CASE IV. EVALUATING CATALYSTS – KINETIC STUDIES

CASE STUDIES IN CONTROLLED POTENTIAL

6.5. CASE IV. EVALUATING CATALYSTS – KINETIC STUDIES

Of course, one of the most important attributes of a catalyst is the rate at which it turns over the substrate species to form products. In many redox catalysis systems, an electrode can replace one of the reactants. In other words, the electrode can donate or accept electrons to recycle the freely diffusing catalyst. The strategy of using an electrode to recycle the mediator is called electrocatalysis. This scheme is pictured for a net reduction of a substrate molecule in Figure 6.14. In addition to regenerating the catalyst, the electrode current is proportional to the turnover rate of the overall reaction. This fact makes voltammetry a powerful tool for studying the reaction kinetics. There are many promising technologies that are presently being investigated using voltammetric techniques such as hydrogen gas production for wind and solar energy storage [17], electrochemical incineration of organic wastes [5], and carbon dioxide reduction [18, 19].

The most widely used voltammetric method for investigating catalysis is cyclic voltammetry. Here the motivation for using a catalyst is usually the fact that the substrate molecule (AOx in Figure 6.14) does not exchange electrons easily with the electrode. In many cases, electron transfer between the substrate and the electrode does occur, but only at much more extreme voltages than the formal potential for the substrate. This problem is illustrated in Figure 6.15. Curve 4 is a CV for the substrate, AOx, alone. An electrode voltage that is slightly more negative than the formal potential for the AOx/ARed redox pair (Eo′A) should be enough to reduce the substrate directly at the electrode according to thermodynamics, but kinetic problems prevent that until much more negative voltages are applied. That leads to a large waste of energy. Adding a catalyst with a formal potential slightly more negative thanEo′Acan be more efficient. Curve 1 is a CV for the catalyst alone and curve 2 is the voltammogram for a mixture of the substrate and catalyst. The catalyst mediates the turnover of the substrate at a voltage close to its own formal potential.

Figure 6.15 was created from a study of the catalytic reduction of CO2 to CO by iron complexes. Thermodynamically, the formal potential for the reduction of CO2 to CO is represented by the dotted vertical line in the lower left corner on the graph marked Eo(CO2/P). CO2 reduction is much more favorable (has a more positiveEo′) than that of the catalyst. Therefore, carbon dioxide should be easier to reduce directly at the electrode, but the rate is insignificant until the voltage is quite extreme as is indicated by curve 4.

Adding the catalyst leads to CO2reduction at a less negative voltage (curve 2). The result is that the reduction of CO2mediated by the catalyst saves a lot of energy.

Electrode

Net reaction:

CRed

ARed

ARed COx

AOx

AOx+ ne– ne–

FIGURE 6.14 Redox catalysis with a freely diffusing catalyst is a variant of an EC electrode mechanism where the following chemical step regenerates the catalyst as well as forming the product, ARed, from the substrate, AOx.

k k A lot can be learned about redox catalysis from observing how the shape of the

current–voltage curve changes with different scan rates [20]. The catalytic mechanism gives rise to a variety of voltammogram shapes depending on conditions. The shape of the cyclic voltammogram is influenced by the scan rate and by the relative concentration of the substrate compared to the catalyst. Savéant investigated catalytic mechanisms with experiments and computer simulations and summarized the CV behavior over a wide range of conditions [20]. He used a diagram to organize the trends based on two dimensionless parameters. The first parameter,𝜆, is a kinetic term.

𝜆= (RT

F

) (k[CatOx]o 𝜐

)

(6.35) Equation (6.35) is written for the process depicted in Figure 6.15 where the reduced catalyst reacts with the substrate. Herekis the rate constant for the following chemical step of the catalyst reacting with the substrate in solution,𝜐is the scan rate in V/s, [CatOx]ois the concentration of the catalyst in bulk solution (present originally in the “unactivated”

form), and the other terms have their usual meaning. The only other parameter needed is the ratio,𝛾, of the bulk concentration of the substrate, [AOx], to that of the catalyst. This ratio is sometimes called the “excess factor” because catalysis reactions are normally operated at conditions where the concentration of substrate is in a stoichiometric excess compared to the catalyst.

𝛾 = [AOx]o

[COx]o (6.36)

Dempsey and coworkers have refined Savéant’s diagram by defining zones within which different CV shapes are found [21]. Her version appears in Figure 6.16.

Current (–i) (mA)

Potential (–E) (V)

Catox + ne

CatRed + AOx k ARed + CatOx CatRed

(3) (4)

(1) (2)

icat

Eonset

E°(CO2/P) E°cat

ηcat ΔE ip

FIGURE 6.15 Theoretical cyclic voltammograms for the redox catalysis of carbon dioxide to carbon monoxide by an iron complex. In this diagram, the applied potential increases in the direction to the right. Cyclic voltammograms are overlaid for the catalyst alone (curve 1), for the substrate alone (curve 4), and for the mixture (curve 2). Curve 3 is a control run in the supporting electrolyte solution.

Source: Adapted with permission from Francke et al. [18]. Copyright 2018, American Chemical Society.

k k –2

–2

–1 –1

0 1 2 3

0 1

KD KG

KG* K

KT1 KT2

Total catalysis

No catalysis

D

KS S-shaped voltammograms

log (γ) C0A

C0P ke

log (λ)

2 3

υ

FIGURE 6.16 Zone diagram depicting the shape of cyclic voltammograms for the catalytic mech- anism over a range of conditions. A log/log plot is needed to encompass the order of magnitude changes in scale. The parameters are defined in Eqs. (6.35, 6.36). The kinetic parameter,𝜆, of the y-axis increases with increasing values of the rate constant, k, for the chemical step and decreases with increasing scan rate,𝜐. (Note the set of vectors in the lower left corner.) The excess factor,𝛾, increases with increasing concentration of the substrate, [AOx]. The concentration of the catalyst, [COx]∘, affects

both𝛾and𝜆. Consequently, increasing [COx]∘moves the conditions toward the upper left-hand corner

of the diagram. Source: Adapted with permission from Rountree et al. [21]. Copyright 2014, American Chemical Society.

In experiments with a system that follows a catalytic mechanism, one can observe the different shapes in current–voltage curves by adjusting the scan rate and/or the substrate concentration, [AOx]o. By increasing the scan rate, conditions move vertically downward in the diagram. By increasing [AOx]o, the conditions move horizontally to the right. The one other adjustable variable is the bulk concentration of the catalyst, [COx]o, but since it appears as a term in both𝛾 and𝜆, increasing [COx]o moves conditions in a diagonal direction toward the upper left corner of the diagram.

The diagram is helpful in two ways. First of all, it can help confirm that the mech- anism is a catalytic process. For example, imagine recording a voltammogram on a new system and observing a cyclic voltammogram with the appearance of the curve in zone K. This shape is also similar to a cyclic voltammogram for a noncatalytic ErCi process.

However, faster scan rates lead to different behaviors in these two systems. In the noncat- alytic case, faster scans can reverse the electron transfer process before the product has time to react chemically. When that happens, a return peak is observed in the voltammogram (recall Figure 6.2). In contrast, scanning faster for a catalytic system moves the conditions down from zone K to zone KS and leads to a current–voltage curve that looks more like

k k Potential (–E)/V

(a) (b)

(E0cat–E)/V

Scan rate (v)/V s–1

0.02 Vs–1

[A]0 = 0.005 M [A]0 = 0.02 M [A]0 = 0.1 M [A]0 = 1 M

0.1 Vs–1 2.5 Vs–1 20 Vs–1

Peak current (–ip)/A

0 5 10 15 20

Current (–i)/A i/ip

(E–E0cat

1 + exp nF –1

⎡RT

⎣ ⎡

⎛ ⎣

⎝ ⎛⎝

⎛⎝

⎧⎨

⎩

⎧⎨

⎩

FIGURE 6.17 (a) Simulated curves at different scan rates (increasing from bottom to top). As scan rate increases, the system moves from kinetic zone K in Figure 6.16 vertically down to zone KS. The insert on the upper left of the diagram shows that the plateau current becomes independent of scan rate in this zone. (b) Simulated cyclic voltammograms for different substrate concentrations. As the substrate concentration increases (bottom to top), the cyclic voltammogram transforms from a curve with a shape representative of zone KG to the “S-shaped” curve of zone KS. Increasing the substrate concentration moves the conditions horizontally to the right in Figure 6.16. The plot on the right of box B is a “Foot-of-the-Wave” plot of the normalized current versus{

1+exp[

(nF∕RT)(

E−Eocat)]}−1

. The rate constant for the overall process can be extracted from the slope of the linear portion of this graph. Source: Adapted with permission from Francke et al. [18]. Copyright 2018, American Chemical Society.

a hydrodynamic voltammogram, such as might be seen with a rotated disk electrode.

The current reaches a constant plateau and the curve retraces itself on the return scan.

In fact, this happens because the starting material, COx, is being replenished by the fol- lowing chemical step rather than by convective mass transport. Likewise, scanning faster and moving vertically downward from zone KT2 (already a curious shape) or from zone KG* to zone KG both produce changes in shape that are not expected for a simple EC mechanism. Figure 6.17a shows a series of voltammograms generated from a computer simulation of a catalytic system and illustrates the changes in shape that one might see for a scan rate study. Figure 6.17b depicts the influence of the substrate concentration. At high substrate concentration, the curves take the “S-shape” indicative of total kinetic control as in zone KS.

There are useful equations that are applicable to different zones, and these can be used in order to extract an apparent rate constant. Of course, if the goal of using a catalyst is to speed up a reaction, then the overall rate is a figure of merit for evaluating the catalyst.

Findingkis often a goal of these studies. In zone KS, the plateau current is related to the observed rate constant (also called the apparent rate constant),kobs, for the chemical step as shown in Eq. (6.37) [21].

icat= nFA[COx]o√ DCkobs 1+exp

{nF RT

(E−EoC)} (6.37)

k k In Eq. (6.37), the applied voltage isEandEoCstands for the formal potential for the

catalyst and [COx]ois the bulk concentration of the catalyst.DCis the diffusion coefficient of the nonactivated form of the catalyst, COx,kis the rate constant for the homogeneous reaction between CRedand AOx, andAis the electrode area. (Ais usually the geometric surface area, but the electrochemically active surface area is more rigorously correct. Recall that the active surface area can be obtained from a chronoamperometry experiment.)F is Faraday’s constant andn is the number of moles of electrons transferred per mole of catalyst. When the current is measured on the plateau at a point at least 100 mV beyond EoC(that is, more negative in this case), then the denominator in Eq. (6.37) approaches unity and the equation simplifies to Eq. (6.38).

iplateau=nFA[COx]o√

DCkobs (6.38)

Performing a cyclic voltammogram for the catalyst alone can helpful here. Because the catalyst by itself undergoes a simple, reversible electron transfer process, the peak current, ipc, for this scan is given by the Randles–Sevcik equation:

ipc =0.446 3nFA[COx]∘(nF𝜐Dc RT

)1∕2

=2.69×105n3∕2ACD1∕2

C 𝜐1∕2at T=298 K (6.39) Dividing Eq. (6.38) by Eq. (6.39) eliminates some terms, such as the electrode area and the diffusion coefficient and provides a relationship that is easy to solve for the apparent rate constant,kobs[21].

iplateau ipc = 1

0.4463

√(RT nF𝜐

)

kobs (6.40)

or

kobs= (0.1991)nF𝜐 RT

(iplateau ipc

)2

(6.41) In this context, the observed or apparent rate constant,kobs, is defined as follows:

kobs=k[AOx]o (6.42)

The apparent rate constant,kobs, is also called the maximum turnover rate, TOFmax. It is the maximum number of moles of product generated per mole of catalyst per second. It should be pointed out that more complicated catalysis schemes have been observed [21].

In those cases, Eq. (6.42) is not an adequate definition of the observed rate constant. Fortu- nately, there are ways of handling these problems. In some reactions that involve multiple electron transfer steps and chemical steps, a single elementary step is rate-determining and the observed rate constant can be expressed as in Eq. (6.42).

Because Eqs. (6.37, 6.41) are applicable only in zones KS and KD, workers manipulate the substrate concentration and the scan rate to ensure that their conditions fall within one of those two zones. The prudent approach is to increase [AOx]oand the scan rate until the value of the limiting current (the plateau on the S-shaped curve) reaches a value that is no longer dependent on the scan rate. Then, the rate constant can be calculated from Eq. (6.41).

k k The catalytic mechanism that has been described here is a very simple one. Practical

catalytic systems often involve multiple chemical and electron transfer steps. Furthermore, there are often complications such as instability of the catalyst, depletion of the substrate near the electrode, or inhibition as a result of product adsorbing to the electrode. However, Savéant has demonstrated that one can analyze the data at the foot of the current–voltage curve where the current is less sensitive to those problems [22]. The following example is a study by Savéant and coworkers with different iron–porphyrin complexes, represented here as [(por)Fe(I)], that can catalyze the reduction of CO2 to CO [19]. Figure 6.18 shows the structure of an iron-TDHPP catalyst (one of the complexes represented by [(por)Fe(I)]

in the reaction scheme in Figure 6.18) and the steps in the overall reaction sequence with CO2. In order to evaluate the catalyst one would like to measure the rate constant,k, for the second step in Figure 6.18. The current that one observes for the electrocatalytic reduction is a function of an apparent rate constant,kobs, for the overall process. In this case, the relationship betweenkandkobsis fairly simple.

kobs=2k[CO2] (6.43)

So now the goal becomes finding kobs from the voltammograms for this system.

Figure 6.19A shows the cyclic voltammogram for the Fe(III) form of the complex being reduced in three separate one-electron steps to the corresponding Fe(II), Fe(I), and Fe(0) complexes in dimethyl formamide (DMF) in the absence of CO2. Figure 6.19B is an overlay of the cyclic voltammogram from panel A with a cyclic voltammogram of the same solution after the addition of CO2. The 60-fold increase in current coincides with the third peak in the reduction of the complex alone indicating that the Fe(0) (oxidation state 0) form is the active state of the catalyst. Panel C is the cyclic voltammogram for CO2

FeTDHPP

Iron 5, 10, 15, 20- tetrakis (2ʹ, 6ʹ- dihydroxylphenyl)-

porphyrin

[(por)Fe(I)]– + e– [(por)Fe(0)]2–

[(por)Fe(0)]2– + CO2 + 2AH [(por)Fe(II)CO]+ H2O + 2A–

CO2+ 2AH + 2e– CO+ H2O + 2A– [(por)Fe(II)CO]+ [(por)Fe(0)]2– 2 [(por)Fe(I)]– + CO

k kʹ ≫ k

OH

OH OH

OH Fe

N N

N N HO

HO

HO HO

FIGURE 6.18 Structure of the iron–porphyrin complex used in this case study. In the reaction scheme on the right [(por)Fe(0)]2−represents the activated form of the catalyst. The experiment described used 0.23 M CO2dissolved in dimethylformamide with 0.1 M tetrabutylammonium/phophorushexafluoride electrolyte. Water was added to a level of 2 M to act as the acid, AH. Source: Costentin et al. 2012 [19].

Adapted with permission of The American Association for the Advancement of Science.

k k

0.4

–1 –10

0 10 20 30 40 50 60 70

0 10 20 30 40 50 60 70

Foot of the wave

–0.5 0 0.5 1 1.5 2

2.5 i/i0p i/i0p i/i0p

0 –0.4

(A) (B) (C) (D)

FIT

E (V vs NHE) E (V vs NHE) E (V vs NHE)

–0.8 –1.2 –1.6 0.4 0 –0.4 –0.8 –1.2 –1.6 –1 –1.1 –1.2 –1.3 –1.4 –1.5 –1.6 0 0.01 0.02 0.03 0.04 0.05 0.06 0 10 20 30 40 50 60 70 80

(E–E0Fe(I)/Fe(0)

1 + exp nF –1

⎡RT

⎣ ⎡

⎛ ⎣

⎝ ⎛⎝

⎛⎝

⎧⎨

⎩

⎧⎨

⎩

FIGURE 6.19 Cyclic voltammograms recorded in the presence of 2 M water in DMF with 0.1 M tetra- butylammonium/phophorushexafluoride electrolyte supporting electrolyte at a scan rate of 0.1 V/s.

(A) FeTDHPP catalyst and water only. (B) Cyclic voltammogram for the same solution as in (A) with 0.23 M CO2 overlaid on the cyclic voltammogram of the catalyst without CO2. (C) Cyclic voltammo- gram of the catalytic peak from (B) showing the region for the foot-of-the-wave analysis. (D) Plot of the ratio of the current, i/ipo in (C), normalized to the peak current for the catalyst alone versus the {1+exp[

nF(E−EFe(I)∕Fe(0))∕RT]}−1

. The slope of this plot yields the apparent rate constant,kobsfrom Eq. (6.46). Source: Costentin et al. 2012 [19]. Adapted with permission of The American Association for the Advancement of Science.

and catalyst together with a rectangle framing the foot of the wave. Data from this region was used to construct the plot in panel D.

Savéant chose to work with data from the foot of the wave for the catalytic current in Figure 6.19C because it was less affected by undesirable complications. In this region, the current is also modelled by Eq. (6.37). Here is that equation again written with the appropriate terms for this cyclic voltammogram.

icat= nFA[FeIIITDHPP]o√ Dkobs 1+exp

{nF RT

(

E−EoFe(I)∕Fe(0)

)} (6.44)

In Eq. (6.44), [FeIIITDHPP] represents the concentration of the starting form of the catalyst added to the solution, and [CO2] was 0.23 M for this experiment. The diffusion coefficient,D, also is for the catalyst. The applied potential is Eand the formal poten- tial,EoFe(I)∕Fe(0), is for the reduction of the Fe(I) state of the complex to the Fe(0) form. That formal potential can be obtained from the cyclic voltammogram of the catalyst alone in Figure 6.19A. The return wave for the third reduction peak is difficult to see in this figure, but the authors say that cyclic voltammograms at faster scans (using a much smaller elec- trode) showed a more prominent peak for the return scan. The average of the peaks gave a value of−1.333 V versus SHE for the formal potential.

Savéant applied a strategy that is often a rewarding approach to finding useful infor- mation from experiments, namely, he manipulated the mathematical model describing the signal until he found a way of plotting the data that put the desired quantity in the slope or intercept. One can follow his logic (and contributions of others) in the original papers

k k [18–22], but here is the basic pathway and his endpoint. Savéant divided equation (6.44)

by the Randles–Sevick equation (6.39) to arrive at Eq. (6.45).

icat ipc =

2.24

√(RT nF𝜐

) kobs

1+exp [nF

RT

(

E−EoFe(I)∕Fe(0)

)] (6.45)

That removes several terms, such as the diffusion coefficient of the catalyst and the electrode area, and introduces others, such as the scan rate,𝜐, and the peak current,ipc, for the catalyst alone. Fortunately, these new terms are readily obtainable. A plot of the current ratio,icat/ipc, versus

{ 1+exp

[nF RT

(

E−EoFe(I)∕Fe(0)

)]}−1

is a straight line (see Figure 6.19D) with a slope containingkobs[19].

Slope of graph=2.24

√(RT nF𝜐

)

kobs (6.46)

The slope of the best fit line to the data in panel D of Figure 6.19 appears to have a numerical value of 80/0.052=1.5×102. Given that the scan rate,𝜐, was 0.1 V/s, and the number of electrons,n, in the electron transfer step at the electrode was 1, and the experiment was performed at 21∘C or 294 K, Eq. (6.45) can be solved forkobs:

Slope= 80

0.052 =1.53×103=2.24

√

(8.314)(294)kobs

(1)(96 485)(0.1) = (1.13)√

kobs (6.47)

√kobs= 1.53×103

1.13 =1.35×103 or kobs= (1.35×103)2=1.8×106M∕s (6.48) For the experiment in Figure 6.19, the CO2substrate concentration was 0.23 M, solving Eq. (6.43) forkgives a rate constant for the homogeneous reaction between the catalyst and substrate a value of

k= 1.8×106M∕s

(2)(0.23 M) =3.9×106s−1 (6.49) This value has been used as a figure of merit for comparing this catalyst with others that control this reaction. Of course, a full analysis of this system must also address the role of the acid, side reactions, catalyst stability, and product inhibition as well. However, those considerations are beyond the scope of the discussion here. Ultimately, a good elec- trocatalyst should have a high turnover frequency and a small overpotential (difference between the formal potential of the substrate and the operating potential for the electrode reaction) [19].

Evaluation of more complicated catalytic systems can be approached by using com- puter simulations to predict the shapes of cyclic voltammograms for various conditions based on a proposed model (sequence of reaction steps). Commercial programs are available that run on small computers and are flexible and powerful enough to handle complicated mechanisms. They enabled the chemist to predict voltammograms based on