The Study of Reactive Intermediates by Electrochemical Methods

The Study of Reactive Intermediates by Electrochemical Methods V E R N O N D. P A R K E R Norwegian Institute of Technology, University of Trondheim, Trondheim, Norway 1 Introduction 132 2 Survey of methods 134 Current as the observable 135 Electrode potential as the observable 139 Optical observation of the intermediates I39 The choice of measurement technique 141 3 The role of diffusion 143 Electron-transfer reactions 143 Homogeneous chemical reactions coupled to charge transfer 145 Digital simulation of electrode processes 146 4 The effect of residual impurities in the solvent electrolyte on the electrode response 147 5 Thermodynamic data from electrode measurements 149 Phase-selective second harmonic a.c. (SHAC) measurements 149 Derivative cyclic voltammetry 151 Equilibrium constants for electron-transfer equilibria 152 Closely spaced consecutive electron transfers 154 The use of electrode potentials to determine pK,-values of weak carbon acids 155 Conformational equilibria studied by electrode measurements 156 The entropy of electrode processes 159 Determination of equilibrium constants for equilibria associated with charge-transfer reactions 160 “Absolute” electrode potentials 161 6 Electrode mechanism analysis and the treatment of kinetic data 162 The theoretical working curve 163 Analysis at a constant value of the observable 166 Reaction orders and LSV response I70 Detailed analysis of LSV waves 172 7 Applications to electrode-mechanism studies 174 Radical anion protonation 174 Reactions of radical cations with pyridines 178 Deprotonation of arenemethyl radical cations 18 1 Reactions of diazoalkane radical anions 184 Electrodimerization 195 Haloaromatic radical-anion cleavage 209 131

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8 Conclusion 216 Acknowledgements 2 16 References 2 16

1

Introduction

Since practically all organic reactive intermediates readily undergo electron transfer reactions, electrochemical methods play an important role in the study of their chemistry. The measurement of the electrode potential for the formation of the intermediate can lead directly to the standard free energy of the process. The kinetics of the reactions of intermediates, formed in exceedingly low concentrations can be deduced from the electrode response of the substrate from which the intermediate is derived by an electron transfer. The study of reactive intermediates generated at electrodes is most often referred to as organic electrochemistry. This is somewhat misleading and can give the impression that reactions of intermediates studied in this manner should differ significantly from those in which the intermediate is generated by non-electrochemical means due to the influence of the electrode. It is therefore of interest to examine the role played by the electrode in these reactions. In order to do this, it is necessary to distinguish between volume and surface reactions. In volume reactions, the electrode functions as an electron source or sink and specific interactions between the electrode and substrates or intermediates are weak or insignificant. In this case, the remaining possible influence of the electrode is due to the electric field in its immediate vicinity. Under usual measurement conditions, the potential gradient at the interface between the electrode and the bulk of the solution is of the order of log V m-1 (Albery, 1975). However, this high potential gradient extends only about 1 nm out into the solution. In order for the electric field to have any influence upon reactions of electrode generated intermediates, a significant fraction of the reaction has to take place very close to the electrode. For purposes of illustration, we can consider the first order reactions (2) of intermediate B, generated during electrode reaction (1). The thickness of the reaction layer P A&e-$B

(1)

kr

B-C

(Brdi&ka and Weisner, 1947) can be estimated using (3) where D is the P = (D/k,)+

(3)

diffusion coefficient of B. If we consider 100 nm as the maximum value of p

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ELECTROCHEMICAL METHODS

where the electric field can possibly influence the reactions of B and if B has a typical diffusion coefficient of about 10-5cm2s-1, we arrive at lo's-' as the minimum value of k, for reaction (2) that would be significantly affected by the potential gradient. Since under normal conditions during kinetic studies [B] will not exceed 10-3M, reactions that are second order in B will never be perturbed by the electric field near the electrode surface. During surface reactions the substrate, the intermediates, or both, interact strongly with the electrode and diffusion is restricted. The reactions of intermediates generated under these conditions can be expected to differ substantially from those in homogeneous solution. Electrode potentials measured under such conditions cannot be equated to thermodynamic potentials for the formation of the intermediates. Likewise, it is not possible to make kinetic measurements on the reactions of the intermediates which give information relating to the homogeneous solution chemistry. In order for an electrode process to be suitable for kinetic and thermodynamic studies of reactive intermediate chemistry it must be of the volume type. As we have deduced in the previous paragraphs, the electrode normally has no influence on the reactions of the intermediates under these conditions. We may then ask if there are any unique features of electrode generation of intermediates. One feature inherent in the method is that concentration gradients necessarily exist. The intermediate is formed at the electrode surface at a given concentration depending upon the substrate concentration and the electrolysis time and its concentration drops to zero out in the bulk of the solution. However, this is not a particular complication since the concentration gradients are well defined and are readily taken into account theoretically. In fact concentration gradients are not a unique feature of electrode reactions. Concentration gradients exist any time it is necessary to mix reagents together. In this case the gradients are much less well defined and can represent a significant limitation for kinetic analysis, especially for very rapid reactions (Ridd, 1978). Thus, there do not appear to be any unique detrimental features of electrode generation of intermediates providing that the rates of reactions are not so great that they occur in the region of the electric field near the electrode. If the heterogeneous charge transfer for the generation of the reactive intermediates is complicated by some surface character of the process it may be possible to circumvent the problem by using electrocatalysis. During electrocatalysis (Savkant, 1980) charge transfer at the electrode involves a catalyst redox couple, O/R, in a thermodynamically reversible reaction (4). O&e-+R

(4)

K5

R+A+O+B

(5)

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VERNON D. PARKER

The catalyst redox couple is selected so that K, is of suitable magnitude depending upon the rate of reaction (2). When the solution initially contains only 0 and A with 0 in excess, once electrolysis begins A never reaches the electrode surface due to the fast equilibrium ( 5 ) followed by the homogenous chemical reaction (2) of B. In this manner, the reactions of B are strictly of the volume type even though the direct electrode reaction may have surface character. Electrocatalysis is also appliable when the rate of reaction (2) is sufficiently great that the direct electrode process can be expected to be influenced by the electric field. In this case, the reaction layer thickness can be governed by the proper selection of the catalyst redox couple. The kinetics of the reactions of B can then be deduced in much the same manner as, although somewhat more complicated than, for the direct electrode generation. There are two principal advantages associated with the use of electrode methods for the generation and study of reactive intermediates. The selectivity of the electrode, governed by the electrode potential, is unequalled by other means of generation of intermediates. Furthermore, the means of generation can at the same time act as a highly sensitive and precise means of monitoring the reactions of the intermediates once formed. The study of reactive intermediates by electrochemical means, as well as the electroanalytical methods, are broad topics which cannot exhaustively be covered in a single chapter. Here, only those electroanalytical techniques which have been reduced to practical application in this field will be considered. A great deal of effort has gone into the development of methods to describe electrode processes theoretically. Only a brief introduction to the theoretical methods for handling the diffusion-kinetic problems is included. The applications discussed cover both thermodynamic and kinetic aspects of reactive intermediate chemistry and are a sampling meant to give an indication of the current state of the field.

2 Survey of methods A large number of electrochemical methods exist which are or have the potential to be useful in the study of reactive intermediates. The methods are conveniently categorized according to the quantity measured, usually the current, potential, or some optical property of the reactants or the intermediates. A further classification arises from the manner in which experiments are conducted, i.e. transient or steady state measurements. In this brief survey only those techniques which have been reduced to useful practice are discussed and even then the coverage is not exhaustive. More detailed discussion can be found in several excellent references sources (Bard, 1966-present; MacDonald, 1977; Bard and Faulkner, 1980).

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135

CURRENT AS THE OBSERVABLE

The majority of electrochemical methods involve the electrode potential as the variable and the current as the observable. The potential may be varied smoothly with time in the sweep methods or abruptly in step methods. Of the potential sweep methods, polarography at the dropping mercury electrode occupies a special position in that the early work using this technique provided the foundations upon which most of the modern techniques are based. The method involves low potential sweep rates (less than 10 mV s-l) and the recording of current-potential curves. The most pertinent data features are the limiting currents ( i L ) and the half-wave potential ( E J designated in Fig. 1. While the use of polarography has diminished in recent years due to

FIG.1 Illustration of a polarogram measured at a dropping mercury electrode

the introduction of methods and instrumentation capable of making measurements at much shorter times, it is still a very useful method for both thermodynamic and kinetic studies of the formation and reactions of intermediates. The method has been discussed in detail in a monograph (Galus, 1976). A closely related technique, alternating current (a.c.) polarography (Smith, 1966) differs in that a low amplitude sine wave is superimposed upon the linear potential sweep. With modern phase sensitive detectors, the amount of information derivable from the polarograms is greatly enhanced. Fast Fourier Transform methods have been incorporated into the gathering and processing of data to make a.c. polarography a highly sophisticated technique (Smith, 1975). Since the latter technique is not yet developed to a stage that it is readily implemented into non-specialist laboratories, it will not be discussed further. The aspect of a.c. measurements which is of greatest use at present is phase sensitive second harmonic a.c. voltammetry for the measure-

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ment of reversible potentials of electrode reactions (Bond and Smith, 1976). The method involves measuring the a.c. current at twice the frequency of the perturbing sine wave by means of a phase sensitive recorder or lock-in amplifier. At the present time this method can be recommended as the most precise method of obtaining reversible electrode potentials for the oxidation or reduction of organic compounds. Rotating disk electrode voltammetry (Opekar and Beran, 1976) gives essentially the same type of information as polarography and differs principally in that convection of the solution at the interface with the electrode is accomplished by rotating the electrode rather than by the dropping mercury electrode. The rotating ring disk electrode (Albery and Hitchman, 1971) incorporates an additional feature, i.e. a ring electrode concentric with the disk which allows for the monitoring of products of the electrode process taking place at the disk. All of the methods mentioned so far are essentially steady state measurements as long as the potential sweep rate is sufficiently low that the charging of the electrical double layer at the solution-electrode interface can be considered to be rapid. This is certainly an advantage in the evaluation of data as has been stressed (Albery, 1975). However, the distinction between volume and surface behaviour is often time-dependent during the electrode reactions of organic compounds in non-aqueous solvents. Very often, reactions that appear to have only volume characteristics at short times using transient techniques are accompanied by severe adsorption on the electrode at longer times and become surface processes under steady state conditions. It has been the author’s experience that these problems are so general that transient techniques are usually of more value than the steady state methods in spite of the added complication of having to contend with double layer charging problems. The remaining methods that will be surveyed are of the transient variety. Linear sweep and cyclic voltammetry differ essentially from those already mentioned in that mass transport to the electrode is restricted t o diffusion. In order that convection does not set in, it is necessary to maintain higher (> 10 mV s-l) sweep rates. Sweep rates as high as 10 kV s-1 (Ahlberg and Parker, 1979) have been applied to processes in non-aqueous solvents. Due to differences in the mode of mass transport when stationary electrodes are used, the current-voltage curves differ from the polarogram. In this case the characteristic feature of the response is the occurrence of current peaks during linear sweep voltammetry (LSV). During cyclic voltammetry (CV) the direction of the linear potential sweep is reversed after the peak for the primary electrode process of the substrate is observed. On the return sweep, a peak due to the reverse reaction (I), primary intermediate to substrate, may or may not appear depending upon the stability of the intermediate during the

E LECTROC H EM IC AL M ETH0 DS

137

time scale of the experiment. The form of the cyclic voltammogram for a reversible electron transfer is illustrated in Fig. 2. There are a number of criteria for a reversible process. (i) The peak potential separation (EFd E;) is close to 59/n mV, where n is the number of electrons transferred, at 298 K. The exact value depends upon the difference between the peak potentials and the switching potential (Eh). (ii) The peak current ratio (ZpOX/ZFd) is

FIG.2 Illustration of a cyclic voltammogram for a reversible redox system

equal to 1.0. (iii) The peak current measured on the forward sweep increases linearly with vf, where v is the voltage sweep rate. (iv) The peak width ( E , = E,,2 - E,, where Ep,2is the potential at which I = .) I,) is equal to 2(1.109) RT/nF. When used in this context, reversibility implies. thermodynamic reversibility (i.e. fast electron transfer) as well as chemical stability of both species of the redox couple. The fundamental variable of LSV and CV is v. A process that appears reversible at a particular v need not be at some other sweep rate. The peak current ratio during CV is adirect measure of the chemical stability of the intermediate resulting from the charge transfer. For example, for a reaction following eqns (1) and (2), the peak current ratio will be equal to 0.5 at 10 V s-l if k, is equal to 30 s-l and the same value at 100 V s-l if k, is 300 s-l. The observation of a peak for the primary intermediate on the reverse scan is sufficient to estimate the lifetime of the intermediate to about a factor of 5. Both LSV and CV will be discussed in a more quantitative manner in later sections. Detailed descriptions of the methods can also be

VERNON D. PARKER

138

found in several books (Adams, 1969; MacDonald, 1977; Bard and Faulkner, 1980). The potential step methods are called chronoamperometry and like LSV and CV can deal with only the forward process (single step) or with the reverse process, involving the primary intermediate, as well. The latter is called double potential step chronoamperometry (DPSC) and is by far the most useful in kinetic studies. The applied potential-time wave form as well as the currenttime response for a reversible electrode process are illustrated in Fig. 3. The potential is stepped from a rest value where no current flows, usually 200300 mV from the potential where the process of interest takes place, to one

I

El

I

I

rf

time

I 2Tf

I

FIG.3 Illustration of the potential (E) waveform applied and the current ( I )

response during double potential step chronoamperometry

where the electrode reaction is diffusion controlled, i.e. usually 200 mV or more beyond the peak of a CV for the process. At the end of time, Tf, the potential is stepped once more this time to avalue where the reverse reaction is diffusion controlled. The current is measured at Tf (If)and again at 2 -rt (&). The ratio of the currents for the backward and forward processes, R, = Ib/If, is then a measure of the chemical stability of the intermediate. For the no reaction case, R, = I - 2-* (= 0.2929). In handling data for kinetic measurements a normalized current ratio is calculated by dividing the experimental values by 0.2929, i.e. that for the no reaction case. With reference once again to reactions (1) and (2), the rate constant for (2) can be calculated from k = 0.41 l / ~ where + T* is Tfwhen the normalized current ratio is 0.5 (Childs et al., 1971). The practical limit for the use of DPSC in non-aqueous solvents is pulse widths of the order of 1 ms.

ELECTR 0 C H EM I CAL M ETH 0 DS

139

ELECTRODE POTENTIAL AS THE O B S E R V A B L E

Chronopotentiometry closely resembles chronoamperometry with the exception that the role of current and potential are reversed. In chronopotentiometry the current is controlled and is the variable and the electrode potential is the observable. A single step of the current or a double step can be employed. The double step method called current reversal chronopotentiometry is more information-rich as in previous comparisons. Both the applied currenttime wave form and the potential-time response for a reversible electrode process are illustrated in Fig. 4. The current step from 0 to a predetermined value depending upon the experimental conditions is maintained until time

FIG. 4 Illustration of the current ( I ) waveform applied and the potential ( E ) response during chronopotentiometry

rr and then stepped to a value of the same magnitude but opposite in polarity. The measure of the chemical stability of the intermediate is given by the reverse transition time T ~ where , the rapid potential change due to depletion of the intermediate is observed, in relation to r,. There are practical difficulties with the evaluation of transition times which make the method less useful than CV and DPSC. Since no new information, not available from the other techniques, can be derived, chronopotentiometry cannot at the present state of development be recommended as a technique for the study of reactive intermediates. OPTICAL OBSERVATION OF T H E INTERMEDIATES

The fundamentals and some of the practical aspects of spectroelectrochemistry have been reviewed (Kuwana and Winograd, 1974). The most common modes of operation are either to use optically transparent electrodes or to

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140

reflect the light beam off the electrode surface. In general, the experiments are conducted in much the same manner as in DPSC with the optical absorption of the intermediate serving as the observable rather than the current. The technique has an additional feature which is very useful in kinetic studies. If at the end of the potential step used to generate the intermediate the electrode is disconnected, the homogeneous relaxation of the intermediate giving rise to the optical absorption can be studied (Blount et al., 1970). The generation of an intermediate during the potential step and subsequent behaviour after open circuit is shown in Fig. 5. In this particular case, the

0

LOO

Timelms)

1200

FIG.5 Absorbance time curves for the spectroelectrochemicalgeneration of perylene radical anion at 570 nm in dimethylformamide (a), and with the addition of phenol (b). The time to open circuit (dashed line) is 400 ms. (Ahlberg et al., 1979)

absorbance at 570 nm is due to perylene radical anion in dimethylformamide (Ahlberg et af., 1979a). After 400 ins the electrode was disconnected and curve (a) shows that the intermediate was stable during the experiment. Curve (b) was recorded for the same solution after the addition of phenol and the decay after open circuit was due to the pseudo first order reaction of the radical anion with phenol. Another experimental approach is to modulate the potential of the electrode by a periodic function usually a sine or square wave and observe the synchronous spectral response by means of a phase-sensitive detector (Aylmer-

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141

Kelly et al., 1974; Mollers and Memming, 1973). This method has the advantage that only absorbances synchronized with the electrode potential are detected. An example of the use of the technique is shown in Fig. 6, in which case the spectrum of the perylene radical anion was obtained even though the intermediate was reacting rapidly with acetic acid (Ahlberg et al., 1978). Spectra of intermediates can also be obtained using rapid scanning spectrometers after a potential step (Strojek et al., 1969).

FIG.6 Visible absorption spectra of the perylene radical anion in DMF containing acetic acid (70 mM) measured by modulated specular reflectance at 3 Hz (a), 10 Hz (b), 30 Hz (c), 60 Hz (d), and 80 Hz (e). (Ahlberg, et al., 1978) THE CHOICE OF THE MEASUREMENT TECHNIQUE

The electrochemical techniques do not differ significantly with respect to time resolution. Pseudo first order rate constants ranging from about 0.1 to IO5s-l can be measured by techniques which monitor the response of the intermediate and LSV and electrocatalysis can give estimates of rate constants as high as 1Ogs-l. In the opinion of the author, the factors of most importance to be considered in selecting a measurement method of the first style are (i) the selectivity of the response, ( i i ) the ease of obtaining reliable data, and (iii) the kinetic or thermodynamic information content of the data. Another factor of utmost importance to the non-specialist is (iv) the availability of instrumentation.

142

VERNON D. PARKER

With regard to the selectivity of the response, spectroelectrochemistry is often quoted as being the ultimate technique in this respect. Perhaps it has the capability of being so but in the manner that it is most often employed in kinetic studies, i.e. a potential step while monitoring the absorbance at a fixed wavelength, the selectivity is no greater than when the current is monitored in DPSC. When modulation techniques are used the selectivity is greater and is comparable to cyclic voltammetry where the wave shape gives a direct indication of any complications. The following discussion of point ( i i ) is based on personal experience. In our laboratory we have access to modern equipment for all of the techniques described in the previous paragraphs. For kinetic studies where the response of the intermediate is observed, we find the most convenient techniques to be CV and DPSC. In the past, CV has been a somewhat qualitative method but recent development using the derivative response has contributed to making it a highly precise kinetic tool (Ahlberg and Parker, 1981a,b). We have had considerably greater problems in obtaining reliable spectroelectrochemical or rotating ring-disk electrode data. Part of the problems that we have encountered with both of these techniques is due to the distinction between volume and surface processes. Rotating ring disk electrode voltammetry is a steady state method involving relatively long measurement times. Although spectroelectrochemistry is a transient technique used in the usual way with a potential step, signal averaging is necessary, and after several hundred or thousands of pulses adsorption problems are often quite severe. Ideal systems do not provide these problems. The apparatus for spectroelectrochemistry is somewhat more complex than that for the other techniques. We find LSV to be the kinetic method which gives the most detailed information related to the mechanism of the reaction of the intermediate. As will be discussed in some detail later, the reaction orders in all species appearing in the rate law can be derived from the LSV response (Parker, 1981f). The reaction orders in substrate and primary intermediate are not directly separable using the data from the other techniques. Because of the possibility of obtaining homogeneous relaxation data in addition to the direct response, spectroelectrochemistry can offer more kinetic detail than the other direct techniques. When applicable, second harmonic a.c. voltammetric measurements give the most reliable reversible potentials. Using the first derivative of the response during cyclic voltammetry allows precision to be attained approaching that for the second harmonic a.c. measurements. The most generally useful technique is CV when coupled with the capability of obtaining the first derivative of the response. This single technique allows one to obtain precise electrode potentials for thermodynamic studies or LSV mechanism analysis, as well as kinetic data obtained by measurements on the response due to the primary intermediate of the reaction.

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143

3 The role of diffusion Regardless of the nature of the electrochemical experiment, diffusion plays a major role in the transport of substrate to the electrode. The effect of forced convection is to decrease the thickness of the diffusion layer. Thus, at very high rotation rates using the rotating disk electrode, the diffusion layer becomes very thin during a charge-transfer reaction. The simplest case encountered in electrochemical methods is represented by diffusion to a planar stationary electrode in quiet solution. Under these conditions the system approximates semi-infinite linear diffusion. The semi-infinite term implies that the distance between the electrode surface and the wall of the vessel is great enough that the diffusion layer never extends that far. For a potential step experiment under these conditions where the charge-transfer reaction is diffusion-controlled, the thickness of the diffusion layer (x) can be considered never to exceed the value estimated by (6), where D is the diffusion coefficient x,,,

=

6 (Dt)*

of the species undergoing electron transfer and f is the time after the potential step. In order to have theoretical relationships with which experimental data can be compared for analysis it is necessary to obtain solutions to the partial differential equations describing the diffusion-kinetic behaviour of the electrode process. Only a very brief accountmf the theoretical methods is given here and this is done merely to provide a basis for an appreciation of the problems involved and to point out where detailed treatments can be found. A very lucid introduction to the theoretical methods of dealing with transient electrochemical response has appeared (MacDonald, 1977) which is highly recommended in addition to the classic detailed treatment (Delahay, 1954). Analytical solutions of the partial differential equations are possible only in the most simple cases. In more complex cases either numerical methods are used to solve the equations or they are transformed into finite difference forms and solved by digital simulation. ELECTRON-TRANSFER REACTIONS

In order to demonstrate the mathematical approch to describing the electrode process we can consider the potential-step experiment for a reversible charge transfer without kinetic complications. In this case there are two diffusing species, A and B in (1). However, if the potential of the electrode is sufficiently greater than the reversible potential for reaction (l), the reverse reaction can be neglected so that only the diffusion of A contributes to the current. The equation to be solved results from Fick’s second law and is given by (7). The aCA/at = DA(azcA/aX2)

(7)

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144

first step in the solution of the partial differential equation is to set up the initial and boundary conditions required by the experiment which are eqns @)-(lo) where x is the distance from the electrode surface, C i is the concen-

r > 0, X

= 0: CA(X = 0) = 0, I = nFADA(aCA/aX)

(10)

tration of A in the bulk of the solution and A is the electrode area. The initial conditions before electrolysis (8) state that CA is uniform throughout the solution. The first boundary condition (9) is a consequence of semi-infinite linear diffusion, i.e. at distances far from the electrode CA approaches the bulk value. The second boundary condition (10) states that CAat the electrode surface is 0, a consequence of diffusion-controlled charge transfer, and that the current I gives the flux of A at the surface. The most common approach to solution of partial differential equations of the type represented by (7) involves the use of Laplace transformation (Crank, 1957). The method involves transforming the partial differential equation into a total differential equation in a single independent variable. After solving the total differential equation inverse transformation of the solution can be carried out in order to reintroduce the second independent variable. Standard Laplace transforms are collected in tables. Laplace transformation of (7) leads to eqn (11) where C is the Laplace

C = C i / s - (C;/s)e-"u

(1 1)

transform of the time-dependent concentration of CA and s is defined by (12) which gives the Laplace transform in t of the function f(r) and o! is (DAIS)*. m

f(s) = le-s'f(t)dt 0

(12)

The next step is to differentiate (1 1) with respect to x and substitute into the Laplace transform of the current to give (13). Finally, inverse Laplace

i = nFADiCi/s*

(13)

transformation of (1 3) gives the expression for the decay of current with time (14) called the Cottrell equation.

I

= nFADiCi/xftf

(14)

In order to demonstrate the low degree of complexity necessary to make an analytical solution of the partial differential equation impossible we only

145

E LECTROC H EM I CA L M ETH 0 D S

-

need to include a rate constant for the charge-transfer step. For reaction (15) where kf is the heterogeneous rate constant, boundary condition ( I 0) must

0

+ ne-

kr

R

(15)

be replaced by (16) which takes into account control of the rate by reaction t > 0, x

= 0:

Do(aCo/ax)= kfCo(x= 0), I

= nFAk,Co(x = 0 )

(16)

(15) rather than diffusion. Going through the procedure of Laplace transformation and taking the inverse transformation results in (1 7) to describe

the current-time decay. In (17) erfc is the complement of the error function

I

= nFAkrC,”exp (k,2t/D0)erfc (k,t4/Dd)

(17)

(Doetsch, 1953) and requires numerical evaluation. The quasi-reversible charge-transfer reaction which takes into account reverse reaction (1 5) is an even more difficult theoretical problem and cannot be solved analytically (Nicholson, 1965). HOMOGENEOUS CHEMICAL REACTIONS COUPLED TO CHARGE TRANSFER

A simple first order reaction following reversible charge transfer is one of the few cases for which an analytical solution to the diffusion-kinetic differential equations can be obtained. For reactions (1) and (2) under diffusion-controlled charge-transfer conditions after a potential step, the partial differential equations which must be solved are (18) and (19). After Laplace transforma-

aCAiat = DA(azcA/aXz) aCB/af = DB(a2cB/aX2)- k&B

(18)

(19)

tion and inverse transformation along with a number of other mathematical operations, the expression (20) is obtained for the current for the reverse process following a double potential step (Schwarz and Shah, 1965). In I

=

--nFADACi[+(k, r,

r)/{x(r - r)}*- I/(nt)*]

+

(20)

(20) r is the time in the forward direction and is a complex function of kz, t and r. The example given above sufices to show the complexity of the solution of the differential equations for the most simple of reactions coupled to charge transfer at an electrode. Most reaction schemes of interest result in equations which cannot be solved analytically. Numerical methods have been used extensively to solve the equations for various mechanisms coupled to charge transfer. The most significant efforts in this field are the contributions by

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VERNON D. PARKER

Shain, Nicholson, and SavCant and their collaborators. Much of this work has recently been summarized (MacDonald, 1977). DIGITAL SIMULATION OF ELECTRODE PROCESSES

In recent years, digital simulation has proved to be a very versatile and straightforward method to obtain theoretical data for the electrode response (Feldberg, 1969). The method involves discretization of both space and time, i.e. the diffusion layer is divided into finite volume elements of thickness A x and the processes of diffusion and chemical reactions are allowed to take place during time elements At. During any particular At species are only allowed to move between adjacent volume elements. For example, for the case with initial and boundary conditions (8)-(10), before the first time step CA = C i and CB = 0 throughout the solution. During the first time step Atl all of A is converted to B in volume element 1 and diffusion of A and B is allowed to take place between volume elements 1 and 2. During the second step all A in element 1 is first converted to B and diffusion takes place in volume elements 1 to 3. Thus, if the diffusion layer is divided into k volume elements, k-1 time steps are required before volume element k will be affected. The concentration profiles of A and B generated by the simulation will appear as staircase curves rather than the continuous functions generated in the real experiment. Thus, in order for the simulation to describe the experiment accurately both Ax and At must be small and the smaller they are the better the simulation. The sequence of operations during any At is (i) electrode reaction, (ii) diffusion and (iii) chemical reactions. In order to carry out a simulation of the electrode response it is first necessary to transform the partial differential equations describing the process to the finite difference form. The finite difference form of (19) which describes the diffusion of B generated in (1) and reacting in (2) is given by (21). In (21) D , is the model diffusion coefficient equal to D A f / A x zand is dimensionless.

+

+

CB(X, f f hf) = CB(X, f ) DM{c~(X AX, f ) - 2 + CB(X- Ax, f ) } - k,AfCB(X, f )

cB(X,

f) (21)

The concentrations are converted into dimensionless form by dividing by CAthroughout. In cases where comparisons have been made, theoretical data obtained by digital simulations are always in agreement with those from analytical solutions of the diffusion-kinetic equations within the limit of experimental error of quantities which can be measured. A definite advantage of simulation over the other calculation techniques is that it does not require a strong mathematical background in order to learn and to use the technique. A very useful guide for the beginner has recently appeared (Britz, 1981).

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ELECTROCHEMICAL METHODS

4

The effect of residual impurities in the solvent electrolyte on the electrode response

Since electrode measurements involve low substrate concentrations, reactive impurities have to be held to a very low level. The physical data and purification methods for several organic solvents used in electrode measurements have been summarized (Mann, 1969). But even when careful procedures for solvent and electrolyte purification are employed, residual impurities can have profound effects upon the electrode response. For example, the voltammetric observation of dications (Hammerich and Parker, 1973, 1976) and dianions (Jensen and Parker, 1974, 1975a) of aromatic hydrocarbons has only been achieved during the last ten years. The stability of radical anions (Peover, 1967) and radical cations (Peover and White, 1967; Phelps et al., 1967; Marcoux et al., 1967) of aromatic compounds was demonstrated by cyclic voltammetry much earlier but the corresponding doubly charged ions were believed to be inherently unstable because of facile reactions with the solvents and supporting electrolytes. However, the effective removal of impurities from the electrolyte solutions extended the life-times of the dianions and dications so that reversible cyclic voltammograms could be observed at ambient temperatures even at very low sweep rates. The procedure for removing the traces of residual impurities is very simple. Active neutral alumina, suspended in the voltammetric cell by rapid stimng, was observed to be highly effective (Hammerich and Parker, 1973). Cyclic voltammograms clearly demonstrating the stability of the dications of various aromatic compounds are shown in Fig. 7. Corresponding voltammograms showing reversible radical anion-dianion redox couples are illustrated

1.5

1.2

0.9

I

I 1.8

I

I

1.5 1.2 Z v s SCE

I

1.8

I

1.5

I

1.2

I 1

0.9

FIG.7 Illustration of cyclic voltammogramsfor consecutive oxidations of aromatic compounds to cation radicals and dications. (Hammerich and Parker, 1973)

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148

in Fig. 8. The alumina technique is now widely used for the removal of acidic, basic, nucleophilic and electrophilic impurities from electrolyte solutions during electrode studies (Evans, 1977). Nitrobenzene

-1.85 -225 -2.65

-1.65 -2.05 -2.45

R2

I

u -0.85 -1.25 -1.65 -2.05

E(VvsSCE)

FIG.8 Illustration of cyclic voltammograms for consecutive reductions of aromatic compounds to anion radicals and dianions

ELECTRODES

FIG.9 Apparatus for the purification of solvent-electrolyte systems and the electrochemical preparation of solutions of reactive intermediates. (Lines et a/., 1978)

E LECTRO C H EMICAL M ETH 0 D S

149

The purification techniques have been refined so that the alumina is contained in a separate compartment of the apparatus and the impurities are removed by repeated cycling of the electrolyte through the alumina column and the cell (Lines et al., 1978). A diagram for the apparatus used to prepare stable solutions of radical anions by cathodic reduction in DMF is illustrated in Fig. 9. More recently further refinements have been made and water contents of acetonitrile solutions as low as lo-' M have been estimated (Kiesele, 1981). The purity of the solvent-electrolyte systems during kinetic and thermodynamic investigations by electrode techniques is surely a factor that cannot be neglected. Such neglect has led to the publication of a number of electrode mechanisms which were later shown to be incorrect. 5

Thermodynamic data f rom electrode measurements

The measurement of an electrode potential is the most direct method of obtaining the free energy change or the equilibrium constant of a reaction. In order that electrode potentials be thermodynamically significant they must be reversible values, i.e. the charge transfer must be rapid in comparison to the measurement technique and both species of the redox couple must be stable in solution. Thus, in order to obtain reversible potentials, conditions must be found where both of the criteria of reversibility are satisfied. It is usually necessary first to find conditions where the chemical stability requirement is fulfilled and then to determine whether or not the electron-transfer rate is rapid enough that the potentials are not influenced by this factor. The means of achieving chemical stability are the effective removal of residual impurities, lowering reaction rates by decreasing the temperature, and decreasing the time scale of the measurement. The last two can give rise to increased problems with charge-transfer rates which represents a limitation to both the applicable temperature range and the time scale for the measurements. At temperatures not too far removed from 298 K and voltage sweep rates of 100 V s-' during CV, or at a.c. frequencies of less than 300 Hz, charge transfer to and from most aromatic molecules and ions is sufficiently rapid so that the electrode potentials measured are not greatly influenced by the measurement technique. This will be assumed to be the case in the discussion in the remainder of this section. PHASE-SELECTIVE SECOND H A R M O N I C a.c. (SHAC) MEASUREMENTS

Theoretical studies suggested that SHAC voltammetry should be capable of providing reversible electrode potentials even for processes producing highly reactive intermediates (McCord and Smith, 1969). For a process following

150

VERNON D. PARKER

reactions (1) and (2) the reversible potential was predicted to be accessible as long as k, < 3 w where w is the angular frequency in radians per second. SHAC was applied to a number of processes where k was of the order of 10 s-l or less and a measurement precision of f0.5 mV was observed in Ere' (Bond and Smith, 1974). The criteria for SHAC voltammograms to yield reversible potentials are that the zero-current crossing potentials must be both frequency- and phaseindependent. In practice one measures the in phase ( I ) and quadrature (Q) components of the second harmonic a.c. current by means of a phase-sensitive detector or lock-in amplifier. The response is illustrated in Figs 10-12 obtained during measurements on the oxidation of 9,lO-diphenylanthracene (DPA) in acetonitrile (Fig. 10) and in acetonitrile containing pyridine (Figs 11 and 12). When the electrode-generated intermediate, DPAt in this case, is stable during the time of the d.c. sweep, the I and Q components are symmetrical and appear as mirror images about the current axis. The traces intersect near zero current and the intersection defines Ere' (Fig. 10). The

E 12

Z

C

-

100mV

E

FIGS10-12 Phase-selective second harmonic ax. voltammograms for the oxidation of 9,lO-diphenylanthracene(Fig. 10, Fig. 11) and anthracene (Fig. 12) in acetonitrile.Pyridine concentration equal to 0 (Fig. lo), and 8.4 mM (Figs 11, 12). Voltage sweep rate = 10 mV s-l, a s . frequency = 100 Hz. (Ahlberg and Parker, 1980a)

ELECTROCHEMICAL METHODS

151

theoretical relationships are not followed precisely in this case, the Q current is higher than the Z and the intersection is not exactly at zero current. When the product of the electrode reaction reacts at a moderate rate the reversible potential can still be obtained. In this case (Fig. 1l), the mirror image relationship still holds and the traces cross at zero current. The difference between this case and the previous one is that the traces are not symmetric. The current at the peak before the zero crossing potential is greater than that at higher potentials. The reason for the difference is that substrate and intermediate are being consumed during the potential sweep. The third example (Fig. 12) shows the response under conditions where the radical cation is reacting so fast that neither of the criteria for reversible potential measurements holds and the traces cross far from zero current. It should be noted that it is impossible to tell from the Q component that the process is not reversible under these conditions. If measurements are carried out with the detection of only one phase, the other criterion, the frequency-independence of the measured potentials must be relied upon. The reaction of DPAt with nucleophiles was used as a test reaction to evaluate the use of SHAC for the measurement of Err' in rapidly reacting redox systems (Ahlberg and Parker, 1980a).It was concluded that the theoretical relations can be realized in organic systems up to o equal to about lo4 radians per second (- 1 kHz applied frequency) and that the reversible potential can be estimated to about 0.1 V for much faster reactions, i.e. k about 10%-1.

DERIVATIVE CYCLIC VOLTAMMETRY

The use of the first and higher derivatives of the cyclic voltammograms for data analysis (Perone, 1972) had been examined during the 1960s but due to errors inherent in the analog differentiators then used the method was not recommended for the measurement of electrode potentials. However, it has recently been found that a commercially available selective amplifier (Princeton Applied Research Company, Model 189) can be used as an analog differentiator to give highly precise peak potentials during CV (Ahlberg et al., 1980a). An extensive set of measurements on the reduction of benzonitrile in DMF has been reported which shows that CV can be a quantitative technique and is suitable for highly precise thermodynamic and kinetic studies (Ahlberg and Parker, 1981a). Peak potentials were measured to a precision of f0.2 mV. At low potential sweep rates LSV or CV compete effectively with SHAC as a tool for the precise measurement of electrode potentials. However, in reacting systems requiring high sweep rates or high frequencies the method of choice is clearly still SHAC.

152

VERNON D. PARKER

Both derivative CV and SHAC voltammetry require specialized instrumentation. A much more simple experimental procedure has been described for electrode potential measurements which can be done with respectable precision using rudimentary instrumentation. The measurement of peak potentials during LSV is normally carried out to a precision of the order of f5 mV. This is because the peak resembled a parabola with a rather flat maximum. On the other hand, the half-peak potential PI2,where the current is half the peak value, has just as much thermodynamic significance and can be measured to about fI mV using x-y recording with a suitable expansion on the potential axis. When used in conjunction with a digital data retrieval system the method is as precise as derivative cyclic voltammetry (Aalstad and Parker, 1980). The applications described in the following paragraphs are taken from examples where the measurement techniques were the newer more precise methods or in some cases less precise CV peak potential measurements. In many of the applications precise measurements were not necessary and when this is the case it is often most convenient to make CV measurements without any refinements. EQUILIBRIUM CONSTANTS FOR ELECTRON-TRANSFER EQUILIBRIA

The equilibrium constant for an electron-transfer reaction (22) can be K 22

M + R + N + S M

+e

+N -e

R

-e

+S

+e

determined by the measurement of the electrode potentials for half reactions (23) and (24) and applying eqn (25). In using (25) it does not matter how the In K,,

=

-(RT/F)(&

- EU)

(25)

potentials are measured as long as they are consistent, i.e. if the peak potential is used for E23the same quantity must be used for EZ4. Equilibrium constants for a number of electron-transfer equilibria involving aromatic compounds and radical cations were calculated from CV data and compared to spectroscopically determined values (Svanholm and Parker, 1973). The values of K,, obtained by the two methods corresponded very closely. The differences noted are most probably due to inaccuracies in the spectroscopic values since the preparation of solutions of cation radicals is

ELECTROC H EM I CAL M ETH 0 DS

153

accompanied by some uncertainty in the concentrations. Similar studies had previously been carried out on the formation of anion radicals where the electrochemical method was potentiometric titration (Hoijtink et al., 1956; Jagur-Grodzinski et al., 1965) and once again the correspondence in K2,values was quite good. The disproportionation of radical ions is a special case which has been studied rather extensively. Electron transfer between two anion radicals AT + A-

K 26

+ A2- + A

results in the formation of the dianion and the substrate as in (26). The equilibrium constant for (26) has been found to be very dependent upon the solvent and the nature of the counter-ion, especially in solvents of low polarity (Szwarc and Jagur-Grodzinski, 1974). An example of the determination of K,, where AT is the perylene anion radical is demonstrated by the SHAC voltammograms in Fig. 13. The electrode potentials for the formation

E FIG. 13 Phase-selective second harmonic a.c. voltammograms for the two consecutive one electron reductions of perylene in DMF containing Bu4NBF4(0.2 M); frequency equal to (a) 300 Hz (b) 3000 Hz,and (c) 30 000 Hz.(Ahlberg et al., 1978)

of the anion radical and the dianion were observed to be frequency-independent in the range studied, 300 Hz to 30 kHz. An interesting feature of the figure is that at 30 kHz the phase was the reverse of that in the two voltammograms measured at lower frequencies. This must have been caused by some phenomenon not directly connected with the electron transfer, perhaps to do with double-layer charging. However, in spite of this problem there was no change observed in the zero-crossing potentials. The effect of tetraalkyl-

V E R N O N D. PARKER

154

ammonium ions on disproportionation constants measured in DMF has been studied by CV (Jensen and Parker, I975a,b). Disproportionation of viologens and related radical cations has been the subject of a recent review (Hunig and Berneth, 1980). The structural and environmental factors which contribute to the position of disproportionation equilibria of radical anions of aromatic nitro-compounds have been studied in detail (Ammar and SavCant, 1973; Andrieux and Saveant, 1974). A series of dinitrophenyl compounds of which both the radical anions and dianions are moderately stable in dimethylformamide and acetonitrile was chosen as a model. The differences in the reversible electrode potentials for the two consecutive charge transfers were determined by cyclic voltammetry as a function of temperature. The differences in E were separated into the enthalpic and entropic contributions, AE, and AcS, respectively. In all cases AE, I 0 implying, as expected, that the structuring of the solvent is greater during the second electron transfer than during the first. The enthalpy term was further separated into internal (AEHi) and environmental (AE,,) parts by comparing data obtained in the two solvents. It was found that AEHi decreased as the separation between the two nitro groups in the molecule increased and with increases in the degree of conjugation. The effect of the addition of water and the presence of Li+ on the disproportionation equilibria was also examined (Ammar and Savtant, 1973). The effect of water was observed to be a decrease in AE'"' with little change in the entropy term. On the other hand, Li+ also brought about a decrease in AE'"' but the entropy increased and became positive. The latter brought about an inverse temperature effect; instead of AEreVincreasing with temperature a decrease was observed.

CLOSELY SPACED CONSECUTIVE ELECTRON TRANSFERS

Due to special structural features in the molecules, a number of electrode processes of aromatic compounds appear qualitatively as two electron transfers. In the cases where this has been observed, the molecules are usually large so that the charges in the doubly charged ions can be separated far enough to reduce the coulombic repulsion. The formation of strong ion pairs (Szwarc and Jagur-Grodzinski, 1974) can have the same effect. A pertinent example of this behaviour is found during the voltammetric oxidation of tetrakis-p-methoxyphenylethylene(TME) in acetonitrile (Parker et al., 1969; Bard and Phelps, 1970, Svanholm et al., 1974) as indicated in (27). The peak TME

-e-

-e-

+ TME+ + E,

Ez

TME2+

155

ELECTROCHEMICAL METHODS

separation during cyclic voltammetry is greater than predicted by the theoErd

-

E&

(In IO)RT/nF

(28)

:

retical relationship (28) for n = 2 but less than for the case where n = 1. The analysis of the LSV waves for cases analogous to (27) where E; - EY ranged from -180 to +51 mV (the signs refer to an oxidation process) in terms of the peak width EP - Epiz (Myers and Shain, 1969) and a working curve was presented from which E; - EP could be estimated from experimental peak widths. The theoretical data were re-examined (Svanholm et al., 1974) and linear eqn (29) was found where w refers to the peak width. An log ( W

-

29)

=

(0.00976) AEo

+ 1.095

(29)

obvious drawback of the analysis is the inherent error in peak-potential measurements. A much more precise analysis (Aalstad and Parker, 1982) has been presented using normalized potential sweep voltammetry (Aalstad and Parker, 1981). The method, which is discussed in detail in a later section, involves normalizing the current by dividing by the peak current and a direct linear comparison between experimental and theoretical data can be made. The oxidation of tetrakis-p-dimethylaminophenylethylene analogous to (27) in acetonitrile is a process which fits the theoretical criteria for a reversible two electron transfer and (28) is obeyed (Bard and Phelps, 1970). THE USE OF ELECTRODE POTENTIALS TO DETERMINE THE W E A K CARBON ACIDS

PK,-VALUES

OF

In the absence of activating unsaturated groups the hydrocarbons are exceedingly weak acids. The direct measurement of pK, in such cases has not been achieved. Reversible electrode potentials have been used in conjunction with bond-dissociation energies via thermodynamic cycles (30-3 1) to estimate +e-

RH + ROH + R+ + R' RH+R'

+e-

+e-

-e-

+ R-(+RH)

+ H ' + R - + H'+R'

.

+ H+(+RH)

(30)

(31) the pK, values for even the most weakly acidic hydrocarbons (Breslow and Chu, 1973; Breslow and Mazur, 1973; Wasielewski and Breslow, 1976; Breslow and Goodin, 1976; Breslow and Drury, 1974; Breslow and Grant, 1977; Jaun et al., 1980). Some of the pK,-values estimated in this way are triphenylmethane (31 S ) , propene (47.1-48.0), toluene (44.4-45.2), and 4,4-dimethylpent-2-yne (44.2-45.4). It should be pointed out that this is a case where precision in the electrode potential measurement is not very critical. An error as great as 10 mV in the electrode potential brings about an error of

156

VERNON D. PARKER

less than 0.25 kcal mol-' in the free energies of the steps involving electron transfer. This is certainly not the limiting factor in the precision of the pK, values estimated in this manner. CONFORMATIONAL EQUILIBRIA STUDIED B Y ELECTRODE MEASUREMENTS

Conformational equilibria involving rotations around single bonds are usually too fast to be detected by electrochemical techniques. However, when steric interactions are increased,usually brought about by the restrictions introduced in cyclic systems, the conformers may be detected by differences in the electrochemical response. A classic example of this behaviour involves apparently slow electron transfer to cyclo-octatetraene (COT) to form first the radical anion and then the dianion (Allendoerfer and Rieger, 1965) as in (32). The -e

-e

heterogeneous rate constant for the first step was found to be much lower than that for the formation of the dianion, and this was attributed to the necessity of COT in a tub conformation to undergo first a conformational change involving flattening of the ring which requires about 13 kcal mol-'. The planar radical anion can then undergo electron transfer to the planar dianion without the necessity of undergoing conformational change. However, it is now less clear just how much of the observed activation energy, 13 kcal mol-', is due to the conformational change. It has been found that when the reduction is carried out in the presence of small tetra-alkylammonium ions that the rate of the first electron transfer is significantly increased (Jensen et al., 1975; Fry et ul., 1975). The free energy of activation AGt has been observed to be dependent upon the cation and values of 9 kcalmol-' (Et,N+) and 8 kcal mol-' (Me,N+) have been estimated for the reduction of COT in DMF at 298 K (Jensen and Parker, 1976). The conformational equilibrium (33) has recently been examined using Br

ee

aa

Br

cyclic voltammetry at temperatures ranging from -55°C to -90°C (Klein and Evans, 1979). At room temperature truns-l,2-dibromocyclohexaneexists as a rapidly equilibrating mixture of the ee and au conformers (33). The linear sweep voltammogram consists of a single two Clectron reduction peak regardless of the voltage-sweep rate. However, at temperatures below -55°C

157

ELECTROCHEMICAL METHODS

two distinct peaks separated by several hundred millivolts were observed, the lower potential one corresponding to the reduction of the aa form. The relative peak heights for the two waves were temperature dependent and both K33 and kf could be estimated. The rate constant for ring inversion kf was found to be equal to 29 s-’ at -60°C and A c t was estimated to be about 11 kcal mol-’ over the temperature range investigated. Similar studies had previously been reported involving cyclic hydrazines (Nelson et al., 1975, 1977, 1978). Two related fused-ring systems, 10,IO’-dimethyl-9,9’-biacridylidenedication [ 11 and bianthrone [2] represent extreme cases in electron-transfer Me

PI

I

0

Me

reactions accompanied by large conformational changes. Conformational changes in these ring systems have been the subject of a number of nonelectrochemical investigations (Schneider and Lippert, 1968, 1970; Hoshino et al., 1973; Nakashima et al., 1976; Koukotas and Schwartz, 1969; Korenstein et al., 1973; Bercovici and Fischer, 1969; Dombrowski et al., 1969). Recent voltammetric investigations (Ahlberg et al., 1981; Olsen and Evans, 1981; Hammerich and Parker, 1981a) have established the energetics and kinetics of these intriguing systems. The neutral molecules exist in two conformers A and B illustrated for [I] in Scheme 2 in which A is the more stable form. Upon electron transfer the stable B2+is reduced first to B? and then to metastable B (Scheme 1) which Me

B2

+

Me

B:

Scheme 1

Me

B

VERNON D. PARKER

158

6

3'

B

A

Scheme 2

then undergoes conformation change to A (Scheme 2). The voltammetric response during the reduction of [I] in both dichloromethane (a) and D M F (b) at room temperature is illustrated by the CV's in Fig. 14. In both solvents the reduction processes consist of overlapped closely spaced consecutive

E ( V vs SCE)

FIG.14 Cyclic voltammograms for the reduction of lucigenin (B2+) at room ternperature in (a) dichloromethane, and (b) DMF containing Bu,NBF, (0.1 M); voltage sweep rate 86 mV s-l. (Ahlberg et a/., 1981)

electron transfers and the oxidation peaks observed correspond to the oxidation of the A form. Upon lowering the temperature to -5O"C, the initial reduction peaks become reversible (Fig. 15) at least from the chemical stability criterion. The effect of lowering the temperature was shown to be manifested in a lowering of the rate constant for the conformational change, k,. The kinetics of the conformational change were studied by DPSC and values of k, ranging from 2.8 at -20°C to 365 s-l at 23°C were found (Ahlberg et al., 1981). The activation energy for the transformation was found to be equal t o 16.4 kcal mol-'. The reduction of bianthrone [2] follows a similar pathway (Hammerich and Parker, 1981a; Olsen and Evans, 1981). The kinetics of the conformation

ELECTROCHEMICAL METHODS

159

I

-lob,

I I +0.90 M.60t0.30

1

I

I

0 -0.30-0.60 -C E(VvsSCE)

I0

FIG. 15 Cyclic voltammograms for the reduction of lucigenin (B2+) at -50°C in (a) dichloromethane, and (b) DMF containing Bu4NBF, (0.1 M); voltage sweep rate 86 mV s-l. (Ahlberg et al., 1981) change were studied by spectroelectrochemistry and by derivative cyclic voltammetry. In this case activation parameters were obtained for both the forward and reverse reactions (34), EtB = 15.3 and E,BA = 18.I kcal mol-I in DMF and the activation entropies in both directions were identical at -7 cal K-' mol-' (Hammerich and Parker, 1981a). THE ENTROPY OF ELECTRODE PROCESSES

The relationship between the reversible potential and thermodynamic potential for electrode process (34) is given by (35) wherefand D refer to activity O+e-+R Ere'

=

Eo - (RT/F)ln(f,/f,)

(34)

(Do/DR)*

(35)

and diffusion coefficients, respectively. Providing that the f and D ratios are unity and temperature independent and that AHo is independent of the temperature in the range of the measurements, (36) gives the relationship between Ere' and ASo for reaction (34). The conditions given are expected to be Ere'

= (I/F)(TASo - AHo) =

T(dErev/dT)- A H o / F

(36) fulfilled at low substrate concentrations and over narrow temperature intervals. Investigations of the entropy changes of the electrode reactions of aromatic hydrocarbons have been carried out using d.c. polarography (Hoijtink, 1955) and cyclic voltammetry (Van Duyne and Reilley, 1972). Both studies arrived at the conclusion that the electrode potentials change about 0.4 mV K-' near room temperature. The electrode reactions of a series of alternant aromatic hydrocarbons have been investigated as a function of temperature

160

VERNON D. PARKER

using SHAC (Svaan and Parker, 1981). A very high degree of precision was achieved in the electrode potentials (&O.l mV) which enabled precise values of ASo to be obtained over a 40 K temperature range. The data are summarized in Table 1. The differences in entropy were interpreted to be predominantly due to the differences in entropies of solvation of the radical ions. TABLE 1

Entropies for the reduction of hydrocarbons and radical cations in acetonitrile Substance

Triphenylene Perylene Benzoperylene Benzopyrene Pyrene 9-Phenylanthracene Ant hracene 9,lO-Diphenylanthracene DPA cation radical PA cation radical

AS:,,.,/cal

K-' mol-'

-0.87

2.33 2.47 - 2.67 -2.74 -

-4.43

-4.54

-4.54

$5.53 +11.6

The entropy change for the reduction of the most symmetrical molecule, triphenylene, was only -0.9 cal K-' mol-1 while the corresponding values for the reduction of anthracene, 9-phenylanthracene and 9, lo-diphenylanthracene were -4.5 cal K-' mol-l. The charges in the radical anions of the latter group areconcentrated in the 9- and 10-positions while that for the triphenylene radical anion is expected to be spread uniformly over the structure. Compounds intermediate in symmetry gave entropy values between the two extremes. It follows that the more localized the charge in the ion radicals, the larger the entropy of solvation and hence of the electrode process. The oxidation of 9,lO-diphenylanthracene was accompanied by a comparable entropy change +5.5 cal K-' mol-l while that for 9-phenylanthracene was twice as great + 11.6 cal K-' mol-l. This difference was interpreted as an indication that solvation is more localized in the free 10-position of the radical cation of the latter. The results of this work indicate that the determination of entropy changes of electrode reactions can prove of value in the more detailed understanding of the fundamental changes taking place. DETERMINATION OF EQUILIBRIUM CONSTANTS FOR EQUILIBRIA ASSOCIATED WITH CHARGE-TRANSFER REACTIONS

If charge-transfer reaction (34) is followed by a rapid and reversible chemical equilibrium (37) the electrode potential will not only reflect the contribution

E LECTR OC H EM I CAL M ETH 0 D S

161

R

+ S + R/S K37

(37)

from E, of (34) but also the free energy change of (37). The change in Ere’ brought about by equilibrium (37) is given by (38). Equation (38) has been A Ere’ = (RT/F)ln( 1

+ K3,[S])

(38)

applied to the study of equilibria involving ion pairing (S is the counter ion), hydrogen bonding and charge complex formation (Peover, 1967). “ABSOLUTE” ELECTRODE POTENTIALS

For most purposes, it suffices to have relative electrode potentials in order to gain the thermodynamic information being sought. This is a fortunate situation since the electrode potential for a half reaction cannot be measured. There are instances where it would be very desirable to be able to estimate the energy of such a reaction. Since the gas phase ionization reactions (39) and (40) can be studied, it is possible to relate the gas phase energetics, the ioniza-

R, -+ RB R,

f

e-

-+

+ e- 1.P. = A H o

(39)

R: E.A.

(40)

=

-AHo

tion potential (I.P.) and the electron affinity (E.A.), to the solution redox reactions by (41) and (42). Thus, if it were possible to obtain potentials on

(E“abS’’)R+RS.= E.A. -(AGsolv)Rs (42) this “absolute” scale, the solvation energies of the ions could be determined directly from the electrode potential and the corresponding 1.P.or E.A. One approach to this problem (Parker, 1976) is to assume that the solvation energies for the positive and negative ions of large aromatic hydrocarbons should be equal and then determine the sum of the two from the measurable

A E = I.P. - EA

+ (AG,,,.,)R* + (AGsolv)RT

(43)

quantities in (43). In (43) A E is the difference in the reversible potentials for the oxidation and reduction of the aromatic compound. When this analysis was applied to the ionization and redox reactions of anthracene, the average value of the solvation energies of the ions was estimated to be equal to -1.79 eV and the “absolute” potential for the oxidation of anthracene in acetonitrile was determined to be, according to (41), +5.68 V. The assumption of the equality of the solvation energies of the positive and negative ions of the large aromatic hydrocarbons had previously been made in connection

162

VERNON D. PARKER

with the determination of the surface potential of acetonitrile (Case et al., 1965). An alternative approach to the problem has been reported (Parker and Hammerich, 1977). The reversible potentials for a family of electrode processes (44-46) where A N refers to methyl substituted anthracenes and NA to AN: + e - + A N

(44)

AN I e +AN;

(45)

NA

(46)

+ e-- + NA;

methylnaphthalenes were determined in acetonitrile. Hammett correlations were made on the data for the three reaction series and the p-values were observed to be linearly related to the values of Ere’ for the parent reaction in each series, i.e. for the unsubstituted substrates. The assumption was made that p would equal zero only for a hypothetical reaction series in which the parent electrode process takes place at 0 V on the “absolute” scale. The latter provided a means of scaling the experimental results to an “absolute” scale. This treatment resulted in avalueof +5.42 V for the oxidation of anthracene. It was pointed out that the first value (5.68 V) could be as much as 0.2 V too high because vertical rather than adiabatic I.P. values were used in (43). In any case, the two values are very close, and the fact that they were arrived at by two completely independent methods suggests that the potential for the oxidation of anthracene in acetonitrile can be used as a reference point to estimate solvation energies of electrode reactions. 6

Electrode mechanism analysis and the treatment of kinetic data

In the remaining discussion, reactions are assumed to be of the volume type and electrode mechanism refers to the overall process, including both heterogeneous and homogeneous reactions. The manner in which kinetic data are treated in arriving at an electrode mechanism depends primarily upon whether the technique gives a direct measure of the response of the intermediate or an indirect measure, usually the effect of the chemical reaction on the electrode response of the substrate. In the former case, the conventional way of handling the data is to compare the experimental response with theoretical data in the form of a working curve and determine the mechanism from the best fit with theoretical data. The latter case usually involves the calculation of the electrode response to a particular mechanism and then comparing some measurable quantity, for example the sweep rate dependence of the peak potential, with the theoretical value. Which type of analysis is appropriate, direct or indirect, depends upon the

163

ELECTRO C H EM I CAL M ETH 0 DS

rate of the chemical reactions following charge transfer. If the rates are low enough so that the response of the intermediate can be observed by cyclic voltammetry, the direct methods apply. On the other hand, if the rates of the coupled chemical reactions are so great that the intermediate cannot be observed, the LSV wave will have a limiting shape called a purely kinetic wave (Nadjo and Savtant, 1973~).Purely kinetic waves are only observed under conditions where the charge transfer is fast relative to the measurement. In the ideal case, the response of the system is such that direct methods can be used a t short times and indirect analysis can be applied at longer times. THE THEORETICAL W O R K I N G C U R V E

It is customary to carry out calculations of electrode mechanisms using dimensionless parameters. This greatly reduces the amount of theoretical data necessary to describe the response to a particular mechanism. For example, if real concentrations were used in the calculations, a complete set of calculations would be necessary to describe the relationships between the variables and observables for each and every concentration. Normalizing the concentration by dividing by the bulk concentration of the substrate makes it possible to describe the system theoretically with a single set of calculations. The same considerations hold for rate constants. Using dimensionless rate constants, achieved by multiplying by the time unit of the variable and concentrations, a single response curve, called the theoretical working curve, describes the system. In order to make this point clear we can consider the theoretical working curve calculated for the CV response to the dimerization mechanism as in eqns (47) and (48). The ordinate in Fig. I6 is the ratio of the peak currents in the reverse and forward directions of a CV and the abscissa is 1og(k4RcR/v)where v is the voltage sweep rate (Ahlberg et al., 1980b). This single curve is then valid for all kpsand all C,. If dimensionless R&e-+M

(47)

k48

2M+D parameters had not been used in the calculations a different curve would be necessary for each rate constant or concentration. Although in principle the working curve is a superb manner of treating experimental data in mechanism analysis, there are a number of factors that limit the general utility of the method. Some of these factors are:- ( i ) the theoretical working curves for different mechanisms are often very similar; ( i i ) by including two parameters in rate laws, i.e. two rate constants or a rate constant and an equilibrium constant, it is possible to change the working

VERNON D. PARKER

164

curve almost at will; and (iii) differences in working curves for different mechanisms usually only appear at long times where the data are least reliable. Theoretical working curves simulated in connection witti studies on the reduction of [l] illustrate points (ii) and (iii) (Ahlberg et al., 1981). The working curve in Fig. I7 was constructed for DPSC in a manner previously carried

0I

s

-4

I

-3

1

-2 log ( k C / v )

I -1

I

0

FIG.16 Working curve for the EC dimerization mechanism during cyclic voltammetry. Calculated by digital simulation. (Ahlberg et al., 1980b)

out (Childs et al., 1971). The method involves finding T + defined as the pulse width at which the normalized current ratio R, is 0.5 and then to plot the data in time units of T+. As is evident from the curves, the solid lines are nearly indistinguishable within experimental error up to almost 2 T+ which corresponds to about two half-lives of the intermediate. Thus, it is necessary to make mechanistic conclusions at longer times. If there are any problems with the response such as some surface character these problems become more severe at longer times and can cause the experimental data to deviate. The lower curve is for electron-transfer reaction (49) followed by first order reaction (50). The experimental data (circles) clearly do not fit this curve at

B2'

+ 2e- + B

(49)

kP

B+A times greater than 2 T+.The upper curve was simulated taking into account

165

ELECTROCHEMICAL METHODS

equilibrium (51). The point that is to be made is that by varying K5,(= k,/kb) kf

B2+ + B + 2 B : kb

(51)

the upper curve can be moved at will all the way from the lower one to one higher than that shown. In doing so, the working curves for any number of other mechanisms will have been crossed. Thus, in the opinion of the author, the theoretical working curve is not of very much value in mechanism analysis and should be applied with extreme caution. The data shown in Fig. 17 were

t

'12

FIG.17 Double potential step chronoamperometric results at 23°C for the reduction of lucigenin (B2+) in D M F containing Bu4NBF4(0.1 M). The circles are experimental values, and the lines show the results of digital simulation for the EEC mechanism (a) including, and (b) without the homogeneous redox equilibrium (eqn 51). Potential-step times varied between 1 and 100 ms. (Ahlberg, et af.,1981)

supported by a number of other measurements and there does not appear to be any reason for questioning the validity of the analysis presented. However, if the figure had been the only evidence presented the mechanism would have been very insecurely based. It has also been shown that the electrode response of some processes can appear to fit theoretical working curves in which the reaction order in the intermediate differs from the true value (Parker, 1981b). For example, the deprotonation of hexamethylbenzene radical cation studied by derivative cyclic voltammetry gave data which fitted theoretical data for a simple first order decomposition of the intermediate. However, the observed first order rate constants were found to vary significantly with the substrate concentration indicating a higher order reaction. A method was proposed to treat

VERNON D. PARKER

166

situations of this type which involves the evaluation of the concentration dependence of the observed rate constants. ANALYSIS A.1 A CONSTANT VALUE OF THE OBSERVABLE

The inadequacy of theoretical working curves in electrode-mechanism analysis has prompted the development of an alternative approach which does not involve the use of theoretical data at all in the determination of the mechanism (Parker, 1981e). Theoretical data are used only after the mechanism has been established and then to evaluate rate constants. The new approach will be described using derivative cyclic voltammetry (DCV) but is readily adaptable to any of the direct kinetic techniques. In DCV, the observable is the derivative peak ratio, R ; , and the variable is v. A response curve is illustrated in Fig. 18 (Ahlberg and Parker, 1981b). For an

FIG. 18 Simulated first derivative cyclic voltammograrn for a reversible charge transfer showing the measurement of the derivative of the forward current (Zf’), the backward current ( I ’ b ) and the switching potential (Esw). The plot is for currenttime for a linear potential sweep. (Ahlberg and Parker, 1981b)

electrode reaction involving a kinetic step after charge transfer R; gives a measure of the rate of the reaction at a given value of v. Any change in reaction conditions which brings about a change in the rate constant for the reaction will be reflected in a change in R; if v remains unchanged. On the other hand if R; is held constant by appropriate changes in v, the changes necessary in v will be directly proportional to the corresponding changes in the rate contant. This relationship is expressed in (52) where kappmay be a function of R; = f(’app/v)

(52)

the substrate concentration, the temperature, or the isotopic content of the

167

ELECTROCHEMICAL METHODS

reactants (Parker, 1981e). For the process consisting of reactions (53) and (54), the reaction orders in A and B are not separable by the direct electrochemical techniques and the sum RA + RR = R A ~ Ris given by eqn (55)

B

Afe-+B

(53)

+X

(54)

4

products

while the reaction order in X, R,, is described by (56). The experimental procedure involves selecting a convenient constant value of the observable,

+ z,

RA/B= 1 R, = x ,

(kapp/C;= constant)

(kapp/C$= constant)

(55) (56)

changing the substrate concentration and then making the appropriate change in v necessary for R; to remain constant. The power that CAmust be raised to in order for (55) to hold then allows one to obtain RA/B.The concentration of the other reactant X in (56) is the bulk concentration and assumes that X is in excess. It is usually convenient to hold R;constant at 0.500 and when this is done the necessary value of the sweep rate is defined as vf. Since vt is directly proportional to kapp,the appropriate substitution can be made in (55) and (56). For reaction (54) experimental V+ values would show that z is 0 and x is 1 which is consistent with either rate law (57) or (58). The ambiguity arises because of the inseparability of reaction orders in A and B. The rate rate

= kaPpC&x

(57)

= kappCiCx/CA

(58)

essential feature of the method is that various mechanistic possibilities can be examined without the need for any theoretical calculations. An added feature of importance is that the data can be taken in a range where they are most reliable. For complex reaction mechanisms it is often not possible to evaluate rate constants during electrode studies. This would ordinarily preclude the determination of the activation energy of the process. However, the same approach as was described in the preceding paragraph for reaction orders can give the apparent activation energy of the process (Parker, 1981a). The direct proportionality of kappand V + can be used to derive the Arrhenius-like eqn (59). In

v f = (--Ea/R)I/T

+c

(59)

In (59) c is a correlation parameter which has no significance. It should be noted that in order to use (59), v must be converted into the appropriate units by multiplying by F/RT. Apparent activation energies can be of con-

168

VERNON D. PARKER

siderable value in electrode-mechanism analysis, especially when anomalous or inverse effects are observed (Parker, 1981b). Kinetic isotope effects can readily be evaluated from the changes in vf brought about by a change in isotopic content of the substrate or other reactants. This again does not require that the mechanism be known or that it is possible to evaluate rate constants. REACTION ORDERS A N D LSV RESPONSE

A large number of significant theoretical papers dealing with the calculation of the LSV response to various electrode mechanisms have been published. TABLE 2

Linear sweep voltammetry slopes calculated from reaction ordersa No. Mechanism

Rate law

bb

ub

ib

xb

1 B + X t C

1

0

0

1

0

112

2 B+XtC C+B+D+A

1

0

0

1

0

-1/2

kC6

2

0

0

0

1/3

113

0

kKCiCx/CA

2 - 1

0

1

1/3

0

113

3 2BtC+A C-D K

4 2B+C+A

SIC SZc Sac

C + X l D 2BtC

2

0

0

0

113

113

0

6 B+A:C

1

1

0

0

112

112

0

2

1

0

0

1/3

113

0

2

0 - 1

1

113

0

113

1

0

0

1

114

0

114

1

1

0

0

114

114

0

1

114 -,114

5

K

7 B+A+C C+B$D +A K

8 B+X+C+I C + B ~ D 9 Af2e-+B'

kKCiCx/CI

B ~ + X ~ F

10 B ~ + A ~ G K

11 B ' + X + F + I

F

~

1 0 - 1

114

G

Parker, 1981f Reaction orders in the rate law as defined in (63) c LSV slopes. S1refers to the factor within the braces in (60), Sz to that in (61) and Sa to that in (62) a

169

ELECTROCHEM I CAL M ETHODS

The contributions of Nicholson, SavCant, and Shain are particularly noteworthy (MacDonald, 1977). In carrying out the theoretical calculations it has has been customary to deal with each individual mechanism separately and make a detailed analysis in each case as was outlined in an earlier section. As a consequence of this approach, the origin of the response to a particular mechanism went undetected until recently. It is now apparent that the response is a direct consequence of the reaction orders of all of the species involved in the reaction mechanism (Parker, 1981f). The LSV observables, the voltage sweep rate dependence (dEP/dlogv), the substrate concentration dependence (dEP/dlogCA), and the dependence of the peak potential upon the concentration of an additional reactant (dEP/ dlogCx) are given by eqns (60), (61) and (62), respectively. The symbols a, b,

+ b)}RT/nF + b + i - I)/(l + b)}RT/nF

dEP/dlogv = In 10{1/(1 dEP/dlogCA = In lO{(a

dEP/dlogCx = In lO{x/(l

+ b)}RT/nF

(60) (61)

(62)

i, and x refer to the reaction orders defined in (63) where 1 is a species formed

rate

= kobsC;CiC;Ci

(63)

during the reaction which participates further. This term is frequently encountered in reactions generating H+ or OH- and can be eliminated from (63) when the experiments are conducted in appropriate buffers. The results of the use of (60)-(62) on various electrode mechanisms are illustrated by the summary in Table 2. During theoretical calculations of the electrode response to a complex mechanism, it is generally necessary to make assumptions regarding the relative importance of various steps and only limiting cases can be treated. Even the relatively simple case of disproportionation as in eqns (64) and (65) 2 B-

kr

+ B2- + B kb

(64)

kP

B2-+ products has been treated theoretically for LSV (Nadjo and Savkant, 1973c) as two limiting cases of rate law (66) depending upon the relative magnitudes of the rate = kpK,,C~/(kp+ kbCB)

(66)

terms in the denominator. The advantages of the reaction order approach is that experimental data are treated directly without making any mechanistic assumptions and the

170

VERNON D PARKER

rate law is derived using (60)-(62). Thus reaction mechanisms can be treated even if they are too complex for theoretical analysis. The method can also be used to treat competing mechanisms. DETAILED ANALYSIS OF LSV WAVES

The measurement of peak potentials during LSV neglects much of the information present in the wave. For purely kinetic waves, the wave shape is dependent upon the mechanism of the process and can be used to distinguish between mechanisms. Although conclusions can be drawn by the direct comparison of the shape of the current-potential curve with theoretical data, such a comparison is subjective. Several procedures have been developed to analyse LSV wave shapes quantitatively for mechanism analysis. The mathematically most sophisticated technique involves computing convolution or semi-integrals of the voltammetric data obtained in digital form (Imbeaux and Saveant, 1973; Nadjo et al., 1974; Oldham and Spanier, 1970; Oldham, 1972, 1973). The latter results in the transformation of the LSV wave into a form resembling a polarogram (Fig. 19) which is amenable

1.0

t5

C,(O, f 1 -

cc

In

0.5

0

0

-5

FIG.19 Convolution potential sweep voltammograms.(ImbeauxandSavkant, 1973)

radical anions

171

ELECTROCHEMICAL METHODS

to logarithmic analysis (Imbeaux and SavCant, 1973).The slope of the logarithmic analysis then gives an indication of the mechanism of the electrode process. The logarithmic slopes obtained by theoretical analysis of several mechanisms using convolution potential sweep voltammetry (CPSV) are summarized in Table 3. TABLE 3

Comparison of linear current potential analyses with those of NPSV and CPSV for electrode mechanisms" Mechanism EC ECEh EC (dim) EEC a

LCPb/mV

NPSV'

CPSVd/mV

68.9 68.9 53.2 35.1

0.906

59.2 59.2 39.4 29.6

0.693 0.431

Aalstad and Parker, 1980, 1981 Linear current potential analysis dE/d(l/P) Normalized potential sweep voltammetry Convolution potential sweep voltammetry

Under purely kinetic conditions, the shape of the LSV wave is independent of the rate of the chemical reaction following charge transfer. The effect of the rate of the reaction is manifested in the shift of the entire wave along the potential axis. Thus, if the current along the wave is normalized to the peak current and the potential scale is redefined relative to a measurable point along the wave, the waveform is independent of sweep rate and substrate concentration. Normalized potential sweep voltammetry (NPSV) simply involves a three-dimensional analysis of voltammetric data (Aalstad and Parker, 1981). Theoretical electrode potentials are taken as the x-axis, experimental electrode potentials as the y-axis and the normalized current Z, as the z-axis. The potentials are defined relative to PI2,the potential where Z , = 0.5. An NPS voltammogram is illustrated in Fig. 20 which shows that projection of the curve on to the x-y plane results in a straight line of unit slope which passes through the origin. This relationship holds when the experimental-theoretical data fit is perfect. The method is equivalent to CPSV in terms of the information content of the data and is somewhat easier to apply. For example, it is possible to do NPSV analysis on data obtained by x-y recording as long as suitable expansion is used on the potential axis. Some NPSV slopes for different mechanisms where the data are correlated versus theoretical data for Nernstian charge transfer are included in Table 3. A more simple analysis of LSV waves can give essentially the same information as CPSV and NPSV. Analysis of theoretical current-potential data for Nernstian and purely kinetic waves revealed that a nearly linear region

172

VERNON D. PARKER

l x y I lX z )

I I

'I \: f(X,Y), I

\

\\ '\

FIG.20 Illustration of the normalized current-voltage curves. The projection on to the x-y plane defines the NPSV analysis. (Aalstad and Parker, 1981)

exists where Z , ranges from 0.50 to 0.75 (Aalstad and Parker, 1980). A linear current potential (LCP) analysis involves taking the slope, dEP/dZ,, over data measured at 0.05 intervals of IN over this range. Slightly different fractions were originally reported but this has a negligible influence on the slopes. Unlike CPSV, the LCP slopes do not have any fundamental significance. This does not detract from their utility in electrode mechanism analysis. Because of the simplicity of applying the method and the fact that it gives essentially the same information as the more sophisticated methods, LCP is highly recommended for work where digital data are not available. LCP slopes for various mechanisms are included in Table 3. 7

Applications t o electrode mechanism studies

During the past fifteen years electrochemical techniques have been used widely in the investigation of the reactions of intermediates generated at electrodes. Some of the problems that have been investigated intensively are characteristic of the measurement techniques and do not have very much to do with the chemical behaviour of the intermediates in homogeneous solution. An example of this type is the so-called ECE mechanism illustrated by eqns (67) to (70) in which AR represents an aromatic compound. The symbol AR

+ e- + AR'

E

(67)

173

ELECTROCHEMICAL METHODS

k

ART + HX + AR'-H AR'-H AR'-H

+ X-

+ e- + AR--H + AR' + AR--H + AR

C E E,

(70)

E is for an electron transfer at the electrode, E, indicates a homogeneous electron transfer and C is a homogeneous chemical reaction. During a chronoamperometric study of a process believed to go by a mechanism such as that above, the response did not fit theoretical data for the ECE mechanism and it was necessary to include the homogeneous electron transfer (70) in the mechanism in order to account for the data (Hawley and Feldberg, 1966). A detailed theoretical study of this problem has shown that the E, step predominates over the second E step in situations where it would be possible to distinguish between the two (Amatore and SavCant, 1977, 1978, 1979, 1980). Another general problem, perhaps with somewhat more impact on homogeneous solution chemistry, is whether the reactions of radical ions with nucleophiles or electrophiles, depending upon the charge, go directly via the radical ions or if reactive doubly charged ions must first be formed by disproportionation. The reaction of thianthrene radical cation with water (Murata and Shine, 1969; Shine and Murata, 1969) is a typical example which was proposed to involve the disproportionation mechanism (71 and 72). The K T h t + T h t -+Th2+ + Th k Th2++ H2O -+ Th-0

+ 2 H+

validity of this mechanism was disputed on the basis of potential step-sweep voltammetric data and the radical cation was proposed to be the reactive intermediate (Parker and Eberson, 1970). The disproportionation mechanism was later rendered highly unlikely by the successful measurement of the reversible potential for the formation of the dication (Hammerich and Parker, 1973) and homogeneous kinetic studies (Svanholm et al., 1975, Evans and Blount, 1976) confirmed that the radical cation is indeed the species undergoing attack by water. Disproportionation of radical anions is believed to be an important reaction pathway during protonation in etheral solvents (Levin et al., 1972; Rainus et al., 1973) but is unlikely in polar solvents containing tetra-alkylammonium counter-ions because of the very small equilibrium constants (Jensen and Parker, 1975a). A preoccupation with problems of the nature described in the preceding paragraphs has strongly influenced the nature of electrochemical investigations of reaction mechanisms. For example, kinetic data are very often re-

174

VERNON D. PARKER

ported on reactions that have been investigated at a single temperature and a single concentration. Reaction mechanisms are sometimes even proposed on the basis of the observation of unidentified CV peaks. It is very seldom that the criteria expected for a careful physical organic investigation of a reaction mechanism are fulfilled. Another serious problem in evaluating data in the literature is that the error limits of the measurements are not stated. A factor which contributes to this situation is that electrochemical measurement techniques have been under intense development since the 1960s and 1970s and the primary interests of the investigators who have examined electrode mechanisms have in many instances been in the development of the techniques. Another factor which contributes to the nature of kinetic data reported is related to the philosophy behind the measurements. The theoretical working curve has been considered as a highly effective means of determining the mechanism of an electrode process. The inadequacy of the theoretical working curve has been discussed in an earlier section. The situation in recent years has begun to change. Data presented in support of reaction mechanisms are in many cases more credible. The techniques of measurement and treating kinetic data are now highly developed. The examples that follow are all taken from recent work and involve problems in which the author has been interested. RADICAL ANION PROTONATION

The protonation of radical anions of aromatic compounds in polar aprotic solvents such as N,N-dimethylformamide (DMF), acetonitrile or dimethylsulfoxide (DMSO) has received a great deal of attention. The general conclusions from a large number of such investigations were summarized in 1974 (Fry and Schuettenberg, 1974). The reactions were believed to go through the ECE mechanism (67-69) and in most of the earlier investigations reaction (70) was not considered. The kinetics of the reactions were most often studied by polarography and the kinetic data were treated as pseudo first order reactions with the rate being determined by reaction (68) where HX was usually water, alcohols or phenol. The reduction of 9,IO-diphenylanthracene in D M F (Santhanam and Bard, 1966) was suggested as a model for the study of reactions of this type (Fry and Schuettenberg, 1974). In more recent work concerned with the protonation of anthracene radical anion (AN') by phenol in DMF, no indications of deviations from ECE,, behaviour were found during DPSC (Amatore and Saveant, 1980) or DCV studies (Ahlberg and Parker, 1981b,c). However, when the reaction was examined in the presence of phenoxide ion it became apparent that the protonation step is reversible and the kinetic law is quite complex (Parker, 1981i). The data reproduced in Table 4 are instructive with regard to the use of some

TABLE 4 LSV and DCV mechanism analyses of the protonation of anthracene radical anions by phenol-phenoxide ion buffers in DMF“

([PhoHl/[PhO-l)l(mM/mM)

20120

10/10

40140

80/80

[ANl/mM

0.50

1.00

2.00

0.50

1.00

2.00

0.50

1.00

2.00

0.50

1.00

d E”/d log v corr. coef.

25.0 1.000 27.0 0.326 0.993

22.7

23.5

25.5

26.1

26.1

26.0 0.999 54.9 0.337 1.000

27.6 0.999 46.6 0.342 0.999

28.0 1.000 36.8 0.330 0.999

24.4 0.998 55.4 0.342 0.999

32.0 0.999 41.6 0.347

v*=/v

s-1

-d In R’/d In v - l corr. coef.

1.OOO 1.OOO

1.OOO 1.000 1.000

16.0 12.3 0.295 0.275 0.998 1.OOO

34.3 28.8 22.3 0.322 0.310 0.301 0.999 0.999 0.997

Parker, 1981i. Measurements in solvent containing Bu,N+ (0.1 M) and methanol (2.34 M) at a mercury electrode

2.00

29.1 0.999 29.9 0.367 1.OOO 1.000

176

VERNON D. PARKER

of the kinetic techniques for mechanism analysis. The first row of data gives the LSV sweep rate dependence which according to (60) should equal 29.3 mV decade-' for a reaction first order in the radical anion or 19.5 mV decade-' for a second order reaction. The next row gives the correlation coefficients for dEP/dlogv measured from 100 to 1000 mV s-l. Values of vt for the DCV analysis which from (55) requires that vt be independent of [AN] for a first order reaction in AN' are summarized in the third row. The slope dlnR'/ dln(v-'), where R' is the derivative peak ratio, is used to compare experimental data with linearized theoretical working curves (Ahlberg and Parker, 19814 and under the conditions of the measurements is predicted to be equal to -0.351. The last line gives the correlation coefficients for the slopes. Several features of the data in Table 4 are of interest. The values of dEP/ dlogv give a clear indication of the complexity of the reaction mechanism. The order in AN' depends both on the substrate concentration and on the concentration of the buffer. With the exception of the entries for [AN] = 0.50 mM the data indicate that the reaction order in AN' is approaching 2 at the lowest and 1 at the highest buffer concentration. On the other hand, V + is dependent upon the substrate concentration under all conditions, but purely second order conditions, which require v+/[AN]to be constant, were not observed in any case. Although both the LSV and DCV reaction order analyses clearly indicate that the mechanism is more complex than the simple ECE, scheme, dlnR',/dln(v-') is not in most cases too far removed from the theoretical value for that mechanism. This again reinforces the comments regarding the pitfalls in the theoretical working curve approach to mechanism analysis. The apparent activation energies for the protonation of AN- by phenol, 2,6-dimethylpheno17and 2,6-di-t-butylphenol were all determined to be very close to 8 kcal mol-' while the relative apparent rate constants at 20°C were 20, 10, and 1, respectively. It was proposed that the E,-values primarily reflect the proton transfer step and that the rate differences are the consequence of differences in the entropies of activation. The complex results observed during the reactions of AN- with phenol prompted a reinvestigation of the protonation of 9,lO-diphenylanthracene radical anion (DPA-) under the same conditions (Parker, 1981j). Kinetic results summarized in Table 5 give a clear indication that this reaction is more complex than previously believed as well. In unbuffered solution, vt showed a definite dependence upon [DPA] indicative that RA/Bis greater than 1 and close to 2. In buffered solution the substrate concentration dependence was less pronounced and in the opposite direction. Similar results were obtained for the reactions of 9-phenylanthracene radical anion. A general mechanism for the protonation of radical anions by phenol was proposed in which any of reactions (73), (74) or (75) can play a predominant

177

ELECTROCHEMICAL METHODS

TABLE 5 A comparison of the kinetics of the protonation of 9,IO-diphenylanthraceneradical anion by phenol in buffered and unbuffered DMF@ [DPAl/mM

v+

(unbuffered)/Vs-1

0.20 0.40

1.60

a

(buffered)/V s-l 0.87

0.34 0.86 1.49 1.52

0.80

vt

0.76

0.41

0.44

Parker, 1981b

'The unbuffered solution contained phenol (100 mM) while the buffered solution

contained phenoxide ion (100 mM) as well. Supporting electrolyte was Bu4NBF4 (0.1 M)

role in determining the overall rate of the reaction depending upon the reaction conditions. A'

+ PhOH

k,s

G A'-H k- 7 3

A'-H + A '

ku

+

+ PhO-

A--H + A

(73)

(74)

k-7,

A--H

+ PhOH

k,, -+ AH,

+ PhO-

(75)

The structural feature present in A'-H, structure [3] for the intermediate derived from anthracene, which contributes to the reversibility of reaction (73) is the presence of benzylic protons. This suggests that the design of an A-H which does not have that feature, so that proton addition must occur at a side-chain position to give a structure such as [4], should bring about simple ECE, behaviour.

The intermediate expected to be formed upon protonation of 1 ,I-diphenylethylene anion radical is [4; R = phenyl]. An LSV study has confirmed the structural hypothesis (Lerflaten and Parker, 1982a). Protonation by methanol

178

VERNON

D

PARKER

in D M F was observed to be first order in radical anion. dEP/dlogv was 29.8 & 0.6 mV decade-' as compared to 29.3 predicted by (60) at 22°C and dEP/dlogCA was 0 within experimental error. This is the result required by (61) for the ECE, mechanism. The only complication observed was in dEP/ dlogCx which was predicted to be 29.3 mV decade-' by (62). The observed values were lower than expected and were sweep-rate dependent. It was proposed that the discrepancy is due to equilibrium (76) which results in a (Ph,C=CH,)'

+

MeOH

K7 B

+ (Ph,C=CH,)'/MeOH

(76)

shift of the reversible reduction potential. It was possible to obtain an excellent fit of experimental and theoretical data by taking equilibrium (76) into account. A plot of In K76 1's I/T was linear, an observation that supports the proposed mechanism. The complex mechanism of the protonation of anion radicals in DMF may have some bearing upon the mechanism proposed for the reaction of perylene radical anion with alcohols (Levin et al., 1972) and anthracene radical anion with t-butyl alcohol (Rainus et al., 1973). The disproportionation mechanism was proposed for these reactions in ethereal solvents with alkalimetal counter-ions. The principal evidence for the mechanism was the observation of rate laws of the form of (77) where kappwas suggested to be rate

=

k,p,[Ar]2[ROH]/[A]

2 A' A2-

(77)

K ,8

+ A2- + A

+ ROH

km

-+ products

(79) k,,K,,. While there is no evidence available that conflicts with this mechanism the complex rate laws obtained in polar solvents for reactions that do not involve the dianions suggest that the same type of complexities may play a role in the reactions in less polar media. REACTIONS OF RADICAL CATIONS WITH PYRIDINES

The reactions of DPAt and radical cations of other aromatic hydrocarbons with pyridine and substituted pyridines are among the most intensively studied electrode reactions of positive ions. The first definitive study of the mechanism of the reaction employed the rotating disk electrode (Manning et al., 1969). Data were found to fit ECE working curves (Fig. 21) for the reactions of DPAf with 4-cyanopyridine, 4-acetoxypyridine, pyridine and 4-methylpyridine. Pseudo first order rate constants of about 3, 10, 30, 300

179

ELECTROCHEMICAL METHODS

FIG. 21 Rate of DPA: interactions with pyridine nucleophiles: 0,0.50mM DPA 25 rnM 4-methylpyridine; 0, 0.50 rnM DPA 25 mM pyridine; A, 0.50 mM DPA 25 mM 4-acetoxypyridine; A, 0.50 mM DPA 25 mM 4cyanopyridine. (Manning et a / . , 1969)

+

+

+

+

and 1000 s-', respectively, at nucleophile concentrations of 25 m M were evaluated. The reaction sequence can be summarized by eqns (80)-(83). The

Ph

Ph

VERNON D. PARKER

180

+

(83)

Ph

initial study resulted in the proposal that (81) is rate determining and (82) was not considered. On the basis of a chronoamperometric investigation, the ECE mechanism was disputed and the disproportionation mechanism (84)2 DPAf + DPA2+ + DPA K 8 4

km

DPA2+ + pyr -+ products

(84) (85)

(85) was proposed (Marcoux, 1971). Disproportionation was found to be unlikely when a kinetic analysis of the reaction was made taking into account the small value of KS4(Parker, 1972) and homogeneous kinetic studies confirmed that the reaction is first order in both DPA: and pyridine (Svanholm and Parker, 1973; Evans and Blount, 1978). At this point the reaction mechanism appeared to be established as the ECE, type with step (81) rate determining. The only conflicting observation was the fit of the chronoamperometric data to the theoretical curve for the disproportionation mechanism. However, the details of the mechanism of reaction of DPA: with pyridine are still somewhat ambiguous. Spectroelectrochemical studies have shown that the reaction becomes second order in DPAf at concentrations of about 10-5M and lower (Evans and Blount, 1979). This is not an unexpected consequence of lowering the radical ion concentration in the ECE, mechanism. Regardless of how high the rate constant for the electron transfer is (forward step 82) when the two species on the left side of (82) are in very low concentrations this step is necessarily slow. However, it was proposed that the rate law under the conditions of low [DPAf] is (86). This rate law leads to the

rate

= kaPp[DPAf]z[pyr]

(86)

prediction of dEPldlogv, dEP/dlogCA and dEPldlogCx of 19.7 mV decade-l in all three cases upon application of eqns (60)-(62) at 298 K. An LSV study (Ahlberg and Parker, 1980b) indicated that dEP/dlogv varied from 28.5 to 19 mV decade-' in the concentration range from 1.0 to 0.05 mM. The latter is consistent with a reaction order in [DPAt] ranging from 1 at high to 2 at low DPA concentrations. On the other hand, dEP/dlogCA was observed to

ELECTROCHEMICAL METHODS

181

be 0 within experimental error. The pyridine concentration dependence dEP/dlogCx was measured by a slightly different technique employing the SHAC response and was found to be 18.6 & 0.5 m V decade-' indicating a reaction order of 1 in pyridine under conditions where the order in radical cation is 2. The LSV data indicate that at low [DPA+] rate law (87) is rate

= kaP,[DPA t]2[pyr]/[DPA]

(87)

followed. Mechanism (88)-(90) was proposd in order to account for the data

+ pyr + DPA: /pyr + DPAf + DPA2+/pyr+ DPA

DPA.' DPAf/pyr

DPA2+/pyr-+ DPA+-pyr+

(88) (89) (90)

(Parker, 1980). The'essential feature of this mechanism is that the initial interaction between the radical cation and pyridine involves the formation of a x complex. Under conditions where the reaction is first order, (88) was supposed to be rate-determining. When the concentrations of DPA and the complex becomes very low the steady state concentration of DPA2+/pyr could become so low that (88) and (89) can be treated as equilibria and the rate is determined by (90). This mechanism is very similar to that proposed for the reactions of a number of radical cations with nucleophiles on the basis of homogeneous kinetic studies (Svanholm et al., 1975; Svanholm and Parker, 1976a,b) and reflects the complexities of the type that have been observed during the protonation of DPA;. Since the ambiguity remains between the data from different laboratories, the mechanism of the pyridination of DPAf cannot be considered to be established. DEPROTONATION OF ARENEMETHYL RADICAL CATIONS

Electrode studies of the mechanism of the deprotonation of a number of arenemethyl radical cations have been carried out. Spectroelectrochemical data obtained in acetonitrile during the oxidation of a number of methylbenzenes indicated that the reactions are first order in radical cation and an ECE, mechanism, (91)-(94), in which reaction (92) was considered to be

+ (Ar-CH,) (Ar-CH,)? + Ar-CH; + H + Ar-CH; + (Ar-CHa)f + Ar-CH: + Ar-CH, Ar-CH, - e-

Ar-CH:

+ Nu +-products

(91) (92) (93) (94)

rate-determining and irreversible was proposed (Bewick et al., 1977, 1980).

182

VERNON D PARKER

Studies on the deprotonation of hexamethylbenzene radical cation in acidic dichloromethane indicated that the reaction is second order in radical cation and it was suggested that the electron-transfer reaction (93) was rate-determining and that (92) was reversible under the reaction conditions (Barek ef al., 1980). The latter suggestion prompted an LSV study of the reaction in acidic and neutral acetonitrile (Schmid-Baumberger and Parker, 1980) which indicated a much more complex situation than previous work had revealed. The reaction order in radical cation was observed to be 2 under all conditions, dEP/dIogv was within I m V decade-' and within experimental error of the theoretical value (19.5 mV decade-') as indicated in Table 6 for the reactions TABLE 6 LSV mechanism analysis of the deprotonation of alkylbenzene cation radicals in

acetonitrile"

Radical cation

Conditions

HMB: HMBf DURf DURf

AN

-

TFAC

AN

-.

TFAC

AN^ AN^

dEp/d log vb 21.0 f 0.9 18.9 f 1.7 20.7 f 1.1 18.9 f 1.7

dEp/d log Cob 5.7 6.5 1.3 3.1

f 0.9 f 4.8 f 0.6 f 2.0

" Schmid-Baumberger and Parker, 1980

Values in mV, Measurements made by analog differentiation of the current-voltage response Solvent ratio (19/1) containing Bu4NBF4(0.1 M ) Solvent containing Bu,NBF, (0.1 M), experiments conducted over neutral alumina

of hexamethylbenzene (HMB) and durene (DUR) cation radicals. The value of dEp/dlogCA was close to but not exactly zero. On the basis of these results, the mechanism was proposed to involve the same sequence of reactions, (91)-(94). with the rate described by (95) where B and BH+ are an unspecified rate

=

k,,,[Ar-CH,:

I2[Nu] [B]/[ArCH,] [BH 1'

(95)

base/conjugate acid pair participating in reaction (92). This mechanism accounts for the apparent first order behaviour since RA:Bis one in this case. A closer examination was made of the mechanism of deprotonation of HMB radical cation in acetonitrile. Tables 7 and 8 show the effect of substrate concentration and temperature, respectively, on the apparent rate constants for the deprotonation of the radical cations of HMB and HMB-d18measured by DCV (Parker, 1981b). Although data for both substrates gave a very good fit to theoretical data for the disproportionation mechanism, the observed rate constants were concentration dependent. This indicates that RAIBis greater than 1 and less than 2 suggesting a complex mechanism. The com-

ELECTROCH EM1CAL METHODS

183

TABLE 7 The dependence of the apparent first order rate constant for deprotonation of hexamethylbenzene radical cations on the substrate concentration" Substrate HMB HMB HMB HMB H M B(dis) HMB(d is) HMB(d 1s) HMB(dis)

C/mMb

kobs/S-lc

0.10 0.25 0.50 1.oo 0.125 0.25

172 372 585 1152 41.4 53.8

1.oo

183

0.50

-

101

" Parker, 1981b. Measured in acetonitrile at 22"C, estimated water content 10 m M

supporting electrolyte was Me4NBF4(sat., 0. I M) Substrate concentration. Measured by DCV at 200 V s-l, E,, - Ere, = 500 mV and theoretical data for the rate law, rate = k,b,[A+]*[A]-'

plexity was confirmed by the temperature study. The apparent rate constant for the radical cation of HMB-dl, increased steadily with decreasing temperature while that for HMBZ was less regular but the same trend was observed. The data indicate a deuterium kinetic isotope effect of about 4.5. The data surely show that the mechanism is much more complex than the simple ECE, scheme predicts. It seems most likely that the mechanism proposed on the basis of the LSV study is correct but that in some cases, depending upon the conditions, the electron-transfer step can be rate-determining. The LSV study was carried out using either acetonitrile containing trifluoroacetic acid or in solvent over neutral alumina. In either case, the strongest nucleophile TABLE 8 Kinetic data for the deprotonation of hexamethylbenzene radical cations in acetonitrile as a function of the temperature" T/"C

kobs(HM B)/s-lb

30 22 12 2

427( 12) 66w) 877(38) 8 16(12)

" Parker,

kobs(H MB-d)/s-lb 103(0) 137(I) 180(1) 207(4)

kH/kD 4.2 4.8 4.9 4.0

1981b. Freshly distilled acetonitrile, estimated water content 10 mM Me4NBF4(sat., -0.1 M) Rate constants measured by DCV at 200 V s-l, E,, - Ere, = 500 mV using theoretical data for the rate law, rate = kob,[At]z[~]-l.The numbers in parentheses refer to the standard deviation in 5 replicate measurements

184

VERNON D. PARKER

in solution is expected to be acetonitrile (Hammerich and Parker, 1974). On the other hand, the DCV response was observed to be much more reproducible with some water present in the acetonitrile. In the latter case, reaction (94) is expected to be less likely to contribute to the overall rate of the reaction. REACTIONS OF DIAZOALKANE RADICAL ANIONS

The carbene radical anion [5] was proposed to be an intermediate in the polarographic reduction of tetracyanodiazocyclopentadiene(Webster, 1966). Subsequently, the parent (CH,)? was identified among the products of electric Ph-C-Ph [71

NC [61

[51

discharges through gaseous CH, and CH,N, (Zittel et al., 1976) and the reactions of cyclopentadienyl radical anion have been examined by the flowing afterglow technique (McDonald et al., 1980a). The evidence for the gas phase existence of carbene radical anions is convincing. However, no direct evidence for the participation of [5] in solution was presented. In order to attempt to demonstrate the intermediacy of carbene radical anions in solution, the cathodic reduction of 9-diazofluorene (FI =N2) and diazodiphenylmethane (Ph,C =N,), possible precursors to carbene radical anions [6] and [7] respectively, was investigated (McDonald et al., 1977, 1978, 1980b; Triebe et al., 1980). The first investigations produced positive conclusions. An intermediate was detected by CV in the reduction of FI=N,, and it was proposed that F1 =N,: lost nitrogen to give the carbene radical anion which then slowly reacts with the substrate according to (96). The FI=N,'

-+ N,

+ Fl'

FI=N,

(FI=N-N=Fl)S

(96)

most remarkable feature of this proposal was that the intermediate was observed in DMF at a voltage sweep rate of 75 mV s-l and the voltammogram indicated that it was essentially stable on this time scale. This observation places a minimum value of the lifetime of the species at greater than 10 s at room temperature. This proposal was disputed (Bethel1 et al., 1980) because the lifetime of diarylmethylenes produced during flash photolysis in solution (Closs and Rabinow, 1976) is very low owing to the nearly diffusion controlled dimerization. Rate constants ranging from lo5 to lo9 M-l s-' have been reported for the reactions of fluorenylidene with unsaturated compounds in acetonitrile at 25°C (Zupancic and Schuster, 1980). The CV of FI=N, was reinvestigated and an anomaly was immediately

ELECTROCHEMICAL M ETHODs

185

evident. At a voltage sweep rate of 1 V s-1 the CV at 20°C was essentially the same as that reported earlier (McDonald et al., 1977) and is shown in Fig. 22A. The redox couple (c/c') corresponds to that proposed to be due to the redox reactions of FI'/FI and (a) and (b) are due to the oxidation of (F1= N-N=Fl); and (FI=N-N=F1)2-, respectively. It should be noted that the CV's in Fig. 22 were recorded after steady state had been achieved in order to

i

i d

0

I

I

-0.6

-1.2

v vs SCE

I

+

FIG.22 Cyclic voltammograms of 9-diazofluorene (5 mM) in DMF at (A) 20°C. (B) -2O"C, and (C) -50°C. [Bu,NBFJ = 0.1 M. Voltage sweep rate = lo00 mV s-'. (Bethell et al., 1980)

diminish the contribution of processes due to the substrate. At -2O"C, peak (a) was no longer evident yet (b/b') was observed and the peak currents were nearly identical to those for (c/c') (Fig. 22B). This means that (b/b') at the higher temperature is due to two overlapped couples, one due to the fluorenone mine system and the other associated with the species giving rise to (clc'). This then requires that if (c/c') is in fact due to FF/FI at -20°C'

VERNON D. PARKER

186

(b/b') is due to FI2-/F1' and the carbene dianion, F12- is long lived. These observations rule out the detection of (c/c') as evidence for the existence of F1' in solution. Furthermore, when the temperature was lowered to -5O"C, a new oxidation peak (d) was observed (Fig. 22C) which indicates that the species giving rise to (c/c') is not the first intermediate of the reaction. It was proposed (Bethell et al., 1980) that the first observable intermediate is a dimer of FI=N2'; the dimer then loses N, to give the product dianion in the cis configuration and it is this species that gives rise to (c/c') and part of the current at (b/b'). The slow process is then the isomerization of this intermediate in any of its three oxidation states shown in Scheme 3.

r

fast

[FINII)az-

-50°C

-

(FIN,);

FIN,

-2e

N=N

F1-

I

-50°C

L

I.

\

N=N

FI -I:-, \\ N-N

(F1 = fluoren-9-yl)

"FI

Scheme 3

Attempts to conduct an LSV mechanism analysis of the reduction of FI=N2 in DMF were inconclusive due to the irreproducibility of the response. However, the system was found to be well behaved in CH,CN and quantitative data, reproduced in Table 9, were obtained (Parker and Bethell, 1980). It was necessary to restrict v to 1.0 V or less because of the interference of the rate of heterogeneous charge transfer with the response. Use of analog differentiation of the response resulted in precision of f0.2 mV in the peak potentials and the LSV slopes were observed to be 20.7 f 1.7 and 19.4 f 1.4 mV decade-', for dEP/dlogv and dEP/dlogCA, respectively. The application of (60) and (61) provides the basis for assigning rate law (97) for the reactions rate

= k,pp[FI=N2x]2

(97)

I a7

ELECTROCHEMICAL METHODS

TABLE 9 Linear sweep voltammetric data for the reduction of 9-diazofluorenein acetonitrile' (FIN&/mM 0.20 0.40 0.80 1 .oo

d E/d log C"

-Ep/mV

0.10 V s-l

0.20 V s-'

0.40 V s-l

1.00 V s-l

218.0 211.4 205.1 203.3

221.0 216.6 210.9 208.3

227.3 222.3 218.7 213.1

238.2 232.4 (230.2)* 222.0

-21.0

- 17.9

-

18.3

-

dE/d log v 20.6 21 .o 22.6 18.5

19.6

'Parker and Bethell,

1980. Measurements made at a platinum electrode at 23°C with a supporting electrolyte (Bu4NBF4)concentration of 0.1 M. Measurement precision was better than f 0 . 2 mV in the peak potentials. The EP values are the mean of 15 determinations and are referred to a bias setting of -1.50 6 vs an Ag/Ag+ reference electrode in acetonitrile * This value deviated substantially from the correlation line for the other three points and was not included in determining the slopes

of Fl=N,;

in acetonitrile. Thus, the kinetic data strongly support the mechanism based upon the low temperature CV study. More recently, a detailed investigation of the mechanism of the decomposition of F1=N2' in both CH,CN and D M F was carried out using DCV and DPSC (Parker and Bethell, 1981b). The kinetics of the heterogeneous charge transfer at mercury electrodes was investigated and it was found that the heterogeneous rate constant k, varied by more than a factor of 10 depending upon the nature of the supporting electrolyte cation, in the order Et4N+ > Pr4N+ > Me,N+ > Bu,N+. This order was attributed to double layer and ion association effects. Cyclic voltammograms measured in the presence of Me,N+ at 50, 5 , and 0.5 V s-' in CH,CN (Fig. 23) and DMF (Fig. 24) show the similarities and differences in behaviour in the two solvents. In CH,CN at 50 V s-1 the oxidation peak for the radical anion was observed but the peak current ratio was considerably less than unity and a peak due to a further reaction intermediate was apparent at less negative potential. In comparison, the peak current ratio at 50 V s-l appears to be greater in DMF indicating that the radical anion is somewhat more stable in that solvent. On the other hand, the peak potential separation is considerably greater indicating that heterogeneous charge transfer is slower in DMF. At lower sweep rates the peak due to another intermediate is also observed in D M F but because of the slower heterogeneous charge transfer the two oxidation peaks overlap. The two figures indicate that the reaction pathways are essentially the same in the two solvents, as would be expected because of their similarity, but because of the charge-transfer problem the overlapping of response for FI=N,' and the other intermediate precluded direct kinetic

VERNON D. PARKER

188 I

62

I

-1.12

I

I

-1.62

E ( V vs Ag /Ag+)

FIG. 23 Cyclic voltammograms for the reduction of 9-diazofluorene in acetonitrile at 50 V s-' (a), 5 V s-' (b), and 0.5 V s-1 (c). (Parker and Bethell, 1981b)

measurements in DMF. A DPSC kinetic study of the reactions of FI=N,S in CH,CN in the presence of tetra-alkylammonium counter-ions is summarized by the data in Table 10. The second order rate constant was observed to increase steadily as the size of the tetra-alkylammonium ion decreased changing by a factor of 10 over the series. The counter-ion effect most probably results from an increasing contribution of ion association as the size of the cation is decreased. Ion association is expected to decrease the charge repulsion of the radical ions in the transition state for dimerization. The effect of temperature on the apparent rate constants was revealing. In the presence of MelN+ an apparent activation energy of 2.2 kcal mol-' was observed. Since this value is considerably lower than expected for any simple bimolecular reaction, it was concluded that the dimerization cannot be a one step process. Based on all of the information available on the reactions of F1=NZT generated at electrodes, the mechanism was proposed to consist of reactions (98)-(lOl). Equilibrium (98) was proposed in order to account for the low

ELECT ROCH EMI CAL

M ETH0 DS

I

-1.12

-062

-1.1

I

E ( V v 5 Ag/Ag+)

FIG.24 Cyclic voltammograms for the reduction of 9-diazofluorene in DMF at 50 V s-l (a), 5 V s-l (b), and 0.5 V s-l (c). (Parker and Bethell, 1981b) activation energy, on the basis that the association to the complex would be expected t o be favoured by lower temperatures. The first intermediate, 1-1, was proposed to be the cyclic dimer [8] or more probably a head to head dimer which could, via transition state [9] lead to s-cis-fluorenone azine dianion which was proposed to be 1-2. The basis for the latter proposal is that when

TABLE 10 The effect of the nature of the supporting electrolyte cation on the rate of dimerization of FI = N,' in acetonitrile" R4N+

Temp/"C

q/ms

k/M-l s-l ~

1

Bu~N+ Pr4N+ EtaN+ Me4N+

10.6 11.1 11.5 11.1

40.3 7.04 5.53

4.02

_

_

_

_

0.214 1.22 1.56 2.14 ~

~~

Parker and Bethell, 1981b. The counter-ion was in all cases BF; and the supporting electrolyte concentration was 0.1 M in all cases but Me4NBF, (sat.)

VERNON D. PARKER

190

N

the 15N-labelled substrate [lo] was reduced at a platinum electrode (Bethel1 et al., 1980), a significant amount of the doubly labelled mine [l I] was isolated. Arguments were presented to link the observed CV behaviour to the s-cis-fluorenone azine dianion (Parker and Bethell, 1981b).

+ (Fl=Nz/Fl=N,T)

2 FI=N,'

(FI=N2r/FI=Nzr 1-1

1-2

--t

-+ 1-2

-+ 1-1

+ N,

F1-N=N-Fl2-

(98) (99) (loo) (101)

Since the only structural difference between Fl=N, and Ph,C=N, is that the rings are fused together in the former case, one might expect the reactions of the radical anions to be similar. Indeed, the carbene radical anion [7] was proposed as an intermediate of the decomposition of Ph,C=N, in DMF (McDonald et al., 1977, 1978, 1980b; Triebe et al., 1980). The summarizing paper on this work (McDonald er al., 1980b) relies heavily on the interpretation of a cyclic voltammogram measured at 5OVs-' in DMF which is reproduced in Fig. 25. The reduction peak was believed to involve the formation of the radical anion followed by a very rapid unimolecular cleavage of the C-N bond and the formation of [7] as in (102). The evidence for the Ph,C-N,'

-+ Ph2C'

+ N,

( 102)

rapidity of reaction (102) was the failure to observe an oxidation peak at the expected potential. The oxidation peak that was observed at less negative potentials was assigned to the oxidation of Ph2CH- believed to arise from [7]. Before discussing these conclusions further it is instructive to consider the CV measured at 100 V s-l for the reduction of Ph,C=N, in CD,CN containing Me,NBF, as is shown in Fig. 26. In this case the voltammogram appears as a well-behaved quasi-reversible process and no reaction of the

191

ELECTROCHEMICAL METHODS

t

2 mA

1

'c

0-

I

0.8

1

1

I

I

0

E

-0.8

I

I

I

-1.6

FIG.25 Cyclic voltammogram of 5.30 mM Ph2CN2in DMF-O.l F (n-BU)4NC101 at a planar platinum electrode. The scan rate is 50 V s-l. (McDonald et at., 1980b) radical anion was detected under the reaction conditions (Parker and Bethell, 1981a). If the interpretation of the voltammogram in Fig. 26 is correct that in Fig. 26 indicates remarkable solvent or electrolyte effects. However, a reinvestigation of the voltammetry in DMF revealed that the potential separation between the reduction and oxidation peaks is dependent upon the nature of the supporting electrolyte cation as would be expected for a quasi-

I

R

I

0 I

-1.54

I

- 2.04 E(V

YS

I

-2.54

Ag /AS')

FIG. 26 Cyclic voltammogram for the reduction of diazodiphenylmethane in CD,CN containing Me4NBF4(sat.) at 8°C and 100 V s-l. (Parker and Bethell, 1981a)

VERNON D. PARKER

192 n

FIG.27 Cyclic voltammograms for the reduction of Ph,C=N, in DMF at 21.5"C at 100 V s-l. In order of decreasing current, the supporting electrolyte cations were Et,N+, Pr,N+, and Bu,N+. (Bethell and Parker, 1982)

reversible process (Bethell and Parker, 1982). The peak potential separation was also observed to be greater on platinum than on mercury which is also a common observation for quasi-reversible reductions. The voltammogram in Fig. 25 was obtained under conditions far from ideal; the measurement was at a platinum electrode with the large tetrabutylammonium ion as the counter ion. The voltammograms illustrated in Fig. 27 were obtained at a mercury electrode. The peak separation decreases progressively as the cation size is decreased as has been observed (Jensen et a/., 1975; Fry et a/., 1975) in a number of cases involving quasi-reversible charge transfer. The peak potential separation varied from 700 mV for Bu,N+ to 360 mV when Me,N+ was the cation (not shown on Fig. 27). The corresponding separation on platinum in the presence of Bu,N+ was about 1200 mV (Fig. 25). Thus, it is quite clear that PhzC=Nz is far less reactive than proposed (McDonald et a/., 1980b) and that Fig. 25 illustrates a CV for a quasi-reversible charge transfer. The voltammograms illustrated in Figs 25-27 suggest that direct kinetic analysis can be made on the reactions of Ph,C=N,;. In contrast to the FI=NF voltammograms, the only oxidation peaks observed at high sweep

193

ELECTROCHEMICAL METHODS

TABLE 11 The rate of the reaction of diazodiphenylmethane radical anion generated in acetonitrile at a mercury electrode" [PhBC=Nz]/mM

Solvent

tp/ms

1 .o 2.0 3.0 4.0 1 .o 2.0

CH3CN CH3CN CH &N CH ,CN CD,CN CD3CN

2.27 2.65 2.82 2.68 78.6 75.3

kapp/S-'

181 156 146 154 5.3 5.5 ~

~~

Parker and Bethell, 1981a. Measurements on solutions containing Me4NBF4(sat.) at 8°C * The potential step time for the current ratio &/If), normalized to the no reaction case, to equal 0.500

a

rates are due t o the radical anion and so DPSC could be used t o study the kinetics in both solvents. The data in Table I 1 show that the decomposition in either CH,CN or CD,CN is first order in Ph,C=N,? and a deuterium kinetic isotope effect of about 30 is apparent. An LSV study (Table 12) supported the conclusion that the reaction is a pseudo first order decomposition of the radical anion. The peak potential was observed t o be indeTABLE 12 Linear sweep voltammetric data for the reduction of Ph,C=N," - EP/mV(at v/V s-l)

1 .OOO

dEp/d log v mV decade-'

329.4(0.9) 330.0(0.4) 329.3(0.6) 331.6(0.8)

31.9 29.5 32.1 30.9

donor 300.8(0.2) 308.0(0.1) 316.7(0.1) 329.3(0.1) 299.7(0.3) 307.8(0.1) 316.8(0.1) 329.8(0.1) 298.9(0.3) 307.5(0.1) 315.3(0.1) 327.7(0.1)

28.7 30.2 28.6

C"/mM [DEMIb/mM

0.100

0.200

0.400

(a) Sweep rate and concentration dependence 0.2 0 303.1(1.4) 305.5(0.6) 314.3(0.5) 0.5 0 300.8(0.4) 306.8(0.3) 315.8(0.5) 1 .o 0 297.5(0.2) 305.6(0.6) 316.0(0.6) 2.0 0 301.2(0.5) 308.3(0.8) 318.8(0.8) (b) Effect of a proton 1 .o 5.0 1 .o 10.0 1 .o 20.0

"Parker and Bethell, 1981a. Measurements at an Hg electrode at 23°C with Me4NBF, (sat.) as electrolyte. The numbers in parentheses refer to the standard deviations in 5 measurements. Peak potentials are relative to a bias setting of - 1.680 V vs Ag/Ag+ in acetonitrile. It should be noted that the reduction process does not fulfill the requirements for purely kinetic waves, linear current potential analysis indicates a slope at 100 mV s-' of about 80 mV rather than 69 mV for a purely kinetic wave

VERNON D. PARKER

194

pendent of the presence of diethyl malonate, a much better proton donor than CH3CN, providing evidence that the radical anion is not abstracting protons from the solvent. Of the three first order or pseudo first order reaction only the hydrogen atom abstraction pathways (103)-(105) of Ph,C=N;, Ph2C=N2'+Ph2C' PhzC=NzT PhzC=N,'

+ N2

+ CH3CN + Ph2CH-N i + EH,CN + CH3CN + Ph2CH-N,-' + eH,CN

(103) (104) (105)

reaction (105) is consistent with the kinetic data. The activation energy for the abstraction of hydrogen was found to be 5.5 and of deuterium 7.2 kcal mol-'. Entropies of activation were identical within experimental error at 30 cal K-' mol-' (Bethell and Parker, 1982). The reaction of Ph,C=N; was observed to be somewhat slower in DMF. The results of a DPSC study are reproduced in Table 13. It is interesting to note the effect of the counter-ion on the apparent rate constant. In this case a change of about a factor of 5 was observed between the two extremes in cation size, Bu4N+and Me4N+. It appears that ion association retards the reaction. The reason for the low rate constant when Pr4N+was the electrolyte is not apparent. A deuterium kinetic isotope effect of about 4 was observed when the reaction was studied in DMF-d,. The activation energy observed in DMF, 16.7 kcal mol-l, was larger than in CH3CN. It seems clear that none of the evidence which had previously been claimed for the intermediacy of [6] and [7] during electrode reactions is valid. Whether or not carbene radical anions can be formed during the decomposition of diazoalkane radical anions in solution remains to be seen. The kinetic studies show that in order to optimize the conditions for the formation of the carbene TABLE 13 The effect of the supporting electrolyte cation on the rate constant for the decomposition of PhzC = N,; in DMF and cyclic voltammetric peak separation during reduction of PhzC = N,' R4N+

q/ms

k/s-l

Bu4N+ Pr4N+ Et 4N Me4N+

9.93 36.2 22.0 46.8

44.4 11.4 18.7 8.78

+

(AEp/rnV)* 697.6 607.8 424.1 360.1

' Bethell and Parker,

1982. Supporting electrolyte concentration was 0.1 M in all cases and the counter-ion was BF; at 21.5"C with a substrate concentration of 2.0 mM

* The difference in potentials of the reduction and oxidation peaks on cyclic voltammograms measured by derivative techniques

ELECTROCHEMICAL METHODS

195

radical anions it would be necessary to take steps t o make dimerization of the diazoalkane radical anions and hydrogen atom abstraction less favourable than they are when the substrate concentration is at the millimolar level and the solvent is DMF or CH,CN. ELECTRODIMERIZATION

Free radicals formed in solution, unless generated by the decomposition of a substance which produces two radicals in close proximity, seldom dimerize. This is because there are usually facile first order and pseudo first order reaction pathways open to these reactive intermediates. Due to the heterogeneity of the electrode process, intermediates are formed in relatively high concentration at the electrode solution interface. If the dimerization of the intermediates is an energetically favourable process, conditions can be optimized so that yields of dimer are high. One dimer-forming reaction, the electrohydrodimerization of activated olefins, deserves special mention. This is the basis for the Monsanto process for the dimerization of acrylonitrile to adiponitrile. The development of this process resulted from the pioneering studies of Manuel Baizer (Baizer, 1963, 1964a,b). The number of published papers, both preparative and mechanistic, that deal with this reaction is very impressive and is a direct reflection of the practical importance of the reaction (Baizer and Anderson, 1964a,b, 1965a, b,c,d; Petrovich and Baizer, 1966, 1969a,b, 1971;Anderson etal., 1965; Baizer et al., 1967, 1970; Baizer, 1973; Childs et al., 1971 ; Puglisi and Bard, 1972a,b, 1973; Hazelrig and Bard, 1975; Bard et al., 1973; Vartires et al., 1975; Yeh and Bard, 1977a,b; Goldberg and Bard, 1974; Andrieux et al., 1970, 1973, 1977; Lamy et al., 1973, 1974; Nadjo and Savtant, 1971b, 1973b,c, 1976; Nadjo et al., 1975; Ryan and Evans, 1974; Zoutendam and Kissinger, 1979; Grypa and Maloy. 1975; Bezilla and Maloy, 1979; Parker, 1981c,d,g,h). Before discussing the mechanism of electrohydrodimerization and other electrodimerization reactions the plausible mechanisms and methods of distinguishing between them must be considered. Three basically different mechanisms have been considered theoretically and have been demonstrated in experimental studies. For simplicity all mechanisms are written as involving radical anions but differ from those of radical cations only in charge. Modifications are necessary in the mechanisms if the radicals are uncharged but these cases are more straightforward and will not be discussed. The primary steps in the three mechanisms are shown in equations (106)-(110). Many of the papers referred to in connection with electrohydrodimerization include calculations of the electrode response for various mechanisms, but only a few of these will be cited here so as to give examples using the different measurement techniques. They are for DPSC (Childs et al., 1971), LSV (Nadjo

196

VERNON D. PARKER

and SavCant, 1973c; Olmstead et al., 1969), rotating ring disk electrode (Puglisi and Bard, 1972a,b) CPSV (Imbeaux and SavCant, 1973) and NPSV (Aalstad and Parker, 1981). 2 R' --+ R--R-

+ R + R--R' R--R' + RT + R--R+R R' + E+ + R'-E R'-E + R' --+ R--R-E R'

( 106) ( 107) ( 108)

All of the theoretical work has been carried out by making calculations of the response for a specific mechanism and then manipulating the data so that they can be used in a theoretical working curve or in the case of LSV, CPSV and NPSV as a slope of some function of the observable vs a function of the variable. The inadequacy of the theoretical working curve has already been mentioned a number of times and the newer work on the origin of the LSV response shows that it is more profitable to analyze response without resort to calculations using (60)-(62) (Parker, 198lf). For these reasons only the reaction-order approach will be considered here in analyzing the mechanisms. The simple dimerization reaction (106) gives rise to rate eqn (111). The radical ion-substrate coupling reaction (107H108) can be described by either (1 12) or (1 13) depending upon which step is rate-determining. Reactions (109)-(110) where E+ is a cation or a proton donor gives rise to rate law (1 14). rate rate rate

= k,o,[R']2

(1 11)

= k107[R+][R]

= klo,Klo7[R']2[R]

rate = kl10K109[R7]2[E+] It should be pointed out that all of the rate expressions were derived using the steady state approximation on an appropriate intermediate and represent limiting cases of the complete rate laws. These approximations are always used in the theoretical calculations, but the reaction order approach does not require such approximations since experimental data are treated directly. Considering first the direct kinetic methods for the study of electrode processes, the mechanistic criterion of most consequence is RAIB,the reaction order in substrate and primary intermediate as defined by ( 5 5 ) (Parker, 1981e). Using DCV as an example of a direct kinetic technique we can write V J C= ~ constant

(1 15)

ELECTROCHEMICAL METHODS

197

(115), where C;; is the concentration of the neutral substrate giving rise to R; as the mechanistic probe. The values of RA/Bfor the rate laws are 2 (1 1 l), 2 (1 12), 3 (1 13) and 2 (1 14). The corresponding values of z for (1 15) to hold are 1, 1,2, and 1 respectively. Rate law (1 13) stands out from the other three because of a unique value in RAIB.The reaction order in E+ obtained from (56) allows for the differentiation of rate law (1 14) from the others. This leaves (111) and (112) indistinguishable from the reaction orders. Rate law (112) has never been observed and thus has not shown up as a limitation in the reaction order approach. In order to distinguish between (1 11) and (112) by a direct technique it would be necessary to rely on the use of a theoretical working curve. For example, the theoretical working curves for the two rate laws differ substantially at long times for DPSC (Childs et al., 1971). The relationship most useful in distinguishing between rate laws (1 11)(I 14) by LSV is (61) which gives the dependence of the peak potential on the substrate concentration. As mentioned earlier, LSV has the distinct advantage over the other techniques that the reaction orders in A and B are separable. Thus, application of (61) with the four rate laws results in dEP/dlogC, equal to 19.7 (Ill), 29.6 (112), 39.4 (113) and 19.7 (114) mV decade-’ at 298 K. Rate laws (1 1 I ) and ( I 14) are then differentiated by (62) which predicts that d@/dlogC,+ is 19.7 mV decade-’ for (1 14). The power of these simple equations for LSV mechanism analysis and LSV as a kinetic tool is quite evident from this treatment. The simple radical coupling mechanism (106) with rate law (101) has found general favour among those investigating the mechanism of electrohydrodimerization using diactivated olefins such as diethyl fumarate [I21 or methylcinnamate [13]. These diactivated olefins are considered to be model compounds for acrylonitrile, mechanistic studies with which have not been

0

0

0

I1

EtO-C-CH-CH-C-OEt [121

It

I1

Ph-CH=CH-C-OMe 31

successful. The reactions were studied in DMF or CH,CN by DPSC (Childs, al., 1971), rotating ring-disk electrode voltammetry (Puglisi and Bard, 1972a,b, 1973), LSV (Andrieux et al., 1970, 1973; Nadjo and SavCant, 1971b, 1973a,b, 1976; Lamy et al., 1973, 1974), CPSV (Nadjo et al., 1975) and by monitoring the esr response after a current pulse (Goldberg and Bard 1974). The general conclusions from all of this work on diactivated olefins were expressed as “The coupling between two anion radicals is the most probable reaction pathway not only when the observed kinetics are not dependent upon the water concentration but also in the case where they are” et

198

VERNON D. PARKER

(Lamy et al., 1974). The presence of water was known to affect the rate of dimerization (Childs et al., 1971 ; Lamy et al., 1974) and this was attributed to solvation of the radical anion. A recent study was designed to determine more specifically the effect of water on the electrohydrodimerization of diactivated olefins. During the reactions of D E F , the radical anion of [12] it was found that the reaction in DMF is second order in radical ion as expected from previous work and first order in water, according to rate law ( I 16) (Parker, 1981~). A small deuterium rate

=-

(1 16)

k,,,[DEFz]2[H,0]

kinetic isotope effect of 1.1 1 5 0.03 was found when the reaction was carried out in the presence of D,O. The activation energy for the reaction had previously been observed to be 4.2 kcal mol-l (Childs et al., 1971) which was taken as an indication (Parker, 1981~)that the reaction could not be of the simple radical anion dimerization type. When the kinetic data were extrapolated to zero added water, a “residual” rate constant of 25 M-’ s-1 was obtained. It was concluded that this represents the rate constant for the reaction taking place in the presence of residual water in the solvent-supporting electrolyte system and that there was no evidence for the simple radical anion dimerization mechanism. In order to account for the kinetic data, a mechanism consisting of an initial equilibrium (1 17) which is displaced strongly to the left was proposed. If this were not the case, the most likely mechanism would be the dimerization (1 19) of the radical anion-water com-

R’/H,O

f

RS

kll,

2 R’/H,O

R--R-H

+ HO-

products

(1 19)

plex which would then require that the reaction be second order in water, a prediction inconsistent with the data. This is one of the facts which rule out a general solvation of the radical anion as the role of water. The other is the very low activation energy which can be accounted for if k,,, is very large and that step has a small activation energy while Kll, is either not greatly affected by temperature or inversely affected. Thus, for the general case this mechanism gives rise to rate law (120) which can accommodate not only the most recent data but those from earlier studies as well. rate

= kllRK117[RT]2[HZO]

( 120)

In view of the important role of water in the dimerization mechanism a study was carried out in which the water concentration was kept at a minimum

ELECTROCHEMICAL M ETH 0 DS

199

using the alumina technique (Parker, 1981d). The reactions of MC-, the radical anion of [13], were studied in CH,CN by both LSV and DCV. The data are summarized in Table 14 for the DCV study. In the presence of water (136mM), VJCAwas constant as expected for rate law (120). However, when the water level was maintained at a low level VJCAchanged by nearly a factor of 3 over an 8-fold concentration change. This indicates a significant contribution of a higher order mechanism. The latter was confirmed by the LSV results which showed that dEP/dlogCA was 36.8 f 2.3 mV decade-' in close agreement with 39.4 predicted by (61) for the radical ion-substrate coupling mechanism with rate-determining electron transfer and rate law

TABLE 14 Kinetics of the electrohydrodimerizationof methyl cinnamate in acetonitrile" [MCl/mM 1.oo

2.00 4.00 1.oo 2.00 4.00 8.00

[H 2Ol/mM

V*/V s-1

Vf/C./V S-' mM-l

136 136 136

4.20 7.80 16.90 0.350 0.970 2.52 6.95

4.20 3.90 4.23 0.350 0.485 0.625 0.869


<1 <1 <1

Parker, 1981c. Measured by derivative cyclic voltammetry in solvent containing Me,NBF, (0.05 M) at 18.5"C. v+ refers to the voltage sweep rate at which the derivative peak ratio is equal to 0.500. (113). The difference in the apparent reaction orders using the two techniques is probably due to the fact that the concentration profiles of reactants and intermediates depend upon the time scale. Thus, differences can be expected for concentration dependent competing mechanisms. In general terms where A' represents a diactivated olefin, the major mechanism of dimerization in solvents of low water content was proposed to be given by eqns (121j(122)

x.,,,

A. t A---tA'-A-k m A'-AAx+ A--A-

+

rate

=

(121) -I- A

(1 22)

k,,lkl,,[A']2[A]

with rate law (123). Reaction (121) could also have been treated as an equilibrium as in the case already discussed (107). A detailed study of the electrohydrodimerization of activated olefins in proton-poor solvents has been reported (Parker, 198Ig) and the results further

200

VERNON D. PARKER

support the conclusions of the preliminary study (Parker, 1981d). A point of interest made evident from this work is the conditions which favour the radical anion-substrate coupling over the dimerization mechanism. It has been suggested (Eberson and Nyberg, 1976) that in cases where reactions appear to be radical ion dimerizations under the conditions of analytical studies, i.e. concentrations in the millimolar range, that the mechanism may change on going to higher concentrations. This opinion was also given in another discussion (Andrieux el al., 1977). If one examines this conclusion by comparing the predicted relative rates of reactions (106) and (107), equation (124) is arrived at for the relative rates. Since both A- and A change rate( 106)/rate(107) = k,,,[A’]/k,,,[A]

(124)

with the initial bulk concentration of A, it is not clear how the relative proportions of reaction taking place by the two mechanisms should vary with [A]. The data in Table 15 give a clue to this question. With v ranging from 100 to lo00 mV s-l, dEP/dlogC,,,, was observed to vary smoothly from -32.6 to 4 0 . 3 mV decade-’ during the electrohydrodimerizationof diethylfumarate. This variation is very much too great to be due to experimental error and indicates that under the conditions of the experiments radical anion dimerization is competing with radical anion-substrate coupling and that the competition is time dependent. The changes in v are a reflection of the thickness of the reaction layer which is inversely proportional to d v . The conclusion that one arrives at from the data in Table 15 is that the thinner the reaction layer, the more important the contribution of radical anionTABLE 15

Linear sweep voltammetry of the electrohydrodimerizationof diethyl fumarate in “anhydrous” acetonitrild -

Epat CA/mM

v/mV s-l

0.50

1.00

2.00

4.00

100 200 400 1000

367.9(0.1) 371.0(0.2) 375.8(0.2) 382.6(0.1)

358.3(0.2) 359.9(0.2) 364.0(0.3) 370.4(0.1)

347.8(0.1) 349.2(0.2) 352.9(0.1) 358.3(0.2)

338.7(0.3)

-

C

-c

-c

dEp/d log C A ~ - 32.6 - 36.2 -38.0 -40.3

Parker, 1981g. In solvent containing Me4NBF4(sat.) at 22°C at an Au electrode. Potentials are in mV relative to a potentiostat bias setting of - 1.420 V vs Ag/Ag+ in acetonitrile In mV/decade, correlation coefficients of 0.9997, 1.0000, 0.9998 and 1.OOOO for 100, 200, 400 and 1000 mV s-l, respectively Due to adsorption of products on the electrode at this high concentration, the potential measurements at these sweep rates were not meaningful

201

ELECTROC H EMI C AL M ETH0 DS

substrate coupling. The last two entries in Table 15 are within experimental error of the theoretical value and suggest exclusive radical anion-substrate coupling. Since both reactions involve primary second order steps, the effect of increasing substrate concentration is to increase the rate of the reaction and hence decrease the reaction layer thickness which would be expected to favour radical anion-substrate coupling. However, the reason for this is probably not that the competition between reactions (106) and (107) becomes more favourable as suggested (Eberson and Nyberg, 1976; Andrieux et al., 1977) but because radical anion-substrate coupling that is observed (Parker, 1981d,g) is a third order reaction and the pertinent rate ratio is (125) which clearly gives the expected concentration dependence. However, the conclusion based upon (125), is not valid when (107) is rate determining. rate( I06)/rate( 107,108) = klo,/klo8Klo,[A]

(125)

For reactions of MC- carried out in the presence of Me,N+, it was shown that the cation must be taken into account in the rate law. Reactions (126)(128) were proposed to describe the radical anion-substrate coupling mechanA-

A'/Me,N+ A'-A'/Me,N+

K

126

+ Me,N+ + A'/Me,N+ K

I27

4 A $ A'-A-/Me,N+

+ A'

k I28

-+ A'-A'/Me,N+

rate = klZ8K~Z6KlZ~[~-12[~I[Me4N+l

(1 27)

+A

(128)

(I 29)

ism with rate law (129). At higher cation concentrations the reaction order in Me,N+ became greater than one indicating the dimerization of the ion pair (Parker, 1981g). Strong ion pairing can be viewed as a case of the general reaction (109). It is interesting that these reactions are important in spite of the fact that K,,, is small which was shown by the independence of the reversible electrode potentials upon whether Me,N+ or the large cation (C,H,,),N+, which would not be expected to form strong ion pairs, was the supporting electrolyte cation. It had previously been shown that alkali metal cations, which are expected to ion pair much more strongly, significantly enhance the rate of electrohydrodimerization of activated olefins (Hazelrig and Bard, 1975). A triactivated olefin, p-methylbenzylidenemalononitrile(MBM) [ 141, has also been used as a substrate in electrohydrodimerization studies (Nadjo et al., 1975; Nadjo and Savkant, 1976). Because of the expected extensive delocalization of charge and the odd electron in the anion radical MBM', this structure would appear to be rather extreme to be considered as a model

202

VERNON D. PARKER

for acrylonitrile. The reaction was first studied by LSV and CPSV and an excellent fit of the experimental slope to the theoretical one for the anion

1141

radical dimerization was observed. The peak potential during LSV was observed to be dependent upon the water concentration but the changes were related to those of the reversible potential which indicates that water is not kinetically involved in the reaction. The reaction was later studied by chronopotentiometry at high concentrations in order to test for a change in mechanism with increasing concentration. The conclusion of this study was that the reaction remained of the radical anion dimerization type but that water played a significant role when the concentration of MBM- was increased (Nadjo and SavCant, 1976). The effect of water was rationalized as follows, the symbols used being those in the original reference. When the concentrations of MBM and water are of the same order of magnitude, the preferential solvation of A- by water may be considered essentially as the formation of an adduct and the reactions can be rationalized as (130Hl33) where TH is Kilo

A - I TH + A S * k131

2AS'+DH, AS'

+ 2 T

kl32

+ AT+DH- + Tkl33

2 A- +D2-

(133)

water, AS' is the radical anion-water adduct, and D2- is the dimer dianion. It was concluded that since coulombic repulsions are reduced in AS', step (131) can be considered to play a major role in the overall reaction. Since the dimerization is unaffected by the presence of water when MBM is at the millimolar level (Nadjo et al., 1975), the importance of (130) at high concentrations of MBM would have to be due to the higher concentrations of MBM;. This is rather difficult to reconcile with the data. It would seem that equilibrium (130) would be shifted to the right either by increasing the concentration of MBM; or water. The electrohydrodimerization of MBM was also studied in the presence of acetic acid (Avaca and Utley, 1975a,b). The products of the reaction were observed to be the cyclic dimers [15a] and [15b]. A reinvestigation of the

203

ELECTROCHEMICAL METHODS

kinetics was carried out in CH,CN and DMF both in the presence and absence of HOAc (Lerflaten and Parker, 1982b). It was shown that the proton donors Ph Ph CN

CN

do not take part in the reaction until dimerization of the radical anions has taken place. In view of the near zero apparent activation energy for the dimerization, it was concluded that the radical anions first associate reversibly and bond formation then takes place to form the dimeric dianion. The dimerization of radical anions derived from 9-X-substituted anthracenes (Scheme 4), where X is an electron-withdrawing substituent, is related to electrohydrodimerization and might be expected to be less complex since proton donors are not involved in the formation of the products (Hammerich and Parker, 1981b). The reactions, where X is NO2, CHO, or CN, were studied by LSV and DCV. Primarily on the basis of the near independence of the reaction rates on temperature, the simple dimerization mechanism was excluded. It was proposed that the overall reaction consists of two reversible steps (i) formation of a radical anion dimer complex in which the two anthracene moieties are not bonded at the 10 positions and ( i i ) the rearrangement of the complex to the stable dimeric dianions. The rate of the reaction was found to be independent of the water concentration in DMF. The radical

XX-AN-AN-X

Scheme 4

VERNON D. PARKER

204

anions, AN-X-, like those from MBM must have highly delocalized chargeand odd electron-distributions which must make direct association favourable relative to the diactivated olefin radical anions which prefer either to react with substrate or to complex with a proton donor before undergoing dimerization. The question of dimerization mechanism has also surfaced in the study of reactions of cation radicals. The anodic oxidation of 4,4'-dimethoxystilbene is accompanied by the formation of dimeric products, the nature of which depends upon the nucleophile involved in the reaction as indicated in Scheme 5 (Parker and Eberson, 1969; Eberson and Parker, 1970; Steckhan, 1978; Burgbacher and Schafer, 1979). The reaction was studied by spectroelectrochemistry (Steckhan, 1978) in acetonitrile containing methanol. Competing mechanisms were proposed involving the reactions of the radical cation (Dt) with methanol (134) and by dimerization (135) giving rise to rate law (136). Theoretical working curves were used to find the best fit of the data

+ + CH30H +D'-0-CH, I4 kl34

Dt

kim

2 Df --+D+-D' rate

+ k13,[D~l[CH30H]

= 2k135[Df]2

OAc

An

+

An-CH-CH-An

I

-2e-. Am-, H.0

1

0

0

Ac

Ac

Ac

H

I

I

n,o

8

+

OCH,

I

I

An-CH-CH-CH-CH-An

I

OCH,

Scheme 5

I

An

An CH,OH

I

0

An

-e-.

I

0

I

-e-.

An-CH-CH-An

I

An

(major)

(135) (1 36)

ELECTROCHEMICAL METHODS

205

according to rate law (136), and it was proposed that k135 = 2 k134. A rotating ring disk electrode study in acetonitrile in the presence of water supported the mechanistic assignment. The data fitted theoretical working curves calculated for the dimerization mechanism (Burgbacher and Schafer, 1979). However, an analysis of the kinetics assuming k135= 2 klN indicated that during the spectroelectrochemical study the reaction was going predominantly by way of the pathway first order in D t (Aalstad el af., 1981a). A reinvestigation of the mechanism of the dimer forming reactions of D was carried out using LSV, DCV and SHAC as diagnostic techniques. The reaction was observed to be very much more complex than the previous studies had indicated (Aalstad et a/., 1981a). LSV analysis of the reaction gave the data reproduced in Tables 16, 17 and 18. These data indicate that (i).the reaction order in Dt is 2 under all conditions studied, and ( i i ) the reaction order in D is 1 and CH30H does not enter into the rate law. That the reaction is complex was clearly shown by the near independence of the reaction rate on temperature over the range, 4 ° C to 53°C. That the apparent concentration of Dt at short times during CV at 25°C is greater than is actually present was shown by comparing the derivative CV with that measured at -30°C (Fig. 28). At the higher temperature a peak due to reduction of D?(R’,) is the only one observed on the reverse sweep, while at -30°C the current at R’l is small compared to that due to the oxidation of another intermediate, R’2. This was interpreted as indicating that D: was in equilibrium with the dimeric dication D+-D+. A mechanism consisting of reac-

TABLE 16 Linear sweep voltammetric analysis of the oxidation of 4,4’-dimethoxystilbene(A) in acetonitrilea EPImV CdmM

0.1OOb

0.200b

O.4OOb

l.Wb

e Eld log Y

0.20 0.50 1.oo 2.00

296.4(3) 276.6(2) 269.5(0) 259.6(6)

304.0(3) 281.4(2) 274.3(3) 264.5(4)

310.0(4) 287.2(3) 280.6(6) 270.8(6)

316.3(4) 295.0(7) 288.5(7) 278.5(9)

19.7 18.5 19.1 19.1

d E/d log CA

- 36.1

- 38.5

-

38.2

- 36.8

Aalstad et al. 1981a. Measurements at a platinum electrode at 20T, supporting electrolyte Bu4NBF4(0.1 M). The peak potentials listed are relative to a bias setting of +0.450 V vs Ag/Ag+in acetonitrile. The numbers in parentheses are the standard deviation in five measurements VIV s-’

206

VERNON D. PARKER

TABLE 17 Linear sweep voltammetric analysis of the oxidation of 4.4’-dimethoxystilbene (A) in acetonitrile containing methanol’ Ep/mV

[MeOH]/mM

0.100”

0.200”

0.400”

1.OOOb

0 7.7 15.4 30.8 Mean

356.8(2) 352.9(1) 349.1(1) 349.2(1)

363.5(3) 358.0(1) 355.5(0) 354.3(1)

369.2(1) 364.6(2) 362.5(2) 360.1(2)

377.6(2) 373.9(4) 372.6(4) 369.4(5)

dE/d log v 20.6 21.2 23.6 20.2 21.4( 15)

Aalstad et al., 1981a. Measurements at a platinum electrode at 2 3 T , supporting electrolyte Bu,NBF4 (0.1 M). Peak potentials are relative to a bias setting of 10.400 V vs Ag/Ag+ in acetonitrile. The numbers in parentheses are the standard deviations in five measurements

a

v/v s-’

r-

0 55

I

0 75

I

1 0 95

I

I

I

0 75

1

0 55

1

E ( V vs Ag / Ag +)

FIG. 28 Derivative cyclic voltammograms for the oxidation of 4,4’-dimethoxystilbene in acetonitrile at 25°C (a) and -30°C (b). Voltage sweep rate = 100 V s-l. (Bu4NBF4) = 0.1 M. (Aalstad et al., 1981a)

207

ELECTROCHEMICAL METHODS

TABLE 18

Concentration dependence during LSV mechanism analysis of the oxidation of 4,4'-dimethoxystilbene (A) in acetonitrile containing methanol" CAlmM

Ep/mV Solution lb

0.10 0.20 0.40 0.60 0.80 1.oo

383.6(4) 373.6(2) 361.2(4) 354.9(8) 350.2(7) 347.9(5)

Ep/mV Solution 2b 385.6(10) 373.8(8) 363.2(4) 357.9(6) 353.8(8) 347.7(3)

- 36.7

d EP/d log CAlmV decade-' Correlation coef:

-36.3 0.998

0.999

" Aalstad et al., 1981a. Measurements at a platinum electrode at 22°C in solvent contaning Bu,NBF, (0.1 M) and methanol (25 mM). Voltage sweep rate = 1.00

v s-1

Substrate was added incrementally to the two solutions. The numbers in parentheses are the standard deviations in 5 measurements Data treated by linear regressions analysis tions (137)-(140) and rate law (141) was proposed to account for the data under LSV conditions.

Df D+-D'

K,,,

+ D + D+-D' kim

+ Df

+D+-D+

(137)

+D

(138)

D+-D+ e 2 D! D+-D+

( 1 39)

products

( 140)

rate = k,,,Kl,,[Df]2[D]

(141)

--f

This discussion of electrodimerization will be concluded with another radical cation example. The anodic coupling of 4-methoxybiphenyl has been obseryed to give good yields of the dimer, 4,4"'-dimethoxyquaterphenyl [ 161

c

-

.

3

3

CH,O

[I61

(Ronlhn et al., 1973). A recent kinetic investigation produced a number of interesting results (Aalstad et al., 1981b). A nearly complete changeover in mechanism, from radical cation dimerization at high concentrations to radical

208

VERNON D. PARKER

cation-substrate coupling at low radical ion concentration, was proposed Thedata for the reaction order study are reproduced in Table 19. Theradicalcation dimerization mechanism requires that v&/CA be constant. This appears to be very nearly the case for the entries with substrate concentration greater than 2 mM. On the other hand, the radical cation-substrate coupling mechanism should be characterized by a constant value of v,/C:. This situation TABLE 19

Kinetic analysis of the coupling of 4-methoxybiphenyl radical cationa 8.0 4.0 2.0 1 .o 0.5 0.25 0.125

48.3 23.6 9.63 3.40 1.34 0.49 0.1 1

6.04 5.90 4.82 3.40 2.68 1.96 0.88

0.755 1.48 2.41 3.40 5.36 7.84 7.04

' Aalstad et a[., 1981 b. Measurements in CH,CN containing Bu,NBF, 22°C

(0.1 M) at

appears to be realized at concentrations lower than about 0.5 mM. At intermediate concentrations both terms change dramatically with substrate concentration. Thus, this is clearly a case of competing reaction mechanisms and it seems likely that the competition involves reaction (142) competing with (143)-( 144). However, the observed concentration dependence is con2 MBt

--t

MB+-MB+

( 142)

MBt

+

+MB+-MB'

(143)

MB+-MB'

+ MB;

-+ MB'-MB+

+ MB

(144)

trary to the prediction given earlier based on eqn (125) for the competing mechanisms. A logical alternative, which should have been but was not considered, is that only the radical cation-substrate coupling mechanism is involved with tb.e rate-determining step changing from (143) at high CAto (144) at low CA.As mentioned earlier, RA/Bdetermined from data such as those in Table 19 do not differentiate between the two second order rate laws. The distinction between the two possibilities could readily be made from theoretical relationships available for DCV analysis (Ahlberg and Parker, 1981c). The linear dlnR;/dlnv+ slopes are significantly different for the two second order mechanisms. At the high end of the substrate concentration range the apparent activation energy was observed to be 11.1 kcal mol-' while at the lowest CAthe rate of

ELECTROCH EM1CAL METHODS

209

the reaction was nearly independent of the temperature. As previously observed (Parker, 1981b), unusual temperature effects appear to be very valuable in the assignment of complex mechanisms to electrode reactions. A further point of interest is that when the ring protons were replaced by deuterium a kinetic isotope effect k,lk, of about 0.7 was observed. This was shown to be consistent with the reactions of radical cations in which the carbon atoms becoming bonded in the transition state pass from sp2 to sps hybridization as had been observed in other types of reactions (do Amaral et al., 1972). HALOAROMATIC RADICAL-ANION CLEAVAGE

The lqss of halide ion from the radical anions of aromatic compounds is a facile reaction in solution. This reaction has been studied extensively by electrode techniques (Lawless and Hawley, 1969a,b; Bartek et al., 1970, 1972; Nadjo and Savtant, 1971a; Houser et al., 1973; Nelson et al., 1973; M'Halla et al., 1978, 1980; Savtant and Thiebault, 1978; Gores et al., 1979; Pinson and Savtant, 1974, 1978; Amatore et al., 1979; Parker, 1981kJ). The anion radicals of halonitrobenzenes, halobenzonitrilies, haloanthracenes, halonaphthalenes, halobenzophenones and haloacetophenones have received the most attention. A particularly pertinent study has recently appeared in which the number of electrons transferred during reduction of a number of haloaromatics in CH,CN and DMSO was determined along with the yield of hydrocarbon (M'Halla et al., 1980). In general, very close to 2 electrons were consumed per molecule undergoing reduction and the yields in all cases were 95% or greater. By working in solvents containing D,O or in deuteriated solvents containing H,O, and assuming that H,O acts only as a proton donor, the competition between reactions (145) and (146)-(147) could be determined.

+ S-H

Ar' Ar'

Ar'

+ Ar-X'

+ e-

--f

Ar-

+ Ar-X

+ S'

+ Ar-H H*O

4 Ar-H

H*0

+ Ar- -+

(145)

+ OHAr-H

( 146)

+ OH-

(147)

The competition between electron transfer at the electrode (146) and in solution (147) in turn depends upon the rate of cleavage of the radical anion Ar-X; (148) since this reaction determines the thickness of the reaction Ar-X;

+ Ar'

+ X-

(148)

layer and hence how far Ar' must diffuse to be reduced at the electrode. This ECE reaction had already been shown to occur only when the C step, (148)

21 0

VERNON D. PARKER

in this case, is exceedingly rapid (Amatore and SavCant, 1977, 1978, 1979, 1980). By an analysis making use of the two limiting cases where either (146) or (147) accounts for the electron transfer, it was possible to derive the rate constant ratio kI48/k145 using the deuterium incorporation data. Since (145) is independent of the leaving group in (148), evaluation of k148 for any precursor of Ar' allows for the evaluation of all other k148 involving other leaving groups from the rate constant ratio k148/k145. The rate constants reproduced in Table 20 involve combinations of the deuterium incorporation data with

TABLE20 C-X cleavage rate constants of the ArX radical anions"

Compound

Solvent

9-Chloroanthracene Me,SO 9-Bromoanthracene CH,CN Me,SO 9-Iodoanthracene CH,CN Me,SO 1-Chloronaphthalene CH3CN Me,SO I-Bromonaphthalene Me,SO I-Iodonaphthalene Me,SO CH,CN 4-Chlorobenzonitrile CH3CN 4-Bromobenzonitrile CH3CN 4-Iodobenzonitrile CH3CN

from cyclic voltammetry (a) or redox catalysis (b) (a) 1.5 x lo2 (a) 2.6 x lo2 (b) 3 x lo6

(b) 5 x lo7 (b) 3 x 10, (b) 5 x lo8

from deuterium incorporation experimentsb

7 x 104 1.5 x lob 7 x 106 6 x lo8 2 x 108 6 x loB 4 x 1010

1 x 10'0 5 x 10'0

" M'Halla et a/., 1980

Deuterium incorporation measurements led to kllR/klrlS while k,,, was obtained from CV data corresponding results from redox catalysis (Andrieux et a/., 1980). Rate constants for reaction (148) as high as 5 x 10'" were estimated in this manner. Slower reactions, for example those of the halobenzophenone radical anions, had previously been studied in DMSO (M'Halla et al., 1978), DMF, CH,CN, 2-cyanopropane and liquid NH, (Nadjo and SavCant, 1971a; SavCant and Thiebault, 1978). Typical rate constants for cleavage reaction (148) in D M F at 20°C were reported to be 10 (p-Cl). 740 (m-Br) and 8 x lo4 (P-Br). The halonitrobenzene radical anions are even less reactive than those derived from the benzophenones. The decomposition of some m-,o-, and

21 1

E LECTROC H EM I CAL M ETH0 DS

p-substituted halonitrobenzene radical anions was studied in CH,CN, DMF, and DMSO by chronoamperometry and current reversal chronopotentiometry (Lawless and Hawley, 1969a). The order of reactivity was found to be o-iodo- > o-bromo- > >p-iodo- > rn-iodo-nitrobenzene. The rates were solvent dependent and increased in the order, DMSO < CH,CN < DMF. The addition of iodide ion was found to decrease the rate of decomposition of all of the iodo-substituted radical anions while bromide ion had no effect on the rates of any o f the reactions. Reaction (149) was proposed to account for the

results, written here with the p-iodo isomer as an example. Recently, a series of investigations was initiated in order to gain more detail of the mechanism of the cleavage reactions (Parker, 1981k,l). The work discussed up to this point was primarily aimed at showing that the cleavage of the carbon-halogen bond takes place and to determine the reaction pathways of the aryl radicals generated in the reactions. No information was available on the activation parameters for the reactions. The reactions of the radical anions of the anthracenes [17] and [I81 where X is either bromine or X

X

chlorine, were studied by DCV. The activation parameters and rate constants at 298 K for the reactions in DMF are gathered in Table 21. The rate constants for the cleavage of the radical anions of [18] were observed to be 7.5 times greater than the corresponding reactions of the radical anions of [17]. The Arrhenius activation energy was found to be independent of whether mono- or di-substituted radical anion was decomposing but very dependent upon the nature of the leaving group. Although the differencein E, for chloroand bromo-substituted radical anions was observed to be about 1 1 kcal mol-1, the rate constants differ by only a factor of about 2000. The entropy of activation decreased in the order 9-chloro > 9,lO-dichloro > > 9-bromo > 9,lO-

21 2

VERNON D. PARKER

TABLE 21

Arrhenius activation parameters for cleavage reactions of aryl halide radical anions' Substrate

9-Chloroanthracene 9,lO-Dichloroanthracene 9-Brom~anthracene~ 9,lO-Dibromoanthracene

E,/kcal mol-'

kzsa/s-'

(AH$ss)b

15.3 15.8 (4.5) 4.5

122 16.5 (2.5 x lo6) 3.4 x 104

14.7 15.2 (4) 3.9

(AS:,,)*

0.32

- 3.65 (-21) -24.7

' Parker, 1981k

Activation parameters: enthalpy expressed in kcal mol-' and entropy in cal K-l mol-l ' Data less reliable than for the other ions dibromo. The difference in entropy of activation for mono- and di-substituted radical anions was in both cases of the order o f 4 cal K-l mol-l, with the latter being more negative. The most surprising feature of the data is that the bromo-substituted radical anions undergo decomposition with entropies of activation about 21 cal K-I mol-' more negative than the chloro-derivatives. This very large difference in entropy of activation caused difficulties in the rationalization of the rate differences. If bond cleavage is essentially complete in the transition state and the position of the transition state nearly the same for either leaving group, it was proposed that the entropy of activation should be due primarily to differences in the ordering of the solvation shells around the radical anions as compared to the transition states leading to the formation of halide ions. The latter would have been expected to be accompanied by small differences in the opposite direction. The difference in standard entropies of CI- and Br- in DMF has been evaluated to be 3.4 cal K-' mol-l with that for CI- being the more negative (Criss, 1973). Thus, if the entropies of activation are associated with solvation changes in going from radical anion to the transition state, bond cleavage must be very much more advanced when the leaving group is bromide. The standard entropy of Br- in DMF has been estimated to be - 4 3 . 3 cal K-l mol-' (Criss, 1973); so, in terms of the magnitude of the entropy of activation for the cleavage of 9-bromoanthracene radical anion, this interpretation requires the standard entropy for the radical anion to be considerably less. This would seem to be highly plausible since the large radical anion would be expected to bring about less ordering of the solvent. A comparable study was carried out on the cleavage reactions of p-bromo-, m-iodo- and p-iodo-nitrobenzene radical anions in DMF and CH,CN. The data reproduced in Table 22 show that the relationship between activation parameters with bromo- and iodo-substitution does not exhibit the anomaly observed with the substituted anthracene radical anions. The value of AS;,,

21 3

ELECTROCHEMICAL METHODS

TABLE 22

Activation parameters for the decomposition reactions of halonitrobenzene radical anions in aprotic solvents' Solvent

Electrolyte

DMF DMF DMF CHsCN CH&N DMFb DMFc

E,/kcal rnol-l

ASi,,/cal K-l mol-l

kf,,ls-'

Bu4NBF4 Bu,NI Me,NBF, Bu~NBF~ MeoNBF4

18.1 19.5 17.9 20.2 20.2

4.3 5.2 0.3 7.6 7.3

7.85

Bu4NBF4 Bu4NBF4

18.8 22.2

2.5 4.1

0.96 0.0013

1.13

5.49 1.19

1.04

'Parker, 19811

For the reaction of 3-iodonitrobenzene radical anion For the reaction of 4-bromonitrobenzeneradical anion

was nearly the same for p-iodo- and p-bromo, 4.3 and 4.1 cal K-' mol-l, while that for m-nitrobenzene radical anion was just slightly lower, 2.5 cal K-' mol-', when the reactions were carried out in DMF in the presence of Bu,NBF,. Thus, the fact that the reaction is 6000 times as fast when the leaving group is p-iodo as compared to p-bromo is a reflection of the 4 kcal mol-1 difference in E,. Both E, and AS;,, were observed to be somewhat larger in CH,CN than in DMF giving rise to a difference of about a factor of 6 in rate constants. The activation parameters and rate constants were only slightly dependent upon whether the counter-ion was Bu,N+ or Me,". When the supporting electrolyte was Bu,NI (0.1 M), E, was observed to increase by 1.4 kcal mol-' and AS;,, increased by 0.9 cal K-*mol-l accompanied by a 6-fold decrease in the rate constant. As found in earlier work (Lawless and Hawley, 1969a), this is a consequence of the participation of reverse reaction (148). It was concluded that the small positive entropies of activation are a result of the fact that the charge in the radical anions is localized on the nitro-groups regardless of the position or nature of the leaving group, and little change in solvent ordering takes place upon going to the transition state. A small deuterium kinetic isotope effect, which was temperature dependent, was observed for the cleavage of p-iodonitrobenzene radical anion in CH,CN. The kinetic isotope effect is a consequence of the participation of the hydrogen atom abstraction reaction (145) in determining the overall rate of the reaction. The temperature dependence of the kinetic isotope effect arises because of the differences in activation energies of the cleavage and abstraction reactions. Reverse reaction (148) was examined more closely as well (Parker, 19811). The observed rate constant at constant [I-] is given by eqn (150) arrived at

21 4

VERNON D. PARKER

by application of the steady state approximation to the p-nitrophenyl radical. + ksHISHl)

kobs == k S H I S H l k f / ( k b [ l - l

(1 50)

In (150) SH is acetonitrile, ksH is the rate constant for hydrogen abstraction and k , and k , refer to the cleavage and the reverse reaction. Equation ( I 50) (151)

l/kobs = [ l - l k b / k f k S H I S H l

can be rearranged to (151) which predicts that the inverse of the observed rate constant should be linearly related to the iodide ion concentration and the intercept of a plot will provide the inverse of k,. The fit of the data to (151) is demonstrated by the plot in Fig. 29. The intercept gave 6.7 s-l at 22.3"C, indicating that in the absence of added iodide ion the back reaction does not contribute significantly to the rate of the reaction. The activation parameters determined under those conditions are thus a true reflection of the energetics of the cleavage reaction. The rate constant for the reaction of the aryl radical, generated by the reduction of p-nitrophenyl diazonium ion with iodide (Helgde and Parker, 1980), was estimated to be 2 x lo9 M-ls-l which allowed the equilibrium constant K = kf/kb to be estimated to be 3.4 x 1 0 - 9 ~ . 1. 1

1.0 0.9 0.8 0.7 0.6

1

i;

(8)

0.5 0.4 0.3 0.2 0. 1

t

0 . 0 L 0.00

'

0.02

'

'

0.04

'

'

0.06

I

0.08

[I-I /M FIG.29 Influence of iodide ion concentration on the rate constant observed for the cleavage of 4-iodonitrobenzene radical anion in DMF at 22.3"C. (Parker, 1981)

21 5

ELECTROCHEMICAL METHODS

Aryl radicals electrochemically generated from the cleavage of aryl halide radical anions have been observed to react with nucleophiles other than iodide (Pinson and Savtant, 1974, 1978; Savtant, 1980), a reaction known as the S1, reaction (Bunnett, 1978). The most commonly used nucleophiles are thiophenolate, mercaptides, and cyanide ion. The reactions observed are Ar-Y

+ Ar'

+ X-

(152)

+ Z- + Ar-Z' Ar-Z' + Ar-X + Ar-Z + Ar-X' Ar' + S-H -+ Ar-H + S' Ar'

(153) (1 54) (155)

described by (152)-(155). If the position of equilibrium (154) is favorable, this step can serve as the propagation of a chain process, the most important termination of which is reaction (155). Acetonitrile and DMSO are generally used as solvents since they are less reactive toward the aryl radicals than is DMF. The coulometric n value, which gives the number of Faradays of charge per mol consumed is a guide to the chain length. Values as low as 0.2 were reported (Pinson and Savtant, 1978) which indicates that (155) competes rather effectively with reaction (153). In many cases, the reaction can be detected directly by CV. An example is given in Fig. 30. On the first forward Experimental

-

-

i

'_

0

&

Simulated

- loo

-

-50.4

i

'5

-0

sweep during the reduction of chlorobenzonitrile to the radical anion which subsequently undergoes cleavage, a single reduction peak is observed (Savtant, 1980). The experiment was carried out in liquid ammonia in the presence of potassium diethyl phosphite. On the reverse sweep the oxidation

VERNON D. PARKER

21 6

of a stable species, identified as the radical anion Ar-PO(0Et); where Ar is p-cyanophenyl, was observed and the corresponding reduction peak occurred on the second sweep. The simulated voltammogram is virtually identical to that observed. 8

Conclusion

The discussion in the previous sections has pointed out that the study of reactive intermediates using electrochemical techniques does not differ in any fundamental way from any other method, for example those involving chemical generation of the intermediates and monitoring the decay in spectral absorption bands. There are distinct advantages in the use of electrochemical methods, mainly the selectivity, time resolution, and information content of the results obtained. Thermodynamic as well as kinetic data can be obtained during the same experiments. The ready availability of digital retrieval systems has greatly influenced the nature and the power of electrode kinetic studies. The ability to handle vast amounts of data has greatly improved the reliability of conclusions based on the experiments. In the past, the quality of electrode mechanism studies has varied a great deal, from very thorough, reliable investigations to those involving a minimum of data of questionable nature. The methods of electrode mechanism analysis are now highly developed and can be considered to be sound physical organic techniques. The future will surely bring about a wider usage of the methods, not only by specialists but also by those who require the methods to solve particular problems associated with their mechanistic studies. Acknowledgements

The author thanks Professor Lennart Eberson and Dr. Ole Hammerich for helpful comments on the manuscript. References

Aalstad, B. and Parker, V. D. (1980).J. Electroanal. Chem. 122, 183 Aalstad, B. and Parker, V. D. (1981).J. Electroanal. Chem. 122, 195 Aalstad, B. and Parker, V. D. (1982). J. Electroanal. Chem. 136, 251 Aalstad, B., Ronlan, A. and Parker, V. D. (1981a). Acta Chem. Scund. B35, 247 Aalstad, B., Ronlan, A. and Parker, V. D. (1981b). Acta Chem. Scand. B35,649 Adams, R. N. (1969). “Electrochemistry at Solid Electrodes”. Dekker, New York Ahlberg, E. and Parker, V. D. (1979). Acta Chem. Scand. B33, 696 Ahlberg, E. and Parker, V. D. (1980a). Acta Chem. Scand. B34, 91 Ahlberg, E. and Parker, V. D. (1980b). Acta Chem. Scand. B34, 97

ELECTROCHEMICAL M ETH0 DS

21 7

Ahlberg, E. and Parker, V. D. (1981a).J. Electroanal. Chem. 121, 57 Ahlberg, E. and Parker, V. D. (1981b).J. Electroanal. Chem. 121, 73 Ahlberg, E. and Parker, V. D. (1981~).Acta Chem. Scand. B35, 117 Ahlberg, E., Svensmark, B., Parker, D. P. and Parker, V. D. (1978). Acta Chem. Scand. B32, 5 10 Ahlberg, E., Halvorsen, J. and Parker, V. D. (1979). Acta Chem. Scand. B33, 781 Ahlberg, E., Svensmark, B. and Parker, V. D. (1980a). Acta Chem. Scand. B34, 53 Ahlberg, E., Helgee, B. and Parker, V. D. (1980b). Acta Chem. Scand. B34, 187 Ahlberg, E., Hammerich, 0. and Parker, V. D. (1981). J . Am. Chem. SOC.103,844 Albery, W. J. and Hitchman, M. L. (1971). “Ring-Disc Electrodes”. Clarendon Press, Oxford Albery, W. J. (1 975). “Electrode Kinetics”. Clarendon Press, Oxford Allendoerfer, R. D. and Rieger, P. H. (1965). J. Am. Chem. SOC.87, 2336 Amatore, C. and Saveant, J. M. (1977). J. Electroanal. Chem. 85, 27 Amatore, C. and Saveant, J. M. (1978). J. Electroanal. Chem. 86, 227 Amatore, C. and Saveant, J. M. (1979). J. Electroanul. Chem. 102, 21 Amatore, C. and Saveant, J. M. (1980). J. Electroanal. Chem. 107, 353 Amatore, C., Chaussard, J., Pinson, J., SavCant, J. M. and Thiebault, A. (1979). J. Am. Chem. SOC.101, 6012 Ammar, F. and SavCant, J. M. (1973). J . Electroanal. Chem. 47, 115 Anderson, J. D., Baizer, M. M. and Prill, E. J. (1965). J . Org. Chem. 30, 1645 Andrieux, C. P. and Saveant, J. M. (1974). J. Electroanal. Chem. 57, 27 Andrieux, C. P., Nadjo, L. and Saveant, J. M. (1970). J. Electroanul. Chem. 24, 147 Andrieux, C. P., Nadjo, L. and Saveant, J. M. (1973). J. Electroanal. Chem. 42, 223 Andrieux, C. P., Brown, J. D. and Saveant, J. M. (1977). Nouv. J. Chim. 1, 157 Andrieux, C. P., Blockman, C., Dumas-Bouchiat, J. M., M’Halla, F. and Savkant, J. M. (1980). J. Am. Chem. SOC.102,3806 Avaca, L. A. and Utley, J. H. P. (1975a). J. Chem. SOC.Perkin Trans. 2 161 Avaca, L. A. and Utley, J. H. P. (1975b). J. Chem. SOC.Perkin Trans. 2 971 Aylmer-Kelly, A. W. B., Bewick, A., Cantrill, P. R. and Tuxford, A. M. (1974). Faraday Discuss. chem. SOC.56, 96 Baizer, M. M. (1963). Tetrahedron Lett. 973 Baizer, M. M. (1964a). J. Electrochem. SOC. 111, 215 Baizer, M. M. (196413). J. Org. Chem. 29, 1675 Baizer, M. M. (1973). In “Organic Electrochemistry” (M. M. Baizer, ed.). Dekker, New York, p. 679 Baizer, M. M. and Anderson, J. D. (1964a). J. Electrochem. SOC.111, 226 Baizer, M. M. and Anderson, J. D. (1964b). J. Electrochem. SOC.111, 223 Baizer, M. M. and Anderson, J. D. (1965a). J. Org. Chem. 30,3138 Baizer, M. M. and Anderson, J. D. (1965b). J. Org. Chem. 30, 1351 Baizer, M. M. and Anderson, J. D. (1965~).J. Org. Chem. 30, 1357 Baizer, M. M. and Anderson, J. D. (1965d). J. Org. Chem. 30, 1348 Baizer, M. M., Anderson, J. D., Wagenknecht, J. H.,Ort, M. R. and Petrovich, J. P. (1967). Prog. Phys. Org. Chem. 7, 189 Baizer, M. M., Petrovich, J. P. and Tyssee, D. A. (1970). J. Electrochem. SOC.117, 173 Bard, A. J. (1966-present). “Electroanalytical Chemistry”. Dekker, New York. [A continuing series dealing with electroanalytical chemistry] Bard, A. J. and Faulkner, L. R. (1980). “Electrochemical Methods”. Wiley, New York

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SOC. 94, 7526

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Bewick, A., Mellor, J. M. and Pons, B. S . (1980). Electrochim. Acta 25, 931 Bezilla, B. M., Jr. and Maloy, J. T. (1979). J . Electrochem. SOC. 126, 579 Blount, H. N., Winograd, N. and Kuwana, T. (1970). J. Phys. Chem. 74, 3231 Bond, A. M. and Smith, D. E. (1976). Anal. Chem. 46, 1946 BrdiEka, R. and Weisner, W. (1947). Coll. Czech. Chem. Commun. 12, 39 Breslow, R. and Chu, W. (1973). J. Am. Chem. SOC. 95,411 Breslow, R. and Mazur, S. (1973). J. Am. Chem. SOC.95, 584 Breslow, R. and Drury, R. F. (1974). J. Am. Chem. SOC. 96,4702 Breslow, R. and Goodin, R. (1976). J. Am. Chem. SOC.98, 6077 Breslow, R. and Grant, J. L. (1977). J. Am. Chem. SOC. 99,7745 Britz, D. (1981). “Digital Simulation in Electrochemistry”. Springer-Verlag, Berlin Bunnett, J. F. (1978). Acc. Chem. Res. 11, 413 Burgbacher, B. and Schafer, H. (1979). J. Am. Chem. SOC.101, 7590 Case, B., Hush, N. S., Parsons, R. and Peover, M. E. (1965). J. Electrounul. Chem. 10,360

Childs, W. V., Maloy, J. T., Keszthelyi, C. P. and Bard, A. J. (1971). J. Electrochem. SOC.118, 874

Closs, G. L. and Rabinow, B. E. (1976). J. Am. Chem. SOC.98, 8190 Crank, J. (1957). “The Mathematics of Diffusion”. Oxford University Press, London. Criss, C. M. (1973). In “Physical Chemistry of Organic Solvent Systems” (A. K. Carrington and T. Dickinson, eds) Ch. 2. Plenum, London Delahay, P. (1954). “New Instrumental Methods in Electrochemistry”. Interscience, New York do Amaral, L., Bull, H. C. and Cordes, E. H. (1972). J. Am. Chem. SOC.94, 7579 Doetsch, G. (1953). “Laplace Transformation”. Dover, New York Dombrowski, L. J., Groncki, C. L., Strong, R. L. and Richtol, H. H. (1969). J. Phys. Chem. 73, 3481 Eberson, L. and Parker, V. D. (1970). Acta Chem. Scund. 24, 3553 Eberson, L. and Nyberg, F. (1976). Adv. Phys. Org. Chem. 12, 1 Evans, D. H. (1977). Acc. Chem. Res. 9, 313 Evans, J. F. and Blount, H. N. (1976). J. Org. Chem. 42, 976 Evans, J. F. and Blount, H. N. (1978). J . Am. Chem. SOC.100,4191 Evans, J. F. and Blount, H. N. (1979). J. P h p . Chem. 83. 1970 Feldberg, S. W. (1969). Electroanul. Chem. 3, 199 Fry, A. J. and Schuettenberg, A. (1974). J. Org. Chem. 39, 2452 Fry, A. J., Hutchins, C. S. and Chung, L. L. (1975). J. Am. Chem. SOC.97, 591

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21 9

Galus, Z.(1976).“Fundamentals of Electrochemical Analysis”. Ellis Hanvood Ltd., New York Goldberg, I. B. and Bard, A. J. (1974).J. Phys. Chem. 78,290 Gores, C. J., Koeppe, C. E. and Bartek, D. E. (1979).J . Org. Chem. 44, 380 Grypa, R. D.and Maloy, J. T. (1975).J. Electrochem. SOC.122, 513 Hammerich, 0. and Parker, V. D. (1973).Electrochim. Acta 18,537 Hammerich, 0. and Parker, V. D. (1974).J . Chem. SOC.Chem. Commun. 244 Hammerich, 0 .and Parker, V. D. (1976).J . Am. Chem. SOC.%, 4284 Hammerich, 0. and Parker, V. D. (1981a).Acta Chem. Scand. B35, 395 Hammerich, 0. and Parker, V. D. (1981b). Acta Chem. Scand. B35, 341 Hawley, M. D.and Feldberg, S. W. (1966).J. Phys. Chem. 70,3459 Hazelrig, M. T.and Bard, A. J. (1975).J. Electrochem. SOC.122, 21 1 Helgtk, B. and Parker, V. D. (1980). Acta Chem. Scand. B34, 129 Hoijtink, G. J. (1955). Red. Trav. Chim. Pays-Bas 74, 1525 Hoijtink, G. J., deBoer, E., van der Meij, P. J. and Weijland, J. P. (1956). Red Trav. Chim. Pays-Bas 75,487 Hoshino, M. Kimura, K. and Imamura, M. (1973). Chem. Phys. Lett. 20, 193 Houser, K. J., Bartek, D. E., Hawley, M. D. (1973).J. Am. Chem. SOC.95,6033 Hunig, S.and Berneth, H. (1980). Top. Curr. Chem. 92, 1 Imbeaux, J. C. and SavCant, J. M. (1973). J. Electroanal. Chem. 44,169 Jagur-Grodzinski, J., Feld, M., Yang, S. L. and Szwarc, M. (1965).J . Phys. Chem. 69,628 Jaun, B., Schwartz, J. and Breslow, R. (1980).J. Am. Chem. SOC.102, 5741 Jensen, B. S and Parker, V. D. (1974). J . Chem. SOC.Chem. Commun. 367 Jensen, B. S.and Parker, V. D. (1975a). J . Am. Chem. SOC.97, 5211 Jensen, B. S.and Parker, V. D. (1975b).J. Am. Chem SOC.97, 5619 Jensen, B. S.and Parker, V. D. (1976). Unpublished work Jensen, B. S., Ronlan, A. and Parker, V. D. (1975). Acta Chem. Scand. B29, 394 Kiesele, H. (1981).Anal. Chem. 53, 1952 Klein, A. J. and Evans, D. H. (1979).J. Am. Chem. SOC.101, 757 Korenstein, R., Muszkat, K. A. and Sharafy-Ozeri, S. (1973).J. Am. Chem. SOC. 95,6177 Koukotas, C. and Schwartz, L. H. (1969). J. Chem. SOC.,Chem. Commun. 1400 Kuwana, T. and Winograd, N. (1974). Electroanal. Chem. 7, 1 Lamy, E., Nadjo, L. and SavCant, J. M. (1973).J. Electroanal. Chem. 42, 189 Lamy, E., Nadjo, L. and SavCant, J. M. (1974).J. Electroanul. Chem. 50, 141 Lawless, J. C. and Hawley, M. D. (1969a).J . Electroanul. Chem. 21, 365 Lawless, J. C.and Hawley, M. D. (1969b).J. Electroanal. Chem. 23. Appendix 1 Lerflaten, 0. and Parker, V. D. (1982a). Acta Chem. Scand. B36 193 Lerflaten, 0.and Parker, V. D. (1982b). Acta Chem. Scand. B36 225 Levin, G., Sutphen, C. and Szwarc, M. (1972).J. Am. Chem. SOC.94,2652 Lines, R.,Svensmark, B. and Parker, V. D. (1978).Acta Chem. Scand. B32, 510 MacDonald, D.D.(1 977). “Transient Techniques in Electrochemistry”. Plenum Press, New York Mann, C. K. (1969). Electroanal. Chem. 3, 57 Manning, G., Parker, V. D. and Adams, R. N. (1969).J. Am. Chem. SOC.91,4584 Marcoux, L.S. (1971). J . Am. Chem. SOC.93, 537 Marcoux, L. S.,Fritsch, J. M. and Adams, R. N. (1967). J. Am. Chem. SOC.89, 5766 McCord, T. C. and Smith, D. E. (1969). Anal. Chem. 41, 1423

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