Peter Kissinger, William R. Heineman Laboratory Techniques in Electroanalytical Chemistry, Second Edition, Revised and Expanded

Peter Kissinger, William R. Heineman Laboratory Techniques in Electroanalytical...

(Parte 3 de 5)

In general, electrochemists apply an electrical excitation signal independent variable) to some system (particular electrode-solution and geometry) and then monitor a response signal (dependent variable), together with the excitation allows some description of the properties system at hand. The nomenclature ideally should incorporate enough tion about these three items to describe the experiment (technique) reasonable degree without being cumbersome. The nomenclature expected to provide a phenomenological explanation of the response individual’s ability to understand the experiment thereby described. tional approach implicitly ignores the subtleties of individual techniques, describe the experiment. The term “polarography ” provides a particular bone of contention.

continued use of “polarography” as a general appellation for all faradaic

“polarography ” is generally accepted in connection with techniques a dropping mercury electrode; however, more general usage is strongly aged. Figure 1.3 illustrates a family tree relating the more important The reader unfamiliar with electroanalytical chemistry should be able logic in these associations after reading Chapters 3 to 5. It would be test to be able to identify the essential characteristics of each technique 1.3.

Figure 1.3 Family tree of electroanalytical techniques.

(black circles) can then be reconverted to the starting material. The electrochemi- cal cell can be represented as a circuit element as depicted in the the figure. The potential of the working electrode is monitored in relation reference electrode. The current passes between the auxiliary and working trodes. How and why this is done is the subject of Chapters 2 to tion of molecules or ions to and from the electrode surface is critical. tron transfer occurs at the working electrode and its surface properties therefore crucial. While students new to chemistry are introduced couples such as Fe(I)/Fe(II) and Ce(II)/Ce(IV) , many redox active are far more complex and frequently exhibit instability.

B. Chemical Complications

For introducing techniques and how to instrument them, we will assume eralized system

O+neGR

Figure 1.4 The typical electroanalytical cell consists of three electrodes milliliters of solution. Electron transfer occurs at the surface of the working Reactant and product are transported to and from this surface by diffusion.

(fast, reversible). For dynamic experiments, the sample is often completely either the 0 or the R form, whereas for static experiments both forms ally present.

In the real world, the simple redox couple may be perturbed rates, by adsorption of 0 and/or R on the electrode surface, and neous (i.e., in solution) chemical kinetics involving 0 and/or R. Various binations of heterogeneous ET steps (E) with homogeneous chemical are encountered. It should be clear that if one or more species in in solution are electroactive, electrochemistry can be used to perturb librium and study the solution chemistry.

Many other complications occur, including heterogeneous chemical and homogeneous ET steps. Our understanding of these complications into real chemical systems is at a primitive stage. There is much work before evaluation of such problems becomes a routine matter. The literature displays more optimism than is warranted by the facts. This has disappointments among practical problem solvers. Some investigators come to view analytical electrochemistry with considerable skepticism. should recognize that electrochemistry will always be more useful tative tool than as a diagnostic tool because of its relatively low resolution.

is a tendency in some circles to overinterpret electrochemical results stating the appropriate reservations. Whenever possible, supporting from other sources (usually spectroscopic or chromatographic techniques) be brought to bear on any mechanistic conclusions suggested by electrochemi- cal data. A large portion of the early literature has ignored this principle should therefore be examined with appropriate caution. The following bibliography lists a few of the more recent texts topics of interest to both beginners and experts in electroanalytical

BIBLIOGRAPHY A. J. Bard and L. R. Faulkner, Electrochemicul Methods, John Wiley & Sons,

H. H. Bauer, Electrodics: Modern Ideas Concerning Electrode Reactions, Georg

A. M. Bond, Modern Polarographic Methods in Analytical Chemistry, Marcel C. M. A. Brett and A. M. 0. Brett, Electrochemistry Principles, Methods,

D. R. Crow, Principles and Applications of Electrochemistry, Blackie Academic

1980. Stuttgart, 1972. New York, 1980. cations, Oxford University Press, New York, 1993. fessional, New York, 1994.

New York, 1986.

R. J. Gale, Spectroelectrochemistry Theory and Practice, Plenum Press, New Z. Galus, Fundamentals of Electrochemical Analysis, 2nd ed., John Wiley

E. Gileadi, Electrode Kinetics for Chemists, Chemical Engineers, and Materials D. K. Gossar, Jr., Cyclic Voltammetry: Simulation and Analysis of Reaction H. Lund and M. M. Baizer, eds., Organic Electrochemistry, 3rd ed., Marcel

R. W. Murray, Molecular Design of Electrode Surfaces, John Wiley & Sons, K. B. Oldham and J. C. Myland, Fundamentals of Electrochemical Science,

J. A. Plambeck, Electroanalytical Chemistry: Basic Principles and Applications,

P. H. Rieger, Electrochemistry, Prentice Hall, Englewood Cliffs, NJ, 1987. 1. Rubinstein, Physical Electrochemistry: Principles, Methods, and Applications,

Southampton Electrochemistry Group Instrumental Methods in Electrochemistry

J. T. Stock, and M. V. Orna, Elecfrochernistry, Past and Present, American H. R. Thirsk, and J. A. Harrison, A Guide to the Study of Electrode Kinetics,

B. H. Vassos and G. W. Ewing, Electroanalytical Chemistry, John Wiley J. Wang, Analytical Electrochemistry, VCH Publishers, New York, 1994.

York, 1994. fists, VCH, New York, 1993.

VCH, New York, 1993. New York, 1991. 1 992.

Press, San Diego, 1994. Wiley & Sons, New York, 1982.

Dekker, New York, 1995. Press, New York, 1985.

Society, Washington, DC, 1989. Press, New York, 1972.

York, 1983.

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Fundamental Concepts of Analytical Electrochemistry

Peter T. Kissinger Purdue University and Bioanalytical Systems, Inc., West Lafayette, Indiana

Car1 R. Preddy"

Ronald E. Shoup Will iam R. Heineman

Purdue University, West Lafayette, Indiana

Bioanalytical Systems, Inc., West hfayette, Indiana University of Cincinnati, Cincinnati, Ohio

The common thread binding all electroanalytical methods is heterogeneity. very act of placing an electrode in contact with a solution creates a phase ary that differentiates otherwise identical solute molecules into two at a distance from the electrode, and those close enough to participate fascinating mutual interactions known collectively as electrochemistry not a trivial distinction, for often it is the bulk-phase properties alone of analytical concern. Unlike most spectroscopic methods, electrochemical measurements are actually made on only a minute fraction of the fined to a highly nonhomogeneous environment, the electrode-solution phase. The coupling and interplay within this region of such phenomena terfacial charge transfer, diffusional mass transport, adsorption, chemisorption, homogeneous-phase chemical reaction, convection, and dissolution can interpretation of electrochemical data and discourage the practically analyst. On the other hand, electrochemistry offers an invaluable damental investigation of these processes, each important in its own either case, the ultimate success of the experimenter will depend on of the underlying physical principles.

*Current ufiliution: Kodak Research Labs, Eastman Kodak Company, Rochester,

We acknowledge extensive, intentional bias and abridgment in derivations discussion. Our intent is to convey the feeling that much may be electrochemical investigation without recourse to an entanglement of cal expressions, provided that one develops an insight into the physical ties of electrode processes.

1. MASS TRANSPORT: LINEAR DIFFUSION

Since the electrochemical reduction or oxidation of a molecule occurs electrode-solution interface, molecules dissolved in solution in an electrochemical cell must be transported to the electrode for this process to occur. Consequently, the transport of molecules from the bulk liquid phase of the cell to surface is a key aspect of electrochemical techniques. This movement rial in an electrochemical cell is called mass transport. Three modes transport are important in electrochemical techniques: hydrodynamics, tion, and diffusion.

Hydrodynamic mass transport is caused by the movement of stirring the solution, rotating the electrode, or flowing the solution cell. The moving solution transports reactant to the electrode surface carrying electrogenerated product away.

Migration is the movement of a charged particle due to its interaction an electric field, such as that which exists in the vicinity of an electrode. example, cations are attracted by a negatively charged electrode by a positively charged electrode. In most analytical techniques, migration is minimized by the addition of an inert electrolyte, called electrolyte, which decreases the field strength near the electrode.

In many respects, the simplest and best understood process electrochemistry is diffusion. Diffusion is a factor in virtually every electroanalytical measurement, yet it is most often introduced as a set tal laws, devoid of physical significance. The governing mathematical ships are apt to seem abstruse, but are in fact quite elegant and readily Their derivation follows from simple finite mathematics, using as collection of inert particles in random motion. This microscopic-level relies on statistical rather than thermodynamic concepts, and although orous, Fick’s well-known laws arise directly with few assumptions out losing sight of physical reality.

A. Impulse Relaxation

As with the familiar theoretical treatment of ideal gases, the logical for understanding the process of diffusion is consideration of the

boundaries or thermal, electromagnetic, or concentration gradients), favored direction of motion. An imaginary plane dividing the system continuously traversed by many molecules moving from both sides, significant time interval, the number that has passed from one direction exactly equal the number from the other. Thus there will be no net of material from one side to the other. The concentration, or more the chemical potential, of the solute is uniform throughout, and the therefore at equilibrium.

When regions of dissimilar chemical potential are created, solute will move between them until a homogeneous condition is restored. ation process involves a temporary net mass transport across some plane. The transport of matter from a region of higher chemical potential of lower chemical potential is the process of diffusion. The motive this movement is maximization of entropy. The fully relaxed system most random configuration.

The transition between regions of high and low chemical potential systems cannot be infinitely sharp. There must be a zone over which centration varies with distance. A place in which dC/dx is nonzero exhibit a concentration gradient. A plot of concentration as a function tance is called a concentration profile, so the gradient is the first the profile function. Since diffusional mass transport is always from concentration, the direction of movement will be determined by the gradient. One imagines that molecules diffuse down their respective tion gradient, meaning that direction in which the sign of dC/dx is negative the molecules’ frame of reference. This is a point worth pondering.

damental to the understanding of unrestricted motion under the influence type of potential field-thermal, electrical, or gravitational. The mathematical description of the transfer of heat along temperature gradients is identical diffusion in every respect. Just as objects cool more rapidly at high ture than near room temperature, so the rate of mass transport is expected to be related to the magnitude of the concentration gradient.

of this relationship will be examined presently.

Another useful concept iscftlu:. Flux is defined as the number penetrating a unit area of an imaginary plane in a unit of time. The are mol/(cm2 s), and the sign identifies the direction of motion, positive and negative away from the plane. The prior assertion that equilibrium no net mass transport is equivalent to a requirement that the sum of all components is exactly zero at any test plane within the system. measure of the rate of mass transport at a fixed point. Its electrochemical evance stems from the direct relationship it holds to electrode current.

central box, arbitrarily labeled 0, we introduce a number No of solute at time t = 0. At the starting time, the concentration profile across exhibits a sharp spike at the center. The right side of Figure 2.1 profile as a histogram of a quantity of molecules versus distance from ter. Since the concentration profile is a step function at either boundary 0, the gradient at these points is some huge negative value. According notion of molecular behavior, this impulse of concentration should be when left to itself. Bombardment by solvent molecules and collision other will cause the molecules to wander out randomly from the Isotropy assures that motion to the left is no more probable than motion right. The fluxes across either boundary should be equal at all times.

time T,, half of the original No molecules will have left the 0th box. will be found in box 1, and an equal number will have made their

-1. The situation is now as depicted in the second set of Figure 2.1.

system now consists of three nonempty boxes with N0/2 molecules ter and N0/4 in each of the neighboring boxes. Each box is entirely dent of the other in the sense that each will behave exactly as box first step. At some later time T2, half the original molecules in each have meandered into the adjacent boxes. The distribution ratio across has progressed from 1:2:1 after the first time increment, to 1:4:6:4:1 second, then to 1:6:15:20:15:6:1 at some later time T,. The fraction ecules in the ith box after the kth step is given by the familiar binomial bution function

Ni,k - - 2k! 2-2k No (k + i)! (k - i)!

k=0,1,; i=O ,..., +k

It should be emphasized that the time steps are not evenly spaced.

If the total number of molecules is very large and the distance

Ax, become infinitesimally small (Ax -+ dx), the distribution will by a smooth function (a Gaussian distribution) following the familiar curve of error,

1 -x2 - -- dN

N, (471 DOV2 ex'[ 4Dt J dx where dN/No is the fraction of the total population of molecules located x and (x + dx), and D is a constant known as the diffusion coefficient

Figure 2.1 Schematic representation of the diffusion process units of cm2/s. The preexponential factor in the normal distribution described in terms of [l/o (27~)”~], where 6, the population standard is a measure of distribution width. In the present case, cJ= J2Dt

(Parte 3 de 5)

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