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CHAPTER
INTRODUCTION
AND OVERVIEW
OF ELECTRODE
PROCESSES
1.1 INTRODUCTION
Electrochemistry is the branch of chemistry concerned with the interrelation of electri-
cal and chemical effects. A large part of this field deals with the study of chemical
changes caused by the passage of an electric current and the production of electrical en-
ergy by chemical reactions. In fact, the field of electrochemistry encompasses a huge
array of different phenomena (e.g., electrophoresis and corrosion), devices (elec-
trochromic displays, electro analytical sensors, batteries, and fuel cells), and technolo-
gies (the electroplating of metals and the large-scale production of aluminum and
chlorine). While the basic principles of electrochemistry discussed in this text apply to
all of these, the main emphasis here is on the application of electrochemical methods to
the study of chemical systems.
Scientists make electrochemical measurements on chemical systems for a variety of
reasons. They may be interested in obtaining thermodynamic data about a reaction. They
may want to generate an unstable intermediate such as a radical ion and study its rate of
decay or its spectroscopic properties. They may seek to analyze a solution for trace
amounts of metal ions or organic species. In these examples, electrochemical methods are
employed as tools in the study of chemical systems in just the way that spectroscopic
methods are frequently applied. There are also investigations in which the electrochemi-
cal properties of the systems themselves are of primary interest, for example, in the design
of a new power source or for the electrosynthesis of some product. Many electrochemical
methods have been devised. Their application requires an understanding of the fundamen-
tal principles of electrode reactions and the electrical properties of electrode-solution in-
terfaces.
In this chapter, the terms and concepts employed in describing electrode reactions
are introduced. In addition, before embarking on a detailed consideration of methods
for studying electrode processes and the rigorous solutions of the mathematical equa-
tions that govern them, we will consider approximate treatments of several different
types of electrode reactions to illustrate their main features. The concepts and treat-
ments described here will be considered in a more complete and rigorous way in later
chapters.
2 • Chapter 1. Introduction and Overview of Electrode Processes
1.1.1 Electrochemical Cells and Reactions
In electrochemical systems, we are concerned with the processes and factors that affect the transport of charge across the interface between chemical phases, for example, be- tween an electronic conductor (an electrode) and an ionic conductor (an electrolyte). Throughout this book, we will be concerned with the electrode/electrolyte interface and the events that occur there when an electric potential is applied and current passes. Charge is transported through the electrode by the movement of electrons (and holes). Typical electrode materials include solid metals (e.g., Pt, Au), liquid metals (Hg, amalgams), car- bon (graphite), and semiconductors (indium-tin oxide, Si). In the electrolyte phase, charge is carried by the movement of ions. The most frequently used electrolytes are liq- uid solutions containing ionic species, such as, H + , Na+ , Cl~, in either water or a non- aqueous solvent. To be useful in an electrochemical cell, the solvent/electrolyte system must be of sufficiently low resistance (i.e., sufficiently conductive) for the electrochemi- cal experiment envisioned. Less conventional electrolytes include fused salts (e.g., molten NaCl-KCl eutectic) and ionically conductive polymers (e.g., Nation, polyethylene oxide-LiClO 4 ). Solid electrolytes also exist (e.g., sodium j8-alumina, where charge is car- ried by mobile sodium ions that move between the aluminum oxide sheets). It is natural to think about events at a single interface, but we will find that one cannot deal experimentally with such an isolated boundary. Instead, one must study the proper- ties of collections of interfaces called electrochemical cells. These systems are defined most generally as two electrodes separated by at least one electrolyte phase. In general, a difference in electric potential can be measured between the electrodes in an electrochemical cell. Typically this is done with a high impedance voltmeter. This cell potential, measured in volts (V), where 1 V = 1 joule/coulomb (J/C), is a measure of the energy available to drive charge externally between the electrodes. It is a manifestation of the collected differences in electric potential between all of the various phases in the cell. We will find in Chapter 2 that the transition in electric potential in crossing from one con- ducting phase to another usually occurs almost entirely at the interface. The sharpness of the transition implies that a very high electric field exists at the interface, and one can ex- pect it to exert effects on the behavior of charge carriers (electrons or ions) in the interfa- cial region. Also, the magnitude of the potential difference at an interface affects the relative energies of the carriers in the two phases; hence it controls the direction and the rate of charge transfer. Thus, the measurement and control of cell potential is one of the most important aspects of experimental electrochemistry. Before we consider how these operations are carried out, it is useful to set up a short- hand notation for expressing the structures of cells. For example, the cell pictured in Fig- ure 1.1.1a is written compactly as
Zn/Zn2 + , СГ/AgCl/Ag (l.l.l)
In this notation, a slash represents a phase boundary, and a comma separates two compo- nents in the same phase. A double slash, not yet used here, represents a phase boundary whose potential is regarded as a negligible component of the overall cell potential. When a gaseous phase is involved, it is written adjacent to its corresponding conducting ele- ment. For example, the cell in Figure 1.1.1ft is written schematically as
Pt/H2/H+ , СГ/AgCl/Ag (1.1.2)
The overall chemical reaction taking place in a cell is made up of two independent half-reactions, which describe the real chemical changes at the two electrodes. Each half- reaction (and, consequently, the chemical composition of the system near the electrodes)
4 Chapter 1. Introduction and Overview of Electrode Processes
Electrode Solution Electrode^ Solution
0
Potential
0j
Energy level of electrons
Vacant MO
Occupied MO A + e — > A (a)
0
Potential
0l
Electrode
Energy level of electrons
Solution Electrode Solution
Vacant MO
Occupied MO
A - e -^ A+ (b)
Figure 1.1.2 Representation of (a) reduction and (b) oxidation process of a species, A, in
solution. The molecular orbitals (MO) of species A shown are the highest occupied MO and the
lowest vacant MO. These correspond in an approximate way to the E°s of the A/A~ and A+/A
couples, respectively. The illustrated system could represent an aromatic hydrocarbon (e.g.,
9,10-diphenylanthracene) in an aprotic solvent (e.g., acetonitrile) at a platinum electrode.
Consider a typical electrochemical experiment where a working electrode and a ref-
erence electrode are immersed in a solution, and the potential difference between the elec-
trodes is varied by means of an external power supply (Figure 1.1.3). This variation in
potential, £, can produce a current flow in the external circuit, because electrons cross the
electrode/solution interfaces as reactions occur. Recall that the number of electrons that
cross an interface is related stoichiometrically to the extent of the chemical reaction (i.e.,
to the amounts of reactant consumed and product generated). The number of electrons is
measured in terms of the total charge, Q, passed in the circuit. Charge is expressed in
units of coulombs (C), where 1 С is equivalent to 6.24 X 101 8^ electrons. The relationship
between charge and amount of product formed is given by Faraday's law; that is, the pas-
sage of 96,485.4 С causes 1 equivalent of reaction (e.g., consumption of 1 mole of reac-
tant or production of 1 mole of product in a one-electron reaction). The current, /, is the
rate of flow of coulombs (or electrons), where a current of 1 ampere (A) is equivalent to 1
C/s. When one plots the current as a function of the potential, one obtains a current-poten-
tial (i vs. E) curve. Such curves can be quite informative about the nature of the solution
and the electrodes and about the reactions that occur at the interfaces. Much of the re-
mainder of this book deals with how one obtains and interprets such curves.
1.1 Introduction 5
Power supply
Pt
1МНВГ
-Ag
-AgBr Figure 1.1.3 Schematic diagram of the electrochemical cell Pt/HBr(l M)/AgBr/Ag attached to power supply and meters for obtaining a current- potential (i-E) curve.
Let us now consider the particular cell in Figure 1.1.3 and discuss in a qualitative way the current-potential curve that might be obtained with it. In Section 1.4 and in later chapters, we will be more quantitative. We first might consider simply the potential we would measure when a high impedance voltmeter (i.e., a voltmeter whose internal resis- tance is so high that no appreciable current flows through it during a measurement) is placed across the cell. This is called the open-circuit potential of the cell.^1 For some electrochemical cells, like those in Figure 1.1.1, it is possible to calculate the open-circuit potential from thermodynamic data, that is, from the standard potentials of the half-reactions involved at both electrodes via the Nernst equation (see Chapter 2). The key point is that a true equilibrium is established, because a pair of redox forms linked by a given half-reaction (i.e., a redox couple) is present at each electrode. In Figure 1.1.1/?, for example, we have H +^ and H 2 at one electrode and Ag and AgCl at the other.^2 The cell in Figure 1.1.3 is different, because an overall equilibrium cannot be estab- lished. At the Ag/AgBr electrode, a couple is present and the half-reaction is
AgBr + e ±± Ag + Br (^) = 0.0713 Vvs. NHE (1.1.6)
Since AgBr and Ag are both solids, their activities are unity. The activity of Br can be found from the concentration in solution; hence the potential of this electrode (with re- spect to NHE) could be calculated from the Nernst equation. This electrode is at equilib- rium. However, we cannot calculate a thermodynamic potential for the Pt/H+ ,Br~ electrode, because we cannot identify a pair of chemical species coupled by a given half- reaction. The controlling pair clearly is not the H2,H+ couple, since no H 2 has been intro- duced into the cell. Similarly, it is not the O 2 ,H 2 O couple, because by leaving O 2 out of the cell formulation we imply that the solutions in the cell have been deaerated. Thus, the Pt electrode and the cell as a whole are not at equilibrium, and an equilibrium potential
*In the electrochemical literature, the open-circuit potential is also called the zero-current potential or the rest potential. (^2) When a redox couple is present at each electrode and there are no contributions from liquid junctions (yet to be
discussed), the open-circuit potential is also the equilibrium potential. This is the situation for each cell in Figure 1.1.1.
1.1 Introduction 7
idation of Br~ to Br 2 (and Br^~) occurs. An oxidation current, or anodic current, flows at
potentials near the E° of the half-reaction,
Br 2 + 2 e ^ 2 B r ~ (1.1.8)
which is +1.09 V vs. NHE or +1.02 V vs. Ag/AgBr. While this reaction occurs (right-
to-left) at the Pt electrode, AgBr in the reference electrode is reduced to Ag and Br~ is
liberated into solution. Again, because the composition of the Ag/AgBr/Br~ interface
(i.e., the activities of AgBr, Ag, and Br~) is almost unchanged with the passage of modest
currents, the potential of the reference electrode is essentially constant. Indeed, the essen-
tial characteristic of a reference electrode is that its potential remains practically constant
with the passage of small currents. When a potential is applied between Pt and Ag/AgBr,
nearly all of the potential change occurs at the Pt/solution interface.
The background limits are the potentials where the cathodic and anodic currents start
to flow at a working electrode when it is immersed in a solution containing only an elec-
trolyte added to decrease the solution resistance (a supporting electrolyte). Moving the
potential to more extreme values than the background limits (i.e., more negative than the
limit for H 2 evolution or more positive than that for Br 2 generation in the example above)
simply causes the current to increase sharply with no additional electrode reactions, be-
cause the reactants are present at high concentrations. This discussion implies that one can
often estimate the background limits of a given electrode-solution interface by consider-
ing the thermodynamics of the system (i.e., the standard potentials of the appropriate half-
reactions). This is frequently, but not always, true, as we shall see in the next example.
From Figure 1.1.4, one can see that the open-circuit potential is not well defined in
the system under discussion. One can say only that the open-circuit potential lies some-
where between the background limits. The value found experimentally will depend
upon trace impurities in the solution (e.g., oxygen) and the previous history of the Pt
electrode.
Let us now consider the same cell, but with the Pt replaced with a mercury electrode:
Hg/H+,Br-(l M)/AgBr/Ag (1.1.9)
We still cannot calculate an open-circuit potential for the cell, because we cannot define a
redox couple for the Hg electrode. In examining the behavior of this cell with an applied
external potential, we find that the electrode reactions and the observed current-potential
behavior are very different from the earlier case. When the potential of the Hg is made
negative, there is essentially no current flow in the region where thermodynamics predict
that H 2 evolution should occur. Indeed, the potential must be brought to considerably
more negative values, as shown in Figure 1.1.5, before this reaction takes place. The ther-
modynamics have not changed, since the equilibrium potential of half-reaction 1.1.7 is in-
dependent of the metal electrode (see Section 2.2.4). However, when mercury serves as
the locale for the hydrogen evolution reaction, the rate (characterized by a heterogeneous
rate constant) is much lower than at Pt. Under these circumstances, the reaction does not
occur at values one would predict from thermodynamics. Instead considerably higher
electron energies (more negative potentials) must be applied to make the reaction occur at
a measurable rate. The rate constant for a heterogeneous electron-transfer reaction is a
function of applied potential, unlike one for a homogeneous reaction, which is a constant
at a given temperature. The additional potential (beyond the thermodynamic requirement)
needed to drive a reaction at a certain rate is called the overpotential. Thus, it is said that
mercury shows "a high overpotential for the hydrogen evolution reaction."
When the mercury is brought to more positive values, the anodic reaction and the po-
tential for current flow also differ from those observed when Pt is used as the electrode.
8 • Chapter 1. Introduction and Overview of Electrode Processes
Hg/I-Г, ВГ(1 M)/AgBr/Ag Cathodic
Anodic
Onset of H+ reduction ,
-0.5 (^) -1. Onset of Hg oxidation
Potential (V vs. NHE) Figure 1.1.5 Schematic current-potential curve for the Hg electrode in the cell Hg/H+, Br ( M)/AgBr/Ag, showing the limiting processes: proton reduction with a large negative overpotential and mercury oxidation. The potential axis is defined through the process outlined in the caption to Figure 1.1.4.
With Hg, the anodic background limit occurs when Hg is oxidized to Hg2Br2 at a poten- tial near 0.14 V vs. NHE (0.07 V vs. Ag/AgBr), characteristic of the half-reaction Hg 2 Br 2 + 2e«±2Hg 2Br"^ (1.1.10) In general, the background limits depend upon both the electrode material and the solu- tion employed in the electrochemical cell. Finally let us consider the same cell with the addition of a small amount of Cd2 +^ to the solution, Hg/H+ ,Br"(l M), Cd2+ (10"^3 M)/AgBr/Ag (1.1.11) The qualitative current-potential curve for this cell is shown in Figure 1.1.6. Note the appearance of the reduction wave at about -0.4 V vs. NHE arising from the reduction reaction CdBr|~ + 2e S Cd(Hg) + 4Br~ (1.1.12) where Cd(Hg) denotes cadmium amalgam. The shape and size of such waves will be cov- ered in Section 1.4.2. If Cd2 + were added to the cell in Figure 1.1.3 and a current-poten- tial curve taken, it would resemble that in Figure 1.1.4, found in the absence of Cd2 +. At a Pt electrode, proton reduction occurs at less positive potentials than are required for the reduction of Cd(II), so the cathodic background limit occurs in 1 M HBr before the cad- mium reduction wave can be seen. In general, when the potential of an electrode is moved from its open-circuit value to- ward more negative potentials, the substance that will be reduced first (assuming all possi- ble electrode reactions are rapid) is the oxidant in the couple with the least negative (or most positive) E®. For example, for a platinum electrode immersed in an aqueous solution containing 0.01 M each of F e 3 +^ , Sn4 +^ , and N i 2 +^ in 1 M HC1, the first substance reduced will be F e 3 +^ , since the E° of this couple is most positive (Figure 1.1.7a). When the poten-
10 • Chapter 1. Introduction and Overview of Electrode Processes
0
(V vs. NHE)
-0.
0 +0.
(Pt)- ©
Possible reduction reactions
N i 2 +^ + 2e -> Ni
2 H +^ + 2e - » H (^9) S n 4 +^ + 2e -> S n 2 +
Possible oxidation reactions
Approximate potential for zero current - -^0
\ 2 + 2e<-2£
3+ + (^) e <- F e 2 + Approximate potential for zero current (a)
0
-0.76 - -
-0.41 - -
(Hg)
0 - -
E° (V vs. NHE)
A u 3 +^ + 3e <- Au - -
0 E° (V w. NHE)
(Au)
+0.
+0.
+1.
+1.
0
(Kineticallyslow)
Approximate potential for zero current
© (c) Figure 1.1.7 (a) Potentials for possible reductions at a platinum electrode, initially at ~ 1 V vs. NHE in a solution of 0.01 M each of Fe3 +^ , Sn4+, and Ni2+^ in 1 M HCL (b) Potentials for possible oxidation reactions at a gold electrode, initially at ~0.1V vs. NHE in a solution of 0.01 M each of Sn2+^ and Fe2+^ in 1 M HI. (c) Potentials for possible reductions at a mercury electrode in 0.01 M Cr3+^ and Zn2+^ in 1 M HCL The arrows indicate the directions of potential change discussed in the text.
nonfaradaic processes occur when electrode reactions take place. Although the faradaic
processes are usually of primary interest in the investigation of an electrode reaction (ex-
cept in studies of the nature of the electrode-solution interface itself), the effects of the
nonfaradaic processes must be taken into account in using electrochemical data to obtain
information about the charge transfer and associated reactions. Consequently, we next
proceed by discussing the simpler case of a system where only nonfaradaic processes
occur.
1.2 Nonfaradaic Processes and the Nature of the Electrode-Solution Interface 11
1.2 NONFARADAIC PROCESSES AND THE NATURE OF THE ELECTRODE-SOLUTION INTERFACE
1.2.1 The Ideal Polarized Electrode
An electrode at which no charge transfer can occur across the metal-solution interface, re- gardless of the potential imposed by an outside source of voltage, is called an ideal polar- ized (or ideal polarizable) electrode (IPE). While no real electrode can behave as an IPE over the whole potential range available in a solution, some electrode-solution systems can approach ideal polarizability over limited potential ranges,. For example, a mercury electrode in contact with a deaerated potassium chloride solution approaches the behavior of an IPE over a potential range about 2 V wide. At sufficiently positive potentials, the mercury can oxidize in a charge-transfer reaction:
Hg + С Г -> |Hg 2 Cl 2 + e (at ~ +0.25 V vs. NHE) (1.2.1) and at very negative potentials K +^ can be reduced: , Hg K+^ + e -> K(Hg) (at ~ -2.1 V vs. NHE) (1.2.2) In the potential range between these processes, charge-transfer reactions are not signifi- cant. The reduction of water:
H 2 O + e -> | H 2 + OH" (1.2.3) is thermodynamically possible, but occurs at a very low rate at a mercury surface unless quite negative potentials are reached. Thus, the only faradaic current that flows in this re- gion is due to charge-transfer reactions of trace impurities (e.g., metal ions, oxygen, and organic species), and this current is quite small in clean systems. Another electrode that behaves as an IPE is a gold surface hosting an adsorbed self-assembled monolayer of alkane thiol (see Section 14.5.2).
1.2.2 Capacitance and Charge of an Electrode
Since charge cannot cross the IPE interface when the potential across it is changed, the behavior of the electrode-solution interface is analogous to that of a capacitor. A capaci- tor is an electrical circuit element composed of two metal sheets separated by a dielectric material (Figure 1.2.1a). Its behavior is governed by the equation
| = С (1.2.4)
e Battery —
©
e ^ -
+ +
_ Capacitor + +
e (^) Figure 1.2.1 (a) A capacitor, (b) (b) Charging a capacitor with a battery.
1.2 Nonfaradaic Processes and the Nature of the Electrode-Solution Interface : 13
IHP OHP ф 1 ф 2 Diffuse layer Solvated cation
Metal
Specifically adsorbed anion
= Solvent molecule
Figure 1.2.3 Proposed model of the
double-layer region under conditions
where anions are specifically adsorbed.
cal centers of the specifically adsorbed ions is called the inner Helmholtz plane (IHP),
which is at a distance x. The total charge density from specifically adsorbed ions in this
inner layer is а^1 (/лС/ст^2 ). Solvated ions can approach the metal only to a distance x 2 ; the
locus of centers of these nearest solvated ions is called the outer Helmholtz plane (OHP).
The interaction of the solvated ions with the charged metal involves only long-range elec-
trostatic forces, so that their interaction is essentially independent of the chemical proper-
ties of the ions. These ions are said to be nonspecifically adsorbed. Because of thermal
agitation in the solution, the nonspecifically adsorbed ions are distributed in a three-
dimensional region called the dijfuse layer, which extends from the OHP into the bulk of
the solution. The excess charge density in the diffuse layer is <7d, hence the total excess
charge density on the solution side of the double layer, crs, is given by
= _ом^ (1.2.5)
The thickness of the diffuse layer depends on the total ionic concentration in the solution;
for concentrations greater than 10~^2 M, the thickness is less than ~100 A. The potential
profile across the double-layer region is shown in Figure 1.2.4.
The structure of the double layer can affect the rates of electrode processes. Consider
an electroactive species that is not specifically adsorbed. This species can approach the
electrode only to the OHP, and the total potential it experiences is less than the potential
between the electrode and the solution by an amount ф 2 — </>s , which is the potential drop
across the diffuse layer. For example, in 0.1 M NaF, ф 2 — <£s^ is —0.021 V at E = -0.
V vs. SCE, but it has somewhat larger magnitudes at more negative and more positive po-
tentials. Sometimes one can neglect double-layer effects in considering electrode reaction
kinetics. At other times they must be taken into account. The importance of adsorption
and double-layer structure is considered in greater detail in Chapter 13.
One usually cannot neglect the existence of the double-layer capacitance or the pres-
ence of a charging current in electrochemical experiments. Indeed, during electrode reac-
tions involving very low concentrations of electroactive species, the charging current can
be much larger than the faradaic current for the reduction or oxidation reaction. For this
reason, we will briefly examine the nature of the charging current at an IPE for several
types of electrochemical experiments.
14 Chapter 1. Introduction and Overview of Electrode Processes
- Metal — > Ц Solution >- 'IN i (+) Solvated cation
!©
0
_)_ j ч ~ ' "Ghost" of anion repelled from electrode surface
ф 2
x 2
Figure 1.2.4 Potential profile across the double-layer region in the absence of specific adsorption of ions. The variable ф, called the inner potential, is discussed in detail in Section 2.2. A more quantitative representation of this profile is shown in Figure 12.3.6.
1.2.4 Double-Layer Capacitance and Charging Current in Electrochemical Measurements Consider a cell consisting of an IPE and an ideal reversible electrode. We can approxi- mate such a system with a mercury electrode in a potassium chloride solution that is also in contact with an SCE. This cell, represented by Hg/K+ , CF/SCE, can be approximated by an electrical circuit with a resistor, Rs, representing the solution resistance and a capac- itor, C(j, representing the double layer at the Hg/K+ ,C1~ interface (Figure 1.2.5).^5 Since
нд drop electrode HI Wv II
-AM о SCE Figure 1.2.5 Left: Two-electrode cell with an ideal polarized mercury drop electrode and an SCE. Right: Representation of the cell in terms of linear circuit elements.
Actually, the capacitance of the SCE, С$СЕ, should also be included. However, the series capacitance of Cd and CSCE is CT = CdCSCEJ[Cd + CSCEL and normally C (^) S C E » Q> so that CT « Cd. Thus, C (^) S C E can be neglected in the circuit.
16 P Chapter 1. Introduction and Overview of Electrode Processes
Resultant (/)
- Applied (E)
Figure 1.2.7 Current transient (/ vs. t) resulting from a potential step experiment.
(b) Current Step When the RsCd circuit is charged by a constant current (Figure 1.2.8), then equation 1.2. again applies. Since q = Jidt, and / is a constant,
E = iRK + 4r\ dt (1.2.11)
or E = i(Rs + t/Cd) (1.2.12)
Hence, the potential increases linearly with time for a current step (Figure 1.2.9).
(c) Voltage Ramp (or Potential Sweep) A voltage ramp or linear potential sweep is a potential that increases linearly with time starting at some initial value (here assumed to be zero) at a sweep rate и (in V s"^1 ) (see Figure 1.2.10a). E = vt (1.2.13)
Constant current source
Figure 1.2.8 Current step experiment for an RC circuit.
1.2 Nonfaradaic Processes and the Nature of the Electrode-Solution Interface 17
-Slope = i - Resultants
- Applied (
_ Figure 1.2.9 E-t behavior resulting t from a current step experiment.
If such a ramp is applied to the RSC^ circuit, equation 1.2.8 still applies; hence
vt = Rs(dq/dt) + q/Cd (1.2.14)
lfq = OaU = 0,
The current rises from zero as the scan starts and attains a steady-state value, vCd (Figure
1.2.10b). This steady-state current can then be used to estimate Cd. If the time constant,
(a)
Applied E(t)
Resultant i
(b)
Figure 1.2.10 Current-time behavior resulting from a linear potential sweep applied to an RC circuit.
1.3 Faradaic Processes and Factors Affecting Rates of Electrode Reactions с 19
Galvanic cell Electrolytic cell
0 Zn/Zn2+ //Cu2+ /Cu 0 (Anode) (Cathode) Cu ,2+_
Power supply
0 Cu/Cu2+, H 2 SO 4 /Pt ( 7 ) (Cathode) (Anode) Zn -> Z n 2 + + 2e Cu C u 2 + + 2e -» Cu
Figure 1.3.1 {a) Galvanic and (b) electrolytic cells.
Although it is often convenient to make a distinction between galvanic and elec- trolytic cells, we will most often be concerned with reactions occurring at only one of the electrodes. Treatment is simplified by concentrating our attention on only one-half of the cell at a time. If necessary, the behavior of a whole cell can be ascertained later by com- bining the characteristics of the individual half-cells. The behavior of a single electrode and the fundamental nature of its reactions are independent of whether the electrode is part of a galvanic or electrolytic cell. For example, consider the cells in Figure 1.3.1. The nature of the reaction C u 2 + + 2e —» Cu is the same in both cells. If one desires to plate copper, one could accomplish this either in a galvanic cell (using a counter half-cell with a more negative potential than that of Cu/Cu2+ ) or in an electrolytic cell (using any counter half-cell and supplying electrons to the copper electrode with an external power supply). Thus, electrolysis is a term that we define broadly to include chemical changes accompanying faradaic reactions at electrodes in contact with electrolytes. In discussing cells, one calls the electrode at which reductions occur the cathode, and the electrode at which oxidations occur the anode. A current in which electrons cross the interface from the electrode to a species in solution is a cathodic current, while electron flow from a so- lution species into the electrode is an anodic current. In an electrolytic cell, the cathode is negative with respect to the anode; but in a galvanic cell, the cathode is positive with re- spect to the anode.^6
The Electrochemical Experiment
and Variables in Electrochemical Cells
An investigation of electrochemical behavior consists of holding certain variables of an electrochemical cell constant and observing how other variables (usually current, poten- tial, or concentration) vary with changes in the controlled variables. The parameters of importance in electrochemical cells are shown in Figure 1.3.2. For example, in potentio- metric experiments, / = 0 and E is determined as a function of C. Since no current flows in this experiment, no net faradaic reaction occurs, and the potential is frequently (but not always) governed by the thermodynamic properties of the system. Many of the variables (electrode area, mass transfer, electrode geometry) do not affect the potential directly.
(^6) Because a cathodic current and a cathodic reaction can occur at an electrode that is either positive or negative with respect to another electrode (e.g., an auxiliary or reference electrode, see Section 1.3.4), it is poor usage to associate the term "cathodic" or "anodic" with potentials of a particular sign. For example, one should not say, "The potential shifted in a cathodic direction," when what is meant is, "The potential shifted in a negative direction." The terms anodic and cathodic refer to electron flow or current direction, not to potential.
20 Chapter 1. Introduction and Overview of Electrode Processes
Electrode variables Material Surface area (A) Geometry Surface condition Mass transfer variables Mode (diffusion, convection,...) Surface concentrations Adsorption
External variables Temperature (T) Pressure {P) Time (?)
Electrical variables Potential (£) Current (i) Quantity of electricity (Q)
Solution variables Bulk concentration of electroactive species (Co, cR) Concentrations of other species (electrolyte, pH,...) Solvent Figure 1.3.2 Variables affecting the rate of an electrode reaction.
Another way of visualizing an electrochemical experiment is in terms of the way in
which the system responds to a perturbation. The electrochemical cell is considered as a
"black box" to which a certain excitation function (e.g., a potential step) is applied, and a
certain response function (e.g., the resulting variation of current with time) is measured,
with all other system variables held constant (Figure 1.3.3). The aim of the experiment is
to obtain information (thermodynamic, kinetic, analytical, etc.) from observation of the
(a) General concept Excitation System Response
(b) Spectrophotometric experiment
Lamp-Monochromator (^) Optical cell with sample
Phototube
(c) Electrochemical experiment
Figure 1.3.3 (a) General principle of studying a system by application of an excitation (or perturbation) and observation of response, (b) In a spectrophotometric experiment, the excitation is light of different wavelengths (A), and the response is the absorbance (si) curve, (c) In an electrochemical (potential step) experiment, the excitation is the application of a potential step, and the response is the observed i-t curve.
