ANALYTICAL CHEMISTRY, VOL. 51, NO. 8, JULY 1979
returns only a single point of best fit. Given data with any noise at all,the likelihood of the minima at several wavelengths coinciding would be quite small unless the minimum was very small and deep relative to its surroundings. This is clearly not the case for the mechanism shown here. Finally it is worthy of note that, because of the use of x 2 as the objective function, it is possible to separate those mechanisms which clearly do not fit the experimental data from those which do. There may, of course, be more than one mechanism which could fit, and it is not possible by this method to select from these the correct one. Likely candidates, however, are clearly set apart so that further investigation may focus on differentiating between the members of this smaller group.
(5) E. Steckhan and D. A . Yates, Ber. Bunsenges. Phys. Chem., 81,369 (1977). (6) C.Li and G. S. Wilson, Anal. Chem., 45, 2371 (1973). (7) E. Steckhan, Nectrochim. Acta, 22, 395 (1977). (8) I . M. Warner, E. R. Davison, and G. D. Christian, Anal. Chem., 49, 2155 (1977). (9) G. M. Ridder and D. W. Margerum, Anal. Chem.. 49, 2098 (1977). (10) H. L. S. Hanatey, T. R. Ridgway, and C. N. Reilley, Anal. Chem., 50, 116 (1978). (11) S.W. Feldberg in "Electrochemistry", Vol. 2, J. S. Mattson, H. 8. Mark, and H. C. MacDonald, Ed., Marcel Dekker. New York, 1972. (12) I. Ruzic and S. W. Feldberg, J . Electroanal. Chem., 50, 153 (1974). (13) J. R. Sandifer and R . P. Buck, J . Electroanal. Chern., 49, 161 (1974). (14) T. Joslin and D. Pletcher. J . €/ectroana/. Chem., 49, 171 (1974). (15) P. R. Bevington, "Data Reduction and Error Analysis for the Physical Sciences". McGraw-Hill, New York, 1969. (16) D. W. Marquardt, J . SOC.Ind. Appl. Math., 11, 431 (1963). (17) S. L. Morgan and S. N. Deming, Anal. Chem., 46, 1170 (1974).
LITERATURE CITED (1) (2) (3) (4)
1139
RECEIVED for review January 19, 1979. Accepted March 27, 1979. This work was supported in part by grants from the National Science Foundation PCM 76-10267 and GP-32909 and the Office of Naval Research.
T. Kuwana and W. R. Heineman, Acc. Chem. Res., 9, 241 (1978). M. D. Ryan and G. S. Wilson, Anal. Chem., 4 7 , 885 (1975). T. Kuwana, Ber. Bunsenges. Phys. Chem., 45, 2371 (1973). E. E. Wells, Jr., Anal. Chem., 45. 2022 (1973).
Spectroelectrochemistry and Cyclic Voltammetry of the EE Mechanism in a Porphyrin Diacid Reduction David L. Langhus' and George S. Wilson" Department of Chemistry, University of Arizona, Tucson, Arizona 8572 1
The electrochemical reduction of mesotetra(4-N-methylpyridy1)porphine diacid at a gold electrode has been investigated by cyclic voltammetry and spectroelectrochemistry. The reduction proceeds in two closely-spaced one-electron steps having Eo' values of -0.016 and -0,100 V vs. SCE, respectively. Spectra obtained from potential-step chronoabsorptometry experiments suggest the first electron transfer step to involve formation of a cation radical (P(-I)H4+*) and The latter the second a porphodimethene (P(-II)H,'+). species is unstable and decays to a phlorin monocation (P(-II)H5+). The rate constant for this step is 0.25 f 0.02 s-i (cyclic voltammetry) and 0.3 0.05 s-' (spectroelectrochemistry). Methods for multiparameter estimation in both cyclic voltammetry and spectroelectrochemistry are presented.
*
The porphyrin moiety has been of interest to chemists for many years, stemming primarily from its varied appearance in biological systems. I t is found in such critical centers as chlorophyll, a link in the photosynthetic process, hemoglobin and myoglobin, oxygen transport species in mammalian tissue, and cytochrome c, a component in the mitochondrial electron transport chain. Of particular interest is its behavior in the latter role where the iron atom which it surrounds is found capable of undergoing reversible oxidation and reduction. In cytochrome c, the iron porphyrin is believed buried in a crevice such that only the edge of the ring is exposed, suggesting that the ring itself is involved in electron transfer. The work of Fleischer and Cheung ( I ) , in which homogeneous electron transfer in cobalt porphyrins is postulated to take place *Present address: Department of Chemistry, M o r a v i a n College, Bethlehem, Pa. 18018. 0003-2700/79/0351-1139$01 .OO/O
primarily through the periphery of the molecule rather than axially, lends credence to this hypothesis. The electrochemistry of the porphyrin ring itself is therefore of considerable interest, and may ultimately lead to a better understanding of the role of this moiety in biological systems. Most naturally occurring porphyrins are insoluble in aqueous media, making characterization, especially by means of electrochemistry, inconvenient. Hambright and Fleischer (2) and Pasternack et al. ( 3 ) have prepared several water soluble porphyrins by attaching substituents in the meso position of the ring. Of these, the 4-N-methylpyridyl derivative is water soluble from p H 0 to 7 with no detectable dimerization ( 3 ) . At p H 0, this molecule is believed to exist as a diacid where the ring is buckled in order to expose the central nitrogens more favorably toward protonation ( 4 ) . Acid dissociation constant (pK,) values of 2.0 and 0.7 were obtained in support of a somewhat strained configuration. Neri and Wilson ( 5 ) examined the electrode reaction mechanism of this molecule in 1 M HCl via cyclic voltammetry a t a gold electrode. Reduction to the P(-11) oxidation state, which proceeded through a single, somewhat broadened two-electron wave, was followed at low scan rates by a second two-electron process, corresponding to reduction to the P(-IV) state. Both peaks were clearly irreversible under these conditions. As the scan rate was increased, the second peak decreased in height and the first became increasingly reversible suggesting the existence of an ECE mechanism. Thin-layer coulometry confirmed the two-electron reductions suggested by the size of the first and second waves, respectively. T h e involvement of protons in the first reduction is difficult to interpret, owing to the simultaneous ionization of the diacid to form the free base. When reduction was allowed to proceed only as far as the P(-11) state, a stable product was formed which was shown 0 1979 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 51, NO. 8, JULY 1979
PORPHYRIN
DIACID
PORPHODIMETHENE
PHLORIN MONOCATION
Figure 1. Porphyrin structures. Porphyrin diacid (P(O)H?+); porpho-
dirnethene (P(-II)HB2+); phlorin monocation (P(-II)H5+) t o be a phlorin monocation P(-II)H5+,having the structure shown in Figure 1. (The four positive charges due to the meso pyridinium ions (R) are ignored.) Based on the available data, the simplest mechanism appeared to involve a reversible two-electron reduction to form a n isophlorin followed by protonation to give the phlorin monocation. T h e purpose of the present study is to examine in more detail the mechanism of diacid reduction by comparing experimental curve shapes obtained from cyclic voltammetry with theory and t o obtain spectra of transient intermediates through the use of rapid scan spectroelectrochemistry.
EXPERIMENTAL Reagents. Mesotetra(4-N-methylpyridy1)porphine was synthesized as the tetraiodide salt according to a procedure described previously ( 5 ) . Solutions (0.5 mM) of this porphyrin in 1.0 M HCl were used for all investigations. o-Tolidine M (Matheson, Coleman and Bell) was used as received in concentration for evaluation of the performance of the spectroelectrochemical thin-layer cell. Apparatus. Cyclic voltammetry was performed in an H cell of conventional design fitted with a separate reference electrode compartment, and utilizing a Ag/AgCl/KCl (satd) reference electrode. Potentials are reported however vs. the saturated calomel electrode (SCE). A linear potential sweep provided by an Exact 126B VCF/sweep generator was applied to the cell by means of a Princeton Applied Research Model 173 Potentiostat. A gold wire ( A = 0.5 cmZ, was employed as the indicating electrode. Thin layer cells for the spectroelectrochemistry were assembled from two microscope slides separated by thin strips of 3-mil Fluorofilm DF1700 (Dilectrix, Farmingdale, L.I., N.Y.) and fastened with epoxy. The indicating electrode took the form of an evaporated gold film on one of the sides, having sufficient thickness to yield an absorbance of roughly 0.5 a t 550 nm. The resulting cells had a thickness of 80 km. A fixed wavelength spectrophotometer consisting of a Jarrell-Ash 82-410 monochromator fitted with two 1P28 photomultiplier tubes and an OEI (Tucson, Ariz.) 2534 log ratio amplifier was used to verify Cottrell behavior. Time-dependent spectra were obtained using a Harrick Scientific Gorp. RSS-1 Rapid Scan Spectrophotometer. Spectra over the range 400 to 700 nm were obtained a t intervals of 300 ms. All data were acquired digitally by means of a modified Raytheon Miniverter system (8) controlled by a Hewlett-Packard 2100 minicomputer with 8K core. A Burr Brown UAF16 universal active filter operated in the low pass mode was used to reject signal frequencies in excess of one half the data acquisition rate to suppress errors due to aliasing. Calculations were performed on a separate 2100 computer system equipped with 32K core, 5 megabyte moving head disc drive, and Tektronix 4002A graphics terminal. Hard copy of graphical output was obtained on a Hewlett-Packard 7200A digital X-Y plotter. The facilities of the Hewlett-Packard DOS operating system were used for software monitoring and file management. Procedure. The estimation of electrochemical parameters from cyclic voltammetry was accomplished by simulation using the explicit finite differences method described by Feldberg (7). A significant departure from this treatment lay in the calculation of the concentration change in each volume element due to homogeneous chemical reactions. It was found advantageous to treat this using expressions based upon integration of the differential rate law for a given homogeneous reaction scheme, rather than as a finite differences approximation. Although somewhat
more costly in computational time, the present approach allowed the selection of a wider variety of rate constant values, without causing instability. Care is still necessary to ensure that rate constants do not become so large that biasing errors result owing to improper coupling of the homogeneous reactions with the diffusion kinetics. For the range of rate constants employed in analysis of the porphyrin data, simulations were compared with the results of Nicholson and Shain (9) and found to agree to better than 0.5%. The simulation routine was encoded within an analysis system which, in addition to accepting parameter values, supplying them to the simulation routines and initiating simulation, also provided facilities for plotting, storing in disc files, and comparing current potential curves. Provision was also made for entering experimental data in the same format as simulations, greatly simplifying the process of comparing simulation with theory. The input of parameter values, and other functions requiring operator interaction, make use exclusively of dimensional units. Therefore potentials are entered in millivolts, first-order homogeneous rate constants in s?, concentrations in mol/L, etc. Scaling is performed internally by the simulation routine itself. The completed simulation is then presented in the form of current-potential pairs in millivolts and microamperes. Because the operator is not burdened with the complication of visualizing his data in terms of normalized parameters, using the simulation for the estimation of parameters is intuitive and does not require extensive programming skill or mathematical ability (10). As pointed out previously ( I I ) , the nonideal electrode orientation geometry of the optically transparent thin-layer cell leads to significant uncompensated resistance. However, as long as there is sufficient light throughput, the area of the indicating electrode may be decreased considerably (11). This will decrease the current but more importantly will lower the total double layer capacity. The cell used in these studies (8 X cm thick) showed theoretical Cottrell behavior for both current and absorbance for o-tolidine between 0.05 and 4 s. Deviation occurs predictably at long times owing to the finite thickness of the cell. Similar current response was observed for the porphyrin when the potential is stepped from 0.2 to -0.15 V vs. SCE. Simple Cottrell behavior for the absorbance is not observed in this case because there is no wavelength at which the reactant can be uniquely monitored.
RESULTS AND DISCUSSION Cyclic voltammograms were obtained for the porphyrin system a t several scan rates ranging over three orders of magnitude. Typical results are shown in Figure 2. Qualitatively, those curves obtained a t high scan rates exhibited a single reversible peak at about -50 mV vs. SCE. As the scan rate was decreased, the anodic peak became smaller in size relative to the cathodic peak in a manner characteristic of an EC mechanism in which the following homogeneous chemical step is irreversible. A distinctive feature of the cathodic and, t o some extent, the anodic peak was the presence of an inflection about midway up the rising portion of the wave. Such a feature might be expected if the two-electron reduction were composed of two one-electron steps with a significant separation in Eo', though not so great as t o yield two distinct peaks. T h e shape of this inflection is quite sensitive to the Eo' separation. For a mechanistic scheme to give a reasonable fit, it is necessary that the entire simulated cyclic voltammograms match the data as closely as possible over a wide range of scan rates, In initial estimation of parameters, direct comparison of the total curves is very cumbersome. Therefore a more manageable procedure, consisting of fitting only certain features of the curve was first performed. For final estimation, comparison of the total curves served t o verify the efficacy of this process. The features which were found useful for this analysis were the peak potentials of the anodic and cathodic peaks, E,, and E,, and the ratio of the anodic to cathodic peak current IJIC. T h e anodic peak current, corrected for residual current, was measured from the cathodic switch point to that a t the anodic
ANALYTICAL CHEMISTRY, VOL. 51, NO. 8, JULY 1979
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m V v s SCC Figure 2. Cyclic voltammograms of porphyrin diacid reduction in 1 M HCI as function of scan rate. (0)Experimental, (-)theory. Simulation parameters for EDEC case: Keq = 0.038, k , = 0.25S‘. Scan rate: (A) 0.0074 VIS; (B)0.075 VIS; (C) 0.31 V / s Potentia!
I
I
I
-I
0
I
Scan R o t e
Figure 3. Peak shape features as function of scan rate for porphyrin Simulation diacid reduction in 1 M HCI. (0)Experimental, (-)theory. parameters for EDEC case: k , = 3.8 X IO’ M-’ s-’, k , = 1.0 X IO9 M-’s-’. (A) Cathodic peak potential (€pc), (B)anodic peak potential (€pa), and (C) ratio of anodic to cathodic peak currents ( I J I J
(E)
and Wilson (12) for the mesotetra(2-N-methylpyridy1)porphyrin diacid. The parameters which require estimation are E? and E? for the first and second electron transfer, respectively, k f and hb for the disproportionation step, and k , for the irreversible chemical step. Thermodynamic considerations require that the equilibrium constant for disproportionation be given by:
A will be shown t o correspond to the porphyrin diacid, C to a porphodimethene, and D to a phlorin monocation. B corresponds to a P(-I) species similar to that observed by Neri
Figure 3 shows feature variation for several values of k , with kf/kb = 0.038 as defined by K,,. I t will be noted that at high scan rates, E,, is independent of scan rate because the rate of the irreversible chemical step is insufficiently fast to significantly affect the concentration of C a t the electrode surface. Since Elo’ is quite anodic of E?‘, E,, is dictated primarily by the potential of the last process to take place,
peak potential. The cathodic switch potential must be constant with scan rate because of the time dependence of the following chemical step. T h e following reduction mechanism was found t o yield a satisfactory fit t o the cyclic voltammetric data:
A + e - s B ki
2B$A+C kb
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ANALYTICAL CHEMISTRY, VOL. 51, NO. 8, JULY 1979 I
0 -
/ /
400
500 Wavelength
L:;
SCOl
70'C
Figure 4. Peak current ratio as function of scan rate for EDEC case Simulation parameters same as Figure 2
t h a t is, E2". As scan rate decreases. the consumption of C causes the cathodic peak to rise and shift in an anodic direction as observed by Nicholson and Shain (9). The value of h l , therefore, dictates the scan rate a t which this anodic shift will begin to appear. Because the disproportionation is a reversible process, it has a negligible effect on E,,, except where C is consumed by the C to D reaction to a very large extent. If kf is large enough, it is possible to supply a small amount of C to the electrode by this means. E , is also found to be independent of scan rate at high scan rates. While its value is primarily dependent on Elo', the location of the peak corresponding to E2' also exerts a small influence, causing motion of this peak as scan rate is lowered and the C to D reaction begins to proceed to a significant extent. Because of the large amount of B present through the disproportionation reaction, coupled with the possibility of supplying B from C, the rate of this reaction has a significant effect on E,, also. T h e anodic to cathodic peak current ratio (Figure 3C) is, as expected, very sensitive to the characteristics of following chemical reaction. As in the case of the other features, no scan rate dependence is observed above 1 V / s at which point the system behaves like a reversible E E case. For this system, Figure 3 indicates that h l is clearly about 0.3 s-l. El0' and Ezo' can be estimated from the scan rate independent region. At high scan rates, there is some deviation from theory due to uncompensated resistance and possibly adsorption. More accurate estimates of the Eo' values can be made in the 0.5 V / s region. Final values obtained for Elo'and E? were -0.016 and -0.100 V vs. SCE, respectively. Heterogeneous electron transfer can be shown to be fast for both steps, i.e., k , > 0.1 c m / s (13). Given the value of k l , it is clear that the disproportionation rate must be in excess of IO3 L/mol-s in order to observe the required amount of material available for reoxidation, (see Figure 4). Optimal fitting of all parameters requires comparison of the total current-voltage curves from experiment and theory. Figure 2 illustrates the high quality of the fit obtained for the same parameters as the scan rate is varied over nearly two orders of magnitude. Two simpler reaction schemes which did not involve the disproportionation step were also investigated. These were the simple EEC case (two one-electron transfers followed by an irreversible homogeneous chemical step) and the EECC case in which the two homogeneous reactions follow serially, the first reversible and the second irreversible. Both of these, when f i t to the E,, and E,, data, give IJZ, curves like that in Figure 4 corresponding to the case where h b = 0 for the EDEC reaction scheme. As a result, the anodic peak current a t low scan rates is signifi-antly smaller than that observed experimentally. It is not possible to adjust k l to compensate for the lack of oxidizable products a t the electrode surface.
Figure 5. M HCI
600
700
nm
Time dependent spectra for porphyrin diacid reduction in 1
The mechanism involving disproportionation is, therefore, the simplest mechanism that can account for the cyclic voltammetric behavior observed. Because species B is apparently stable to following chemical reaction, the effect of the disproportionation is to produce B a t the expense of c, thus resulting in a larger anodic current. Spectroelectrochemistry. The observation of Cottrell behavior (current) upon application of a potential step suggests an overall 2e process. If there are intervening chemical steps between the one-electron transfers, they must be extremely fast. The potential step data also permit calculation of the diffusion coefficient for the starting material. A typical set of time-dependent spectra resulting from the potential step is shown in Figure 5 . While 15 spectra were taken in this experiment a t intervals of 0.3 s, only every third spectrum is shown for clarity. The starting material spectrum, obtained before application of the potential step, and the final product spectrum, acquired after exhaustive electrolysis has been allowed to take place. are also shown. A base-line spectrum, obtained in a separate experiment, was subtracted from the raw data to obtain these base-line corrected spectra. Note that, although the final product peak is broad, it occurs at a somewhat shorter wavelength than the rising peak of the time-dependent spectra themselves. This is most clearly seen in the 55Ck570 nm region. This must result from the presence of at least one intermediate with a strong absorption above 500 nm, inasmuch as the starting material has no significant absorbance there. No other information can be obtained through cursory inspection of the raw data. To deduce the spectra of the intermediates, therefore, will require a parameter estimation method. The EDEC mechanism was postulated as the candidate for fitting to the time-dependent spectra obtained from the porphyrin system. For the potential step perturbation, it is reasonable to assume t h a t species A is converted rapidly to C a t the electrode surface such that no significant amount of B would be present there. However, as C diffuses from the electrode surface, it encounters molecules of A and can reproportionate, forming additional B which may then diffuse back to the electrode to be reduced, or out into solution where it is assumed unreactive. If equilibrium is favorable toward reproportionation, significant quantities of B may be present, and must be accounted for when calculating the theoretical total absorbance (14). The physical parameters which require assignment to simulate the absorbance-time behavior of this mechanism include the molar absorptivities of all four species, as well as the diffusion coefficient of the diacid, the rate constants for disproportionation, kf and kb, and the following chemical step rate constant, kl. Of these, the molar absorptivities of A and D at each wavelength are known since these species are stable and their spectra may be recorded. The diffusion coefficient
ANALYTICAL CHEMISTRY, VOL 51, NO. 8, JULY 1979 ~
~
1143
-_
3 h
-0 5
0 0 -I
- 1.5
Waveenc
n
nm
Figure 7. Estimated spectra for intermediates B and C
CONCLUSIONS 2
-I Log
0
i
kl
Figure 6. Contour plot of experimental spectral data for porphyrin reduction at 500 nm Shaded area indicates value of k , l k , determined from cyclic voltammetry
is estimated from the current vs. t profile. The results of the cyclic voltammetry analysis indicate that the disproportionation rates, k f and h b , are sufficiently fast that the equilibrium only between species A, B, and C need be considered as long as k l is less than about 100 s While this assumption IS not necessary, considerable simplification of the simulation results if it is made. There remain then four parameters which must be estimated: the molar absorptivities of B and C , the disproportionation equilibrium constant. kf/kb, and k,. Since the molar absorptivities appear linearly in the expression for total absorbance, they may be estimated via linear least squares, for any set of parameters. Thus k , / k b and h i are the only nonlinear parameters yet to be assigned, a situation ideally suited for the plotting of a two-dimensional contour map. The contour lines are expressed in terms of the reduced x2 statistic. A value of unity represents the best possible fit of theoretical and experimental data consistent with such considerations as the variance of individual measurements and the number of adjustable parameters. T h e details of these calculations and the advantage of this approach are described in more detail elsewhere (15). Figure 6 is typical of the contour map for these data at different wavelengths. The region bounded by the ''1" contour line therefore constitutes the interval of best fit of experiment and theory. The nature of this mechanism makes the shape of the absorbance-time curve rather insensitive to the k , / h h ratio. Further, noise on the absorhance signal also tends to obscure minima. If the k f / f b ratio obtained from cyclic voltammetry is used, it is then possible to suggest a region in which k l might lie. Taking into account the behavior at several wavelengths and assuming that the optimum value lies within the X2-unity region, I ; ! may be estimated as 0.3 IO.05 s-'. While there is yet a roughly 30% chance that the optimum lies outside this region, the agreement with the cyclic voltammetry value of 0.25 f 0.02 s-l is nonetheless impressive. Given these values for the mechanistic parameters, it is now possible to employ the linear least squares algorithm to obtain spectra for the intermediates from the time-dependent spectra. Intermediate B is found to have a large absorption > lo5 M cm-') in the Soret region around 450 nm, but shifted slightly toward shorter wavelength, as well as the possibility of some smaller absorption bands toward the red. C exhibits a single broad absorption centered at 510 nm. This band also has a molar absorptivity greater than lo5. The spectra are shown in Figure 7 .
On the basis of both cyclic voltammetry and rapid scan spectroelectrochemistry, the first two-electron reduction of the porphyrin diacid has been shown to fit an EEC mechanism with dispropwtionation of the one-electron product. The disproportionation equilibrium constant (K,) is 0.038 f 0.005 aiid the rate constant of the final chemical reaction (K,) is 0.25 f 0.02 s-'. For reasons discussed above, it is not possible to interpret definitively the p H dependence of the two oneelectron steps. However, the initial two-electron reduction product yields a distinctive spectrum with a strong absorption maximum a t 510 nm. A similar spectrum was observed by Dolphin (6) for a porphodimethene formed during the oxidation of a phlorin monocation to the corresponding porphyrin diacid. Formation of a porphodimethene (P(-II)H6") requires the addition of two protons and two electrons to the diacid (P(0)H:'). The ring strain in the porphodimethene is relieved by loss of a proton to form the stable phlorin monocation. We had previously suggested an isophlorin as the initial product of the two-electron reduction ( 5 ) . Although we see no spectral evidence for such an intermediate, it may still have a very short transient existence prior to protonation resulting in formation of the porphodimethene. The one-electron reduced product has a spectrum very similar to the previously reported cation radical \P(-I)H,+.) of mesotetra(2-hr-methylpyridyllporphine diacid (12), a stable species. The following mechanism is therefore suggested:
2H'
+ 2P(-I)H4+*
kf
P(0)Hd2+
+
kb
P(-1I)He2+
P(--I)H4+.+ e-
K,, = 0.038
+ 2H+ r? P(-II)H62+
-
k , = 0.25
P(-II)H~*+
E20'
P(-II)H~++ H+
The combination of spectroelectrochemistry and cyclic voltammetry has made possible mechanistic interpretation which could not be accomplished by either technique alone. In particular, the observation of spectra of reactive intermediates has facilitated measurement of both structural and dynamic properties of porphyrin redox reactions.
LITERATURE CITED (1) E. 8. Fleischer and S. K. Cheung, J . Am. Chem. SOC..98, 8381 (1976). (2) R. Hambright and E. B. Fleischer, Inorg. Chem.. 9, 1757 (1970). (3) R. G. Pasternack et all, J . Am. Chem. Soc., 94, 4511 (1972). (4) R. G. Pasternack, N. Sutin, and D. H. Turner, J . Am. Chem. SOC.,98, 1908 (1976) (5) B. P. Neri and G. S. Wilson, Anal. Chem., 44, 1002 (1972). (6) D. Dolphin, J . Heferocycl. Chem., 7, 275 (1970). (7) S.W. Feldberg in "Electroanalyticai Chemistry", Vol. 2, A . J. Bard, Ed., Marcel Dekker, New York, 1969, pp 199-296.
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ANALYTICAL CHEMISTRY, VOL. 51, NO. 8, JULY 1979
(8) L. Ramaley and G. S. Wilson, Anal. Chem., 42, 606 (1970). (9) R. S. Nicholson and I . Shain, Anal. Chem., 37, 178 (1965). (10) D. L. Langhus, Ph.D. Dissertation, University of Arizona, Tucson.Ariz., 1978. (11) F. R. Shu and G. S. Wilson, Anal. Chem., 48, 1676 (1976). (12) 8.P. Neri and G. S. Wilson, Anal. Chem., 45, 442 (1973). (13) M. D.Ryan, J . Nectrochem. Soc., 125, 547 (1978). (14) T. Kuwana, Ber. Bunsenges. Phys. Chem.. 77, 858 (1973).
(15) D. L. Langhus and G. S. Wilson, Anal. Chem., preceding paper in thls issue.
RECEIVED for review January 19, 1979. Accepted March 27, 1979. This work was supported in part by grants from the National Science Foundation PCM 76-10267 and G P 32909 and the Office of Naval Research.
Comparison of Spinning Dropping Mercury Electrode Response with Polarographic and Rotating Disk Electrode Theory H. J. Mortko' and R. E. Cover" Department of Chemistry, St. John's University, Jamaica, N e w York
The relationships between the responses of the spinning dropping mercury electrode (SDME) and polarographic theory are examined. The parameters utilized included droptime, speed of rotation, rate of mercury flow, and electrode area. Although diffusion-controlledmass transfer is not applicable to the SDME, close correlation exists between SDME response and polarographic theory. The relationship between current density and angular velocity at the SDME is consistent with that predicted for the rotating disk electrode (RDE) and the rotating spherical electrode (RSE). Finally, an evaluation of the Reynolds Number ( R e ) reveals that the disk electrode theory is adhered to by the SDME in both the laminar and turbulent flow regions.
T h e improved analytical response of the spinning dropping mercury electrode (SDME) in systems containing undesirable polarographic phenomena has been demonstrated ( I , 2). Significantly, maxima of the first and second kinds are completely eliminated without the addition of a maximum suppressor. This advantage is not shared by Kolthoffs rotating dropping mercury electrode (RDME) (3). The RDME generates a maximum of the second kind and therefore requires the constant use of a surface active material before useful data can be obtained. Moreover, catalytic and kinetic waves and the undesirable effects of adsorption and convection are greatly minimized if not completely eliminated. These advantages as a n analytical detector are not shared by any other electrode except the vibrating dropping mercury electrode (VDME) ( 4 , 5 ) . In addition to these advantages, the ability to seal the SDME capillary into a small stream permits adaptation t o stream analysis and automated equipment. These advantages of the SDME as a n analytical detector have prompted a study of the theoretical nature of the electrode response. Because of the unquestionably complex hydrodynamics a t the electrode surface, conformity to existing theory was sought rather than a new theory based on a detailed consideration of the transport phenomena involved. T h e range of parameters over which the electrode was studied are: total head pressure, 30 to 50 cm; rotational speed, 0 t o 7000 rpm; drop time, 3.0 x lo-' to 12.1 s; and rate of mercury flow, 0.35 t o 1.1 mg sxl. Present address: Vick Research and Development Laboratories, 1 Bradford Road, Mt. Vernon, N.Y. 10553. 0003-2700/79/0351-1144$01 .OO/O
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EXPERIMENTAL Apparatus. The SDME apparatus has been previously described ( I ) . The capillaries used had an 0.d. of 0.63 cm and a bore of about 59 pm. All polarograms were recorded with a Sargent Model (XVj polarograph. No auxiliary damping was used in obtaining any of the data beyond that inherent in the recorder. .411 currents were mean currents determined by conventional extrapolation techniques. All experiments were performed at 25 0.05 "C. All drop times were measured, with the working electrode potential set at the beginning of the plateau of the wave, by amplification of the voltage drop across a suitable precision resistor in series with the cell. A variable gain operational amplifier circuit patched on an Electronics Associates Inc. Model TR-20 analog computer was used to amplify this voltage drop. The amplified voltage drop was displayed on the Y-axis of a Model 453 Tektronix oscilloscope using an internally time-calibrated X-axis. Several drop times were photographed with a Model C-30A Tektronix camera while the oscilloscope was set in the single-sweep mode. The mean drop time was determined from the measurement of a minimum of five individual drop times. All mercury flow rates were measured using conventional techniques for a minimum of 5 min with the working electrode potential set at the beginning of the plateau of the wave. All other apparatus used have been previously described ( 4 ) . Reagents. All reagents were J. T. Baker or Mallinckrodt reagent grade. RESULTS AND DISCUSSION All polarograms, except where noted, refer to the reduction of 4.00 m M Cd(I1j in 0.1 M KNO,. Cadmium(I1) in this system is well known to be reversible and diffusion-controlled under polarographic conditions. For these reasons, this system was chosen to evaluate SDME responses. D r o p Time. T h e drop time a t the SDME is primarily controlled by the rotational speed of the capillary and, from 5000 to 7000 rpm, is unaffected by head pressure, Figure 1. This combination of head pressures and capillary characteristics produced a nearly constant drop time of 0.03 s over this rpm range. The small drops formed a t the SDME fall straight down from the capillary tip, as with the DME. Rate of M e r c u r y Flow. Under polarographic conditions, the rate of mercury flow, m, in mg s-l from a capillary has been demonstrated to obey an equation of the form where h is the head pressure, N is a constant which can be related to capillary dimensions and the properties of mercury, and Bexp is the experimental back pressure. C 1979 American Chemical Society
