2. THE CHARGE AND CURRENT
•Electrochemistry studies the processes which involve charge
•The charge is a source of electric field
Element of charge: 1.602·10-19 C
The energy change is ±1.602·10-19 J if we move the charge across the potential
drop of 1V
If we do the same with 1 mol of charges, we obtain…
A
+
B
1V
-
-
The current is the change of charge per time
I=
dQ
dt
3. FARADAY’S LAWs (1834)
“The chemical power of a current of electricity is in
direct proportion to the absolute quantity of electricity
which passes”
“Electrochemical Equivalents coincide, and are the
same, with ordinary chemical equivalents”
m
Q
=
M zF
MIt
m=
zF
t
M
m=
∫ Idt
t =0
zF
Area under current-time curve (and freqently the currentpotential curve also) is the charge!! This way can be deduced
how much material was transformed.
4. CONDUCTIVITY
R≈
l
A
l
(Ω)
A
E
R = (Ohmś law)
I
+
+
-
Electrolytes: same principle, but
conductivity is preferred
A
G=χ
l
The unit for conductivity is
Siemens, what is the unit
of specific conductivity?
For species KXAY:
Migration velocities can be different
Stokes force is balanced by force induced by electric field
Only the cations distant from the plane by vA or nearer will
cross the plane. In unit field (1V) and unit area will cross the
boundary xcαFz cat ucat cations
χ = xcαFzcat ucat + ycαFz anuan
5. CONDUCTIVITY
V
A
Solutions can have different concentrations:
χ S m3
2
−1
Λ=
m mol = Sm mol
c
Λ ΟΟ
This is used for measurements of
dissociation constants:
AB
c (1 -α)
Λ
α=
Λ∞
C
A
+
cα
+
B
-
cα
Λ
c
Λ
2 2
cα
KD =
= ∞
c (1 − α ) 1 − Λ
Λ∞
2
6. HOW AND WHERE THE POTENTIAL
DIFFERENCE DEVELOPS
s o lu tio n 1
s o lu tio n 2
Junction potential
(Henderson)
Donnan potential
m e m b ra n e
Potential difference develops where a charge
separation in space occurs
7. THE NERNST EQUATION
The combination of two basic physical chemistry
equations:
− ∆G = zFE
and
− ∆G = RT ln K
All processes in which charge separation occurs go
to equilibrium
…but what is K?
8. DANIEL CELL
Zn | ZnSO4 | | CuSO4 | Cu
Zn+CuSO4→ Cu+ZnSO4
[ Cu ][ ZnSO4 ]
zFEMN = RT ln
[ Zn][ CuSO4 ]
…is it OK?
9. BACK TO NERNST EQUATION
RT aox
E=E +
ln
zF ared
0
RT ared
E=E −
ln
zF
aox
0
aox
2.303RT
E=E +
log
zF
ared
0
2.303RT
= 0.059 V
F
(at 25°C )
10. ELECTRODES OF THE FIRST KIND
The term electrode is here used in a sense of a half-cell.
Metal immersed into the solution of its own soluble salt. The potential is
controlled by the concentration of the salt.
E=E
0
Me / Me +
RT
+
ln aMe+
zF
Zn in ZnCl2, Ag in AgNO3, Cu in CuSO4 etc.
Non-metallic electrodes – gas electrodes (hydrogen and chlorine electrode)
13. ELECTRODES OF THE SECOND KIND
Argentochloride Ag | AgCl | KCl | |
Calomel Hg | Hg2Cl2 | KCl | |
Mercurysulphate Hg | Hg2SO4 | K2SO4 | |
0
SHE
197 m V 244 m V
640 m V
SCE
. A
g /A
gC
l
s a t. H g /H g 2S O
sat
4
REDOX ELECTRODES
F e 2+
e-
F e 3+
e-
Fe
3+
The electrode serves as an electron sink
Redox combo
F e 2+
P t e le c tr o d e
14. ELECTRODES OF THE THIRD KIND
..just a curiosity
Zn | Zn2C2O4 | CaC2O4 | CaCl2 | |
We can measure the concentration of Ca2+, but
there’s a better device to do this…
15. THE ABSOLUTE SCALE OF POTENTIALS
R E D (v a c u u m )
-∆ G
s o lv
∆G
IO N
O X (v a c u u m )
-∆ G
(R E D )
zF∆E
s o lv
(O X )
Reference to vacuum
(instead of hydrogen electrode)
ABS
R E D (s o lu tio n )
O X (s o lu tio n )
H
Thermodynamic cycle for hydrogen
-∆ G
H
0
-∆ G
(v a c u u m )
H
.
(v a c u u m )
-∆ G
s o lv
+
-F ∆ E
(s o lu tio n )
d is s
/2
0
ABS
1 /2 H
2
4420 m V
0
Vacuum
IO N
SHE
197 m V 244 m V
SC
sa
t.
The most commonly accepted
value is 4.42V, but values
around 4.8V are also reported
+
E
640 m V
s a t. H g /H g 2S O
4
Ag
/A
gC
l
16. ION SELECTIVE ELECTRODES
Membrane potential reflects the
gradient of activity of the analyte ion in
the inner and outer (sample) solutions.
•The trick is to find a membrane material, to
which an analyte is selectively bound. The
membrane must be conductive (a little bit, at
least), but it should not leak
Liquid junction for
reference electrode
(sometimes is high)
Li
Li
+
H
Si
Li
O
h y d r a te d H a u g a a r d la y e r s
+
L i io n s p a r tia lly fr e e
+
400 M Ω
+
Si
Nikolski eq.
E = Eassym +
RT
RT
ln aH O + + X ⋅
ln a Na +
3
F
F
17. MEMBRANES FOR ISEs
•Glass membranes (H+, for other cations change in the composition of glass
membrane (Al2O3 or B2O3 in glass to enhance binding for ions other than H + (Na+,
Li+, NH4+, K+, Rb+, Cs+ and Ag+)
•Crystalline Membranes (single crystal of or homogeneous mixture of ionic
compounds cast under high P, d~10 mm, thickness: 1-2 mm. Conductivity: doping or
nonstechiometry, Ag+ in AgCl or Ag2S, Cu+ in Cu2S. Fluoride electrode: determines
F-, LaF3 crystal doped with EuF2).
•Liquid membranes (organic, immiscible liquid held by porous (PVC) membrane
with ion exchange properties or neutral macrocyclic compouds selectively binding
the analyte in their cavities)
18. POTENTIOMETRY
Cell and voltmeter behaves as a
voltage divider circuit
E(cell)
Ri
RM
V
E(measured)
R2
E2 = E1
R1 + R2
R1
E1
Emeasured = Ecell
R2
E2
RM
RM + Ri
19. POTENTIOMETRY AND PHYSICAL CHEMISTRY
1. Activity coefficients determination
2. Solubility products determination
3. Ion product of water determination
Pt | H2 | HCl | AgCl |Ag
Ag | AgNO3 | |KNO3 | | KX, AgX | Ag
Pt | H2 | KOH | |KCl | AgCl |Ag
Ionic product of water: 1.008·10-14 (25°C) – good agreement with
conductivity measurement
21. ELECTRODE MATERIALS
Inert metals (Hg, Pt, Au)
•Polycrystalline
•Monocrystals
Carbon electrodes
•Glassy carbon
•reticulated
•Pyrrolytic graphite
•Highly oriented (edge plane, )
•Wax impregnated
•Carbon paste
•Carbon fiber
•Diamond (boron doped)
Potential window available for experiments
is determined by destruction of electrode
Semiconductor electrodes (ITO)
material or by decomposition of solvent (or
Modified electrodes
dissolved electrolyte)
22. ELECTRON TRANSFER PHENOMENON
1-10 nm
1-10 nm in thickness
↓
↓
↓
↓ ↓ ↓
↓
~1 volt is dropped across this region…
Which means fields of order 107-8 V/m
↓
↓
↓
↓
↓
↓
l
↓
+
+
↓
↓
↓
+
+
↓
↓
l
↓
Where the truncation of the metal’s
Electronic structure is compensated for
in the electrolyte.
+
+
↓
↓
↓
l
↓ ↓
Solvated
ions
↓
↓
↓
l
↓ ↓ ↓
Electrode
surface
↓
The double-layer region is:
↓
↓
↓
↓ ↓ ↓
+
+
↓
↓
l
↓
“The effect of this enormous field at the electrodeelectrolyte interface is, in a sense, the essence of
electrochemistry.” [1]
l
IHL
OHL
[1] Bockris, Fundamentals of Electrodics, 2000
23. BUTLER-VOLMER AND TAFEL EQUATIONS
-
ne
+
ox
=
re d
E
∆G
E
#
-
2
zF ∆E
E
αzF ∆E
(E 2)
∆G
#
-
(E 1)
∆G
#
+
(E 1)
∆G
#
+
(E 2)
1
E 2< E
1
r e a c tio n c o o r d in a te
24. BUTLER-VOLMER AND TAFEL EQUATIONS
i
i0 , α = 0 .7
i0 , α = 0 .5
Exchange current density
Depends
on
the
species
undergoing redox transformation
and on the electrode material
i0 . α = 0 .3
0
i0 ' < i0 , α = 0 .5
η
exp (1−α ) nF ( E − E ° ) − exp αnF ( E − E ° )
0
RT
RT
i=i
In fact, large overpotential for
hydrogen evolution on Hg
surfaces enables us to observe
reductions in aqueous solutions
Also, the development of modern
modified electrodes is based on
finding the modifying layer
which increase the exchange
current density on the electrode
surface
25. BUTLER-VOLMER AND TAFEL EQUATIONS
i
lo g (a b s ( i0 ) )
η
i0
η
α
i = i0 exp (1−RT) zF ( E − E ° ) −exp αzF ( E − E ° )
RT
2.303αzF
log( i ) = log( i0 ) −
(E − E ° )
RT
27. TRANSPORT BY DIFFUSION
t1
C
t2
t3
t= 0
1st Fick Law
j = − D ∂C
∂x
C s
0
x ... d is ta n c e fr o m th e e le c tr o d e
C
t= 0
Nernst diffusion layer
c0 − cs
i = zFD
δN
Cs
ilim
0
δN
x
∂c
i = zFD
∂x x =0
c0
= zFD
δN
η D = E − E′ =
η D = E − E′ =
RT cS
ln
zF c0
RT
i
ln1 −
i
zF
lim
28. THE COTTRELL EQUATION
t1
C
t2
t3
t= 0
E
C s
t= 0
0
x ... d is ta n c e fr o m th e e le c tr o d e
t
∂c
∂ 2c
=D 2
∂t
∂x
Mathematical solution for boundary conditions of CA
experiment is very complicated, but the result is
simple:
Second Fickś law
i
c0 − cs
i = zFD
πDt
This is how Nernst layer thickness changes over time
t
29. TRANSPORT BY CONVECTION
Rotating disk electrode (RDE)
Rotating ring disk electrode
(RRDE)
c u rre n t ta k e -o ff
r o ta tin g c y lin d e r
s o lu tio n
" ro ta tin g d is k "
A c tiv e a re a o f
th e e le c tro d e
IL = (0,620)∙z∙F∙A∙D2/3∙ω1/2∙ν–1/6∙c Levich Equation
ω speed of rotation (rad∙s-1),
ν kinematic viscosity of the solution (cm2∙s-1),
kinematic viscosity is the ratio between solution viscosity and its specific weight.
For pure water: ν = 0,0100 cm2∙s-1, For 1.0 mol∙dm-3 KNO3 is ν = 0,00916 cm2∙s-1
(at 20°C).
c concentration of electroactive species (in mol.cm-3, note unusual unit)
D diffúsion coefficient (cm2∙s-1), A electrode area in cm2
31. CYCLIC VOLTAMMETRY
CV – the most important electrochemical method
One or more cycles …CV
Half cycle … LSV
0 ≤ t ≤ t r : E = Ei + vt
t r ≤ t ≤ 2t r : E = Ei + v( t − t r )
v… the scan rate
32. REVERSIBLE CYCLIC VOLTAMMOGRAM
Electroactive species attached
to the electrode, both redox
forms stable
I
(
)
F
exp
E − E0
F
RT
I = FAΓ0 v
2
RT
F
E − E 0
1 + exp
RT
(
E
0
E
)
33. REVERSIBLE CYCLIC VOLTAMMOGRAM
4.0×10 -6
B
O
fo rw a rd
scan
0
-2.0×10 -6
-0.50
Electroactive species in
solution, both stable
C
2.0×10 -6
I/A
R
A
re ve rs e
scan
R
IUPAC convention
O
D
-0.25
0.00
0.25
E/V vs. reference electrode
Randles-Sevcik equation:
0.50
Peak separation is 59 /z mV
Ipc = Ipa = 2,69.105 ∙ A ∙ z3/2 ∙ D1/2 ∙ c ∙ v1/2
A in cm2, D in cm2s-1/2, c in molcm-3, v in V/s
35. BASIC MECHANISMS IN CV
E, C notation
(E… electron transfer,
C… coupled chemical reaction)
E, EE, CE, EC, ECcat etc.
Mechanisms can be very complex
even for simple systems
Two electron-two proton system =
„square scheme“
37. THE EC MECHANISM
I/A
3.0×10 -6
O X
RED
Black: kf=0 cm.s-1
Blue: 0.2
Red: 0.5
Orange: 1
Green: 10
RED
Z
1.0×10 -6
-1.0×10 -6
-3.0×10 -6
-0.5
0.0
0.5
E/V vs. reference electrode
There are many variations of this mechanism:
Reaction with solvent
Dimerization
Radical substrate reaction
EC catalytic … etc.
38. EC catalytic
3.5×10 -5
I/A
2.5×10 -5
O X
R ED
RED + A
O X + Z
1.5×10 -5
Black : no A
Blue: A (c=1)
Red: A (c=10)
Green: A (c=100)
5.0×10 -6
-5.0×10 -6
-0.5
0.0
E/V vs. reference electrode
0.5
40. MICROELECTRODES
Microelectrode: at least one dimension must be comparable to diffusion layer
thickness (sub μm upto ca. 25 μm). Produce steady state voltammograms.
Converging diffusional flux
E le c tro d e
M e ta l c o n ta c t
C o n d u c tiv e jo in t
1 1
I = nFADc0 +
δ r
E le c tro d e b o d y
F ib e r
A )
In s u la to r
B)
C)
δ = 2πDt
Advantages of microelectrodes:
• fast mass flux - short response time (e.g. faster CV)
• significantly enhanced S/N (IF / IC) ratio
• high temporal and spatial resolution
• measurements in extremely small environments
• measurements in highly resistive media
