7. Introduction to electrometric methods

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7. Introduction to electrometric methods 7.1
Structure of the metal interface
neutrality condition
interface two capacitors in series
OHP- outer Helmholtz plane distance of the
closest approach of solvated ions IHP inner
Helmholtz plane plane in which specifically
adsorbed ions are located Diffuse layer layer
within which ionic cloud screening the charge on
the metal is located
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Capacity of an Au electrode
adsorbed anions
Nonadsorbing electrolyte
adsorbed neural organic molecules
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Capacity of an electrode changes with potential
the changes reflect changes in the Coverage by
specifically adsorbed ions or molecules


true capacity
pseudo capacity
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Potential drop across the metal solution interface
no specific adsorption
specific adsorption of anions
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7.2 Electrochemical cell in the presence of a
current flowing through the cell
Two electrode cell
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when potential E is applied from an external
source current flows through the cell
From Ohms Law
Zi impedance of the indicator electrode Ze
impedance of the electrolyte ZRef impedance of
the reference electrode Zext impedance of the
external circuits
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In an electrochemical experiment Ze, ZRef, Zext
must be eliminated
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a. Elimination of ZRef
- specific resistivity
- length
- area
- capacity
-angular frequency
hence
then
Consequently if
The surface area of an indicator electrode should
be much smaller than the surface area of the
reference or auxiliary electrodes
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b) Elimination of Ze
Use 3-electrode system and Luggin capillary
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Luggin capillary and uncompensated resistance Ru
For a planar electrode
For a spherical electrode
- radius of the spherical electrode
- distance from the electrode surface
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7.3 Three electrode system potentiostat
Summing amplifier
E1
E2
E3
E
E
E
E
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Simple potentiostat
Note that if
than
Problem with this circuit current flows through
the reference electrode
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Voltage Follower
Eo
Ei
( or counter electrode)
auxiliary electrode
working electrode
reference electrode
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7.4 Current flowing through a simple RC circuit
When a potential step is applied to the circuit
the current is described by
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Change of potential across the capacitor as a
function of time
since
EC across the capacitor
one obtains
t
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Linear potential sweep or voltage ramp
where
is the sweep rate in V s-1
or
if q0 at t0
if tgtgtRsCd
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Cyclic-linear potential sweep
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8.1 Electrode reaction as a series of multiple
consecutive steps
A charge transfer reaction provides an additional
channel for current to flow through the
interface. The amount of electricity that flows
through this channel depends on the amount of
species being oxidized or reduced according to
the Faraday law
Faraday law links electrical quantity such as
current to the chemical quantity such as
concentration or mass of the analyte
This expression may be rearranged to give
expression for current
n- number of electrons in a redox reaction,
N-number of moles, MA- molecular weight, F-
Faraday constant, C-concentration, V-volume
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Currents which are described by the Faraday law
are called faradaic currents
This equation described average current flowing
through the electrode During time t. During
infinitesimal period dt the number of
electrolyzed moles is dN and the expression for
the instantaneous current is
The rate of a chemical reaction is
Hence faradaic current is a measure of a reaction
rate
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Current flowing in the absence of a redox
reaction nonfaradaic current In the presence
of a redox reaction faradaic impedance is
connected in parallel to the double layer
capacitance. The scheme of the cell is
The overall current flowing through the cell is
i if inf Only the faradaic current if
contains analytical or kinetic information
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Non-faradaic ( capacitive ) current constitutes a
limitation to the detection limit of
electrometric techniques
Experimental conditions for electroanalytical
measurements
( large concentration of electroactive
species, long times of experiment)
1.
( correction for non-faradaic current)
2.
are different functions of time
and
Under a steady state condition
but
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Current voltage characteristics of an ideal
polarizable and ideal non-polarizable electrode
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(No Transcript)
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For a multistep reaction
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8.2 Mechanism of electron transfer at the
electrode solution interface
Solution contains Red-Ox system
Ox species provide unoccupied electronic levels
Red species provide occupied electronic levels
Metal
Conductive band provides unoccupied electronic
levels Valence band provides occupied electronic
levels Electron transfer across the
interface Results from a quantum mechanical
resonance between the energy levels of this same
energy on the metal and the solution side of the
interface
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antibonding
- is the resonance energy
bonding
is the distance between the energy levels
is the overlap integral
Rate of the charge transfer reaction
is the probablity of electron transfer
is the density of electronic levels in the metal
is the density of electronic levels in solution
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• Quantum mechanical probability of an electron
  transfer from an electrode
• to solution

The bonding state is not formed instantaneously
but requires a certain time to be formed. This
time is given by the Heisenbergs uncertainty
principle.
The energy levels in solution have limited life
time. They may be deactivated by a) diffusion
jumps
b) rotation of the solvent molecule in the
coordination shell
c) vibrations in the coordination shell
To have an effective electron transfer
but
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Probablity of the electron transfer is a function
of
Properies of
if
if
recalling that
and that
ln P
adiabatic
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non-adiabatic
0.5 to 0.8nm
x
( distance between energy levels)
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b) Density of electronic levels in the metal
Enegy of Fermii level equal to electrochemical
potential of electron in the metal
Fermi statistics describes distribution of
electrons between electronic levels. N-total
number of electronic levels
Fermi function
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if
Energy
Density of states
N
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c. Density of electronic levels in solution
Occupied electronic level provided by Reduced
species (Red) Unoccupied electronic level
provided by Oxidized specied ( Ox) Energy of an
occupied level in solution work done in
reaction Redsolv? Oxsolv evacuum Energy of
an unoccupied level in solution work done in
reaction Oxsolv evacuum ? Redsolv Distribution
of energy levels in solution Electron transfer
in solution is subject to Frank-Condon constrain.
Electron Transitions take place at fixed nuclei
positions
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Page 110
U
Oxv ev
Redv
?
unoccupied at T0
at T gt 0
occupied at T0
?
?Red
?Ox
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Metal
Solution
? P DM DS
?
?Ox
?F
?Red
?
DM
DS
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