**Introduction.**

This experiment is offered as an alternative Lab #4. If you find this
experiment more interesting and at least another student who
shares your choice, you should **discuss it with the
instructor on the last day of your Lab #1 or #2**
whichever comes last. No switching will be allowed after that.

**Objective:** In this lab you will study the **cyclic
voltametry** technique and measure redox potentials of a
few compounds.

**Cyclic voltammetry** is the most widely used
technique for acquiring qualitative information about
electrochemical reactions. The power of cyclic voltammetry
results from its ability to rapidly provide considerable
information on the thermodynamics of redox processes and the
kinetics of heterogeneous electron-transfer reactions, and on coupled chemical reactions or
adsorption processes. Cyclic voltammetry is often the first
experiment performed in an electroanalytical study. In
particular, it offers a rapid location of **redox
potentials** of the electroactive species, and convenient
evaluation of the effect of media upon the redox process.

Let us begin by discussing what happens near an **electrode**
in a polar solution (water or other highly polar solvent) with
high concentration of a** background electrolyte **(an
electrochemically inert salt such as NaCl or tetra butylammonium
perchlorate, TBAP; usually added in high concentration ~0.1M to
allow the current to pass). If an **analyte or reactant**
, say Fe^{3+}(aq), is present at a low concentration (*ca.*
10^{-3} M), its distribution near the electrode surface
is initially uniform (see picture to the right). If at time zero
a voltage sufficient to initiate electrochemical reaction is
applied, a current starts flowing due to the reaction:

Fe

^{3+}(aq) + e^{-}(from the electrode) --(k_{red})--> Fe^{2+}(aq)

The concentration of Fe^{3+}(aq)
near the electrode will gradually decline and thus the current
will decrease in time as well (see Figure to the right).

d[Fe

^{3+}]dt = Dd^{2}[Fe^{3+}]dt^{2}(1)

i_{c}= - nFAk_{red}[Fe^{3+}]_{surface }(2)

|i_{c}| = nFAk_{red}[Reactant]_{bulk}(D/pt)^{1/2}(3)

**Linear Sweep Voltammetry (LSV)**

Now let us assume that the voltage is changed from
value V_{1} (where electrochemical reaction of interest
is thermodynamically unfavorable) to a value V_{2}
linearly increasing in time (see Figure to the left), opposite to
an abrapt change considered above. The **voltage scan rate**
(**n**) is calculated
from the slope of the line. Clearly by changing the time taken to
sweep the range we alter the scan rate. The characteristics of
the linear sweep voltammogram recorded depend on a number of
factors including:

-The rate of the electron transfer reaction(s)

-The chemical reactivity of the electroactive species

-The voltage scan rate, **n**

In LSV measurements the current response is plotted
as a function of voltage rather than time, unlike potential step
measurements. For example if we return to the **Fe**^{3+}**/Fe**^{2+}
system

Fe^{3+}+ e^{-}-->Fe^{2+}

then the following voltammogram would be seen for a single
voltage scan using an electrolyte solution containing only **Fe**^{3+}
resulting from a voltage sweep (see Figure to the right). The
scan begins from the left hand side of the current/voltage plot
where no current flows. As the voltage is swept further to the
right (to more reductive values) a current begins to flow and
eventually reaches a peak before dropping. To rationalise this
behaviour we need to consider the influence of voltage on the
equilibrium established at the electrode surface. If we consider
the electrochemical reduction of **Fe**^{3+} to
**Fe**^{2+}, the rate of electron transfer is
fast in comparsion to the voltage sweep rate. Therefore at the
electrode surface an equilibrum is established identical to that
predicted by thermodynamics. You may recall from equilibrium
electrochemistry that the Nernst equation

E = E

^{o}+ RT/nF ln([Fe^{3+}]/[Fe^{2+}]) (4)

predicts the relationship between concentration and voltage
(potential difference), where E is the applied potential
difference and E^{o} is the standard electrode potential.
So as the voltage is swept from V_{1} to V_{2}
the equilibrium position shifts from no conversion at V_{1}
to full conversion at V_{2} of the reactant at the
electrode surface.

The exact form of the voltammogram can be rationalised by
considering the voltage and mass transport effects. As the
voltage is initially swept from V_{1}, the equilibrium at
the surface begins to alter and the current begins to flow: The
current rises as the voltage is swept further from its initial
value and the equilibrium position is shifted further towards
products (Fe^{2+}), thus converting more reactant. The
peak occurs, since at some point the diffusion layer has grown
sufficiently above the electrode so that the flux of reactant to
the electrode is not fast enough to satisfy that required by the
Nernst equation. In this situation the curent begins to drop just
as it did in the potential step measurements. In fact the drop in
current follows the same behaviour as that predicted by the
Cottrell equation. The above voltammogram was recorded at a
single scan rate. If the scan rate is altered the current
response also changes. The figure on the left shows a series
of linear sweep voltammograms recorded at different scan rates
for the same solution containing only **Fe**^{3+}.
Each curve has the same form but it is apparent that the total
current increases with increasing scan rate. This again can be
rationalised by considering the size of the diffusion layer and
the time taken to record the scan. Clearly the linear sweep
voltammogram will take longer to record as the scan rate is
decreased. Therefore the size of the diffusion layer above the
electrode surface will be different depending upon the voltage
scan rate used. In a slow voltage scan the diffusion layer will
grow much further from the electrode in comparison to a fast
scan. Consequently the flux to the electrode surface is
considerably smaller at slow scan rates than it is at faster
rates. As the current is proportional to the flux towards the
electrode the magnitude of the current will be lower at slow scan
rates and higher at high rates. This highlights an important
point when examining LSV (and cyclic voltammograms), although
there is no time axis on the graph the voltage scan rate (and
therefore the time taken to record the voltammogram) do strongly
effect the behaviour seen.

A final point to note from the figure is the position of the
current maximum, it is clear that the peak occurs at the same
voltage and this is a characteristic of electrode reactions which
have rapid electron transfer kinetics. These rapid processes are
often referred to as **reversible** electron
transfer reactions

For the reactions that are 'slow' (so
called **quasi-reversible or irreversible **electron
transfer reactions) the voltage applied will not result in the
generation of the concentrations at the electrode surface
predicted by the Nernst equation. This happens because the
kinetics of the reaction are 'slow' and thus the equilibria are
not established rapidly (in comparison tothe voltage scan rate).
The figure on the left shows a series of voltammograms recorded
at a single voltage sweep rate for different values of the
reduction rate constant (**k**_{red}) In this
situation the overall form of the voltammogram recorded is
similar to that above, but unlike the reversible reaction now the
position of the current maximum, E_{p}) shifts depending
upon the reduction rate constant (and also the voltage scan
rate). This occurs because the current takes more time to respond
to the the applied voltage than the reversible case.

**Cyclic
voltammetry** consists of scanning linearly the potential
of a stationary **working electrode**, using a
triangular potential waveform (see Figure on the right).
Depending on the information sought, single or multiple cycles
can be used. During the potential sweep, the potentiostat
measures the current resulting from the applied potential. The
resulting plot of current vs. potential is termed a cyclic
voltammogram. The cyclic voltammogram is a complicated,
time-dependent function of a large number of physical and
chemical parameters.

Figure to the right illustrates
the expected response of a reversible redox couple during a
single potential cycle. Here it is assumed that only the oxidized
form O is present initially. Thus, a negative-going potential
scan is chosen for the first half cycle, starting from a value
where no reduction occurs. As the applied potential approaches
the characteristic E° for the redox process, a **cathodic
current** begins to increase, until a peak is reached.
After traversing the potential region in which the reduction
process takes place, the direction of the potential sweep is
reversed.

**O + e**^{-}**
--> R**

During the reverse scan, R molecules (generated in the forward
half cycle, and *accumulated near the surface*) are
reoxidized back to O and an **anodic peak **results.

**R --> O + e**^{-}** **

The characteristic peaks in the cycle voltammogram are caused
by the formation of the diffusion layer near the electrode
surface. These can be best understood by carefully examining the
concentration-distance profiles during the potential sweep. For
example, Figure illustrates four concentration gradients for the
reactant and product at different times corresponding to (B) the
initial potential value, (D) and (G) to the formal potential of
the couple (during the forward and reversed scans, respectively),
and (C) to the achievement of a zero reactant surface
concentration. Note that the continuous change in the surface
concentration is coupled with an expansion of the diffusion layer
thickness (as expected in quiescent solutions). The resulting
current peaks thus reflect the continuous change of the
concentration gradient with the time. Hence, the increase to the
peak current corresponds to the achievement of diffusion control,
while the current drop (beyond the peak) exhibits a t^{ -1/2}
dependence (independent of the applied potential). For the
above reasons, the reversal current has the same shape as the
forward one. The use of ultramicroelectrodes – for which the
mass transport process is dominated by radial (rather than
linear) diffusion – results in a sigmoidal-shaped cyclic
voltammogram.

**Data Interpretation**

The cyclic voltammogram is characterized by
several important parameters. Four of these observables, the two **peak
currents** and two **peak potentials**,
provide the basis for the diagnostics developed by Nicholson and
Shain (2) for analyzing the cyclic voltammetric response.

*Reversible Systems*

The peak current for a reversible couple (at 25°C), is given by the Randles-Sevcik equation:

**i**_{p}
= (2.69x10^{5}) n^{3/2}ACD^{1/2}v^{1/2}
(5)

where n is the number of electrons, A the electrode area (in
cm^{2}), C the concentration (in mol/cm^{3}), D
the diffusion coefficient (in cm^{2}/s), and v the scan
rate (in V/s). Accordingly, the current is directly
proportional to concentration and increases with the square root
of the scan rate. The ratio of the reverse-to-forward peak
currents, **i**_{pr}/**i**_{pf
}, is unity for a simple reversible couple. This peak ratio
can be strongly affected by chemical reactions coupled to the
redox process. The current peaks are commonly measured by
extrapolating the preceding baseline current. The position of the
peaks on the potential axis (E_{p}) is related to the
formal potential of the redox process. The formal potential for
a reversible couple is centered between E_{pa} and E_{pc}:

E° = (E_{pa}
+ E_{pc})/2
(6)

The separation between the peak potentials (for a reversible couple) is given by:

DE_{p}
= E_{pa} - E_{pc} =
59mV/n
(7)

Thus, the peak separation can be used to determine the number
of electrons transferred, and as a criterion for a Nernstian
behavior. Accordingly, a fast one-electron process exhibits a DE_{p} of about 59 mV.Both the
cathodic and anodic peak potentials are independent of the scan
rate. It is possible to relate the half-peak potential (E_{p/2}
, where the current is half of the peak current) to the
polarographic half-wave potential, E_{1/2}

E_{p/2} = E_{1/2}
±
29mV/n
(8)

(The sign is positive for a reduction process.) For
multielectron-transfer (reversible) processes, the cyclic
voltammogram consists of several distinct peaks, if the E^{o}
values for the individual steps are successively higher and are
well separated. An example of such mechanism is the six-step
reduction of the fullerenes C_{60} and C_{70} to
yield the hexaanion products C_{60}^{6-} and C_{70}^{6-}
where six successive reduction peaks can be observed.

The situation is very different when the redox reaction is slow or coupled with a chemical reaction. Indeed, it is these "nonideal" processes that are usually of greatest chemical interest and for which the diagnostic power of cyclic voltammetry is most useful. Such information is usually obtained by comparing the experimental voltammograms with those derived from theoretical (simulated) ones.

*Irreversible and Quasi-reversible Systems*

For irreversible processes (those with sluggish electron exchange), the individual peaks are reduced in size and widely separated. Totally irreversible systems are characterized by a shift of the peak potential with the scan rate:

E_{p} = E° - (RT/an_{a}F)[0.78
- ln(k^{o}/(D)^{1/2}) + ln (an_{a}Fn/RT)^{1/2}] (9)

where a is the transfer coefficient
and n_{a} is the number of electrons involved in the
charge-transfer step. Thus, E_{p} occurs at potentials
higher than E°, with the overpotential related to k° and a.
Independent of the value k°, such peak displacement can be
compensated by an appropriate change of the scan rate. The peak
potential and the half-peak potential (at 25°C) will differ by
48/an mV. Hence, the voltammogram
becomes more drawn-out as a**n**
decreases.

The peak current, given by:

**i**_{p}
= (2.99x10^{5})**n**(an_{a})^{1/2}ACD^{1/2}n^{1/2} (10)

is still proportional to the bulk concentration, but will be
lower in height (depending upon the value of a).
Assuming a = 0.5, the ratio of the
reversible-to-irreversible current peaks is 1.27 (*i.e.*
the peak current for the irreversible process is about 80% of the
peak for a reversible one). For quasi-reversible systems (with 10^{-1}
> k° > 10^{-5} cm/s) the current is controlled by
both the charge transfer and mass transport. The shape of the
cyclic voltammogram is a function of the ratio k°/(pnnFD/RT)^{1/2}. As the ratio
increases, the process approaches the reversible case. For small
values of it, the system exhibits an irreversible behavior.
Overall, the voltammograms of a quasi-reversible system are more
drawn out and exhibit a larger separation in peak potentials
compared to a reversible system. In Eq.(10), n is equal to the
number of electrons gained in the reduction, A is the surface
area of the working electrode in cm^{2}, D is the
diffusion coefficient in cm^{2}/s, n
is the sweep rate in V/s, and C is the bulk molar concentration
in mole/cm^{3}.

*Nonfaradeic current*

So far we have only considered faradeic
current, *i.e.*, the current resulted from charge transfer
at the electrode, but when the potential is changing with time,
another **nonfaradeic** contribution to the **current
**takes place as well. More on that can be found in Lab 14. The easiest interpretation of such
current is as due to charging the double layer capacaitance, as
given in the figure to the right. Here C_{dl} is the
capacitance of the double layer :

C_{dl} = ee_{o}A/d_{dl}
(11)

and R_{F }is the resistance of the
Faradaic reaction, in parallel to it. The resistance of the
solution to the motion of ions can be represented a series
resistance R_{cell}. As a result, the equivalent
electrical circuit for the cell can be presented as shown in the
same figure.

In the cyclic voltammetry
experiment, the nofaradeic current appears as hysteresis current
proportional to the *first power* of the sweeping rate, n:

**i**_{nF} = (I_{a}-I_{c})/2 =
AC_{dl}dE/dt = nAC_{dl}
(12)

The double layer capacitance does depend on the applied potential and the electrolyte, as well as, its concentration but we will not delve into that for now.

For more detailed information on the theory of cyclic voltammetry, and the interpretation of cyclic voltammograms, see references.

**References**

1. Wang, J., Analytical Electrochemistry, Chapter 2, John
Wiley & Sons (2000)

2. Nicholson, R.S.; Shain, I., Anal. Chem., 36, 706 (1964).

*Last updated 05/05/14.*