Physical Electrochemistry & Electrocatalysis
Viktoriia Saveleva Electrochemical Kinetics
. Methods to Measure Electrode Reactions Cyclic Voltammetry
4/26/2019 Physical Electrochemistry & Electrocatalysis 2 Cyclic Voltammetry
Recording of current density when the electrode potential is linearly changed between two potential limits with defined sweep rate
Linear Sweep Voltammetry (single sweep from E1 to E2)
Cyclic Voltammetry (cyclic sweep between E1 to E2 and back to E1)
E1: negative potential limit E2: positive potential limit dE n: sweep rate (in V/s) n dt During potential scan diffusion processes (=transport of electroactive species to electrode surface) and faradaic charge transfer processes at the electrode surface are occuring, resulting in a defined current peak
4/26/2019 Physical Electrochemistry & Electrocatalysis 3 Cyclic Voltammetry
0.6
E 0.4 pos
0.2
0.0
E [V]
-0.2
-0.4
Eneg -0.6 0 20 40 60 80 time [s]
4/26/2019 Physical Electrochemistry & Electrocatalysis 4 Cyclic Voltammetry A A e Diffusion effect starts to dominate
0.08
Start of noticeable 0.06 effect of diffusion
as jd falls with time
0.04 Rate controlled
by jd
j [mA/cm²]
0.02Exponential increase with potential
0.00
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 E [V]
4/26/2019 Physical Electrochemistry & Electrocatalysis 5 Cyclic Voltammetry A A e
0.08
0.06
0.04
j [mA/cm²] 0.02 A A A cx0 0 cx0 cbulk 0.00
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 E [V]
4/26/2019 Physical Electrochemistry & Electrocatalysis 6 Diffusion Equation A A e Basis: Linear Diffusion, no migration, no convection Single potential sweep c A 2c A D t A x 2 c A 2c A D t A x 2
c A c A Boundary conditions j nFDA nFDA t x0 t x0
4/26/2019 Physical Electrochemistry & Electrocatalysis 7 Diffusion Equation A A e Basis: Linear Diffusion, no migration, no convection Single potential sweep
Boundary conditions If no A+ in solution present
A A t 0 x 0 c cbulk A A t 0 x c cbulk
t 0 x 0 c A 0 t 0 x c A 0
4/26/2019 Physical Electrochemistry & Electrocatalysis 8 Diffusion Equation, CV A A e
Case 1: reversible reaction, very fast electron transfer single potential sweep LSV
2.3RT c A Nernst Behavior: E E 0 log x0 nF A cx0 dE n E E nt dt 1 2.3RT c A E E 0 log x0 E nt nF A 1 cx0
c A nFE nt E 0 t 0 x 0 x0 exp 1 A RT cx0
4/26/2019 Physical Electrochemistry & Electrocatalysis 9 Reversible vs Irreversible A A e
Reversible voltammetry was seen for “fast” electrode kinetics, irreversible for “slow”. What are they fast or slow related to? to rate of mass transport to the electrode
풌ퟎ measures the rate of electron transfer kinetics 푫 풎 = measures the rate of mass transport 푻 휹 푹푻 푫 휹~ 푫풕 풕~ 풎 ~ 푭υ 푻 푹푻/푭υ
Reversible Quasi-reversible Irreversible
ퟎ ퟎ 풌 ≫ 풎푻 풌 ≪ 풎푻
풌ퟎ Λ = Λ ≥ ퟏퟓ 15 > Λ > ퟏퟎ−ퟑ Λ ≤ ퟏퟎ−ퟑ 푭푫υ ퟏ/ퟐ 푹푻 @ RT
4/26/2019 Physical Electrochemistry & Electrocatalysis 10 Diffusion Equation, CV A A e
Case 1: reversible reaction, very fast electron transfer Λ ≥ ퟏퟓ 풌ퟎ ≥ ퟎ. ퟑυퟏ/ퟐ single potential sweep LSV
1/ 2 nF 1/ 2 A 1/ 2 Function j nF DA cbulk PnE E1/ 2 RT
3/ 2 1/ 2 A 1/ 2 j peak 0.4463n DA cbulk Randles-Sevcik Equation
4/26/2019 Physical Electrochemistry & Electrocatalysis 11 Diffusion Equation, CV A A e Case 1: reversible reaction, very fast electron transfer ퟎ ퟏ/ퟐ single potential sweep LSV Λ ≥ ퟏퟓ 풌 ≥ ퟎ. ퟑυ
=P
At peak maximum
4/26/2019 Physical Electrochemistry & Electrocatalysis 12 Diffusion Equation, CV A A e
Case 1: reversible reaction, very fast electron transfer Λ ≥ ퟏퟓ 풌ퟎ ≥ ퟎ. ퟑυퟏ/ퟐ single potential sweep LSV
1/ 2 0 2.3RT DA Half-wave Potential E1/ 2 E log nF DA
RT E E 1.1 Peak Potential peak 1/ 2 nF
4/26/2019 Physical Electrochemistry & Electrocatalysis 13 Cyclic Voltammetry A A e j 0.4463n3/ 2 D1/ 2c A 1/ 2 peak A bulk Λ ≥ ퟏퟓ 풌ퟎ ≥ ퟎ. ퟑυퟏ/ퟐ
0.08 E E peak 1/2
0.08 0.06 0.07
0.06
0.05 0.04
0.04
[mA/cm²]
P 0.03 100 mV/s
j
j [mA/cm²] 0.02 0.02 0.01
0.00 10 mV/s 0 5 10 n0.5 0.00 1mV/s
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 E [V]
4/26/2019 Physical Electrochemistry & Electrocatalysis 14 Diffusion Equation, CV A A e
Case 2: reversible reaction, Cyclic Potential Sweep Λ ≥ ퟏퟓ 풌ퟎ ≥ ퟎ. ퟑυퟏ/ퟐ
0.09 0.08 Epeak 0.07 E1/2 0.06 0.05 0.04 0.03 100 mV/s 0.02 0.01 10 mV/s 0.00 1mV/s -0.01 j [mA/cm²] -0.02 -0.03 -0.04 -0.05 -0.06 -0.07 -0.5 0.0 0.5 E [V]
4/26/2019 Physical Electrochemistry & Electrocatalysis 15 Diffusion Equation, CV A A e
Case 2: reversible reaction, Cyclic Potential Sweep Λ ≥ ퟏퟓ 풌ퟎ ≥ ퟎ. ퟑυퟏ/ퟐ
0.09 0.08 Epeak 0.07 E1/2 0.06 0.05 0.04 0.03 100 mV/s 0.02 0.01 0.00 -0.01 j [mA/cm²] -0.02 -0.03 -0.04 -0.05 -0.06 -0.07 57mV -0.5 0.0 0.5 E [V]
4/26/2019 Physical Electrochemistry & Electrocatalysis 16 Diffusion Equation, CV A A e
Case 3: irreversible reaction, single potential sweep LSV Λ ≤ ퟏퟎ−ퟑ 풌ퟎ ≤ ퟐ ∙ ퟏퟎ−ퟓυퟏ/ퟐ
1/ 2 1/ 2 0 RT D nF E peak E 0.780 ln ln Peak Potential nF k0 RT
nF 0 j peak 0.227nFc Ak0 exp EPeak E Peak current RT
F 3 / 2 1/ 2 A 1/ 2 j peak 0.496 n DA cbulk RT
4/26/2019 Physical Electrochemistry & Electrocatalysis 17 Cyclic Voltammetry A A e
F 3 / 2 1/ 2 A 1/ 2 j peak 0.496 n DA cbulk RT
0.06 E peak E1/2 0.36 0.35 0.05 0.34 Slope = 1.15RT/nF 0.33 0.04 0.32 0.31 100 mV/s 0.30 0.03
0.29
[V] P 0.28
E
0.27 j [mA/cm²] 0.02 0.26 10 mV/s 0.25 0.01 0.24 0.23 1mV/s 0.22 0.00 1 10 100
n -0.5 0.0 0.5 E [V]
4/26/2019 Physical Electrochemistry & Electrocatalysis 18 face-centered cubic structure (fcc) of Pt: 1 Pt atom at each cube corner & face center (100) surface (“number 5”): 1.28·1015 atoms/cm2 = 2.13·10-9 mol/cm2 = 205mC/cm2 (110) surface (“number 6”): 0.92·1015 atoms/cm2 = 1.53·10-9 mol/cm2 = 147mC/cm2 (111) surface (“hexagonal”): 1.5·1015 atoms/cm2 = 2.49·10-9 mol/cm2 = 240mC/cm2
average: 197mC/cm2 commonly used for polycrystalline Pt: 210mC/cm2
2 2 2 (note: 210mC/cm Pt = 2.04 nmolPt/cm Pt 235m Pt/gPt using MPt =195.7 gPt/molPt) (100)-face (110)-face (111)-face
2 2 Charge (Coulombs) from cyclic voltammetry divided by 210mC/cm : cm Pt surface
2 2 2 specific surface area: cm Pt/gPt m /gPt - from 30-120m /gPt for Pt/C (catalyst property)
2 2 2 2 roughness factor: 0.4mgPt/cm MEA · 60m Pt/gPt = 240cm Pt/cm MEA
4/26/2019 Physical Electrochemistry & Electrocatalysis 19 Peaks in the HUPD Region: Pt Single Crystals 2 (0.283cm Pt electrodes at 50mV/s)
shape in the HUPD-region depends on surface orientation
Pt/C HUPD-signature is less specific
Markovic et al., J. Chem. Soc. Farad. Transactions 92, 3719 (1996)
4/26/2019 Physical Electrochemistry & Electrocatalysis 20 + - + - H2 2H + 2e Pt-Had Pt + H + e RDE Nafionfilm Catalysts In-situ cathode CV's at 20mV/s and 25°C:
MEA: H2(500sccm) / N2 (62sccm); both overhumidified
RDE: N2 (1000sccm) in 0.1M HClO4 20 ~1µm Glassy-Carbon (RDE) 10 + - Pt + H2O PtOHad + H + e ~6mm
] 0 Pt MEA
A/g PtOH + H+ + e- Pt + H O
i [ -10 ad 2
N
H
Electrode
2
Reference
Electrodes
, , Working
2 , , Counter/ -20 thin-film GC in 0.1M HClO4 50cm2 MEA w. 63 sccm N2 -30 + - Pt + H + e Pt-Had -40 0.0 0.2 0.4 0.6 0.8 1.0 1.2 E/V [RHE] + - 2H + 2e H2
2 2 . H-adsorption/desorption on RDE (13mgPt/cm ) or in MEA (0.4mgPt/cm ): “H-titration” of Pt 2 2 . State-of-the-art 47%wt Pt/HSC (TKK): 92/79m /gPt (RDE/MEA) vs. 235 m /gPt theoretical limit
. H-adsorption/desorption is independent of H2 partial pressure, H2-evolution is not
4/26/2019 Physical Electrochemistry & Electrocatalysis 21 Electrochemical Kinetics
. Methods to Measure Electrode Reactions Stripping Voltammetry
4/26/2019 Physical Electrochemistry & Electrocatalysis 22 Anodic Stripping Voltammetry (ASV)
ASV is an extremely sensitive electro-analytical technique that can determine trace quantities of analyte at the parts-per-billion level.
I step: pre-concentration phase, where analyte is reduced/deposited at the working electrode surface in a stirred solution at a suitable reduction potential 푴풏+ 풂풒 + 풏풆− → 푴(풆풍풆풄풕풓풐풅풆)
II step: working electrode potential is scanned so that the reduced/deposited analytes are oxidizes back to their ionic form, i.e. are anodically stripped from the electrode surface 푴 풆풍풆풄풕풓풐풅풆 → 푴풏+ 풂풒 + 풏풆−
4/26/2019 Physical Electrochemistry & Electrocatalysis 23 Anodic Stripping Voltammetry (ASV)
4/26/2019 Physical Electrochemistry & Electrocatalysis 24 Anodic Stripping Voltammetry (ASV)
4/26/2019 Physical Electrochemistry & Electrocatalysis 25 Electrochemical Kinetics
. Methods to Measure Electrode Reactions Hydrodynamic Voltammetry
4/26/2019 Physical Electrochemistry & Electrocatalysis 26 Measurements under mass-transport control
Often, it is preferable to measure steady state curves, i.e., curves where the mass transport is controlled to the electrode and the diffusion layer thickness remains constant.
Rotating Electrodes e.g., rotating disk electrodes (RDE), rotating ring-disk electrodes (RRDE), rotating cones, rotating cylinders
Measurements are often called Hydrodynamic Voltammetry
4/26/2019 Physical Electrochemistry & Electrocatalysis 27 The Rotating Disk Electrode (RDE)
from: Gileadi
4/26/2019 Physical Electrochemistry & Electrocatalysis 28 The Rotating Disk Electrode (RDE)
• Uniformely accessible electrode
• Laminar solution flow on the surface (Reynolds number < 105)
v(velocity)l(length) Re v(kinematicviscosity) • For RDE Re w r 2 / v 10 5 w: angular velocity [rad/s]; r: radius disk
• w [rad/s] = 2p f [1/s] • 1 rad/s = 9.549 rpm (rotations per minute or revolution per minute) • 1 rpm = 0.105 rad/s
4/26/2019 Physical Electrochemistry & Electrocatalysis 29 RDE: Ruling Equations A A e
D A A A limiting current density jlim nFm A cbulk nF cbulk
With definition of the diffusion layer thickness at rotating disk electrode:
1.61D1/ 3v1/ 6w 1/ 2
2 / 3 1/ 6 A 1/ 2 jlim 0.62nFDA v cbulk w
Levich Equation
V.G. Levich (1917-1987) Deviation of these equations: See e.g., J.S. Newman, Electrochemical Systems, Wiley
4/26/2019 Physical Electrochemistry & Electrocatalysis 30 RDE: Ruling Equations A A e
j 0.62nFD 2 / 3v 1/ 6 c A w1/ 2 lim A bulk Levich Equation B
A 1/ 2 B: Levich constant Or jlim Bcbulk w
Note: This is the pure diffusion limited current density at a RDE!
The limiting current density is only dependent on the rotation rate!
4/26/2019 Physical Electrochemistry & Electrocatalysis 31 RDE: Ruling Equations
1.61D1/ 3v1/ 6w 1/ 2 Diffusion layer thickness
400 -5 2 RDE D=10 cm /s 350 Stagnant electrolyte rpm d [µm] 300
400 25 250
900 17 ] 200
m
m
1600 13 [
2500 10 150
3600 8 100 Stirred Solution 4900 7 50 RDE 0 0 5 10 15 20 25 30 35 40 t [s]
4/26/2019 Physical Electrochemistry & Electrocatalysis 32 Kinetic vs. Diffusion control
I 0.62AnFD 2 / 3v 1/ 6 c w1/ 2 I lim A bulk Levich Equation j B A
I I kFc 1 and Generally: bulk I k kFcbulk I lim
Diffusion control kinetic control 1 1 1 I I I I I I k 1 k lim I lim 1 1 1 1/ 2 I I k Bcbulkw
4/26/2019 Physical Electrochemistry & Electrocatalysis 33 10mM K3[Fe(CN)6] in 0.1M NaOH an Pt(pc)
Diffusion control Kinetic control Levich-Koutecky Plot
mixed control
DISK
-3 0.5 Bcbulk=6.96 10 mA/(cm²rpm )
-2 1/ik=2.18 10 cm²/mA
4/26/2019 Physical Electrochemistry & Electrocatalysis 34 Rotating Ring-Disk Electrode
3 3 2 / 3 2 / 3 1/ 6 A 1/ 2 I lim,Ring 0.62nFp r3 r2 DA v cbulk w
Note: in RRDE experiments, typically currents are used rather than current densities
Why RRDE?
The ring acts as an analytical electrode to determine (short lived) reaction intermediates
There is a defined transfer of the disk produced species to the ring electrode, where these species can be detected under pure diffusion control!
4/26/2019 Physical Electrochemistry & Electrocatalysis 35 Rotating Ring-Disk Electrode
3 3 2 / 3 2 / 3 1/ 6 A 1/ 2 I lim,Ring 0.62nFp r3 r2 DA v cbulk w
Collection efficiency: Fraction of disk produced species transported to the ring electrode and collected there!
N I Rring / I Disk
=f(r1;r2;r3)
4/26/2019 Physical Electrochemistry & Electrocatalysis 36 Ring Determination of collection efficiency Ring reaction:
10mM K3[Fe(CN)6] in 0.1M NaOH an Pt(pc) Fe2+ Fe3+ +e-
The Disk potential is swept (20mV/s)
The Ring potential is kept constant at a potential, where the reaction proceeds under pure diffusion control
Disk reaction:
Fe3+ +e- Fe2+
DISK
4/26/2019 Physical Electrochemistry & Electrocatalysis 37 + - + - Example:½ O2 + 2H Oxygen+ 2e H Reduction20 O2 + 2H + 2e H2O2 4e-
- - O 2e 2e 2 O2,ad H2O2,ad H2O RDE
H2O2
Pt(111) Pt(100) Pt(110-1x2)
N.M. Markovic, T.J. Schmidt, V. Stamenkovic, P.N. Ross, Fuel Cells 1 (2001) 105. N.M. Markovic, T.J. Schmidt, V. Stamenkovic, P.N. Ross, Fuel Cells 1 (2001) 105.
4/26/2019 Physical Electrochemistry & Electrocatalysis 38 100 0.05 M H2SO4, 50 mV/s, 900 rpm
50 O + 2H+ + 2e- H O
I I [µA] 2 2 2
I [mA]
0.00 + - ½ O2 + 2H + e H20 -0.5 Pt(111)
I [mA] Pt(110) -1.0 Pt(100)
0.0 0.2 0.4 0.6 0.8 1.0 Fuel Cells 1 (2001) 105. E [VRHE] Pt(111) Pt(100) Pt(110-1x2)
< <
4/26/2019 Physical Electrochemistry & Electrocatalysis 39 4/26/2019 Physical Electrochemistry & Electrocatalysis 40 2.3RT j j lim conc log nF jlim
Hydrogen oxidation in acid is mainly under pure diffusion control
Schmidt et al, JES 146 (1999) 1296
4/26/2019 Physical Electrochemistry & Electrocatalysis 41 Ring-Disk Shielding Experiments
Principle:
ring Disk ring
E =0.01 V (RHE) ring Edisk=0.8 V – 0.3 V 50mV/s Ring reaction: Bi3+ +3e- Bi0 Disk reaction: 3+ - 0 Bulk deposition, pure Bi +3e Bi diffusion control Underpotential deposition
-5 3+ Solution: e.g. 0.1M HClO4 + 5 10 M Bi
4/26/2019 Physical Electrochemistry & Electrocatalysis 42 Pt(111)/Bi (a) Disk Potentiodynamic ring-shielding experiment with a -5 3+ 20 0.1M HClO4, 5×10 M Bi -5 3+ RRDPt(111)E in 0.1 M HClO4 and 5·10 M Bi at 50 mV/s and 900 rpm. (a) straight line: cyclic voltamogramm of Pt(111)
after holding the electrode at Edisk=0.25 V for three minutes. The dashed line shows the second consecutive sweep. 0 (b) Corresponding ring-shielding currents (ERing=0.01 V) for Bi-deposition; notation as described in (a); (c) bismuth adsorption isotherm evaluated from the anodic 50mV/s potentiostatic 0.2 sweep after holding the disk electrode at Edisk=0.25 V for potentiodynamic 900rpm -20 three minutes (straight line). The black dots represent the
[ML]
Bi adsorption isotherm evaluated from a potentiostatic
A]
m
i [ (c) experiment after jumping from 0.8 V to the indicated potentials. 0.0 (b) Ring 1 0.2 0.4 0.6 0.8 E [V]
ir
-1
0.2 0.4 0.6 0.8 E [V/RHE]
Schmidt et al. PCCP 2 (2000) 4379
4/26/2019 Physical Electrochemistry & Electrocatalysis 43 20
A]
m
i [ 10 TDC
ISCBi 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 E [V/RHE] Comparison of the Bi3+ ion specific partial current (ISC) with the total disk current (TDS) for Bi underpotential deposition in 0.1 M HClO . 4 Schmidt et al. PCCP 2 (2000) 4379
4/26/2019 Physical Electrochemistry & Electrocatalysis 44