Supplementary Material on
Kinetically Induced Irreversibility
in Electro-oxidation and Reduction
of Pt surface
Ryosuke Jinnouchi, Kensaku Kodama, Takahisa Suzuki and Yu Morimoto
Toyota Central R&D Labs., Inc.
41-1 Yokomichi Nagakute, Aichi 480-1192, Japan
1
A. Experimental methods to obtain Fig. 1
Sample preparations
A Pt (111) surfaced single crystal (99.99%, 0.196 cm2, MaTecK) and a Pt
polycrystalline (0.283 cm2) disks were annealed using electromagnetic inductive heating
for 10 minutes at approximately 1300 K in the flow of a mixture of H2 and Ar (3 % H2,
Taiyo Nippon Sanso, the purity of each gas: H2: 99.99999%, Ar: 99.999%). The annealed
specimens were cooled slowly to room temperature in the flow of the gas mixture.
Afterward the Pt (111) and polycrystalline surfaces were covered with water (Milli-Q,
18.2 MΩ) and then immersed in 0.1 M HClO4 (MERCK, Suprapur) saturated with Ar
(Taiyo Nippon Sanso, 99.999%) at 0.07 V.
The Pt/C electrode was prepared by depositing and then drying the catalyst ink of
Pt/Vulcan (TKK, TEC10V50E, 50wt%Pt) dispersed in 24vol% isopropanol aqueous
solution on a glassy carbon (0.246cm2, TOKAI CARBON) with the total amount of
1.1μgPt, and was treated with potential cycling from 0.07 V to 1.2 V (RHE) for cleaning
before the electrochemical measurements.
Electrochemical procedures
For Pt(111) and Pt poly-crystals, the electrode potential was cycled from 0.07 V to
1.1 V (RHE). For Pt/C, the electrode potential was cycled from 0.07 V to 1.2 V (RHE).
In all measurements, the electrode potential was swept at 50 mVs1.
Calculations of current densities and surface coverages
Current densities shown in Fig. 1 (A) are normalized with respect to geometric surface
areas of used electrodes for Pt(111) and poly-Pt. For Pt nanoparticles, the current density
is normalized with respect to the electrochemical surface area (ECSA) obtained by
converting Faradaic charges generated through H-desorptions during the voltammetry
using an empirically determined Faradaic charge per surface area of 210 Ccm2 for
removing 1 monolayer of adsorbed H. The oxide amounts ox=OH+2O shown in Fig. 1
(B) are obtained by converting Faradaic charges generated through the oxide formations
and reductions at U  0.4 V during voltammetries using empirically determined Faradaic
charges per surface area of 240 Ccm2, 210 Ccm2 and 210 Ccm2 for Pt(111), polyPt and Pt nanoparticles, respectively, for forming or reducing 1 ML of adsorbed OH. To
2
obtain the Faradaic charges generated by H-desorptions, oxide formations and oxide
removals from CVs, contributions from double layer charging and discharging need to be
subtracted. In this study, the background charges for Pt(111), Poly-Pt and Pt/C were set
as 1.0 Acm2, 3.5 Acm2 and 14.8 Acm2, respectively, for the anodic scan
conditions and 2.0 Acm2, 2.3 Acm2 and 10.1 Acm2 for the cathodic scan
conditions.
B. Basic equations of DFT-MPB method
Detailed forms of energy terms in Eq. (6) are summarized below,
 1 
K   f nk  dr nk r    2  nk r  ,
 2 
n k 
Ees   dr e r    c r     r     r  r    dr
(S1)
 r 
2
 r  ,
8
(S2)
E xc   drf xc   ,   ,   ,    ,
(S3)
     2 
e
  ,
Se 
exp   nk

2  n k 
  k BTe  
(S4)
Fcav   bulkS ,
(S5)
Fdis   a IdisS I  bIdis  ,
(S6)
1
I
Frep   a Irep S I  bIrep  ,
(S7)
I
Fion   dr    r     r  rep r  ,
S MPB  
(S8)
kB
dr[   r  a 3 ln    r  a 3     r  a 3 ln    r  a 3 
3 
,
a
3
3
3
3
 1    r  a    r  a ln 1    r  a    r  a ]
(S9)
where fxc is a function given by the generalized gradient approximation, bulk is the surface
tension of the solvent, S is the molecular surface area, aIi and bIi (i = dis or rep) are
dispersion and repulsion interaction parameters for Ith atom, SI is the Ith atomic surface
area, rep is the repulsive interaction potential between atoms in the DFT region and ions
in the MPB region, and a is the ion radius. The dielectric permittivity  and molecular (or
3
atomic) surface area S (or SI) are defined as functionals of a sum of ground state atomic
electron densities na as shown below,
  r   1  1   na r  /  0 2 
1 
 r   1 
 1   r  /  2 
2
na
0


,


(S10)
 bulk , for molecular systems

,
  r     bulk  1 
 z  z0  
1  erf 
    bulk , for surface systems




2 
 z 

(S11)
S   drsr  ,
(S12)


s  na ,  na    r  0  / 2 r   0  / 2 r  
 na r 
,

1, for molecular systems

,
 r    1 
 z  z0  
   1, for surface systems
 1  erf 

 2
 z 


(S13)
(S14)
2
1   na r  /  0   1 
(S15)
 1 ,

2   na r  /  0 2   1 
is the dielectric permittivity of the bulk solution, z0 is the zposition of the
 r  
0
where bulk
bottom of the slab, and other parameters (0, ,  and z) are the parameters needed for
defining cavity shapes. Parameters 0 and  are particularly important parameters
affecting the solvation interactions strongly and were determined to reproduce the
solvation free energies of small molecules and ions as described in Ref. 51.
The repulsive interaction potential rep is introduced to prevent ions in the MPB region
from approaching atoms in the DFT region too closely and is defined as a function
adaptive to atomic motions in the DFT region as follows,
rep r    u I  r  R I  R  ,
R
(S16)
I
where RI is the position vector of Ith atom, and R is the lattice vector. uI is the repulsive
field from Ith atom acting on ions in the MPB region, and its details are shown also Ref.
51.
The forces acting on atoms in the DFT region are calculated using analytically
obtained derivatives of Helmholtz free energy functional with respect to atomic positions
summarized below,
4
 R I F  FHF  FPulay  Fsolv ,
(S17)
FHF    drR I  c r  r  ,
(S18)


FPulay    dr[R I nk r  Ĥ   nk  nk r 

k
n

Fsolv 

nk
r Ĥ   nk R  nk r ]
,
(S19)
I
 Fcav  Fdis  Frep 
1
2




d
r




r

d
r


r
R
R
na

I
I
8 
na
.
  dr    r     r   R I rep r 
(S20)
C. Enthalpies and entropies of nuclear motions
Enthalpies Hn and entropies Sn in Eq. (13) at the reference state are tabulated in Table
C.
5
Table C Thermal enthalpies and entropies calculated by ideal gas models and harmonic
oscillator models. The vibration frequencies of local reaction complexes were calculated
from their partial Hessian matrices obtained by a numerical finite difference method using
a 0.005 Å atomic displacement.
Chemical specie
Hn / eV
TSn / eV
0.064
0.665
0.337
0.673
OH(ad)
O(ad)
0.724
0.984
0.400
0.098
0.126
0.092
0.130
0.041
H2OHHOHOH [TS of (R1)]
H2O HHOHO [TS of (R2)]
HOHO [TS of (R3)]
2.036
1.802
0.787
0.269
0.323
0.128
+
a
H (g)
H2O(g)b
H2O(c)
H3O+(c)
Free energy of H+(aq) was calculated by adding a solvation free energy of 11.240 eV
obtained from a free energy difference of H+(g)+(H2O)4(aq)H+(H2O)4(aq) calculated
by using the DFT-MPB method as described in Ref. 50, where (g) indicates a chemical
specie in vacuum, and (aq) indicates a chemical specie in the continuum solvation
medium.
a
b
Enthalpy and entropy of H2O at an empirical vapor pressure of 0.035 atm was used.
D. Empirically determined equilibrium surface coverage
Oxide coverage obtained by integrating current densities in cyclic voltammograms is
the most reliable and reproducible experimental data, and an equilibrium surface coverage
should be obtained from voltammograms at a small scan-rate condition sufficient to
achieve the equilibrium condition. It is, however, still difficult to detect small current
densities generated purely by the oxide formations and their removals at slow scan rate
conditions accurately, and therefore, some approximated methods are necessary. In this
study, as indicated in Fig. S1, an equilibrium surface coverage was estimated by linearly
extrapolating non-equilibrium surface coverages at scan-rates of 0.002 and 0.005 Vs1
reported in Ref. 8 to a sufficiently small scan-rate of 0.0004 Vs1, where the peak
potential a shown in Fig. 9 is estimated to match with that for b.
6
1.2
0.002 V/s
0.005 V/s
Extrapolated data
1.0
ox / ML
0.8
0.6
0.4
0.2
0.0
0.4
0.6
0.8
1.0
1.2
U / V (RHE)
Figure S1
Equilibrium surface coverage obtained by linearly extrapolating non-
equilibrium surface coverages at scan-rates of 0.002 and 0.005 V s1. The experimental
data were taken from Ref. 8 using a digitizer program.
E. Symmetry factor and the number of electrons transferred by a redox reaction
To derive the equation (48), the activation free energy G* is formulated using a
thermodynamic integration along a reaction coordinate  of a redox reaction as follows,
P


  R  , R   pV

 2M 



d 
k BT
 k BT ln  e
dP  dP dR  dV  d ,
 

d 




2
G   
 TS
0
 TS
dG
d  
0
d
(S21)
where 0 and TS are positions of a reactant state and a transition state, respectively, on
the reaction coordinate , M, P and R are an effective mass, momentum vector and
position vector regarding a coordinate , respectively, and p and V are pressure and
volume of the system, respectively.
The symmetry factor  equals the partial derivative of G* with respect to U and is
derived as follows,
7
P


 R ,R  pV

 2 M




1 dG
1 TS d  
k BT


 k BT ln  e
dP  dP dR  dV  d
 

eN e dU
eN e 0 d U 




2
P


 R ,R  pV

 2 M


1 TS d  1 
 1  
k BT

e
dP dR  dV  d

dP 


N e 0 d  Q 
 e U 




2
P


 R ,R  pV

 2 M



1 TS d  1
k BT

e
N e R  dP  dP dR  dV  d
 

N e 0 d  Q 




2

1
N e
TS

d N e R  
d
0
d 
N e
N e
,
(S22)
where the partial derivative of the grandpotential  with respect to the electrode potential
U is converted to Ne using the Janak’s theorem (F/Ne=e) as follows,
 F   e N e    N     N  
N e
1 
F


 N e  e
e U
 e
 e
 e
N F
N e
N e
N e
 e
 N e  e
  e
 N e  e
 Ne
 e N e
 e
 e
 e
.
(S23)
In Eq. (S20), the symbol Q indicates the partition function described below,

Q  e
F.


P
2
2M 
  R  , R 
k BT
 pV
dP  dP dR dV .
 
(S24)
Disappearance of irreversibility at a slow scan-rate condition
At a very slow scan rate of 0.0001 Vs1, removals of O(ad) become to proceed mainly
through the backward reaction (R3), and the shape of the voltammogram become
symmetric as indicated in Fig. S2. This trend is observed also in experimental
voltammograms at room temperature reported in Ref. 8, where the reduction current peak
is shown to become sharper and closer to the oxidation current peak. The clearer trend is
8
observed also in our voltammograms obtained at a higher temperature as shown in Fig.
S3. The calculation indicates that when the electrode potential is scanned very slowly,
removals of O(ad) are completed mainly by the reaction (R3) before the backward
reaction (R2) is activated by the decrease in the electrode potential.
0.25
j / A cm-2
0.002
R1
R2
R3
R1+R2
0.20
(A) Anodic scan
0.15
0.001
v / s-1
0.30
0.10
0.05
0.00
0.000
0.6
0.8
1
1.2
E / V (RHE)
0.00
0.000
-0.10
R1
R2
R3
R1+R2
-0.15
-0.20
-0.25
-0.001
(B) Cathodic scan
-0.30
0.6
0.8
-v / s-1
j / A cm-2
-0.05
-0.002
1
1.2
E / V (RHE)
H2Oaq
(C)
H2OaqOHad+H+aq+e-
OHad
2OHadOad+H2Oaq
Oad
Figure S2
Simulated voltammogram at anodic (A) and cathodic scans (B) with a scan
rate of 0.0001 Vs1. Figure (C) shows the reaction scheme at this condition.
9
-2
Current density / 10 A・cm
-2
Current density / 10 A・cm
-1
30
50mVs
301K
333K
20
10
0
-10
0
10mVs
301K
333K
20
10
0
-10
0
0.5
1
Electrode potential (vs.RHE) / V
0.5
1
Electrode potential (vs.RHE) / V
1.1
-2
-1
30
1mVs
Oxidation
301K
333K
20
Peak potential / V
Current density / 10 A・cm
-1
30
10
0
1
333K
0.9
-10
Reduction
0
0.5
1
Electrode potential (vs.RHE) / V
100
101
Scan rate / mVs-1
301K
102
Figure S3 Experimental cyclic voltammograms measured with scan-rate of 0.0010.05
Vs1 at 301K and 333 K. Although there are significant effects by contaminations at the
high temperature and slow scan rate conditions, oxidation and reduction current peaks
observed at 0.8 U<1.2 V (RHE) are shown to become more symmetric at the high
temperature.
Section G
Driving forces acting on reactions (R1), (R2) and (R3)
Reaction free energies G1R, G2R and G3R, which correspond to driving forces
acting on reactions, (R1), (R2) and (R3), respectively, are summarized in Fig. S4, and
activation free energies G1*, G2* and G3* for the reactions, (R1), (R2) and (R3),
respectively, are summarized in Fig. S5. By using these figures, details of the reaction
mechanism at the anodic scan condition is described in this section. Because of a lot of
similarity, the reaction mechanism at the cathodic scan condition is not described, and
only numerical data are shown in the figures.
As indicated by Fig. S4, the reaction free energy G1R=e(UOHU) for the reaction
10
1
(R1) is nearly zero at 0.9  U < 1.0 V (RHE) because of the fast kinetics of the reaction
(R1). To achieve this quasi-equilibrium condition (G1R  0), the free energy of OH(ad)
needs to be increased with the increase in the electrode potential U, and the increase in
the free energy is achieved by the increase in the surface coverage of OH(ad) . The
coverage increase at this potential range is, however, very small as indicated by Fig. 9 (B)
because the repulsive interactions among OH(ad) are very strong as indicated by Fig 6.
In other words, the small changes in the OH(ad) coverage can realize the necessary
increase in the free energy of OH(ad). In contrast, because O(ad) does not have large
repulsive interactions, the free energy of O(ad) does not change considerable by the slight
changes in the OH(ad) coverage. Accordingly, the free energy of OH(ad) increases more
sharply than that of O(ad), and this selective increase in the free energy generates the
driving forces promoting formations of O(ad) from OH(ad) through the reactions (R2)
and (R3). The driving force acting on the reaction (R2) (G2R) is further shown to be
almost the same as that acting on the reaction (R3) (G3R) because the quasi-equilibrium
condition G1R0 indicates that the free energy of OH(ad)+H+(aq)+e nearly equals that
of H2O(aq). The relation G2RG3R is in fact observed in the obtained reaction free
energies shown in Fig. S4.
Although the driving forces are almost the same, activation free energies are totally
different between the reaction (R2) and (R3) as indicated by Fig. S5 because of the large
difference in the symmetry factor as described in Section 3.2.2.
11
0.8
(A) Anodic scan
Gi R / eV
0.6
(R1)
(R2)
(R3)
Fitted
0.4
0.2
0.0
-0.2
GiR1.5eU
-0.4
0.6
1.0
1.2
U / V (SHE)
0.2
G i R / eV
0.8
(B) Cathodic scan
0.0
(R1)
(R2)
(R3)
Fitted
-0.2
GiR0.7eU
-0.4
0.6
0.8
1.0
1.2
U / V (SHE)
Figure S4 Reaction free energies GiR (i=1, 2 and 3) for the reactions (R1), (R2) and
(R3) obtained from the simulations of the cyclic voltammogram. For eliminating the
effects by the concentration terms, the simulations were carried out at 1 molL1 of H+(aq).
12
1.2
G f* / eV
1.0
0.8
0.6
0.4
0.2
(R1)
(R2)
(R3)
(A) Anodic scan
0.0
0.6
0.8
1.2
1.0
U / V (SHE)
1.2
G b*/ eV
1.0
0.8
0.6
0.4
0.2
(R1)
(R2)
(R3)
(B) Cathodic scan
0.0
0.6
0.8
1.0
1.2
U / V (SHE)
Figure S5 Activation free energies Gi,f* and Gi,b* (i=1, 2 and 3) for respective
forward and backward directions of the reactions (R1), (R2) and (R3) obtained from the
simulations of the cyclic voltammograms.
13