Voltammetry

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Chapter 23

• Voltammetry

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23 A Excitation signals in voltammetry Figure
23-1 Voltage versus time excitation signals used
in voltammetry.
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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. (a) Disk electrode. (b)
Hanging mercury drop electrode (HMDE). (c)
Microelectrode. (d) Sandwich-type flow electrode.
(e) Dropping mercury electrode (DME).
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Figure 23-4 Potential ranges for three types of
electrodes in various supporting electrolytes.
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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.
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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.
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The half-reaction at the working electrode is the
reversible reaction A ne- ? P E0 -0.26
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.
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23 C Hydrodynamic voltammetry
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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.
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Figure 23-7 Current response to a stepped
potential for a planar electrode in an unstirred
solution. (a) Excitation potential. (b) Current
response.
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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.
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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.
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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.
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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.
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Figure 23-11 Concentration profiles at an
electrode/solution interface during the
electrolysis A ne- ? P from a stirred solution
of A.
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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
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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,
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Substitution and rearrangement gives Eappl is
the half-wave potential, that is, kA/kP
is nearly unity, thus
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A voltammogram for a mixture is just the sum of
the waves for the individual components.
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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.
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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.
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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.
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• 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.

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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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• 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 23-20 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.

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• 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.

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

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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 25C, the
difference in peak potentials, ?Ep, is expected
to be where n is the number of electrons
involved in the half-reaction.
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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 25C is ip 2.686 ?
105n3/2AcD1/2v1/2
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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.
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The first cathodic peak (A) results from a
four-electron reduction of the parathion to give
a hydroxylamine derivative ?NO2 4e- 4H ?
?NHOH H2O The first cathodic peak (A) results
from a four-electron reduction of the parathion
to give a hydroxylamine derivative ?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
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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.
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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.
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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).
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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.
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• 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.

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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.
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Figure 23-30 (a) Excitation signal for stripping
determination of Cd2 and Cu2. (b) Stripping
voltammogram.
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Figure 23-31 Differential-pulse anodic stripping
voltammogram in the analysis of a mineralized
honey sample spiked with GaCl3
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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.