Electrochemical Studies of Rapid Photolytic Processes A Theoretical and Experimental Evaluation of Potentiostatic Analysis in Flash Photolyzed Solutions J. R. Birk' and S . P. Perone Department of Chemistry, Purdue University, Lufayette, Ind. 47907 The application of electrochemical techniques to the study of rapid photolytic processes i n solution has been limited previously by serious electronic disturbances caused by flash photolytic instrumentation, by a lack of theory relating second-order photolytic rate steps t o observed electrolysis currents, and by the lack of a quantitative evaluation of the effects of electrochemical measurements of nonhomogeneous solutions produced by flash irradiation. The work reported here attempts to examine and minimize these limitations. The electrochemical monitoring technique utilized was potentiostatic analysis a t a hanging mercury drop electrode located i n the flash-photolyzed solution. Instrumental improvements have been made extending the time resolution by a factor of 20 over that previously attained; theoretical expressions correlating second-order photolytic rate processes with current-time behavior a t a stationary electrode have been described and evaluated; and a theoretical and experimental evaluation of solution nonhomogeneity and its effects in these photo-electrochemical experiments has been presented. Kinetic data for the dimerization of the ketyl radical and ketyl radical anion produced in the flash photolysis of benzophenone are reported with time resolution as short as 50 psec. I n addition, derived relationships correlating transmittance characteristics with electrochemical response have been evaluated experimentally.
BOTHBERGet al., (1-6) and Perone and Birk (7) have demonstrated the general applicability of electroanalytical techniques to the study of photolytic processes. Qualitative information has been obtained from current-potential plots with the polarographic technique using continuous irradiation (2, 4, and with the stationary-electrode potentiostatic technique using flash irradiation (7). Rate data have been obtained by a variety of techniques which have included time-delayed potentiostatic analysis (7), classical kinetic analysis (3, 4), and theoretical electrochemical kinetic-diffusion studies (3,6). The technique of time-delayed potentiostatic analysis was developed previously in this laboratory and was found to be generally applicable to rate studies of photolytic processes (7). Because it is equally applicable to second- as well as first-order processes, this technique is particularly advantageous for unknown systems. It was found to be especially useful for the 1 Present address, Chemistry Department, Atomics International, Canoga Park, Calif.
(1) H. Berg and H. Schweiss, Elecfrochim. Acra, 9, 425 (1964). (2) H. Berg, Z.Ana/. Chem., 216, 165 (1966). (3) H. Berg and H. Schweiss, Monarsber. Deuf. Akad. Wiss. Berlin, 2, 546 (1960). (4) H. Berg and H. Schweiss, Nafure, 191, 1270 (1961). (5) H. Berg, H. Schweiss, and D. Tresselt, Exprl. Tech. Physik, 12, 116 (1964). (6) K. E. Reinert and H. Berg, Monatsber. Deur. Akad. Wiss. Berlin, 4, 26 (1962). ( 7 ) S. P. Perone and J. R. Birk, ANAL.CHEM., 38, 1589 (1966).
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ANALYTICAL CHEMISTRY
study of second-order processes for which rigorous theoretical electrochemical relationships have not been obtained, However, the technique could not be applied to very fast photolytic reactions because charging current limits the measurement time. Because the delay time must be considerably larger than the measurement time, reactions with half lives of about 5 msec or less cannot be studied accurately with this technique under the present experimental limitations. Another difficulty encountered in electrochemical monitoring of flash photolysis processes is that there is an extremely complex nonhomogeneous distribution of intermediate produced by the flash. This nonhomogeneity around the electrode might handicap the electroanalytical approach because theoretical electrochemical relationships are usually derived with assumption that the solution is homogeneous. Also, the direct study of second-order rate processes requires knowledge of absolute concentrations of the species undergoing reaction. The primary objectives of the work reported here were to improve the time response of potentiostatic analysis of photolytic processes, to develop mathematically and to evaluate experimentally a technique to obtain second-order kinetic data directly from analysis of potentiostatic current-time curves, and to evaluate the effect of the nonhomogeneity of the electroactive intermediates due to absorption by the solution and also due to shadows from the electrode. To evaluate the theory developed, the flash photolytic reduction of benzophenone was investigated. The mechanism has been described in detail elsewhere (8, 9). To evaluate the equation derived for the determination of second-order rate constants from current-time data, the reaction of the ketyl radical with the ketyl radical anion was investigated: OH
I
Cp-c-Cp-
OH 0-
0I
k
+ +-c-r#l+
I 1 I 1
Cp--c-c-Cp-
(1)
$ 6 This reaction was chosen because the rate can be conveniently changed over a wide range by varying the pH (9); the rate constants at several pH values have been determined previously using spectrophotometric monitoring (9); and the electrochemistry has been well defined (10-13).
(8) A. Beckett, Ph.D. thesis, The University, Sheffield, England, 1963. (9) A. Beckett and G. Porter, Trans. Faraday SOC.,59,2038 (1963). (10) P. J. Elving and J. T. Leone, J. Am. Chem. SOC.,80, 1021 (1958). (11) W. Kemula, 2. R. Grabowski, and M. K. Kalinkowski, Nufurwiss, 22, 514 (1960). (12) S. P. Perone, Ph.D. thesis, Univ. of Wisconsin, Madison, Wis., 1963. (13) M. Suzuki and P. J. Elving, J. Phys. Chem., 65, 391 (1961).
EXPERIMENTAL Cell, electrodes, monitoring instrumentation, previous flash instrumentation, procedure for time-delayed potentiostatic analysis, general experimental procedure, and reagents, except for buffers, were described earlier (7). The hanging mercury drop electrode (HMDE) was the working electrode. The cell used for electrochemical measurements on irradiated solutions was modified such that a 1-inch diameter open quartz tube was sealed in the cell. The bottom half of the quartz tube was fitted with a stainless steel reflector, and the flash lamp was positioned within the tube for flash experiments. Trigger and Flash Instrumentation. Poor time resolution in the previous application of potentiostatic analysis to flash photolytic studies (7) was the result of current saturation of the potentiostat amplifiers coincident with the flash. The initial instability apparently was associated with capacitive loading of the controlling potentiostat amplifiers. Because the potentiostat was attempting to control the potential across the capacitive double layer of the working electrode, it was assumed that that was the source of instability when coupled with the flash discharge. A series of empirical studies (14) designed to eliminate the source of the instability and/or minimize the effects resulted in the development of a novel flash-lamp triggering technique which was used in this work. The procedure adopted was to connect the negative end of the floating high voltage to a length of hook-up wire wrapped around the flash lamp after a potential near the self-flash potential was applied to the flash lamp. The flash voltage used was 10,000 V across a 6-pF capacitor bank (yielding better than 300 J of energy). In addition, a resistance of 1 ohm (rated at 75 W) was added in series with the flash lamp so as not to exceed its maximum current capabilities. Also, the leads between the capacitor bank and flash lamp were kept as short as possible so that inductance was minimized. Calculated and measured flash-times were the order of 7 psec. In order to provide magnetic as well as electric shielding all leads used in the work presented here were covered with flexible steel conduit, and the flash box described previously (7) was also covered with sheets of galvanized steel. Improvement of time resolution by about an additional factor of two was obtained with this degree of shielding. The result of using magnetic shielding along with the new triggering procedure and flash instrumentation is shown in Figure 1 where the time resolution has been improved by a factor of about 20 over what had been attained previously (7).
(14) J. R. Birk, Ph.D. thesis, Purdue University, Lafayette, Ind., 1967.
Figure 1. Continuous potentiostatic analysis following flash irradiation, 50-psec time resolution Top: Analysis of benzophenone solution (8 X 10-3M in 0.25M NaOH, 80 ethanol). Bottom: Analysis of a blank (0.25MNaOH, 80% ethanol). Horizontal: 50 Msec/div. Vertical: 50 pA/div. Potential: -0.700 V us. SCE. The straight horizontal trace across each photograph is the zero current line; the curved trace in the upper photograph is due to the oxidation of the ketyl radical and/or ketyl radical anion Reagents. All chemicals used were reagent grade. Water was purified by distillation and passage through a mixedbed ion-exchange column. Solvent-saturated, deoxygenated high purity nitrogen was used to deaerate all solutions before photolysis, and the nitrogen continued to flow through the upper half of the sample solution during all experiments, ~
~~
~~
Table I. The Effect of pH on the Rate of Dimerization of the Ketyl Radical with Radical Anion PH tl/P k, M-1 sec-1 kb, M-1 sec-1 Buffer 1o.w 90 psec (0.9 =k 0.3) X 108 1 . 8 X 108 0 . 1M glycine/NaOHd 11.0 600 psec (1.3 =t 0.4) X 107 1 . 8 x 107 0.04M NarCOp' 12.0 5 . 5 msec (1.6 =t 0.5) X 106 1 . 8 X 108 0.01M NaOHd 13.0 64 msec (1.4 =k 0.4) X 106 1 . 8 X 106 0.1M NaOHd 13.0 1 . 3 x 106E 0.1 M NaOH. 0.25M OH(4.9 f 1.5) x 1041 7.1 x 104 0.25M NaOH 0.25M OH48 msec (5.3 f 1.6) x 104 7 . 1 x 104 0.25M NaOH 0.50M OH0.21 sec (3.6 f 1.1) X 10' 3 . 6 x 104 0.50M NaOH a Average value of l/kCRo for series of experiments at each pH. Using Beckett and Porter's (9) results: Log(k,bJ = -pH 18.25. 5 Kinetic measurement made after the half life for this pH. Enough tetramethyl ammonium chloride added to make ionic strength = 0.25. From Berg and Schweiss (4). Time-delayed potentiostatic analysis.
+
'
VOL. 40, NO. 3, MARCH 1968
497
because this did not interfere with the photo-electrochemical studies. The buffers were prepared in aqueous solutions and measurements of pH were on the buffer diluted to the proper concentrations with water. Beckett (8) reports that this pH and the actual pH of the aqueous-alcohol solution are very close assuming the pK, in the S O X alcohol solution is 14. The buffers and their concentrations after dilution are included in Table I. RESULTS AND DISCUSSION
Theory for Simultaneous Electrolysis and Photochemical Reaction. The potentiostatic current-time relationship for
uncomplicated diffusion-controlled potentiostatic electrolysis at a planar electrode is given by the Cottrell equation: id = nFADR112CRo/(?rt)112
(2)
Here, the diffusion current, id, is determined as a function of the number of electrons, n, the Faraday, F, the area of the electrode, A , the diffusion coefficient, DR,and the bulk concentration, C R o at , time t . However, if the electrolysis is complicated by a simultaneous chemical decomposition of the reactant, the corresponding kinetic-diffusion boundary value problem must be evaluated to obtain the appropriate currenttime relationship. The process under consideration here is as follows:
O t -neA RI
2R4Z
(3)
f# =
id(cR/cRo)
(10)
Thus, one might postulate at least a limiting form of the solution to the second-order case. Using Equation 10 and solving for CR/CRO from the second-order rate law, Equation 11 is obtained: id/it = 1 d k2CRot
(11)
This equation ought to be valid for the second-order case at time zero before a concentration gradient is estabbshed at the electrode surface. Solving a second-order equation by analogy with the firstorder case is not ordinarily legitimate for heterogeneous electrochemical schemes; however, this approach has not been applied previously to a situation where the reactive species is present homogeneously in solution around the electrode, as is the case described. It is expected in this case that, at short times at least, the current will be influenced primarily by bulk concentration changes, as predicted by Equations 9 and 11, rather than by the shape of the concentration gradient near the electrode. Severe distortion of the diffusion-dependent concentration gradient by the second-order rate process should not be encountered at times which are short compared to the half-life times. Thus, it is proposed that Equation 11 might be used for the kinetic analysis of potentiostatic data obtained at times which are sbort compared to t t i z in flash photolysis experiments. EXPERIMENTAL RATE STUDY
where kz is the second-order rate constant. Here the photolytic production of R is assumed to be instantaneous and homogeneous in the vicinity of the electrode. Thus, it is equivalent to saying that an unstable chemical system is set up at time zero. The subsequent measured electrolysis of R is assumed to be controlled by kinetics and diffusion only. Mathematically, the situation involving kinetics and diffusion at a planar electrode can be described by Fick‘s laws to obtain the following boundary value problem: (4)
Flash photolysis experiments were performed with 4 x lO-4M benzophenone in 50% ethanol at various pH values between 10 and 14 where the ketyl radical reacts with the ketyl radical anion (Equation 1). The hanging mercury drop working electrode (HMDE) was held at -0.700 V us. SCE at which point the radical species are oxidized to benzophenone ( I I , 1 2 ) . Current-time curves were obtained at the appropriate time resolutions, and 1/it(t)l/2 was plotted against t as shown in Figures 2 and 3. This plot arises from the following equation: I/it(f)”’ = I/K’
+ (kzCRo/K’)f
(12)
Equation 12 was derived from Equation 11 by dividing through by K‘ which is a constant term defined as : Here x is the distance from the electrode; t is the time after R is initially produced around the electrode, which is being held at constant potential; i r is the current at time t ; k2 is the second-order rate constant; and CR(x, t ) is the concentration of R at x and t . The boundary conditions are:
CR(0, t ) = 0
limit CR(x,t ) = c R o / l X+rn
(1
> 0)
+ kzCRot (t 2 0)
(7) (8)
Unfortunately, an explicit solution to this boundary value problem for the second-order case cannot be obtained. However, the analogous case involving a first-order chemical reaction is amenable to solution (6). The solution for the first-order case is: it = id exp (-kit)
(9)
where kl is the first-order rate constant. Solving for exp( - k d ) from the first-order rate law and substituting into Equation 9, the following equation is obtained: 498
ANALYTICAL CHEMISTRY
K’ =
id(f)’/’
(13)
Equation 13 was obtained from Equation 2 where
K’ = nFADR1/2CRo/(?r)1/2
(14)
showing the relationship between K’and CEO. The value for K’ was obtained from the intercept of an experimental plot of Equation 12. C R ocould be directly related to K’ using Equation 14; however, the diffusion coefficient for the radical is not known. Therefore, Equation 15 was used to obtain the initial concentration of the radical. CRo = K’(Coo/K”)A,
(15 )
Here K” is i,&)1/2, experimentally measured for the electroreduction of benzophenone in acid solution where n = 1; C O O is the bulk concentration of benzophenone involved in the determination of K“; and Ar is the electrode area ratio between experiments performed on benzophenone alone as compared to the flash experiments where the radical is being observed. The assumption used in deriving this equation from Equation 14 was that the diffusion coefficients for benzophenone and the ketyl radical are very close.
20
40 TIME, MSEC
60
Figure 3. Second-order kinetic plot from continuous potentiostatic current-time curve following flash irradiation, pH 13
K' (from intercept) Figure 2. Continuous potentiostatic analysis following flash irradiation, pH 13 4 X lO-'M benzophenone in50%ethanol, pH 13. Horizontal: 10
msecldiv. Vertical: 0.5 pA/div. Potential: -0.700 V cs. SCE. The upper two traces represent current due to oxidation of the radical; the lower trace is the instrumental response to the trigger only, where the potential across the electrodes of the flash lamp was not sufficient for a flash
By multiplying the slope of the kinetic plot (Equation 12) by K ' , k2CRocould be determined. The rate constant, kp,could then be calculated by using Equation 15, with the appropriate limits for A,, to determine C R o(these limits are discussed below). Rate constants obtained in this manner as a function of pH are given in Table I. The validity of this kinetic technique is demonstrated in several ways: (1) the plot of l/il(t)l'* cs. t yields a straight line as predicted by Equation 12 (deviations at long times are discussed below); (2) the average value of K' obtained from the intercepts was (7.5 =t1.3) X lo-' amp -set*/*, which compares favorably with the value of 7.8 X lO-'amp -sec1I2obtainedfor oxidation of the radical under conditions where the rate of the second-order reaction was negligible-Le., 0.5M base, 500psec time resolution; and (3) the rate constants obtained by Beckett and Porter (9), by Berg and Schweiss at pH 13 (4),and by time-delayed potentiostatic studies here at 0.25M OH- are all consistent with those obtained by this technique. It should be pointed out that the rate constant obtained here in 0.5M NaOH (see Table I) is significantly higher than that obtained previously (7). This may result from the fact that in this set of experiments 50% instead of 80% ethanol was used, and the method of estimating the concentration of radical used previously was inaccurate. EXPERIMENTAL DEVIATIONS
Evaluation of kinetic data from a plot of Equation 12 did not always appear applicable. For example, at pH 1 1 , measurements made after the half life did not fall on the same straight line as those obtained before the half life (Figure 4). Also, the rate constant calculated for pH 10 (obtained from measurements after the half life) appeared to be low. This problem was not observed for higher pH's where the secondorder reaction was slower, and all measurements could be taken before t,;z.
= 6.1 X 106M-l sec-l, r + = 64 msec
A-seck, k2
=
(1.43 i. 0.45) X
This result was not surprising because the boundary value problem for the second-order case was not solved rigorously. Undoubtedly, severe distortions of the electrolytic concentration gradient at the electrode surface by the second-order process at times long compared to the half life were responsible for this phenomenon. However, by restricting measurements to times less than the half life, it appeared that valid secondorder rate data could be obtained. Also, it appeared that rate constants obtained by measurements after 1 1 1 2might be low by about a factor of 2. Uncertainty in Initial Concentration of Intermediate at the Electrode. Just after the flash, nonhomogeneous solutions of photolytic intermediate and product are caused by shadows cast during the flash by the HMDE, and by a decrease of quanta with length from the flash lamp because of absorption. The first of these will be considered later in this section. By a derivation (14) analogous to that used in fluorescence studies (15) an expression has been obtained for the concentration of intermediate initially formed CRo(b),as a function of the light path length, b; concentration of reactant before the flash, Coo; quantum efficiency, a; instantaneous initial quanta of monochromatic light per unit area, Qo; and the absorption coefficient, a : CRo(b)= ~Qo[aCoolexp(&Coo)
(16)
From Equation 16 it is apparent that, at a given distance in solution, there is a certain initial concentration of reactant that will yield the maximum amount of intermediate. Equation 16 was derived under ideal conditions where Coo does not change during the flash, the light is monochromatic, and no other absorbing species are produced during the flash. In the more realistic situation these assumptions are not valid. The effects of the discrepancies between the real and ideal situation are discussed below. Because the reactant is depleted and other species are being produced from the reactant throughout the duration of the flash, the transmittance term-i.e., the exponential term in Equation l b w h i c h accounts for the absorption of light in increment b, is only approximate at best. The quantity in (15) D. M. Hercules, ANAL.CHEM., 38,29A (1966). VOL 40, NO. 3, MARCH 1968
499
Table 11. Effect of Nonmonochromatic Irradiation on Concentration of Intermediate Produced Relative average value of Area Ca0(b) when under absorption radiant energy curve between falls between (humax
- Xu)
+
(Xumax
- Xu)
+
XU)* and (XU.,,, XU)C - a ) / a ' ~ and (XU,,, 0.05 17.8 0.90 0.10 25.2 0.90 0.25 39.4 0.94 0.45 52.4 0.98 0.80 68.8 1.05 1.25 83.8 1.10 1.75 95.8 1.06 2.00 100.0 0.98 a Assume amax = 2a' where a' is defined by Equation 17. (a,,,
* a is considered a Gaussian function of wavelength.
Obtained by integrating Equation 16 with respect to CY between the limits of amax. and a,and dividing result by (amax -a). Assume Coo~opt) = Coo,and that Qo, @, and b are constant. c
doubt in the exponential term is doo; however, all of the uncertainty can be accounted for to a first approximation by the absorption coefficient which, in this case, can be considered as an effective absorption coefficient, a'. Essentially, the use of a' attempts to account for absorption of all the absorbing species produced from the reactant as well as the reactant itself. Thus, it is critically dependent on many of the experiQo, and the identity of the mental parameters including reactant. The effective absorption coefficient can be experimentally determined with the aid of Equation 17
+,
where Coo(opt) is the concentration of the reactant required for Obtaining the maximum possible concentration of intermediate at distance b. Equation 17 was obtained by differentiating equal Equation 16 with respect to Cooand setting dCEo(b)/dCoo to zero. The assumptions used in deriving Equation 17 are that a' is independent of Coo,and that Cooat distance b does not change appreciably. The effective absorption coefficient can be determined, then, by experimentally obtaining In addition, by estimating a' (I priori one can obtain from Equation 17 a rough prediction of The effect of a light source that has a continuum of irradiation (as opposed to monochromatic light) appears to be minor if Coois in the vicinity of Coo~opt). This is demonstrated in Table I1 where CR'(b) is calculated theoretically for increasingly broader irradiation over a given absorption band. The first column represents the difference between the absorption coefficient and the maximum absorption coefficient, and the second shows how much of the absorption band is being considered. The last column demonstrates the fact that C,"(b) deviates from the average only by *lox over the entire absorption band (assuming constant Qo and +). These results imply that Equation 16 is applicable to the determination of CRo(b)despite the use of nonmonochromatic light. From the practical standpoint of applying potentiostatic analysis to quantitative photolysis studies, it is important to utilize the preceding discussion to predict the nonhomogeneity of the solution after a flash. This can be estimated by taking a ratio of C R oat b and (6 Ab). This expression follows:
+
500
ANALYTICAL CHEMISTRY
4
L w
-b
v) I
s
0 -
0 X
1
I
I
0.4
0.8
I
I
1.2
1.6
I
TIME, MSEC Figure 4. Second-order kinetic plot from continuous potentiostatic current-time curve following flash irradiation, pH 11 K' (from intercept) = 8.2 X 10- amp-secf, ka = (1.3 f 0.4) X lO'M-1 sec-1, r t = 600 Isec A direct measure of the solution nonhomogeneity was obtained experimentally by measuring the current at two different lengths from the flash lamp after flash irradiation of 1.6 x 10-4M benzophenone in 0.5M base. The ratio of currents at short times after the flash (Ab = 0.17 crn) was 1.65. This ratio is directly related to the ratio of CRo(b)/CRo(b Ab). By substitution into Equation 18 an effective absorption coefficient of 1.8 X 104M-' cm-l was calculated. In addition, the value of for benzophenone was determined experimentally by varying Coo in a series of flash experiments and obtaining C R O in each case by potentiostatic analysis. The maximum response in this series of experiments was for 8 x 10-4M benzophenone at a distance, b, of 0.07 cm. This result indicates an effective absorption coefficient, again, of about 1.8 X lO4M-I cm-1. These values for a' are not unreasonable, considering that the maximum absorption coefficient for benzophenone at 252 mp is 4.1 X 104M-l cm-1 (9) and that roughly half of the benzophenone i s photolyzed between the flash lamp and electrode during the flash. Therefore, Equations 17 and 18, despite the necessary assumptions, appear to be useful, at least for rough predictions. When Equation 18 and the experimental value of a' obtained above are used, and Ab equals the radius of the HMDE (0.06 cm), the calculated value of CR"(b)varies only by a factor of about 1.2 over Ab. Therefore, the use of the HMDE can be justified for the work presented here and, probably, for most photolytic work. However, for more exact results, especially with very large concentration gradients, planar electrodes would be required. Additional uncertainties in the solution conditions as seen by the working electrode arise from possible shadows caused by the shape of the HMDE and its position with respect to the flash lamp in this work. It is questionable whether significant photolysis occurs at the back half of the drop. This question becomes particularly critical for determining CROfrom Equation 15. Thus, a compromise value of l .5 for A R(in Equation 15) was used to determine CRo(b);the uncertainty in this value is reflected in the limits specified for the second-order rate constant in Table I.
+
RECEIVED for review September 20, 1967. Accepted December 14, 1967. Work supported by Public Health Service Grant No. CA-07773 from the National Cancer Institute. J. R. B. received Fellowships granted by Lubrizol Corp. and the Analytical Division of the American Chemical Society.
