599
Anal. Chem. lS81, 5 3 , 599-603
Potential-Dependent Chronoamperometry in the Study of Electrode Reactions with Comproportionation or Disproportionation Chemical Steps Franco Magno" and Gin0 Bontempelli Istituto di Chimica Analitica, Universiw of Padova, Via Marrolo 1, 35100 Padova, Italy
The EE mechanlsm (two-electron transfer) for potentlal-dependent chronoamperometry has been lnvestlgated In detall along wlth the effect of either a comproportlonatlon or a dlsproportlonatlon reactlon. The relevant potentlal-dependent chronoamperometric proflles have been developed, under the appropriate boundary condltlons, by the flnite dlflerence simulation technique. When a cornproportionation chemical step competes with an EE mechanlsm, the anomalous shape of chronoamperometrlc curves reveals within itself the occurrence of such a kinetic compllcation, whlle for the compettllon wlth a disproportlonatlonchemlcal reactlon the Ivs. f curves do not exhlblt any unusual trend. I n both cases, the klnetlc parameters can be determlned by the slmplex flttlng procedure. The calculations were then applied to the analysis of the reduction of nickel(I1) In the presence of triphenylphosphine In acetonitrile.
Among the different electroanalytical techniques, potential-dependent chronoamperometry has been little used to elucidate mechanisms of homogeneous reactions coupled with charge-transfer steps. This is the consequence of the fact that the critical dependence of the experimental results on the applied potential makes the technique more suitable to study steps of heterogeneous charge transfers rather than associated chemical reactions. The potential dependence of the current, in fact, not only can introduce an additional slow step in the overall reaction sequence but requires also high-quality potential control because the knowledge of the exact value of the applied potential is critical in this technique. However, in the literature some examples of useful application of this technique have been described. In particular, it has been applied to the study of mechanisms involving a chemical reaction: (i) following the charge transfer (EC) (1, 2 ) , (ii) interposed between two electrode reactions (ECE) (3), and (iii) partially regenerating the depolarizer through a disproportionation reaction (DISP) (4). In this connection, we wish to point out that, in our study (5-8) of the electrochemical properties of coordination compounds of nickel, we found to be opertive a fairly unusual mechanism involving a comproportionation reaction (COMP), i.e., a redox chemical reaction between the depolarizer (Ni") and the product of its twoelectron reduction (NiO) giving a nickel complex containing the metal in the intermediate oxidation state (NiI) (7). For the study of such a process, the potential-dependent chronoamperometry appeared to be the most suitable technique thanks to the clarity of the informations which it was able to provide. Consequently, the relevant i vs. t curves have been calculated by the digital simulation technique. Moreover, as a disproportionation chemical reaction can also be, in principle, involved as an alternative route in a two-electron process, depending on the relative E" values of the two charge-transfer steps, we have also explored the applicability of potential-dependent chronoamperometry in 0003-2700/81/0353-0599$01.25/0
studying mechanisms in which such a reaction is competitive with the second heterogeneous charge-transfer step. The calculations have been utilized to fully rationalize the above mentioned cathodic reduction of nickel perchlorate in acetonitrile in the presence of a large excess of triphenylphosphine (PPhB).
EXPERIMENTAL SECTION Chemicals. All the chemicals employed were of reagent grade quality. Reagent grade acetonitrile was further purified by distilling repeatedly from phosphorus pentoxide and stored over molecular sieves (3-A) under nitrogen atmosphere. The supporting electrolyte tetrabutylammonium perchlorate (TBAP) was prepared from perchloric acid and tetrabutylammonium hydroxide, recrystallized from methanol and dried in a vacuum oven at 50 "C. Stock solutions of anhydrous nickel(I1) perchlorate in acetonitrile were prepared by anodic oxidation of metallic nickel in TBAP-acetonitrile solutions as previously described (9). Triphenylphosphine was crystallized from methanol and stored in a vacuum oven in the dark. Nitrogen (99.99%), previously equilibrated to the vapor pressure of acetonitrile, was used in the removal of dissolved oxygen. Apparatus and Procedure. Voltammetric and chronoamperometric experimentswere carried out in a three-electrodecell. The working electrode was a platinum disk with a diameter of 0.5 mm, surrounded by a Pbspiral counterelectrode. The potentid of the working electrode was probed by a Luggin capillary-reference electrode compartmentwhose position was made adjustable by mounting it on a syringe barrel. In all cases an aqueous SCE was used as reference electrode. The voltammetric unit employed was a three-electrodesystem assembled with the MP-system 1000 equipment in conjunction with a digital logic function generator made in these laboratories. It provides, as previously described (IO),a stable and accurate value of the selected potential, thanks to the high resolution of the digital-analoguedevice utilized and the great accuracy of the hold times available by the employment of a quartz oscillator. The recording device was either a Hewlett-Packard 7040-A XY recorder or a Hewlett-Packard Memory Scope type 1201-A. The electroanalytical measurementswere performed at 20 O C . RESULTS AND DISCUSSION Theoretical Considerations. It is recognized (11,12)that a generalized two-electron mechanism (EE) has to be considered, as a rule, the combination of two associated oneelectron transfers
A B
+ e-
+ e-
--
B C
E O A p
EoBIC
(1)
for which the relative values of the parameters E O , K,, and CY will influence the shape of the overall voltammetric response. In particular, the analysis of the problem can be divided in two major sections depending upon whether two successive one-electron waves or a single two-electron wave are detected. The last situation, a two-electron step, can occur either for thermodynamic or kinetic reasons. For E O B I C > E " A p only 0 1981 American Chemical Society
600
ANALYTICAL CHEMISTRY, VOL. 53, NO. 4, APRIL 1981
one wave will be always observed but, if the second charge transfer is kinetically hindered, the mechanism
+
-
(2)
involving a disproportionation reacton takes place. In this connection, it must be noted that a disproportionation reaction can occur also for a potential sequence EOAIB > E o B / C if this reaction is not the rate-determining step and one of the products, obviously the species C, undergoes an irreversible chemical reaction which affects the overall process. This case, "mechanism 6", will not be treated by us as it has been the subject of a previous report ( 4 ) . When the normal thermodynamic sequence is found, E o A / B > E o B / C , the first cathodic step can occur, in principle, at potential values even more negative than E o B / ~if it is affected by overvoltage; if this is the case, a single irreversible twoelectron process is again observed, but the occurrence of a comproportionation reaction between the depolarizer (species A) and the electrode product (species C) may be expected.
+ 2e-
k,
C
k
A+C-+2B
A
100
2A 2e2B 2Bk-A+C
A
y.
(3)
2B + 2e- 8 2C Similar behaviors are sometimes exhibited by the coordination compounds where any modification in the coordination sphere can cause dramatic changes in the degree of reversibility of their electrode processes. Potential-step chronoamperometry performed at potential values at which the diffusion is the only controlling process allows the evaluation of the kinetic constant of a disproportionation reaction (13),but it completely fails in studying a mechanism involving a comproportionation reaction because no change of the so-called nappvalue has to be ever detected since the diffusive step is rate determining. Quite different results are to be expected, on the contrary, when the working potential is chosen in the potential-dependent region; the overall slow electrochemicalprocess, in fact, can be catalyzed by the homogeneous comproportionation reaction which generates the depolarizer of the second fast electrode process (reaction sequence 3). Finite Difference Simulation and Simplex Fitting of Chronoamperometric Curves. Explicit finite difference programs, based on the method described by Feldberg (14, 15),were written (Fortran IV) to generate current-time curves with different boundary conditions. A suitable number (1200) of time steps were employed in the calculation to obtain a good accuracy (16). In this way, the agreement of simulated values of current, for the diffusion-limited case, with the theoretical response predicted by the Cottrell equation was less than 0.13% after the 200th iteration. In particular, 200 time steps in the calculation were made to correspond to 1 s of the experimental time scale. In order to fit the experimental chronoamperometric profiles, we calculated both the puTely diffusive and the charge-transfer controlled currents with appropriate parameters in model units. Their ratios were then multiplied by the experimental diffusive currents thus obtaining simulated currents in experimental units. Therefore, the fitting was made without employing the experimental electrode surface and the diffusion coefficient values. This procedure was adopted to make as unambiguous as possible the assignment of the operative mechanism. The numerical values of the experimental kinetic constants were drawn from the simulator system by using appropriate combinations of variables so that the dimensional terms cancelled. In particular for the charge-transfer constant, the dimensionless
c
Ev'
v 1oc LOX
Figure 1. Cyclic voltammetric curve recorded on a platinum microelectrode in a 3 X lo-, M Ni(II), 0.1 M PPh,, 0.1 M TBAP, CH&N solutlon. Scan rate was 0.1 V s-'. The potential values are referred to an aqueous SCE.
parameter was kht1/2D-'/2( k h = heterogeneous charge-transfer constant at the applied potential), while for the chemical rate constant the usual dimensionless group ktC"-l (n = homogeneous reaction order) was used. In the calculations all the species were assumed to have the same diffusion coefficient; its value (3.66 X lo4 cm28) had been determined by inserting the apparent electrode area and the concentration value of the depolarizer in the equation of the purely diffusion current. This quite high value, even in acetonitrile, can be explained by considering that the effective electrode area was obviously larger than the apparent geometric one. However, the inaccuracy of the D value affects only the accuracy of the POtential-dependent heterogeneous kinetic constant but does not affect the value of the chemical constant thanks to the procedure adopted. Comproportionation Mechanism. The voltammetric behavior of nickel(I1) perchlorate in acetonitrile at a platinum electrode in the presence of a large excess of PPh3 is shown in Figure 1. In a previous work (7) we have demonstrated that the cathodic peak must be attributed to the irreversible two-electron reduction of the [Ni11(PPh3)2(CH3CN)4]2+ complex to the [Nio(PPh3)4]species, while the two associated anodic peaks are due to the stepwise oxidation of [Nio(PPh3)4] to [Ni1(PPh3)$ and to [Nin(CH3CN)4(PPh3)2]2+, respectively. Unambiguous evidences of the occurrence, in the cathodic process, of the mechanism
-
+ 2ek NiO + Ni'I Ni'I
-
Nio 2NiI
(4)
2Ni' + 2e- P 2Ni0 had been gained by several electroanalytical and chemical experiments. In order to check the correctness of this mechanism and to determine the rate constant of the comproportionation chemical reaction, we performed potentialdependent chronoamperometric experiments at different potential values corresponding to the rising portion of the cathodic peak. Figure 2 shows, as typical examples, several chronoamperometric profiles obtained in the investigated system (Ni", PPh3, CH3CN),under mixed control conditions (charge transfer, kinetic, diffusion) together with a pure diffusive current-time curve. These curves illustrate the large effect of the comproportionation reaction which acts indeed as a catalytic step in the overall cathodic process. In particular, this effect becomes more evident for increased values of the homogeneous kinetic constant and decreased values of the heterogeneous consiant of the first charge-transfer step, as shown by the calculated curves reported in Figures 3 and 4. The fitting, by the modified simplex optimization procedure (13,of theoretical curves (see Figure 5) on the experimental ones (Figure 2) gave, at the same time, both the numerical values of the potential-dependentheterogeneous rate constants
ANALYTICAL CHEMISTRY, VOL. 53, NO. 4, APRIL 1981
*
J
Figure 2. Potential-dependent chronoamperometric curves obtained M Ni(II), 0.1 M on a stationary platinum microelectrode in a 4 X PPh3, 0.1 M TBAP, CH3CN solution. The reported potentials are the employed experimental values (vs. SCE). c
sac
t
601
1000
530
1 -
'
II I I
1LC'J
Figure 4. Theoretical single-step potentialdependent curves calculated for the same kinetic constant of the comproportlonatlon reaction and different heterogeneous charge-transfer constants. The values of the homogeneous constant (2 X 10-7, of the heterogeneous ones and of the coordinates,time, and faradaic flux (FF), are In simulator system units: (1) kh = io? (2) kh = 2 X (4) k (3) = 4 X (5) kh = 8 x io? (6) kh = 10- ; (7) kh = 2 x 10-6 =6x (8)kh = 10'.
5
0 15C FF
Figure 3. Theoretical single-step potentialdependent curves calculated for the same overall heterogeneous charge-transfer constant and different kinetic constants of the comproportionation reaction. The values of the heterogeneous constant (lo-*), of the homogeneous ones, and of the Coordinates, time, and faradaic flux (FF) are in simulator system units: (1) k = 0.0; (2) k = (3) k = (4) k = lo-'; (5)k = 1.
as well as the value of the potential-independenthomogeneous rate constant; the mean value of this last quantity was 519 M-l s-' if the calculations were stopped when the final relative standard deviation was 0.02. In order to test the accuracy of kinetic data derived from the potential-dependent approach, some calculations were performed by changing the homogeneous kinetic constant at fixed heterogeneous ones. The results indicated for k an accuracy of *15% if the calculations were stopped when the
final relative standard deviation was 0.05. An additional important consequence of the occurrence of the comproportionation reaction is its influence on the potential value at which the overall process takes place. Thus, even if the irreversibility of the first step were so high, as a limit case, to shift the relevant cathodic peak beyond that associated to the second charge transfer, the autocatalytic character of the overall process causes the occurrence of both electrode processes at the potential values of the second one. Therefore,the larger the homogeneous rate constant, the closer will be the coincidence of the potentials. Disproportionation Mechanism. If the disproportionation reaction is an alternative route to the EE mechanism ( E O B p > EA^) the overall process can be depicted as A+e-+B B+e--C
(5)
k
2 B s A + C When both the two charge-transfer steps are reversible in character, the overall electrochemicalreaction appears as an uncomplicated EE process. On the contrary, when the second step becomes more and more kinetically hindered (irreversible in character), the homogeneous reaction becomes concomitantly more competitive until the usual DISP mechanism (eq 2) becomes consequently operative. The competition between the two last reactions can be observed only when working in a suitable potential range. If the applied potential corresponds in fact to the potential-independent current region, the effect of the chemical reaction can be detected in the chronoamperometric responses only when the second charge-transfer
802
ANALYTICAL CHEMISTRY, VOL. 53, NO. 4, APRIL 1981 3 O
l
4
115
5
r
ks=lO-‘ 5-
ks=10-3 :k, 0
15-
10-
10
0
20
30
5
3
log t
Figure 7. Single-step potentialdependent n, vs. log t curves, calculated at E = with fixed values of A€’ (60 mV) and k (lo-’) for “mechanism 5” as a function of k,. The values of the homogeneous and heterogeneous constants and of the time are in simulator system units. 2 04
Figure 5. Theoretical single-step potentialdependent curves used in the fitting of the experimental curves reported in Figure 2. The values of the heterogeneousand of the homogeneous constants drawn from the fitting are as foilows: (1) kh = 6.0 X lo4 cm-s-‘, k = 440 M-‘*s-’; (2)kh = 9.7 x io-4 CmS-’, k = 450 M-’.S-’; (3) kh = 17.0 x io-‘ cmqs-‘, k = 585 M - k i ; 14) k h = 39.5 X lo-‘ cm.s-‘, k = 600 M-1‘s-1., (5)k = 10’ cm-s- and any value of k .
k=m
k =lo-’ k =lo-*
15-
k z’O-~
10-
1
,
10
20
30
log t
40
Figure 8. Single-step potentialdependent n, vs. log t curves, calculated at E = EoMBwith fixed values of A d (60 mV) and k, (10-7 for “mechanism 5” as a function of k. The values of the homogeneous and heterogeneous constants and of the time are in simulator system units.
10
20
30
log t
40
Figure 6. Single-step potentialdependent nappvs. log f curves, calwith fixed values of k, (lo-’) and k (lo-’) for culated at E = “mechanism5” as a function of the A€’ parameter. The values of the homogeneous and heterogeneous constants and of the time are In sirnulator system units. step is not operative at the working potential. If this is not the case, when working in the plateau region for both the electrochemical reactions, the nappvalue results to be always 2 (nappis defined as the ratio between ( i t 1 / 2 ) k t g o and (it1/2/ 2)kt-) as both the electrode reactions occur at their maximum rate which is only conditioned by the mass transfer process. For all these reasons, the observation of the effect of the disproportionation reaction will be possible only at working potential values at which the second electrode reaction is no longer diffusion controlled, that is, by employing potentialdependent chronoamperometry. For the generalized “mechanism 5”, in which the first charge-transfer step has been assumed reversible in character for the sake of simplicity, the neppvs. log t curves have been calculated as a function of the three independent parameters AEo ( E o B / C - E’A/B),k, (heterogeneous standard rate constant
of the second charge transfer), and k (homogeneous kinetic constant for the disproportionation reaction). Figures 6 , 7 , and 8 summarize the effects on the nappvalue of these three quantities at the working potential E = E o A / B . In particular, Figure 6 shows that an increase in AEo causes an enhancement of the nappvalues, which is obviously due to the larger overvoltage available to the second charge transfer process. An increase of the reversibility of the second heterogeneous step, at a fixed AEo value, produces a similar effect as shown in Figure 7. Finally, Figure 8 shows that an enhancement of the nappvalue is produced by an increase of the parameter k. Moreover, inspection of this last figure reveals that for the same kt value, different nappfigures are found depending on the homogeneous kinetic constant employed in the calculation. This circumstance prevents the pwibility of summarizingall the observed effects in a single working curve, and, consequently, the trend of the experimental i vs. t curves cannot be used as a diagnostic criterion. For this reason, such a mechanism can be recognized (and the associated parameters can be determined) only by employing a fitting procedure. It can be noted that our curves resemble to some extent those previously reported (4) for the rather similar mechanism
A+e-+B 2BeA+C k
C+Z-D
(6)
ANALYTICAL CHEMISTRY, VOL. 53, NO. 4, APRIL 1981
Figure 9, Single-step working curves for “mechanism 2”: (a) potentiai-dependentcurve calculated at E = EoA,*; (b) potentlal-independent curve.
in which a disproportionationequilibrium, followed by a slower rate-determining chemical step, is involved. However, the curves of Figures 6-8 result to be more drawn out than those related to “eq 6” since for this mechanism the chemical step exhibita a reaction order of 1(4) while in our “mechanism 5” the disproportionation reaction results to be of the second order. Consequently, for “process 5” the reaction order with respect to the depolarizer species A ranges between 1and 2 depending on the relative contributes of the two competitive reactions. Finally, Figure 9 compares two curves which correspond to “mechanism 2” (Le., “mechanism 5” with (kh)B/C = 0) calculated for different applied potential values. Curve “a” refers to a working potential E = E o A / B (potential-dependent chronoamperometry),while curve “b” has been calculated for diffusive conditions (potential step technique) of the species A and therefore it is expected to agree perfectly, as it does, with that previously reported by Feldberg (13). It can be noted that in this borderline case the curve calculated for E = E o ~ p can be employed as a working one as a consequence of the absence of the contribution of the heterogeneous charge transfer. In conclusion, in the study of an electrochemicalmechanism involving a disproportionation reaction, potential-dependent chronoamperometry might be preferred to the potential step technique as it offers two advantages. The first one can be
603
inferred by comparing the two curves reported in Figure 9, which shows that a higher napprange is available when the potential step is carried out at E = E O A / B ; at this potential the newvs. log t plot exhibita a higher slope which makes more precise the determination of the kinetic parameter by the fitting procedure. The second advantage comes from the circumstance that only a fraction of the total electroactive species (A) is converted to the reactive form (B),so that the chemical reaction proceeds at a much slower rate than if total conversion to the reduced species had occurred. Therefore, as also reported in ref 2, an expansion of the time frame of the experiment becomes available and faster chemical reactions can be hence investigated. However, severe limitations for adopting this experimental approach are to be expected. These are, on the one hand, the requirement of a strict control of the working potential and, on the other hand, the difficulty in determining an accurate E’AIBvalue under dynamic conditions (e.g., by employing high scan rates in cyclic voltammetric experiments) which are necessary to cancel the effect of the following chemical reaction.
ACKNOWLEDGMENT We thank the Italian National Research Council (C.N.R.) for financial support. LITERATURE CITED Marcoux, L.; OBrlen, T. J. P. J. Phys. Chem. 1972, 78, 1966-1968. Cheng, Hung-Yuan; McCreery, R. L. Anal. Chem. 1978, 50, 645-648. Marcoux, L. J. Am. Chem. Soc. 1971, 93, 537-539. Marcoux, L. J. Phys. Chem. 1972, 78, 3254-3259. Bontempelll, G.; Corain, B.; Magno, F. Anal. Chem. 1977, 49, inns-inm .--- .---. Magno, F.; Bontempelli, G.; Corain, B. J. Chem. Soc., Faraday Trans. 11979, 75, 1330-1336. Bontempelli, G.; Magno, F.; Coraln, B.; Schiavon, 0.J. Electroanal. Chem. 1979. 103.. 243-250. _ . -. Magno, F.; Bontempelll, G. Anal. Chem. 1980, 52, 329-331. Coraln, B.; Bontempelll, 0.; De Nardo, L.; Mazzocchln, G. A. Inofg. Chim. Acta 1978, 28, 37-40. Magno, F.; Bontempelli, G.; Mazzocchin, G. A,; Patane’, I. Chem. Instrum. (N. Y.) 1975, 6 , 239-257. Mohilner, D. M. J. Phys. Chem. 1984, 68, 623-629. Ryan, M. D. J. Electrochem. Soc. 1978, 125, 547-555. Feldberg, S. W. J. F’hys. Chem. 1989, 73, 1238-1243. Feldberg, S. W. In “Electroanaiytical Chemlstry”; a r d , A. J., Ed.; Marcel Dekker: New York, 1969; Vol. 3, pp 199-296. Feldberg, S. W. In “Electrochemistry”; Mattson, J. S., Mark, H. B., MacDonald, H. C., Eds.; Marcel Dekker: New York, 1972 Vol. 2, Chapter 7. Hanafey, M. K.; Scott, R. L.; Rldgway, T. H.; Rellley, C. N. Anal. Chem. 1978, 50, 118-137. Deming, S. N.; Morgan, S. L. Anal. Chem. 1973, 45, 278A-283A.
RECEIVED for review June 12,1980. Accepted December 15, 1980.
