!? THINGS THAT WE ARE FAMILIAR WITH : !?
Ohm’s law ( and Kirchoff’s…) (ABC... electrical circuits)
U = I  R , R =  L / S
Faraday’s law (ABC... electrolysis)
m = k  Q , k = M / n  F ( F = ?)
Fick’s laws (ABC... diffusion)
J =  D  dC/dx
C/t = D  2C/x2
Electrical properties of condensed phases – conducting electrical current (metals ,
semiconductors)
Ionic compounds , properties of solutions, ionic conductivity
Redox reactions ( np. 2Cr3+ +3 H2O2 + 10 OH- = 2 CrO4 - + 8H2O )
Phase boundary electrolyte - electrode
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Me+
transport
Me
Me+
electrode
electrolyte
Charge transfer
Oxidation – reduction
reaction rate
Diffusion
transport rate
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Each stage can determine the overall reaction rate
1. „obligatory” stages
charge transfer
Transport (diffusion, convection , migration )
2. other possible stages
Chemical reaction before or after (c t)
Crystallisation of new phases
Adsorption at the electrode
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=

A  ne  B
Reaction rate
v = ∆ cA / ∆t , ( or v = kA-B · cA )
( cA - volumetric concentration – we must do something about it)
In electrode kinetics the transferred charge is a measure of reaction rate
Following Faraday’s law:
mA = kF · I · ∆t = k · Q (here k – electrochem equivalent, not
reaction rate constant)
And back to general reaction rate formula
mA = cA · V or cA surface · S = kF · I · ∆t
v= k·I·/S
v ( mol · s-1 m) = kF (mol/C) · j
,
j – current density (A/m2)
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CURRENT DENSITY = MEASURE OF
ELECTRODE PROCESS RATE
And what makes the reaction happen at all??
Equilibrium – no products ( is anything happening?)
Deviation from equilibrium - energy impuls needed
Reaction – transformation to new equilibrium state
What might be an energy impuls?
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 energy state of a particle – chemical potential
μi= μ o + RT ( ai)
Charged particle - electrochemical potential , possible responce to
electrical field
φ= φo + RT/nF ln ( ai(n+) )
Equilibrium - equal potentials of a particle in two phases (electrode –
electrolyte)
E = E0 + RT/nF ln ( aelectrode / aelectrolyte )
Change in concentration, temperature
ENERGY IMPULS
Overpotential applied to the electrode
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At equilibrium
Redox transitions on molecular scale
Identical overall charge for oxidation and reduction
jk = ja , overall current density jk - ja = 0
At overpotential ∆E
j = jk - ja ≠ 0 as measure for reaction rate, so
j/nF = v = krr × C
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Reaction rate constant - overpotential:
krr = ks exp[ α n F ΔE / RT]
(one equilibrium – two constants: anodic and cathodic)
Combining v = .. And k = ….
(To get current-overpotential dependence)
i = nF S ks [ cutl exp(-αn F ΔE / RT ) – cred (βn F ΔE / RT)]
where
ks - standard reaction rate constant
α i β coefficients for energy barrier symmetry
ΔE overpotential
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• Electrode process – heterogenous, charge transfer at
phase boundary + transport
• Electrode = element of electrical circuit
• Measurement = two electrodes form a cell
• Circuit – measurable : voltage and current
• Difference in V/I response for a.c and d.c.
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Transport properties
• Structure of electrolytes, dissociation
•
• Movement of ionic species
• Mobility, velocity of part i vi = E · ui
• Conductivity  = e · Ni · zi · ui
• Transference number
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Cell voltage or electrode potential
• Equilibrium at the electrode – Nernst pot.
• Overpotential – driving force for the reaction
• Current – electrical measure of reaction rate
• Voltage – measure of potential difference !
• For kinetics – we must know the potential of a single
electrode!
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3 –electrode cell
•3-electrode cells : WE and CE - „working circuit”
reactions at electrodes , current flow
WE- RE - measuring circuit , high input impedance
on RE
no current flow
•Reference electrodes : very precise potential,
examples : Hg/ Hg2Cl2 , Ag/ AgCl ,
•Quasi-reference : W, Ta, other non-reactive metals
idea : stable potential, easy assembly,
•Function current-potential – diffusion and kinetics in the
cell must be described
electroanalysis
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Electrolytic cell and potentiostat
Electrodes:
Meas. Parameters:
CE - counter
RE - reference
WE - working
E - WE potential
Ez - applied potential
I - current in CE-WE circuit
I
RE
CE
E
WE
Cell
Ez
Potentiostat
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EIS
• Electrotechnical aspect : a.c.circuit
• Electrochemical aspect : approximation of
electrode process with circuit elements
Charge transfer
Conductivity
Resistance of layer
Resistances R
Z=R
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Double layer capacity
Capacity of layers
Capacities C
Z = -j/C
Diffusion phenomena
Roughness of surface
Inhomogenity of layer
Constant phase element
Admittance Y = Yo (j)n
for n=0 resistance
For n=1 capacity
Corrosion processes
(many reactions
and equilibria)
Inductance L
Z = j L
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Equivalent circuits
• Electrical model of electrode
• Connections in series and parallel –
interpretation of consecutive or
simultaneous reactions / phenomena
• Physical sense vs. numerical possibilities
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Our lab sessions
EIS – dr Regina Borkowska ( 5h basic electrode kinetics)
Voltammetry – dr Regina Borkowska 5h
Conducting polymers dr M. Siekierski 5h
Batteries – dr Marek Marcinek (5h basic cells + 5h Li- cells)
Transference numbers – Msc Michał Piszcz(5h diffusion coefficient + 5h
transference numbers in Li systems)
Ion associations – Dr Leszek Niedzicki (5h Fuoss-Kraus formalism –
electrochemical approach)
Corrosion dr Andrzej Królikowski 5h
Instructions and auxillary materials: download from
http://pirg.ch.pw.edu.pl/
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