1. Unit Three
3. Interfacial Electrochemistry
Outline:
3.1. Introduction
3.2. Potential differences across interfaces
3.3. Electric Double Layer
3.4. Thermodynamics of electrified
interface
3.5. Electrochemical Kinetics
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2. 3.1 Introduction
The term “electrode potential” combines two basic notations:
“electrode” and “potential”.
The electrical potential φ, represents the electrical energy, which is
necessary for transferring a unit test charge from infinity in
vacuum into the phase under consideration.
It is only affected by external field, sufficiently small to induce
any charge redistribution inside the phase.
In actual practice, the charges exist only in a combination with
elementary particles, particularly, electrons, and ions.
Hence the value of φ appears to be beyond the reach of
experimental determination, a fact that posses the problems
concerned with interpretation of the electrode potential and brings
to existence numerous potential scales.
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3. 3.2. Potential differences across interfaces
One can measure the potential difference across a system of
interfaces or cell, not potential difference across one electrode-
electrolyte interface.
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4. In attempting to measure potential difference PDM1/S, one cannot avoid
including PDM2/S, etc within overall measured potential difference (PD).
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5. Non-polarizable interface: e.g. calomel or other reference
electrode, whose potential is a constant, i.e. it act as a leaky
capacitor, or any chare flowing into interface from external
source promptly leaks across interface.
Further, constant potential difference between two metals
depends on composition of the two metals and is unaffected by
potential difference across cell: hence,
δV ≈ δPDM1/S,
assuming that the M1/S interface is completely polarizable.
Example of an ideally polarizable interface:
Hg in contact with aqueous solution of an electrolyte. Equivalent
circuit of electrified interface:
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7. Work done in bringing unit +ve from infinity up to a point P (just
outside rich of image forces) and hence, the potential at this point,
is determined purely by the charge on the electrode and is not
influenced by any image interactions between test charge and
electrode.
This potential just outside the charged electrode is termed the outer
potential, Ψ(Volta potential). A simple potential may be defined for
the solution phase, so that
M∆SΨ = ΨM - ΨS
where M∆SΨ is the outer φ, that contribution to the potential difference
across an electrified interface arising from the charges on the two
phases (i.e. metal and solution).
M∆SΨ can be measured experimentally. Charge on solution is
removed, and solution is wrapped in an oriented-dipole layer.
Work done to transport charge across oriented dipole layer defines
the surface potential, χ.
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10. Since surface potentials cannot be measured, inner potentials
are not measurable.
Potential difference recorded by a measuring instrument is
sum of all the potential differences across several interfaces:
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12. Therefore the potential difference V registered by a measuring
system, i.e. V across the system is effectively equivalent to a
difference of inner potentials between the two pieces of the same
metal (or two phases of the same composition)which constitute
the terminals of the measuring instruments.
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14. 3.3. Electric Double Layer
List the different types of double layer structures.
What are the limitations of Helmhotz double layer model?
How Stern Double Layer structures differ from Gouy-Chapman
Double Layer structure?
The double layer model is used to visualize the ionic
environment in the vicinity of a charged surface.
It can be either a metal under potential or due to ionic groups
on the surface of a dielectric.
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15. Matter at the boundary of two phases possesses properties
which differentiate it from matter freely extended in either of
the continuous phases separated by the interface.
In solid solution interface, it may easier to visualize a
difference between the interface and the solid than between the
interface and the extended liquid phase.
Where we have a charged surface, however, there must be a
balancing counter charge, and this counter charge will occur in
the liquid.
The charges will not be uniformly distributed throughout the
liquid phase, but will be concentrated near the charged surface.
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16. Thus, we have a small and finite volume of the liquid phase
which is different from the extended liquid.
This concept is central to electrochemistry, and reactions
within this interfacial boundary that govern external
observations of electrochemical reactions.
It is also of great importance to soil chemistry, where colloidal
particles with different surface charges play a crucial role.
There are several theoretical treatments electrified double layer
interface.
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17. A. Helmholtz Double ( compact) Layer
It is the first theory of double layer, which considered the
ordering of +ve and -ve charges in a rigid fashion on the two
sides of the interface, giving rise to the designation of double
layer, the interactions not stretching any further into solution.
This model of the interface is comparable to the classic
problem of a parallel-plate capacitor.
One plate would be on the contact surface metal/solution and
other, formed by the ions of opposite charge from solution
rigidly linked to the electrode, would pass through the centers
of these ions (Figure 4.5).
So xu would be the distance of closest approach of the
charges, i.e. ionic radius, which, for the purpose of calculation,
were treated as point charges.
By analogy with a capacitor the capacity would be
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19. The Helmholtz theoretical treatment does not adequately explain
all the features, since it hypothesizes rigid layers of opposite
charges. This does not occur in nature.
The two principal faults of this model are;
1. it neglects interactions that occur further from the electrode than
the first layer of adsorbed species,
2. secondly that it does not take into account any dependence on
electrolyte concentration.
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20. B. Gouy-Chapman Double Layer
Gouy suggested that interfacial potential at the charged
surface could be qualified to the presence of a number of ions
of given sign attached to its surface, and to an equal number of
ions of opposite charge in the solution.
Counter ions are not rigidly held, but tend to diffuse into the
liquid phase until the counter potential set up by their
departure restricts this tendency.
The kinetic energy of the counter ions will, in part, affect the
thickness of the resulting diffuse double layer.
Gouy and, independently, Chapman developed theories of this
so called diffuse double layer.
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21. Figure 3.4 The Gouy-Chapman model of the double layer,
(a) Arrangement of the ions in a diffuse way;
(b) Variation of the electrostatic potential, ф, with distance, xy
from the electrode, showing effect of ion concentration, с.
(c) Variation of Cd with potential, showing the minimum at the
point of zero charge Ez.
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23. Already, however, we are in error, since derivation of this form
of the Boltzman distribution assumes that activity is equal to
molar concentration.
This may be an OK approximation for the bulk solution, but
will not be true near a charged surface.
It concerns about a diffuse double layer with the volume
charge density rather than a rigid double layer with surface
charge density when studying the columbic interactions
between charges.
The volume charge density, ρ, of any volume, i, can be
expressed as;
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24. Where - ψ varies from ψo at the surface to 0 in bulk solution.
Thus, we can relate the charge density at any given point to the
potential gradient away from the surface.
Combining the Boltzmann distribution with the Poisson
equation and integrating under appropriate limits, yields the
electric potential as a function of distance from the surface.
The thickness of the diffuse double layer:
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25. The Gouy-Chapman theory describes a rigid charged surface,
with a cloud of oppositely charged ions in the solution, the
concentration of the oppositely charged ions decreasing with
distance from the surface.
This is the so-called diffuse double layer. This theory is still
not entirely accurate.
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26. Experimentally, the double layer thickness is generally found
to be somewhat greater than calculated.
This may relate to the error incorporated in assuming activity
equals molar concentration when using the desired form of the
Boltzman distribution.
Conceptually, it tends to be a function of the fact that both
anions and cations exist in the solution and with increasing
distance away from the surface the probability that ions of the
same sign as the surface charge will be found within the
double layer increase as well.
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27. C. Stern Modification of the Diffuse double Layer
The Gouy-Chapman theory provides a better approximation of
reality than does the Helmholtz theory, but it still has limited
quantitative application.
It assumes that ions behave as point charges, which they
cannot, and it assumes that there is no physical limits for the
ions in their approach to the surface, which is not true.
Stern, therefore, combines the Gouy-Chapman and
Helmholtz model.
His theory states that ions do have finite size so cannot
approach the surface closer than a few nm.
The first ions of the Gouy-Chapman Diffuse Double Layer are
not at the surface, but at some distance δ away from the
surface.
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28. This distance will usually be taken as the radius of the ion.
As a result, the potential and concentration of the diffuse part
of the layer is low enough to justify treating the I Stern also
assumed that it is possible that some of the ions are
specifically adsorbed by the surface in the plane δ, and this
layer has become known as the Stern Layer.
Therefore, the potential will drop by ψo - ψδ over the
"molecular condenser" (ie. the Helmholtz Plane) and by ψδ
over the diffuse layer.
ψδ has become known as the zeta (ζ) potential.
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29. • Figure 3.5 The Stern model of the double layer, (a) Arrangement of the ions
in a compact and a diffuse layer; (b) Variation of the electrostatic potential,
ф, with distance, x, from the electrode; (c) Variation of Cd with potential.
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30. The double layer is formed in order to neutralize the charged
surface and, in turn, causes an electro kinetic potential between
the surface and any point in the mass of the suspending liquid.
This voltage difference is on the order of millivolts and is
referred to as the surface potential.
The magnitude of the surface potential is related to the surface
charge and the thickness of the double layer.
3.4. Thermodynamics of electrified interface
The interfacial tension at an interface is force acting on a unit
length of the interface against an increase in the interface area.
The region around the interface in which interfacial tension is
produced is very narrow.
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31. Tolman, Kirkwood and Buff state that this distance is only about
0.1- 0.3 nm for the liquid-vapour interface, corresponding to a
monolayer at the surface of the liquid, still affecting the next
nearest layer.
In order to derive a relationship that would qualitatively
characterize the formation of interfacial tension at the interface
between two homogeneous single component phases, the
following cycle will be considered.
First a free surface area of A is formed in each of phases α and β.
These surfaces are then brought into contact, forming the inter-
phase s.
The work required to separate these two phases and to return the
system to the original state is -γA, where γ is the interfacial
tension.
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32. Thus, γA = ∆G(α) + ∆G(β) - ∆G(s)
where ∆G(α) and ∆G(β) are the Gibbs energies required for
reversible separation (i.e. the formation of two free surfaces A)
of the phases α and β both divided by two.
∆G(s) is the Gibbs energy required for interrupting the contact
between phases α and β. The ∆G(s) are given by the equations
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33. where no(α) and no(β) are the numbers of nearest neighbors that
the particle has in the bulk of phases α and β, respectively,
ns(α) and ns(β) are the numbers of nearest neighbors from phase
α or β that the particle has at the interface,
εc(α) and εc(β) are the bond energies between this particle and its
nearest neighbour,
εr's are the energies required for rearrangement of the particle in
the inter-phase in order to be able to form a bond to a particle in
the neighbouring phase,
εv(α), εv(β), and εv(s) are the changes in the thermal vibrational
energies of the particle at the interface as a result of formation of
the free surface and contact between the phases,
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34. N(α) and N(β) are the numbers of particles per unit surface
area for the free surface of phases α and β,
εc(s) is the bond energy between the particles of phases α and β
in the interphase and N(s) is the number of such bonds per unit
surface area at the interphase.
If we assume that N(α) = N(β) = N(s), that species at the
surface have only one free bond (n0 - ns = l) and that εc » εr, εv,
then
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35. This expression can be roughly interpreted as the difference
between the Gibbs energy of adhesion of the two phases and
the sum of the Gibbs energies of cohesion for the two phases.
These considerations can also be used to derive the Dupre
equation, where ∆G(s) is the Gibbs energy of adsorption of the
solvent per unit area of the metal surface:
∆G(s) = γm/a + γ1/a - γ
where γm/a is the interfacial tension of the metal-air interface,
γ1/a is the interfacial tension of the solution-air interface and γ
is the interfacial tension of the metal-solution interface.
Now the relationship between the interfacial tension and the
composition of the two phases in contact will be analyzed
thermodynamically by using the approach of J. W. Gibbs.
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36. The inter-phase can be considered as a particular phase s of
thickness h.
This phase differs from the homogeneous phases only in that
the effect of pressure is accompanied by the effect of the
interfacial tension γ.
Consider a rectangle with sides h (perpendicular to the
interphase) and l (parallel with the interphase) located
perpendicular to the interphase.
The force acting on the rectangle is not equal to the product
phl (as for an area in the bulk of the solution) but phl - γl.
If the volume of the interphase V(s) is increased by dV(s) by
increasing the thickness of the interphase by dh, then area A =
V(s)/h increases by dA.
The overall work, W, connected with this process consists of
volume work accompanying the increase in the thickness of
the interphase and volume and surface work connected with an
increase of the surface area:
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37. W (s) = - pAdh + (-ph + γ) dA = - pdV (s ) + γ dA
• Because of this formation, a different definition of the enthalpy
must be introduced for the interphase, differing from the usual
expression for a homogeneous phase:
H(s) = U(s) +pv(s) - γ A
where U(s) is the internal energy of the interphase. For the differential
Gibbs energy of the interphase we have
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39. This relationship is termed the Gibbs adsorption equation.
It is often useful (e.g. for dilute solutions) to express the
adsorption of components with respect to a predominant
component, e.g. the solvent.
The component that prevails over m components is designated
by the subscript 0 and the case of constant temperature and
pressure is considered.
In the bulk of the solution, the Gibbs-Duhem equation,
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41. • When the adsorbed components are electrically charged, then
the partial molar Gibbs energy of the charged component
depends on the charge of the given phase, and thus the
chemical potentials in the above relationships must be replaced
by the electrochemical potentials.
• The Gibbs adsorption isotherm then has the form
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42. The interfacial tension always depends on the potential of the
ideal polarized electrode.
In order to derive this dependence, consider a cell consisting of
an ideal polarized electrode of metal M and a reference non
polarizable electrode of the second kind of the same metal
covered with a sparingly soluble salt MA.
Anion A- is a component of the electrolyte in the cell.
The quantities related to the first electrode will be denoted as
m, the quantities related to the reference electrode as m' and to
the solution as 1.
For equilibrium between the electrons and ions M+ in the
metal phase, the Gibbs adsorption isotherm can be written in
the form (s = n - 2)
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47. This quantity is, in general, a function of the electrode
potential.
An important point on the electro capillary curve is its
maximum. It follows from the surface charge density equation
that σ(m) = σ(1) = 0 at the potential of the electrocapillary
maximum.
This potential is termed the zero-charge potential and is
denoted as Epzc.
In earlier usage, this potential was also called the potential of
the electro capillary zero; this designation is not suitable, as
Epzc is connected with the zero charge σ(m) rather than the
zero potential.
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49. Figure 3.6 Electro capillary curves of 0.1 M aqueous solutions of
KF, KC1, KBr, KI and K2SO4 obtained by means of the drop-
time method.
The slight deviation of the right-hand branch of the SO4
2- curve is
caused by a higher charge number of sulphate. (By courtesy of L.
Novotny) Further, the concept of the integral capacity K will be
introduced:
The differential capacity is given by the slope of the tangent to
the curve of the dependence of the electrode charge on the
potential, while the integral capacity at a certain point on this
dependence is given by the slope of the radius vector of this point
drawn from the point Ep = Epzc.
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50. The zero-charge potential is determined by a number of
methods. A general procedure is the determination of the
differential capacity minimum which, at low electrolyte
concentration, coincides with Epzc.
With liquid metals (Hg, Ga, amalgams, metals in melts) Epzc
is directly found from the electro capillary curve.
As a material function, the zero-charge potential of various
metals (and even of different crystallographic faces of the
same metal) extends over a wide range of values.
How it is related to other material functions like the electron
work function Φe has not yet been elucidated.
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51. However, S. Trasatti found two empirical equations, one for sp
metals with the exception of Ga and Zn (i.e. for Sb, Hg, Sn, Bi,
In, Pb, Cd, Ti), Epzc(H2O) = Φe /F -4.69 V versus SHE, and the
other one for the transition metals (Ti, Ta, Nb, Co, Ni, Fe, Pd),
Epzc = Φe /F - 5.01 V versus SHE.
For solutions of simple electrolytes, the surface excess of ions
can be determined by measuring the interfacial tension.
Consider the valence symmetrical electrolyte BA (z+ = -Z- = z).
The Gibbs- Lippmann equation then has the form
while
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53. In this manner, the surface excess of ions can be found from
the experimental values of the interfacial tension determined
for a number of electrolyte concentrations.
These measurements require high precision and are often
experimentally difficult.
Thus, it is preferable to determine the surface excess from the
dependence of the differential capacity on the concentration.
By differentiating the surface excess, ΓB+ equation with
respect to EA and using the surface charge density and the
differential capacity of the electrode, C, in turn we obtain the
Gibbs-Lippmann equation
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54. Double integration with respect to EA yields the surface excess
ΓB+; however, the calculation requires that the value of this
excess be known, along with the value of the first differential
dΓB+/dEA for a definite potential.
This value can be found, for example, by measuring the
interfacial tension, especially at the potential of the electro
capillary maximum.
The surface excess is often found for solutions of the alkali
metals on the basis of the assumption that, at potentials
sufficiently more negative than the zero-charge potential, the
electrode double layer has a diffuse character without specific
adsorption of any component of the electrolyte.
The theory of diffuse electrical double layer is then used to
determine ΓB+ and dΓB+/dEA.
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55. In practical measurements, the differential capacity values are
determined with respect to a reference electrode connected to
the studied electrolyte through a salt bridge.
The measured data are then recalculated for an anionic
reference electrode by adding the value RT/F lna±2 to the Ep
value.
The quantity dγ/dna±2at the potential of the electrocapillary
maximum is of basic importance.
As the surface charge of the electrode is here equal to zero, the
electrostatic effect of the electrode on the ions ceases.
Thus, if no specific ion adsorption occurs, this differential
quotient is equal to zero and no surface excess of ions is
formed at the electrode.
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56. This is especially true for ions of the alkali metals and alkaline
earths and, of the anions, fluoride at low concentrations and
hydroxide.
Sulphate, nitrate and perchlorate ions are very weakly surface
active.
The remaining ions decrease the surface tension at the
maximum on the electro capillary curve to a greater or lesser
degree.
In the case of a specific ('super equivalent') adsorption we have
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57. where Γsalt is the surface excess for both components of the
electrolyte.
One of them may be specifically adsorbed and the second
compensates the corresponding excess charge by its excess
charge of opposite sign in the diffuse layer.
3.5. Electrochemical Kinetics Current density
The rate of a homogeneous reaction, vr:
Vr =
1𝑑𝑛
𝑉𝑑𝑡
where the unit for Vr is mol dm-3 s-1
Taking stoichiometric number to be one, V =1, Vr =
𝑑𝑛
𝑑𝑡
The reaction rate of a heterogeneous process (e.g., an electrode
process) depends on the surface of the electrode at constant
polarization potential.
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58. The rate, v refers to unit surface area:
Vr =
1𝑑𝑛
𝐴𝑑𝑡
, where the unit for Vr is mol dm-1s-1
The rate of an electrode process is proportional to the current
density: j=
1𝑑𝑞
𝐴𝑑𝑡
1
The current density is proportional to rate of an
electrochemical reaction and it makes rate independent of the
area of electrode.
An infinitesimal amount of charge dq is proportional to the
amount of material passed through the interface; dq = zF .dn
j=
zF
𝐴
dn
𝑑𝑡
2
From equations 1. and 2. we get j = zF .v 3
The reaction rate of a unit surface electrode is proportional to
current density.
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59. Polarization, overvoltage
Polarization: the shift in the voltage across a cell caused by the
passage of current, departure of the cell potential from the
reversible(or equilibrium or nernstian) potential.
For a simple reversible redox reaction Mz+ + ze- ↔ M
the cathodic process is a reduction at a rate jc, cathodic current
density, while the anodic process is an oxidation at a rate ja,
anodic current density.
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60. At equilibrium a rest or equilibrium potential εe is measured
against a proper reference electrode.
When electrochemical equilibrium is established |jc| = |ja| = jo
the anodic and cathodic current densities are the same and
equals to exchange current density.
Increasing the negative potential:
|jc| > |ja|
• The portion of potential differs from equilibrium potential is
called overvoltage (η ).
η =𝜀pol - 𝜀e 4
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62. Mass transport:
reactants are transported from the bulk of solution to the electrode
surface by diffusion
products are transported from electrode to the bulk by diffusion
Charge transfer: the electron jump between the metal and liquid
phase.
The slowest process determines the net rate of the electrode
reaction.
Mass transport and charge transfer are the most important steps in
controlling the rate of electrochemical processes.
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63. Fast mass transport but rate limiting electron transfer kinetics.
Normal homogeneous kinetics at a temperature is
characterized a rate constant independent of the composition
of reaction mixture.
Why can an applied voltage affect the kinetics of a reaction?
Question can be answered at the level of equilibrium
electrochemistry?
∆Go = -RT ln K
∆Go = -nFEo
And Question can be answered at the level of electrochemical
kinetics by using the transition state theory (TST).
Consider a reduction reaction: O + ze- →R
By TST, the species, O with gain an electron and goes through
a transition state.
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64. The energy barrier to forming this is called ΔG‡c. The c
subscript denotes this to be a cathodic reaction – that is a
reduction reaction.
The free energy barrier of an electrochemical reaction is linked
to the applied potential.
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65. When a potential is applied, the free energy of reactants (O + ne-)
is raised by an amount zFE where E is the applied potential.
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73. This is the equation of a polarization curve giving current
potential characteristics of an electrochemical process for a metal
electrode of clean surface, crystal parameters, electrolyte
composition concentration are known and the process is charge
transfer controlled.
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