Triarylaminium Radical Coupling Rate Constants
(48) C. J. Winscon and A. H. Maki, Chem. Phys. Lett., 12,264 (1971). (49) J. Schmidt and J. H. van der Waals, Chem. Phys. Left., 3,546(1989). (50) J. Schmidt, D. A. Antheunis, and J. H. van der Waals, Mol. Phys.,
22, l(1971). (51) A. L. Kwiram, MTPInt. Rev. Phys. Chem., Ser. One, 4 (1972). (52) S. Yamauchi and T. Azumi, Chem. Phys. Lett., 21, 603 (1973). (53) N. Nishi and M. Kinoshita, Chem. Phys. Left., 27, 342 (1974). (54) H. Hayashi and S. Nagakura, Mol. Phys., 24, 801 (1972).
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(55) N. Kanamaru and E. C. Llm, J . Chem. Phys., 62,3252 (1975). (56) B. R. Henry and W. Siebrand, J . Chem. Phys., 54, 1072 (1971). (57) F. Metz, Chem. Phys. Lett., 22, 186 (1973). (58) M. Koyanagi, K. Higashi, and Y. Kanda, Chem. Phys. Lett., 52,184 (1977). (59) N. Kanamaru and E. C. Lim, J . Chem. Phys., 65,4055 (6976). (60) D. A. Antheunis, J. Schmidt, and J. H. van der Waals, Mol. Phys., 27, 1571 (1972).
Electrochemical and Spectroscopic Studies of Cation Radicals. 4. Stopped-Flow Determination of Triarylaminium Radical Coupling Rate Constantst Robert F. Nelsont Department of Chemistry, University of Georgia, Athens, Georgia 3060 1
and Robert H. Phllp, Jr. * Deparfment of Chemistry, University of South Carolina, Columbia, South Carolina 29208 (Received March 11, 1977; Revised Manuscript Received November 1, 1978)
The reactions of nine different mono-para-substituted triphenylaminium cations produced by oxidation of the parent amines by Cu(I1) in acetonitrile have been studied. The cation radicals undergo apparent second-order coupling reactions giving rate constants ranging from 4.4 X lo3to 8.8 X M-' s-l. These values correlate well with rate constants for these reactions previously determined by chronoamperometricmeasurements and their determination should better establish the reliability of electrochemical methods for studying similar systems.
Introduction The digital simulation method, coupled with standard electrochemical techniques, has proven to be a powerful tool for both quantitatively measuring homogeneous rate constants for chemical reactions associated with electrode processes and for differentiating between alternate mechanisms in such systems. As with any physicochemical technique, correlation with another independent method is highly desirable. Spectrophotometry would be the method of choice for monitoring the stabilities and decay pathways of electrochemically generated intermediates, since these are quite often highly colored. In fact, this has been done for a limited number of systems, specifically the spectroelectrochemical studies by Kuwana and co-workers' and the electrochemical/spectrophotometric rate determinations for the benzidine rearrangement carried out by Reilley2 and Nichol~on,~ as well as the comparison of stopped-flow and electrochemicalmethods for studying the Ti(II1)-hydroxylamine reaction by Murray and coworker~.~ In an effort to better characterize the properties and reactions of triarylminium cation radicals and to correlate homogeneous rate constants previously determined electrochemically with a totally nonelectrochemical spectroscopic method we have carried out extensive studies using both conventional visible spectrophotometric and stopped-flow techniques. The ions were generated in acetonitrile using Cu(I1) as the oxidant. Although kinetic analysis of the system was complicated, bimolecular rate constants for coupling in nine different 'For part 3 see J. R. Ambrose, L. L. Carpenter, and R. F. Nelson,
J.Electrochem. t
Soc., 122, 876 (1975).
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compounds were found to be in good agreement with those previously determined by chron~amperometry.~,~ In so doing, we have gained a better understanding of the properties and reactions of triarylaminium cation radicals, have tested the validity of the digital simulation/electrochemical approach, and have partially defined the capabilities and drawbacks of the stopped-flow techniques for such studies.
Experimental Section Reagents. The synthesis and purification of the amines employed in this study have been reported previously.6 The acetonitrile was double distilled from PzO5 after standing in contact with CaHz for several days; in each distillation the middle 70% fraction was collected for use. The copper(I[) perchlorate oxidant was prepared according to the method given by Kratochvil,' and the concentration was verified by coulometry. Apparatus. Kinetic studies were carried out using the Aminco-Morrow stopped-flow apparatus in conjunction with an Aminco (4-8459) grating monochromator. The tungsten-iodine source was powered by a Hewlett-Packmd Model 6274B dc power supply. High voltage to the PM tube was provided by a Kepco Model ABC 1000M-20316 power supply and it was monitored by a Hewlett-Packard 5326B DVM. Data acquisition was carried out with the Aminco DASAR system. A 1.0-cm cell thermostatted at 25.0 "C was employed. Generation of Radicals. The radicals were generated by direct mixing of the oxidant and the parent triphenylamine (TPA) in the stopped-flow apparatus. In order to maximize the initial concentration of the cation radical and to avoid formation of the tetraphenylbenzidine dication (see Results and Discussion 0 1979 American
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spectrum, obtained using the stopped-flow apparatus, is shown in Figure 1. In most of the systems studied the disappearance of the absorption near 650 nm was accompanied by a simultaneous growth of absorption around 480 nm. This latter absorption grew in at precisely half the rate of the disappearance of the 650-nm band (dAdW/dt= - 1/2dA6,/dt) during the initial stages of the reaction (usually about one half-life). The reaction scheme appears to be adequately described by the following sequence of reactions: kl
Cu(I1) + TPA e Cu(1) + TPA+*
(2)
k-1
K,, = [CU(I)I[TPA+~I/(~CU(II)I[TPAI)
-
2TPA+* Cu(I1) + T P B 400
500 600 WAVELENGTH, NM
700
Flgure 1. Spectra of initial and final oxidation products of triphenylamine: recorded spectrum, excess Cu(I1); plotted spectrum, excess (50X) triphenylamine, points taken at 500 ms.
section) it was necessary to mix the oxidant with a solution containing a 10-100-fold excess of the amine. The Cu(I1) concentrations which were employed ranged from 2.8 X 10-5 to 2.8 x 10-4 M. Acquisition of Spectral Data. The spectra for the primary radicals were obtained either from the recorded Cary 14 output (for the more stable aminium ions) or from point-by-point data acquisition using the stopped-flow system.
Results and Discussion General Description o f the Reactions. Mixing of an excess of the Cu(I1) oxidant with TPA results in the formation of a stable deep blue substance which is apparently the dication, TPB2+. This can be mistaken for
R
R
TPBZ+
the primary TPA cation radical and, in the case of the unsubstituted TPA, probably corresponds to the blue nonparamagnetic product reported by Walteras If significant amounts of the unoxidized tetraphenylbenzidine are present, the solution tends toward the formation of the benzidine cation radical which absorbs near 480 nm via the previously described reaction5 TPB2+ + T P B 2TPB+. (1) Highly oxidized TPA solutions tend to show absorptions of both TPB'. and TPB2+. It is, however, possible to generate and study the TPA cation radical (TPA+-)provided the Cu(I1) is present in deficiency to avoid oxidation to TPB2+. By making observations at short times under these conditions, spectra of the initial cation radicals can be obtained. Such a -+
k2
TPB
fast
+ 2H+
CU(I) + TPB+.
(3)
(4)
The products of the reaction are unoxidized T P B in the cases where reaction 2 is complete and rapid compared to reaction 3 or a mixture of T P B and TPB++in cases where reaction 4 must be considered. Because of the apparent second-order nature of reaction 3 it was generally not possible to observe the reactions for a sufficiently long time in the stopped-flow system to eliminate the possibility of a small residual absorption near 650 nm due to the TPB2+, formed either by some oxidation by Cu(I1) or by disproportionation of TPB+.. The preponderance of evidence is that the formation of TPB2+was not significant under the conditions of our study. Preliminary kinetic analysis of the data indicated a second-order disappearance of TPA+. consistent with a radical-radical mechanism as opposed to a radical-parent mechani~m.~ Evidence for a second-order process was (a) no trend in rates with changes of concentration of parent amine was observed, (b) the second half-life for the decay was very near twice the first half-life, and (c) the data clearly followed second-order plots better than first-order plots. Exact kinetic analysis is complicated by two factors. The initial redox reactions between the amines and Cu(I1) were found to be surprisingly slow and easily observable at short times by stopped-flow. In some cases half-times for this reaction were of the order of 1 s. It was normally possible, however, by working with a large excess of the TPA to establish a half-time for this reaction that was less than one tenth the first half-time of the radical coupling reaction. Secondly, reaction 2 was incomplete, even in most cases in as high an excess of the TPA as was practical for the experiments. From the E l l z values reported for the various TPA's6 and the value of 0.96 V vs. SCE for the Cu(II)/Cu(I) system reported by Kratochvi17 one can estimate K,, values for reaction 2. While these serve as useful guides we have generally found that the extent of reaction 2 is significantly less than that predicted under the conditions of our experiments. In the case of the CN and NO2 derivatives no appreciable oxidation could be observed. In an effort to observe oxidation of these two compounds, other stronger oxidants such as Pb(1V) and Tl(II1) were tried but were found to be unsatisfactory as alternatives to Cu(I1). Kinetic Analysis of t h e Data. If the initial redox reaction 2 is treated as a prior equilibrium and if the parent amine is present in large excess, the correct kinetic expression for the coupling of TPA+. is
The Journal of Physical Chemistry, Vol. 83, No. 6, 1979 715
Triarylaminium Radical Coupling Rate Constants
TABLE I: Long Wavelength Absorptions of TPA's and Related Compounds
[L+ [TPA+*] + ~[TPA+*]CT K,,[TPA][TPA+*](Ke,[TPA] + [TPA+.]) 2CT [TPA] + [TPA+.] --K,,[TPA]CT
(Keq[TPAI)'
In Keq
[TPA+*]
TPA +. substituent
-
1
z= [TPA+*]~/CT
H F Br
= 2kzt
evaluated between [TPA+*lo(at t = 0) and [TPA'.], (at time t after mixing) where [TPA] is the initial concentration of the parent amine (which remains essentially constant) and CT is the total copper con~entration.~ If the system is coupled through reaction 4 the resulting kinetic expression is identical except that the right side is 3h2t rather than 2k2t. The systern is conveniently discussed in terms of the initial extent, of reaction 2 which may be defined as (6)
If 2 is greater than about 0.5 an ordinary second-order plot of Ao/A- 1,where A. is the initial absorbance of the TPA+., will be quite linear through more than one half-life. ~ The slope of such a plot can be shown to be 2 h 2 Z 2 C (or 3k2Z2CTif reaction 4 is important). Approximate kinetic analysis can thus be carried out by treating the data as simple second order if 2 is known. In only one case, that of the OEt derivative, was it possible to treat the data as an ordinary second-order reaction. In this system the coupling reaction is very slow and the initial redox reaction is apparently complete (2 = 1) in a moderate excess of the amine. In one other compound, the phenyl, it was possible to determine an accurate value of the molar absorptivity, E, by use of large excesses of the amine. In subsequent experiments this value was used to calculate [TPA+.] and the data were then plotted according to eq 5. Results of rate constant measurements for this compound are shown in Table 11. Rates measured by stopped-flow showed good agreement with those measured from recorded spectra in this system which could be observed by both techniques. Rate constants for most of the other compounds were extracted by use of a three-parameter (E, 2, k,) non-linear least-squares curve fit to a form of eq 5 based on SIMPLEX.^^ Fourteen data points over from two to three half-lives were employed in the fit. In computing hz, the factor of 3 in eq 5 was employed if the data indicated that 2 was significantly less than one and there was evidence for concomitant formation of TPB+- (via eq 4). Otherwise, a factor of 2 was employed. Figure 2 shows a kinetic plot based on eq 5. The same data plotted as a first-order reaction is shown for comparison. In two compounds, the Br and Et derivatives, the initial redox reaction was sufficiently slow to call into question the assumption of rapid prior equilibrium. It was not possible to find an analytical expression for the rate law in this case and these data were treated by a numerical integration coupled with a curve fit to kl, 2, kz, and E over the entire time of observation. Rate constants €or these two systems were 20-50% lower if calculated by the curve fit neglecting the initial formation reaction. In the OPh system in which the initial reaction was much faster than the coupling reaction data treatment by the two methods gave rate constants that agreed to within 6 % . Table I11 is a summary of rate constants determined in this study and these values are plotted vs. previously
(e
x
645 (2.4) 640 (2.6) 668 (5.5) 655 (7.3) 770(5.1) 668 (1.3) 665 (1.1) 698 (1.9) 666(7.4)
CHO Ph Et OPh OEt SO,NEt,
TPB'.
TPB2*
481 480
68 0
490
-770
500 483
-670
TABLE 11: Coupling Rate Constants for TPA(Ph)
-
CTPA, M
4.8 x 7.4 x 1.0 x
k,,
Ccu,M M-' s-' method 3.5 x 27 recorded spectra 2.7 x 20 recorded spectra 8.6 x l o - ' 25 stopped-flow
TABLE 111: Rate Constants substituent
SO,NEt, CHO H Br F
k,,
M'I
-
s-' substituent k , , M-' s-'
4.4 x l o 3 1.8 X l o 3 1.1 x l o 3 1.1X l o 3 2.7 x 10,
Ph Et OPh OEt
2.4 x 10' 1.1x 10' 3.5 8.8 x
4 4 ln
'ti 2
Time Isec)
Figure 2. Kinetic plot of data for unsubstituted TPA. CT = 3.74 X [TPA] = 3.75 X Z f r o m curve fit is 0.45. The data are also plotted as first order for comparison.
reported values determined by chronoamperometry6 in Figure 3. The line representing 1:l correspondence is drawn to facilitate comparison. It can be seen that the spectroscopic rate constants are uniformly lower than those determined by chronoamperometry, although in view of the wide range of rates studied and the known chemical and computational complications in both the spectroscopic and electrochemical systems, the agreement must be considered good. It should be noted that the slowest system, OEt, shows the poorest agreement. If the spectroscopic rates are taken as more reliable, such EI deviation might be expected because of the sigmoid form of the working curves used to obtain the electrochemical rates. Such an observation is, however, tenuous with the limited data presented here. Unfortunately, the fastest systems reported by chronoamperometry (CN, NOz) were not accessible in this study for reasons cited above.
Comparison of the Two Methods The limitations of the chronoamperometric measure. ments have been adequately d i s c u ~ s e d . ~They , ~ include
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Frank, J. W. Otvos and M. Calvin
While the chemical oxidation-spectroscopic method must be considered the more straightforward and better established it was found to present analogous problems. These centered around difficulties in obtaining rapid and complete formation of the initial cation radical. In this system, formation of the reactive species a t an electrode is an attractive alternative. For compounds exhibiting slower rates the electrochemical method presents other experimental advantages. For example, in the slowest systems, employing concentrations favoring good spectral measurements the first half-time can be hours. The fact that these rates can be measured from current-time curves requiring only a few seconds is a definite “plus” for the electrochemical technique.
Acknowledgment. The contribution of E. E. Mercer to the kinetic analysis is gratefully acknowledged. References a n d Notes (1) J. W. Strojek, T. Kuwana, and S. W. Feldberg, J . Am. Cbem. SOC., 90, 1353 (1968); N. Winograd and T. Kuwana, bid., 92, 224 (1970); N. Winograd, H. N. Blount, and T. Kuwana, J. Pbys. Cbem., 73, 3456 (1969). (2) b. M. Oglesby, J. D. Johnson, and C. N. Reilley, Anal. Cbem., 38, 385 (1966). (3) J. T. Lundquist, Jr., and R. S.Nicholson, J . Elecfroanal. Chem., 16, 445 11968). (4) M. Patek, T. E. Neal, R. L. McNeely, and R. W. Murray, Anal. Cbem.,
k, (electro)
Comparison of rate constants determined by spectrophotometric and by electrochemical measurements, logarithmic scale. For comparison with substituted compounds the rate constant for the unsubstituted TPA has been multiplied by the statistical factor 4/9 (see ref 6). Figure 3.
45. . - , 32 - - (1973). \
- I
(5) R. F. Nelson and S.W. Feldberg, J. Pbys. Cbem., 73, 2623 (1969). (6) S.C. Creason, J. Wheeler, and R. F. Nelson, J . Org. Cbem., 37, 4440 (1972). (7) B. Kratochvll, D. Zatko, and R. Markuszewski, Anal. Cbem., 38, 770 (1966). (8) R. I. Walter, J . Am. Cbem. Soc., 88, 1923 (1966). (9) E. E. Mercer, private communication. (10) S.N. Deming and S. L. Morgan, Anal. Cbem., 45, 2782 (1973).
lack of knowledge of diffusion coefficients, difficulties in separating the effects of possible competing reactions, and the well-known experimental problems associated with chronoamperometric measurements a t long and a t very short times.
Quenching of Rhodamine 101 Emission in Methanol and in Colloidal Suspensions of Latex Particles Arthur J. Frank,*+ John W. Otvos, and Melvin Calvin Laboratory of Chemical Biodynamics, Lawrence Berkeley Laboratory, University of California, Berkeley, California 94 720 (Received August 21, 1978) Publication costs assisted by the U.S. Department of Energy
The quenching of rhodamine 101 emission in methanol by triethylamine, N,N-dimethylaniline, diphenylamine, and N-methyldiphenylamine was attributed to electron transfer. The values of the rate constants, which range from lo8 to 1O1O M-’ s-l, are in agreement with theoretical predictions of electron transfer. A comparison is made between the redox processes in methanol and on the surface of hydrocarbon latex particles suspended in aqueous solution. The association constants for the equilibria of rhodamine 101 and diphenylamine between the latex and bulk solution are 3.0 X lo4 and 1.6 X lo4 M-l, respectively. The quenching efficiency of diphenylamine in solutions containing 17 to 98 ppm latex is 22-72-fold higher than that in the methanolic solution. The fluorescence lifetime of rhodamine 101 is 4 ns in methanol. The fluorescence quantum yields in methanol (+F = 0.99) and water (& = 0.71) were also determined. The implications of these results to photochemical storage reactions are discussed. Introduction Efficient conversion of light quanta into chemical free energy requires that energy losses of the absorbing system due to luminescence and nonradiative heat production be minimized. In homogeneous solutions, intermolecular Solar Energy Research Institute, Golden, Colo. 80401. 0022-3654/79/2083-0716$01 .OO/O
electron transfer usually proceeds from the excited triplet state rather than the excited singlet state of a molecule because the lifetime of the latter is short compared with encounter times. Formation of the triplet state, however, entails the loss of the singlet-triplet splitting energy which may be as much as several tens of kilocalories per mo1e.l In turn, the decrease in excitation energy is associated with 0 1979 American Chemical Society
