Introduction to voltammetry
using CV Sim
N. Murer, J.-P. Diard
CV Sim
1
Objectives
Understand what is performed during a
voltammetry experiment.
Understand what information can be obtained
on the studied electrochemical system.
Simplest case : The redox reaction (E)
A+e↔B
Example : [Fe(CN)6] 3- + e- ↔ *Fe(CN)6]4A≡O and B≡R
other reactions (EE), (EC), (CE) not presented here
CV Sim
2
Outline
1. Study by linear voltammetry
1. Influence of the scan rate
1. Reversible reaction, high k°
2. Irreversible reaction, low k°
2. The double layer capacitance and the ohmic drop
2. Study by cyclic voltammetry
1. Influence of the first vertex
2. Influence of the k°
3. Influence of the number of scan
4. Influence of the scan rate
CV Sim
3
Two types of voltammetry
Linear
CV Sim
Cyclic
4
Outline
1. Study by linear voltammetry
1. Influence of the scan rate
1. Reversible reaction, high k°
2. Irreversible reaction, low k°
2. The double layer capacitance and the ohmic drop
2. Study by cyclic voltammetry
1. Influence of the first vertex
2. Influence of the k°
3. Influence of the number of scan
4. Influence of the scan rate
5
Influence of the scan rate
Experimental conditions
Only A in solution, support electrolyte, unstirred solution, no ohmic drop,
negligible double layer capacitance current.
The CVSim tool in EC-Lab is used to simulate an I vs. E curve corresponding to a redox
reaction.
Linear Voltammetry
6
Influence of the scan rate
Scan
direction
We define the peak
current Ip and the potential
at which the peak current
is reached Ep.
CA≠0 at Ep.
E° = 0.2 V
Peak current: Ip
Ep
During the potential sweep, CA decreases and approaches 0
after Ep.
Linear Voltammetry
7
Outline
1. Study by linear voltammetry
1. Influence of the scan rate
1. Reversible reaction, high k°
2. Irreversible reaction, low k°
2. The double layer capacitance and the ohmic drop
2. Study by cyclic voltammetry
1. Influence of the first vertex
2. Influence of the k°
3. Influence of the number of scan
4. Influence of the scan rate
8
Influence of the scan rate
Which information can we get ?
Limit case #1: Reversible reaction, high reaction standard constant ko
k°=10 cm s-1
A = 0.03142 cm2
CA* = 10-5 mol cm-3
Red curve : 10 V s-1
Green curve : 40 V s-1
Purple curve : 160 V s-1
Pink curve : 640 V s-1
Blue curve : 2560 V s-1
Scan
direction
If the scan rate v is 4 times larger, Ip is √4 times larger.
For high ko, Ip is dependent on the scan rate but Ep is not.
Linear Voltammetry
9
Influence of the scan rate
Which information can we get ?
Limit case #1: Reversible reaction, high ko
Ip vs Scan rate
Ip (A)
Ip is proportional to the square root of the scan rate.
Linear Voltammetry
10
Influence of the scan rate
Which information can we get ?
Limit case #1: Reversible reaction, high ko
Knowing all the other parameters we can
recalculate
v (V/s) M
10
40
160
640
2560
0.4461
0.4458
0.4453
0.4441
0.4420
As the scan rate increases,
the factor M goes further
away from 0.446.
The system becomes less
and less reversible (more
and more irreversible).
It shows that
Linear Voltammetry
11
Influence of the scan rate
Which information can we get ?
Limit case #1: Reversible reaction, high ko
Ep vs Scan rate
D A 1.109
1
E p= E −
ln −
2 nf DB
nf
o
Ep can be used to determine the standard potential of the redox
couple A/B.
If Ep does not change with v, it means it is a reversible redox reaction,
then k° cannot be determined.
Linear Voltammetry
12
Outline
1. Study by linear voltammetry
1. Influence of the scan rate
1. Reversible reaction, high k°
2. Irreversible reaction, low k°
2. The double layer capacitance and the ohmic drop
2. Study by cyclic voltammetry
1. Influence of the first vertex
2. Influence of the k°
3. Influence of the number of scan
4. Influence of the scan rate
13
Influence of the scan rate
Which information can we get ?
Limit case #1: Ireversible reaction, low ko
k°=10-3 cm s-1
A = 0.03142 cm2
CA* = 10-5 mol cm-3
Red curve : 10 V/s
Green curve : 40 V/s
Purple curve : 160 V/s
Pink curve : 640 V/s
Blue curve : 2560 V/s
Scan
direction
Ip and Ep depend on the scan rate :
the higher the scan rate, the higher |Ip|and the lower Ep .
What can we measure from this dependence ?
Linear Voltammetry
14
Influence of the scan rate
Which information can we get ?
Limit case #1: Irreversible reaction, low ko
The peak current Ip is
proportional to the
square root of the
scan rate.
Ip
The slope above can be used to determine the diffusion coefficient
DA or the symmetry factor r.
Linear Voltammetry
15
Influence of the scan rate
Which information can we get ?
Limit case #1: Irreversible reaction, low ko
Ep
The dependence of Ep with v can be used to determine
Linear Voltammetry
r
and k°.
16
Summary
To investigate a redox system in the standard condition, one can make several
CV's with different scan rates v :
if Ep is invariant and Ip is proportional to v1/2 → reversible behaviour (high
ko). Possible measurements : diffusion coefficient DA and the standard
potential Eo of the reaction.
if Ep varies with log(v) and Ip is proportional to v1/2 → irreversible behaviour
(low ko).
Possible measurements : the symmetry factor αr and the standard constant ko
of the reaction.
Whichever the value of ko, it is possible to shift from an reversible to a
irreversible behaviour by increasing the potential scan rate.
In reality there is an ohmic drop and the double layer capacitance current is
not negligible. They must be taken into account, which is possible with CVSim.
Linear Voltammetry
17
Outline
1. Study by linear voltammetry
1. Influence of the scan rate
1. Reversible reaction, high k°
2. Irreversible reaction, low k°
2. The double layer capacitance and the ohmic drop
2. Study by cyclic voltammetry
1. Influence of the first vertex
2. Influence of the k°
3. Influence of the number of scan
4. Influence of the scan rate
18
Cdl
For a « random » k°, v = 10 V/s
Scan
direction
Itotal = Ic + If
(with CV Sim the two
contributions can be
separated)
Ic = Cdl(dE(t)/dt) = -Cdlv
For a constant scan rate the capacitive current is also constant.
Linear Voltammetry
19
Cdl
For a « random » k°, v = 1000 V/s
Scan
direction
Itotal = Ic + If
Ic = Cdl(dE(t)/dt) = -Cdlv
For a high scan rate, the value of the capacitive current Ic can be
higher than the faradaic current If and cannot be neglected.
Linear Voltammetry
20
RΩ
For a « random » k°, v = 1 V/s
Scan
direction
RΩ = 0 Ω, RΩ = 20 Ω, RΩ = 100 Ω
The actual potential seen by the electrode is not linear.
E(t) = vt + RI(t). The ohmic drop leads to a shift of Ip and Ep.
The potential shift is due to the term –RI.
Linear Voltammetry
21
Cdl and RΩ
For a « random » k°, v = 10 V/s
Scan
direction
Itotal = Ic + If
Ic(t) = Cdl(dE(t)/dt)
Because of the ohmic drop dE(t)/dt = v – RΩdI(t)/dt, Ic(t) is not constant even
if the scan rate is constant.
Linear Voltammetry
22
Cdl and RΩ
For a negligible faradaic current i.e. at short times, the system is
equivalent to an R+C electrical circuit.
Ic = -Cdl v (for t > 0.01 s)
τ = RΩ Cdl
A time constant, RΩ Cdl can be
measured at short times.
Linear Voltammetry
Ic
τ
23
Outline
1. Study by linear voltammetry
1. Influence of the scan rate
1. Reversible reaction, high k°
2. Irreversible reaction, low k°
2. The double layer capacitance and the ohmic drop
2. Study by cyclic voltammetry
1. Influence of the first vertex
2. Influence of the k°
3. Influence of the number of scan
4. Influence of the scan rate
24
Cyclic Voltammetry
Einit
E vs. t
Vertex 2
Vertex 1
25
Cyclic Voltammetry
Ep ox, Ip ox
CVsim .m pr
I vs. Ew e
600
Oxidation
B
Vertex 2
A
400
I/mA
200
Einit
0
-200
Vertex 1
Reduction
-400
-600
B
A
-800
0
Ep red, Ip red
0,5
Ewe/V
26
Outline
1. Study by linear voltammetry
1. Influence of the scan rate
1. Reversible reaction, high k°
2. Irreversible reaction, low k°
2. The double layer capacitance and the ohmic drop
2. Study by cyclic voltammetry
1. Influence of the first vertex
2. Influence of the k°
3. Influence of the number of scan
4. Influence of the scan rate
27
Influence of the first vertex
Vertices : -0,3 V
0V
0,1 V
Reversible system (k° = 10 cm2 s-1)
B
B
A
A
Ip,ox and to a smaller extent Ep,ox depend on the value of the Vertex 1.
The correct vertex value is the one after which Ip, ox and Ep, ox
do not vary.
Cyclic Voltammetry
28
Influence of the first vertex
Ep difference
B
B
A
A
For a vertex 1 of -0,3 V, the difference ΔEp is equal to 57,7 mV.
It was calculated1 that for a vertex 1 of -∞, this difference is 57 mV.
It can be considered that -0,3 V is a sufficiently low vertex 1
potential. 1. A. J. Bard, L. R. Faulkner, Electrochemical Methods, Wiley, p. 242
Cyclic Voltammetry
29
Outline
1. Study by linear voltammetry
1. Influence of the scan rate
1. Reversible reaction, high k°
2. Irreversible reaction, low k°
2. The double layer capacitance and the ohmic drop
2. Study by cyclic voltammetry
1. Influence of the first vertex
2. Influence of the k°
3. Influence of the number of scan
4. Influence of the scan rate
30
Influence of k°
k° = 10 cm/s
k° = 0.001 cm/s
The peak difference increases as the value of ko decreases.
The red curve is characteristic of an irreversible system.
Cyclic Voltammetry
31
Outline
1. Study by linear voltammetry
1. Influence of the scan rate
1. Reversible reaction, high k°
2. Irreversible reaction, low k°
2. The double layer capacitance and the ohmic drop
2. Study by cyclic voltammetry
1. Influence of the first vertex
2. Influence of the k°
3. Influence of the number of scan
4. Influence of the scan rate
32
Influence of the number of scan
Reversible system (k° = 10 cm2 s-1)
B
B
A
A
When the scan number increases, reduction |Ip| decreases and
oxidation |Ip| increases to reach a limit value. It is due to the fact
that after one scan the initial conditions are not recovered : there is
less A and more B.
Cyclic Voltammetry
33
Influence of the number of scan
Reversible system (k° = 10 cm2 s-1)
(obtained using Peak Analysis and integral calculation in EC-Lab )
For each cycle (1 reduction and 1 oxidation scans) there are more A species
reduced into B than produced by the oxidation of B. The integral function
available in EC-Lab allows to calculate the charge involved in the reduction
scan and the oxidation scan.
Cyclic Voltammetry
34
Influence of the number of scan
Reversible system (k° = 10 cm2 s-1)
B
B
A
A
Qreduction : -6.2 µC
Qoxidation : 4.1 µC
If vertex 2 is more positive (0.7 V compared to 0.5 V), more B are
oxidized in A and the value Ip, ox shows little variation from one
scan to another.
Cyclic Voltammetry
35
Influence of the number of scan
Reversible system (k° = 10 cm2 s-1)
2.m pr
CA vs. time
CB vs. time #
0,01
0,01
0,009
0,009
0,008
0,008
0,007
0,007
CA/mol.L-1
CB/mol.L-1
0,006
0,006
0,005
0,005
0,004
0,004
0,003
0,003
0,002
0,002
0,001
0,001
0
0
0
0,5
time/s
The evolution of the interfacial concentration CA does not vary from one cycle to another
because the chosen reaction constant is characteristic of a Nernstian system.
Consequently :
with DA = DB, A(0,t) + B(0,t) = A*
Whatever the cycle number, to any E(t) corresponds one ratio A(0,t)/B(0,t) and
E(t) does not vary from one cycle to another.
Cyclic Voltammetry
36
Outline
1. Study by linear voltammetry
1. Influence of the scan rate
1. Reversible reaction, high k°
2. Irreversible reaction, low k°
2. The double layer capacitance and the ohmic drop
2. Study by cyclic voltammetry
1. Influence of the first vertex
2. Influence of the k°
3. Influence of the number of scan
4. Influence of the scan rate
37
Influence of the scan rate
Reversible system (k° = 10 cm2 s-1)
2.5 V/s
10 V/s
40 V/s
Increasing the scan rate leads to an increase of Ip and Ep but
all scans intersect at a specific point.
If all the curves were divided by (v)½, they would all look the same.
Cyclic Voltammetry
38
Summary
• The magnitude of the oxidation peak depends on the value of the potential of
the first vertex.
• The difference between the two peak potentials depends on the potential of
first vertex and also on the value of k° of the reaction.
• As the number of scans increases, the oxidation peak current decreases due to
the fact that the reverse reaction is less complete than the forward reaction.
• Choosing a sufficiently high potential of second vertex makes the reverse
reaction more complete.
• Increasing the scan rate has the same effect as with a linear scan. All the
curves intersect at I=0 on the reverse scan.
Cyclic Voltammetry
39
To be continued…
Cyclic Voltammetry
40