The most commonly employed techniques used by coordination chemists undertaking electro- chemical experiments are:
Voltammetry under transient (e.g., cyclic voltammetry) or steady-state (e.g., rotated disk or microelec- trode) conditions2–5which requires the interpretation ofcurrent–potential–time (I–E–t) curves.
Spectroelectrochemical measurements9,10 in which a spectroscopic or other (e.g., mass spectrometric) method ofmeasurement is used in conjunction with electrochemistry to characterize intermediates or products ofelectrode processes.
Bulk electrolysis2for the purpose of electrosynthesis or for a coulometric determination of the number ofelectrons (n) associated with a half-cell reaction of the kind A!Bþne (A is the compound being oxidized and B is product, with charges being omitted for simplicity, and n is the overall number ofelectrons transferred per molecule ofA oxidized as determined by coulometry and application of Faraday’s Law ofelectrolysis).
Ru(bpy)2(NCS)2 Clear conducting
oxide
Electrolyte containing I–/I3–
Pt catalyst Porous TiO2/
RuII dye sensitized solar cell
Glass Load
Figure 1 Schematic diagram ofa ruthenium dye-sensitized photoelectrochemical cell. Provided courtesy of Leone Spiccia and Douglas MacFarlane.
excitation: RuII(bpy)2(NCS)2 [RuIII(bpy•–)(bpy)(NCS)2]*
e– injection: [RuIII(bpy•–)(bpy)(NCS)2]* [RuIII(bpy)2(NCS)2]+ + e– dye regeneration: [RuIII(bpy)2(NCS)2]+ + El– RuII(bpy)2(NCS)2 + El electrolyte regeneration: El + e– El
hν
Pt
TiO2
Scheme 1
The basic concept ofthe most common form ofelectrochemical investigation ofthe redox chemistry ofa coordination compound is that voltammetric data are initially collected and a mechanism for the half-cell reaction that occurs at the working electrode is postulated. A simple process, often used as a voltammetric reference potential standard,2would be (Equation (1)) oxidation of ferrocene (Fc) to the ferrocenium cation (Fcþ) in an organic solvent (acetonitrile, dichloromethane, etc.) containing 0.1 M ofan electrolyte such as Bu4NPF6(added to lower the resistance):
FcéFcỵ ỵ e ð1ị
The reduction ofpotassium ferricyanide in water (0.1 M KCl) as summarized inEquation (2),
ẵFeðCNị63 ỵ eé ẵFeðCNị64 ð2ị and the reduction ofcytochromecin its oxidized form (FeIIIcytc) to the reduced (FeIIcytc) form in a buffered aqueous environment (Equation (3))
FeIIIcytcỵ eéFeIIcytc ð3ị
represent other very well known redox systems that have been widely studied by voltammetric techniques.
Ideally, the proposed mechanism may be theoretically simulated by solving the appropriate mathematical problem.2,11–13 Satisfactory agreement between experiment and theory is used to provide a quantitative description for the postulated mechanism, but as with any kinetic study, ideally the identity of proposed reaction intermediates and the final product will be confirmed by an independent technique (e.g., a spectroscopic method). It is inherently dangerous to assume the structure ofa reaction intermediate or product solely on the basis ofa voltammetric response.
A general procedure for obtaining quantitative data related to an electrode mechanism using a voltammetric technique is summarized inFigure 2.
2.15.2.1 Basic Definitions of Voltammetry
Voltammetric techniques involve monitoring the current when a time-dependent potential is applied to an electrochemical cell. Even in a simple process, in which the oxidized and reduced forms of the electrode process are soluble in solution, the measured current frequently results from a complex combination of heterogeneous electron charge transfer processes that occur across the solution–electrode interface and homogeneous processes which occur in the solution phase. If a redox active solid is adhered to the electrode surface, then significantly greater complexity is introduced.2Comprehensive information concerning a particular electrode reaction mechanism can be obtained from examining how the current varies as a function of time (or frequency) and the applied electrode potential. It is the variation of this current–potential–time relationship that is commonly crucial for the quantitative determination of the mechanistic details ofan electrochemical reaction.
A typical electrochemical cell for a voltammetric experiment is illustrated in Figure 3. The processes that are probed in a voltammetric experiment occur at or in the region ofthe working electrode, which is the electrode of critical interest. The reference electrode merely provides a fixed reference potential and the counter electrode, present when a potentiostatted form of apparatus is used, completes the electrical circuit.2,6–8,13,14 Other noteworthy features of the cell depicted in Figure 3 are that N2 or Ar gas is introduced into the cell to remove oxygen, and a Luggin capillary is present in order to minimize the distance between working and reference electrode, thereby also minimizing the influence of uncompensated resistance.
The importance ofthe time element may be understood by briefly considering the commonly used transient and steady-state voltammetric methods.
2.15.2.1.1 Transient voltammetry
In these experiments, a potential perturbation to the working electrode is applied to the system of interest and the resulting current response is measured as a function of potential (time). Transient Electrochemistry: General Introduction 199
techniques include cyclic, linear sweep, staircase, square wave, pulsed, alternating current, etc.
voltammetries.2–5,13 In the former two cases, and in the traditional format (analog instrumenta- tion), the potential at the working electrode is scanned in a linear fashion with time with the current being continuously monitored. The temporal aspect arises from the rate at which the potential is ramped, known as the scan rate,. When the potential is swept in only one direction the technique is known as linear sweep voltammetry. Ifthe potential is swept in one direction and then reversed, this technique is known as cyclic voltammetry (Figure 4). (It should be noted that the International Union ofPure and Applied Chemistry (IUPAC) recommended convention of positive potential to the right and oxidation current being positive is indicated in Figure 4.
Unfortunately, even present-day literature all too often fails to comply with this official conven- tion. Until uniformity is achieved via widespread use of IUPAC recommendations, confusion that presently exists with respect to the format used to present voltammetric data will remain.) With
Apply external
New species generated stimulus,
e.g., light Electrode potential swept in a well defined manner
Electron transfer between electrode and species in solution
Record how current
associated with electron-transfer processes varies with potential
I vs. E voltammogram obtained for chemical system
Interpret voltammetric data
Postulate a mechanism
Compare with theoretical model
Confirm using spectroscopic techniques Is
agreement satisfactory
Quantification of electrode reaction
mechanism
No Yes
Solid electrode probe in chemical solution
of interest
Suggested complete description
of system
Figure 2 Schematic diagram ofa systematic procedure recommended for the elucidation ofthe details ofan electrode reaction mechanism; (reproduced by courtesy:Adv. Phys. Org. Chem.1999,32, 1;#Academic Press).
digital instrumentation, the linear ramp is often replaced by a staircase waveform, which mimics a linear ramp if the potential steps in the staircase waveform are sufficiently small. In the other techniques, a time- (square wave or pulse) or frequency- (alternating current) dependent perturb- ation usually is superimposed onto the linear or staircase waveforms and the current measured as a function of time or frequency. Cyclic voltammetry is the prime transient technique used by coordination chemists.
2.15.2.1.2 Steady state voltammetry
In this form ofvoltammetry, the concentration distributions ofeach species in the electrode reaction mechanism are temporally invariant at each applied potential. This condition applies to a
Connections to potentiostat
Solution (ca.20mL)
N2/Ar to purge
Counter electrode
Water in from thermostatic bath Working
electrode Water
out Reference
electrode Luggin capillary
Figure 3 Schematic representation ofa typical electrochemical cell employed in a voltammetric experiment (reproduced by courtesy:Adv. Phys. Org. Chem.1999,32, 1;#Academic Press).
E(t)
E2
E1
(a)
∆E
∆E
∆t
∆t
oxidative current
oxidation
reductive current
reduction (b)
/ mV
ox
red
E E
E (vs. arb. reference electrode) E2 E1
I
υ =
p
p
p p
red ox 56
n
t
I
I
Figure 4 (a) Waveform used in cyclic voltammetry and (b) the readout obtained with this technique for a reversible oxidation process ofthe type A(solution)ÐB(solution) þ e.
Electrochemistry: General Introduction 201
good approximation, despite various processes still occurring such as mass transport (e.g., diffu- sion), heterogeneous electron transfer, and homogeneous chemical processes. Theoretically, it takes an infinite time to reach the steady state. Thus, in a practical sense, steady state voltam- metric experiments are conducted under conditions that approach sufficiently close to the true steady state that the experimental uncertainty ofthe steady state value ofthe parameter being probed (e.g., current) is greater than that associated with not fully reaching the steady state. The time scale ofa near steady state process is determined by the rate at which material reaches the electrode surface.11This time scale may be varied in a number ofways:
Altering the convective rate oftransport, e.g., by changing the rotation frequency ofa rotating disk electrode or the flow rate in a channel electrode. Experiments in which the convective rate of transport can be altered are known as hydrodynamic techniques.
Decreasing the size ofthe electrode so that the rate ofradial diffusion ofmaterial to the electrode surface is enhanced. This is a key component in many important applications of microelectrode volt- ammetry.11
2.15.2.2 A Reversible Electrode Process
Almost all publications containing descriptions ofcyclic voltammetric experiments related to coordination compounds introduce concepts of‘‘reversible’’ or ‘‘irreversible’’ when summarizing the nature ofthe measured electrode process. Figure 4billustrates the asymmetrical peak shaped curve obtained under conditions ofcyclic voltammetry for the ‘‘reversible’’ process,
Aðsolutionịé
Eof
Bðsolutionị ỵne ð4ị when both A and B are solution soluble and Efo is the reversible formal potential. For this process, the average ofthe oxidation (Epox) and reduction (Eredp ) peak potentials, or (Eoxp þEredp )/2, is equal to Efo (assuming the diffusion coefficients of A and B are equal). Furthermore, the magnitude ofcorresponding peak currents,Ipox andIpred is unity andIpox is given by the Randles–
Sevcik equation2–5,13 which realizes a square root dependence on scan rate. To obtain the cyclic voltammogram depicted inFigure 4b, the potential was scanned at a rate(V s1) from an initial potential (E1), which is considerable less positive thanEfo, to a value E2, which is considerably more positive thanEfo, and then back toE1(Figure 4a).
The equivalent reversible voltammogram obtained under steady state conditions is shown in Figure 5, where the half-wave potential orE1/2-value obtained at halfthe limiting current (Ilim) is equal to Eof. In this case the wave shape is readily defined by the equation
EẳEof ỵ RT
nFlnIlimI
I ð5ị
whereIlim is a linear function of concentration and electrode radius for a microdisk electrode or square root ofrotation rate for a rotated disk electrode. Use ofthe ‘‘log plot’’ in Equation (5) enables the values ofbothEfoand n to be calculated from the intercept and slope respectively. The theory for the different steady state techniques is available in the following references.2–5,11 Both the cyclic and steady state voltammograms depicted in Figures 4 and 5 assume perfect Ohmic compensation and correction for background current, which is rarely achieved.14 Distortions introduced by the presence ofuncompensated resistance and background current are explained in Eklundet al.11
C
R R S ..
S
N (1)
Voltammetric measurement of Efo has been widely employed by coordination chemists.
Commonly, these reversible potentials are compared for a series of compounds and the system- atics ofthe redox chemistry ofa particular class ofcompound are established in this manner. For
example, Chantet al.15have studied the voltammetric reduction and oxidation ofa very extensive series ofiron(III) dithiocarbamate (Fe(R2dtc)3or Fe(R,R0dtc)3) complexes (R2dtcis the dithio- carbamate ligand (1)) and examined the redox chemistry as a function of substituent, R, R0. Reversible potentials for the
FeIIIðR2dtcị3é ẵFeIVðR2dtcị2ỵ ỵe ð6ị and
FeIIIðR2dtcị3ỵ eé ẵFeIIðR2dtcị3 ð7ị processes have been obtained. Figure 6shows that a linear relationship is obtained between the reversible potentials for these oxidation and reduction processes. Analogous ligand substituent effects are observed with other metal dithiocarbamate complexes.16A plot ofreversible potential for a series of compounds having the same central metal atom with the substituent on the ligand being varied also often may be correlated with Taft, Hammett or other substituent parameters.
These linear free energy vs. substituent parameters of the kind illustrated in Figure 7are widely encountered in both organic17and coordination chemistry.18–20
The role ofthe central metal ion also is important as indicated by the voltammetrically determined reversible potentials of4d and 5d hexafluoro and hexachlorometallate complexes in acetonitrile.21,22 Thus, as shown inFigure 8a,Efo-values (E1/2) for the [MF6]n/(n1)couples (nẳ0, 1,2; MẳTa, W, Ro, Os, Nb, Mo, Tc, Rh) 4d and 5d complexes follow linear progressions related to central ion nuclear and electronic structures ford0!d1,d1!d2, andd2!d3. Deviations observed for thed3!d4and subsequent effects are attributable to spin-pairing effects.21It can also be noted from data inFigure 8that the corresponding 4dand 5dcouples are almost uniformly separated by 1 V. The even more extreme data set for the [MCl6]n/(n1)couples (nẳ0,1,2,3; MẳZr–Pd for 4dmetals, and Ta–Pt, excluding Tc for 5dmetals) also reveal orderly trends (Figure 8b) that have been interpreted in terms ofcore charge and inter-electronic correlations.22Links to data obtained by electronic spectroscopy have also been reported in many studies20and, for example, a linear correlation of hmax (ligand to metal charge transfer) and Efo has emerged with a gradient of 1.35 eV V1for the above mentioned [MCl6]n/n1systems.23
Extensive data are now available to quantify ligand additivity effects onEfovalues. In a detailed study by Lever,24 ligand electrochemical parameters for over 200 ligands are presented and the model proposed has been tested with a wide range ofcoordination complexes (seeSection 2.15.2.4). In the more sophisticated models, the Efo value is described in terms ofthe sum offactors involving the ligand electrochemical parameter and the metal. As expected,Efo depends on the
E (vs. arb. reference electrode)
E1/2 E2
E1
Ilim
Ilim
2 I
Figure 5 Sigmoidal-shaped, steady state voltammogram obtained at a microdisk or hydrodynamic electrode for a simple process of the type A(solution)ÐB(solution) þ e.
Electrochemistry: General Introduction 203
metal, ligand, redox couple, spin state, and stereochemistry, but is generally insensitive to the net charge or the species involved in the redox process. A recent review of different ligand additivity models has been reported by Lever and Dodsworth.20Ligand electrochemical parameters perform a similar role to that oftheDqparameter in electronic spectroscopy.
Ease of reduction
Ease of oxidation Ph, Me
morph Bz2
Me2 Ph, Et
Ph2
Et2 n-Bu2
n-Hx2 i-Pnt2
i-Pr2
i-Bu2 n-Pr2 2.6-Me2pip
c-Hx2
pyrr 4-Mepip
pip n-Bu, Me 2-Mepip
Potential of the Fe(III) (R, R′dtc)3/[Fe(IV)(R, R′dtc)3]+ couple (V vs. Ag/AgCl)
Potential of the Fe(III) (R,R′dtc)3/[Fe(II)(R,R′dtc)3]– couple (V vs. Ag/AgCl) –0.2
–0.3
–0.4
–0.5
–0.6
0.4 0.5 0.6 0.7
Figure 6 Relation between the reversible potentials for oxidation and reduction of Fe(R,R0dtc)3complexes (reproduced by courtesy:Inorg. Chem.1975,14, 1894;# American Chemical Society).
Potential of the couple (V vs. Ag/ACl) NiL2 + e [NiL2]–
Ni S S
Me, Me
Ph, Ph Ph, Me
R H R′ 2
0/–
CF3, Me NR2, Me
OEt, Me OMe, Me
∑σm per ligand –0.2
–0.4 –0.2 –0.6 –1.0 –1.4
0 0.2 0.4
Figure 7 Correlation between substituent effects (approximated by the Taft parameter "m and the reversible potentials for reduction of nickel(II) dithioacetylacetonate complexes Ni(R-Sac R0-Sac)2
(reproduced by courtesy:Inorg. Chem.1976,15, 1118;# American Chemical Society).
In a reduction process, an electron is usually added to the LUMO, whereas in an oxidation process, an electron usually is removed from the HOMO. This is the reason why it is commonly assumed thatEfovalues for oxidation and reduction processes correlate with HOMO and LUMO energies respectively. However, the redox potential reflects the relative free energies of both the oxidized and reduced forms of a redox couple, whilst the HOMO and LUMO energies belong to only one species. Thus, it is only in the absence ofnuclear and electronic rearrangement and change in solvation energy thatEfovalues ofa series ofrelated molecules would correlate linearly
3.0
2.0
1.0
–1.0
–2.0
–3.0 0
2.0
1.0
–1.0
–2.0 0
Zr Hf
Ta W Re Os Ir Pt
Nb Ta
Mo W
(Tc) Re
Ru Os
Rh Ir
Pd Pt d0/d1
d0/d1 d1/d2 d2/d3 d3/d4 d4/d5 d5/d6 d0/d1
d1/d2 d2/d3
d2/d3 d2/d3
d5/d6 d5/d6
d5/d6 d5/d6
d5/d6 d4/d5
d4/d5 d/d
d4/d5 d4/d5 d3/d4
d3/d4
d3/d4 d0/d1
d0/d1
d0/d1 d1/d2
d1/d2
d1/d2 d1/d2
[MCl6]1–/2–(b) [MCl6]2–/3–
[MCl6]3–/4–
[MCl6]00/–(a)
{
{
{ {
(d)
(c)
Eẵ (V)Eẵ (V)
Figure 8 Dependence ofreversible potential on metal ion. (Upper curves): trends in half-wave potentials, E1/2in V vs. SCE of[MCl6]n/n1couples in CH2Cl2; O: 4d-hexachlorometallates;~: 5d-hexachlorometallates.
(a)nẳ0; (b)nẳ 1; (c)nẳ 2; (d)nẳ 3. (Lower curves): comparison ofhalf-wave potentials for [MX6]1/2 couples of5d-hexafluorometallates (~; XẳF) and hexachlorometallates (; XẳCl) (reproduced by
courtesy:J. Chem. Soc. Chem. Commun.1985, 1503;#Royal Society ofChemistry).
Electrochemistry: General Introduction 205
with HOMO or LUMO orbitals as appropriate. It is this linear relationship approximation which forms the basis of many ligand additivity or substituent models. Clearly, the concept works in many cases, but caution should be maintained as the models contain approximations. The concept that the energy difference between the HOMO and LUMO corresponds with the optical energy ofthe HOMO!LUMO electronic transition has a similar basis. However, again this widely used concept is also not strictly correct.20 The origin ofthese and other energy relation- ships, such as those associated with metal-to-ligand and ligand-to-metal charge transfer electronic transitions (see above), and their limitations, have all been discussed in detail by Lever and Dodsworth.20Consequently, readers wishing to employ these relationships in experimental studies are urged to carefully consult this article.
2.15.2.2.1 Electrochemical reversibility and irreversibility
Despite the fact that thermodynamic Efo values may be calculated under some conditions, an understanding ofthe basics ofthe technique ofvoltammetry actually requires a kinetic rather than thermodynamic theoretical treatment. In a voltammetric experiment, current flows in response to the reaction in Equation (8), being driven in either the forward or
Aðsolutionịékf
kb
Bðsolutionịỵne ð8ị reverse directions at a rate which is governed by the forward (kf) and back (kb) rate constants as well as by the value ofthe potential, E, relative toEfo. Consequently, whenever current flows, the half-cell reaction can never be genuinely in equilibrium, since this requires that no net reaction takes place (zero current) or that the rate ofthe forward reaction equals the rate ofthe back reaction. However, ifthe rate ofthe forward and backward reactions in Equation (8) are both sufficiently fast relative to the voltammetric timescale, then the electrode process can readjust to equilibrium conditions, within experimental error, as the potential is varied. This is equivalent to being able to provide a theoretical description ofthe cyclic voltammogram or other technique by assuming that the Nernst relationship (Equation (9)) is valid at the electrode surface,
EẳEfoRT
nFlnẵA ðxẳ0ị
ẵB ðxẳ0ị ð9ị
where xis the distance from the electrode surface.
The terminology of‘‘reversible’’ and ‘‘irreversible’’ is therefore clearly an operational one which must be defined in terms of the timescale (e.g., scan rate in cyclic voltammetry). To provide a full theoretical description, the electrode process in Equation (8) can be rewritten in terms ofpara- meters contained in Equation (10)
Aðsolutionịé
Eof;ks;
Bðsolutionịỵne ð10ị where ks (cm s1) is the heterogeneous charge transfer rate constant at potential Eof, is the charge transfer process (usually 0.5) and where the rate constant kfandkbcontained inEquation (8) are related to potential and ks via the Butler–Volmer or other relationship.2,3 Reversibility requires that the electron transfer kinetics (ks) are fast enough to maintain the surface concentra- tions [A]x=0and [B]x=0at the values required by the Nernst equation. Thus, reversibility depends on the relative values of ks and the rate ofchange ofpotential or scan rate, , in a cyclic voltammetric experiment. Ifthe ratio ofks/ is sufficiently small that Nernstian surface concentrations cannot be maintained as the potential is swept, then the process is said to be nonreversible. Terms widely used in the literature to cover this case are quasi-reversible (some back reaction) or irreversible (no back reaction). Unlike a reversible process (Figure 4b), a quasi-reversible process is characterized by Ep>57/n mV at 25C, with the value becoming larger with increasing . The effect of decreasingks from a value where reversibility is achieved (kslarge), to where nonreversibility is exhibited (kssmall) is illustrated by the cyclic voltammograms displayed in Figure 9 (upper part) (note that the magnitude of Ipox/Ipred only remains unity if ẳ0.5 when the process is quasi-reversible).