Transcript Slide 1

Lecture 6.1
Kinetics of Electron Transfer at the Solid Electrode-Solution Interface
Examination of the Eyring Equation under various conditions.
Case II: At applied potentials E different than Eeq such that we
are applying an overpotential, h = E- Eeq
Skipping the derivation (you should be able to do it):
CO (0,t ) -nfh CR (0,t ) (1- ) nfh
i  i0 [
e
e
]
*
*
CO
CR
NB: Not corrected for DL effects- see page 571
At E = Eeq, Ci(0,t) = Ci*, and so i = i0
 C R (0, t ) 

i  F 
*
 CR 
 CO (0, t ) 

i  F 
*
 CO 
High h, MT control
Low h, Exponential control
Lecture 6.2
Kinetics of Electron Transfer at the Solid Electrode-Solution Interface
This expression makes it difficult to extract key information.
Must use approximations resulting from certain limiting conditions:
Approximation A : 1) Well-stirred solution, and 2) i is small
That means that Ci(0,t) = Ci* and E is near Eeq
Butler-Volmer
Eqn.
-nfh
i  i0[e
(1- ) nfh
-e
This is a good approximation of the i-h Eqn. when:
0.9 ≤ Ci(0,t)/Ci* ≤ 1.1
Or
i is ≤ 10% of ilim
]
Lecture 6.3
Kinetics of Electron Transfer at the Solid Electrode-Solution Interface
Because MT is not a component of the measured i, then i is
based solely on the activation energy of the process.
i0  F(k 0 )  F' (h -1 )
So, the observed potentials for oxidation are more positive and
those for reduction more negative than E0’.
i0 is merely a measure of a system’s ability to provide a net
current w/o a significant energy loss due to activation effects.
Approximation A, with Small h:
-nfh
i  i0[e
Linearized
Butler-Volmer
Eqn.
(1- ) nfh
-e
]
For small x, ex ≈ 1+x
(be able to derive)
i  i0fh
jc
Use for Fast ET
Region
of
interest
+h
h
ja
Lecture 6.4
Kinetics of Electron Transfer at the Solid Electrode-Solution Interface
Approximation A, with Large ±h:
-nfh
(1- ) nfh
i  i0[e
-e
]
For large -h
i  i0e
-nfh
Tafel Eqn.
Holds when:
1. ib is < 0.01 if
Or
2. |h| > 118/n mV
Or
i0
ln  nfh
i
RT
RT
h
ln i0 
ln i
nF
nF
Use for Slow ET
(Typically for Totally Irreversible Systems)
Tafel Plots to Obtain Kinetic and Other Information
ln i  ln i0 ln i  ln i0
nFh
h large negative
RT

1   nFh
+
RT
h large positive
Lecture 6.5
Kinetics of Electron Transfer at the Solid Electrode-Solution Interface
When h is large, must recognize that MT limitations occur.
n should be there
When h is small, near 0,
must be cognizant of
back reactions.
Anodic
Branch
Cathodic
Branch
Extrapolate to 0 h and obtain log i0.
Obtain h from slope.
Read about exchange current plots (pp. 105-107)
on your own and learn about methods to obtain 
and other parameters independently (see problem
3.11).