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Adsorption and coupled chemical reactions in the electroreduction of ferriheme in alkaline solutions
J Electroanal Chem, 163 (1984) 277-296
277
Elsewer Sequoia S A., Lausanne - Pnnted in The Netherlands
ADSORPTION AND COUPLED CHEMICAL REACTIONS IN THE ELECTROREDUCTION OF FERRIHEME IN ALKALINE SOLUTIONS
JAMES F. R U S L I N G * and M A R G A R E T Y BROOKS
Department of Chemzstry, U-60, Unwerstty of Connectmut, Storrs, CT 06268 (U S A ) (Received 8th June 1983, in rewsed form 20th August 1983)
ABSTRACT Electroanalytlcal techmques were used to investigate adsorption, charge transfer, and coupled chemacal reactions In the electroreductlon of a ferrtheme dlmer at mercury electrodes in 0 1 M N a O H over a wide range of experimental conditions. Current-sampled polarography confirmed that the overall reaction is a two-electron, Fe(III) dlmer to Fe(II) monomer process, as previously found in solutions of K O H A preceding reaction influences the shape of the wave at tugher concentrations. Cychc voltammetry (CV) at low concentrations (c < 0.06 m M ) revealed the reversible reduction and oxadatlon of an adsorbed redox couple. Ferroheme, the reduction product, ts more strongly adsorbed than the ferriheme darner reactant The total hmatmg surface concentration of ferroheme was 7 X 10-11 mol cm-2. Analysis of the shape of the adsorption prepeak m CV usmg nonhnear regression showed that the adsorbate featured large repulsive interactions. The shape of the two-electron, diffusion-controlled peak m CV suggested a fast EE or ECE process. The value of E~ for the femheme dlmer was estimated at - 0 486 V vs. N H E The standard potentml E~ for the one-electron intermediate was about 10 mV more positive than E~' At c > 0 3 m M and v < 2 V s -a, voltammograms reflected the influence of aggregation of both femheme d~mer and ferroheme monomer. Approxamate kinetic and e q m h b n u m parameters for these reactions were estimated from the voltammetric data.
INTRODUCTION
Metalloporphyrins have received considerable attention in the recent electrochemical literature [1-3] because of their importance in biological reactions and their electrocatalytic properties. Since the major emphasis in studies of the electroreduction of biologically important iron porphyrins has been on charge transfer processes [4-8] and ligand exchange reactions [9-13], most work on these compounds has been done under conditions where adsorption and aggregation were minimized. In the case of ferriheme (iron(III) protoporphynn), it has been realized that adsorption and aggregation of reactants and products can occur during electroreduction in aqueous media [5-7,9,13,14]. Nevertheless, little use has been made of electroanalytlcal techniques to investigate these phenomena. One recent paper [14] has discussed * To whom correspondence should be addressed. 0022-0728/84/$03.00
© 1984 Elsevier Sequoia S A
278
electrochemical properties of ferriheme dimer adsorbed on mercury from 0.2 M KOH, but this study was of limited scope and emphasized electrocatalysis of the reduction of oxygen. Ferriheme in 0.1 M K O H forms dimers which undergo a two-electron reversible reduction of Fe(III) to Fe(II) at mercury cathodes to yield a ferroheme monomer [4,5]. Our initial interest in the reduction of ferriheme dimer was as a model for dimer-to-monomer reduction in a computerized system for mechanistic elucidation [15] using deviation-pattern recognition [16]. When current-sampled polarograms of ferriheme in 0.1 M N a O H were analyzed by our computerized method [15], it was found that the dimer-to-monomer mechanism was strictly followed only in a limited range of concentrations (c < 0.7 m M ) . At c > 1.0 mM, small but significant deviations from the theoretical behavior for the dimer-to-monomer reaction were observed. Bednarski and Jordan [4,5] provided a mathematical analysis of the polarographlc wave shape assuming equal adsorption of oxidized and reduced forms, which we used in our fitting procedure [15]. When a more rigorously derived equation [17], free from the above restriction about adsorption, was used to fit the data, nearly identical deviations were observed at c > 1.0 mM, as with the Bednarski-Jordan expression. In order to explain the above observations and to clarify the role of adsorption and chemical reactions coupled to the charge-transfer process, we have undertaken a more extensive study of the reduction of ferriheme in 0.1 M N a O H at mercury electrodes over a wide range of experimental conditions. EXPERIMENTAL
Crystalline bovine hemln (ferriheme), obtained from Aldrich Chemical Co., was used as received. Solutions of sodium hydroxide were prepared by dilution of a 50% solution obtained from Baker Chemical Co. All water used in this work was prepared by treating distilled water with a Sybron/Barnstead NANOpure wateipurification system. The final product had a specific resistance greater than 10 Mf~ cm. To avoid irreversible aggregation and decomposition, ferrlheme solutions were always prepared immediately prior to the experiment. Cyclic voltammograms, and current-sampled and pulse polarograms were obtained with a Princeton Applied Research (PAR) Model 170 Electrochemistry System and a PAR Model 174A Polarographic Analyzer. Three-electrode cells and procedures outlined previously were used [18]. All solutions were purged with purified nitrogen [18] for 20 min prior to the start of an experiment. The hangingdrop-mercury electrode (HDME) for cyclic voltammetry (CV) had a corrected area of 0.0208 cm2; the dropping mercury electrode (DME) for polarography had a flow rate of 1.88 mg s -1 and a natural drop time of 4.00 s (1 M KC1) at a mercury column height of 70 cm. All polarograms were recorded using a controlled drop time of 2 s. Both saturated calomel and Ag/AgC1 reference electrodes were used, and reported potentials, unless otherwise stated, are referred to Ag/AgC1. The resistance of assembled cells containing 0.1 M N a O H averaged 400 ~2. At scan rates (v) in CV above 0.2 V s-1, positive feedback compensation of ohmic drop and oscillographic
279 recording of current-potential curves was employed. To check the performance of electrochemical cells and instruments, CV's of k n o w n reversible systems were periodically recorded. Separation of anodic and cathodic peaks for Cd(II) in 1.0 M N a N O 3 and U(VI) in 0.1 M HC1 were always ( 6 0 / n ) _+ 1 mV. All computations utilized a Radio Shack TRS-80 Model I microcomputer (48K) and the Level II B A S I C language. Nonlinear regression analysis was carried out with a general p r o g r a m for this purpose [16,19]. Appropriate modifications, described in the text, were made to the p r o g r a m to obtain the desired fitting procedures. In all regression analyses, the absolute, rather than the relative, error in the dependent variable was assumed to be r a n d o m l y distributed. Digitization and corrections for residual current of experimental current-potential curves were accomplished at 5 or 10 mV intervals as previously described [20]. RESULTS AND DISCUSSION Behavtor at low concentrations (c < 0.06 m M ) Cyclic voltammetric behavior of ferriheme at low concentrations is illustrated by Fig. 1. The labels given to peaks in Fig. 1A are used throughout the discussion. Two major reduction peaks, Ic and IIc, were observed; on the reverse scan three oxidation peaks, Ia, IIa, and Ilia, were present. The shapes of CV's were qualita-
Ic
(o)
01
o
,
,
0,~
, -E
0.4
-01
cb
-20~
Fig. 1 Cychc voltammograms of 0.05 mM femheme m 0.1 M NaOH. (a) v = 0 20 V S -1, (b) v = 20 V s-1. Sohd hnes are experimental curves (©) Points calculated from nonlinear regression onto eqns. (1) and (4). (O) Points calculated from reversible current function [24] with n(app)= 1.15
280
7 7
.= z~
0
8 "6 0
II \
7 "6
7
"6
281
0
0 O < c~
0
LC L)
0 0
0
•
OoOO_@_ooO .
_o?_@_O_o_O_o I
-5
I
I
-4 -3 log (cv-I/2/mol dm-3 V -1/2 s 1/2 )
F i g 2 Plot of ratio of current function (lpc-lv -1/2) of p e a k l l c to the value of the current function as co -1/2 ---, oo, t a k e n as avg. lpc-lo -1/2 at v < 0 1 V s -x, against log(co-I~2). ( O ) 0.05 m M f e r n h e m e , (n) 0 6 m M ferrlheme, a n d (@) 1.0 m M ferrlheme
tively similar to those obtained in 0.2 M K O H at v < 0.2 V s-1 [14]. At higher scan rates (v), peaks Ia and Ic increased in height relative to the heights of IIa, IIc, and IIIa. The width at half height of Ic was about 140-150 mV and its peak current varied linearly with v. The ratio of currents of peaks Ic and Ia was approximately one, and their peak potentials were nearly equal at all v (Table 1), except at 50 V s-1. At this highest scan rate, a slightly greater peak separation could be attributed to the influence of charge-transfer kinetics or a small uncompensated ohmic drop. A small shift in the potential of Ic of - 4 . 5 _+ 1.4 m V / l o g v was observed. These data are consistent with the reactions of an adsorbed redox couple in peaks Ic and Ia [21-231. The current function [lp(C 01/2)- 1] of peak IIc was reasonably constant at v < 1 V s-a (Table 1, Fig. 2). A large increase in current function, caused [21] by adsorption of the ferriheme dimer, was observed at higher scan rates. The ratio of currents of peaks IIa and IIc was approximately one (Table 1). The potentials of peaks I I a and IIc were independent of scan rate and differed by an average of 35 mV. Although subject to some uncertainty because of overlap of Ic with IIc, ]Ep - Ep/21 for IIc at v < 0.2 V s-1 was about 40-45 mV. These data are in agreement with the interpretation of the polarographic reduction of ferriheme in 0.1 M K O H [4,5]. The height of peak I I I a was proportional to v, rather than to 01/2, at v < 1V s -1. A small cathodic counterpart to I I I a was observed (IIIc) but it was severely overlapped with Ic. Peak IIIc became smaller relative to Ic at lower concentrations
282
05
L/~A
°7 -025
E, v vsAg gc,
VIva
Fig. 3. Cyclic voltammogram of 0.6 mM fernheme in 01 M NaOH at 002 V s -1 Solid hne is experimental curve, points calculated from reversiblecurrent function [24] with n(app)= 1 19
at v = 0.2 V s-1. However, because of poor resolution peaks I l i a and IIIc were not investigated in any detail. In order to obtain the area under peak Ic, a correction for overlap with IIc was necessary. For this purpose, the shape of IIc was investigated at 0.3 < c ~< 1 m M , and at v < 0.05 V s -1, where the influence of adsorption and aggregation on the shape of the peak was rmnlmal. When these data were fit with the current function of Nicholson and Shain [24] for a reversible two-electron reduction, it was found that the theoretical peak was much too narrow to describe the experimental voltammograms. A good fit to experimental data could be obtained when an apparent number of electrons [n(app)] of 1.15 to 1.2 was used with the reversible current function (Fig. 3). Justification for this procedure is based on the assumption that the electron-transfer mechanism can be described by a fast EE process, but that the reduction potential E~ of the one-electron intermediate is close to that ( E ? ) of the ferriheme dimer. Theoretical calculations for the EE mechanism have shown [25,26] that only in the case where E~ >> E~ (for reductions) is the separation between cathodic and anodic diffusion peaks expected to be 57/n mV or 28.5 mV for n = 2. Larger peak separations are predicted as the value of E~ approaches that of E~. For an EE process with E~' = E~, a peak separation of 42 mV is predicted [22] as well as a reversible reduction peak with the same shape as one with n = 1. A peak shape described by the reversible current function with n ( a p p ) = 1.15 would lead to a peak separation of about 39 mV, close to that observed for peaks I I a and IIc of the ferriheme dimer. The fitting procedure described provided an adequate method of calculating the rising portion of peak lIc and subtracting it from adsorption peak Ic. Following this subtraction, numerical integration of peak Ic was begun at - 0 . 4 V vs. Ag/AgC1 to eliminate part of peak IIIc from contributing to the charge. The charge density (Qc) under peak Ic (Table 1) was reasonably constant at scan rates between 0.05 and 50 V s -1, with an average value of 6.7 _+ 0.6 /tC cm - 2.
283
The width at half height of peak Ic was much greater than the 9 0 / n mV expected for the reversible reduction of an adsorbed redox couple [23]. Broadening of the peak can be attributed to repulsive interactions within the adsorbed layer [27,28]. To confirm this assignment, we subjected data from peak Ic, corrected for overlap with IIc, to nonlinear regression analysis onto eqn. (1), which takes into account the influence of interactions between electroactwe molecules in reversible adsorption peaks in CV [28]. l = / p f(1 - f ) ( 4 - 2 r F t ) / [ 1 - 2rFtf(1 - f ) ]
(1)
where: ip = n2F2F, v / R T ( 4
- 2rF,)
(2)
f, the fraction of adsorbed molecules in the oxidized form, is defined by: 0 = exp[(nF/RT)(E
- E°)] = f ( 1 - f ) - '
exp - [ I', (2fr - r)]
(3)
with E ° = E p , 1"t 1S the total concentration of material adsorbed on the electrode surface in mol cm -2, r is the interaction parameter in cm 2 mo1-1, and the other symbols have their usual meanings. For use in nonhnear regression, eqn. (3) was rewritten as: 0(1 _ f ) f - 1
exp[ Ft (2fr _ r)] - 1 = 0
(4)
and solved by a Newton-Raphson subroutine [29] using Ep and R as regression parameters. This subroutine provided a value of f at each experimental value of E. These f ' s were then used within the regression program to calculate the
TABLE 2 Results of nonlinear regression analysis of major catho&c adsorption peak (Ic) xn cychc voltammograms of fernheme
C/mM
v / V s -1
- Ep/V (Ag/AgCI)
tp/l~A
10 n F t /
-lO-l°r/
RSD '~
Meas
Calc.
Meas
Calc
mol c m - 2
cm 2 m o l - 1
%t p
0 05
0.1 0.2 05 10 20 50 10 20 50
0.522 0 528 0.540 0.540 0(535 0 540 0 528 0.535 0 5¢35
0 521 0.529 0.534 0.532 0.530 0 532 0.525 0 530 0 530
0 100 0.193 0.627 1.018 1.82 4.75 9.00 17 9 41 6
0.093 0 181 0.575 0.952 1 72 4 53 8.68 16 8 39 4
36 35 3.9 3.2 33 33 32 32 3.1
41 41 25 37 42 37 35 42 5.0
71 7.0 6.4 7.9 6.7 6.3 6.7 67 5.3
0.3
20
0 540
0.527
16.0
15 0
2.7
4.7
9.3
0.6
05 20
0.530 0.530
0 526 0 517
0 44 15.6
0.43 14 5
3.1 2.8
4.4 5.6
5.0 5.8
a Relative standard devaatlon of the regression calculated as percent of peak current.
284
current-potential curve from eqn. (1), using the additional regression parameter lp. Thus, with eqns. (4) and (1), the nonlinear regression program [19] minimized the sum of squares of the residuals of t [i.e., t(meas) - t(calc)] and yielded the best values of the parameters Ep, R, and tp. This fitting procedure was tested with a voltammogram of 9,10-phenanthrenequinone adsorbed onto a pyrolytic graphite electrode [28]. An interaction parameter close to that previously reported, as well as a random deviation plot, were obtained. Moreover, final values of parameters were independent of variations in their initial estimates, within the hmits of error of those estimates. Nonlinear regression analyses of data from peak Ic resulted (Table 2) in an average interaction parameter of - 4 . 1 _+ 0.8 × 101° cm 2 mol-1, indicating strong repulsive interactions within the adsorbed layer. Calculated values of tp and Ep were very close to the measured ones, although the calculated tp was consistently about 5% smaller than the measured value. The average standard deviation of the regression was about 6% of tp. These small deviations from the model are attributed to uncertainties in corrections for the residual current and the diffusion peak IIc, and the fact that the small wave IIIc was not completely subtracted. Figure 1 illustrates that the combined procedure of fitting peak IIc with the reversible current function and fitting Ic to eqns. (4) and (1) gave good representations of the cathodic current-potential curves at low concentrations of ferriheme. Similar results to those discussed above were obtained with solutions 0.03 m M in ferriheme. The voltammetric data for ferriheme at low concentrations indicate a reversible, two-electron reduction involving strong adsorption of the product and weaker adsorption of the reactant. Strong adsorption [21,23] of the reduction product is confirmed by the observation of peaks Ic and Ia at potentials more positive than the diffusion peak IIc. The weaker adsorption of the reactant ferriheme dimer is indicated by the large increase in current function of IIc at large v (Fig. 2), predicted for the proposed mechanism when c / e x p ( - A G o / R T ) > 4 [21], where AGO is the
~
P
2/
o
-
o
-
/
4'0
'
8'0
'
1C)-3V 112 C -1/V 1/2s-1/2dr'N3 tool-1
Fig. 4. Plot of ratio ( 0 ) of peak currents of Ic and IIc agmnst ol/2c -1 at 0.05 m M fernheme.
285
standard Gibbs energy of adsorption of the reactant, assuming a Langmuir adsorption isotherm. Further support for this interpretation is given by a plot of the ratio (p) of the peak currents of Ic and IIc (Fig. 4). p is a linear function of v]/Z/c at low v ]/2, but deviates negatively from linearity at high v 1/2, as predicted ]for the proposed mechanism when c/exp( - A G o / R T ) > 1 [21]. The approximately equal potentials of peaks Ia and Ic and the constant 35 mV separation of peaks IIa and IIc reflect the reversibility of the surface and diffusion-controlled reductmns. The small shift in potential of peak Ic ( - 4 . 5 + 1.4 mV/log v) is also in agreement [21] with the proposed mechanism. Behavtor at higher concentranons (0.3 m M <~c <~3 mM) Data from current-sampled polarograms of ferriheme were regressed onto the equation: i + O~2 - ~1 = 0
(5)
using the parameters E ° = El~2, S = R T / n F , and q, the limiting current. Equation (5) is the exponential form of an expression describing the polarographic dimer-tomonomer reduction [4,5], and its use in nonlinear regression analysis has been described previously [30]. By conventional measures, good agreement between experiment and theory was obtained at 0.66 and 1.0 m M ferriheme (Fig. 5). However, smoothed deviation plots [30] obtained from the residuals of the regression analyses provide more discriminating criteria for goodness of fit [16]. The deviation plot obtained from the data at 0.66 m M (Fig. 6) was nearly featureless, suggesting a good fit to eqn. (5). The average value of S at this concentration was 0.0139 V, close
f
S
1C
{./~A o
b
O~
03
03
-E/V
vs SCE
Fig. 5. Current-sample.xl pol~o~mms m 0.] M NaOH. Sobd hne is expenmental curve; points calculated from results of nonhnear regression onto eqn. (5). (a) 0 66 m M fernhem¢, (b) 1 0 m M fernheme.
286
I
t~
I
I ~a
I I I I I~
~ ° ~ ° ~
ol \ t~
I
~a \
I
;> e-, 0
'-6
I
287
41 0
0
0
Ds
0000
0
00
0_(3 0
0 0
0 0
O0
0
00 0
0
0
-4
- E / V vs
0)75
SCE
Fig 6 Smoothed deviation plot [30] obtained from residuals after nonlinear regression of data In Fig 5a. N+2
D s = ~ [ t ( m e a s ) - l ( c a l c ) ] / s where N is the data point number and s is the standard deviation of 7=N regression.
4
0
0
Os
0000
0
0 0
0 0
0
0 0
O
O 0
0
0
O0 0
0
0o 0 i
0.65
0.75 - E / V vs SeE
Fig 7. Smoothed deviation plot for data in Fig. 5b
1.5
30
i/~A 0
0
-1.5"
-30
Fig 8. Cychc voltammograms of 1.0 m M fernheme m 0.1 M NaOH. (a) o = 0.5 V s -1, (b) v = 0 5 V with swltchmg potential at the foot of peak llc, and (c) v = 50 V s - i
S -1
288 to the theoretical value of 0.01285 V at 25°C. A similar plot for the data at 1.0 m M (Fig. 7) exhibited a large m i n i m u m at - 0 . 7 1 V a n d a large m a x i m u m at - 0 . 7 3 V, i n d i c a t i n g significant deviations from eqn. (5). D e v i a t i o n plots with similar shapes, respectively, were o b t a i n e d for several sets of data at each concentration. As discussed previously, cyclic v o l t a m m e t r i c peak IIc at c > 0.3 m M a n d v < 0.05 V s-1 was adequately fit b y the current f u n c t i o n for a reversible diffusion-controlled r e d u c t i o n with n ( a p p ) = 1.15 to 1.2 (Fig. 3). However, overall CV's at 0.05 < v < 2 V s - t a n d c > 0.3 m M had shapes significantly different from those observed at lower concentrations. U n d e r the former conditions, Ic was small with respect to IIc, IIa was not observed, a n d a new anodic peak, IVa, appeared (Figs. 3 a n d 8a). The c u r r e n t f u n c t i o n for IVa (Table 3) r e m a i n e d c o n s t a n t with increasing v up to 1 V s-1. A CV with a switching potential at the foot of IIc showed only peak Ia, without peak IVa, o n the reverse scan (Fig. 8b). A second negative scan following the usual triangular-wave CV revealed n o a d d i t i o n a l cathodic peaks. As v was increased b e t w e e n 0.5 a n d 5 V s - t , peak IVa decreased in height a n d was replaced b y IIa. CV's at c > 0.3 m M a n d v > 2 V s -1 (Fig. 8c) were strikingly similar in shape to those o b t a i n e d at lower c o n c e n t r a t i o n s (c.f. Fig. 1). U n d e r the former conditions, Ia a n d Ic were of a p p r o x i m a t e l y equal height a n d potential, a n d their peak currents were p r o p o r t i o n a l to v. I n addition, peaks I I a a n d IIc were of equal height at v > 2-V s -1 a n d separated b y a b o u t 35 mV. The peak c u r r e n t of Ic was i n d e p e n d e n t of c o n c e n t r a t i o n (Table 4), i n d i c a t i n g complete coverage of the surface with adsorbate u n d e r all c o n d i t i o n s studied. TABLE 4 Effect of concentration of ferrlheme on cychc voltammograms
o//V S - 1
c/mM
Peak Ic Peak IIc tp/p,A
lpC-1/p,A
Peak IVa -Ep/2/V
mM-1 0 20
0 05 0.30 0.60 1.0 2.0 3.0
0 225 0.228 0 213 0.220 0.270 0.280
3 14 1.96 1.73 1 80 1 45 1.04
0.656 0.668 0.678 0.688 0 695 0 700
a [Ep
- E p / V a [Ep
lpC-l/#A
_ Ep/2[/g
mM -1
0 043 0.067 0.072 0.082 0 105 0 130
--1.9 1.3 1.2 1.1
_ Ep/2[/g
--0.578 0.582 0 580 0 590
---0 042 0 050 0 050
Peak lla - Ep/V a
20
0 05 0.30 0 60 1.0 2.0 3.0
17 8 14.9 15 7 15.9 14.2 14.6
90 21 13 8.0 4.3 33
0.700 0.690 0 690 0 705 0 700 0 695
b b b b b b
t~/l~
-- Ep/V
1 24 1 28 0.81 1.07 1.14 1 10
0 665 0 660 0.660 0.670 0 660 0.665
a Vs. Ag/AgCI b Not accurately measurable because of overlap with Ic, but IIc 1s peak shaped
a
289 Thus, peaks Ia and Ic behaved similarly at high and low concentrations. Peak IIc, however, exhibited significant differences at c > 0.3 m M from its behavior at low concentrations. The current function of IIc at 0.6 and 1.0 m M was constant at low scan rates (Table 3, Fig. 2), decreased as v increased, and increased again at the highest scan rates. Concurrently, IEp - Ep/2l for IIc increased as v increased up to 2 V s-1 (Table 3). This broadening of IIc can be seen as a tendency toward a wave shape by comparison of Figs. 3 and 8a. A similar broadening of IIc was observed at 0.2 V s-1 with increasing concentration of ferriheme (Table 4). Moreover, IIc shifted to negative potentials and lp c -1 decreased at v = 0.2 V s 1 as the concentration of ferriheme increased. Ep for IIc was independent of c at 20 V s -1, but iv c -1 decreased as c increased (Table 4). Ep/2 for IIc was essentially independent of v. Normal-pulse polarograms of ferriheme at 0.6 and 1.0 m M exhibited a distinct peak shape, rather than the familiar wave shape [23]. Such peak shapes can be attributed to adsorption of the reactant [31].
Charge transfer processes The shapes of current-sampled polarograms at 0.66 m M ferriheme are m accord with the interpretation [4,5,14] that the reduction of ferriheme dlmer in alkaline media is an overall two-electron process yielding ferroheme monomer. CV results are in general agreement with this picture, but can provide additional information concerning the charge-transfer processes. Under conditions where peaks IIa and lIc were both observed, their heights were equal and their potentials were independent of scan rate, as expected for reversible electron-transfer processes [23,24]. Nevertheless, peak separations (AEp = 35 mV) and [ E p - Ep/2l (40-45 mY) for IIc were slightly larger than expected for a two-electron, reversible reaction, 1.e., AEp = 29.5 mV and I E p - Ep/21 = 28.3 mV. Moreover, fitting of peak IIc with the reversible current function [24] required a non-integral n(app) (Figs. 1 and 3). Although an approximation in the present case, the ferriheme charge-transfer can be treated as a fast EE process, as mentioned previously. However, EE voltammograms have shapes identical to those arising from an ECE reaction, provided the chemical step is fast [22,26] with respect to the time window of the experiment. As eqn. (6) shows, the reduction involves the exchange of two axial ligands and the breaking of a bond [4,5] in addition to two electron-transfer reactions. Assuming A 2 is the reducible species, one could expect chemical steps to be interposed between, a n d / o r occur subsequent to, the two-electron transfers. OH
OH
/ \ ,,/,
/\Jg\ L.
H20
H20 (A2)
H20
+
2OH-
(6)
\/!\/ H20 (M)
All ot tlae steps implied in eqn. (6) are fast on the CV time scale; therefore, no
290 inferences about their sequence can be made from our results. Assuming that the ECE or EE mechanism applies, the value of n ( a p p ) = 1.15 for fitting the voltammograms suggests that E~ for the intermediate product of the first electron transfer is positive of E? by about 10 mV [22,25]. This is also consistent with the estimated value of [Ep - E p : I at low v and low c. The difference in E°-values ( A E °) can be used with the average peak potential of IIc under conditions where the overall reaction is reversible ( - 0 . 7 0 0 V vs. Ag/AgC1) to estimate [26] a value of E~' = - 0 . 6 8 5 V vs. Ag/AgC1 ( - 0 . 4 8 6 V vs. NHE). This value is identical to the El~ 2 obtained by current-sampled polarography [15] at c = 0.66 raM, and in good agreement with the polarographic El~ 2 in 0.1 M K O H of - 0.480 + 0.006 V vs. N H E determined by Bednarski and Jordan [5]. The rate of the overall charge-transfer process appears to be very fast. Since no shift in the potential of IIc was observed at low c/v, even at the highest scan rates, both electron-transfer reactions must have standard heterogeneous rate constants (k°h)> 0.8 cm s - l , estimated for ferriheme dimer at p H 10 from CV peak shifts between 20 and 32 V s-1 [7]. Second-order disproportionatlon of the intermediate one-electron product has been observed in the electroreductlon of ferriheme dimers between p H 9 and 11 [6,7]. We have found no evidence for disproportionation in the reduction in 0.1 M N a O H . The absence of a disproportionation reaction is in agreement with the small AE °, which implies that disproportionation would not be highly thermodynamically favored [32]. There may also be chemical reasons for the lack of disproportionation and the increase in ks°h at the higher pH, since the dlmer formed at p H 13 may have a different structure than that formed between p H 9 and 11 [5,33]. It should be mentioned that the influence of preceding chemical reactions on the shape of IIc at intermediate concentrations and low v cannot be completely ruled out. However, since the reversible current function with the same n (app) fit the data at both low and intermediate c, such effects are considered unlikely.
Adsorptzon of ferroheme and ferriheme dlmer Results of CV at low co -1 indicate strong adsorption on the electrode of the ferroheme monomer and weaker adsorption of the ferriheme dimer, as discussed for low concentrations. Data at higher concentrations support this view. The current function of IIc increases at the highest scan rates (Fig. 2) and the shapes of plots of p VS. 131/2¢-1 (Fig. 9) shows negative deviations from linearlty [21]. These latter plots had shapes which were qualitatively invariant with concentration. The width of the adsorption peaks is accounted for by large repulsive interactions between molecules in the adsorbate. The average total surface concentration of ferriheme dimer (3.5 × 10 -11 mol cm -2, or 7 × 10 -11 mol cm -2 as ferroheme monomer) was slightly smaller than values of F t measured in buffered ethanolic solutions by chronopotentiometry and polarography (1.1 × 10 -1° mol cm -2, p H 9.5 [9]) but close to one measured in a similar solvent by CV (7.6 × 10 -11 mol cm -2, p H 11.4 [33a]), both calculated for monomer. However, because of the inherent variance in the respective measurements, and the controversy surrounding the structure of the dimer [33b], no
291
2
1
•
•
o
5
10 10-3 v 1/2 c -1/Vl/2s-112dm3 tool-1
Fig. 9 Plot of peak current ratio (#) vs
vl/2c-1
for (©) 0.6 m M fernheme and (O) 1 0 m M fernheme
conclusions have been drawn regarding these differences. Moreover, the observation of small overlapped adsorption peaks (e.g. III, Fig. 1) suggest adsorption of small amounts of species in addition to ferroheme and ferriheme dimer on the electrode surface. Peak IIIc does not appear to involve reduction of ferriheme monomer, since its relative height decreases with decreasing concentration. Our value of Ft is also shghtly smaller than the value of 5.3 × 10-11 mol cm-2 obtained for ferriheme dimer in 0.2 M K O H by differential capacitance measurements [14]. This is not unexpected, since differential capacitance reflects the adsorption of all species on the electrode surface. CV in 0.2 M K O H also showed double adsorption peaks [14], suggesting adsorption of species in addition to ferriheme dimer and ferroheme monomer in this medium as well. Furthermore, the higher ionic strength of the 0.2 M K O H solutions favors aggregation [5], and a significant fraction of aggregated species may be adsorbed. The large increase in current function at small cv-1/2 and the curved shapes of p vs. vl/2c -1 plots (Fig. 4) at low concentrations indicate [21] that even at c < 0.06 m M adsorption of ferriheme dlmer is significant. A theoretical study of the type of mechanism proposed here showed [21] that adsorption of the reactant should be more important at higher concentrations. Direct experimental verification of this in the present system is precluded by the onset of coupled chemical reactions as c is increased. The model of equal adsorption of oxidized and reduced forms was followed under polarographic conditions in a hmited range of concentrations. Under conditions of CV, however, especially at low cv -1, the equal adsorption model is invalid and the stronger adsorption of the ferroheme monomer is clearly evident.
Coupled chemtcal reacttons Results of CV at c > 0.3 m M and v < 2 V s -1 can be explained in terms of coupled chemical reactions preceding and following the fast charge transfer process (eqn. (6)). Because the potential of peak IIc shifts negatively with increasing c, and because changes in the shape of IIc and in the anodic peaks occur only at higher
292
O
+
I
, ?
I
I
+
I
O
8
II
II
~
O
O
,~
O
A v 0 0
? II
I~ ~ -~ IL-~ ~ ~
8
"6
U
g E
E
293
concentrations of ferriheme, aggregation phenomena are strongly implicated. Aggregation of both Fe(II) and Fe(III) porphyrins is well known and has been extensively studied [33b]. Initial steps in the aggregation of ferriheme dlmer (A 2) and ferroheme monomer (M), respectively, are shown in eqns. (7) and (8). kt
(A2) 2 ~ 2 A 2
2 M
k
(7)
(8)
and M 2 c a n then undergo further aggregation [33b]. As a first approximation, we assumed that reactions (7) and (8) dominate the kinetic processes of the relevant aggregates. In that case, the diagnostic criteria summarized in Table 5 can be used to analyze the results of CV. The predominant influence on changes in peak IIc as C and o increase can be seen to involve aggregate dissociation preceding charge transfer (Table 5, mechanisms 1 and 2). The appearance of peak IVa at high cv-1 apparently reflects the influence of a follow-up aggregation of ferroheme (Table 5, mechanism 3). The broadening of peak IIc with increasing c and o, the decrease in current function of IIc with increasing v, and the negative shift in the potential of IIc with increasing c all can be explained by dissociation of an aggregate of the ferriheme dimer preceding charge transfer (Table 5). Aggregation of ferroheme, conversely, does not appear to have significant effects on the behavior of IIc. At low values of v and intermediate c, the shape of IIc ( I E p - Ep/2], Table 3) indicates that the reaction (mechanisms 1 and 2) involving preceding dissociation resides in the diffusion zone [34]. Increases in either c or v tend to drive the reaction toward an intermediate or general kinetic zone between the diffusion (mechanism 2) and kinetic (mechanism 1) zones [34], as evidenced by the tendency of IIc to broaden and attain a wave shape (Fig. 8a, Tables 3 and 4). This peak broadening does not occur with an increase in concentration at v = 20 V s -1 because the experimental time window is now too small for the preceding dissociation to affect the peak shape. Other supporting results are the negative value of dEp/E/d log c and the value of dEp/2/d log v of zero for IIc. Quantitative agreement of d E p / J d log c with the predicted value for the preceding dissociation mechanism may be less than satisfactory because of the oversimplified representation of the dissociation by the single reaction in eqn. (7). The interpretation presented here of the CV of ferriheme in 0.1 M N a O H at c > 0.3 m M is consistent with that proposed by Bednarski and Jordan [5,37] to explain a kinetic component of the polarographic limiting current of ferriheme at c > 1.0 m M in 0.1 M KOH. The preceding dissociation reaction is also expected to influence the shapes of polarograms at higher concentrations. To further test the validity of mechanisms 1 and 2, we have used the current function ratios (cf. Fig. 2) of peak IIc to obtain the kinetic parameter K R = klb/2g3/a[DA2/D(A2)2 ]1/2 using a working curve from ref. 34 for the general case of mechanisms 1 and 2. To avoid the influence of adsorption, current functions at v > 1 (A2) a
294 TABLE 6 Kanet~c parameters of preceding and follow-up chemical steps Preceding reactton a
v/V s- 1
K R = k l / 2 K 3/4( DA2//DtA2)2)I/2//moll/4 ]-1/4 s - l / 2
c=0.6 m M 0.05 0.1 02 05 10 Average Overall average
c =10 mM
0.68 0 63 0 65 0.56 0 59 0.62 + 0.05
-0 81 0 65, 0.76 1 02 0.85 0.81 + 0 14 0 72 _+0 14
Follow - up reactton b
k=56×102lmo1-1
s -1
a Mechanisms (1) and (2), Table 5 Calculated from working curve in Fig 6, ref 34 D, diffusion coeffloent b Mechamsm (3), Table 5 Calculated from t a / t ~ between 0 5-2 0 V s -1 following ref 36
V s-a were not used. Values of K R at five scan rates and two concentrations showed good agreement (Table 6), giving further support to our hypothesis. Average values of K R at the two concentrations were not slgmficantly different at the 95% confidence level, as shown by a t test. Anodic peak IVa, observed at large c o - 1 , can be attributed to the oxidation of the product of a chemical reaction of ferroheme formed at the electrode. A current function for IVa which is nearly independent of v 1/2 suggests that adsorption does not play a role in this oxidation. However, because of overlap of the anodlc peaks, there is a large uncertainty in the current function of IVa and some influence of adsorption cannot be totally ruled out. Likewise, the order of the chemical reaction leading to IVa cannot be directly ascertained from the voltammetrac results, but the fact that IVa appears only at c > 0.3 m M and that it does not appear when a switching potential at the foot of IIc is used (Fig. 8b) suggests that the reaction involves aggregation. Irreversible aggregation of ferroheme was observed by Bednarski and Jordan [5,37] following controlled-potential electrolytic reduction of ferriheine dimer in 0.1 M KOH. In the latter study, an anodic polarographic wave attributed to ferroheme monomer splat into two waves, then dissappeared, over the period of a 2 h electrolysis. In light of this result, peak IVa can be attributed to an intermediate aggregate of ferroheme, possibly a dimer, which is stable on the CV time scale but probably aggregates further at longer times. A rate constant, k, for the dimerization (mechanism 3, Table 5) was estimated (Table 6) from the ratio of peak heights of I I a / I I c [36]. The extent of aggregation of ferriheme dimer can be estimated from the electroanalytical results. Polarographic hmiting currents [37] showed mixed diffusion and
295
kinetic control at c > 1.0 m M in 0.1 M K O H , indicating significant unaggregated ferriheme dimer in the bulk of solution. We have estimated an equlhbrtum constant ( K ) for reaction (7) using [38] the CV current function ratios under conditions where the influence of adsorption is small. Assuming negligible aggregation in solutions 0.05 m M in ferriheme, the current function at this c and at v < 0.2 V s -1 reflects the prolSortionality between peak current and the total concentration of fernheme. Peak IIc at 0.6 and 1.0 m M and 5 < v < 20 V s -1 is diffusion controlled and the current function under these conditions reflects the concentration of unaggregated ferriheme dimer. The ratios of the average current function under the latter conditions to the one at 0.05 m M are 0.48 and 0.51 at 0.6 and 1.0 m M , respectively. These values are estimates of the fraction of unaggregated ferriheme dirner in the bulk of solution, and were used to estimate an average K = 4 × 10 -4. Using K, the average K R (Table 6), and assuming equal diffusion coefficients, we obtained k b = 6.5 × 10 4 1 m o l - : s - : and kf = 26 s -1. Given the assumptions made, these rate constants can be considered only approximate. Nevertheless, k r is about 20 times smaller than k (cf. Table 5), in qualitative agreement with the observation that only the preceding reaction, with the slower rate, influences the shape of the diffusion peak IIc. ACKNOWLEDGEMENT
Development of computational methods in this work was partially supported by U.S. Public Health Service G r a n t No. l-R01 CA33195 awarded by the National Cancer Institute, Department of Health and H u m a n Senves. REFERENCES 1 (a) D.G. Davis, in D Dolplun (Ed), The Porphynns, Vol V, Acaderruc Press, New York, 1979, pp 127-152; (b) K.M. Kadlsh (Ed.), Electrochemical and Spectrocheimcal Studies of Blologxcal Redox Components, Amer Chem. Soc., Waslungton DC, 1982 2 G. Dryhurst, Electrochemastry of Biological Molecules, Academic Press, New York, 1977, pp. 392-472. 3 M.R. Tarasevich and R.A Radyushkma, m D.A Cadenhead and J.F. Danlelh (Eds.), Progress m Surface and Membrane Soence, Vol. 14, Acadenuc Press, New York, 1981. 4 J. Jordan and T.M Bednarska, J. Am Chem. Soc., 86 (1964) 5690. 5 T.M. Bednarska and J Jordan, J. Am Chem Soc, 89 (1967) 1552 6 K M Kadish and J. Jordan, Anal. Lett, 3 (1970) 113 7 K M Kadlsh and J. Jordan, J. Electrochem Soc, 125 (1978) 1250 8 R. Bury and J Jordan, Anal Chem, 49 (1977) 1573 9 D G. Davis and R.F. Martm, J. Am Chem Soc, 88 (1966) 1365. 10 D G. Davis and D.J. Orleron, Anal. Chem., 38 (1966) 179 11 J G. Montalvo and D.G. Davis, J. Electroanal. Chem., 23 (1969) 166 12 L.A Constant and D.G. Daws, Anal. Chem, 47 (1975) 2253 13 R Brdlcka and K. Wlesner, Coil Czech. Chem. Commun, 12 (1947) 39 14 T. Osaka, J. Mlyata and T. Yosluda, Denlo Kagaku Oyobi Kogyo Butsun Kagaku, 49 (1981) 642. Chem. Abstr., 95 (1981) 227962a. 15 J.F. Rusling, Anal. Chem., 55 (1983) 1719
296 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38
L. Meltes, Cnt Rev. Anal Chem, 8 (1979) 1 R.I. Gelb, J Electroanal. Chem., 19 (1968) 215 J.F. Rushng, J Electroanal Chem., 125 (1981) 447. L. Meltes, The General Nonlinear Regression Program CFT4A, privately pubhshed, 1983 J.F. Rushng and T F Connors, Anal. Chem., 55 (1983) 776. R H. WopshaU and I. Shmn, Anal Chem., 39 (1967) 1514 R.H Wopshall and I Sham, Anal Chem, 39 (1967) 1527. A J Bard and L.R Faulkner, Electrochemacal Methods, Wdey, New York, 1980 R.S Nlcholson and I. Sham, Anal Chem., 36 (1964) 706. D S. Polcyn and I Sham, Anal. Chem., 39 (1966) 370 R L Meyers and I. Shain, Anal. Chem., 41 (1969) 980. E. Lavlron, J. Electroanal Chem, 52 (1974) 395 A.P. Brown and F C. Anson, Anal Chem., 49 (1977) 1589. K J. Johnson, Numerical Methods m Chemistry, Marcel Dekker, New York, 1980 J.F Rushng, Anal. Chem, 55 (1983) 1713 J B Flanagan, T. Takahasba and F.C Anson, J Electroanal. Chem., 57 (1977) 257 M. Mastragostino, L. Nadjo and J M Sav6ant, Electrochlm Acta, 13 (1968) 721 (a) C F. Kolpln and H.S. Swofford, Anal Chem, 50 (1978) 916, (b) W I White, m D Dolphm (Ed), The Porphynns, Vol V, Acadenuc Press, New York, 1979, pp. 303-338 J.M. Sav6ant and E. Vlanello, Electrocham. Acta, 12 (1967) 1545 C.P. Andneux, L. Nadjo and J.M. Sav6ant, J Electroanal. Chem, 26 (1970) 147 M.L Olmstead, R.G Hamalton and R S. Nlcholson, Anal. Chem. 41 (1969) 261. T M Bednarskl, Ph.D. Thesis, Pennsylvania State Umverslty, College Park, PA, 1966. J F. Rushng, J.P Segretarlo and P Zuman, J Electroanal Chem, 143 (1983) 291
277
Elsewer Sequoia S A., Lausanne - Pnnted in The Netherlands
ADSORPTION AND COUPLED CHEMICAL REACTIONS IN THE ELECTROREDUCTION OF FERRIHEME IN ALKALINE SOLUTIONS
JAMES F. R U S L I N G * and M A R G A R E T Y BROOKS
Department of Chemzstry, U-60, Unwerstty of Connectmut, Storrs, CT 06268 (U S A ) (Received 8th June 1983, in rewsed form 20th August 1983)
ABSTRACT Electroanalytlcal techmques were used to investigate adsorption, charge transfer, and coupled chemacal reactions In the electroreductlon of a ferrtheme dlmer at mercury electrodes in 0 1 M N a O H over a wide range of experimental conditions. Current-sampled polarography confirmed that the overall reaction is a two-electron, Fe(III) dlmer to Fe(II) monomer process, as previously found in solutions of K O H A preceding reaction influences the shape of the wave at tugher concentrations. Cychc voltammetry (CV) at low concentrations (c < 0.06 m M ) revealed the reversible reduction and oxadatlon of an adsorbed redox couple. Ferroheme, the reduction product, ts more strongly adsorbed than the ferriheme darner reactant The total hmatmg surface concentration of ferroheme was 7 X 10-11 mol cm-2. Analysis of the shape of the adsorption prepeak m CV usmg nonhnear regression showed that the adsorbate featured large repulsive interactions. The shape of the two-electron, diffusion-controlled peak m CV suggested a fast EE or ECE process. The value of E~ for the femheme dlmer was estimated at - 0 486 V vs. N H E The standard potentml E~ for the one-electron intermediate was about 10 mV more positive than E~' At c > 0 3 m M and v < 2 V s -a, voltammograms reflected the influence of aggregation of both femheme d~mer and ferroheme monomer. Approxamate kinetic and e q m h b n u m parameters for these reactions were estimated from the voltammetric data.
INTRODUCTION
Metalloporphyrins have received considerable attention in the recent electrochemical literature [1-3] because of their importance in biological reactions and their electrocatalytic properties. Since the major emphasis in studies of the electroreduction of biologically important iron porphyrins has been on charge transfer processes [4-8] and ligand exchange reactions [9-13], most work on these compounds has been done under conditions where adsorption and aggregation were minimized. In the case of ferriheme (iron(III) protoporphynn), it has been realized that adsorption and aggregation of reactants and products can occur during electroreduction in aqueous media [5-7,9,13,14]. Nevertheless, little use has been made of electroanalytlcal techniques to investigate these phenomena. One recent paper [14] has discussed * To whom correspondence should be addressed. 0022-0728/84/$03.00
© 1984 Elsevier Sequoia S A
278
electrochemical properties of ferriheme dimer adsorbed on mercury from 0.2 M KOH, but this study was of limited scope and emphasized electrocatalysis of the reduction of oxygen. Ferriheme in 0.1 M K O H forms dimers which undergo a two-electron reversible reduction of Fe(III) to Fe(II) at mercury cathodes to yield a ferroheme monomer [4,5]. Our initial interest in the reduction of ferriheme dimer was as a model for dimer-to-monomer reduction in a computerized system for mechanistic elucidation [15] using deviation-pattern recognition [16]. When current-sampled polarograms of ferriheme in 0.1 M N a O H were analyzed by our computerized method [15], it was found that the dimer-to-monomer mechanism was strictly followed only in a limited range of concentrations (c < 0.7 m M ) . At c > 1.0 mM, small but significant deviations from the theoretical behavior for the dimer-to-monomer reaction were observed. Bednarski and Jordan [4,5] provided a mathematical analysis of the polarographlc wave shape assuming equal adsorption of oxidized and reduced forms, which we used in our fitting procedure [15]. When a more rigorously derived equation [17], free from the above restriction about adsorption, was used to fit the data, nearly identical deviations were observed at c > 1.0 mM, as with the Bednarski-Jordan expression. In order to explain the above observations and to clarify the role of adsorption and chemical reactions coupled to the charge-transfer process, we have undertaken a more extensive study of the reduction of ferriheme in 0.1 M N a O H at mercury electrodes over a wide range of experimental conditions. EXPERIMENTAL
Crystalline bovine hemln (ferriheme), obtained from Aldrich Chemical Co., was used as received. Solutions of sodium hydroxide were prepared by dilution of a 50% solution obtained from Baker Chemical Co. All water used in this work was prepared by treating distilled water with a Sybron/Barnstead NANOpure wateipurification system. The final product had a specific resistance greater than 10 Mf~ cm. To avoid irreversible aggregation and decomposition, ferrlheme solutions were always prepared immediately prior to the experiment. Cyclic voltammograms, and current-sampled and pulse polarograms were obtained with a Princeton Applied Research (PAR) Model 170 Electrochemistry System and a PAR Model 174A Polarographic Analyzer. Three-electrode cells and procedures outlined previously were used [18]. All solutions were purged with purified nitrogen [18] for 20 min prior to the start of an experiment. The hangingdrop-mercury electrode (HDME) for cyclic voltammetry (CV) had a corrected area of 0.0208 cm2; the dropping mercury electrode (DME) for polarography had a flow rate of 1.88 mg s -1 and a natural drop time of 4.00 s (1 M KC1) at a mercury column height of 70 cm. All polarograms were recorded using a controlled drop time of 2 s. Both saturated calomel and Ag/AgC1 reference electrodes were used, and reported potentials, unless otherwise stated, are referred to Ag/AgC1. The resistance of assembled cells containing 0.1 M N a O H averaged 400 ~2. At scan rates (v) in CV above 0.2 V s-1, positive feedback compensation of ohmic drop and oscillographic
279 recording of current-potential curves was employed. To check the performance of electrochemical cells and instruments, CV's of k n o w n reversible systems were periodically recorded. Separation of anodic and cathodic peaks for Cd(II) in 1.0 M N a N O 3 and U(VI) in 0.1 M HC1 were always ( 6 0 / n ) _+ 1 mV. All computations utilized a Radio Shack TRS-80 Model I microcomputer (48K) and the Level II B A S I C language. Nonlinear regression analysis was carried out with a general p r o g r a m for this purpose [16,19]. Appropriate modifications, described in the text, were made to the p r o g r a m to obtain the desired fitting procedures. In all regression analyses, the absolute, rather than the relative, error in the dependent variable was assumed to be r a n d o m l y distributed. Digitization and corrections for residual current of experimental current-potential curves were accomplished at 5 or 10 mV intervals as previously described [20]. RESULTS AND DISCUSSION Behavtor at low concentrations (c < 0.06 m M ) Cyclic voltammetric behavior of ferriheme at low concentrations is illustrated by Fig. 1. The labels given to peaks in Fig. 1A are used throughout the discussion. Two major reduction peaks, Ic and IIc, were observed; on the reverse scan three oxidation peaks, Ia, IIa, and Ilia, were present. The shapes of CV's were qualita-
Ic
(o)
01
o
,
,
0,~
, -E
0.4
-01
cb
-20~
Fig. 1 Cychc voltammograms of 0.05 mM femheme m 0.1 M NaOH. (a) v = 0 20 V S -1, (b) v = 20 V s-1. Sohd hnes are experimental curves (©) Points calculated from nonlinear regression onto eqns. (1) and (4). (O) Points calculated from reversible current function [24] with n(app)= 1.15
280
7 7
.= z~
0
8 "6 0
II \
7 "6
7
"6
281
0
0 O < c~
0
LC L)
0 0
0
•
OoOO_@_ooO .
_o?_@_O_o_O_o I
-5
I
I
-4 -3 log (cv-I/2/mol dm-3 V -1/2 s 1/2 )
F i g 2 Plot of ratio of current function (lpc-lv -1/2) of p e a k l l c to the value of the current function as co -1/2 ---, oo, t a k e n as avg. lpc-lo -1/2 at v < 0 1 V s -x, against log(co-I~2). ( O ) 0.05 m M f e r n h e m e , (n) 0 6 m M ferrlheme, a n d (@) 1.0 m M ferrlheme
tively similar to those obtained in 0.2 M K O H at v < 0.2 V s-1 [14]. At higher scan rates (v), peaks Ia and Ic increased in height relative to the heights of IIa, IIc, and IIIa. The width at half height of Ic was about 140-150 mV and its peak current varied linearly with v. The ratio of currents of peaks Ic and Ia was approximately one, and their peak potentials were nearly equal at all v (Table 1), except at 50 V s-1. At this highest scan rate, a slightly greater peak separation could be attributed to the influence of charge-transfer kinetics or a small uncompensated ohmic drop. A small shift in the potential of Ic of - 4 . 5 _+ 1.4 m V / l o g v was observed. These data are consistent with the reactions of an adsorbed redox couple in peaks Ic and Ia [21-231. The current function [lp(C 01/2)- 1] of peak IIc was reasonably constant at v < 1 V s-a (Table 1, Fig. 2). A large increase in current function, caused [21] by adsorption of the ferriheme dimer, was observed at higher scan rates. The ratio of currents of peaks IIa and IIc was approximately one (Table 1). The potentials of peaks I I a and IIc were independent of scan rate and differed by an average of 35 mV. Although subject to some uncertainty because of overlap of Ic with IIc, ]Ep - Ep/21 for IIc at v < 0.2 V s-1 was about 40-45 mV. These data are in agreement with the interpretation of the polarographic reduction of ferriheme in 0.1 M K O H [4,5]. The height of peak I I I a was proportional to v, rather than to 01/2, at v < 1V s -1. A small cathodic counterpart to I I I a was observed (IIIc) but it was severely overlapped with Ic. Peak IIIc became smaller relative to Ic at lower concentrations
282
05
L/~A
°7 -025
E, v vsAg gc,
VIva
Fig. 3. Cyclic voltammogram of 0.6 mM fernheme in 01 M NaOH at 002 V s -1 Solid hne is experimental curve, points calculated from reversiblecurrent function [24] with n(app)= 1 19
at v = 0.2 V s-1. However, because of poor resolution peaks I l i a and IIIc were not investigated in any detail. In order to obtain the area under peak Ic, a correction for overlap with IIc was necessary. For this purpose, the shape of IIc was investigated at 0.3 < c ~< 1 m M , and at v < 0.05 V s -1, where the influence of adsorption and aggregation on the shape of the peak was rmnlmal. When these data were fit with the current function of Nicholson and Shain [24] for a reversible two-electron reduction, it was found that the theoretical peak was much too narrow to describe the experimental voltammograms. A good fit to experimental data could be obtained when an apparent number of electrons [n(app)] of 1.15 to 1.2 was used with the reversible current function (Fig. 3). Justification for this procedure is based on the assumption that the electron-transfer mechanism can be described by a fast EE process, but that the reduction potential E~ of the one-electron intermediate is close to that ( E ? ) of the ferriheme dimer. Theoretical calculations for the EE mechanism have shown [25,26] that only in the case where E~ >> E~ (for reductions) is the separation between cathodic and anodic diffusion peaks expected to be 57/n mV or 28.5 mV for n = 2. Larger peak separations are predicted as the value of E~ approaches that of E~. For an EE process with E~' = E~, a peak separation of 42 mV is predicted [22] as well as a reversible reduction peak with the same shape as one with n = 1. A peak shape described by the reversible current function with n ( a p p ) = 1.15 would lead to a peak separation of about 39 mV, close to that observed for peaks I I a and IIc of the ferriheme dimer. The fitting procedure described provided an adequate method of calculating the rising portion of peak lIc and subtracting it from adsorption peak Ic. Following this subtraction, numerical integration of peak Ic was begun at - 0 . 4 V vs. Ag/AgC1 to eliminate part of peak IIIc from contributing to the charge. The charge density (Qc) under peak Ic (Table 1) was reasonably constant at scan rates between 0.05 and 50 V s -1, with an average value of 6.7 _+ 0.6 /tC cm - 2.
283
The width at half height of peak Ic was much greater than the 9 0 / n mV expected for the reversible reduction of an adsorbed redox couple [23]. Broadening of the peak can be attributed to repulsive interactions within the adsorbed layer [27,28]. To confirm this assignment, we subjected data from peak Ic, corrected for overlap with IIc, to nonlinear regression analysis onto eqn. (1), which takes into account the influence of interactions between electroactwe molecules in reversible adsorption peaks in CV [28]. l = / p f(1 - f ) ( 4 - 2 r F t ) / [ 1 - 2rFtf(1 - f ) ]
(1)
where: ip = n2F2F, v / R T ( 4
- 2rF,)
(2)
f, the fraction of adsorbed molecules in the oxidized form, is defined by: 0 = exp[(nF/RT)(E
- E°)] = f ( 1 - f ) - '
exp - [ I', (2fr - r)]
(3)
with E ° = E p , 1"t 1S the total concentration of material adsorbed on the electrode surface in mol cm -2, r is the interaction parameter in cm 2 mo1-1, and the other symbols have their usual meanings. For use in nonhnear regression, eqn. (3) was rewritten as: 0(1 _ f ) f - 1
exp[ Ft (2fr _ r)] - 1 = 0
(4)
and solved by a Newton-Raphson subroutine [29] using Ep and R as regression parameters. This subroutine provided a value of f at each experimental value of E. These f ' s were then used within the regression program to calculate the
TABLE 2 Results of nonlinear regression analysis of major catho&c adsorption peak (Ic) xn cychc voltammograms of fernheme
C/mM
v / V s -1
- Ep/V (Ag/AgCI)
tp/l~A
10 n F t /
-lO-l°r/
RSD '~
Meas
Calc.
Meas
Calc
mol c m - 2
cm 2 m o l - 1
%t p
0 05
0.1 0.2 05 10 20 50 10 20 50
0.522 0 528 0.540 0.540 0(535 0 540 0 528 0.535 0 5¢35
0 521 0.529 0.534 0.532 0.530 0 532 0.525 0 530 0 530
0 100 0.193 0.627 1.018 1.82 4.75 9.00 17 9 41 6
0.093 0 181 0.575 0.952 1 72 4 53 8.68 16 8 39 4
36 35 3.9 3.2 33 33 32 32 3.1
41 41 25 37 42 37 35 42 5.0
71 7.0 6.4 7.9 6.7 6.3 6.7 67 5.3
0.3
20
0 540
0.527
16.0
15 0
2.7
4.7
9.3
0.6
05 20
0.530 0.530
0 526 0 517
0 44 15.6
0.43 14 5
3.1 2.8
4.4 5.6
5.0 5.8
a Relative standard devaatlon of the regression calculated as percent of peak current.
284
current-potential curve from eqn. (1), using the additional regression parameter lp. Thus, with eqns. (4) and (1), the nonlinear regression program [19] minimized the sum of squares of the residuals of t [i.e., t(meas) - t(calc)] and yielded the best values of the parameters Ep, R, and tp. This fitting procedure was tested with a voltammogram of 9,10-phenanthrenequinone adsorbed onto a pyrolytic graphite electrode [28]. An interaction parameter close to that previously reported, as well as a random deviation plot, were obtained. Moreover, final values of parameters were independent of variations in their initial estimates, within the hmits of error of those estimates. Nonlinear regression analyses of data from peak Ic resulted (Table 2) in an average interaction parameter of - 4 . 1 _+ 0.8 × 101° cm 2 mol-1, indicating strong repulsive interactions within the adsorbed layer. Calculated values of tp and Ep were very close to the measured ones, although the calculated tp was consistently about 5% smaller than the measured value. The average standard deviation of the regression was about 6% of tp. These small deviations from the model are attributed to uncertainties in corrections for the residual current and the diffusion peak IIc, and the fact that the small wave IIIc was not completely subtracted. Figure 1 illustrates that the combined procedure of fitting peak IIc with the reversible current function and fitting Ic to eqns. (4) and (1) gave good representations of the cathodic current-potential curves at low concentrations of ferriheme. Similar results to those discussed above were obtained with solutions 0.03 m M in ferriheme. The voltammetric data for ferriheme at low concentrations indicate a reversible, two-electron reduction involving strong adsorption of the product and weaker adsorption of the reactant. Strong adsorption [21,23] of the reduction product is confirmed by the observation of peaks Ic and Ia at potentials more positive than the diffusion peak IIc. The weaker adsorption of the reactant ferriheme dimer is indicated by the large increase in current function of IIc at large v (Fig. 2), predicted for the proposed mechanism when c / e x p ( - A G o / R T ) > 4 [21], where AGO is the
~
P
2/
o
-
o
-
/
4'0
'
8'0
'
1C)-3V 112 C -1/V 1/2s-1/2dr'N3 tool-1
Fig. 4. Plot of ratio ( 0 ) of peak currents of Ic and IIc agmnst ol/2c -1 at 0.05 m M fernheme.
285
standard Gibbs energy of adsorption of the reactant, assuming a Langmuir adsorption isotherm. Further support for this interpretation is given by a plot of the ratio (p) of the peak currents of Ic and IIc (Fig. 4). p is a linear function of v]/Z/c at low v ]/2, but deviates negatively from linearity at high v 1/2, as predicted ]for the proposed mechanism when c/exp( - A G o / R T ) > 1 [21]. The approximately equal potentials of peaks Ia and Ic and the constant 35 mV separation of peaks IIa and IIc reflect the reversibility of the surface and diffusion-controlled reductmns. The small shift in potential of peak Ic ( - 4 . 5 + 1.4 mV/log v) is also in agreement [21] with the proposed mechanism. Behavtor at higher concentranons (0.3 m M <~c <~3 mM) Data from current-sampled polarograms of ferriheme were regressed onto the equation: i + O~2 - ~1 = 0
(5)
using the parameters E ° = El~2, S = R T / n F , and q, the limiting current. Equation (5) is the exponential form of an expression describing the polarographic dimer-tomonomer reduction [4,5], and its use in nonlinear regression analysis has been described previously [30]. By conventional measures, good agreement between experiment and theory was obtained at 0.66 and 1.0 m M ferriheme (Fig. 5). However, smoothed deviation plots [30] obtained from the residuals of the regression analyses provide more discriminating criteria for goodness of fit [16]. The deviation plot obtained from the data at 0.66 m M (Fig. 6) was nearly featureless, suggesting a good fit to eqn. (5). The average value of S at this concentration was 0.0139 V, close
f
S
1C
{./~A o
b
O~
03
03
-E/V
vs SCE
Fig. 5. Current-sample.xl pol~o~mms m 0.] M NaOH. Sobd hne is expenmental curve; points calculated from results of nonhnear regression onto eqn. (5). (a) 0 66 m M fernhem¢, (b) 1 0 m M fernheme.
286
I
t~
I
I ~a
I I I I I~
~ ° ~ ° ~
ol \ t~
I
~a \
I
;> e-, 0
'-6
I
287
41 0
0
0
Ds
0000
0
00
0_(3 0
0 0
0 0
O0
0
00 0
0
0
-4
- E / V vs
0)75
SCE
Fig 6 Smoothed deviation plot [30] obtained from residuals after nonlinear regression of data In Fig 5a. N+2
D s = ~ [ t ( m e a s ) - l ( c a l c ) ] / s where N is the data point number and s is the standard deviation of 7=N regression.
4
0
0
Os
0000
0
0 0
0 0
0
0 0
O
O 0
0
0
O0 0
0
0o 0 i
0.65
0.75 - E / V vs SeE
Fig 7. Smoothed deviation plot for data in Fig. 5b
1.5
30
i/~A 0
0
-1.5"
-30
Fig 8. Cychc voltammograms of 1.0 m M fernheme m 0.1 M NaOH. (a) o = 0.5 V s -1, (b) v = 0 5 V with swltchmg potential at the foot of peak llc, and (c) v = 50 V s - i
S -1
288 to the theoretical value of 0.01285 V at 25°C. A similar plot for the data at 1.0 m M (Fig. 7) exhibited a large m i n i m u m at - 0 . 7 1 V a n d a large m a x i m u m at - 0 . 7 3 V, i n d i c a t i n g significant deviations from eqn. (5). D e v i a t i o n plots with similar shapes, respectively, were o b t a i n e d for several sets of data at each concentration. As discussed previously, cyclic v o l t a m m e t r i c peak IIc at c > 0.3 m M a n d v < 0.05 V s-1 was adequately fit b y the current f u n c t i o n for a reversible diffusion-controlled r e d u c t i o n with n ( a p p ) = 1.15 to 1.2 (Fig. 3). However, overall CV's at 0.05 < v < 2 V s - t a n d c > 0.3 m M had shapes significantly different from those observed at lower concentrations. U n d e r the former conditions, Ic was small with respect to IIc, IIa was not observed, a n d a new anodic peak, IVa, appeared (Figs. 3 a n d 8a). The c u r r e n t f u n c t i o n for IVa (Table 3) r e m a i n e d c o n s t a n t with increasing v up to 1 V s-1. A CV with a switching potential at the foot of IIc showed only peak Ia, without peak IVa, o n the reverse scan (Fig. 8b). A second negative scan following the usual triangular-wave CV revealed n o a d d i t i o n a l cathodic peaks. As v was increased b e t w e e n 0.5 a n d 5 V s - t , peak IVa decreased in height a n d was replaced b y IIa. CV's at c > 0.3 m M a n d v > 2 V s -1 (Fig. 8c) were strikingly similar in shape to those o b t a i n e d at lower c o n c e n t r a t i o n s (c.f. Fig. 1). U n d e r the former conditions, Ia a n d Ic were of a p p r o x i m a t e l y equal height a n d potential, a n d their peak currents were p r o p o r t i o n a l to v. I n addition, peaks I I a a n d IIc were of equal height at v > 2-V s -1 a n d separated b y a b o u t 35 mV. The peak c u r r e n t of Ic was i n d e p e n d e n t of c o n c e n t r a t i o n (Table 4), i n d i c a t i n g complete coverage of the surface with adsorbate u n d e r all c o n d i t i o n s studied. TABLE 4 Effect of concentration of ferrlheme on cychc voltammograms
o//V S - 1
c/mM
Peak Ic Peak IIc tp/p,A
lpC-1/p,A
Peak IVa -Ep/2/V
mM-1 0 20
0 05 0.30 0.60 1.0 2.0 3.0
0 225 0.228 0 213 0.220 0.270 0.280
3 14 1.96 1.73 1 80 1 45 1.04
0.656 0.668 0.678 0.688 0 695 0 700
a [Ep
- E p / V a [Ep
lpC-l/#A
_ Ep/2[/g
mM -1
0 043 0.067 0.072 0.082 0 105 0 130
--1.9 1.3 1.2 1.1
_ Ep/2[/g
--0.578 0.582 0 580 0 590
---0 042 0 050 0 050
Peak lla - Ep/V a
20
0 05 0.30 0 60 1.0 2.0 3.0
17 8 14.9 15 7 15.9 14.2 14.6
90 21 13 8.0 4.3 33
0.700 0.690 0 690 0 705 0 700 0 695
b b b b b b
t~/l~
-- Ep/V
1 24 1 28 0.81 1.07 1.14 1 10
0 665 0 660 0.660 0.670 0 660 0.665
a Vs. Ag/AgCI b Not accurately measurable because of overlap with Ic, but IIc 1s peak shaped
a
289 Thus, peaks Ia and Ic behaved similarly at high and low concentrations. Peak IIc, however, exhibited significant differences at c > 0.3 m M from its behavior at low concentrations. The current function of IIc at 0.6 and 1.0 m M was constant at low scan rates (Table 3, Fig. 2), decreased as v increased, and increased again at the highest scan rates. Concurrently, IEp - Ep/2l for IIc increased as v increased up to 2 V s-1 (Table 3). This broadening of IIc can be seen as a tendency toward a wave shape by comparison of Figs. 3 and 8a. A similar broadening of IIc was observed at 0.2 V s-1 with increasing concentration of ferriheme (Table 4). Moreover, IIc shifted to negative potentials and lp c -1 decreased at v = 0.2 V s 1 as the concentration of ferriheme increased. Ep for IIc was independent of c at 20 V s -1, but iv c -1 decreased as c increased (Table 4). Ep/2 for IIc was essentially independent of v. Normal-pulse polarograms of ferriheme at 0.6 and 1.0 m M exhibited a distinct peak shape, rather than the familiar wave shape [23]. Such peak shapes can be attributed to adsorption of the reactant [31].
Charge transfer processes The shapes of current-sampled polarograms at 0.66 m M ferriheme are m accord with the interpretation [4,5,14] that the reduction of ferriheme dlmer in alkaline media is an overall two-electron process yielding ferroheme monomer. CV results are in general agreement with this picture, but can provide additional information concerning the charge-transfer processes. Under conditions where peaks IIa and lIc were both observed, their heights were equal and their potentials were independent of scan rate, as expected for reversible electron-transfer processes [23,24]. Nevertheless, peak separations (AEp = 35 mV) and [ E p - Ep/2l (40-45 mY) for IIc were slightly larger than expected for a two-electron, reversible reaction, 1.e., AEp = 29.5 mV and I E p - Ep/21 = 28.3 mV. Moreover, fitting of peak IIc with the reversible current function [24] required a non-integral n(app) (Figs. 1 and 3). Although an approximation in the present case, the ferriheme charge-transfer can be treated as a fast EE process, as mentioned previously. However, EE voltammograms have shapes identical to those arising from an ECE reaction, provided the chemical step is fast [22,26] with respect to the time window of the experiment. As eqn. (6) shows, the reduction involves the exchange of two axial ligands and the breaking of a bond [4,5] in addition to two electron-transfer reactions. Assuming A 2 is the reducible species, one could expect chemical steps to be interposed between, a n d / o r occur subsequent to, the two-electron transfers. OH
OH
/ \ ,,/,
/\Jg\ L.
H20
H20 (A2)
H20
+
2OH-
(6)
\/!\/ H20 (M)
All ot tlae steps implied in eqn. (6) are fast on the CV time scale; therefore, no
290 inferences about their sequence can be made from our results. Assuming that the ECE or EE mechanism applies, the value of n ( a p p ) = 1.15 for fitting the voltammograms suggests that E~ for the intermediate product of the first electron transfer is positive of E? by about 10 mV [22,25]. This is also consistent with the estimated value of [Ep - E p : I at low v and low c. The difference in E°-values ( A E °) can be used with the average peak potential of IIc under conditions where the overall reaction is reversible ( - 0 . 7 0 0 V vs. Ag/AgC1) to estimate [26] a value of E~' = - 0 . 6 8 5 V vs. Ag/AgC1 ( - 0 . 4 8 6 V vs. NHE). This value is identical to the El~ 2 obtained by current-sampled polarography [15] at c = 0.66 raM, and in good agreement with the polarographic El~ 2 in 0.1 M K O H of - 0.480 + 0.006 V vs. N H E determined by Bednarski and Jordan [5]. The rate of the overall charge-transfer process appears to be very fast. Since no shift in the potential of IIc was observed at low c/v, even at the highest scan rates, both electron-transfer reactions must have standard heterogeneous rate constants (k°h)> 0.8 cm s - l , estimated for ferriheme dimer at p H 10 from CV peak shifts between 20 and 32 V s-1 [7]. Second-order disproportionatlon of the intermediate one-electron product has been observed in the electroreductlon of ferriheme dimers between p H 9 and 11 [6,7]. We have found no evidence for disproportionation in the reduction in 0.1 M N a O H . The absence of a disproportionation reaction is in agreement with the small AE °, which implies that disproportionation would not be highly thermodynamically favored [32]. There may also be chemical reasons for the lack of disproportionation and the increase in ks°h at the higher pH, since the dlmer formed at p H 13 may have a different structure than that formed between p H 9 and 11 [5,33]. It should be mentioned that the influence of preceding chemical reactions on the shape of IIc at intermediate concentrations and low v cannot be completely ruled out. However, since the reversible current function with the same n (app) fit the data at both low and intermediate c, such effects are considered unlikely.
Adsorptzon of ferroheme and ferriheme dlmer Results of CV at low co -1 indicate strong adsorption on the electrode of the ferroheme monomer and weaker adsorption of the ferriheme dimer, as discussed for low concentrations. Data at higher concentrations support this view. The current function of IIc increases at the highest scan rates (Fig. 2) and the shapes of plots of p VS. 131/2¢-1 (Fig. 9) shows negative deviations from linearlty [21]. These latter plots had shapes which were qualitatively invariant with concentration. The width of the adsorption peaks is accounted for by large repulsive interactions between molecules in the adsorbate. The average total surface concentration of ferriheme dimer (3.5 × 10 -11 mol cm -2, or 7 × 10 -11 mol cm -2 as ferroheme monomer) was slightly smaller than values of F t measured in buffered ethanolic solutions by chronopotentiometry and polarography (1.1 × 10 -1° mol cm -2, p H 9.5 [9]) but close to one measured in a similar solvent by CV (7.6 × 10 -11 mol cm -2, p H 11.4 [33a]), both calculated for monomer. However, because of the inherent variance in the respective measurements, and the controversy surrounding the structure of the dimer [33b], no
291
2
1
•
•
o
5
10 10-3 v 1/2 c -1/Vl/2s-112dm3 tool-1
Fig. 9 Plot of peak current ratio (#) vs
vl/2c-1
for (©) 0.6 m M fernheme and (O) 1 0 m M fernheme
conclusions have been drawn regarding these differences. Moreover, the observation of small overlapped adsorption peaks (e.g. III, Fig. 1) suggest adsorption of small amounts of species in addition to ferroheme and ferriheme dimer on the electrode surface. Peak IIIc does not appear to involve reduction of ferriheme monomer, since its relative height decreases with decreasing concentration. Our value of Ft is also shghtly smaller than the value of 5.3 × 10-11 mol cm-2 obtained for ferriheme dimer in 0.2 M K O H by differential capacitance measurements [14]. This is not unexpected, since differential capacitance reflects the adsorption of all species on the electrode surface. CV in 0.2 M K O H also showed double adsorption peaks [14], suggesting adsorption of species in addition to ferriheme dimer and ferroheme monomer in this medium as well. Furthermore, the higher ionic strength of the 0.2 M K O H solutions favors aggregation [5], and a significant fraction of aggregated species may be adsorbed. The large increase in current function at small cv-1/2 and the curved shapes of p vs. vl/2c -1 plots (Fig. 4) at low concentrations indicate [21] that even at c < 0.06 m M adsorption of ferriheme dlmer is significant. A theoretical study of the type of mechanism proposed here showed [21] that adsorption of the reactant should be more important at higher concentrations. Direct experimental verification of this in the present system is precluded by the onset of coupled chemical reactions as c is increased. The model of equal adsorption of oxidized and reduced forms was followed under polarographic conditions in a hmited range of concentrations. Under conditions of CV, however, especially at low cv -1, the equal adsorption model is invalid and the stronger adsorption of the ferroheme monomer is clearly evident.
Coupled chemtcal reacttons Results of CV at c > 0.3 m M and v < 2 V s -1 can be explained in terms of coupled chemical reactions preceding and following the fast charge transfer process (eqn. (6)). Because the potential of peak IIc shifts negatively with increasing c, and because changes in the shape of IIc and in the anodic peaks occur only at higher
292
O
+
I
, ?
I
I
+
I
O
8
II
II
~
O
O
,~
O
A v 0 0
? II
I~ ~ -~ IL-~ ~ ~
8
"6
U
g E
E
293
concentrations of ferriheme, aggregation phenomena are strongly implicated. Aggregation of both Fe(II) and Fe(III) porphyrins is well known and has been extensively studied [33b]. Initial steps in the aggregation of ferriheme dlmer (A 2) and ferroheme monomer (M), respectively, are shown in eqns. (7) and (8). kt
(A2) 2 ~ 2 A 2
2 M
k
(7)
(8)
and M 2 c a n then undergo further aggregation [33b]. As a first approximation, we assumed that reactions (7) and (8) dominate the kinetic processes of the relevant aggregates. In that case, the diagnostic criteria summarized in Table 5 can be used to analyze the results of CV. The predominant influence on changes in peak IIc as C and o increase can be seen to involve aggregate dissociation preceding charge transfer (Table 5, mechanisms 1 and 2). The appearance of peak IVa at high cv-1 apparently reflects the influence of a follow-up aggregation of ferroheme (Table 5, mechanism 3). The broadening of peak IIc with increasing c and o, the decrease in current function of IIc with increasing v, and the negative shift in the potential of IIc with increasing c all can be explained by dissociation of an aggregate of the ferriheme dimer preceding charge transfer (Table 5). Aggregation of ferroheme, conversely, does not appear to have significant effects on the behavior of IIc. At low values of v and intermediate c, the shape of IIc ( I E p - Ep/2], Table 3) indicates that the reaction (mechanisms 1 and 2) involving preceding dissociation resides in the diffusion zone [34]. Increases in either c or v tend to drive the reaction toward an intermediate or general kinetic zone between the diffusion (mechanism 2) and kinetic (mechanism 1) zones [34], as evidenced by the tendency of IIc to broaden and attain a wave shape (Fig. 8a, Tables 3 and 4). This peak broadening does not occur with an increase in concentration at v = 20 V s -1 because the experimental time window is now too small for the preceding dissociation to affect the peak shape. Other supporting results are the negative value of dEp/E/d log c and the value of dEp/2/d log v of zero for IIc. Quantitative agreement of d E p / J d log c with the predicted value for the preceding dissociation mechanism may be less than satisfactory because of the oversimplified representation of the dissociation by the single reaction in eqn. (7). The interpretation presented here of the CV of ferriheme in 0.1 M N a O H at c > 0.3 m M is consistent with that proposed by Bednarski and Jordan [5,37] to explain a kinetic component of the polarographic limiting current of ferriheme at c > 1.0 m M in 0.1 M KOH. The preceding dissociation reaction is also expected to influence the shapes of polarograms at higher concentrations. To further test the validity of mechanisms 1 and 2, we have used the current function ratios (cf. Fig. 2) of peak IIc to obtain the kinetic parameter K R = klb/2g3/a[DA2/D(A2)2 ]1/2 using a working curve from ref. 34 for the general case of mechanisms 1 and 2. To avoid the influence of adsorption, current functions at v > 1 (A2) a
294 TABLE 6 Kanet~c parameters of preceding and follow-up chemical steps Preceding reactton a
v/V s- 1
K R = k l / 2 K 3/4( DA2//DtA2)2)I/2//moll/4 ]-1/4 s - l / 2
c=0.6 m M 0.05 0.1 02 05 10 Average Overall average
c =10 mM
0.68 0 63 0 65 0.56 0 59 0.62 + 0.05
-0 81 0 65, 0.76 1 02 0.85 0.81 + 0 14 0 72 _+0 14
Follow - up reactton b
k=56×102lmo1-1
s -1
a Mechanisms (1) and (2), Table 5 Calculated from working curve in Fig 6, ref 34 D, diffusion coeffloent b Mechamsm (3), Table 5 Calculated from t a / t ~ between 0 5-2 0 V s -1 following ref 36
V s-a were not used. Values of K R at five scan rates and two concentrations showed good agreement (Table 6), giving further support to our hypothesis. Average values of K R at the two concentrations were not slgmficantly different at the 95% confidence level, as shown by a t test. Anodic peak IVa, observed at large c o - 1 , can be attributed to the oxidation of the product of a chemical reaction of ferroheme formed at the electrode. A current function for IVa which is nearly independent of v 1/2 suggests that adsorption does not play a role in this oxidation. However, because of overlap of the anodlc peaks, there is a large uncertainty in the current function of IVa and some influence of adsorption cannot be totally ruled out. Likewise, the order of the chemical reaction leading to IVa cannot be directly ascertained from the voltammetrac results, but the fact that IVa appears only at c > 0.3 m M and that it does not appear when a switching potential at the foot of IIc is used (Fig. 8b) suggests that the reaction involves aggregation. Irreversible aggregation of ferroheme was observed by Bednarski and Jordan [5,37] following controlled-potential electrolytic reduction of ferriheine dimer in 0.1 M KOH. In the latter study, an anodic polarographic wave attributed to ferroheme monomer splat into two waves, then dissappeared, over the period of a 2 h electrolysis. In light of this result, peak IVa can be attributed to an intermediate aggregate of ferroheme, possibly a dimer, which is stable on the CV time scale but probably aggregates further at longer times. A rate constant, k, for the dimerization (mechanism 3, Table 5) was estimated (Table 6) from the ratio of peak heights of I I a / I I c [36]. The extent of aggregation of ferriheme dimer can be estimated from the electroanalytical results. Polarographic hmiting currents [37] showed mixed diffusion and
295
kinetic control at c > 1.0 m M in 0.1 M K O H , indicating significant unaggregated ferriheme dimer in the bulk of solution. We have estimated an equlhbrtum constant ( K ) for reaction (7) using [38] the CV current function ratios under conditions where the influence of adsorption is small. Assuming negligible aggregation in solutions 0.05 m M in ferriheme, the current function at this c and at v < 0.2 V s -1 reflects the prolSortionality between peak current and the total concentration of fernheme. Peak IIc at 0.6 and 1.0 m M and 5 < v < 20 V s -1 is diffusion controlled and the current function under these conditions reflects the concentration of unaggregated ferriheme dimer. The ratios of the average current function under the latter conditions to the one at 0.05 m M are 0.48 and 0.51 at 0.6 and 1.0 m M , respectively. These values are estimates of the fraction of unaggregated ferriheme dirner in the bulk of solution, and were used to estimate an average K = 4 × 10 -4. Using K, the average K R (Table 6), and assuming equal diffusion coefficients, we obtained k b = 6.5 × 10 4 1 m o l - : s - : and kf = 26 s -1. Given the assumptions made, these rate constants can be considered only approximate. Nevertheless, k r is about 20 times smaller than k (cf. Table 5), in qualitative agreement with the observation that only the preceding reaction, with the slower rate, influences the shape of the diffusion peak IIc. ACKNOWLEDGEMENT
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