefore, if the bimolecular electron transfer to solution is to be the rate-limiting process, the flux for this reaction must be less than lo-' mol/(cm2 s). As discussed by Murray, this flux, f E X ,is given by', fEX
=
k12rsC*
(7)
where k , , is the bimolecular rate constant for electron transfer
From this equation it is seen that the intercept of the Koutecky-Levich plot (Figure 5b) definesf= and thereby kI2rs.From the experimentally obtained values of kI2rsvalues of k12are mol/cm2. These values have the obtained assuming rs= added uncertainty associated with rs. However, from the earlier described relationship between iL and r showing no I' dependence for J? > 10 monolayers, the value of rscan be off by no more than 1 order of magnitude, and a detailed kinetic analysis of 25 electrodes with varying coverages indicates that rsand thus k , , are correct within a factor of 2 or 3.20 The values obtained for klzFsand k 1 2by using eq 8 are listed in Table 11 and represent results of four sets of electrodes of different coverage. Each electrode was carried through all five supporting electrolytes. All supporting electrolytes yield data qualitatively similar to that shown for LiNO, in Figure 5 . Marcus Theory Analysis. As can be seen from Table 11, there is a definite dependence of k12on ERS,supporting the qualitative linear sweep voltammetry results. Of particular interest is the observation that even in the presence of Cs+, where the free energy of the forward reaction is positive ( A E = -100 mV), a small, but appreciable, rate constant for the charge transfer is observed. This observation has previously been noted for polymer-coated elec(20) In determining the value of ra,one must take into consideration the percentage of the surface species in the reduced oxidiation state, as well as the ability of solution species to access the surface material. Since in the Fe3+(aq)reduction only 60-70% of the surface is in the reduced form, not all accessible surface sites lead to a reaction.
Charge Transfer at Derivatized Interface
d
The Journal of Physical Chemistry, Vol. 91, No. 3, 1987
l
591
I
,
I
I
.om
4.~11
om
om
MB AE (VOLTS)
a12
ale
Figure 6. Log of the bimolecular charge-transfer rate constant vs. AE using a set of typical data for the reduction of Fe3+(aq) at the derivatized interface and showing fit to eq 11. The cations indicate the supporting electrolyte employed as the nitrate salt.
trodes in which high self-exchange rate solution charge-transfer reagents have been employed.I2' It can qualitatively be seen that as the free energy for the system becomes more negative, the rate constant k I 2increases. As defined by eq 9 and 10, the free energy AE12' =
ER
- ERS
-AGO nF = log K12 = -AE12' 2.3RT 2.3RT
'
ao
04
Potential. 08 1V YI 5b CE
a
s
(9) = 16.9AEI2'
(10)
for the reaction can be related to the difference in redox potential of the surface-attached material and the solution species (for a one-electron process at room temperature). In this framework it can be seen that values of k12have been attained over a potential range (300 mV) corresponding to equilibrium constant values, in the K12,ranging over 5 orders of magnitude from 2.0 X present Cs+ ions to 1.1 X 1O3 in the present Li+. The relationship between the redox potential of the surfaceattached material and the observed electrocatalytic rate constant was quantitatively evaluated by using the Marcus relationship for outer-sphere electron-transfer kinetics, as given in the equation2' kl2
b f
= [kllkzzK12f11'2
(1la)
= (log K1A2/[4 log ( k l 1 k d Z 2 ) 1
(1lb)
where Z is the bimolecular collision frequency of the two charge-transfer reagents (lo-" M-l s- for two solution species interacting) and k l l , k22are the self-exchange rates for the surface-attached complex and the Fe2+/3+couple in solution, respectively. In order to relate the experimental data to this relationship, it was combined with eq 9 and recast into its log form: log
k12
= (8.47Y')AE12~+ Y z [ b
(kiik22)I
+ Y2(logA
(12)
The comparison between the data in Table I and eq 12 was made as follows: Initially, it was assumed logf
