1. Chapter 23
Voltammetry

2. 23 A Excitation signals in voltammetry
Figure 23-1 Voltage versus time excitation signals used in voltammetry.

3. 23 B Voltammetric instrumentation
Figure 23-2 A manual potentiostat for voltammetry.
The cell is made up of three electrodes immersed
in a solution containing the analyte and also
an excess of a nonreactive electrolyte called a supporting electrolyte.
The potential of the working electrode (WE),
versus a reference electrode is varied
linearly with time.
The reference electrode (RE) has a potential
that remains constant.
The third electrode is a counter
electrode(CE), which is often a coil of
platinum wire or a pool of mercury.

4. Figure 23-3 Some common types of commercial voltammetric electrodes
Figure 23-3 Some common types of commercial voltammetric electrodes. (a) Disk electrode. (b) Hanging mercury drop electrode (HMDE). (c) Microelectrode. (d) Sandwich-type flow electrode. (e) Dropping mercury electrode (DME).

5. Figure 23-4 Potential ranges for three types of electrodes in various supporting electrolytes.

6. Modified electrodes
Modifications include applying irreversibly adsorbing substances with desired
functionalities, covalent bonding of components to the surface, and coating the
electrode with polymer films or films of other substances.
They can be applied in the area of electrocatalysis.
In this application, electrodes capable of reducing oxygen to water have been sought
for use in fuel cells and batteries.
Another application is in the production of electrochromic devices that change color
on oxidation and reduction.
Such devices are used in displays or smart windows and mirrors.

7. Figure 23-5 Linear-sweep voltammogram for the reduction of a hypothetical species A to give a product P.
The limiting current il is proportional to the analyte concentration and is used for quantitative analysis.
The half-wave potential E1/2 is related to the standard potential for the half-reaction and is often used for qualitative identification of species.
The half-wave potential is the applied potential at which the current i is i1/2.

8. The half-reaction at the working electrode is the reversible reaction
A + ne-  P E0 = V
Linear-scan voltammograms generally have a sigmoidal shape and are called voltammetric waves.
The constant current beyond the steep rise is called the limiting current, il.
iI = kcA
The potential at which the current is equal to one half the limiting current is called the half-wave potential, E1/2.
Linear-scan voltammetry in which the solution or the electrode is in constant motion is called hydrodynamic voltammetry.

9. 23 C Hydrodynamic voltammetry

10. Concentration profiles at electrode surfaces
Assume that the initial concentration of A is cA while that of the product P is zero.
We also assume that the reduction reaction is rapid and reversible so that the
concentrations of A and P in the film of solution immediately adjacent to the electrode
is given at any instant by the Nernst equation:
Eappl is the potential between the working electrode and the reference electrode
and c0P and c0A are the molar concentrations of P and A in a thin layer of solution
at the electrode surface only.

11. Figure 23-7 Current response to a stepped potential for a planar electrode
in an unstirred solution. (a) Excitation potential. (b) Current response.

12. Figure 23-8 Concentration distance profiles during the diffusion- controlled reduction of A to give P at a planar electrode. (a) Eappl = 0 V. (b) Eappl = point Z.
The concentration profiles for A and P are shown after 0, 1, 5, and 10 ms of electrolysis.

13. The concentration of A increases linearly with distance and approaches cA at about 0.01 mm from the surface.
A linear decrease in the concentration of P occurs in this same region.
The current I required to produce the gradients is proportional to the slopes of the
straight line portions of the solid lines, that is,
where i is the current in amperes,
n is the number of moles of electrons per mole of analyte,
F is the faraday,
A is the electrode surface area in cm2,
DA is the diffusion coefficient for A in cm2s-1, and
cA is the concentration of A in mol cm-3.

14. Figure 23-9 Visualization of flow patterns in a flowing stream.
Turbulent flow, shown on the right, becomes laminar flow as the average velocity decreases to the left.
In turbulent flow, the molecules move in an irregular, zigzag fashion, and there are swirls and eddies in the movement.

15. Figure 23-10 Flow patterns and regions of interest near the working electrode in hydrodynamic voltammetry.
At a distance d cm from the electrode surface, frictional forces give rise to a region
where the flow velocity is essentially zero. The thin layer of solution in this region is
a stagnant layer, called the Nernst diffusion layer.

16. Figure Concentration profiles at an electrode/solution interface during the electrolysis A + ne-  P from a stirred solution of A.

17. Voltammetric Currents
The current at any point in the electrolysis is determined by the rate of transport of A
from the outer edge of the diffusion layer to the electrode surface.
This rate is given by cA/ x, where x is the distance in centimeters from the electrode
surface.
The earlier equation thus can be expressed as
when

18. Current/Voltage Relationships for Reversible Reactions
To develop an equation for the sigmoidal curve, substitution and rearrangement gives
The surface concentration of P can also be expressed in terms of the current as
Throughout electrolysis, the concentration of P approaches zero in the bulk of the
solution and, therefore, when cP  0,
Rearranging gives,

19. Substitution and rearrangement gives
Eappl is the half-wave potential, that is,
kA/kP is nearly unity, thus

20. A voltammogram for a mixture is just the sum of the waves for the individual components.

21. Figure 23-13 Voltammetric behavior of iron(II) and iron(III) in a citrate medium.
Curve A: anodic wave for a solution in which cFe2+ = 1  10-4 M.
Curve B: anodic/cathodic wave for a solution in which cFe2+ = cFe3+ = 0.5  10-4 M.
Curve C: cathodic wave for a solution in which cFe3+ = 1  10-4 M.

22. Oxygen Waves
Figure 23-14 Voltammogram for the reduction of oxygen in an air-saturated 0.1 M KCl solution. The lower curve is for a 0.1 M KCl solution in which the oxygen is removed by bubbling nitrogen through the solution.
An aqueous solution saturated with air exhibits two distinct oxygen waves.
The first wave results from the reduction of oxygen to hydrogen peroxide; the second wave shows the overall reduction of oxygen to water and is a voltammogram of an oxygen-free solution.

23. Voltammetric measurements offer a convenient and widely used method for determining dissolved oxygen in solutions.
The presence of oxygen often interferes with the accurate determination of other species.
Therefore, oxygen removal is usually the first step in amperometric procedures.
Oxygen can be removed by passing an inert gas through the analyte solution for several minutes (sparging).
A stream of the same gas, usually nitrogen, is passed over the surface of the solution during analysis to prevent reabsorption of oxygen.

24. Applications of Hydrodynamic Voltammetry
The most important uses of hydrodynamic voltammetry include
detection and determination of chemical species as they exit from chromatographic columns or flow-injection apparatus;
(2) routine determination of oxygen and certain species of biochemical interest, such as glucose, lactose, and sucrose;
(3) detection of end points in coulometric and volumetric titrations; and
(4) fundamental studies of electrochemical processes.

25. Voltammetric Detectors in Chromatography and Flow-Injection Analysis
Hydrodynamic voltammetry is widely used for detection and determination of oxi-
dizable or reducible compounds or ions that have been separated by liquid chro-
matography or that are produced by flow-injection methods.
Figure 23-15 A schematic of a voltammetric system for detecting electroactive species as they elute from a column. The cell volume is determined by the thickness of the gasket.

26. Figure 23-16 (a) Detail of a commercial flow cell assembly
Figure 23-16 (a) Detail of a commercial flow cell assembly. (b) Configurations of working electrode blocks. Arrows show the direction of flow in the cell.

27. Figure 23-17 The Clark voltammetric oxygen sensor. Cathodic reaction:
O2 + 4H+ + 4e-  2H2O.
Anodic reaction: Ag + Cl-  AgCl(s) + e-.
It is used for the determination of dissolved oxygen in a variety of aqueous environments.

28. Enzyme-based Sensors
A number of enzyme-based voltammetric sensors are available.
Example, a glucose sensor that is widely used in clinical laboratories for the routine determination of glucose in blood serums.
When this device is immersed in a glucose-containing solution, glucose diffuses through the outer membrane into the immobilized enzyme, where the following reaction occurs catalyzed by glucose oxidase:
glucose + O2  H2O2 + gluconic acid
The hydrogen peroxide diffuses through the inner layer of membrane and to the electrode surface, where it is oxidized to give oxygen.
The resulting current is directly proportional to the glucose concentration of the analyte solution.

29. Figure 23-18 Typical amperometric titration curves
Figure 23-18 Typical amperometric titration curves. (a) Analyte is reduced;
reagent is not. (b) Reagent is reduced; analyte is not. (c) Both reagent and
analyte are reduced.

30. There are two types of amperometric electrode systems.
One uses a single polarizable electrode coupled to a reference, while the other uses a pair of identical solid-state electrodes immersed in a stirred solution.
Amperometric titrations with one indicator electrode have been confined to titrations in which a precipitate or a stable complex is the product.

31. Precipitating reagents include silver nitrate for halide ions, lead nitrate for sulfate ion, and several organic reagents, such as 8-hydroxyquinoline, dimethylglyoxime, and cupferron, for various metallic ions that are reducible at working electrodes.
The second type of system has been incorporated in instruments designed for routine automatic determination of a single species, usually with a coulometrically generated reagent.
An instrument of this type is often used for the automatic determination of
chloride in samples of serum, sweat, tissue extracts, pesticides, and food products.

32. Figure 23-19 (a) Side view of a rotating disk electrode showing solution flow pattern.
(b) Bottom view of a disk electrode. (c) Photo of a commercial RDE.
The RDE is a common method for obtaining a rigorous description of the hydrodynamic flow of stirred solution.

33. A rigorous treatment of the hydrodynamics is possible and leads to the Levich equation
iI = 0.620nFAD1/2v-1/6cA
is the angular velocity of the disk in radians per second, and
n is the kinematic viscosity in centimeters squared per second
Figure Disk (a) and ring (b) current for reduction of oxygen at the rotating ring-disk electrode.
(a) depicts the voltammogram for the reduction of oxygen to hydrogen peroxide at the disk electrode.
(b) shows the anodic voltammogram for the oxidation of the hydrogen peroxide as it flows past the ring electrode.

34. 23 D Polarography
Linear-scan polarography differs from hydrodynamic voltammetry in two significant ways.
There is essentially no convection or migration, and
There is no dropping mercury electrode (DME)
Polarographic Currents
Figure 23-21 Polarogram for 1 M solution of KCl that is 3  10-4 M in Pb2+.

35. The residual current in polarography is the small current observed in the
absence of an electroactive species.
Diffusion current is the limiting current observed in polarography when the current is limited only by the rate of diffusion to the dropping mercury electrode surface.
The diffusion current in polarography is proportional to the concentration of analyte.

36. Diffusion Current at the Dropping Mercury Electrode
The Ilkovic equation for polarographic diffusion currents includes
t, time in seconds
the rate of flow of mercury through the capillary m in mg/s
D, the diffusion coefficient of the analyte in cm2/s,
(id)max, the maximum diffusion current in mA and
c the analyte concentration in mM.

37. Figure 23-22 Residual current for a 0.1 M solution of HCl.

38. The residual current has two sources.
1. the reduction of trace impurities that are inevitably present in the blank solution.
2. the so-called charging, or capacitive, current resulting from a flow of electrons that charge the mercury droplets with respect to the solution.
A faradaic current in an electrochemical cell is the current that results from an oxidation/reduction process.
A nonfaradaic current is a charging current that results because the mercury drop is expanding and must be charged to the electrode potential.

39. 23 E Cyclic voltammetry
In cyclic voltammetry (CV), the current response of a small stationary electrode in an
unstirred solution is excited by a triangular voltage waveform.
Figure 23-23 Cyclic voltammetric excitation signal.
The voltage extrema at which reversal takes place are called switching potentials.

40. Figure 23-24 
Potential versus time waveform.
(b) Cyclic voltammogram for a solution that is 6.0 mM in K3Fe(CN)6 and 1.0 M in KNO3.

41. Important variables in a cyclic voltammogram are
the cathodic peak potential Epc,
the anodic peak potential Epa,
the cathodic peak current ipc, and
the anodic peak current ipa.
For a reversible electrode reaction at 25°C, the difference in peak potentials,
Ep, is expected to be
where n is the number of electrons involved in the half-reaction.

42. To detect slow electron transfer kinetics and to obtain rate constants,
Ep is measured for different sweep rates.
Quantitative information is obtained from the Randles-Sevcik equation, which at 25°C is
ip =  105n3/2AcD1/2v1/2

43. Figure 23-25 Cyclic voltammogram of the insecticide parathion in 0
Figure 23-25 Cyclic voltammogram of the insecticide parathion in 0.5 M pH 5 sodium acetate buffer in 50% ethanol.
The primary use of CV is as a tool for fundamental and diagnostic studies that
provides qualitative information about electrochemical processes under various conditions.

44. The first cathodic peak (A) results from a four-electron reduction of the parathion to give a hydroxylamine derivative
NO2 + 4e- + 4H+  NHOH + H2O
NHOH  NO + 2H+ + 2e-
The cathodic peak at C results from the oxidation of the nitroso compound to the
hydroxylamine, as shown by the equation
NO + 2e- + 2H+  NHOH

45. 23 F Pulse voltammetry
The two most important pulse techniques are: differential-pulse voltammetry and
square-wave voltammetry.
Figure 23-26 Excitation signals for differential-pulse voltammetry.

46. We get a differential curve consisting of a peak the height of which is directly proportional to concentration.
For a reversible reaction, the peak potential is approximately equal to the standard potential for the half-reaction.

47. Figure 23-28 Generation of a square-wave voltammetry excitation signal.
The staircase signal in (a) is added to the pulse train in (b) to give the square-wave excitation signal in (c).

48. Figure 23-29 Current response for a reversible reaction to excitation signal.
This theoretical response plots a dimensionless function of current versus a function of potential, n(E - E1/2) in mV. In this example, i1 = forward current; i2 = reverse current; and i1 - i2 = current difference.

49. 23 G Applications of voltammetry
Voltammetry is applicable to:
the analysis of many inorganic substances.
the analysis of such inorganic anions as bromate, iodate, dichromate, vanadate,
selenite, and nitrite.
the study and determination of organic compounds.

50. 23H Stripping methods
Stripping methods encompass a variety of electrochemical procedures having a common characteristic initial step:
In anodic stripping methods, the working electrode behaves as a cathode during
the deposition step and as an anode during the stripping step, with the analyte being oxidized back to its original form.
In a cathodic stripping method, the working electrode behaves as an anode during the deposition step and as a cathode during stripping.

51. Figure 23-30 (a) Excitation signal for stripping determination of Cd2+ and Cu2+. (b) Stripping voltammogram.

52. Figure 23-31 Differential-pulse anodic stripping voltammogram in the analysis of a mineralized honey sample spiked with GaCl3

53. 23 I Voltammetry with microelectrodes
Figure 23-32 Optical image using brightfield microscopy showing a carbon fiber microelectrode adjacent to a bovine chromaffin cell from the adrenal medulla.
The dimensions of microelectrodes are typically smaller than about 20 m and may be as small as a 30 nm in diameter and 2 m in length.
They are a very useful tool to study chemical processes in single cells or processes inside organs of living species, such as in mammalian brains.