Kinetic Analysis of Competitive Electrocatalytic Pathways: New Insights into Hydrogen Production with Nickel Electrocatalysts

Article abstract of DOI:10.1021/jacs.5b10853

The hydrogen production electrocatalyst Ni(P^Ph₂N^Ph₂)₂²⁺⁺, the mechanism of H₂ formation by 1 changes from an ECEC to an EECC mechanism as the potential approaches the Ni(I/0) couple. Two electrochemical methods, current-potential analysis and foot-of-the-wave analysis (FOWA), were performed on 1 to measure detailed kinetics of the competing ECEC and EECC pathways. A sensitivity analysis was performed on the methods using digital simulations to understand their strengths and limitations. Chemical rate constants were significantly underestimated when not accounting for electron-transfer kinetics, even when electron transfer was fast enough to afford a reversible noncatalytic wave. The EECC pathway of 1 was faster than the ECEC pathway under all conditions studied. Buffered DMF:DMF(H)⁺ mixtures afforded an increase in the catalytic rate constant (k_obs) of the EECC pathway, but k_obs for the ECEC pathway did not change when using buffered acid. Further kinetic analysis of the ECEC path revealed that base increases the rate of isomerization from exo-protonated Ni(0) isomers to the catalytically active endo-isomers, but decreases the rate of protonation of Ni(I). FOWA did not provide accurate rate constants, but FOWA was used to estimate the reduction potential of the previously undetected exo-protonated Ni(I) intermediate. Comparison of catalytic Tafel plots for 1 under different conditions reveals substantial inaccuracies in the turnover frequency at zero overpotential when the kinetic and thermodynamic effects of the conjugate base are not accounted for properly.

Full text of DOI:10.1021/jacs.5b10853

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Article
Kinetic Analysis of Competitive Electrocatalytic Pathways: New
Insights into Hydrogen Production with Nickel Electrocatalysts
Eric S. Wiedner, Houston J. S. Brown, and Monte L Helm
J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.5b10853 • Publication Date (Web): 21 Dec 2015
Downloaded from http://pubs.acs.org on December 26, 2015
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Kinetic Analysis of Competitive Electrocatalytic Pathways: New Insights into
Hydrogen Production with Nickel Electrocatalysts
Eric S. Wiedner,* Houston J. S. Brown, and Monte L. Helm
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Center for Molecular Electrocatalysis, Pacific Northwest National Laboratory,
P.O. Box 999, K2-57, Richland, Washington 99352, USA
*
E-mail: eric.wiedner@pnnl.gov
Abstract
The hydrogen production electrocatalyst Ni(P N ) (1) is capable of traversing multiple
Ph
Ph 2+
2 2
2
+
electrocatalytic pathways. When using dimethylformamidium, DMF(H) , the mechanism of H
2
formation by 1 changes from an ECEC to an EECC mechanism as the potential approaches the Ni(I/0)
couple. Two electrochemical methods, current-potential analysis and foot-of-the-wave analysis
(
FOWA), were performed on 1 to measure detailed kinetics of the competing ECEC and EECC
pathways. A sensitivity analysis was performed on the methods using digital simulations to understand
their strengths and limitations. Chemical rate constants were significantly underestimated when not
accounting for electron transfer kinetics, even when electron transfer was fast enough to afford a
reversible non-catalytic wave. The EECC pathway of 1 was faster than the ECEC pathway under all
+
conditions studied. Buffered DMF:DMF(H) mixtures afforded an increase in the catalytic rate constant
(
kobs) of the EECC pathway, but kobs for the ECEC pathway did not change when using buffered acid.
Further kinetic analysis of the ECEC path revealed that base increases the rate of isomerization from
exo-protonated Ni(0) isomers to the catalytically active endo-isomers, but decreases the rate of
protonation of Ni(I). FOWA did not provide accurate rate constants, but FOWA was used to estimate the
reduction potential of the previously undetected exo-protonated Ni(I) intermediate. Comparison of
catalytic Tafel plots for 1 under different conditions reveals substantial inaccuracies in the turnover
frequency at zero overpotential when the kinetic and thermodynamic effects of the conjugate base are
not accounted for properly.
Keywords
hydrogen production, electrocatalysis, foot-of-the-wave analysis (FOWA), homoconjugation, proton
relays, nickel phosphine complexes
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Introduction
Replacing fossil fuels with energy generated from renewable sources, coupled with the desire to
use energy more efficiently, has driven a resurgence in research and development of electrocatalysts for
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energy storage and use. A wide variety of molecular complexes have been studied as electrocatalysts
2
-6
for production of H and reduction of CO . Enabling the rational design and improvement of
2
2
molecular electrocatalysts requires careful mechanistic studies to determine key catalytic intermediates
and kinetic bottlenecks.
Electrocatalytic cyclic voltammetry has become an indispensable tool for understanding overall
7
, 8
rates of molecular catalysis, overpotential, and catalytic mechanisms. A seminal report by Costentin
and Savéant in 2014 provides the groundwork for detailed kinetic analysis of multi-electron
9
, 10
electrocatalysis by molecular compounds.
In electrochemical nomenclature, electron transfers and
chemical steps are denoted as “E” and “C”, respectively. From an electrochemical perspective,
electrocatalytic H production can be simplified into two proton transfer steps (C) and two electron
2
transfer steps (E), which can occur in five possible orders: ECEC, EECC, ECCE, CECE, and CCEE.
Costentin and Savéant provided a current-potential analysis for each the three mechanisms that begin
9
with an electron transfer step, allowing for determination of the rate constant for each chemical step
without the use of digital simulation software.
As with digital simulation techniques, incorrect assignment of the catalytic mechanism can lead
to misleading or incorrect kinetic information. This problem can be exacerbated if the catalyst is capable
of traversing multiple competing pathways for catalytic turnover, as frequently observed with molecular
11-21
complexes that catalyze the reduction of protons or CO2.
The careful delineation of the possible
relevant mechanisms, the methods and expressions for extracting the kinetic data, and sensitivity
analysis of different electrochemical methods are crucial for thorough and accurate analysis of
electrocatalytic data. Herein we report an electrochemical mechanistic analysis for proton reduction
Ph
2
Ph 2+
2 2
22-24
catalysis by the well-established Ni(P N )
(1) complex
using the multi-electron, multi-
9
chemical step analysis recently reported by Costentin and Savéant. Using this catalyst, we present
methods for analyzing competing ECEC and EECC catalytic pathways and evaluate the error associated
with these methods.
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Results
Identification of Relevant Mechanisms
Ph
Ph 2+
2 2
23-26
The reduction of protons to form H using Ni(P N ) (1) has been previously reported,
and
As previously
reported, cyclic voltammograms of 1 recorded in acetonitrile display two reversible waves
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R
R' 2+
22, 27-29
mechanistic studies on Ni(P N ) derivatives have appeared in the literature.
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2 2
2
3, 24
corresponding to the Ni(II/I) couple (–0.83 V) and the Ni(I/0) couple (–1.03 V).
A representative
+
cyclic voltammogram of 1 recorded in the presence of protonated dimethylformamide, DMF(H) , is
shown in Figure 1. The wave approximates an ideal S-shaped catalytic wave, and the maximum catalytic
current (i ) is independent of the scan rate employed. However, the catalytic wave also displays a
cat
discernible inflection point near –0.9 V, located approximately halfway between the Ni(II/I) and Ni(I/0)
couples. This inflection is a deviation away from ideal electrocatalytic behavior and suggests a change in
the catalytic mechanism as the potential is swept more negative.
+
Figure 1. Cyclic voltammogram of 1 (0.7 mM) in the presence of DMF(H) (158 mM) in MeCN (0.2
M NBu PF ), showing the E of the non-catalytic Ni(II/I) and Ni(I/0) couples relative to the catalytic
4
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1/2
-1
wave. Conditions: υ = 0.05 V s , 1 mm diameter glassy carbon working electrode.
The appearance of a single inflection point in the catalytic wave of 1 (Figure 1) suggests that the
majority of the catalytic current stems from only two of the five possible E/C mechanisms for H2
production. Several of the candidate mechanisms for catalysis by 1 can be reasonably excluded based on
experimental observations and estimated pK values of the protonated pendant amines in the
a
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Ph
Ph 2+
+
30, 31
R
R' 2+
Ni(P N )
complex relative to the pK of DMF(H) in CH CN (6.1).
For Ni(P N )
2 2 2
2
2 2
a
3
complexes that can be protonated in the Ni(II) state, the catalytic half-wave potential is ~350 mV more
32, 33
positive than the Ni(II/I) couple of the unprotonated complex.
The shift in Ecat/2 versus the Ni(II/I)
couple of 1 is smaller than 200 mV, therefore the mechanisms involving protonation of Ni(II) before
electrochemical reduction (CECE and CCEE) can be ruled out as major pathways The ECCE
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mechanism can also be eliminated as protonation of a mono-protonated Ni(I) species by DMF(H) is
unlikely. Based on electrostatic arguments, the basicity of a protonated Ni(I) species (overall +2 charge)
would be similar to that of a Ni(II) complex (overall +2 charge). These pK approximations are well
a
R
R' 2+
2 2
34, 35
supported by previous computational studies on the Ni(P N ) family of complexes.
The two
2
remaining mechanistic candidates are the ECEC and EECC mechanisms, both of which are discussed
below.
The non-ideal inflection in the catalytic wave of proton reduction by 1 can be attributed to either
a change from an ECEC to an EECC mechanism or from two distinct ECEC mechanisms occurring at
different potentials. For example, protonation of Ni(I) at a pendant amine can occur in either an endo or
an exo position (Chart 1). If the reduction potentials of the endo and exo protonated intermediates are
sufficiently different, two catalytic waves corresponding to an ECEC mechanism could be observed.
The protonated Ni(I) intermediates of 1 have not been observed previously, but comparison of 1 with
R
R' 2+
2 2
related Ni(P N )
complexes suggests that the reduction potentials of both the endo- and exo-
2
protonated Ni(I) forms of 1 are more positive than the Ni(II/I) couple (see Discussion section for further
details). Therefore the observed inflection point in the electrocatalytic wave is most likely due to a
change in mechanism from an initial ECEC mechanism to an EECC mechanism, both of which are
depicted generically in Scheme 1 to show the overall stoichiometry (and not structure or connectivity).
+
0
Ph
Ph
Ph
2
Ph +
For instance, Ni(0)H could be either an exo-protonated Ni(0) complex, Ni (P N -H)(P N ) , or a
2
2
2
II Ph
Ph
+
2 2
formal Ni(II)-hydride, HNi (P N ) .
2
Chart 1. Endo vs exo protonation isomers of Ni(I). The groups on P and N have been omitted for
clarity.
4
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Scheme 1. Generalized ECEC and EECC Mechanisms for 1.
ECEC:
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2+
–
+
Ni(II) + e ⇌ Ni(I)
E1
C1
E2
C2
+
+
2+
Ni(I) + H ⇌ Ni(I)H
2
+
–
+
Ni(I)H + e ⇌ Ni(0)H
+
+
2+
Ni(0)H + H ⇌ Ni(II) + H
2
EECC:
2
+
–
+
Ni(II) + e ⇌ Ni(I)
E1
E2
C1
C2
+
–
Ni(I) + e ⇌ Ni(0)
+
+
Ni(0) + H ⇌ Ni(0)H
+
+
2+
Ni(0)H + H ⇌ Ni(II) + H
2
Defining the Kinetic Parameters
For a two-electron electrocatalytic process in which both electron transfers occur at the electrode,
the maximum catalytic current (i ) is given by equation 1, where F is Faraday’s constant, A is the area
cat
2
2 –1
of the electrode in cm , [Cat] is the concentration of catalyst, D is the diffusion coefficient in cm s ,
T
–1 36-38
and kobs is the observed catalytic rate constant in s .
When a reversible non-catalytic wave can be
observed in the absence of substrate, dividing equation 1 by the non-catalytic peak current (i ) results in
p
cancellation of A, [Cat] , and D, and the ratio i /i becomes a function of k , the scan rate (υ), and the
T
cat
p
obs
electrochemical parameter f, which is equal to F/RT (equation 2). Equation 2 is readily rearranged to
give equation 3, thus kobs can be determined from the measured electrochemical parameters icat and ip
without prior knowledge of the specific 2-electron catalytic mechanism.
푖푐푎푡 = 2퐹퐴[퐶ꢀꢁ] √퐷ꢂ푘
(1)
(2)
푇
표푏푠
푖푐푎푡
푘표푏푠
푓휐
=
4.48ꢃ
푖푝
ꢋ
ꢅꢆꢇꢈ
푘표푏푠 = 0.0497푓휐 ꢄ ꢅꢉ
ꢊ
(3)
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Costentin and Savéant recently described the dependence of kobs on k and k , the rate constants
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9
for the two individual chemical steps (C), in the ECEC, EECC and ECCE mechanisms. Additionally,
they described the potential at half-height of the catalytic wave (Ecat/2) according to equation 4, where
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kinetic parameter. Equation 4 can be rearranged to give equation 5, thus λ can be determined directly
from the measured E1/2 and Ecat/2 values.
1
퐸푐푎푡/ꢋ = 퐸ꢌ/ꢋ + ln(1 + 휆)
푓
(4)
(5)
휆 = 푒푥ꢍꢎ푓ꢏ퐸푐푎푡/ꢋ − 퐸ꢌ/ꢋꢐꢑ − 1
Determination of λ allows for calculation of the two individual chemical step rate constants, k1
and k in terms of experimental observables. Table 1 gives the expressions for ꢂ푘 and λ in terms of k1
2
표푏푠
and k (expressed as pseudo-first order rate constants, e.g. k = k ′[HA]) for ECEC and EECC
2
1
1
mechanisms in which the second electron transfer is easier than the first (E < E ). These expressions
1
2
9
are obtained from algebraic rearrangement of the reported equations. As seen in Table 1, the ECEC
and EECC mechanisms possess the same general form of ꢂ푘obs, but differ in the form of λ. After
algebraic manipulation, k can be expressed in terms of the experimental measurables, k and λ, and
1
obs
similarly, k can be expressed in terms of and k and λ (see SI for derivations).
2
1
Table 1. Kinetic Parameters for ECEC and EECC Mechanisms.
a
–1
b
–1
b
–1/2 a
Mechanism
휆
k (s )
k (s )
ꢂ푘표푏푠 (s
ꢂ푘ꢌ
+ 휆
)
1
2
ꢂ푘ꢌ
푘ꢌ
휆ꢋ
c
푘표푏푠(1 + 휆)ꢋ
푘표푏푠(1 + 휆)ꢋ
c
ECEC
1
ꢂ푘ꢋ
ꢂ푘ꢌ
1
1 4 + 휆
1
ꢂ푘ꢌ
+ 휆
EECC
ꢔ − ꢃ
+ ꢕ 푘
ꢌ
ꢂ푘ꢋ
휆
2
휆
2
1
ꢂ푘ꢋ ꢒ1 +
ꢓ
ꢂ푘ꢌ
a
b
Reported in Ref 9. Derived from ꢂ푘 and 휆 (see the SI). For the case in which the second
표푏푠
electron transfer is easier than the first electron transfer (E < E for a reduction). A different set of
1
2
ꢂ푘표푏푠 and 휆 are obtained for an ECEC mechanism in which the second electron transfer is more
9
difficult than the first (E > E ).
1
2
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A common approximation in multi-step electrocatalytic mechanisms is that kobs corresponds to a
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single rate-limiting step in the catalytic cycle. The dependence of kobs on the values of k and k reveal
1 2
that this assumption is only valid when the rates for the two steps differ by several orders of magnitude,
and that the precise relationship depends on the mechanism. For example, this relationship is illustrated
for the kinetic regime of k ≥ k in Figure 2, where k /k expresses the relationship between the
0
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obs
2
catalytic rate (k ) and the slow step (k ) as a function of log(k /k ), which defines the relative
obs
2
1
2
magnitude of the two individual rate constants. For an ECEC mechanism (red trace), kobs will not be
equivalent to k until log(k /k ) ≥ 4, i.e. the first step is at least four orders of magnitude faster than the
2
1
2
second step. The kinetics are different for an EECC mechanism (blue trace), where kobs becomes
equivalent to k at a much smaller value of log(k /k ) ~ 2. These examples illustrate the importance of
2
1
2
understanding the catalytic mechanism and relationship between the rate constants for the elementary
reaction steps before drawing general conclusions about rate determining steps from the overall rate
constant, k . In situations where both k and k contribute to k , it is important to be able to measure
obs
1
2
obs
the individual rate constants to gain insight into how to improve catalytic bottlenecks.
Figure 2. Plot of k /k versus log(k /k ) for ECEC and EECC mechanisms.
obs
2
1
2
Before analyzing catalytic data to determine the individual k and k rate constants it is important
1
2
to understand the assumptions and limitations of the equations in Table 1. One important assumption in
the derivation of the expressions for λ in Table 1 is that electron transfer from the electrode to the
9
catalyst is fast enough to obey the Nernst law. The limitations of this assumption do not appear to have
been tested in the literature, and electron transfer kinetics might be especially important for very fast
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-
1
catalysts (i.e. kobs > 100 s ). To demonstrate how the catalytic response might be affected, the Butler-
Volmer model of electron transfer (equation 6) is considered:
푘 = 푘 푒푥ꢍꢎ−훼푓ꢏ퐸 − 퐸ꢌ/ꢋꢐꢑ
(6)
ꢖ
푠
0
1
2
3
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6
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8
9
0
1
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9
0
1
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0
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9
0
1
2
3
4
5
6
7
8
9
0
–
1
where k is the forward rate constant for reduction by the electrode (cm s ), k is the standard
f
s
–1
heterogeneous electron transfer rate constant (cm s ), and α is the transfer coefficient (0 ≤ α ≤ 1), a
unitless term that describes the symmetry of the energy barrier for electron transfer (α = 0.5 for a
10, 39
perfectly symmetrical barrier).
At the plateau of a catalytic wave, the applied potential (E) is
negative of E1/2 and k will be large. However, k will be much smaller at potentials positive of E , such
f
f
1/2
as at Ecat/2. Equation 4 describing Ecat/2 can only be rigorously correct if k is large enough to generate
f
the reduced catalyst (e.g. Ni(I) in the case of 1) faster than it is consumed in the catalytic cycle, thus
requiring large values of ks.
Digital simulation was employed to test the effect of k on the value of k calculated from k
obs
s
1
–
–1
and λ. A reversible, 1e reduction wave was simulated with values of k ranging from 100 cm s to 0.01
s
–
1
40
–1
cm s (for reference, ferrocene has been reported to have k = 0.25 cm s relative to a glassy carbon
s
electrode in acetonitrile). Next, the non-catalytic reduction wave was simulated as a catalytic ECEC
–
1
mechanism with k arbitrarily chosen to be 100 s and variable values of k such that k ≥ k . The
2
1
1
2
apparent k value was then determined from i /i and E of the simulated voltammograms using
cat/2
1
cat
p
different values for k . The accuracy of the k measurement was evaluated from the percent error relative
s
1
to the value used in the simulation. Figure 3 shows a plot of % error versus log(k ), with negative error
s
6
-1
values corresponding to an underestimation of k . For a very large value of k = 1 × 10 s (blue
1
1
–1
diamonds), an error of –20% was measured at k = 3.2 cm s , and further decreases in k cause a rapid
s
s
–1
drop in the accuracy; at k = 0.1 cm s , an error of –99% was obtained, corresponding to an
s
underestimation of 2-orders of magnitude for k . Similar trends are observed for smaller values of k
1
1
(red and green traces), except that the decrease in accuracy begins at smaller values of k . For example,
s
–
1
–1
for k = 100 s (green triangles), errors of less than –10% are only observed at k < 1.0 cm s . Using
1
s
-1
the k of ferrocene as a benchmark, catalysts that operate at k ≥ 100 s and have electron transfer rates
s
obs
-1
slower than that of ferrocene (< 0.25 cm s , or log(k ) = –0.6) will result in an underestimation of the
s
calculated values of k using the equations in Table 1.
1
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60
Figure 3. Plot of % error in k measured from E
versus log(k ) at different values of k . ECEC
s 1
1
cat/2
-1
-1
-5
2 -1
Model: E –E = –0.5 V, k = 100 s , υ = 0.05 V s , D = 1 × 10 cm s .
1
2
2
5, 9, 41
Equation 4 can be modified to account for heterogeneous electron transfer kinetics,
which
would allow determination of λ from Ecat/2 after independent measurement of k and α. However,
s
accurate measurement of k values in non-aqueous solvents presents a variety of experimental
s
4
2
challenges. In particular, a simple and popular voltammetric method for measuring k values is to
s
4
3, 44
measure the increase in the peak-to-peak separation of a redox wave at high scan rates.
The major
challenge of this technique is to completely compensate for the solution resistance, which also causes
4
4
the peak-to-peak separation to increase at high scan rates due to Ohmic potential drop. As an example,
+
/0
the value of k that is obtained for the Cp Fe couple in acetonitrile relative to a glassy carbon electrode
s
2
–
1 45
is much smaller when measured by cyclic voltammetry with iR compensation (k = 0.009 cm s ) than
s
–1 40
by AC voltammetry techniques (k ≅ 0.25-0.5 cm s ). Additionally, most studies of homogeneous
s
electrocatalysts for proton reduction are performed using a glassy carbon electrode due to its large
4
6, 47
overpotential for acid reduction,
yet k values measured at glassy carbon electrodes have been shown
s
4
8, 49
50
to be highly sensitive to the surface microstructure
and polishing history. Given the above
considerations, experimental measurements of k values for molecular electrocatalysts are likely
s
underestimated. With regard to determining chemical rate constants, an underestimate of k will lead to
s
an overcorrection of Ecat/2, which will afford an overestimate of k when E
occurs positive of E°′.
1
cat/2
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6
Foot-of-the-Wave Analysis
Foot-of-the-Wave analysis (FOWA) has been reported as a method for obtaining kinetic
information on catalysts for which a plateau-shaped catalytic wave cannot be obtained due to competing
41, 51, 52
side phenomena, such as substrate depletion or catalyst decomposition.
In general, a catalytic
0
1
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0
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9
0
wave normalized to i can be described in terms of equation 7:
p
푖
푖푐푎푡⁄푖푝
=
(7)
푖푝 1 + 푒푥ꢍꢎ푓ꢏ퐸 − 퐸ꢌ/ꢋꢐꢑ
In equation 7, the function 1/{1+exp[f(E–E )]} describes the fraction of catalyst that is reduced at a
1/2
given potential under non-catalytic conditions. For example, 1/{1+exp[f(E–E )]} has a value of 0.5 at
1
/2
E = E , indicating half of the catalyst is reduced at the formal reduction potential. When the applied
1/2
potential becomes more negative than E , the exponential term approaches 0 and equation 7 simplifies
1
/2
to equation 3. In FOWA, the normalized catalytic current (i/i ) is plotted versus 1/{1+exp[f(E–E )]},
p
1/2
and the shape of the resulting plot depends on the kinetic regime of catalysis, as illustrated next.
–
1
Simulations were performed for several ECEC models, each having kobs = 100 s and different
values of the kinetic parameter λ (recall that λ = ꢂ푘 ⁄푘 for the ECEC mechanism). In the first model,
ꢌ
ꢋ
k is much smaller than k such that λ = 0.01, resulting in a catalytic wave having E equal to E1/2 of
cat/2
1
2
the non-catalytic wave (Fig. 4a, black trace). FOWA on this model affords a straight line with a slope
(m) that is equal to i /i (Fig. 4b, black trace), thus providing access to k (which is equal to k in this
cat
p
obs
1
kinetic regime) according to equation 3. Note that in this kinetic regime, k cannot be measured from the
2
catalytic wave since it occurs after the rate-determining step of the catalytic cycle.
1
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Figure 4. Plot of i/i versus E-E (A) and 1/{1+exp[f(E-E )]} (B) for ECEC mechanisms having k =
obs
p
1/2
1/2
-1
4
-1
100 s but different values of k and k . General ECEC Model: E –E = –0.5 V, k = 1 × 10 cm s , υ =
1
2
1
-1
2
S
-1
-5
2
-1
6
-1
0
1
1
.05 V s , D = 1 × 10 cm s ; Red trace (λ=100): k = 1 × 10 s , k = 100 s ; Green trace (λ=10): k =
.2 × 10 s , k = 120 s ; Blue trace (λ=1): k = k = 400 s ; Black trace (λ=0.01): k = 100 s , k = 1 ×
1
2
1
4
-1
-1
-1
-1
2
1
2
1
2
6
-1
0 s .
When k is no longer the sole rate-determining step, Ecat/2 becomes more positive than E , as
1
1/2
shown in Figure 4a for ECEC models having k = k (λ = 1, blue trace) and k > k (λ = 10, green trace;
1
2
1
2
λ = 100, red trace). FOWA plots of these waves are nonlinear, with the amount of curvature increasing
as λ increases (Fig 4b). This phenomenon is best understood through expansion of the i /i term in
cat
p
equation 7, providing equation 8 for an ECEC model, as shown below. At the foot of the wave, i.e.
positive values of E–E , the term exp[f(E–E )] is much larger than λ. Consequently, kinetic data on k
1
1
/2
1/2
(the fast chemical step) can be obtained from the linear slope measured at the foot-of-the-wave (mF)
9
according to equation 9, illustrated by the dashed traces in Figure 4b. As the potential is swept through
the catalytic wave, exp[f(E–E )] becomes smaller than λ, and equation 8 simplifies to equation 2 for
1
/2
i /i . Similar FOWA plots are obtained for other mechanisms, such as EECC, when k ≥ k .
cat
p
1
2
1
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ꢂ푓휐
.48
ꢂ푘ꢌ
푖
=
(8)
푖푝 {1 + 휆}ꢗ1 + 푒푥ꢍꢎ푓ꢏ퐸 − 퐸ꢌ/ꢋꢐꢑꢘ
푘ꢌ
0
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0
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9
0
푚 ≅ 4.48ꢃ
(9)
F
푓휐
A consideration that has not been clearly addressed in the literature is how much of the catalytic
wave should be used in FOWA when the idealized FOWA plot is non-linear. This was tested for the
-
1
simulated ECEC model in the “fast k ” regime (i.e. E
> E ) using k = 100 s , several different
1/2 2
1
cat/2
4
–1
values of k , and fast electron transfer (k = 1 × 10 cm s ). The accuracy of the measured k values were
1
s
1
described by the percent error and were plotted against the fraction of i /i used in the FOWA (Figure
cat
p
5
a). An error of approximately -5 to -13% was measured using only 3% of i /i in the FOWA, and the
cat p
error in k clearly increases as more of the catalytic wave is employed in the FOWA. The analysis was
1
-1
repeated on the same model using a slower electron transfer rate constant of k = 0.1 cm s (Fig 5b). In
s
this case, the inaccuracies in the measured k become even greater as more of the foot is utilized, as
1
expected given the effect of k on E
determined above (Fig 3). However, utilizing only 3% of icat/ip
s
cat/2
afforded an error of -20 to -30% for the measured k values, which is much improved over the error
1
of -40 to -84% obtained from the Ecat/2 analysis performed on the same catalytic waves (see Fig 3).
While the specific errors in FOWA will depend on the values of k and the ratio k /k , these simulations
S
1
2
demonstrate a clear benefit in using less of the catalytic wave in FOWA when a kinetic potential shift is
observed.
1
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Figure 5. Plots of % error in k measured from FOWA vs fraction of i /i used in FOWA for (A) k =
1
cat
p
s
4
–1
–1
–1
–1
1
1
× 10 cm s and (B) k = 0.1 cm s . ECEC Model: E –E = –0.5 V, k = 100 s , υ = 0.05 V s , D =
s 1 2 2
× 10 cm s .
–
5
2 –1
The FOWA plots shown in Figure 4 bear a resemblance to FOWA plots obtained when either the
8, 51
substrate or catalyst is depleted within the diffusion layer.
Therefore, care should be taken to identify
the correct rate constant being measured by FOWA, since accidental misrepresentation of k as k
1
obs
could lead to an overestimation of the catalytic rate. One possible way to confirm the kinetic regime is to
substitute Ecat/2 for E1/2 in the FOWA plot, i.e. a plot of i/i versus 1/{1+exp[f(E–Ecat/2)]}, which will
p
afford a linear FOWA plot under all kinetic regimes. If k ≥ k , then the FOWA plot using E will give
cat/2
1
2
a smaller rate constant than the FOWA plot using E .
1
/2
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Applying the Electrochemical Methods to 1
In order to apply the above analyses to voltammograms of 1, the degree to which the ECEC and
EECC mechanisms contribute to the observed catalytic wave must be better understood. Digital
simulation was used as an initial assessment of the competition between the ECEC and EECC pathways
0
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(Figure 6a) using the experimentally observed potentials of the Ni(II/I) (–0.83 V) and Ni(I/0) (–1.03 V)
couples. Simulation of the full model affords a voltammogram (Figure 6b, black trace) that is similar in
appearance to the experimental voltammograms of 1, suggesting that this model is a reasonable
approximation of the relevant catalytic processes. Next the individual reaction pathways were “isolated”
by turning off the chemical steps of the opposing mechanism in the simulation. For example, the ECEC
–
1
pathway was isolated by setting k of the EECC pathway to 0 s , while maintaining the Ni(I/0)
1
reduction in the model. Figure 6b shows the simulated voltammograms of the isolated ECEC pathway
(dashed blue trace) and the isolated EECC pathway (dashed red trace).
Figure 6. a) Simulation model for competing ECEC and EECC pathways, and b) simulated
voltammograms for the competing ECEC and EECC pathways (black trace), isolated ECEC pathway
(dashed blue trace), and isolated EECC pathway (dashed red trace). ECEC Model: E = –0.83 V, E = –
1 2
1
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0.50 V, k = 1 × 10 s , k = 200 s . EECC Model: E = –0.83 V, E = –1.03 V, k = 1 × 10 s , k = 300
1
2
1
2
1
2
-1
-1
-5
2
-1
-1
s . General parameters: υ = 0.05 V s , D = 1×10 cm s , k = 0.5 cm s .
s
At potentials positive of the Ni(II/I) couple (–0.83 V), the catalytic wave of the isolated ECEC
pathway (blue trace) is superimposed over the wave simulated from competing ECEC and EECC
mechanisms (black trace). This indicates that the current at the beginning of the catalytic wave arises
solely from the ECEC pathway, with little to no contribution from the EECC pathway. The catalytic
current of the isolated ECEC wave reaches a plateau approximately halfway between the Ni(II/I) and
Ni(I/0) couples, then begins to decrease as the potential becomes more negative. This phenomenon
indicates that at sufficiently negative potentials, reduction of Ni(I) by the electrode becomes faster than
protonation of Ni(I). Consequently, the catalytic current at the most negative potentials corresponds
solely to the EECC pathway, as evidenced by the equivalent plateau regions of the isolated EECC wave
0
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0
(red trace) and the wave for the competing ECEC and EECC pathways (black trace). Similar
2
2
conclusions were reached in a recent computational microkinetics study of 1.
Given the above considerations, the maximum icat value at the catalytic plateau of 1 originates
predominantly from an EECC pathway (Fig. 7a). This maximum i value is typically used to measure
cat
R
R' 2+
2 2
23, 53-57
the proton reduction activity of many Ni(P N )
derivatives,
therefore the kobs values
2
previously reported for these catalysts likely reflect the activity of an EECC pathway. Direct
measurement of an accurate icat value for the ECEC pathway is less straightforward since the plateau
region for this pathway is obscured by the rise in current associated with the following EECC pathway.
However, Ecat/2 for the ECEC pathway is readily identified by the potential of the first maximum
5
8
observed in the first derivative of the i–E trace (Figure 7b). In the cyclic voltammogram, the current at
Ecat/2 is equal to half of icat by definition (Figure 7a), thus icat and kobs for the ECEC pathway can be
measured in this manner. Additionally, the first derivative trace can be used to approximate the potential
at which the EECC begins to compete with the ECEC pathway by reflecting the early portion of the
trace through the potential of the first maximum (Figure 7b, dashed blue trace). The resulting reflection
does not deviate from the real derivative at potentials positive of the Ni(II/I) couple (–0.83 V), indicating
that the EECC pathway does not become kinetically competitive with the ECEC pathway prior to the
Ni(II/I) couple.
1
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0
Figure 7. a) Cyclic voltammogram of 1 showing the methods for measuring i and E
and EECC mechanisms, and b) first-derivative plot of the cyclic voltammogram of 1, with the dashed
for the ECEC
cat
cat/2
blue line illustrating the reflection of the derivative across the potential of the first maximum.
+
-1
Conditions: 1 (0.7 mM) and DMF(H) (158 mM) in MeCN (0.2 M NBu PF ), υ = 0.05 V s , 1 mm
4
6
diameter glassy carbon working electrode.
For a given mechanism, k and k can be determined from E and icat or by using FOWA as
cat/2
1
2
described above. Both of these techniques can be used to examine of the kinetics of the ECEC pathway
for 1 by using the value of the Ni(II/I) couple for the non-catalytic reduction potential E°'. More difficult
is analysis of the EECC pathway of 1, as the voltammetric response is perturbed by the preceding ECEC
pathway until the catalytic plateau is reached. The second maximum observed at –0.96 V in the first
derivative plot does not provide Ecat/2 for the EECC pathway, but instead identifies the potential at which
the catalyst has an equal chance of entering either an ECEC or an EECC pathway. Therefore, the present
electrochemical analysis cannot be used to experimentally determine the k and k values of the EECC
1
2
pathway of 1 when both the ECEC and EECC pathways are operative.
1
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Acid and Base Dependence of Electrocatalytic Proton Reduction by 1
Understanding the acid and base dependence of kobs for the individual ECEC and EECC
pathways is a crucial step for gaining mechanistic insights into the catalytic production of H . Cyclic
2
voltammograms of 1 were recorded in acetonitrile solution (0.2 M NBu PF electrolyte) in the presence
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+
+
+
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0
of 0.005 – 0.25 M of DMF(H) , 1:3 DMF:DMF(H) , and 1:1 DMF:DMF(H) . The value for k of each
obs
pathway was determined from the corresponding icat value, measured either from the plateau-limiting
current (EECC) or from twice the current at the potential of the first maximum in the first derivative
+
trace (ECEC). The resulting plots of kobs versus concentration of DMF(H) are shown for both the ECEC
pathway (Figure 8a) and the EECC pathway (Figure 8b). The EECC pathway is clearly faster than the
2
3
ECEC pathway under similar conditions. However, as noted previously, 1 displays slower rates of
+
catalysis for both pathways when using buffered DMF:DMF(H)] mixtures. This observation is
counterintuitive since base is required to deprotonate the exo-protonated intermediates that are believed
28
to inhibit catalytic formation of H . We address this discrepancy next by considering the effect of
2
homoconjugation.
1
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5
5
5
6
+
Figure 8. Plots of kobs versus acid concentration. A) ECEC, [DMF(H) ] (uncorrected for
o
+
+
homoconjugation), B) EECC, [DMF(H) ] (uncorrected for homoconjugation), C) ECEC, [DMF(H) ]
corrected for homoconjugation), D) EECC, [DMF(H) ]EQ (corrected for homoconjugation).
o
EQ
+
(
In the homoconjugation reaction, an acid and its conjugate base react to form a hydrogen bonded
pair (equation 10). Proper treatment of this phenomonenon is essential for understanding the kinetics of
0
1
2
3
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5
6
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9
0
1
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3
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9
0
1
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9
0
1
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7
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9
0
1
2
3
4
5
6
7
8
9
0
–
1
protonation of 1 (and related catalysts) since a homoconjugation constant (K ) of 49 M has been
f
+
59
measured for DMF(H) in acetonitrile. A critical question is whether the homoconjugate pair is
capable of directly protonating or deprotonating the catalytic intermediates. For the present case,
+
+
(
DMF) (H) is a poorer acid than DMF(H) on the basis of thermodynamic and steric considerations,
2
and is therefore unlikely to directly protonate the Ni intermediates. Similarly, we will assume that
+
(DMF) (H) does not play a significant role as a base. The actual concentration of the monomeric acid in
2
+
+
solution, [BH ] , can be determined from the initial concentrations of acid and base ([BH ] and [B] )
EQ
o
o
and the homoconjugation constant (K ), according to equation 11. A similar equation can be written to
f
determine [B] , the concentration of monomeric base in solution (equation 12). Therefore, the
EQ
+
homoconjugation reaction serves to decrease the concentrations of DMF(H) and DMF (the substrates)
in solution (Figure S2 in the Supporting Information), and the kinetics for electrocatalysis must account
for this phenomenon.
ꢙ
ꢙ
BH + B ⇌ BHB
퐾f (10)
ꢙ
ꢙ
ꢋ
ꢙ
−{퐾 ([B] − [BH ] ) + 1} + ꢂ{퐾 ([B] − [BH ] ) + 1} + 4퐾 [BH ]
f
o
o
f
o
o
f
o
[
BHꢙ]EQ
=
(11)
(12)
2
퐾f
ꢙ
ꢙ
ꢋ
−
{퐾 ([BH ] − [B] ) + 1} + ꢂ{퐾 ([BH ] − [B] ) + 1} + 4퐾 [B]
f
o
o
f
o
o
f
o
[B]EQ
=
2퐾f
+
Returning to the acid dependence of 1, the plots of kobs versus [DMF(H) ] (Figures 8a-b) can be
o
+
converted into plots of kobs versus [DMF(H) ] (Figures 8c-d). After correcting the acid concentration
EQ
for homoconjugation in the buffered solutions, kobs is linear with respect to the acid concentration under
the range of acid concentrations examined. Catalysis is also first-order in acid at low concentrations of
+
+ 23
DMF(H) with no buffer, but becomes independent of the acid concentration at ~0.2 M DMF(H) .
Notably, correction of the acid concentrations due to homoconjugation reveals that kobs of the ECEC
1
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pathway is independent of the base concentration, while kobs of the EECC pathway increases in the
presence of added base. The latter finding for the EECC pathway is consistent with an increased rate of
isomerization from exo- to endo-protonated species in the presence of added base.
The absence of a base concentration dependence of kobs for the ECEC pathway was further
0
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0
examined through determination of k and k from the E values (Tables S1-S3). Second-order rate
cat/2
1
2
+
constants were measured from plots of the pseudo first-order rate constants versus [DMF(H) ]
EQ
60
–1 –1
(Figures S7-S9) and are listed in Table 2. A large k value of 220,000 M s was measured using
1
+
+
–1 –
unbuffered DMF(H) , and was found to decrease by half using 1:3 DMF:DMF(H) (k = 125,000 M s
1
1
+
–1 –1
)
and over an order of magnitude with 1:1 DMF:DMF(H) (k = 12,000 M s ). This finding indicates
1
that the protonated Ni(I) intermediate is readily deprotonated in the presence of added base, leading to a
slower net rate of protonation. In contrast to k , a three-fold increase in k is observed upon moving from
1
2
+
+
–1 –1
unbuffered DMF(H) to 1:1 DMF:DMF(H) . In the presence of a 1:1 buffer, k (12,000 M s ) is only
1
–1
–1
two-fold larger than k2 (7,400 M s ), which implies that both steps contribute to the observed
–1 –1
catalytic rate since kobs (2,300 M s ) is smaller than either of the individual rate constants. Thus, there
is a tradeoff for the ECEC pathway, where added base facilitates the second catalytic step but hinders
the first.
–1 –1
Table 2. Second order rate constants (M s ) for electrocatalytic hydrogen production by 1 measured
by Ecat/2 analysis.
+ a
+
+
BH
1:3 B:BH
125,000
2,800
1:1 B:BH
12,000
7,400
ECEC k1
220,000
2,400
k2
kobs
2,000
2,100
2,300
EECC kobs
2,600
3,600
5,700
a
Rate constants measured from the linear region prior to acid saturation.
Unlike the ECEC pathway, an accurate Ecat/2 for the EECC path of 1 cannot be identified under
these conditions, due to the transition from an ECEC to EECC mechanism. However, an approximate
kinetic analysis of the EECC pathway indicates that the second chemical step is rate-determining for
catalysis (see Supporting Information). A similar conclusion was reached by Dempsey et al. in studies
61
of 1 using a much weaker acid, anilinium (pK =10.6), where catalysis through the ECEC pathway is
a
2
9
negligible. Therefore, kobs can be approximated to be equal to k for the EECC pathway of 1.
2
1
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FOWA of ECEC Pathway
FOWA was performed on 1 using E°′ = –0.83 V (the potential of the Ni(II/I) couple) and i/ip
values up to 3% of the maximum i /i of the ECEC pathway. The ratio of the k values determined from
cat
p
1
+
Ecat/2 analysis and FOWA was plotted versus [DMF(H) ] (Figure 9a). Under buffered conditions, the
EQ
0
1
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0
k1 values measured from Ecat/2 analysis were 1.5-3.0 times larger than the values measured by FOWA.
This trend is opposite to that expected from simulations, and suggests that an unexpected phenomenon is
occurring at the foot of the wave.
+
Figure 9. a) Plot of the ratio of k obtained from E
analysis and FOWA versus [DMF(H) ] , and b)
1
cat/2
EQ
+
plot of k versus the percent of i /i used in the FOWA for [DMF(H) ] = 57 mM with 1:1 DMF:
1
+
cat
p
EQ
DMF(H) .
2
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The behavior at the foot of the wave was further explored by examining the dependence of k on
1
+
the percent of i /i used for FOWA of 1 in the presence of 1:1 DMF:DMF(H) (Figure 9b).
cat
p
4
5
6
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9
1
1
1
1
1
1
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1
1
1
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5
6
Surprisingly, the value of k was found to increase linearly as the percentage of i /i used in FOWA was
1
cat p
increased from 3% to 20%, while further increases in the percentage of i /i led to a decrease in k . This
cat
p
1
trend again contradicts the simulations, which afforded larger k values as less of the wave was used in
1
0
1
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3
4
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8
9
0
1
2
3
4
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7
8
9
0
1
2
3
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9
0
1
2
3
4
5
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7
8
9
0
1
2
3
4
5
6
7
8
9
0
FOWA (Figure 5). A possible cause of this phenomenon is that the reduction potential of the protonated
Ni(I) intermediate lies near the foot of the wave, leading to an increase in current as more of the
intermediate is reduced. This hypothesis was tested through simulation of a model ECEC mechanism
having E°′ = –0.83 V for the Ni(II/I) couple and E°′ = –0.75 V for reduction of the protonated Ni(I)
1
2
intermediate. FOWA on the simulated voltammograms of this model led to a qualitative reproduction of
the behavior shown in Figure 9b, thus providing support for the hypothesis (Figures S12-S14).
Additionally, FOWA can be used to estimate the reduction potential of the protonated Ni(I)
intermediate of the ECEC mechanism. This is accomplished by converting the current axis in Figure 9b
into a potential axis, so that the k values obtained from FOWA are plotted versus the most negative
1
potential used in FOWA. The reduction potential of the protonated Ni(I) intermediate is approximately
equal to the potential providing the largest k value by FOWA. Simulations can be used to show that this
1
approximation is most appropriate when the kinetic parameter λ is small, i.e. k is not much larger than
1
+
k (Figures S15-S16). These conditions are met for 1 when using 1:1 DMF:DMF(H) as the proton
2
source, and the potential analysis provides a value of –0.79 V for the protonated Ni(I) intermediate
(Figure S17).
+
Thus far, FOWA of 1 has only been discussed using DMF:DMF(H) mixtures as the proton
+
source. When unbuffered DMF(H) is employed, the pseudo first-order k values obtained from FOWA
1
are larger than those obtained from Ecat/2 analysis at acid concentrations greater than 30 mM (Figure 9a,
+
blue diamonds). Plots of k measured from FOWA versus concentration of DMF(H) show two distinct
1
linear regions at low and high acid concentrations (Figures S18-S19). We interpret these data to mean
+
that at the foot of the catalytic wave, increasing the concentration of unbuffered DMF(H) causes 1 to
transition from an ECEC mechanism to a CECE mechanism involving reduction of a protonated Ni(II)
species. However, the CECE pathway does not appear to be operative at more negative potentials, since
the k values measured by E
analysis showed a first-order dependence on acid over the entire
1
cat/2
+
concentration range of DMF(H) . For this reason, it is likely that the CECE pathway is only operative at
2
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the foot of the wave, and that catalytic turnover quickly generates enough DMF in the diffusion layer to
deprotonate any protonated Ni(II) species that may be present.
Discussion
0
1
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3
4
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7
8
9
0
Electrocatalytic Mechanism
The proposed electrocatalytic network for production of H by 1 is shown in Scheme 1.
2
Protonation of the catalytic intermediates at the pendant amines forms endo and exo isomers. In the
nomenclature of Scheme 1, endo and exo protonation isomers are designated by e and x, and the formal
oxidation state of nickel is given in parentheses. The k and k rate constants for both the ECEC and
1
2
EECC pathways are global rate constants comprising multiple chemical steps. For the ECEC pathway,
both endo- and exo-protonation of Ni(I) can potentially contribute to k (solid green arrows), while
1
endo- and exo-protonation of Ni(0) can affect k of the EECC pathway (dashed green arrows). The
1
ECEC and EECC pathways share a common set of steps corresponding to k , namely protonation to
2
form doubly protonated Ni(0) species and subsequent isomerization to the ee(0) isomer (purple arrows).
In principal elimination of H from the ee(0) isomer could also contribute to the measured k values.
2
2
5
–1
25,
However, turnover frequencies as high as 5 × 10 s have been measured for 1 in protic ionic liquids,
2
6
indicating that H elimination is much faster than the turnover frequencies observed under the present
2
–
1
conditions (< 500 s ).
Scheme 1. Proposed catalytic cycle for electrocatalytic production of H by 1. The Ph groups on P and
2
N have been omitted for clarity.
2
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3
Despite being unsuitable for accurate kinetic measurements under these conditions, FOWA
afforded valuable mechanistic insight on the intermediate(s) formed under electrocatalytic conditions.
Using FOWA, a reduction potential of –0.79 V was estimated for the singly protonated Ni(I)
intermediate. This potential is 250 mV more positive than the Ni(I/0) couple of 1 (E1/2 = –1.03 V), and
comparisons to related complexes suggest that this species is the exo-protonated isomer, x(I), rather than
4
5
6
7
8
9
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
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5
5
5
5
5
5
5
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0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
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5
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7
8
9
0
1
2
3
4
5
6
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8
9
0
I
tBu
Bn
2 2
+
the endo-protonated isomer, e(I). Recent studies on Ni (P N ) demonstrated that reduction of e(I)
2
62
occurs approximately 400 mV more positive than the corresponding Ni(I/0) couple. Applying this
relationship to 1 allows one to estimate a reduction potential of –0.63 V for the e(I) isomer of 1, which is
approximately 100 mV more positive than the foot-of-the-wave region observed for 1 with 1:1
+
DMF:DMF(H) and implies the e(I) isomer is not significantly populated under these conditions. Mono-
exo Ni(I) or Ni(0) species have not been observed experimentally; however, the xx(0) isomer of the
0
tBu
Bn
2+
related complex Ni (P 2N 2-H)2 displays a quasi-reversible oxidation that is 680 mV positive of the
6
3
Ni(I/0) couple as a result of electrostatic and inductive effects. A reasonable estimate of the singly-
protonated x(0) complex would be that it is oxidized 340 mV positive of the Ni(I/0) couple, which is
close to the experimentally observed difference of 240 mV for 1, providing support for this structural
assignment.
For the ECEC pathway, FOWA analysis indicates that exo-protonation of Ni(I) is kinetically
preferred over endo-protonation, as observed in prior spectroscopic studies of other doubly-protonated
0
R
R′
2+
28, 32
Ni (P N -H) complexes.
This finding differs from a recent computational microkinetics study
2
2
2
–1
of 1, which estimated the free-energy barrier for protonation of Ni(I) in an endo position is 2 kcal mol
22
lower than for the exo-position. Despite this minor discrepancy, both the microkinetics study and the
present findings demonstrate that exo-protonation at Ni(I) impedes catalytic turnover due to
accumulation of exo-protonated Ni(0) isomers in the diffusion layer. This conclusion is supported by
+
the three-fold increase in k for the ECEC pathway upon switching from DMF(H) to 1:1 DMF:
2
+
DMF(H) as the acid, corresponding to an increased rate of exo to endo isomerization of the doubly-
protonated Ni(0) intermediates in the presence of added base.
A k value for the EECC pathway could not be measured due to interference from the preceding
1
ECEC pathway, but was estimated to be significantly larger than kobs (see Supporting Information). In a
complementary study of 1 using anilinium as the proton source, Dempsey et al. measured a k value (6.5
1
6
–1 –1
–1 –1
×
10 M s ) that is approximately five orders of magnitude larger than k (~ 50 M s ) for the
obs
2
9
EECC pathway. Information on the endo versus exo regioselectivity of Ni(0) protonation cannot be
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obtained from the magnitude of k , but can be inferred from comparison of the k values measured for
1
2
the ECEC and EECC pathways. While the catalytic steps corresponding to k appear to be identical for
2
both mechanisms, the measured k values could be significantly different if Ni(0) has a greater
2
probability to be protonated in an endo position than Ni(I). Comparison of the measured k values,
2
approximated as kobs for the EECC pathway, does not reveal a significant difference between the two
mechanisms (Table 2). Therefore the first chemical step of the EECC pathway for 1 is most likely
exo-protonation of Ni(0), similar to the ECEC pathway in which Ni(I) is protonated in an exo position.
0
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Catalytic Tafel Plots
In general terms, overpotential (η) for the electrocatalytic production of H is the difference
2
+
between the potential of catalysis (E) and the thermodynamic potential of the H /H couple (E ) under
2
H+
the specific reaction conditions (equations 13-14). The potential at which catalysis occurs for molecular
electrocatalysts is traditionally reported using Ecat/2, where the turnover frequency (TOF) is equal to
4
6
0
.5 × k . FOWA has recently been suggested as an improved method for analyzing η in molecular
obs
51, 52, 64
electrocatalysis.
The FOWA equations can be adapted to obtain a “catalytic Tafel plot” (equation
1
5), where the TOF is described as a function of the amount of catalyst that is reduced at a given
overpotential. The turnover frequency at zero overpotential (TOF , equation 16) is obtained when η = 0
o
in equation 15. For a given catalyst, TOF is no more significant than TOF at E
since the two are
o
cat/2
linked on the overpotential axis by a common slope of f/ln10. However, use of TOF does simplify the
o
comparison between different catalysts, as the TOF–η landscape is reduced to a single dimension (TOF)
6
4
at η = 0.
휂 = 퐸퐻
ꢚ
− 퐸
(13)
(14)
ꢙ
푅ꢛ 퐾 [퐵ꢜ ]
푎
퐸퐻
ꢚ
= 퐸°퐻
ꢚ
+
푙푛
푛퐹
푃 [퐵]
퐻
ꢝ
푘obs
TOꢞ =
(15)
1
퐻ꢚ
+ expꢎ푓ꢏ퐸 − 휂 − 퐸푐푎푡/ꢋꢐꢑ
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푘obs
TOꢞ =
(16)
o
3
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1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
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3
3
4
4
4
4
4
4
4
4
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5
5
5
5
5
5
5
5
5
5
6
1
+ 푒푥ꢍꢎ푓ꢏ퐸퐻 − 퐸푐푎푡/ꢋꢐꢑ
ꢚ
6
4
Artero and Savéant reported catalytic Tafel plots for 1 and several related complexes using
23,
kinetic data from the literature that did not account for the competing ECEC and EECC mechanisms.
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
2
4
Here we examine the TOF–η plots for the different mechanisms of 1 in the presence of 185 mM
+
DMF(H) , which provides the limiting k values for this acid (Figure 8). In keeping with common
obs
+
46
practice, EH+ is defined by assuming [DMF(H) ] = [DMF] and P = 1 atm. A value of E = –0.50 V
H2
H+
6
4
58
was used by Artero and Savéant based on a method for estimating E for acids that homoconjugate.
H+
However, we use the more accurate value of EH+ = –0.38 V, which was measured directly for 1:1
+
DMF:DMF(H) using equilibrium open circuit potential measurements that inherently account for
5
9
homoconjugation. Values of Ecat/2 for the ECEC (–0.76 V) and EECC (–0.96 V) pathways were
measured from the two maxima observed in the d(i)/dt–E trace (illustrated in Figure 7b), and the
resulting Tafel plots are shown in Figure 10.
+
Figure 10. Catalytic Tafel Plots for 1 in the presence of 185 mM DMF(H) using E = –0.38 V.
H+
–
1
–1
ECEC: E
kobs = 480 s .
= –0.76 V, kobs = 270 s ; EECC: E
= –0.96 V, kobs = 480 s ; global: E
= –0.79 V,
cat/2
cat/2
cat/2
–
1
The transition from the ECEC pathway to the EECC pathway is accompanied by an increase in
both kobs and in the overpotential, as the EECC pathway occurs at more negative potentials than the
ECEC path. TOF for the two mechanisms of 1 differ by about three orders of magnitude, indicating that
o
the ECEC pathway is more efficient than the EECC pathway. The kinetic analysis described above
reveals that the difference in kobs between the two mechanisms is due primarily to the greater rate of exo-
protonation of Ni(0) compared to Ni(I). This trend is most likely due to an increase in the basicity of the
2
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pendant amines upon reduction from Ni(I) to Ni(0). DFT calculations support this interpretation, as the
2
2
computed pK of x(0) (10.9) is greater than x(I) (5.5). Therefore, the TOF of 1 is fundamentally
a
connected to η by the thermodynamic properties of the intermediates along the ECEC and EECC
pathways.
0
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A third Tafel plot (Figure 10, red dots) was generated using the global analysis that is
traditionally reported for 1 and related complexes. In the global analysis, kobs is measured from i and
cat
corresponds to the EECC mechanism, and Ecat/2 is measured at half of i , providing a potential where
cat
both the ECEC and EECC mechanisms are occurring. The catalytic Tafel plot generated from the global
analysis is nearly identical to the plot for ECEC mechanism (Figure 10), which suggests that it is
R
R' 2+
2 2
reasonable to generate catalytic Tafel plots for other Ni(P N ) complexes using previously reported
2
data.
Benchmarking studies are ideally conducted under identical reaction conditions to obtain the
6
5
most meaningful comparisons of different catalysts. This presents a challenge for comparison of
molecular electrocatalysts since a wide range of reaction conditions are commonly employed. Artero
and Savéant have proposed reporting catalytic Tafel plots at 1 M acid concentration as a means to
6
4
improve the comparison of molecular H production electrocatalysts, and several catalyst studies have
2
6
6-68
adopted this approach.
In principle, this convention is a good idea, but unfortunately its
implementation leads to the use of several assumptions that might limit the accuracy of data reported in
this manner. These considerations are examined below using 1 as an illustrative example, with data
tabulated in Table 3 and catalytic Tafel plots displayed in Figure 11.
Kinetic data for H production is often measured at low concentrations of acid (< 0.1 M) and
2
64
extrapolated to 1 M acid. This practice can be problematic since it precludes the possibility of
saturation kinetics that would limit the TOF at acid concentrations less than 1 M. As an example, the
+
TOF for 1 is first-order in [DMF(H) ] at low acid concentrations, but becomes independent of the acid
+
concentration at [DMF(H) ] ~ 0.19 M. Extrapolation from the low acid concentration regime to 1 M
+
–1
–1
DMF(H) provides a TOF of 2000 s , which is 7× larger than the maximum TOF of 270 s observed in
the acid-saturation regime. This difference in rates also translates to the TOF values measured from a
o
catalytic Tafel analysis. Therefore, the catalytic performance of 1 is overestimated by extrapolating the
TOF from low acid concentrations to 1 M acid. Similar effects could be important for other catalysts,
but are typically not reported.
2
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+
Table 3. Parameters for generating catalytic Tafel plots for the ECEC mechanism of 1 at 1 M H .
4
5
6
7
8
9
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
+
+
a
Conditions [DMF(H) ]o [DMF]o [DMF(H) ]
[DMF]EQ
EH+
(V)
Ecat/2
(V)
TOF
log(TOFo)
EQ
-
1
(M)
(M)
0
(M)
0.19
1.0
(M)
0
(s )
b
b
c
acid only
0.19
-0.38
-0.38
-0.19
-0.38
-0.28
-0.76
-0.76
-0.76
-0.78
-0.78
-0.81
270
2000
2000
1400
1400
300
-4.0
-3.2
-6.3
-3.7
-5.3
-4.7
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
.0
0
0
1.0
1.0
0
1.0
0
b
d
1
:3 buffer
0.33
0.33
1.0
0.66
0.66
0.13
0.01
0.01
0.13
1
.0
1:1 buffer
1.0
-0.38
a
–1 –1
+
b
c
Determined from kobs (M s , Table 2) and [DMF(H) ] . Using the value for 1:1 buffer as an estimate.
EQ
d
Open circuit value determined according to method of Roberts and Bullock (reference 59).
Obtained from
+
substituting [DMF(H) ] and [DMF]EQ into equation 14 assuming P = 1 atm.
EQ
H2
Another concern is that the value used for EH+ frequently does not reflect the actual solution
conditions in the electrochemical diffusion layer. Molecular electrocatalysts for hydrogen production are
commonly studied in organic solvents using an organic acid with no added conjugate base and no
dihydrogen. The conventional approach for determining EH+ is to assume that half of the acid substrate
is consumed at Ecat/2, which permits ready estimation of EH+ from E°H+ and the pK of the acid since
a
+
46, 58
[
BH ] = [B] and P = 1 atm (i.e. a solution saturated in H2).
However, this assumption does not
H2
accurately represent the conditions present at the foot-of-the-wave or for a canonical S-shaped catalytic
5
1,
wave, since consumption of acid within the diffusion layer is minimal in each of these kinetic regimes.
6
9
The errors introduced by the assumption of a 1:1 buffer could be minimal if catalysis is unaffected by
either H or conjugate base, but this is not typically reported for most catalysts.
2
The findings reported here for 1 can be used to highlight several ways that a catalytic Tafel plot
might be affected by different ratios of acid and base. Tafel plots for the ECEC mechanism of 1 at 1 M
+
acid were generated for the different ratios of DMF:DMF(H) using the common approximation that
EH+ is identical to the value for a 1:1 buffer under all conditions (Figure 11). The Tafel plot for
+
unbuffered DMF(H) (solid blue diamonds) was obtained by extrapolation from low acid
concentrations, as described above. Some of the monomeric acid is trapped in the homoconjugate pair
+
under buffered conditions, resulting in a concentration of DMF(H) that is less than 1 M (Table 3).
+
Consequently, the catalytic Tafel plots for 1:3 DMF:DMF(H) (solid red squares) and 1:1
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+
DMF:DMF(H) (solid green circles) display maximum TOF values that are lower than observed for
+
unbuffered DMF(H) . Additionally, E
for the ECEC pathway shifts to more negative potentials in the
cat/2
presence of base, which causes a shift in the entire Tafel plot to higher η under buffered conditions. The
net result of these effects, when using a common value of E , is that TOF decreases by approximately
H+
o
+
+
30-fold upon moving from 1 M of unbuffered DMF(H) to 1:1 DMF:DMF(H) .
0
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0
+
Figure 11. Catalytic Tafel plots for the ECEC mechanism of 1 with different ratios of DMF:DMF(H)
+
(
1 M H ) and different values of E .
H+
Since the presence of base clearly affects the kinetics of H production by 1, more accurate
2
determinations of E will provide more meaningful Tafel plots. A value of P = 1 atm can be assumed
H+
H2
since the catalytic response of 1 is known to be unaffected by performing catalysis under an atmosphere
59
+
+
of H2. Therefore EH+ for 1:1 DMF:DMF(H) remains unchanged, and E for 1:3 DMF:DMF(H) at
H+
+
1 M H is readily determined to be –0.28 V using equation 14 and the concentrations of monomeric acid
+
and base. A value of EH+ for unbuffered DMF(H) cannot be estimated from equation 14 due to the
absence of conjugate base. However, open circuit potential measurements performed on acetonitrile
+
solutions of unbuffered DMF(H) under an atmosphere of H were found to display a logarithmic
2
+
dependence on the concentration of DMF(H) , which allows a value of E = –0.19 V to be estimated
H+
+
59
for 1 M DMF(H) .
+
These corrections to EH+ afford revised Tafel plots for 1:3 DMF:DMF(H) (open red squares)
+
and unbuffered DMF(H) (open blue diamonds) as shown in Figure 11. Notably, accurate determination
of EH+ causes a reversal in the ordering of TOF for the different buffer conditions, with TOF
o
o
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increasing approximately 40-fold by switching from unbuffered DMF(H) to 1:1 DMF DMF:DMF(H) .
Perhaps most significant is the observation that the TOF for 1 is overestimated by three orders of
o
magnitude when using the conventional assumption of buffered conditions for determination of E with
H+
+
catalytic data obtained using unbuffered DMF(H) . These findings suggest that greater care is required
in reporting accurate TOF values for meaningful catalyst benchmarking.
o
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Conclusions
We have reported a detailed kinetic analysis on electrocatalytic proton reduction by
Ph
Ph 2+
2 2
Ni(P N ) (1) using recent methodologies developed by Costentin and Savéant. The presence of
2
competing ECEC and EECC mechanisms complicates the kinetic analysis, but with the aid of digital
simulations, a strategy was developed to measure the catalytic rate constant (k ) for each of the two
obs
pathways using the first-derivative plot of the voltammograms. Notably, the EECC pathway results in a
larger kobs than the ECEC pathway due to an increased rate of protonation of Ni(0) over Ni(I). FOWA of
1
did not afford accurate rate constants due to competing side-phenomena at the foot-of-the-wave, but
allowed for an estimate for the reduction potential of the protonated Ni(I) intermediate, corresponding to
R
R′ 2+
2 2
the second electron transfer in the ECEC mechanism. Comparison to other Ni(P N ) derivatives
2
suggests the Ni(I) intermediate is protonated in an exo-position, which is known to be detrimental to
catalysis.
The methods detailed here could potentially be implemented in the kinetic analysis of other
electrocatalysts capable of operating by multiple mechanisms. Proper kinetic analysis requires careful
scrutiny of transitory regions between mechanisms, as well as the strengths and limitations of the
electrochemical methods employed for the kinetic analysis. The findings in our kinetic analysis of 1, a
catalyst with a well-understood mechanism, provide an initial foundation for analysis of other
electrocatalysts displaying complex mechanisms.
Experimental
Materials
Acetonitrile (Alfa-Aesar, anhydrous, amine-free) and dimethylformamide (Burdick & Jackson)
were purified by sparging with N and passage through neutral alumina. Tetrabutylammonium
2
2
9
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