by a single weighing of a pure substance, and a buffer ratio very close to unity is assured. The usefulness of some buffer substances such as potassium hydrogen tartrate and, to a lesser potassium hydrogen phthalate is impaired by a tendency'to support mold growth. Although molding in solutions of sulfosalicylates was not specifically investigated, it seems likely that the presence of a phenol group in the sulfosalicylate molecule may provide built-in mold inhibition.
(3)G.D. Pinching and R. G. Bates, J. Res. Nat. Bur. Stand., 40,405 (1948). (4)G.D. Pinching and R. G. Bates, J. Res. Nat. Bur. Stand., 45,322 (1950). (5)R. G.Bates and V. E. Bower, J. Res. Nat. Bur. Stand., 53, 283 (1954). (6)H. T. S.Britton, "Hydrogen Ions", 4th ed., Vol. I., Van Nostrand, Princeton, N.J., 1956,Chap. 3. (7) R. G , Bates, J. Res. Nat, Bur, Stand,, 47, 127 (1957). (8) H. s. Harned and B. 6. Owen, "The Physical Chemistry of Electrolytic solutions", 36 ed., Reinhold Publishing Corp., New York, N.Y., 1958, p 608. (9) H. S.Harried and W. J. Flamer, J. Am. Chem. Sot., 5 5 , 2194 (1933). (10)H. S. Harned and R . A. Robinson, Trans. Faraday Soc., 36, 973 (1940). (11) N. W. Please, Biochern. J., 56, 196(1954).
LITERATURE CITED
RECEIVEDfor review April 28,1976. Accepted June 24,1976. This work was supported in part by the National Science Foundation under Grant CHE73-05019 A02.
(1) N. Konopik and 0. Leberl, Monatsh. Chem., 80, 655 (1949). (2)0.Mendius, Ann. Chem., 103, 39 (1857).
Semiintegral Electroanalysis: The Shape of Irreversible Neopolarograms Masashi Goto' and Keith B. Bidham* Trent University, Peterborough, Ontario, Canada
The equatlon of the m vs. E curve during the totally Irreversible reduction of an electroactive species is derived: it resembles an irreversible polarogram at a stationary electrode, but is less asymmetric. The effects of ramp-rate and of initial potential are evaluated, and the relationship to linear scan voltammetry is explored. Neopolarogramshave been determined experimentally, using the IO3- and Ni2+ electroreductions, and correlation between theory and experiment is sought by comparing transfer coefficlent values determined from various features of the neopolarograms.
When an electrode in contact with a solution containing a reducible species is polarized by a potential E that becomes progressively and linearly more negative, the curve which results from displaying the semiintegral m of the faradaic current vs. -E is termed a neopolarogram. If the electrode reaction is reversible, the shape of the neopolarogram is identical to that of a classical reversible polarogram (1-3). The usual equation describing this shape
may be rephrased as
Conditions wherein the electrochemical reduction
+
k(E)
Ox Ne--Rd (5) is totally irreversible or quasi-reversible have also been considered (1,2). One of the major advantages of the semiintegral method, that has been exploited by Saveant and coworkers ( 5 ) ,is its ability to analyze electrochemical kinetics without preassuming any particular dependence of the heterogeneous rate constant k ( E ) upon potential. For the present purpose, however, it will be assumed that the rate of reduction is governed by a volmerian,
h ( E ) = h , exp
(sF [E - E , ] )
dependence on potential. If the rate-determining step of the electroreduction mechanism is an initial transfer of n electrons, then a is the transfer coefficient of that step. The shape of such irreversible neopolarograms is not independent either of Eo or of u , so that it is impossible to write an equation of the form m = f ( E ) in which the function f is independent of the starting potential and the ramp-rate. However, it is possible to derive an expression of the form f(m,i,E)= 0, relating potential to both the faradaic current and its semiintegral, and in which neither Eo or u appears. Such a relationship (1, 2 ) is (7)
where m is the semiintegral ( 4 ) ,d-l12 i/dt-lI2, of the faradaic current i, m, is an abbreviation for the constant
NAFC d m,
(3)
and other symbols have the significance commonly accorded them in electroanalytical chemistry. Note that the shape of a reversible neopolarogram depends on neither the initial potential Eo nor the ramp-rate u , the two constants that jointly determine how the potential
E = Eo - vt
(4)
changes with time. 1 Present address, Department of Applied Chemistry, Faculty of Engineering, Nagoya University, Chikusa-ku, Nagoya, Japan.
and has been verified experimentally. Though it certainly holds when the potential varies with time according to the linear relation 4, the validity of Equation 7 is not restricted to any particular temporal dependence of potential (6). Equation 7 cannot be said to describe the shape of an irreversible neopolarogram; what it does is to provide an interrelationship between the shape of a neopolarogram and the shape of a linear-potential-scan voltammogram. The object of the present study is to produce and test an equation that, in fact, does describe the shape of an irreversible neopolarogram by giving the value of m as an explicit function, m = f(E,Eo,u),of the variable E and the constants Eo and v. If Eo is sufficiently positive, then its precise value is irrelevant. We shall see that, in this circumstance, the equation that relates m and E is
ANALYTICAL CHEMISTRY, VOL. 48, NO. 12, OCTOBER 1976
1671
Tabie I. Values of m/m,as a Function of the Parameter (an Undimensionalized Potential, Defined in Equation 8b), Giving the Shape of an Irreversible Neopolarogram That Starts at a Sufficiently Positive Potential E
0 0.00091 0.00249 0.00671 0.01810 0.04810 0.12333 0.14768 0.17612 0.20904 0.24672 0.25000 0.28930 0.33669 0.38850 0.44401 0.50000 0.50212 0.56140 0.62020
-7.0000 -6.0 0 00 --5.0000 -4.0 0 00 -3.0000 -2 .o 000 -1.8000 -1.6000 -1.4000 -1.2000 -1.1837 -1
E
mlm,
-m
.oooo
-0.8000 -0.6000 -0.4000 -0.2072 -0.200 0 -0 .ooo 0 +0.2000
+0.4000 +0.6000 +0.6829 +0.7802* +0.8000
+1.0000 +1.2000
+1.4000 +1.6000 +1.8000 +1.9346 +2.0000 +2.1292 +2.5185 +3.2969 +4.0000 +5.0000 +6.0000 +7.0000 +m
mlm,
0.67678 0.72955 0.75000 0.77277 0.77725 0.81909 0.85476 0.88445 0.90867 0.92811 0.9389 0.94361 0.9517 0.9699 0.9880 (0.99483) (0.99830) (0.99943) (0.99981) 1
m/m, values given to only four decimal places were derived from data in Ref. ( I O ) , while parenthesized values are from Expression 18. The asterisked entry corresponds to the peak of a linear scan voltammogram.
0.4
1 5
-3
-2
I
,
I
I
I
I
0
I
2
3
Figure 1. Comparison of the shape of an irreversible neopolarogram (full line) with a reversible (neo)polarogram(dashed line) and an irre-
versible polarogram (unconnected points) The three curves, which are given by the expressions 1 - Z()l)-i’z(-exp[)/ %tanh(NF[€- Ei/2]/RT);and where[+ 0.2072 = a n F [ € ~ / ~€]/RT;1/2&A exp(X2)erfcX where X = 0.433 exp(anF[€l/p - €]/RT); have been scaled by assuming an = N/2 and by adjusting the half-wave potentials to coincide
-
proach to solving Equation 10 will be to first consider its solution in the y 0 limit (as appropriate to neopolarograms which start at an arbitrarily large positive potential), before going on to a more general solution. Initial Potential Indefinitely Positive. Definitions 8b, 1 2 and 13 imply ( = T In y, an identity which converts Equation 10 to
+
where t is the abbreviation anF
-[E,-EI RT
1 +-In 2
(A) = t k2RT anFuD
(8b)
The derivation of Equation 8, and of the more complex relationship that covers cases in which Eo is not indefinitely positive, is accomplished in the next section. This is followed by an experimental section which attempts to verify the theoretical predictions using the reductions of iodate and nickel ions at a mercury electrode. THEORETICAL On recognition that the current i is the temporal semiderivative, i = d112m/dt112,of m, Equation 7 may be recast as
fid112m - [mc - m] exp (-a n F [E, - E O
+ ut]) (9) RT after incorporation of relationship 4. This so-called semidifferential equation (7) contains m and t as the only variables. Simplification to k , dt112
follows from the definitions m mC
-= - Y
and anFvt -= 7
RT of two undimensionalized variables to play the roles of m and t , and of one dimensionless constant,
whose value decreases as Eo becomes more positive. Our ap1672
This becomes
-
in the y 0 limit. Notice that is simply a suitably undimensionalized potential. The d1l2/[d(( m)I1/2 operator, corresponding to a lower limit of -a, is an instance of the Weyl differintegration operator (7), a class to which the rule
+
dq exp(ux) = u q exp(ux), u > 0, all q (16) [d(x + a ) l q applies. This simple rule permits immediate recognition of
as a solution to Equation 15. From here it is just a matter of changes of variable to generate the final result, Equation 8. Table I contains accurate numerical data corresponding to Equation 17 and Figure 1includes a graph of p vs. E; that is, it shows the shape of an irreversible neopolarogram. For comparison, the shapes of a reversible neopolarogram (Equation 1or 2) and of an irreversible polarogram a t a stationary electrode (8)are also included in this diagram. (By the phrase “polarogram at a stationary electrode” we mean the i vs. -E curve produced by a series of potential step experiments in which the current is measured after a constant time interval. The applied potential is changed slightly between experiments.) The three curves have been “fitted” at the half-wave point. As expected, the irreversible neopolarogram is decidedly less steep than the reversible curve. The irreversible neopolarogram is an asymmetric curve, its point of inflection lying somewhat negative of its half-wave potential. The asymmetry is mild enough to escape casual notice, how-
* ANALYTICAL CHEMISTRY, VOL. 48, NO. 12, OCTOBER 1976
Table 11. Comparison of Polarographic Features. D’Is the Diffusion Coefficient of the Reduction Product Reversible neopolarogram or polarogram
Feature
E%
E , + NF E l n B
RT 1.099 -
NF
RT
1.099 -
NF
NF
Slope at E%
4RT NF 4RT
Maximum slope Height of maximum slope (inflection point) Potential of maximum slope “Log plot” slope
(
E,+- RT In 1.23k, anF RT 0.977anF RT 0.890 anF anF -0.295RT anF -0.297RT
0.500
0.545
E%
RT E I~ 0.151-
NF
1.178 a n F
2.303 RT
2.303 RT
1 [E, - E,] + -In RT 2 to yield
m
(=)LvnFuD
E,+RT h(2.31ksE) anF RT 0.940anF RT 0.809anF anF -0.313RT anF
4.320RT
at E%
RT
E1h- 0.241anF 1.279 a n P at Eih 2.303 RT
0.5
a4
exp(-E)
(18)
Dependence on Ramp-Rate. We have established that, for irreversible neopolarograms which start at arbitrarily positive potentials, Y is a function of 6only. It follows, therefore, that the change with u of any point on the neopolarographic wave (e.g., the half-wave potential, El/,, corresponding to p = %) is that required to maintain a constant value of 6. Then by differentiating anF
-
Irreversible stationary electrode polarogram
0.576 anF
ever, and is certainly not as great as that of a classical stationary electrode irreversible polarogram. Features of the three curves are compared in Table JI. Early entries in Table I were calculated by using Equation 17. For ,$values in excess of about 2.0, the retention of sufficient computational precision makes this straightforward approach unrewarding. The parenthesized values listed in the tabulation for large 6 were calculated from the asymptotic expression l-p--
E)
Irreversible neopolarogram
0.3
0.2
= 6, = constant (19) 0.I
d In u --a n F dE, - --0 RT 2
(20)
we find that
hE, - -2.303RT (21) Alogu 2anF In words, Equation 21 states that a tenfold increase in ramp-rate will shift the potential corresponding to any particular height up the wave (Ellz,El/d,etc.) cathodically by 29.6/an mV a t 298 K. Note that changing the ramp-rate merely shifts the entire wave along the potential axis, the shape of the wave remaining unaltered. This is in contrast to linear-potential-scan voltammetry, wherein changes in u also affect the height of the response. Solution f o r Arbitrary Initial Potential. An exact solution of Equation 14, namely
is possible in terms of functions s, ( ) that are repeated semiintegrals of the exponential function. The recurrence
Flgure 2. The upper curve is the foot of an irreversible neopolarogram that started at an indefinitely large positive potential The four incomplete curves show the effect (from left to right) of making €0 increasingly less positive. The fragment marked with an asterisk shows the start of the neopolarogram for which p acquires the value 0.4900 at El,*
defines all these functions, SO( ) being unity. Via polynomial tabular values of s, (7) approximations to these functions (9)) were prepared and these enabled Figure 2 to be constructed. This diagram compares the theoretical shapes of the feet of neopolarograms that commence at various potentials. Note that the late-starting neopolarographic curves are initially vertical but that they soon veer to follow a course almost
ANALYTICAL CHEMISTRY, VOL. 48, NO. 12, OCTOBER 1976
1673
Table 111. Values of y at E% for Various Initial Potentials Y 1.000 1.500 2.000 2.500 2.622 3.000 3.500 4.000 4.500 5.000 m
0.2990 0.1814
0.1100 0.0667 0.0591 0.0405 0.0246 0.0149 0.0090 0.0053 0
LL a t E%
0.4267 0.4617 0.4792 0.4885 0.4900 0.4935 0.4963 0.4979 0.4988 0.4993 0.5000
parallel to, but slowly converging with, the neopolarogramthat started at an indefinitely positive potential. Some time after the commencement of a neopolarogram, T becomes large enough that an asymptotic summation (9) may be employed to replace that in Equation 22. Introduction of this simplification leads eventually to the result
where pm is the value that p would have had if Eo had been infinite. The integrand in result 24 is the same function that appears in the expression (Equation 17) for p m itself. Values of the integral were calculated and were, in fact, used as an aid in the construction of Figure 2. Though its restriction to large 7 must not be overlooked, Equation 24 tends to be more useful than Equation 22. The former correctly predicts that is invariably less than pm,but that these two values converge as y approaches zero or as T approaches infinity. Choice of Initial Potential. Though irreversible neopolarograms are simplest when the initial potential is very positive, in practice one must choose Eo such that no electrooxidations occur. In this subsection, the effect upon the neopolarographic half-wave potential of starting the ramp a t a less-than-infinitely positive potential will be evaluated. It will be demonstrated that, provided that the initial potential is a t least 67.4/an mV more positive than Ell2, effects are confined to the foot of the wave. Making use of Table I1 and of Equations 12 and 13, one may demonstrate that at the true neopolarographic half-wave potential (E112,correspondingto km = I&, T acquires the value -ln(1.23 y). Substitution of this value into Equation 24 gives
-1 -
1 y m (-expu)j du (25) 2 .\/-4sln(1.23y) as the expression for I* at E1/2. Values of this expression,which is a function of y alone, are to be found in Table 111. From Table 111,it is seen that y must not exceed 0.0591 to ensure that I.L lies between 0.4900 and 0.5000 at Ell2. At T = 298 K, this corresponds to the inequality
J ZOa
RT an[Eo - Ell21 2 2.622 -= 67.4 mV (26) F Of course, the foot of the irreversible neopolarogram that just satisfies this inequality will be considerably distorted (the start of this neopolarogram is shown by the asterisk in Figure 2), but, in the vicinity of Ell2 and at more negative potentials, the curve lies within experimental error of the ideal neopolarogram. Relation to Linear Scan Voltammetry. Obviously,since a neopolarogram is the semiintegral of a linear-potential-scan voltammogram, the known shapes (10) of the latter curves 1674
E ( m V va.SCE) Figure 3. Neopolarograms for iodate reduction Solution: 2.00 mM K103 in 100 mM KNOB;electrode area: 46.8 mm2; initial potential: -800 mV vs. SCE ramp-rates (mv s-’): 0 20.5, A 50.3,0 102, 205, and V 509
B
-I350
u) 0
-
-1300
P -1250
-
-1200
-
1v >
f
w
-1150
1.0
1-5
2.0
2.5
3.0
log E (mv/sec)
Figure 4. Dependence of the characteristic potentials(0,Ell4. 0 Ell*, and A 1 5on ~the ~ )logarithm of the ramp-rate. Conditionsas in Figure 3
could have been used to predict neopolarographic behavior. This method has not been followed here, because to have done so would have obscured the fundamentality of the semiintegral approach. As Reinmuth ( I I ) , in a different terminology, stressed: the linear relationship of m to the surface concentrations of electroactive species lends to m a basic significance that i does not share. In evidence of this, the shape of a reversible linear-potential-scan voltammogram (10-12) is described by the unfamiliar infinite sum
whereas m is expressed by Equation 2, in terms of a single elementary transcendental function. From a mathematical viewpoint, the neopolarogram is far the simpler curve and consequently it is appropriate to regard the linear scan voltammogram as derived from it by semidifferentiation. That Equation 27 is indeed the semiderivativeof Equation 2 follows immediately from the identity
ANALYTICAL CHEMISTRY, VOL. 48, NO. 12, OCTOBER 1976
0.e
-
0.6
-
0.4
-
0.2
-
5+ -
0
-
k
-0.2
Table IV. Summary of an Results a n for reduction of
Method
Ni2+
10,-
E x vs. log u slope E% vs. log u slope E3/4 vs. log u slope E x - Eih separation Eih - E3/4 separation Eih - E3/4 separation Slope at u = 20.5 mV s-’ Slope at u = 50.3 mV s-’ Slope at u = 102 mV s-’ Slope a t u = 205 mV s-’ Slope at u = 509 mV s-’ Mean : log (mc - m)/i vs. E slope
x
0.55 0.56 0.53 0.47-0.50 0 . 53-0.55 0.58-0.69 0.52 0.51 0.48 0.48 (0.43) 0.53 i 0.04 0.50
0.47 0.46 0.45 0.53-0.54 0.55-0.57 0.58-0.61 0.57 0.61 0.59 0.53 (0.49) 0 . 5 4 f: 0.04 0.52
2 range. Note that the cited data were not prepared using Equation 29 (which suffers the same limitations as Equation 8 at the more cathodic potentials) but by a numerical integration scheme.
EXPERIMENTAL The apparatus and technique are unchanged from those described in previous articles of this series (2,4, 14). A hanging mercury drop electrode was employed; in all cases the drop was “second hand” ( 2 ) . Reagent grade chemicalswere used without further purification. A supporting electrolyte of 0.10 M KN03 was used throughout. Two electroreducible species were examined: the iodate ion as 2.00 mM KIO3 and the nickel(I1) ion as 4.00 mM Ni(N03)~. Both these ions have been extensively studied and their reduction at a mercury electrode is well known to be irreversible.Because a rather large initial current was observed in the case of the 103- reduction, the working electrode was regularly maintained at the initial potential for about 45 s to eliminate such currents prior to the recording of the neopolarogram. Analog semiintegration was employed,using a ladder network in the feedback loop of the Princeton Applied Research Model 170’s integrator,as previously described (15). (Please note a typographical error in Figure 10 of this article; the resistor shown as 830 kS1 should have read 8300 kS1.) The m values so measured were corrected for electrode sphericity ( I , 12) by subtraction of the q D 1 / * / rterm ( q = Ji dt, r = drop radius). RESULTS AND DISCUSSION Experimental neopolarograms for iodate reduction are shown in Figure 3 for a variety of ramp-rates, u . Figure 4,de-
-.
Q-
0.2 0
I
-850
-1000
I
-IO50
I
-1100
E (mVva.SCE)
Flgure 6. Plot based on Equation 7 for nickel reduction Solution: 4.00 mM Ni(NO&in 100 mM K N 0 3 ; electrode area: 87.3 mm2; initial potential: -650 mV vs. SCE; ramp-rates: as in Figure 3
rived from Figure 3, shows how the quarter-wave, half-wave, and three-quarters-wave potentials depend on ramp-rate. As predicted in Equation 21, each characteristic potential is seen to depend logarithmically on u . The equation was applied to the slopes of the Figure 4 lines, the an values listed in Table IV being thereby calculated. Values of an may be calculated, not only from the slopes of the lines in Figure 4,but also from the displacement of these lines from each other. This is evident from the predictions in Table 11, which show that
a t 298 K. The an values calculated from these relations are also displayed in Table IV; ranges of an are reported because the lines in Figure 4 are not quite parallel. For iodate electroreduction, data determined from relations in Equation 30 demonstrate rather poor self-consistency; this reflects the fact, evident in Figure 3, that the iodate neopolarogram is slightly less symmetrical than theory predicts. Yet another way of determining an from the neopolarograms uses their slopes. According to Table 11,the irreversible neopolarographic wave has a maximum slope almost equal to its slope a t El/z,both these slopes being given within experimental precision by
ANALYTICAL CHEMISTRY, VOL. 48, NO. 12, OCTOBER 1976
1675
200
ii
150
%
-;
100
E
SO
-06x1
-BW
-
950
-1100
-1250
E I m V v s . SCE)
Figure 7. Neopolarograms for nickel(l1)reduction with various initial
potentials Ramp-rate: 102 mV s-'; other conditions: as in Figure 6
1 dm --=
-an
slope = m, d E 86.8mV at 298 K. Using this equation and the curves shown in Figure 3, an values were calculated for each ramp-rate, the results again being collected in Table IV. Apart from the datum obtained from the 509 mV/s ramp-rate (where pen response may have been a complicating factor), the values agree well and give an an average value of 0.50. Table IV permits an intercomparison of an values determined for iodate reduction by all three neopolarographic methods. Though the agreement is less than might have been hoped, the scatter averages only 0.04 and confirms that theory and experiment are in broad agreement. Possible causes of the discrepancies include: imperfect correction for sphericity, interference from nonfaradaic and other background effects, and neglect of the role of the double-layer structure (1)on the kinetics of 103- reduction. Essentially similar results were obtained for Ni2+reduction. Values of an were calculated by the same method used for 103- and the data are likewise assembled into Table IV. The agreement between an values determined by the various methods is no better than in the iodate case, but it is interesting to note that the results for the two electroreducible species do not parallel each other. This suggests that divergencies arise from idiosyncrasies of the individual systems,
rather than reflecting any general inadequacy of the theory* Finally, a method of determining an was employed that does not hinge on the theory presented in this article. This method uses Equation 7 and consists of plotting log (m, m)/i vs. E . Figures 5 and 6 show these plots for iodate and nickel ion reductions respectively. From the slopes of the lines shown in these diagrams, which, it should be noted, embrace several ramp-rates, the an values reported as the final items in Table IV were calculated. Agreement with the other tabulated values is good. Figure 7 shows neopolarograms for the reduction of Ni2+ for a variety of initial potentials. We have not attempted to correlate these curves quantitatively with theory, but the qualitative agreement with Figure 2 is evident.
ACKNOWLEDGMENT The computational assistance provided by Penny Dalrymple-Alford and Chummer Farina is gratefully acknowledged.
LITERATURE CITED (1) J. C. lmbeaux and J. M. Saveant, J. Electroanal. Chem., 44, 169 (1973). (2) M. Goto and K. B. Oldham, Anal. Chem., 45, 2043 (1973). (3) P. E. Whitson, H. W. VandenBorn, and D. H. Evans, Anal. Chem., 45, 1298 (1973). (4) M. Grenness and K. B. Oldham, Anal. Chem.. 44, 1121 (1972). (5) J. M. Saveant and D. Tessier, J. Electroanal. Chem., 65, 57 (1975). (6) K. B. Oldham and J. Spanier. J. Electroanal. Chem., 26, 331 (1970). (7) K. B. Oldham and J. Spanier, "The Fractional Calculus", Academic Press, New York, 1974. (8) P. Delahay and J. E. Strassner, J. Am. Chem. SOC.,73, 5219 (1951). (9) K. B. Oldham, unpublished work, details available on request. (IO) R. S. Nicholson and I. Shain, Anal. Chem., 36, 706 (1964). (11) W. H. Reinmuth, Anal. Chem., 34, 1446(1962). (12) A. Sevcik, Collect. Czech. Chem. Commun., 13, 349 (1948). (13) W. H. Reinmuth, Anal. Chem., 33, 1793 (1961). (14) M. Goto and K. 8. Oldham, Anal. Chem., 46, 1522 (1974). (15) K. B. Oldham, Anal. Chem., 45, 39(1973).
RECEIVEDfor review February 11,1974. Resubmitted March 16,1976.Accepted May 10,1976. The financial support of the National Research Council of Canada is gratefully acknowledged.
Optical PathIength Considerat ions in Transmiss ion Spectroelectrochemical Measurements F. R. Shu' and G. S. Wilson" Chemistry Department, University of Arizona, Tucson, Ariz. 8572 I
A transmission spectroelectrochemical cell is described in which the optical path length can be varied to enable consideration of its effect on electrochemical characleristlcs such as cell time constant. The utility of the short pathlength cell was demonstrated in the measurement of the second order homogeneous electron transfer rate constant for the reaction of horse heart cytochrome c and hexaammineruthenium(11).
Present address, Smith Kline Instruments, Inc. 880 W. Maude Ave., Sunnyvale, Calif. 94086 1676
In the course of investigating electron transfer reactions involving fast kinetics via transmission spectroelectrochemical techniques, it is necessary to measure the absorbance changes corresponding to chemical reactions taking place at the electrode surface or in the diffusion layer of the working electrode. Under these conditions, the diffusion layer constitutes only a small fraction of the total optical path length. Thus, it is necessary to measure a small difference between two large numbers if the original reactant absorbs appreciably. Clearly, greater sensitivity can be achieved by reducing the total path length. Such an approach might lead to the use of optically transparent thin-layer electrodes (OTTLE). These have been used to considerable advantage for both chemical and biochemical applications ( 1 4 ) , especially where final spectral
ANALYTICAL CHEMISTRY, VOL. 48, NO. 12, OCTOBER 1976
