Some Considerations in Spectroelectrochemical Evaluation of Homogeneous Electron Transfer Involving Biological Molecules Michael D. Ryan’ and George S. Wilson2 Department of Chemistry, University of Arizona, Tucson, AZ 85721
Potential-step chronoabsorptometry was used to measure the rate of the second-order homogeneous electron transfer between horse heart cytochrome c and methyl viologen radical. A rate constant of 1.0 X 10’ f 0 . 3 W ’ sec-’ was obtained at pH 7.2. Theoretical and experimental considerations affecting the measurement of rate constants are discussed. These include the deconvoiution of time-dependent spectra and the influence of concentration and dlffusion coefficient ratios.
The ability to monitor changes in the absorbance of reacting species during an electrochemical experiment enables one to make a more definitive analysis of the mechanism involved. In recent years, significant advances have been made in developing the theoretical relationships for most of the common mechanisms [see Ref. ( I ) and references therein). The use of the catalytic mechanism to measure homogeneous electron transfer rates of reactions has greatly expanded the opportunities to apply electrochemistry to problems in other areas of chemistry (2-4). Most of the work thus far has been addressed exclusively a t examining the fate of the product of the electron transfer and not on the variations of other species involved, except for the work done by Grant and Kuwana (5) for the EC mechanism and Li and Wilson ( I ) for several other cases. Thus, it is the purpose of this paper to examine the theoretical and experimental considerations involved in monitoring all the species in the second-order catalytic mechanism (Reactions 1 and 2) and its application to the methyl viologen radical cation-cytochrome c reaction. The ultimate objective is to account for all spectral changes over a wide wavelength range, thus making possible the identification of transient intermediates. EO
A + e - e B kf
B + Z - A + Z ’ EXPERIMENTAL Apparatus. A Hewlett-Packard 2100 computer with an A/D converter system described previously ( 6 ) was used along with a PAR-173/176 potentiostat under computer control. The-absorbance data were plotted on a Tektronix 4010 graphics terminal during the experiment to determine when a sufficient number of steps had been time-averaged. The absorbance was monitored on a Harrick Scientific Corp. rapid-scan spectrometer. Reagents. Horse-heart cytochrome c (Type VI) was obtained from Sigma Chemical Co., St. Louis, MO, while methyl viologen was obtained from K&K Laboratories, Plainville, NJ. All solutions were 0.10M potassium phosphate buffers a t pH 7.2 (ionic strength 0.2). Other chemicals used were reagent grade. Procedure. At the beginning of each potential step, the initial absorbance and initial current were measured (several values were averaged each time). The potential was then switched from 0.0 V Present address, Department of Chemistry, Marquette UniverMilwaukee, WI 53233. I ’ T o whom communications concerning this paper should be addressed.
sit
vs. SCE to -0.800 V vs. SCE and the absorbance and current were measured up to time T , when the potential was returned to 0.0 V vs. SCE. The absorbance and current change were then calculated as the difference between the value a t time t and the initial value. At the end of each step, the solution was stirred for 8 sec. A new step was then initiated 30 sec after the stirring stopped. The correct wavelength was found a t the beginning of each experiment from a spectrum of reduced cytochrome c. The data were obtained a t a fixed wavelength. The instrument was calibrated to ensure photometric accuracy. A spectroelectrochemical cell similar to that described by Hawkridge et al. (7) was positioned so that the incident light beam passed first through the solution and then through the tin oxide optically transparent electrode. In this way, possible photochemical effects a t the electrode surface were minimized.
THEORY Absorbance of B. The variation of the absorbance of B as a function of $ (where $ = k f C z t ) has been derived by Blount et al. ( 4 ) and is shown in Figure 1. The normalized absorbance of B, AB^, (see Equation 3 ) depends upon the ratio of CZICA (if CZICA < 10) where Cz and CA are the bulk molar concentrations of Z and A, respectively.
ABN =
A , (t)fi 2rn€,C,
(3)
This derivation assumes that the diffusion coefficient of B, D B , is equal to the diffusion coefficient of Z, Dz. This assumption will not, in general, be valid, especially if high molecular weight species such as proteins are involved. The effect of the DzIDB ratio on the normalized absorbance change of B, AB^, is shown in Figure 2 for CZ/CA = 1. There are two limiting situations in this curve. First, if D z / D B is 0.1 or less, then the results are independent of the ratio of the diffusion coefficients. In this case, it appears that the Z species is almost motionless in the diffusion layer compared to B. In the second limit, Z is diffusing so fast compared to B that Z is not appreciably depleted near the electrode surface. Thus, as the D z / D B ratio becomes very large, the reaction approaches the limit of a first-order catalytic case. The effect of the diffusion coefficient ratio is greatest when the concentration ratio, CZICA,is low. The effect of the DzIDB ratio can also be seen in the double-potential step experiment. At time t = 0, the potential is stepped to a potential Ef> Eo. The effect of the Dz/DB ratio is greatest for CZ/CA values less than one. In Figure 3, the variation of the ratio of the absorbance of B at 27, A2,, to the absorbance at T, A , , as a function $ is shown for CZICA = 0.25. If D z / D B < 0.1, the A2,/A, ratio does not approach zero but about 0.11. As before, if the diffusion coefficient ratio becomes very large, the results approach the firstorder catalytic case. For values of CZICA> 0.5, the ratio of A ~ , / A Tapproaches zero. When the effect of D Z concomitantly becomes important ($ becomes large), kinetic parameters cannot be measured in any case. Experimentally, for full verification of a second-order catalytic mechanism, a large range of CZICAvalues must be used and significant errors can result if the effect of D Z is not included. Absorbance of Z. The variation of A z N (see Equation 4) ANALYTICAL CHEMISTRY, VOL. 47, NO. 6, MAY 1975
885
1.0
c'
0.8
-
0.6
-
0.4
-
0.2
-
I
I
I
0
1.0
0
LOG $'
A2 JA, ratio as a function of log $ for various values of D z l h . CZICA= 0.25
Figure 3. -I
0
I O
0 LOG
Figure 1. Normalized absorbance of
20
Y I
B, AsN, vs. log $ ($ = kfCzt).
I
Dzlh=1 0 25 20
4
I O C
/
IO
osc
1
0.6
001
I
I
I
0
IO
lQQ
*
I 20
LOG
I
I
I
2
9
Figure 4. Normalized absorbance of 2 , AzN, as a function of log Dzl&= 1
Figure 2. Normalized absorbance of B, AsN, vs. log $ for various values of D z l h . CZ/CA = 1.0. Curve A, first-order catalytic case
I
1
3z -
-
2 5-
.' E
as a function of $ and CZICA 2
is shown in Figure 4 for D z I D B = 1. It will be noted that the greatest total change in the normalized values occurs for small CZICA ratios. In addition, AzN values vary from zero to some maximum value. This has an advantage over using ABN values especially for small CZICAvalues or small $ values because AB^ approaches unity as a limit when CZ = 0. For small values of C Z / C Aor small $ values, one must measure a value of AB^ near one, or in other words, measure the difference between two large numbers. But AzN values are measured from zero giving a much more accurate number. This conclusion, of course, must be weighed against an inherent experimental difficulty in transmission spectroelectrochemistry. If, for example, only species Z absorbs, it will still be necessary to measure a small absorbance change which might be 0.01-0.1% of the initial absorbance. Thus, depending on the photometric characteristics of the measurement system, it might well prove advantageous to monitor AB^ instead. In Figure 5 , the effect of the DzIDB ratio on AzN as a function of $ is shown for CZICA = 1. As can be seen, the effect of the D z I D B ratio is even more pronounced on AzN than on AB^ (CZICA = 1). For example, a t $ I= 100, the value of AzN is 25% lower for D z I D B = 0.1 than when the 886
*
ANALYTICAL CHEMISTRY, VOL. 47, NO. 6, MAY 1975
1 $.
-
0-
"
-40
20
0 LOG i
Flgure 5. Normalized absorbance of Z, AzN, for various values of D z l h . CZ/CA = 1.0
as a
function of log
$
ratio is unity. A difference of 10% is seen in the AB^ curve for the same ratio value. Therefore, for fast electron transfer reactions or a t long times, the error in the normalized absorbance of Z is much greater than that for B. I t is not likely, of course, that the D z / D B ratio would exceed unity for the reaction of a small electrogenerated molecule with a protein. Even in the more likely range of 0.1 to 0.5, significant error will result. Since Z and Z' are essentially electroinactive, the time dependent absorbance of Z and Z' are only useful for mea-
~
~~~
~~
~
Table 11. Effect of) I on Spectral Overlap for Case IVa
Table I. Possible Cases of Spectral Overlap Spectral overlap
Case
N o spectral overlap
... z,Z '
I
II
A, A or B, Z, Z' A o r 13, Z o r 2' A, B, 2 , Z '
I11 IV
V
A B N EBCA
A,B,Z,Z' A' B z , 2' B or A B o r A, 2 or Z '
...
suring the rate of the forward step. The product, Z', cannot be directly oxidized back to Z. This means that, in timeaveraging experiments, the absorbance a t the beginning of each experiment is somewhat different from the initial absorbance of the previous potential-step. This is because the concentration of Z' is constantly increasing. Thus, the initial absorbance a t the beginning of each potential step must be determined, necessitating computer control of the experiment. Spectral Overlap. The analysis of spectroelectrochemical data is straightforward if there is no significant overlap a t the wavelengths studied. In general, overlap of a t least some of the species will occur. The total overall change in absorbance, AAx(t), is:
(5)
0.05 0.5
5 50 a
9.7 x 102
8.8 x 10' 6.7 X 10' 5.9 x 102
AzN(IZ
- €zz')Cz
1.20 x 1.00 x 2.96 x 3.80 x
Fb
102
0.89
103
0.47
103
0.18
0.13
103
CzICp = 0,5; DzlDB = 1; t g = cz = lo3; c z , = 5 Fraction of total absorbance due to B.
X
lo3; CA = 0.
and/or B can be determined separately while Z and Z' both adsorb appreciably a t the wavelength used. In this case t ~ , = C B , ~and , Equation 11 reduces to: U , ( t ) = MZNCZ(EZ,, -
EZ',,)
(13)
The change due to Z alone, AAz,h(t), is
U,,,(n= ~ z N C z E z , ,
(14)
Combining Equations 13 and 14, the effect of spectral overlap a t A A i ( t ) can be seen from Equation 15.
Conversely, (16)
where ANi(t) = number of moles of species i a t time t , t r , i = molar absorptivity of i a t wavelength A, b pathlength, V = volume. From Equations 1 and 2, we see that, ANz(t) = -ANz,(t)
(6)
and
(7)
ANA@) = -ANB(t)
Combining Equations 5 through 7 , we obtain,
b
u,(t)
F[ANA(~)(EA,,
-
