Electrochemical kinetics at electrode / solution interface and electrochemical overpotential

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Chapter 4 Electrochemical kinetics at
electrode / solution interface and
electrochemical overpotential
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Effect of potential on electrode reaction

• Thermodynamic aspect
• If electrode reaction is fast and
  electrochemical equilibrium remains, i.e., Nernst
  equation is applicable. Different potential
  corresponds to different surface concentration.

2. Kinetic aspect If electrode reaction is
slow and electrochemical equilibrium is broken.
Different potential corresponds to different
activation energy.
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4.1 Effect of potential on activation energy
4.1.1 basic concepts
For Elementary unimolecular process
Rate expressions
At equilibrium
Exchange rate of reaction
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Some important empirical formula
Arrhenius equation
According to Transition State Theory
Corresponding to steric factor in SCT
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For electrode reactions
For reversible state
Nernst equation
For irreversible state
Tafel equation (1905)
Overpotential
How to explain these empirical formula?
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Potential curve described by Morse empirical
equation
In electrochemistry, electrochemical potential
was used instead of chemical potential (Gibbs
free energy)
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4.1.2 net current and exchange current
Net current
Net current
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If cOx cRed activity 1 at ?re
At equilibrium condition
standard exchange current
Then i net 0
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4.1.3 effect of overpotential on activation energy
Ox
Red
Na(Hg)x
Na e?
Ox
Na(Hg)x
Na e?
The energy level of species in solution keeps
unchanged while that of the species on electrode
changes with electrode potential.
Red
Na e?
Na(Hg)x
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polarization
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Fraction of applied potential alters
activation energy ? for oxidation and ? for
reduction
Anode side
cathode side
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?
?
?
x
? is usually approximate to 1/2
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4.1.4 Effect of polarization on reaction rate
Marcus theory transition state theory
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No concentration polarization
If initial potential is 0, then
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At equilibirum
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4.2 Electrochemical polarization
4.2.1 Master equation
Master equation
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Theoretical deduction of Nernst equation from
Mater equation
At equilibrium
Nernst equation
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4.2.2 Butler-Volmer model and equation
Butler-Volmer equation
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4.2.3 discussion of B-V equation
1) Limiting behavior at small overpotentials
Current is a linear function of overpotential
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Charge transfer resistance
False resistance
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2) Limiting behavior at large overpotentials
One term dominates
Error is less than 1
When cathodic polarization is larger than 118 mV
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Taking logarithm of the equation gives
Making comparison with Tafel equation
One can obtain
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At 25 oC, when n 1, ? 0.5
The typical Tafel slope
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Tafel plot ? ? log i plot
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4.2.4 determination of kinetic parameters
For evolution of hydrogen on Hg electrode
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active dissolution
active dissolution
?n ?n
Ag /Ag 0.5 0.5
Hg2 /Hg 0.6 1.4
Cu2 /Cu 0.4 1.6
Zn2 /Zn 0.47 1.47
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Anode side
cathode side
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Master equation
Nernst equation
Butler-Volmer equation
Tafel equation
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4.2.5 Exchange current density
1) The exchange current of different electrodes
differs a lot
Electrode materials solutions Electrode reaction i0 / A?cm-2
Hg 0.5 M sulfuric acid H2e H2 5?10-13
Cu 1.0 M CuSO4 Cu22e Cu 2?10-5
Pt 0.1 M sulfuric acid H2e H2 1?10-3
Hg 1?10-3 M Hg2(NO3)2 2.0M HClO4 Hg222e 2Hg 5?10-1
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2) Dependence of exchange currents on electrolyte
concentration
Electrode reaction c (ZnSO4) i0 / A?cm-2
Zn22e Zn 1.0 80.0
Zn22e Zn 0.1 27.6
Zn22e Zn 0.05 14.0
Zn22e Zn 0.025 7.0
High electrolyte concentration is need for
electrode to achieve high exchange current. Use
of Ag/AgCl electrode.
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When i0 is large and i ltlt i0, ?c is small.
When i0 ?, ?c0, ideal nonpolarizable
electrode, basic characteristic of reference
electrode.
When i0 is small, ?c is large. When i0 0, ?c
?, ideal polarizable electrode
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The common current density used for
electrochemical study ranges between 10-6 1
A?cm-2. If exchange current of the electrode i0
gt 10100 A?cm-2, it is difficult for the
electrode to be polarized. When i0 lt 10-8
A?cm-2, the electrode will always undergoes sever
polarization.
For electrode with high exchange current,
passing current will affect the equilibrium a
little, therefore, the electrode potential is
stable, which is suitable for reference
electrode.
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Influence of impurity
If an impurity undergoes reduction at electrode
The influence of impurity on equilibrium is
negligible.
If
If
Oxidation of electrode and reduction of impurity
take place. There is net electrochemical
reaction.
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Single/couple electrode and Mixed potential
Icorro
Electrode with exchange current less than 10-4 A
cm-2 is hard to attain equilibrium potential.
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4.3 Diffusion on electrode kinetic
When we discuss situations in 4.2, diffusion
polarization is not take into consideration.
When diffusion take effect
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At high cathodic polarization
Therefore
Electrochemical term
Diffusion term
The total polarization comprises of tow terms
electrochemical term and diffusion term.
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Discussion
1. id gtgt i gtgt i0
No diffusion
ec polarization
At large polarization
At small polarization
i
?0
?c
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2. id ? i ltlt i0
diffusion
No ec
is invalid
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0
-100
-200
-300
300
200
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3. id ? i gtgt i0 both terms take effect
4. i ltlt i0, id no polarization (ideal
unpolarizable electrode)
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When id gtgti0, diffusion control
At half wave potential
The half wave potential depends on both id and i0
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Tafel plot with diffusion control
i0 ltlt i lt 0.1 id Electrochemical polarization
i between 0.1id ? 0.9id mixed control
i gt0.9 id diffusion control
Question
How to overcome mixed / diffusion control?
please summarize the ways to elevate limiting
diffusion current
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4.4 EC methods under EC-diff mixed control
4.4.1 potential step
Using B-V equation with consideration of
diffusion polarization
at high polarization ?c
At constant ?c, it ? cOx(0,t)
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at low polarization
is very small
Constant for potential step
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Numerical solution
is the current density at no concentration
polarization at ?
That is
At t 0
i(0) i??
no concentration polarization
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When
at time right after the potential step it
?t1/2 is linear Extrapolating the linear part to
y axes can obtain
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Making potential jump to different ? can obtain
i?? at different ?. Then plot i?? against ?c
can obtain i?c without concentration
polarization.
The way can be used to eliminate concentration
polarization.
?c ? time constant ??s
it gt i?? due to charge of double layer
capacitor
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4.4.2 current step
cathodic current 0 ? ic
constant
? ? transition time when potential steps to next
reaction.
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The slope of the linear par of ?c (t) can be used
to determine n and ?.
When t?0 the second term 0
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4.4.3 cyclic voltammetry (CV)
for reversible single electrode
Potential separation
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for the reversible systems , use the forward
kinetics only
can be solved only by numerical method
Nicholson-Shain equation
for fast EC reaction i ltlt i0 controlled by
diffusion

• ? tramper coefficient
• n number of electrons involved in charge
  transfer step

is tabulated
x (bt) max 0.4958
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For irreversible single electrode
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For totally irreversible systems
peak potential shift with scan rate
for slow EC reaction i?i0 ( quasi? reversible,
irreversible) in comparison to the same rate,
equilibrium can not establish rapidly. Because
current takes more time to respond to the applied
voltage, Ep shift with scan rate .
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Dependence of ??p on ?
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4.5 effect of ?1 potential on EC rate
??10, validate at high concentration or larger
polarization ?G ?nF??
effect of ?1 1. on concentration
2. ?? ? ? ?1
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This means ?1 has same effect on the forward
(reduction) and reverse (oxidation) reaction.
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When zO lt0 ( minus ), ?n ?zO is large, therefore,
for anion reduced on cathode , ?1 effect is more
significant.
When zO ? n
?1 made ?c shift positively
so if ?1 increases, i decreases
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if n zO Cu2 2e- Cu
MnO4? e? MnO42?
? 0.5 H e- 1/2 H2
if zO 0
adsorption of anion slow reaction
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without specific adsorption ??? reduction
of 1 cation reduction of ?1 anion ?1
accelerates reduction of cation, slows reduction
of anion
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Rotation rate of RDE on reduction of 1?10-3 mol/L
K2S2O8 without supporting electrolyte
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Effect of potential of zero charge on
polarization curve of RDE for reduction of K2S2O8
without supporting electrolyte
Only when the electrode potential is near to the
potential of zero charge, ?1 has large effect on
the reaction rate, while at higher polarization,
?1 take less effect.
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Effect of concentration of supporting electrolyte
(sodium sulfate) on the polarization curve of RDE
for reduction of K2S2O8 .
1 0 2 2.8 ?10-3 3 0.1 4 1.0 mol/L Na2SO4
Problem how to eliminate the effect of ?1?
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4.6 EC kinetics for multi-electron process
For a di-electron reaction Ox 2e? ??
Red Its mechanism can be described by
At stable state
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If
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Therefore
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For a multi-electron reaction Ox ne? ??
Red Its mechanism can be described by
Steps before rds, with higher i0 at equilibrium
Steps after rds, with higher i0 at equilibrium
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Therefore
At small overpotential
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At higher overpotential
For cathodic current
For anodic current
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4.7 Marcus theory for electron transfer
Effect of reactant, solvents, electrode materials
and adsorbed species on electrochemical reaction.
Electron-transfer between two coordination
compounds.
No strong interaction between electrode
surface and reactant. Reduction of Ru(NH3)63
reactant, intermediate and product interact
with electrode surface strongly. Reduction of O
and oxidation of H
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Microscopic theories of electron transfer
Electron transfer reaction, a radiationless
electronic rearrangement, sharing commonalities
with radiationless deactivation of excited
molecules.
For a homogeneous redox reaction
O R ?? R O Electron transfer between
tow isoenergetic points ----
isoenergetic
electron transfer
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Franck-Condon principle Nuclear coordinates do
not change on time scale of electronic
transitions. Reactants and products share common
nuclear configuration at moment of
transfer. Deduce expression for standard Gibbs
energy of activation as a function of structural
parameters of reactant, so as to calculate rate
constant of the reaction.
activation
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Transition state
isoenergetic electron transfer
g global reaction coordinate for 1 dimensional
process, related to solvation.
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For homogeneous electron transfer
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Work of assemblying reactants, i.e., ion pair
electrostatic work to bring charged species next
to charged electrode, wO and wR not considered.
Improved model
Predictions from Marcus theory
½ factor seems like first order term in expansion
of ?, rest are corrections
Classical Butler-Volmer theory regards ? as
constant, cannot predict potential dependence of
?.
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Electron transfer occurs between empty levels of
electrode (or species in solution) and filled
levels of species in solution (or electrode) of
the same energy. For reduction - energy of
occupied level of electrode must match energy
level of empty state of species in solution. For
oxidation - energy of empty level of electrode
must match energy level of occupied state of
species in solution. Energy levels of metal and
species in solution form a continuum Overall rate
must be evaluated by summing or integrating over
all energy matched pairs.
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Since filled electrode states overlap with
(empty) O states, reduction can proceed. Since
the (filled) R states overlap only with filled
electrode states, oxidation is blocked.
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Number of electronic states of electrode in
energy range E and E dE is
area of the electrode
density of states
Total number of states of electrode in given
energy range
At absolute zero, energy of highest filled state
is called Fermi level, At higher temperatures,
thermal energy promotes electrons to higher
levels Electron distribution given by Fermi
function f(E)
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concentration density function
Number concentration of R species in the range
between E dE is
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Rate Constant for Reduction
Rate Constant for Oxidation
FURTHER CONSIDERATIONS Electron transfer occurs
almost entirely at the Fermi level Rate
constant proportional to local rate at Fermi
level. Integrals reduce to single value
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R
P
tunneling