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
Exchange rate of reaction
At equilibrium
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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
Tafel equation
For irreversible state
How to explain these empirical formula?
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In electrochemistry, electrochemical potential
was used instead of chemical potential (Gibbs
free energy)
Potential curve described by Morse empirical
equation
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4.1.2 net current and exchange current
Fe3
Cu
Cu2
Fe2
Net current
Net current
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If cOx cRed activity 1 at ?re
At equilibrium condition
Then i net 0
standard exchange current
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4.1.3 effect of overpotential on activation energy
transfer coefficient
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
deuce
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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 equilibrium
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0
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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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Butler-Volmer 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
At cathodic polarization 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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log i0
?re
Tafel plot ? ? log i plot
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4.2.4 determination of kinetic parameters
For evolution of hydrogen over Hg electrode
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4.2.5 Exchange current density
1) The exchange currents of different electrodes
differ 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.
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When i0 is large and i ltlt i0, ?c is small.
When i0 ?, ?c0, ideal nonpolarizable 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 gt 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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4.2 potential on electrode kinetics
Shift of potential
?1 keeps constant
The nature of potential -dependence of rate
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At equilibrium cox(0,t) cox0
i0,ci0,ai0
Master equation
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Master equation
At equilibrium
Nernst equation
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Master equation
Butler-Volmer equation
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Butler-Volmer equation
at small overpotentials
Charge transfer resistance
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at large overpotentials
Tafel equation
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4.3 Diffusion on electrode kinetic
When we discuss situations in 4.2, we didnt take
diffusion polarization into consideration
When diffusion take effect
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At high cathodic polarization
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Taking logarithm yields
Therefore
Electrochemical term
Diffusion term
At this time 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
is invalid
diffusion
No ec
i
?
?
log i
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3. id ? i gtgt i0 both terms take effect
4. i ltlt i0, id no polarization
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diff
id
When id gtgti0
ec
?
?1/2
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0
-100
-200
-300
-400
300
200
100
400
Tafel plot under diffusion polarization
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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
How to overcome mixed / diffusion control? 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
?c ? constant
it ? CO(0,t)
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at low polarization
is very small
Constant
Constant
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is the current density at no concentration
polarization at ?
t0
i(0) i??
no concentration polarization
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When
it
at time right after the potential step it
?t1/2 is linear Extrapolating the linear part to
y axes can obtain
Double-layer charge
i??
EC control
diff control
?C
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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 to eliminate concentration polarization
effect
?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
3.8.2 Current step / jump
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? ? transition time when potential step to next
rxn.
?i i charge
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The slope of the linear relationship between ?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)
Typical CV diagram for reversible single
electrode
Potential separation
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For typical CV diagram of irreversible single
electrode
for fast EC reaction i ltlt i0 controlled by
diffusion
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for the reversible systems , use the forward
kinetics only
can be only by numerical method
Nicholson-Shain equation

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

is tabulated
x (bt) max 0.4958
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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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per decade of change in scan rate
drawn - out
ip? COx0 lower due to ?
if ?0.5 n 1
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lnip ? Ep ?E0 is linear with S ??RT/nF,
intercept is linearly proportional to k0
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4.4.4 effect of ?1 potential on EC rate
??10, validate at high concentration or larger
polarization ?nF??
effect of ?1 1.on concentration
2.?? ? ? ?1
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When z0 lt0 ( minus ) ?n ? ?1 large . For anion
reduced on cathode , ?1 effect is more
significant.
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When z0 ? n
?1 made ?c shift positively
minus lt0
plus gt0
so if ?1 increases, i decreases
?-?0
without specific adsorption ??? reduction of
1 cation reduction of ?1anion ?1
accelerates reduction of cations slow reduction
of anion
lgi
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if n z0 Cu2 2e- Cu
MnO4? e? MnO42?
?0.5 H e- 1/2 H2
if z0 0
adsorption of anion slow reaction
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Electrochemistry of LB film
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exam
1.Draw the potential change versus distance away
from electrode surface according to Stern
electric double-layer and indicate ?1 potential
2. When the electrode was positively charged, the
surface concentration of action is still more
than that of bulk solution. Explain this
phenomenon using specific adsorption model
3.The differential double layer capacitance of
Cu/H2O surface is 10-5 F?cm-2 while that for
Cu/HS(CH2)11CH3 is 10-9F?cm-2 (can be taken as
zero). If the differential Cdl for a
Cu/HS(CH2)11CH3 system is measured to be 10-7
F?cm-2. Please calculate the coverage of
HS(CH2)11CH3 on copper.
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4. Electro-capillary curves of Hg in KI and K2S
solution are shown in the Figure.
Please indicate the PZC of Hg on the curves and
explain the difference in PZC. The curves
coincide with each other when potential is quite
negative but differ a lot when potential is
positive, please give explanation.
5.Tell how to determine whether or not a
electrode process is governed by diffusion.
Given id for RDE can be expressed as id 0.62 nF
Di2/3?1/2?-1/6 ci0
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6.This is a water drop with contact angle of ? on
Pt surface. When potential shift negatively, plot
the change of ? with potential, i.e., ? ?.
7.Deposition of Cu nanowire in microspore of
anodic alumina membrane (AAO) can be taken as
ideal stable diffusion process. If the thickness
of (AAO) is 1?m 0.1 mol? cm-1,
105cm2? s-1. Please calculate the limiting
diffusion current.
8. Convection affects diffusion. If the slope of
concentration gradient is ,The
effective thickness of diffusion layer ?E
and the dimity diffusion
current id
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9.a typical CV peak is shown in the figure.
Please Indicate EP, EP/2, Ere, and iP on it. How
can you determine whether or not this
electrochemical process is electrochemical
reversible?