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BASIC PRINCIPLES OF ELECTRODE PROCESSES
Heterogeneous kinetics
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Charged interfaces
/ora a/?(i dipoles in the volume element:
•     solutions (random distribution, isotropic) (charge Q = O)
•     charged interface: electrode/electrolyte (anisotropic) (Q •£ O)
Metal l/^\                                                                 \
+   )           Electrolyte
Electric (electrode) double layer
(EDL):
^-^ - metals/electrolytes (Ag/Ag+); Q+J        (Hg/NaF); (Hg/KI)
-non-metallic elements/ electrolyte (gas, glass, polymers, membranes,
colloides...)
- liquid I/liquid II
Potential creation on interface
Heterogeneous system
solid conductive phase - interface - liquid conductive phase
1.    Ag (Ag+)
2.   Pt ( Pt-Ir, graphite)
Ag+ NO3-Fe2+ , Fe3+ ( S04 2 )
spontaneous ion crossing 1. or electron transfer 2,
spontaneous interface charging:
1.	Ag+   + e	0	Ag
2.	Fe3+   +   e	<=>	Fe2+
	Ox     + z e	<=>	Red
balance stabilization   => electrochemical potential
equality of ion i in both phases:
Mi (i) = Mi (s)
+
Mi (i) =
chemical work
electrical work
Chemical potential:     //,-  =   juf  +RTlnUi
Aft    =   Aft  + zFA(p   = 0
Aßi =lzl F A(p
in balance
A<p = potential difference between solid phase and solution A(p inner (Galvani) potential, immeasurable!
Measurable    => cell potential EMN , made from 2
hemi-cells: standard hydrogen electrode    SHE   E° = 0 V measured electrode  E  = b   + A(p          b = constant
EMN  =   E  -   0 = E
_   ,o        RT_
redox       J~Jredox          j-p iri uOi                                             R T
Nernst: 1. E„,   = £„°,   +----In a,
E      . = E      . H------lna
Ag/Ag+           Ag/Ag+         p            Ag
iE      =E°     +—ln-^
Zá •       redox           redox           1-^
ZF        ared
F            = F°          H-------In——
Fe2+/Fe3+           Fe2+/Fei+          rp
That was a balance                                                ť      aFe
RT .   a^
2+
From within entered potential on electrode:
^ charge goes through an interface
impossible of charging =>
impolai izedable interface
(impolarizedable electrode, Ag / Ag+)
^ charge doesn't go through an interface
possible of charging=> polarizedable interface
(polarizedable electrode, Pt, graphite, Hg, without Hgz+ in solution)
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ELECTRODE DOUBLE LAYER
(EDL)
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electrode surface water molecule
+      L-;i1liin ff)    anion
A    adsorbed neutral species
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ELECTRODE DOUBLE LAYER (EDL)
electrostatic potential cp
charge density o
surface tension y
capacity C
adsorption r
Solution
Electrojlé'
+CTS
+
Solution
+
+
Electron
Solution
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surface tension y
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A
Y
VFg
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a) capillary elevation
F =F
Y           g
2 n r y cos© = n r 2h p g
y =
rhpg 2 cos0
b) stalagmometr (also DME)
m g = 27rry
y =
mg
2n r
y :y0 =m:m
o
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charge density o
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3y 3Ě]
= —o
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Lippman equation
capacity C
differential capacity Cd
integral capacity C{
M _
3E
= C
d
a
M       _
{cßE
adsorption T
Langmuir isotherm
E-EA
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= c.
dE
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1-0
= ßi ai
0      fraction of coverage T ľ      surface or maximum surface excess
Pi      adsorption coefficient
q .   activity of species i in bulk         Q —
solution
oo
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Temkin isotherm
r=RT
2g
ln(p.a.)
g .... parameter treating the
interaction energy between the
adsorbed species
Frumkin isotherm
Pi a{ =       !     exp  & '
r -r
oo
RT
Esin-Markov effect
The degree of specific adsorption should vary with electrolyte concentration, just
as there should be a change in the point of zero charge
YE-M ~
RT
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models             electrode double layer structure on

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Electrode (metal)
INTERFACE ELECTRODE - ELECTROLYTE
charges - points
+
+
GO©
C,
H
Helmholtz Model (1879)
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XH
LH
about 10-20 jiF/cm2
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ELECTRODE   DOUBLE   LAYER STRUCTURE   ON INTERFACE ELECTRODE - ELECTROLYTE
diffuse layer
Electrode (metal)
C
d
H
Gouy-Chapman Model (1910-1913)



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Gouy-Chapman Model (1910-1913)
distribution of species with distance from electrode
(xDL =  distance characteristic of the diffuse layer)
0
ni =nt   exp
<Pa=<P-<P;
r-Zie^A^
V
kBT
Bolztmann's law
J
p(*)=Xnizie=Zn>°zie exp
-z.e^A
V
kBT
J
d2q>Jx)_-p(x)
dx
Poisson's equation
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Poisson-Bolztmann equation
dx2
£r£0     i
Yjn°iziexp
r
w <p.
\
v
kBT
J
xDL =  distance characteristic of the diffuse layer
XDL —
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£r£0 kßT
0 _2_2
V
2nľ zze
diffuse layer thickness
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xDL for water at 298 K is 3.04*\0r*zrlc-m cm if c = IM and z = 1, then xDL is 0.3 nm.
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ELECTRODE DOUBLE LAYER   STRUCTURE ON INTERFACE ELECTRODE - ELECTROLYTE
Electrode (metal)
C,
OHP
Stern Model (1924)
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Stern Model (1924)
1
C,     c
1       1
- +
d
H
C
GC
X
H
Wo
+
1
[2£ľ£0z2e2nj /kBT)   cosh(zeyA0/2kBT)
close to Ez, CH » CGC   and so Cd ~ CGC far from Ez, CH « CGC and so Cd ~ CH
separation plane between the two zones is called the
outer Helmholtz plane (OHP)


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Electrode (metal)
ELECTRODE DOUBLE LAYER   STRUCTURE ON
INTERFACE ELECTRODE - ELECTROLYTE
IHP - Inner Helmholtz Plane IHP                  OHP - Outer Helmholtz Plane
&
: +
OHP
E = E
CJ(3ľ5(^)E<E
C
d
Grahame Model (1947)
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Diffuse Layer
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ELECTRODE   DOUBLE LAYER   STRUCTURE ON INTERFACE ELECTRODE - ELECTROLYTE
Electrode (metal)
Layer of oriented molecules of supporting electrolytes or solvents
Electrolyte
BDM Model
Bockris, Devanathan, Müller Model (1963)
CHARACTERISTIC OF ELECTRODE POTENTIAL IN
DOUBLE LAYER
OHP
0
OHP
<P
<Pi „
adsorption
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ELECTRODE DOUBLE LAYER   STRUCTURE ON INTERFACE
ELECTRODE - ELECTROLYTE
Chemical Models - the electronic distribution of the atoms in the electrode
( not only electrostatic forces)
- difference between (sp) metals and transition (d)metals
- IHP as an electronic molecular capacitor jellium model
Classical                              ______   i       The jellium
representation                     M            \ |           model
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Variation of the electrostatic potentials with distance from a metallic electrode
Chemical Model    (Damaskin and Frumkin)
(Trasatti) (Parsons)



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ELECTRODE DOUBLE LAYER   STRUCTURE ON INTERFACE
ELECTRODE - ELECTROLYTE
C/}
C
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U
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-2
-1           0
Distance
Positive charges distribution profile
Electrons distribution profile
1
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Electron spill-over at the surface of a metal according to the Jellium model.