Transcript Electron transfer in heterogeneous systems (on electrodes)

Electron transfer in heterogeneous
systems
(on electrodes)
Impacts on our society
• Most of the modern method of generating
electricity are inefficient, and the development of
fuel cells could revolutionize the production and
deployment of energy.
• The inefficiency can be improved by knowing
more about the kinetics of electrochemical
processes.
• Applications in organic and inorganic
electrosynthesis.
• Waste treatments.
25.8 The electrode-solution
interface
• Electrical double layer
Helmholtz layer model
Gouy-Chapman Model
• This model explains why
measurements of the
dynamics of electrode
processes are almost
always done using a large
excess of supporting
electrolyte. ( Why??)
The Stern model of the electrodesolution interface
• The Helmholtz model
overemphasizes the
rigidity of the local solution.
• The Gouy-Chapman
model underemphasizes
the rigidity of local solution.
• The improved version is
the Stern model.
The electric potential at the interface
1. Outer potential
2. Inner potential
3. Surface potential
The potential difference
between the points in
the bulk metal (i.e.
electrode) and the bulk
solution is the Galvani
potential difference
which is the electrode
potential discussed in
chapter 7.
The origin of the distanceindependence of the outer potential
The connection between the
Galvani potential difference and the
electrode potential
• Electrochemical potential (û)
û = u + zFø
• Discussions through half-reactions
25.9 The rate of charge transfer
• Expressed through flux of products: the amount of material produced over a
region of the electrode surface in an interval of time divided by the area of the
region and the duration of time interval.
• The rate laws
Product flux = k [species]
The rate of reduction of Ox,
vox = kc[Ox]
The rate of oxidation of Red,
vRed = ka[Red]
• Current densities:
jc = F kc[Ox] for Ox + e- → Red
ja = F ka[Red] for Red →Ox + ethe net current density is:
j = ja – jc = F ka[Red] - F kc[Ox]
The activation Gibbs energy
•
Write the rate constant in the form suggested by activated complex theory:

k  B e   G / RT

j  FBa [Red ]e   Ga / RT
•

 FBc [Ox]e   Gc / RT
Notably, the activation energies for the catholic and anodic processes
could be different!
The Butler-Volmer equation
Variation of the Galvani potential difference across the electrode –
solution interface
The reduction reaction, Ox + e → Red
 Gc   Gc (0)  F
 Gc   Gc (0)  F
 Ga   Ga (0)  (1   ) F
The parameter α is called the transient coefficient and lies in the range 0 to 1.
Based on the above new expressions, the net current density can be expressed
as:


j  FBa [RED ]e   Ga ( 0) / RT e (1 ) F / RT  FBc [Ox]e   Gc ( 0 ) / RT e F / RT
assuming f 
then
F
RT
ja  FBa [RED ]e

  Ga ( 0 ) / RT (1 ) f
e
jc  FBc [Ox]e   Gc ( 0) / RT e f
j  ja  jc
• Example 25.1 Calculate the change in
cathodic current density at an electrode
when the potential difference changes
from ΔФ’ to ΔФ
• Self-test 25.5 calculate the change in
anodic current density when the potential
difference is increased by 1 V.
Overpotential
• When the cell is balanced against an external source, the
Galvani potential difference, , can be identified as the
electrode potential.
• When the cell is producing current, the electrode potential
changes from its zero-current value, E, to a new value, E’.
• The difference between E and E’ is the electrode’s
overpotential, η.
η = E’ – E
• The ∆Φ = η + E,
• Expressing current density in terms of η
ja = j0e(1-a)fη
and
jc = j0e-afη
where jo is called the exchange current density, when ja = jc
• The butler-Volmer
equation:
j = j0(e(1-a)fη - e-afη)
• The lower
overpotential limit
( η less than 0.01V)
• The high
overpotential limit
(η ≥ 0.12 V)
The low overpotential limit
• The overpotential η is very small, i.e. fη <<1
• When x is small, ex = 1 + x + …
• Therefore ja = j0[1 + (1-a) fη]
jc = j0[1 + (-a fη)]
• Then j = ja - jc = j0[1 + (1-a) fη] - j0[1 + (-a fη)]
= j0fη
• The above equation illustrates that at low overpotential limit, the
current density is proportional to the overpotential.
• It is important to know how the overpotential determines the property
of the current.
Calculations under low overpotential
conditions
• Example 25.2: The exchange current density of a Pt(s)|H2(g)|H+(aq)
electrode at 298K is 0.79 mAcm-2. Calculate the current density
when the over potential is +5.0mV.
Solution: j0 = 0.79 mAcm-2
η = 5.0mV
f = F/RT =
j = j0fη
• Self-test 25.6: What would be the current at pH = 2.0, the other
conditions being the same?