Low-Temperature Electrochemistry I I . for Homogeneous Chemical Reactions Coupled to Charge Transfer

Evaluation of Rate Constants and Activation Parameters

Richard P. Van Duyne’ and Charles N. Reilley Department of Chemistry, University of North Carolina, Chapel Hill, N .C . 27514

A simple method is presented for analyzing the tem- perature dependence of pseudo first order chemical reaction(s) coupled to a heterogeneous charge transfer process. The temperature dependent factors asso- ciated with the mass transport and heterogeneous charge transfer processes have been specifically separated from those pertaining to the coupled chem- ical reactions. The following kinetic cases have been treated in some detail: EC, simple ECE, catalytic, regeneration scheme, and the more general ECEC decay scheme. Single and double potential step and cyclic voltammetry methods have been treated theo- retically via finite difference or analytical solutions and their potential utility for analyzing the pertinent rate constants is discussed.

IN THE PRECEDING paper ( I ) , it has been demonstrated that electrochemical experiments such as cyclic voltammetry and the potentiostatic relaxation techniques, chronoamperom- etry and chronocoulometry, can, in fact, be performed in cryogenic environments. Low-temperature electrochemical cells have been designed to perform these experiments with reasonable facility, and a variety of solvent/supporting electrolyte systems have been evaluated for low-temperature use.

Cyclic voltammetry under low-temperature conditions is characterized by complex temperature dependences relative to the rather simple behavior of the potentiostatic chrono- methods. For this reason, we recommend cyclic voltam- metry for strictly quantitative investigations, deferring to chronoamperometry and chronocoulometry for more quan- titative results. Double potential step chronoamperometry and chronocoulometry have the special advantage for low- temperature work that their characteristic ratio responses, &/io and Qb/Q,, respectively, are temperature independent in the absence of chemical reactions coupled to the heterogeneous charge transfer. Similar temperature independent ratios have been formulated for other two-step electrochemical techniques.

Having established conditions under which all tem- perature dependences characteristic of two-step electro- chemical techniques are eliminated for electrode reactions without coupled chemical reactions, it is now possible to examine the effect of homogeneous kinetics on the otherwise temperature independent ratios. Furthermore, under cer- tain conditions it will be shown that single potential step techniques also can give temperature dependent information characteristic of only the coupled chemical reactions. Dis- cussion will be restricted to post-kinetic reaction sequences commonly found in radical ion decay processes as studied by cyclic voltammetry and the potential step techniques.

1 Present address, Department of Chemistry, Northwestern University, Evanston, Ill. 60201

(1) R. P. Van Duyne and C. N. Reilley, ANAL. CHEM. 43, 142 (1971).

EC MECHANISM

Since the concentration profile of 0 is not altered by the

(1)

only two-step techniques should be used to measure the low temperature kinetics. The small peak potential shifts that are indicative of the kinetics in single sweep peak voltammetry would be difficult to interpret under low-tkmperature con- ditions in view of the complex potential temperature de- pendence noted earlier ( I ) . This reaction sequence has been treated in considerable detail for cyclic voltammetry (2), double potential step chronoamperometry (3), and double potential step chronocoulometry (4).

Recently, we have conducted a theoretical and experimental reinvestigation of EC kinetics in double potential step chrono- coulometry (5) and have found a quantitative discrepancy in the 1 Qb/Qrl us. (k7)lI2 function, although use of the previously published working curve ( 4 ) would not have qualitatively altered the low-temperature behavior of the Q ratio reported here. Using the new results for the Q - t behavior:

conversion of R to Z in the EC scheme

0 + ne-* R + Z k

where

E(k, t , 7) = e - k t X

[k(t - ~)1’1Fl ( j + l /2 , j + 1, k ~ ) ~ F d l , j + 3/2, k(t - 7)) j = O 2 j ! ( 2 j + 1)

(3) the Q ratio, including the kinetic contribution, is:

(4)

In Equation 3, lFl(a, b, 2) refers to the confluent hypergeo- metric function .(6).

Inspection of Equation 4 shows that the only temperature dependent factor in the Q ratio is the chemical reaction rate constant. An extremely simple method is therefore available for graphically calculating the temperature dependence of any of the parameters in Table I11 of the preceding paper ( I ) once the working curve for that parameter as a function of

(2) R. Nicholson and I. Shah, ANAL. CHEM., 36, 706 (1964). (3) W. Schwarz and I. Shah, J. Phys. Chem., 69, 30 (1965). (4) J. Christie, J. Electroanal. Chem., 13, 79 (1967). (5) T. H. Ridgway, R. P. Van Duyne, and C. N. Reilley, ibid.,

in press. (6) L. J. Slater, in “Handbook of Mathematical Functions,”

M. Ambramowitz and I. Stegun, Ed., National Bureau of Standards Applied Mathematics Series 5 5 , US. Government Printing Office, Washington, D.C., 1967, 6th edition.

ANALYTICAL CHEMISTRY, VOL. 44, NO, 1, JANUARY 1972 153

L -

- ~h ........................................ \ 4- g -,+ X 5,15Kc1

........................

10 Kca lmo le

0 3.3 -1.0 - 0.5 0 0.5 1.0 log lkfl

10

Figure 1. Double potential step chronocoulometry working curves for the EC mechanism and the ECE mechanism with a stable second electron transfer product and superimposed Arrhenius temperature dependence of the chemical reaction rate constant

the logarithm of the appropriate kinetic variable is at hand. For example, let us calculate the temperature dependence of the I Q b / Q I l ratio in double potential step chronocoulometry at a fixed switching time, r, and room temperature rate con- stant. Since k is the only temperature dependent factor in the l Q b / Q f l us. log ( k ~ ) expression, the effect of lowering the temperature is to translate the horizontal axis of the work- ing curve according to the activation energy of the chemical reaction. For a particular chemical system at T = 298 OK and fixed 7 , the kinetic variable, kr, has a defined value, say 10. Therefore, lowering the temperature will cause the point log kr = 1.0 to shift according to the Arrhenius-type equation:

log (kr) log (AT) - EA/2.303 RT ( 5 ) Superposition of the Arrhenius plot for the temperature dependence of the log k r axis on the l Q b / Q / i us. log ( k r ) working curve for the EC mechanism and the ECE mech- anism with stable second electron transfer product is shown in Figure 1. In order to obtain lQb/Q, l at any temperature of interest, simply move horizontally to the Arrhenius plot of proper activation energy, vertically to the desired working curve, and horizontally again to i Q b / Q / l . The dotted lines in Figure 1 illustrate this operation. The variation of lQb/Qll as a function of temperature calculated in this

60

1 I I I 0300' 260 220 180

5 'K

Figure 2. Temperature dependence of the Q b / Q / ratio in double potential step chronocoulometry for fixed and room temperature follow-up reaction rate constant Solid lines are calculated for the EC mechanism while the dotted lines are for the ECE mechanism with a stable second electron transfer product

718'K ID l98'K B

A -.is -.$ VOLTS V I . S C E

Figure 3. Finite differences simulation of temperature dependent cyclic voltammograms for the case of an irreversible following chemical reaction Parameter values at T = 298 O K : DO and DR = 10-6 cm2- sec-I, E" = -0.300 V, Co* = 1 mM, and kia = 10. Tem- perature coefficients: bE"/bT = V Kc-*, solvent density = -9.8 X 10-4 g . ~ m - ~ KO-' (7). Activation energies: diffusion, EaD"'. = 4.0 Kcal mole-' K O - ' ; chemical reaction, EA = 5.0 Kcal mole-' KO-'.

manner for k (298 OK) = 500 sec-I and r = 0.020 sec is shown in Figure 2. From Figure 2 it is seen that very nearly complete thermal quenching of the follow-up reaction is possible (i ,e. , 1 Qb/Qrl + 0.5858) near the low-temperature limit of the BNjPN solvent system even for a reaction of only 3 Kcal/mole activation energy.

The activation parameters for the follow-up reaction can be calculated from a plot of log(k7) us. 1/T. For the greatest reliability, r should be readjusted at each temperature to give a lQb/Qrl ratio which occurs in the region of steepest slope on the working curve. For the EC case this corresponds to a I Q b / Q / l near 0.274 (5).

The low-temperature characteristics of cyclic voltammetry for the EC case were obtained by calculating theoretical 1st cycle voltammograms for a reduction by the finite difference technique. The effect of solvent volume contraction has been included in these calculations (7). As shown in Figure 3 at

(7) M. Szwarc, J . Amer. Chenz. Soc., 87, 5548 (1965).

154 ANALYTICAL CHEMISTRY, VOL. 44, NO. 1, JANUARY 1972

Figure 4. Low-temperature peak potential shifts calculated by the finite difference method for cyclic voltammetry of an ir- reversible chemical reaction coupled to charge transfer All parameter values at 298 O K same as Figure 3. Low-temperature (LT) limit is the freezing point of the butyronitrile/propionitrile solvent mixture 141 "K. A ) cathodic peak potential k/a = 0; B ) cathodic peak potential k/a (298 "K) = 10, EA = 10 Kcal mole-'; C ) cathodic peak potential k/a (298 O K ) = 10, EA = 5 Kcal mole-'; D) anodic peak potential k/a (298°K) = 0

room temperature, there is no recovery on the back sweep of product species generated on the forward sweep. As the tem- perature is decreased, more and more product is recovered until at 158 OK perfectly reversible behavior is achieved as indicated by the anodic/cathodic peak current ratio of 1.00. The peak potential shifts as a function of temperature can be inter- preted as a competition between an anodic shift (cathodic shift for an oxidation) resulting from the Eo temperature dependence and a cathodic shift (anodic for oxidation) due to thermal quenching of the chemical reaction. These predicted potential shifts are presented in Figure 4 as a func- tion of temperature for various activation energy processes. The nonkinetic case data are presented for comparison. In practice, however, interpretation of peak potential shifts for purposes of characterizing the low temperature kinetics is difficult a t best due to the iR drop and electrode surface problems noted earlier (I).

Cyclic voltammetry at low-temperatures is thus seen to be fully analogous to room temperature measurements made at high sweep rates. This similarity is emphasized in Figure 5 where the corresponding temperatures and/or scan rates required to achieve a given ipa/ipc ratio, R, are shown for vari- ous activation energies at fixed room temperature rate constant. For example, a peak current ratio of 0.8 for a reaction with 7 Kcal/mole activation energy and room tem- perature first order rate constant of 500 sec-' can be attained with a sweep rate of 246 volts/sec at 298 OK or with a sweep rate of 31.5 volts/sec at 256.5 OK (E112 - Ex = 0.10 V) where EA is the potential at which the forward sweep is reversed. Similar analogies could be made with the other two-step techniques; for example, the corresponding double potential step time 7 and temperatures required t o give a particular lib/i,l value for chronoamperometry.

ECE AND REGENERATION MECHAh'ISMS In contrast to the EC mechanism, the concentration profile

of the electroactive species 0 is perturbed by the influence of coupled chemical reaction(s) in the pseudo-first order mechanisms :

1 4 i R '.E

I

I I I I J .5 10 5 10 50 100

V k(Ep2- E A )

Figure 5. Corresponding temperatures and sweep rates required to achieve a particular peak current ratio, R , for cyclic voltammetry of an irreversible chemical reaction following charge transfer All parameter values at 298 O K and temperature coefficients are the same as for Figures 3 and 4

(8) 0 2 + me- e R2 E2"

where IE2" < E1"I; X is any pseudo-first order reactant.

CATALYTIC-FULL REGENERATION

where p 2 = k C , (see Table I)

' / 2 REGENERATION

0 + ne- + R (11)

(1 2) R + X"- 0' + Z

0' + R -% 0 + Z' (13)

(where Z and Z' are electroinactive and k2 >> kl: applying a steady state treatment to 0', the observed k is 2k1) either by regeneration of 0 as in the catalytic and regeneration schemes or by formation of a species more easily reduced (oxidized) than 0 as in the ECE mechanism. As a result, one-step as well as two-step techniques can be used to extract the kinetic information.

Single Potential Step Methods. All temperature de- pendent factors other than those associated with the coupled chemical reaction(s) can be eliminated in at least three ways for single potential step techniques : normalization of the kinetically controlled current, charge, etc. with respect to some long time limiting behavior; normalization with re- spect to short time limiting behavior; and normalization using the ratio of two kinetically controlled parameters with different time dependences (e.g., charge/current). A representative but not exhaustive listing of normalized pa- rameters whose only temperature dependence is k is given in Table I. Unlike the double potential step, EC situation where the elimination of all nonkinetic temperature de- pendences was rigorous, the single potential step ratios in

ANALYTICAL CHEMISTRY, VOL. 44, NO. 1, JANUARY 1972 155

Table I. Single Potential Step Technique Ratios Normalized for Temperature Dependent Factors Other than Kinetics. Measured Mechanism response ECE Catalytic l/% Regenerationb

i k - Ik-0

[e-kt - 11 2kt +

Assuming all diffusion coefficients are the same at T = 298 “K and have equal activation energies of diffusion. A steady state treatment applied to 0’ (see Equations 11-13) gives observed k = 2kl.

Table I depend on the validity of the approximation that all diffusion coefficients are equal a t all temperatures. Choice of the normalization procedure to be used depends on the magnitude of k over the temperature range of interest. For slow rate constants, the short time normalization pro- cedure is used since it may be difficult t o attain the long time limiting behavior due t o spherical diffusion and/or convection complications. For fast rate constants, the long time nor- malization is used since the low-temperature time resolution may be insufficient to reach the short time limit. The normalization procedure using the ratio of two kinetically controlled parameters is applicable to all accessible k’s since it does not depend on reaching a limiting situation.

Double Potential Step Methods. The double potential step theory for chronocoulometry pertaining to coupled chemical reactions of the catalytic type has appeared in the literature (4). The chronoabsorptometric theory has been given by Winograd (8) and recently extended to include second order kinetics (9). Analysis of the temperature de- pendence of the measured parameter lQbiQl .1 or IAb/Ajl is carried out as described above once the working curve is obtained in the log (k7) form.

Double potential step theory has not previously been pre- sented for the ECE or regeneration cases. We have, therefore, undertaken such calculations for the ECE mech- anism since it appears so frequently in radical ion decay reactions (10, 11).

Solution of the diffusion-kinetics problem for the ECE reaction scheme consisting of Reactions 6-8 is sufficient to predict the electrochemical responses for the single step techniques chronoamperometry, chronocoulometry, rotating disk voltammetry, etc. since the electrical variable that is measured is influenced only by chemical kinetics preceding

(8) N. Winograd, H. N. Blount, and T. Kuwana, J. Phys. Chem.,

(9) H. Blount, N. Winograd, and T. Kuwana, ibid. 74, 3231 (1970). (10) R. N. Adams, “Electrochemistry at Solid Electrodes,” Marcel

Dekker, New York, N.Y., 1969. (1 1) M. E. Peover, “Electrochemistry of Aromatic Hydrocarbons

and Related Substances,” in ‘‘Electroanalytical Chemistry,” Vol. 2, A. J. Bard, Ed., Marcel Dekker, New York, N.Y., 1967,

73, 3456 (1969).

pp 1-51.

an electron transfer step. For completeness, however, the homogeneous redox reaction between O1 and R? should also be considered (12):

k/ 01 + RP 0 2 + RI (14)

k b where

Keq = -

When double potential step techniques are considered, one must allow for various possibilities concerning the reverse step recovery of the second electron transfer product, R?. Consider a double potential step experiment in which the potential is stepped from some initial value, E;, where no electrode processes take place to a potential, El, sufficiently positive of Elo (in the case of an oxidation) to cause Reaction 6 t o proceed at a diffusion controlled rate. At the applied potential, El, Reaction 8 also proceeds a t a diffusion con- trolled rate since IE20 < Eloi (otherwise the ECE scheme collapses t o an EC scheme which has been considered in the previous section). After a suitable generation time, 7, the reverse step is applied returning the potential t o its initial value E , (symmetrical double potential step experiment) thereby causing the reverse of Reaction 6 to proceed a t a diffusion controlled rate. If both Elo and Ezo lie within the potential step “window” bounded by E, and El, then the reverse of Reaction 8 will proceed a t a diffusion controlled rate as well. If, however, E P O is quite far positive, the ap- plied potential during the reverse step, E,, may not be suffi- cient t o allow the reduction of electrogenerated Rz or 0 2 t o occur. In this latter case no current or charge will be con- tributed by the Oz/Rz couple t o the reverse step response.

Let us consider in more detail the former situation in which the Rz - O2 conversion can take place under diffusion control during the reverse potential step. It is highly conceivable that R2 can undergo a decay reaction analogous to Equation 7. Thus the reaction:

R Z + X - % Z

(12) M. D. Hawley and S. Feldberg, J. Phys. Chem., 70, 3459 ( 1966).

156 ANALYTICAL CHEMISTRY, VOL. 44, NO. 1, JANUARY 1972

Table 11. Numerical Results, I Q b / & us. (k1~)1/2 , for the ECEC Mechanism Using Double Potential Step Chronocoulometry. Comparison of the Finite Difference (FD) and Analytical Solutions (A)

1 Q d Q s 1 kzlki = 0 10-2 lo-’ 100 - 10’ 102 m

(k27)’” A FD A FD A FD A FD A FD A 0.0 0 .1 0 .2 0 .3 0.4 0 .5 0 .6 0 .7 0.8 0 .9 1 . o 1 .1 1 .2 1 . 3 1 .4 1.5 1 .6 1.7 1.8 1.9 2.0

0.5858 0.5676 0.5678 0.5465 0.5199 0.4899 0.4587 0.4283 0.3998 0.3743 0.3523 0.3336 0.3185 0,3063 0.2968 0.2894 0.2839 0.2798 0.2769 0.2748 0.2733

0.5858

0.5669 . . .

. . .

. . .

. . .

. . .

. . .

. . .

. . . 0.3502

0.3157

0.2931

0.2792

0.2710

0.2660

. . .

. . .

. . .

. . .

. . .

0.5858 0.5811 0.5676 0.5464 0.5196 0.4892 0.4574 0.4266 0.3961 0.3689 0.3446 0.3234 0.3051 0.2894 0.2766 0.2643 0.2542 0.2450 0.2369 0.2293 0.2220

0,5858

0.5669 . . . . . . . . . . . . . . . . . . . . . . . .

0.3434

0.3038

0.2746

0.2528

0.2355

0.2207

. . .

. . .

. . .

. . .

0.5858 0.5811 0.5674 0.5456 0.5171 0.4837 0.4471 0.4090 0.3767 0.3335 0.2981 0.2649 0.2348 0.2074 0.1830 0.1612 0.1423 0.1255 0.1112 0.0987 0.0878

0.5858 . . . . . . . . . . . . . . . . . . . . . . . . . . .

0.2968

0.2334

0.1815

0 . ‘1408

0.1097

0.0863

. . .

. . .

. . .

. . .

0.5858 0.5810 0.5660 0.5400 0.5030 0.4589 0.4180 0.3816 0.3146 0.2710 0.2314 0.1966 0.1667 0.1412 0.1198 0.1018 0.0871 0.0747 0,0646 0.0563 0.0492

0.5858 . . . . . . . . . . . . . . . . . . . . . . . . . . .

0.2302

0 .‘1654

0.1185

0.0858

0.0635

0.0483

. . .

. . .

. . .

. . .

0.5858 0.5803 0,5610 0.5000 0.4895 0.4437 0.3953

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . . . . . . . . . . . . . I

. . .

0.5858 . . . . . . . . . , . .

. . .

. . .

. . .

. . .

. . . 0.2190

0.1566

0.1115

0.0804

. . .

. . .

. . . . . . . . . . . . . . .

0.5858 0.5789 0,5586 0.5275 0.4875 0.4419 0.3937 0.3436 0.2996 0.2572 0.2191 0.1857 0.1570 0.1326 0.1122 0.0952 0.0812 0.0696 0.0602 0,0524 0.0458

must be considered. If Z is also electroactive at the potential El then an ECEC. . , . .cascade mechanism can develop. The electrooxidation of single ring aromatic hydrocarbons such as benzene is thought to follow this sort of scheme (13). The restriction will be made here that Z is electroinactive, thus limiting the cascade t o the ECEC stage. The now classical Hoijtink mechanism for radical anion protonation (11):

(17) R + e- J_ R;

R ; + H X % R H . +x- (1 8)

R H . + e-= RH- (19)

RH: + HX kz_ RHZ (20) is an excellent example of such an ECEC mechanism.

We have obtained both finite difference (14) and Laplace transform analytical solutions to the diffusion-kinetics bound- ary value problem describing the (pseudo) first order ECEC reaction sequence (Reactions 6-8 and Reaction 16) for double potential step chronamperometry and chronocoulom- etry. The chronocoulometry results are presented here in the usual lQb/Q,i us. (k17)1’2 form where the kinetic Q ratio is defined as:

The functional dependence of the charge ratio 1 Q b / Q , i on the kinetic parameters of the coupled chemical reactions of the ECEC mechanism is shown in Figure 6 for several values of the rate constant ratio k2/kl. Table I1 provides the numer- ical results of these calculations; and compares the results

(13) T. Osa, A. Yildiz, and T. Kuwana, J. Amer. Chem. SOC., 91, 3994 (1969).

(14) S. Feldberg, “Digital Simulation: A General Method for Solving Electrochemical Diffusion-Kinetic Problems,” in “Elec- troanalytical Chemistry,” Vol. 3, A. J. Bard, Ed., Marcel Dekker, New York, N.Y., 1969, pp 199-296.

0.6

0.5

0.4 92. Qf

0.3

0.2

0.1

t L

Figure 6. Double potential step chronocoulometry working curves for the pseudo first ECEC mechanism

obtained by the finite difference technique with the analytical solution results obtained via Laplace transforms. In all cases, excellent agreement was obtained between the two approaches. The assumptions used in deriving the results of Figure 6 are the same as those given by Christie (4) . It is understood that here these assumptions apply to both the Or/R1 and O2/R2 couples. Additionally it is assumed that the lE1” - Ez”~ separation is sufficiently large that the in- fluence of Reaction 14 on the ECEC decay scheme is negli- gible. A more detailed discussion of the analytical solution results for chronocoulometry, chronoamperometry, and

ANALYTICAL CHEMISTRY, VOL. 44, NO. 1, JANUARY 1972 157

chronoabsorptometry will form the substance of a succeeding communication (25).

It is apparent from Figure 6 that double potential step methods provide a means for determining both rate constants in the ECEC sequence provided the rate constant ratio lies in the range 0.1 5 k2/kl 5 10. The rate constant kl can be obtained independently of k2 from an analysis of the for- ward step charge-time data in a manner analogous to that previously used by Shain (16) and by Herman (17). Double potential step measurements t o define the iQb/Qll us. T

behavior will allow determination of the ratio kz/kl by a curve-fitting procedure. From a knowledge of kl and the ratio kz/kl, the value of kz can be calculated.

Determination of the temperature dependence of 1 Qb/Q,I at a fixed r for the ECEC mechanism is as straightforward as for the EC mechanism only in those special cases where one

(15) T. H. Ridgway, Ph.D. Thesis, University of North Carolina,

(16) G. S. Alberts and I. Shain, ANAL. CHEM., 35, 1859 (1963). (17) H. B. Herman and H. N. Blount, J . Phys. Chem., 73, 1406

Chapel Hill, N.C., 1971.

(1969).

of the kinetic steps is rate determining, for example, k2/kl = 0 and kz/kl = m . The iQb/Q,l VS. temperature profile has already been presented for the k2/kl = 0 case in Figure 2. For the cases of intermediate kz/kl , the best procedure is to calculate lQb/Q,l at each temperature of interest from the finite difference computer program or the results of the analytical equations (15).

The extension of these ideas to other electrochemical tech- niques and reaction mechanisms is straightforward. One must only identify a measurable parameter (see Table 111, Reference 1) whose sole temperature dependence is that of the coupled chemical reaction(s) and apply a graphical analysis analogous to that in Figure 1.

RECEIVED for review March 29, 1971. Accepted August 2, 1971. One of the authors (R.P.V.D.) wishes to acknowledge support of a National Aeronautics and Space Administration Fellowship (1967-70). In addition, various aspects of this work were supported by the Advanced Research Projects Agency under Contract SD-100 with the U.N.C. Materials Research Center and Air Force Office of Scientific Research (AFSC), USAF, Grant AF-AFOSR-69-1625.

Low-Temperature Electrochemistry 111. Application to the Study of Radical Ion Decay Mechanisms Richard P. Van Duynel and Charles N. Reilley Department of Chemistry, University of North Carolina, Chapel Hill, N. C. 27514

The ability of low-temperature techniques to isolate the primary one-electron transfer oxidation or reduc- tion process with a cryoquench of the coupled chem- ical reactions responsible for the radical ion decay mechanism is demonstrated. Successful cryoquench- ing, producing radical ion lifetimes of at least 2 sec, was achieved for: a radical anion fragmentation decay reaction (reduction of 0- and p-iodonitrobenzene in dimethylformamide); a radical cation dimerization reaction (oxidation of triphenylamine in butyronitrile); a radical cation scavenging reaction by nucleophilic solvent impurity (oxidation of 1,2,3,6,7,&hexahydro- pyrene in butyronitrile); and a radical cation scaveng- ing reaction by nucleophilic solvent (oxidation of 9,lO- diphenylanthracene in dimethylformamide). In con- trast, the lifetime of the 9,lO-dimethylanthracene cation radical in butyronitrile is less at low tempera- tures; the decay reaction involves a prior equilibrium reaction of the cation radical (DMAt) with another cation radical (DMAt) or with parent (DMA) and rep- resents a case where new information has been pro- vided by the low-temperature technique.

A SURVEY OF THE RECENT literature concerning the preparation and characterization of radical ions indicates that electro- chemical methods provide a very facile approach to their generation (1-4). The purported reason for this facility of

1 Present address, Department of Chemistry, Northwestern University, Evanston, Ill. 60201

(1) “Radical Ions,” E. T. Kaiser and L. Kevans, Ed., John Wiley

(2) R. N. Adams, “Electrochemistry at Solid Electrodes,” Marcel and Sons, New York, N.Y., 1968.

Defier, New York, N.Y., 1969.

electrochemical radical generation is the ready availability of a controlled potential redox agent (i.e., the electrode) which, in principle, permits a selectivity not easily obtained with chem- ical redox agents. For example, reduction of an aromatic hydrocarbon with an alkali metal in an ether-type solvent to form the hydrocarbon radical anion is often accompanied by dianion formation due to the large reducing potential of the metal. Electrochemical techniques, however, suffer from the fact that the high dielectric constant, nonaqueous solvents used in electrochemistry, which are capable of supporting a dissociated electrolyte to provide a reasonably low resistance pathway for passage of electrical current, either act as rela- tively efficient radical ion traps themselves, or they contain notoriously difficult to remove, trace level, impurities that scavenge the radical ions. Recent reviews of oxidative organic electrochemistry (2 , 5 ) point out that the chemical fate of an electrogenerated cation radical is frequently dictated by its reaction with residual water in nominally nonaquous sol- vents. In addition to scavenging by water, radical ions may decay by unimolecular as well as a variety of bimolecular path- ways including : unimolecular decomposition (fragmenta- tion) and intramolecular rearrangement, interaction with

(3) M. E. Peover, “Electrochemistry of Aromatic Hydrocarbons and Related Substances,” in “Electroanalytical Chemistry,” Vol. 2, A. J. Bard, Ed., Marcel Dekker, New York, N.Y., 1967,

(4) M. Szwarc, ‘‘Carbanions, Living Polymers, and Electron Transfer Processes,” Interscience Publishers, John Wiley and Sons, New York, N.Y., 1968.

( 5 ) N. L. Weinberg and H. R. Weinberg, Chem. Rec., 68, 449 (1968).

pp 1-51.

158 ANALYTICAL CHEMISTRY, VOL. 44, NO. 1, JANUARY 1972