Methods to Investigate Mechanisms of Electroorganic Ractions

1

1Methods to InvestigateMechanisms of ElectroorganicReactions

Bernd SpeiserInstitut f

..ur Organische Chemie, Auf der Morgenstelle 18, T

..ubingen, Germany

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.1.1 Scope: Methods of Molecular Electrochemistry . . . . . . . . . . . . . . . 31.1.2 Historical Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Why and How to Investigate Mechanisms of Electroorganic Reactions 41.2.1 Steps of Electrode Reaction Mechanisms . . . . . . . . . . . . . . . . . . . 41.2.1.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2.1.2 Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2.1.3 Electron Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2.1.4 Chemical Kinetic Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2.1.5 Adsorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.2.2 Organic Electrode Reaction Mechanisms . . . . . . . . . . . . . . . . . . . 61.2.2.1 Electron Transfer Initiates Chemistry . . . . . . . . . . . . . . . . . . . . . 61.2.2.2 Nomenclature of Electrode Reaction Mechanisms . . . . . . . . . . . . . 61.2.3 Formal Description of Events at an Electrode . . . . . . . . . . . . . . . . 71.2.3.1 Current-Potential-Time Relationships . . . . . . . . . . . . . . . . . . . . . 71.2.3.2 Concentration Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2.4 Methods of Mechanistic Electroorganic Chemistry . . . . . . . . . . . . 71.2.4.1 Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2.4.2 Controlled-Potential Techniques . . . . . . . . . . . . . . . . . . . . . . . . 71.2.4.3 Controlled-Current Techniques . . . . . . . . . . . . . . . . . . . . . . . . . 111.2.4.4 Hydrodynamic Voltammetry . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.2.4.5 Exhaustive Electrolysis Techniques . . . . . . . . . . . . . . . . . . . . . . . 13

1.3 How to Gain Access to Kinetics, Thermodynamics, and Mechanismsof Electroorganic Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.3.1 Qualitative and Quantitative Investigation of Electrode ReactionMechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.3.2 General Recommendations for Mechanistic Analysis . . . . . . . . . . . 14

3

1.1Introduction

1.1.1Scope: Methods of MolecularElectrochemistry

Reaction mechanisms divide the transfor-mations between organic molecules intoclasses that can be understood by well-defined concepts. Thus, for example, theSN1 or SN2 nucleophilic substitutions areexamples of organic reactionmechanisms.Each mechanism is characterized by tran-sition states and intermediates that arepassed over while the reaction proceeds.It defines the kinetic, stereochemical, andproduct features of the reaction. Reactionmechanisms are thus extremely importantto optimize the respective conversion forconditions, selectivity, or yields of desiredproducts.Reaction mechanisms are also defined

for electroorganic reactions, induced byor including an electron transfer at anelectrode. Knowledge of such electrodereaction mechanisms includes, prefer-ably but not exclusively, the potential atwhich the reaction proceeds, the proofof intermediates, the electron stoichiom-etry, the kinetics of the various reactionsteps, and the transport properties ofthe species involved. Recently, the terms

molecular electrochemistry [1] or dynamicelectrochemistry [2] have been used for thatpart of electrochemistry that studies themechanistic events at or near an electrodeon a molecular level.There are a large number of methods

(often also called electroanalytical methods)for such studies of which only the mostimportant ones can be covered in thischapter. Moreover, technical details ofthe methods cannot be described, andemphasis will be placed on their use inmechanistic electroorganic chemistry.

1.1.2Historical Development

Although organic electrochemistry hadalready been established in the nineteenthcentury, only the 1960s saw the adventof detailed electroorganic mechanisticstudies.Most of the techniques employed can be

traced back to polarography, which was al-ready in use in 1925, to determine theconcentrations of organic molecules [3].Technical developments in instrumenta-tion (potentiostats) [4], the use of nonaque-ous electrolytes [5], and the digital controlof experiments [6] led to the spread ofelectroanalytical techniques. For example,cyclic voltammograms are frequently androutinely used today to define the redox

4 1 Methods to Investigate Mechanisms of Electroorganic Reactions

properties of newly synthesized organiccompounds similar to the use of NMRspectra for structural characterization.Numerical simulation of the experi-

ments [7] became increasingly availableduring the 1980s, and ultramicroelec-trodes [8] opened the way not only toever-faster timescales but also to finerlateral resolutionwhen characterizing elec-trode processes. Finally, combinationswith spectroscopic and mass-sensitive de-vices opened new ways to augment infor-mation available from molecular electro-chemical experiments.This development contributes to a still-

increasing body of knowledge about thefate of organic molecules upon oxidationand reduction.

1.2Why and How to Investigate Mechanismsof Electroorganic Reactions

1.2.1Steps of Electrode Reaction Mechanisms

1.2.1.1 GeneralAs heterogeneous reactions at the inter-face electrode–electrolyte, electrochemicalreactions are intrinsically more complexthan typical (thermal) chemical transfor-mations (Figure 1). We mostly neglect theexact structure of the interface in the fol-lowing description. Transport of the educt

(substrate) from the bulk of the electrolyteto the electrode plays an important, oftenrate-determining role. The electron trans-fer step occurs at the interface. The productof the redox reaction is transported backto the bulk. Purely chemical reactions mayprecede or follow these steps. Specific in-teractions of any species present in theelectrolyte with the electrode surface leadsto adsorption, which may considerably in-fluence the overall process.

1.2.1.2 TransportThree types of mass transport are impor-tant at an electrode:

1. Diffusion (along a concentration gradi-ent) is observed if the solution near theelectrode is depleted from a substrate ora product is accumulated. Diffusion ischaracterized by a diffusion coefficientD (typical value: 10−5 cm2/s) and ex-tends over a diffusion layer (thickness:δ) that develops from the electrode intothe electrolyte. At the outward bound-ary the concentrations approach theirbulk values.

2. Migration (in the electrical field be-tween the anode and the cathode)contributes to themovement of chargedspecies. In most practical experiments,however, the concentration of support-ing electrolyte ions is much higher(100–1000 : 1) than that of other ions.

P

d

E

Electrontransfer

Adsorption

Chemicalreactions

E E’

P P’

P

Ele

ctro

de

Transport

Transport

Diffusion layer Bulk

E

Fig. 1 Steps constituting atypical organic electrodereaction; E, E′: educt, P, P′:product; circles indicateadsorbed molecules.

1.2 Why and How to Investigate Mechanisms of Electroorganic Reactions 5

Hence, migration of the latter is sup-pressed. On the other hand, migrationbecomes important at modified elec-trodes or in electrolytes of low ionconcentration [9].

3. Convection (of the electrolyte liquidphase as a whole) can be natural (dueto thermal effects or density gradients)or forced (principal mass transportmode in hydrodynamic techniques).Still, however, close to the electrodesurface a diffusion layer develops.

If we neglectmigration, experiments canbe performedunder conditions ofminimalconvection, which are thus dominatedby diffusion. Since δ increases withtime t in such a case, nonstationaryconditions exist. On the other hand, ifconvection dominates in the electrolytebulk, δ �= f (t), and we approach stationaryconditions, as far as diffusion is concerned.

1.2.1.3 Electron TransferThe electron transfer (ET) at the interfacebetween electrode and electrolyte is centralto an electrode reaction. Electrons passthrough the interface. Macroscopically weobserve a current i.The transfer of an electron to (reduc-

tion) or from (oxidation) the substrate is anactivated process, characterized by a rateconstant ks, defined as the standard (orformal) potentialE0, and the transfer coef-ficient α. The three situations mentionedbelow can be distinguished:

1. ET much faster than transport (trans-port control). Electrochemical equilib-rium is attained at the electrode surfaceat all times and defined by the electrodepotentialE. The concentrations cox andcred of oxidized and reduced forms ofthe redox couple, respectively, followthe Nernst equation (1) (reversible ET)

cox

cred= exp

[nF

RT(E − E0)

](1)

(n = number of electrons transferred,F = Faraday constant, R = gas con-stant, T = temperature). The current isproportional to the amount of materialtransported to the electrode in a timeunit.

2. ET much slower than transport (ETcontrol). The current follows the But-ler–Volmer equation (2)

i = i0

{exp

[−αnFRT

(E − E0)

]

− exp

[(1 − α)nF

RT(E − E0)

] }(2)

where i0 defines the exchange currentat E = E0 (irreversible ET). A physicalinterpretation of α is related to the ETtransition state (see the comprehensivediscussion in ref. [10]). It is furthermoreexpected that α is potential dependentand importantmechanistic conclusionsfollow [11, 12].

3. ET and transport have comparablerates. This mixed-control situation ischaracterized as quasi-reversible.

A given electrode reaction may corre-spond to any of these situations dependingon the experimental conditions, in particu-lar on the external control ofmass transfer.

1.2.1.4 Chemical Kinetic StepsMost electrode reactions of interest to theorganic electrochemist involve chemicalreaction steps. These are often assumed tooccur in a homogeneous solution, that is,not at the electrode surface itself. They aredescribed by the usual chemical kineticequations, for example, first- or second-order reactions and may be reversible(chemical reversibility) or irreversible.


Chemical steps may precede or followthe transport and ET processes. In theformer case, the electroactive species isformed in a preequilibrium. In the lattercase, we produce by ET some reactivespecies, which undergoes a (possiblycomplex) chemical transformation to amore stable product.

1.2.1.5 AdsorptionThe involvement of specific attractive in-teractions of molecules with the electrodesurface (adsorption) makes the electrodeprocess even more complex. The inten-sity of such interactions ranges from weak(physisorption) to strong (chemical bondsformed between adsorbate and electrode).For some common organic electrochem-

ical reactions, for example, the Kolbeelectrolysis of carboxylates [13], the adsorp-tion of intermediates has been discussed.

1.2.2Organic Electrode Reaction Mechanisms

1.2.2.1 Electron Transfer InitiatesChemistryThemajority of organic electrode reactionsis characterized by the generation of areactive intermediate at the electrode by ETand subsequent reactions typical for thatspecies. Thus, the oxidation or reductionstep initiates the follow-up chemistry tothe reaction products (‘‘doing chemistrywith electrodes’’ [14]).Species with electron deficiency (e.g.

carbocations), unpaired electrons (e.g.radicals, radical ions), electron excess(e.g. carbanions), or those with unusualoxidation states (e.g. metal complexes withlow- or high-valent central atoms) areproduced at the electrode. Electrochemicalgeneration of such intermediates may beadvantageous because of the mild reactionconditions employed (room temperature,

strong acids or bases are not necessary)and/or the additional selectivity introducedin controlled-potential experiments.The reaction mechanisms of organic

electrode reactions are thus composed of atleast one ET step at the electrode as well aspreceding and follow-up bond-breaking,bond-forming, or structural rearrange-ment steps. These chemical steps maybe concerted with the electron trans-fer [15, 16]. The instrumental techniquesdescribed in this chapter allow the in-vestigation of the course of the reactionaccompanying the overall electrolysis.

1.2.2.2 Nomenclature of ElectrodeReaction MechanismsIn order to classify the various mech-anisms of organic electrode reactions,a specific nomenclature has been de-veloped [17]. It is often extended in aninformal way to accommodate particularreaction features, and one may find addi-tional or deviant symbols.Usually, however, electron transfers

at the electrode are denoted by ‘‘E’’,while chemical steps not involving theelectrode are denoted by ‘‘C’’. The ETmay further be characterized as ‘‘Er’’,‘‘Eqr’’, or ‘‘Ei’’ in the reversible, quasi-reversible, or irreversible case. It is usuallynot indicated how transport occurs. If theC-step is a dimerization, the symbol ‘‘D’’ iscommon, while an ET between two speciesin a (homogeneous) solution is denoted‘‘SET’’ (for solution electron transfer) [18]or ‘‘DISP’’ (see, e.g. [19]).For more complex mechanisms, pic-

turesque names such as square, ladder,fence [18] or cubic schemes [20] have beenselected. In redox polymer films, addi-tional transport of counterions, solvation,and polymer reconfiguration are impor-tant and four-dimensional hyper-cubes areneeded to describe the reactions [21].


1.2.3Formal Description of Events at anElectrode

1.2.3.1 Current-Potential-TimeRelationshipsThe equations given in Section 1.2.1 in-clude the most important quantities forunderstanding a reaction mechanism atan electrode: current i, potential E, andtime t . Consequently, most techniques toinvestigate electroorganic reaction mecha-nisms involve the determination of i or Eas a function of time (while the other oneof these quantities is kept constant) or as afunction of each other (while one is variedwith t in a defined manner).Similar i–E– t relationships are derived

theoretically from basic equations (simu-lation, see Section 1.4.1), on the basis ofa hypothesis for the reaction mechanism,and the experimental and the theoreticalresults are compared. In this way, the hy-pothesis is either disproved, or proven tobe consistent with the events at the elec-trode.

1.2.3.2 Concentration ProfilesThe current through the electrode is pro-portional to the flux of redox-active mate-rial to the surface, which, in turn is relatedto the concentrations c of various speciesnear the interface. Thus, an equivalent de-scription is based on the dependence ofc on space x and t . Often a single space-coordinate suffices.More complex systems(e.g. ultramicroelectrodes) may require upto three space-coordinates.Although it is difficult to determine the

spatial distribution of species experimen-tally, it provides an illustrative view ofthe electrode reaction. Simulations usu-ally provide values of c = f (x, t) for eachspecies as the primary result. The spacedependence of c is termed a concentration

profile. In general, the electrode is locatedat x = 0, and the electrolyte extends intothe positive x half-space. The bulk ofthe solution is assumed at the right-handside of the profile. Often, concentrationvalues are normalized with respect tothe bulk concentration of one species,and space coordinate values are normal-ized with respect to the extension ofthe diffusion layer δ. Such concentra-tion profiles will be used in the followingdiscussion.

1.2.4Methods of Mechanistic ElectroorganicChemistry

1.2.4.1 ClassificationOne of several possibilities to classify elec-troanalyticalmethods is based on the quan-tity that is controlled in the experiment,that is, current or potential. Alternatively,since diffusion is an important mode ofmass transport in most experiments, wedistinguish techniques with stationary ornonstationary diffusion. Finally, transientmethods are different from those that workin an exhaustive way.Only a small selection of the variants in

the electrochemical literature can be men-tioned here. Thus, impedance techniques(small amplitude sinusoidal perturbationat the electrode with observation of thesystem’s response [22]) as well as polaro-graphic methods (at mercury electrodes)will not be described. Since the notion ofa reaction mechanism requires consump-tion of substance, equilibrium techniques(such as potentiometry) will also not bediscussed here.

1.2.4.2 Controlled-Potential TechniquesControl of the potential E of that elec-trode where the electrode reaction occurs(working electrode) is accomplished by a


C WR

E

Electrolyte

Potentio/galvanostat

Computer,Recorder

Functiongenerator

Fig. 2 Schematic representation of experimental set-up forcontrolled-potential experiments; W: working, C: counter, R:references electrodes.

potentiostat in a three-electrode arrange-ment (Figure 2). The current is passedthrough the working (W) and counter(C) electrodes, while E is measured withrespect to a currentless reference (R) elec-trode. Often, a recording device and afunction generator complement the exper-imental setup.We will assume a simple reversible one-

electron redox process A±e−

−−−⇀↽−−− B in allcases to introduce the techniques.An important property of the solution

to be investigated is the rest or open-circuitpotential ER. This is the potential that theworking electrode develops in the solutionat equilibrium, that is, when no currentflows through the electrode. The value ofER depends on the components of thesolution and the electrode itself.Chronoamperometry is a technique in

which a potential step is applied to theworking electrode in a quiet solution at t =0 (Figure 3). Initially (t < 0), the electrodeattains ER. For t > 0, a potential isselected,which drives the desired electrodereaction. Often, but not necessarily (see,e.g. References [23–25]) the latter is in the

transport (diffusion) limited region. Aftersome (pulse) time τ , E may be switchedback to ER or another appropriate value(double-step chronoamperometry).Starting at ER guarantees that at t <

0, the concentration of the redox-activecompound A, cA, equals c0A at all x.The product concentration cB is usuallyassumed to be zero. After E is stepped,the concentrations of A and B at x = 0adjust to conform to equation (1). Theseconcentrations deviate from the bulkconcentrations that remain at their initialvalues throughout the experiment, anda concentration gradient develops. As aresult, A diffuses to the electrode,while B isproduced at x = 0 and diffuses to the bulk.The resulting diffusion layer grows intothe solution with t (typically 10−2 cm after10 s in common organic solvents). Thesteepness of the concentration gradientis high shortly after t = 0, and decreasesthereafter. This is reflected in the currentresponse given by the Cottrell equation (3)

i = nFAc0A

√D√

πt(3)


0.0−0.1

0.00.10.20.30.40.50.6

0.5

(a)

1.0 1.5

Time, t[s]

Pote

ntia

l, E

[V]

2.0 0.0−40−30−20−10

0102030

0.5

(b)

1.0 1.5

Time, t[s]

2.0

0.0−0.2

0.00.20.40.60.81.01.2

0.2(c)

0.60.4 1.00.8

Distance, x

Con

cent

ratio

n, c

1.2 0.0−0.2

0.00.20.40.60.81.01.2

0.2(d)

0.60.4 1.00.8

Distance, x

Con

cent

ratio

n, c

1.2

Cur

rent

, i

106

[A]

•

Fig. 3 Chronoamperometry: (a) typicalexcitation signal; (b) current response; andconcentration profiles [(c) first step; (d) secondstep; educt: solid lines, product: dotted lines; five

profiles respectively at various times, increasingtime shown by arrows] for a double-stepchronoamperometric experiment (pulse timeτ = 1s).

in the most simple case (with A =electroactive area of the electrode). Thus,i√t is a constant, and a plot of i vs. t−1/2

is a straight line.Switching back E to ER causes the

concentrations at x = 0 to return to theiroriginal values with the concentrationprofiles changing accordingly. Now, B,which has accumulated in the diffusionlayer, diffuses toward the electrode andis transformed back to A. We observe acurrent in the opposite direction.Any reaction that removes B from the so-

lution will influence the current response,allowing qualitative mechanistic conclu-sions. Furthermore, quantitative analysisof chronoamperometric curves includesdetermination of n, A, or D, provided twoof these quantities are known.Chronocoulometry is similar to chrono-

amperometry, but the time integral of i,

the charge Q, is recorded (Figure 4). Thisquantity continuously increases during thefirst part of the experiment (0 < t < τ ).Integration of equation (3) yields

Q = 2nFAc0A√D√

π

√t (0 < t < τ) (4)

As soon as the potential is stepped backsuch that a current in the reverse directionflows, the accumulated charge decreasesas shown:

Q = 2nFAc0A√D√

π(√t − √

t − τ )

(τ < t < 2τ) (5)

Thus, a plot of Q vs.√t for the first, and

Q vs.√t − √

t − τ for the second partof the curve results in two straight lines(‘‘Anson plot’’ [26]). Adsorption of redoxactive species can simply be diagnosed


0.0−3−2−1

01234

0.60.2 0.4

(b)

0.8

Square root of time, t1/2

[s1/2]

1.21.0−0.2−0.3

0.20.71.21.72.23.23.7

0.80.3

(a)

1.3

Time, t[s]

2.31.8

Cha

rge,

Q

106

[C]

•

Cha

rge,

Q

106

[C]

•

Fig. 4 Chronocoulometry: (a) typical charge response; (b) Anson plot for a double-stepchronocoulometric experiment.

if the extrapolated Anson plot lines do notcross close to the origin [27]. An interestingcharacteristic of the chronocoulometriccurve is that Q(2τ)/Q(τ) = 0.414, if nofollow-up reaction destroys B. If B reacts,however, this charge ratio increases.Because of its integral nature, chrono-

coulometry is less susceptible to noise

than chronoamperometry. Again, n, A, orD are accessible from chronocoulometricdata.Linear sweep and cyclic voltammetry (LSV

and CV) are probably the most widelyused techniques to investigate electrodereaction mechanisms. They are easy toapply experimentally, readily available in

0.00−0.1

0.00.10.20.30.40.5

0.70.6

0.02

(a)

0.06 0.08 0.10 0.120.04

Time, t[s]

Pote

ntia

l, E

[V]

0.14 −0.1 0.0−300−200−100

0100200300400

0.1

(b)

0.2 0.3 0.5 0.60.4

Potential, E[V]

0.7

0.0−0.2

0.00.20.40.60.81.01.2

0.2(c)

0.60.4 1.00.8

Distance, x

Con

cent

ratio

n, c

1.2 0.0−0.2

0.00.20.40.60.81.01.2

0.2(d)

0.60.4 1.00.8

Distance, x

Con

cent

ratio

n, c

1.2

Cur

rent

, i

106

[A]

•

Fig. 5 Linear sweep and cyclic voltammetry: (a)typical excitation signal; (b) current response;and concentration profiles [(c) forward scan;(d) reverse scan; educt: solid lines, product:

dotted lines; five profiles respectively at varioustimes, increasing time shown by arrows] for acyclic voltammetric experiment.


commercial instruments, and provide awealth of mechanistic information. Insuch experiments, the potential of theworking electrode is controlled by apotential ramp (LSV) or one or morepotential triangle(s) (CV, Figure 5, see alsoVolume 3, Chapter 2).The potential changes with a scan (or

sweep) rate v = dE/dt . This quantity iseasily variable and is one of the mostimportant parameters for mechanisticanalysis, defining the timescale of theexperiment.In these techniques, the concentrations

at the electrode do not immediatelyattain their extreme values after the startof the experiment. Rather, they changewith E or t according to equation (1).While the steepness of the concentrationprofiles increases with E (forward scan),simultaneously δ increases in the quietsolution. The latter effect slows down theincrease of i with E, and finally (close tothe limiting current region) leads to theformation of a peak with a characteristicasymmetric shape. On the reverse scan(after switching the scan direction at Eλ),products formed in the forward scan canbe detected (B, in the case discussed).The peak current in the forward scan is

given by [28]

ip = 0.4463nFAc0A

√nF

RTvD (6)

or, for T = 298 K,

ip = (2.69 × 105)n3/2Ac0A√vD (7)

(Randles-Sevcik equation). The peak po-tential in the forward scan, Ef

p, is related

to E0 of the redox couple by Efp = E0 +

28 mV, and E0 = (Efp + Eb

p)/2, where Ebp

is the potential of the peak on the reversescan.

Besides determination of n, A, or D,follow-up kinetics are accessible fromthe influence on the position of thepeaks, and in particular, the intensity ofthe reverse peak. Formation of productsthat are electroactive within the potentialwindow scanned causes the appearance ofadditional peaks. Furthermore, the shapeof the peaks allows conclusions to bedrawn about the involvement of adsorptionprocesses.

1.2.4.3 Controlled-Current TechniquesCurrent control of an electroanalyticalexperiment is accomplished by a galvano-or amperostat [29].Chronopotentiometry is a transient cons-

tant-current technique in which the po-tential of the electrode is followed, asa function of time, in a quiet solution(Figure 6). Double-step applications [30],as well as programmed current experi-ments [31] have been described.Starting at ER, as soon as a current i

is imposed, the equivalent flux of redox-active substrate A to the electrode isestablished. Since i is constant, the slopeof the concentration profile must also beconstant. Thus, depletion of the substratecauses an increase in the diffusion layerthickness, while the steepness of theprofile does not change. The concentrationof A at x = 0 necessarily decreases.Simultaneously, cB(x = 0) increases. Asa consequence, E adjusts according toequation (1).After some transition time τ , cA(x = 0)

reaches a value of zero and no moredecrease is possible. Since δ still keepsincreasing, the concentration gradientbecomes less steep. The current can nolonger bemaintained by the redox reactionof A. Now, E increases steeply untilanother electrode process is possible (notshown in Figure 6).


0.0

0

2

4

6

8

10

12

0.2

(a)

0.4 0.6

Time, t[s]

1.00.8 0.0−0.13

−0.08

−0.03

0.02

0.07

0.12

0.2

(b)

0.4 0.6 0.8

Time, t[s]

Pote

ntia

l, E

[V]

1.0

0.00.0

0.2

0.4

0.6

0.8

1.0

1.2

0.2

(c)

0.60.4 1.00.8

Distance, x[m]

Con

cent

ratio

n, c

[mol

l−1]

1.2

Cur

rent

, i

106

[A]

•

Fig. 6 Chronopotentiometry: (a) typical excitation signal; (b) potentialresponse; (c) concentration profiles of educt for a chronopotentiometricexperiment (three profiles at various times, increasing time shown by arrow).

The relation between i and τ is given bythe Sand equation (8)

iτ 1/2 = nFAc0A

√πD

2(8)

Again, n, A, or D can be determined fromchronopotentiometric experiments.

1.2.4.4 Hydrodynamic VoltammetryIn hydrodynamic techniques, convectionis the principal mode of mass transport,and is brought about by the controlledmovement of the electrode in the solutionor by pumping the electrolyte through apipe or channel.In a simple model, one assumes that

convective mass transport keeps the con-centration constant at some fixed distanceδ from the solid wall. Thus, the diffusionlayer thickness is constant.

Rotating disk voltammetry uses a po-tential scan to control the potential ofa specially designed working electrode,consisting of a disk embedded into thelower cross section of a perpendicularlymounted insulating shaft. The shaft isinserted into the electrolyte and rotatedaround its vertical axis with an angu-lar velocity ω (RDE [32], Figure 7). Theelectrolyte is set into a circular motionand moves centrifugally along the elec-trode surface. It is replenished by freshsolution dragged up vertically from thebulk.Diffusion occurs across a distance of

δ = 1.61D1/3ω−1/2ν1/6 (ν is the kine-matic viscosity of the electrolyte). AtER, cA(x = 0) ≈ c0A, diffusion is negligibleand no current flows. Scanning E causescA(x = 0) to change, and a current results.Eventually, cA(x = 0) = 0 and a limiting


0.0

0.2

0.4

0.6

0.8

1.0

1.2

(c)(a) (b)

−0.6 −0.4 −0.2 0.0 0.2 0.4

Potential, E[V]

0.6

Cur

rent

, i

106

[A]

•

Fig. 7 Construction [section and bottom view, (a) RDE; (b) RRDE] ofrotating disk electrodes; and (c) typical RDE response.

current

ilim = 0.620nFAc0AD2/3ω1/2ν−1/6 (9)

is reached [Levich equation (9)].Since products of the electrode process

are quickly transported out of the vicinity ofthe electrode disk, use of the rotating diskelectrode complements the more complexrotating ring disk electrode (RRDE) [32].Here, redox active products can be detectedat the ring electrode, which is held at aseparately controlled potential.Channel techniques employ rectangu-

lar ducts through which the electrolyteflows. The electrode is embedded intothe wall [33]. Under suitable geomet-rical conditions [2] a parabolic veloc-ity profile develops. Potential-controlledsteady state (diffusion limiting condi-tions) and transient experiments are pos-sible [34]. Similar to the Levich equationat the RDE, the diffusion limiting cur-rent is

ilim = 1.165nFc0AD2/3U

1/3h−1/3wx

2/3E(10)

(with U = mean solution velocity, xE =electrode length, h = half-height of chan-nel, w = width of the electrode). Experi-mental variables include U and xE (arraysof microbands) [35, 36].

The fact that transport limits the rateof the overall electrode reaction affectsthe fastest timescale accessible. Oncetransport controls the rate, faster reactionsteps cannot be characterized. It is thusimportant to enhance mass transfer, forexample, by increased convection withhigh flow rates [37, 38].

1.2.4.5 Exhaustive Electrolysis TechniquesIn contrast to the techniques discussedup to now in which only a small partof the substrate present in the electrolyteis consumed, we will now considerapproaches that exhaustively convert thesubstrate to the product. Typically, theelectrodes used have a comparatively largearea, and the electrolyte is stirred in orderto increase mass transport. Exhaustiveelectrolyses can be performed potentio- orgalvanostatically.In potentiostatic exhaustive electrolysis,

the potential of the working electrodeis constant throughout the experiment.The substrate is transported by convectionand diffusion to the working electrodesurface. The current decreases with thebulk concentration of the substrate, ifno further electron transfers occur. Thecharge transferred is

Q =∫ tend

0i dt (11)


with tend denoting the time when theexperiment is stopped. A frequent, but notunique stopping criterion is the remainingcurrent, for example, 1% of the initial i.One could also test for disappearance ofthe substrate or some intermediate, in situor in samples taken from the electrolyte.Typically, the duration of a potentiostaticelectrolysis is much larger than that of atransient experiment as discussed above.Q can be related to the amount m

of substrate with molecular mass M

consumed. From Faraday’s first law (Q =nFm/M), n is available.From an exhaustive potentiostatic elec-

trolysis, the product(s) formed at theselected electrode potential can be isolated.Preparative and analytical techniques areavailable to determine the compositionof the product mixture and the structureof its components. Mechanistic reason-ing will often allow defining the reactionsteps. Even more information about thereaction can be gained from electrolysisexperiments at various defined potentials,for example, after each peak in the cyclicvoltammogram of the substrate.In contrast, in galvanostatic exhaustive

electrolysis the current through the workingelectrode is kept constant. As in chronopo-tentiometry, this will result in a constantflux of electroactivematerial to the surface.Consequently, the electrode potential willvary during the experiment. As a result, atdifferent times various electrode processesmay be induced. Hence, the results of gal-vanostatic and potentiostatic electrolyseswill not necessarily be identical.The determination of charge in galvano-

static electrolysis is particularly simple,since i �= f (t): Q = it . Again, a suit-able protocol for endpoint detection mustbe defined [39], and product isolation ispossible.

1.3How to Gain Access to Kinetics,Thermodynamics, and Mechanisms ofElectroorganic Reactions

1.3.1Qualitative and Quantitative Investigationof Electrode Reaction Mechanisms

Two extreme forms of mechanistic inves-tigations in organic electrochemistry arefrequently applied:

1. Qualitative analysis has the main objec-tive of confirming a given mechanistichypothesis by rejection of conflicting al-ternatives. Thismay be applied to singleelementary steps, the intermediates, orhow the steps are linked together.

2. Quantitative analysis relies on a highlyprobable mechanistic hypothesis anddetermines as many as possible kinetic,thermodynamic, and/or transport pa-rameters for the various steps. Thisis often a complex problem, since thevalues of the parameters are usually cor-related, their relation to experimentaldata is nonlinear, and the data containartifacts and statistical errors [40, 41].

Both types of mechanistic analysis aresupported by the instrumental techniquesdiscussed here.

1.3.2General Recommendations for MechanisticAnalysis

In general, for a mechanistic analysis, asmany facets as possible of the investigatedelectrode reaction should be taken intoaccount and the various experimentalparameters be varied as widely as possible.Among these are

• Time scale: This is particularly importantfor kinetic studies and the determina-tion of rate constants.

1.3 How to Gain Access to Kinetics, Thermodynamics, and Mechanisms of Electroorganic Reactions 15

• Concentration: The dependence of re-sults on concentration indicates chem-ical reactions of an order higher thanunity.

• Presence of reagents: Formation ofintermediates may be proven bytheir reaction with intentionally addedreagents, for example, nucleophilesto quench electrogenerated carbeniumions. Characteristic changes areexpected, for example, peaks in CV maydisappear.

Usually, the experimental results arecompared with the theoretical modelsimulations. Again, it is important toconsider wide ranges of experimentalconditions that have to be adequatelymodeled using a single set of parameters.Comparison is done by

• data transformation. Suitable transfor-mations of the experimental data leadto straight lines (e.g. Anson plot inchronocoulometry) or similar simplecurves (semi-integration or differentia-tion [42]).

• feature analysis. The experimental curvesexhibit features (e.g. peaks in CV)that change characteristically with theexperimental conditions. The results areusually compared to working curves [28]or surfaces [43, 44].

• full curve analysis. Global analysis ofexperimental and theoretical data isapplied by comparing entire curves. Thisis used to great advantage in simulationprocedures [45, 46].

Of course, experimental artifacts shouldbe avoided. In particular, in mechanisticelectroorganic work these are

• Background currents are current compo-nents not related to the ET of substratesor products, but rather to impurities

or are caused by non-Faradaic pro-cesses (charging of the double layer).They are at least approximately cor-rected by subtraction of a blank curverecorded in the electrolyte without sub-strate.

• iR drop is caused by the resistance Rbetween the reference and the work-ing electrode in a three-electrode cell.It is particularly awkward in low-conductivity electrolytes and distortscurves in a nonlinear way. Compen-sation in commercial instruments isoften possible, and procedures for cor-rection have also been given [47, 48].However, it is best to avoid an iR dropby decreasing i [decreasing c or A (ul-tramicroelectrodes, Section 1.4.2)] or R(increasing conductivity or decreasingdistance between reference andworkingelectrodes).

1.3.3Some Mechanistic Examples

1.3.3.1 Pure ET ReactionsIf no chemical steps are coupled to the ETat the electrode, the reactionmechanism isfully described by E0 (thermodynamics),n (stoichiometry),D (transport), as well asks, and α (kinetics). It is characteristic tofind a fully developed reverse peak in thecyclic voltammogram [49]. Qualitatively, itis important to diagnose full diffusioncontrol (Er). Cyclic voltammetry allowsthis by inspection of the peak potentialdifference %Ep = Ef

p − Ebp. For Er, %Ep

is independent of v, while for Eqr anincrease of v (faster timescale) causes%Epto increase (Figure 8a) [50].While E0 follows from CV directly (Sec-

tion 1.2.4), determination of the other pa-rameters is more complex. For diffusion-controlled ETs, n follows from %Ep =58/nmV, and D is calculated from


−0.1 0.0−30−20−10

010203040

0.1

(a)

0.2 0.3 0.5 0.60.4

Potential, E[V]

0.90.80.7 −0.1 0.0−80−60−40−20

020406080

0.1

(b)

0.2 0.3 0.5 0.60.4

Potential, E[V]

0.90.80.7

Cur

rent

, i

106

[A]

•

Cur

rent

, i

106

[A]

•

Fig. 8 Typical cyclic voltammograms of pureelectron transfer reactions; (a) effect ofquasi-reversibility (ks decreases from solid todashed line); (b) effect of relative values of

formal potentials in an ErEr reaction (differenceof formal potentials, %E0, decreases fromdash-dotted through dashed to solid line; in thelatter case, potential inversion occurs).

equation (7). Alternatively, a combinationof equations (7) and either (3) or (4) yieldsn [51]. Exhaustive electrolyses also give nand allow product generation. Because ofthe longer timescale as compared to tran-sient methods, the results may differ fromthe CV or potential step techniques. Of-ten, starting with stable organicmolecules,radical ions are produced, which can be in-vestigated by ESR spectroelectrochemistry(Section 1.4.4). Note, that n must be aninteger value.Kinetic information for Eqr reactions is

not available from techniques that work inthe diffusion-controlled regime. However,again, CV allows determination of ks fromthe dependence of %Ep on v [50, 52, 53].The transfer coefficient is also accessiblefrom cyclic voltammograms [53]. Often α

is assumed to be 0.5 in organic electrodereactions, but clearly this is only a roughapproximation.Transfer of several electrons yields n > 1

from the above procedures, but CV addi-tionally shows the relative thermodynam-ics and depending on the individual E0

values, various shapes of i/E curves areobtained (Figure 8b). If the twoE0 are suf-ficiently different (%E0 > 100 mV), twoseparated peak couples occur (dash-dottedline). On the other hand, if%E0 decreasesbelow ≈100 mV, the voltammetric signalsmerge (dashed line).Further, interesting cases are encoun-

tered in ‘‘inverted potential’’ [54] situations(solid line in Figure 8b, second ET thermo-dynamically easier than the first one), andfor dendrimers with a large number of

−0.1 0.0−30−20−10

010203040

0.1 0.2 0.3 0.5 0.60.4

Potential, E[V]

0.7

Cur

rent

, i

106

[A]

•

Fig. 9 Typical cyclicvoltammograms of an ECreaction system; rate offollow-up reaction increasesfrom short-dashed throughdotted, dash-dotted andlong-dashed to solid curve.

1.3 How to Gain Access to Kinetics, Thermodynamics, and Mechanisms of Electroorganic Reactions 17

redox-active units, which undergo ET atapproximately the same potential [55].

1.3.3.2 Follow-up ReactionsIrreversible follow-up reactions (mostsimple case: EC mechanism) decreasethe concentration of the primary redoxproduct. This is again diagnosed in CV(Figure 9) and also in chronocoulome-try. Timescale variation in CV allowsto modulate the importance of the C-step: at fast v the chemical reaction willhave no influence on the curves, whileat slower v all product has reacted andthe reverse peak disappears. A govern-ing factor is k/a (k = rate constant ofC-step, a = nFv/RT ). Thus, for a qual-itative interpretation, the peak currentratio in CV is evaluated as a func-tion of v (and Eλ) in order to calcu-late k [49]. Also, Ep and ip depend onk/a [28].Reversible follow-up reactions may just

shift the entire voltammetric signals (fastequilibration) on the E axis, or lead to ef-fects approaching those of the irreversiblecase [28].The most important are cases in which

the product of the C-step is again electroac-tive [ECE mechanism, Reaction (12)]:

A−e−

−−−⇀↽−−− Bk−−−→ C

−e−−−−⇀↽−−− D (12)

(for an oxidation; extension to reduction isobvious). In such cases, homogeneous ETs[disproportionation, Reaction (13)] havealso to be considered:

B + C−−−⇀↽−−−A + D (13)

where the equilibrium constant is relatedto the E0 of the two heterogeneous ETs.Several variants are discussed in the

literature [18, 56, 57]. Figure 10 showssome cyclic voltammograms. The heightof the second peak depends on the rateof the C-step. In chronoamperometry, theformation of a redox-active product leadsto an increase in the apparent n during theexperiment (e.g. from n = 1 to n = 2). Aplot of i vs. t−1/2 switches from a straightline for n = 1 at small t to the one for n = 2at large t .If, for an oxidation step, the chemical

reaction of B leads to the oxidized form ofthe second redox couple B′ (and not thereduced one as in the earlier case) and asecond chemical transformation from A′leads back to A [reaction (14)], we arriveat a square scheme (Figure 11), whichforms the basis for many important redoxsystems [18, 58]. Again SET steps

A + B′−−−⇀↽−−−A′ + B (14)

can be involved, resulting in rather un-usual voltammograms under certain con-ditions [18, 59].

Fig. 10 Typical cyclicvoltammograms of ECEreaction systems; rate of C-stepincreases from dash-dottedthrough dashed and dotted tosolid curve.

−0.10.0−30−20−10

010203040

0.1 0.2 0.3 0.5 0.80.70.60.4

Potential, E[V]

Cur

rent

, i

106

[A]

0.9

•


± e−

A

A′

B

B′

± e− Fig. 11 The square schemereaction mechanism.

1.3.3.3 Preequilibria to ETsThe square scheme discussed above al-ready includes a further common motifin electroorganic mechanisms: reactionA−−−⇀↽−−−A′ forms a preequilibrium to bothETs in the scheme. The response of sucha system in CV depends particularly onthe equilibrium constantK = [A]/[A′] andthe rate constants kA→A′ and kA′→A. If thek are large (reaction at equilibrium), onlythat ET will occur, which is thermody-namically easier (smaller E0). All materialconsumed by that ET will immediately bereplenished through the equilibrium re-action. On the other hand, if the k aresmall, two peaks will be observed withtheir relative heights proportional to theequilibrium concentrations of A and A′,thus allowing determination of K .Both partners of the preequilibrium are

not always electroactive (CE mechanism).

Kinetics and thermodynamics will influ-ence the exact appearance of the concen-tration profiles. Figure 12 shows some CEvoltammograms. In particular, chronopo-tentiometry was used for analyses[60, 61],since for high i

iτ 1/2 =√π

2nFAc0

√D

K

1 +K(15)

(with total concentration c0 = c0A +c0A′ ) [62]. Furthermore, hydrodynamictechniques were also employed [63, 64].

1.3.3.4 Catalytic ReactionsIn some reactions the product of anET at the electrode reacts back to the

starting compound: A±e−

−−−⇀↽−−− Bk−−−→ A.

This mechanistic motif is found in me-diated electrode reactions [65] or in sen-sor applications [66]. The reformation of

−0.1 0.0−1.9−1.4−0.9−0.4

0.10.61.11.6

0.1 0.2 0.3 0.5 0.60.4

Potential, E[V]

0.7

Cur

rent

, i

106

[A]

•

Fig. 12 Typical cyclicvoltammograms ofpreequilibrium systems; kineticsof preequilibrium becomeslower from dotted throughdashed to solid curve.

1.4 How to Gain Additional Information about Electroorganic Reaction Mechanisms 19

0.0−100

0

100

200

300

400

500

(a)

0.2 0.6 0.80.4

Time, t[s]

1.21.0 −0.1 0.0−100

1020304050607080

0.1

(b)

0.2 0.3 0.5 0.60.4Potential, E

[V]

0.7

Cur

rent

, i

106

[A]

•

Cur

rent

, i

106

[A]

•

Fig. 13 Typical (a) chronoampero- and (b) cyclic voltammogram of a catalytic system.

the electroactive A leads to an increasein current and a decrease of diffu-sional effects. Thus, in chronoamperom-etry, i reaches a nonzero limiting value(Figure 13a), while in CV the peak disap-pears in favor of an S-shaped i/E curve(Figure 13b). From the limiting CV cur-rent, the rate constant k is accessiblefrom [28, 67]

i = nFAc0√Dk (16)

1.4How to Gain Additional Information aboutElectroorganic Reaction Mechanisms

1.4.1Simulation

A simulation (Volume 3, Chapter 3.1) isthe reproduction of an electroanalyticalexperiment in the form of a set of math-ematical equations and their solutions,usually on a digital computer [7]. The equa-tions express a physical model of the realexperiment. Thus, the main steps of theelectrode process (see Section 1.2.1) areincluded.Various numerical techniques are em-

ployed, and commercial programs areavailable, mostly for the CV technique [7].For the elucidation of electrode reaction

mechanisms, simulation is an indispens-able tool for both types of analyses de-scribed in Section 1.3.1. For a simulation,one needs amechanistic hypothesis that insome programs is translated into the gov-erning equations automatically [45, 68, 69].There are various parameters defining thereaction steps in detail, for example, rateconstants or formal potentials. One solvesthe equations for given values of theseparameters and compares the results to ex-perimental curves in an iterative process,until a ‘‘best fit’’ is obtained. Automaticfitting is also available [45]. Alternatively,it is illustrating to see how variations inmechanism and/or parameters change theresulting curves.It is of particular importance to follow

the guidelines provided in Section 1.3.2in comparing experiments and simula-tions.

1.4.2Ultramicroelectrodes

In previous sections we have implicitly as-sumed that diffusion occurs perpendicularto the electrode surface (semi-infinite lin-ear diffusion). If we decrease the size ofthe electrode to values roughly in the orderof the size of diffusion layers, this assump-tion becomes invalid. Now, additional


Quartz crystal withelectrodes

RW

Electrolyte

Oscillator

Computer,Recorder

Functiongenerator

C

Potentio/galvanostat

Frequencycounter

Fig. 14 Set-up of an electrogravimetric experiment with anelectrochemical quartz crystal microbalance.

diffusion components parallel to the sur-face become important. Thus, the currentdensities are increased. It is common tocall disk electrodes with radii ≤20 µm ‘‘ul-tramicroelectrodes’’ (UMEs) [8].UMEs decrease the effects of non-

Faradaic currents and of the iR drop.At usual timescales, diffusional transportbecomes stationary after short settlingtimes, and the enhanced mass transportleads to a decrease of reaction effects.On the other hand, in voltammetry veryhigh scan rates (v up to 106 Vs−1)become accessible, which is importantfor the study of very fast chemical steps.For organic reactions, minimization ofthe iR drop is of practical value andhighly nonpolar solvents (e.g. benzeneor hexane [8]) have been used with lowor vanishing concentrations of supportingelectrolyte. In scanning electrochemicalmicroscopy (SECM [70]), the small sizeof UMEs is exploited to localize electrodeprocesses in the µm scale.

1.4.3Electrogravimetry

If the electrode process results in thedeposition of some product at the electrodesurface, or in changes of composition of aprecipitate or film on the electrode, masschanges are coupled to the ET. Usually,these changes are small (ng–µg) andspecial techniques are necessary for theirexact determination.A technique for such measurements

is the electrochemical quartz crystalmicrobalance (EQCM; Figure 14) [71].Here, the working electrode is part of aquartz crystal oscillator that is mountedon the wall of the electrochemical celland exposed to the electrolyte. Theresonance frequencyf of the quartz crystalis proportional to mass changes %m:%f ∼ %m. With base frequencies around10 MHz, the determination of %m in theng range is possible.Electrogravimetric experiments lead to

a mechanistic understanding of polymer

1.5 Conclusion 21

film formation on electrodes, supportthe study of film morphology and thediffusional as well as the migrationaltransport into and within such films [72].

1.4.4Spectroelectrochemistry

Although the instrumental techniques de-scribed here give detailed mechanisticinformation, they do not provide an in-sight into the structure of intermediates.If we, however, combine electrochemicaland spectroscopic methods, this is ad-vantageously accomplished (spectroelec-trochemistry) [73]. Various spectroscopieshave been coupled with electrochemicalexperiments, among them ESR [74], opti-cal [75], and NMR spectroscopy [76, 77], aswell as mass spectrometry [78, 79].Three types of spectroelectrochemical

experiments are useful for mechanisticstudies:

• Spectral resolution records spectra atdifferent potentials, for example, duringa CV scan. This allows structuralcharacterization of intermediates.

• Temporal resolution records the inten-sity of a spectroscopic signal with t ,giving access to formation and decaykinetics.

• Spatial resolution [80] leads to informa-tion on the distribution of species withinthe diffusion layer. Distinction betweenalternative mechanisms has been re-ported [81].

1.5Conclusion

This chapter discussed some of themore important electroanalytical tech-niques with particular emphasis on their

use in electroorganic chemistry. Thesetechniques greatly help determine andunderstand the mechanistic course ofelectrode reactions in a qualitative andquantitative way. Besides briefly describ-ing the methods themselves, the chapterprovides examples for their applicationfor some frequently encountered reactionmechanisms. In particular, cyclic voltam-metry is probably the most often usedof these techniques, but other methodsshould also be applied if necessary, andextensions, as discussed in Section 1.4, areexpected to gain additional importance inthe future.

Acknowledgment

The authors thankKai Ludwig for technicalassistance in preparing Figures 6 and 7.

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1.3.3 Some Mechanistic Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . 151.3.3.1 Pure ET Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151.3.3.2 Follow-up Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171.3.3.3 Preequilibria to ETs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181.3.3.4 Catalytic Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

1.4 How to Gain Additional Information about Electroorganic ReactionMechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

1.4.1 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191.4.2 Ultramicroelectrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191.4.3 Electrogravimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201.4.4 Spectroelectrochemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

1.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Methods to Investigate Mechanisms of Electroorganic Ractions

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