of 27
JOUL, Volume
2
Supplemental Information
Trapping an Iron(VI) Water-Splitting
Intermediate in Nonaqueous Media
Bryan M. Hunter, Niklas B. Thompson, Astrid M. Müller, George R. Rossman, Michael G.
Hill, Jay R. Winkler, and Harry B. Gray
S1: Tafel Behavior
Figure S1
: Tafel plot of [NiFe]
-
LDH on a rotated disk (900 RPM). (Top)
1% 1
M
aqueous KOH in acetonitrile
; (bottom)
1
M
aqueous KOH
. The y
-
axis represents
arbitrary potential, since the overpotential
in acetonitrile is undefined. The x
-
axis is the
logarithm of the current density. The 1%
1
M
aqueous KOH in acetonitrile plot curves
upward at high applied potential due to mass transport limitation at low substrate
concentration.
The units for
j
are mA/cm
2
.
Table S1
: Least
-
squares fitting parameters for Tafel behavior of [NiFe]
-
LDH in 1
M
aqueous KOH.
-1
-0.5
0
0.5
1
Applied Potential
log(
j
)
100 mV
Y
=
M0
+
M1*X
Upper
95%
Lower
95%
P
Value
t Value
Std.
Error
Value
477.1
475.95
5.9385e-195
1634.1
0.29161
476.52
M0
60.505
57.792
1.7499e-85
86.686
0.68233
59.149
M1
Goodness of Fit
0.99433
R
0.98855
Adj.
R
2
2.7333
Std.
Error
7514.5
F Value
1.7499e-85
P
Value
S2: Kinetics Simulations
We have simulated the kinetics of a compressed version of the
mechanism
illustrated in Fig. 5
. We assume that two electrons and two protons are removed from the
catalyst in the first step to produce the highly oxidized intermediate; two hydroxide ions
react with the oxidized catalyst in the second step to generate oxygen. When ample
hydroxide ion
is present as in 1
M
KOH, the population of the intermediate is very low
and would be difficult to detect in
operando
measurements. When H
2
O and HO
concentrations are restricted as in acetonitrile solvent, oxygen production is inhibited and
the population
of the oxidized catalyst intermediate increases substantially to the point
that it would be spectroscopically detectable. The simulation results closely mirror our
experimental observations.
A compressed version of the mechanism outline in Figure
5
is given by the following
reaction steps, where CAT is the resting form of the electrocatalyst and CAT
ox
is the
oxidized form in which 2 electrons, 2 protons, and 1 water molecule have been removed.
The two reaction steps defined by rate constants
k
1a
and
k
1b
differ only in the identity of
the proton acceptor (HO
or H
2
O).
Under the assumption of instantaneous mixing of electrode products with the bulk
solution, the c
onversion rates of all reagents are given by following differential
equations:
The differential equations were solved numerically using the MATLAB function
ide23s
(for stiff equations, Set 1), and
ide23
(Set 2). The accuracy of the numerical solutions was
-
-
+
+
¾
¾
®
¾
+
e
a
k
4
CAT
O
H
3
CAT
HO
2
ox
2
1
-
+
+
+
¾
¾
®
¾
+
e
b
k
4
CAT
O
H
2
CAT
O
H
ox
3
2
1
CAT
O
HO
2
CAT
O
H
2
ox
2
2
+
¾
®
¾
+
+
-
k
[
]
18
3
3
2
2
3
2
10
25
.
3
O
H
HO
O
H
O
H
2
3
3
-
-
-
+
́
=
=
=
+
¾
¾
®
¬
-
k
k
K
K
w
eq
k
k
]
O
H
[
]
[HO
]
[CAT
]
O
H
][
CAT
[
]
[HO
]
CAT
[
]
CAT
[
2
2
ox
2
2
1
2
1
2
-
-
+
-
-
=
÷
ø
ö
ç
è
æ
k
k
k
s
cm
mol
dt
d
b
a
]
O
H
[
]
[HO
]
[CAT
]
O
H
][
CAT
[
]
[HO
]
CAT
[
]
CAT
[
2
2
ox
2
2
1
2
1
2
ox
-
-
-
+
=
÷
ø
ö
ç
è
æ
k
k
k
s
cm
mol
dt
d
b
a
]
HO
][
O
H
[
]
O
H
[
]
O
H
[
]
HO
][
CAT
[
10
2
]
HO
][
CAT
[
10
2
]
HO
[
3
3
2
2
3
2
2
ox
2
3
2
1
3
-
+
-
-
-
-
-
-
-
+
́
-
́
-
=
÷
÷
ø
ö
ç
ç
è
æ
k
k
k
k
s
L
mol
dt
d
a
]
HO
][
O
H
[
2
]
O
H
[
2
]
O
H
[
]
HO
][
CAT
[
10
1
]
O
H
][
CAT
[
10
1
]
HO
][
CAT
[
10
3
]
O
H
[
3
3
2
2
3
2
2
ox
2
3
2
1
3
2
1
3
2
-
+
-
-
-
-
-
-
+
-
́
-
́
-
́
=
÷
÷
ø
ö
ç
ç
è
æ
k
k
k
k
k
s
L
mol
dt
d
b
a
]
HO
][
O
H
[
]
O
H
[
]
O
H
][
CAT
[
10
2
]
O
H
[
3
3
2
2
3
2
1
3
3
-
+
-
-
+
-
+
́
=
÷
÷
ø
ö
ç
ç
è
æ
k
k
k
s
L
mol
dt
d
b
]
O
H
[
]
HO
][
CAT
[
10
1
]
O
[
2
2
ox
2
3
2
-
-
́
=
÷
÷
ø
ö
ç
ç
è
æ
k
s
L
mol
dt
d
tested by numerically differentiating the six time
-
dependent concentration profiles for
each reagent and comparing those to the combinations of rate constants and
concentrations defined by the different
ial equations.
Using an estimated catalyst surface area of 193 m
2
g
1
and assuming a 20% population of
Fe centers, the initial catalysts concentration was taken to be [CAT]
0
= 10
9
mol cm
2
.
The initial concentrations of oxidized catalyst, [CAT
ox
]
0
, and o
xygen, [O
2
], were set
equal to zero. Two sets of initial substrate concentration conditions were considered. Set
1 corresponds to aqueous conditions: [H
2
O]
0
= 55.5 M; [HO
]
0
= 1 M; [H
3
O
+
]
0
= 10
14
M. Set 2 corresponds to nonaqueous electrolyte conditions:
[H
2
O]
0
= 5
́
10
3
M; [HO
]
0
= 9
́
10
12
M; [H
3
O
+
]
0
= 9
́
10
12
M.
The rate constants were given the following values:
k
1a
= 3
́
10
6
M
2
s
1
; defined to produce O
2
at a rate of 2.6
́
10
6
M
s
1
k
1b
= 1
́
10
2
M
1
s
1
; defined to not contribute to O
2
production under aqueous pH
14 conditions (set 1)
k
2
= 1
́
10
8
M
3
s
1
; defined to be large enough relative to
k
1a
so that the steady
state ratio of [CAT
ox
]:[CAT] is less than 10
3
under aqueous pH 14
conditions (set 1)
k
3
= 1
́
10
10
M
1
s
1
; assumed to be
diffusion controlled
k
3
= 3.25
́
10
8
M
1
s
1
; defined by
k
3
and
K
eq
With these parameter sets, the simulations produce the time
-
dependent concentration
profiles and [CAT
ox
]
:[CAT] ratios shown in Figure S2
(set 1 conditions) and Figure S3
(set 2 conditions). Under aqueous pH 14 conditions (set 1), O
2
is produced at the
specified rate and the [CAT
ox
]:[CAT] ratio remains less than 10
3
. Under nonaqueous
conditions (set 2), the concentration of CAT
ox
builds up over time and the
[CAT
ox
]:[CAT]
ratio becomes greater than 1 after 1 s.
The simulations are not intended to accurately reproduce the experimental
electrochemical kinetics. Rather, they are meant to sho
w that the mechanism in Figure 5
is plausible and can lead to the general be
havior fou
nd experimentally. In
particular, the
simulations demonstrate that while no oxidized
intermediate would be detected d
ur
ing
turnover conditions in aqueous alkaline solution, the intermediate would be expected to
build up when a nonaqueous
electrolyte is employed.
10
-3
10
-2
10
-1
10
0
10
1
10
-20
10
-15
10
-10
10
-5
10
0
10
5
Seconds
Concentration
Set 1, Aqueous, pH 14
2.6 x 10
-6
M
[CAT] mol cm
-2
[CAT
ox
] mol cm
-2
[HO
-
] M
[H
2
O] M
[H
3
O
+
] M
[O
2
] M
10
-3
10
-2
10
-1
10
0
10
1
10
-6
10
-5
10
-4
10
-3
[CAT
ox
]/[CAT]
Seconds
Figure S2.
Simulated concentration versus time profiles generated by numerical integration
of differential equations listed in the supporting text. Initial conditions were aqueous pH 14
electrolyte (Set 1).
Figure S3.
Simul
ated concentration versus time profiles generated by numerical integration
of differential equations listed in the supporting text. Initial conditions were nonaqueous
electrolyte (Set 2).
S3:
Estimation of the Standard Electrode Potential for the Fe(IV)/
Fe(III) Couple in “Dry”
Acetonitrile
Fe
IV
(O)
(s)
+ H
+
(aq)
e
-
Fe
III
(OH)
(s)
(
Equation S1
.
)
The standard elect
rode potential for Equation S1 in terms of the free energies of
formation of
Fe
IV
(O)
(s)
(
x
)and
Fe
III
(OH)
(s)
(
y
) can be estimated from
thermodynamic
cycle
s
as shown in Schemes S1 and S2. Here, “dry” is taken to mean the condition where
[H
2
O] approaches the limit of a dilute acetonitrile solution of H
2
O, as per Matsubara (ref.
17
).
A
ll values taken from reference 17
unless otherwise stated.
Scheme
S
1
. A thermodynamic cycle to estimate the potential for equation S1 at standard
conditions (1
M
H
+
(aq)
) and 298 K.
Fe
IV
(O)
(s)
+ H
+
(aq)
e
-
Fe
III
(OH)
(s)
r
G
aq
°
kJ/mol
Fe
IV
(O)
(s)
Fe
(s)
+ 1/2O
2(g)
-
f
G
FeO
°
-
x
Fe
(s)
+ 1/2O
2(g)
+ 1/2H
2(g)
Fe
III
(OH)
(s)
f
G
FeOH
°
y
H
+
(aq)
H
+
(sol)
tr
aq
à
CH3CN
G
1
°
46.2
H
+
(sol)
+ e
-
1/2H
2(g)
r
G
1
°
2.5
(
vs
Fc
+
/Fc)
Scheme
S
2
. A thermodynamic cycle to estimate the potential for equation S1 in “dry”
acetonitrile at 298 K.
As in
reference C, the subscripts “(g)”, “(aq)”, “(sol)”, and “(sol,
x
)” denote substances in gas, aqueous solution, acetonitrile solution, and acetonitrile
solution phases, whose activities are expressed in units of pressure (bar), molarity (M),
molarity (M), a
nd mole fraction (
x
), respectively. Matsubara notes that “H
2
O
(sol, x
à
0)
denotes H
2
O at the limit of a dilute acetonitrile solution of H
2
O where the standard state
for H
2
O is taken to be unit mole fraction of H
2
O (i.e., pure liquid water).”
Fe
IV
(O)
(s)
+ H
+
(aq)
e
-
Fe
III
(OH)
(s)
r
G
acn
°
kJ/mol
3H
+
(sol)
+ 3e
-
3/2H
2(g)
r
G
1
°
2.5(3)
(Fc
+
/Fc)
H
2(g)
+ 1/2O
2(g)
H
2
O
(g)
r
G
2
°
-
228.582
H
2
O
(g)
H
2
O
(sol,x
à
0)
tr
g
à
CH3CN
G
2
°
-
3.2
2H
2
O
(sol,x
à
0)
2H
+
(sol)
+ 2OH
-
(sol)
G
w
°
79.9(2)
2OH
-
(sol)
1/2O
2(g)
+ H
2
O
(sol
,x
à
0
)
+ 2e
-
r
G
ox
°
199
a
Fe
IV
(O)
(s)
Fe
(s)
+ 1/2O
2(g)
-
f
G
FeO
°
-
x
Fe
(s)
+1/2O
2(g)
+ 1/2H
2(g)
Fe
III
(OH)
(s)
f
G
FeOH
°
y
a
Calculated from
E
° =
-
0.401
vs
NHE [
Dean, J. A., & Lange, N. A. (1999).
Lange's
handbook of chemistry
. New York: McGraw
-
Hill.
]
referenced to Fc
+
/Fc [
Pavlishchuk, V.
V., Addison, A. W. Conversion constants for redox potentials measured versus different
reference electrodes in acetonitrile solutions at 25°C.
Inorg. Chim. Acta
1
, 97
-
102
(2000)
] and converted to free energy by
G
° =
-
nF
E
° for n = 2.
Following Schemes
S
1 and
S
2, the standard electrode potentials for Equation S1 are:
r
G
aq
°=
-
(
-
f
G
FeO
°+ ∆
f
G
FeOH
°+ ∆
tr
aq
à
CH3CN
G
1
°+ ∆
r
G
1
°
)
F
=
0
.
505
,
where
=
>
?
@
A
.
r
G
acn
°
=
-
(3
r
G
1
°
+
r
G
2
°
+
tr
g
à
CH3CN
G
2
°
+
2
G
w
°
+
r
G
ox
°
-
f
G
FeO
°
+
f
G
FeOH
°
)
F
=
+
1
.
39
.
Thus, the potential of the Fe(IV)/Fe(III) couple is shifted positive by over 1.5V in
the theoretical limit of “dry” acetonitrile.