1. Overpotential
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

2. The low overpotential limit
The overpotential η is very small, i.e. fη <<1
When x is small, ex = 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.

3. Calculations under low overpotential conditions
Example: 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 = 6.0mV
f = F/RT =
j = j0fη

4. The high overpotential limit
The overpotential η is large, but could be positive or negative!!!
When η is large and positive
j0e-afη = j0/eafη becomes very small in comparison
to ja
Therefore j ≈ ja = j0e(1-a)fη
ln(j) = ln(j0e(1-a)fη ) = ln(j0) + (1-a)fη
When η is large but negative
ja is much smaller than jc
then j ≈ jc = j0e-afη
ln(j) = ln(j0e-afη ) = ln(j0) – afη
Tafel plot: the plot of logarithm of the current density against the over potential.

5. Calculations under high overpotential conditions
The following data are the anodic current through a platinum electrode of area 2.0 cm2 in contact with an Fe3+, Fe2+ aqueous solution at 298K. Calculate the exchange current density and the transfer coefficient for the process.
η/mV
I/mA
Solution: calculate j0 and a
Note that I needs to be converted to J

6. The general arrangement for electrochemical rate measurement

7. Voltammetry
Voltammetry: the current is monitored as the potential of the lectrode is changed.
Chronopotentiometry: the potential is monitored as the current density is changed.
Voltammetry may also be used to identify species and determine their concentration in solution.
Non-polarizable electrode: their potential only slightly changes when a current passes through them. Such as calomel and H2/Pt electrodes
Polarizable electrodes: those with strongly current-dependent potentials.

8. Concentration polarization
Concentration polarization: The consumption of electroactive species close to the electrode results in a concentration gradient and diffusion of the species towards the electrode from the bulk may become rate-determining. Therefore, a large overpotential is needed to produce a given current.
Eqns to will be discussed in class
Example 29.3: Estimate the limiting current density at 298K for an electrode in a 0.10M Cu2+(aq) unstirred solution in which the thickness of the diffusion layer is about 0.3mm.

9. Experimental techniques in voltammetry

10. Experimental techniques in voltammetry

11. Experimental techniques in voltammetry

12. Electrolysis
Cell potential: the sum of the overpotentials at the two electrodes and the ohmic drop due to the current through the electrolyte (IRs).
Electrolysis: To induce current to flow through an electrochemical cell and force a non-spontaneous cell reaction to occur.
Estimating the relative rates of electrolysis.