Impedance of the Catalytic EC’ Processes

P. Połczyoski, R. Jurczakowski

10th International Symposium Electrochemical Impedance Analysis 2014

Department of Chemistry, University of Warsaw, Warsaw, Poland rafjur@chem.uw.edu.pl

Outline:

• Introduction

• The model – Impedance, surface concentrations, spectra

– novel impedance element

• Experimental results – Fenton reaction

– Silver(I) oxidation in H2SO4

• Other possible applications

• Conclusions

Catalytic EC’ Processes

EC’ processes - why are they important? • electrocatalysis, • electrochemical sensors, • catalytic hydrogen evolution, • carbon dioxide electroreduction, • bioanalytical applications:

- electrochemistry of enzymes, nucleic acids and amino acids.

Previous ac treatments

Impedance: • Solution involving unevaluated integrals1

• Approximate solution assuming „diffusion layer theory”2

Cot(ϕ) analysis:1

• Non-measurable directly, • Not an additive function, • reduced dimensionality (cot ϕ =Z′/Z″), • mathematical complexity,

[1] D. Smith, Anal. Chem. 1963, 35, 602−609 [2] Sluyters-Rehbach et al., J. Electroanal. Chem. 1969, 23, 457−474

𝑑2𝐶 𝑜𝑥

𝑑𝑥2 = 𝑠𝑜𝑥2 𝐶 𝑜𝑥 + 𝑞𝐶 𝑟𝑒𝑑

𝑑2𝐶 𝑟𝑒𝑑

𝑑𝑥2 = 𝑠𝑟𝑒𝑑2 𝐶 𝑟𝑒𝑑

𝜕∆𝐶𝑜𝑥

𝜕𝑡= 𝐷𝑜𝑥

𝜕2∆𝐶𝑜𝑥

𝜕𝑥2 + 𝑘∆𝐶𝑟𝑒𝑑

𝜕∆𝐶𝑟𝑒𝑑

𝜕𝑡= 𝐷𝑟𝑒𝑑

𝜕2∆𝐶𝑟𝑒𝑑

𝜕𝑥2 − 𝑘∆𝐶𝑟𝑒𝑑

𝑠𝑟𝑒𝑑 =𝑘 + 𝑗𝜔

𝐷𝑟𝑒𝑑 and 𝑠𝑜𝑥 =

𝑗𝜔

𝐷𝑜𝑥

∆𝐶ox = 𝐶 ox exp 𝑗𝜔𝑡 ;

∆𝐶red = 𝐶 red exp 𝑗𝜔𝑡

d𝐶 ox

d𝑥= −

𝑖 f

𝑛𝐹𝐴𝐷ox ;

d𝐶 red

d𝑥=

𝑖 f

𝑛𝐹𝐴𝐷red ;

d𝐶 ox

d𝑥+

d𝐶 R𝑒𝑑

d𝑥= 0

Initial and boundary conditions

𝐶 ox → 0 and 𝐶 red → 0

𝑥 = 0

𝑥 → ∞

The model

𝑂𝑥 + 𝑛𝑒−

𝑘𝑓

𝑘𝑏

𝑅𝑒𝑑

𝑅𝑒𝑑 + 𝑆𝑘𝑐→ 𝑂𝑥 + 𝑃

𝑧f = 𝐸

𝑖 f =

𝑅𝑇

𝑛2𝐹2𝐴

1 +𝑘f

𝐷ox𝑠ox+

𝑘b𝐷red𝑠red

−𝑘𝑘𝑓

𝑗𝜔 𝑘 + 𝑗𝜔 𝐷𝑜𝑥 𝑘 + 𝑗𝜔 + 𝐷𝑟𝑒𝑑 𝑗𝜔

𝛽𝑘b 𝐶red 0 + α𝑘f𝐶ox(0)

Faradaic impedance

where

𝑠𝑟𝑒𝑑 =𝑘 + 𝑗𝜔

𝐷𝑟𝑒𝑑 and 𝑠𝑜𝑥 =

𝑗𝜔

𝐷𝑜𝑥

d2𝐶ox

d𝑥2=

𝑘

𝐷ox𝐶ox

d2𝐶red

d𝑥2 = −𝑘

𝐷red𝐶ox

𝑥 = 0

𝑥 → ∞

d𝐶 ox

d𝑥= 𝑘f𝐶ox 0 − 𝑘b𝐶red 0

𝐶ox → 0 and 𝐶red → 𝐶red∗

𝐶red(𝑥) = 𝐶red∗ 1 −

𝐷ox𝑘b

𝐷ox𝐷red 𝑘 + 𝐷ox𝑘b + 𝐷red𝑘f

𝑒−

𝑘

𝐷ox 𝑥

𝐶ox 𝑥 = 𝐶red∗ 𝐷red𝑘b

𝐷ox𝐷red 𝑘 + 𝐷ox𝑘b + 𝐷red𝑘f

𝑒−

𝑘

𝐷ox 𝑥

𝜕𝐶ox

𝜕𝑡= 𝐷ox

𝜕2𝐶ox

𝜕𝑥2− 𝑘𝐶ox

𝜕𝐶red

𝜕𝑡= 𝐷red

𝜕2𝐶red

𝜕𝑥2+ 𝑘𝐶ox

Surface concentrations

boundary conditions:

Solution:

0

1

5

5

4

3

2

Lo

g R

ct

E-E 0

1

𝑅𝑐𝑡 =𝑅𝑇

𝑛2𝐹2𝐴𝐶𝑜𝑥∗ 𝐷𝑜𝑥𝑘𝑓

𝐷𝑟𝑒𝑑𝑘𝑓 + 𝐷𝑜𝑥 𝐷𝑟𝑒𝑑𝑘 + 𝑘𝑏

𝛼 𝐷𝑟𝑒𝑑𝑘 + 𝛼 + 𝛽 𝑘𝑏

𝑅𝑐𝑡(𝐸 ≪ 𝐸0′) =𝑅𝑇 𝐷𝑟𝑒𝑑

𝑛2𝐹2𝐴𝛼𝐶𝑜𝑥∗ 𝐷𝑜𝑥 𝑘

k/ko [cm-1]: (1) 100, (2) 102, (3) 104, (4) 106, (5) 108.

R. Jurczakowski, P. Połczyoski, The Journal of Physical Chemistry C, 2014, 118, 7980–7988.

Rct – potential dependence

0 3 6

0

-3

(1) = 0.707

(2) = 1

(3) = 1.414

21

Z '' /

Rct

Z ' / Rct

3

The influence of diffusion coefficients

(theoretical spectra for the EC’ process)

𝜉 =𝐷𝑜𝑥

𝐷𝑟𝑒𝑑

0 50 100 150 200 250 300 350

0

-50

-100

-150

421

(1) 0.050 V

(2) 0.100 V

(3) 0.130 V

(4) 0.150 V

Z''

/

cm

2

Z' / cm2

3

= 0.707

-5 -4 -3 -2 -1 0 1 2 3 4 5 6

0

-10

-20

-30

-40

= 0.707 (1) 0.050 V

(2) 0.100 V

(3) 0.130 V

(4) 0.150 V

/ d

eg

log(f / Hz)

4

3

2

1

0 400 800 1200 1600 20000

-300

-600

-900

-1200

(1) 0.050 V

(1) 0.100 V

(1) 0.130 V

(1) 0.150 V

421

Z''

/

cm

2

Z' / cm2

3

= 1.414

-5 -4 -3 -2 -1 0 1 2 3 4 5 60

-10

-20

-30

-40

-50

-60

4

3

2

= 1.414 (1) 0.050 V

(2) 0.100 V

(3) 0.130 V

(4) 0.150 V

/ d

eg

log(f / Hz)

1

The influence of diffusion coefficients

(theoretical spectra for the EC’ process)

0 50 100 150 2000

-20

-40

-60

-80

-100

-120

0.15Hz

=1.118

=1.414

Gerischer

HN

Z''

/

cm

2

Z' / cm2

0.15Hz

Spectra fitting

(theoretical spectra for the EC’ process)

𝜉 =𝐷𝑜𝑥

𝐷𝑟𝑒𝑑

𝑍 𝑓 = 𝑅𝑐𝑡 + 1

𝑗𝜔 + 𝑘 𝑍 𝜉 𝑍 𝜉= 𝑍1

𝜉 + 𝑎

1 + 𝜉𝑎 𝑎 =

𝑗𝜔

𝑗𝜔 + 𝑘

𝑍1 =𝑅𝑐𝑡 𝑘𝑓

𝐷𝑟𝑒𝑑

; 𝜉 =𝐷𝑜𝑥

𝐷𝑟𝑒𝑑

R. Jurczakowski, P. Połczyoski, The Journal of Physical Chemistry C, 2014, 118, 7980–7988.

Faradaic impedance

Fenton reaction. Cyclic voltammetry

-0.2 0.0 0.2 0.4-5

-4

-3

-2

-1

0

1

0 mM H2O

2

1 mM H2O

2

4 mM H2O

2

8 mM H2O

2

j /

mA

cm

-2

E vs. MMS / V

Impedance of Fenton reaction

0 50 100 150 200 2500

-30

-60

-90

-120

-150

-0.05 V

0.05 V

0.10 VZ

'' /

c

m-2

Z ' / cm-2

-2 -1 0 1 2 3 40

-25

-50

-75

/ d

eg

0.10 V

0.05 V

-0.05 V

log(f /Hz)

ξ = 1.17 ξ =Dred

Dox

Fenton reaction - Impedance parameters

-0.2 -0.1 0.0 0.1 0.210

0

101

102

103

104

105

Zger

Rct

k

Rct /

, Y

-1 0 /

s

-1/2, k / s

-1

E / V

[Fe3+]= 5mM

k = 4.0 s-1

k0 = 3.2 10-4 cm s-1

0.0 0.5 1.0 1.5 2.0 2.5 3.00

100

200

k-1/2

s-1/2

limit R

ct /

c

m2

𝑅𝑐𝑡(𝐸 ≪ 𝐸0′) =𝑅𝑇 𝐷𝑟𝑒𝑑

𝑛2𝐹2𝐴𝛼𝐶𝑜𝑥∗ 𝐷𝑜𝑥 𝑘

Rct – cathodic limit at E<<E0 ̓

P. Połczyński, R. Jurczakowski, W. Grochala, Chem. Commun., 2013, 49, 7480-7482.

50mM Ag(I)

0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7-10

-5

0

5

10

15

j /

mA

cm

-2

E vs. SSE (sat.) / V

1000mVs-1

500mVs-1

100mVs-1

v=500 mV∙s–1

0.6 0.9 1.2 1.5 1.8 2.1 2.4

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

E / V vs. SSE (sat.)

j /

j pa

50mM

25mM

10mM

1mM

Ag+ + 2HSO4 ̶ → Ag(HSO4)2

• (solv) + e−

Ag(HSO4)2(solv) → Ag+ + HSO4(solv) ̶ + HSO4(solv)

•

Silver(I) oxidation – cyclic voltammetry

10-1

100

101

102

103

104

0

-10

-20

-30

-40

d

eg

Freq / Hz

Fitting of the experimental spectra for Ag(I) oxidation

0 100 200 300 400 500 600 700

0

50

100

150

Z"

/

Z' /

ξ = 0.69

1.7 1.8 1.9 2.0 2.1 2.2 2.3100

1000

Rct / c

m2

E / V

CAg+= 5mM

k = 0,1 s-1

k0 = 10-6 cm s-1

Dox= 2,5·10-7cm2 s-1

Dred = 4.2·10-7 cm2 s-1,

α=0.4 β=0.6

Potential dependence of Rct Ag(I) oxidation

Other possible applications. Solid state ionics

Lu, X; Kreller, C; Adler, S., J. Electrochem. Soc., 2009, 156, B513-B525

La0.8Sr0.2CoO3-δ

1. Boukamp, B.A.; Bouwmeester, H.J.M., Solid State Ionics, 2003, 157, 29-33

2. Gonzalez-Cuenca, M.; Zipprich, W.; Boukamp, B. A.; Pudmich, G.; Tietz, F., Fuel Cells 2001, 1, 256-264.

Impedance Studies on Chromite-

Titanate Porous Electrodes under

Reducing Conditions.2

Other possible applications. Solid state ionics

Zr0.636Y0.091Tb0.273O2-δ

Conclusions

Analytical solution for EC’ processes was obtained in the rigorous treatment together with the potential-dependence of all impedance parameters. The analytical expression for this limiting Rct value allows for determination of many important kinetic and thermodynamic parameters of the catalytic systems. Systems with unequal diffusivities of the redox mediator have a strong effect on the impedance characteristics of the catalytic EC′ systems. This behavior is related to the novel impedance element derrived in this study. Impedance features characteristic to the novel element have been frequently reported in the experimental studies in solid state Ionics.

Acknowledgement

N N204 275638 grant

Polish Ministry of Science and Higher Education

Homogeneous reaction rate constants

2.6 2.8 3.0 3.2

1

10

100

70%

80%

95%

100%

110%

k /

s-1

E vs RHE