spiral.imperial.ac.uk€¦ · • • abstract the behaviour of the sulphide-sulphur redox couple...
TRANSCRIPT
0
(±)
ELECTROCHEMICAL STUDIES OF' SULPHUR ELECTRODES
g...1a1AUISAITI
A THESIS
submitted for the degree of
DOCTOR OF PHILOSOPHY
BY
MICHAEL JOHN WEAVER, B.Sc.
Department of Metallurgy
Imperial College
London.
Illgust 1972.
•
•
•
•
ABSTRACT
The behaviour of the sulphide-sulphur redox couple at gold, platinum
and carbon electrodes was studied in fused lithium chloride - potassium
chloride, fused sodium nitrate-potassium nitrate, and alkaline aqueous
media.
In the chloride solvent, the redox couple exhibited complete reversi-
bility with respect to electron transfer. However, the anodic oxidation
of sulphide ion appeared to be strongly inhibited by the formation of
a polymeric sulphur film on the electrode surface. The properties of this
film were studied using various electrochemical perturbation techniques.
In the nitrate solvent, a similar anodic inhibition was seen, along
with a degree of irreversibility with respect to electron-transfer.
wds In the aqueous media, the anodic mechanism A dependent on the presen-
ce of dissolved sulphur. With solutions containing both sulphide and
sulphur (including sulphur electro-generated under pulse conditions),
the rate-determining step was found to be a two-electron transfer,
probably involving two sulphide ions. In the absence of sulphur, a rate-
determining one-electron oxidation step was found.
On platinum electrodes in the chloride system, thick films of platinum
sulphide were formed. A concerted platinum ion-sulphide ion rearrangement
step has been postulated to explain the galvanostatic film reduction
kinetics.
Very thin (", few molecular layers) oxide films were observed to
form on platinum electrodes under anodic polarization in solutions of
oxide in aqueous LiCl-KC1 melt. Some similarities with the analogous
aqueous system were seen, particularly with regard to hysteresis between
formation and reduction and the low ("J 2.3 PT/2F) Tafel slopes for reduction.
Again, the most likely mechanism for film formation and removal was
considered to be a concerted platinum ion-oxide ion rearrangement step
under the influence of a high field, thus involving mainly incorporated oxide.
Iodide ions were found to be completely electroinactive in fused
LiCl-KC1. This has been attributed to a necessary formation of 13 ions
being prevented by preferential co-ordination of any iodine produced to
form 12C1-.
•
•
"SOMEHOW IT SEEMS TO FILL MY HEAD WITH IDEAS -
ONLY I DON'T EXACTLY KNOW WHAT THEY ARE. "
Lewis Carroll
•
(iv)
LIST OF CONTENTS
PAGE
1
1.1 General 1 1.2 Charge-transfer reactions involving non-metals
2 1.2.1 Electrode mechanisms 1.3 Fused salts 4 1.4 Present work 5
SECTION 2 THEORY AND LITERATURE SURVEY 8
2.1 Interfaces - general 8 2.2 Thermodynamics of electrochemical interfaces -
charge transfer equilibria 9 2.3 Electrochemical kinetics 12 2.3.1 Absolute reaction rate theory 2.3.2 Basic factors in ion discharge 2.3.3 The effect of potential on the activation energy 2.3.4 Effect of reverse reaction 2.3.5 Electrochemical reaction orders 2.3.6 The transfer coefficient 2.3.7 Derivation of the Nernst equation with varying
intermediate adsorption energy 2.3.8 High-field ion transport processes 2.3.8.1 General 2.3.8.2 The ion-transport mechanism 2.4 Surface chemistry aspects 23 2.4.1 General -'thermodynamics 2.4.2 Nature of surface forces 2.4.3 Adsorption models 2.4.4 Surface kinetics 2.4.5 Chemisorption - equilibria 2.4.5.1 Isotherms - the Temkin model 2.4.5.2 Explanations of adsorption heat fall with coverage 2.4.5.3 Surface potentials 2.4.6 Chemisorption kinetics 2.4.6.1 General - the Elovich equation 2.4.6.2. Experimental applicability 2.4.6.3 Models for the Elovich equation 2.4.6.4 Other applications 2.4.7 Other adsorption types 2.4.7.1 Physical adsorption 2.4.7.2 "Insoluble monolayer" films 2.5 Electrochemical adsorption 38 2.5.1 Introduction 2.5.2 Experimental methods 2.5.3.1 General 2.5.3.2 Galvanostatic charging 2.5.3.3 Potentiostatic techniques
SECTION 1
INTRODUCTION
(v)
PAGE
2.5.3.4 Linear potential sweep 2.5.3.5 A.C. bridge method 2.5.3.6 Open-circuit decay 2.5.3.7 General limitations of the methods 2.5.4 Electrochemical adsorption equilibria 2.5.4.1 General 2.5.4.2 The Langmuir isotherm 2.5.4.3 The Temkin isotherm 2.5.5 Electrochemical Adsorption kinetics 2.6 Electrochemical adsorption - previous results
and discussion 51 2.6.1 General 2.6.2 Hydrogen adsorption 2.6.3' Oxygen adsorption and oxide formation 2.6.3.1 Introduction 2.6.3.2 General behaviour 2.6.3.3 Film formation 2.6.3.4 Film reduction 2.6.3.5 The high-field growth model 2.6.3.6 Limitations of the model 2.6.3.7 Mechanism involving a quasi-equilibrium intermediate 2.6.3.8 Comparison with gas-solid systems 2.6.3.9 Other oxide films on platinum 2.6.3.10 Miscellaneous anodic films 2.7 Other electrochemical techniques 68 2.7.1 Steady-state techniques 2.7.1.1 The irreversible case 2.7.1.2 The reversible case 2.7.2 Transient techniques - chronopotentiometry 2.7.2.1 Introduction 2.7.2.2 Chronopotentiometry - general 2.7.2.3 Deviations from the Sand equation 2.7.2.4 Current reversal 2.7.2.5 Potential-time curves 2.7.2.6 Measurement of the transition time 2.8 Passivation and inhibition processes 83 2.8.1 General 2.8.2 Galvanostatic studies of passivity 2.8.3 Inhibition mechanisms 2.9 Electrode processes involving simple anions 86 2.9.1 Electrode reaction rates 2.9.2 Sulphur electrodes 2.9.2.1 Aqueous media 2.9.2.2 Other room temperature systems 2.9.2.3 Fused salts 2.9.2.4 Sulphur species 2.9.3 Oxygen electrodes in aprotic solvents 2.9.3.1 Fused salts - general 2.9.3.2 Fused alkali nitrates
2.9.3.3 Fused alkali chlorides 2.9.3.4 Other aprotic solvents 2.9.4 Iodine electrodes
PAGE
SECTION 3 : EXPERIMENTAL ASPECTS 98
3.1 Apparatus 98 3.1.1 Electronic equipment 3.1.2 Furnace and temperature control 3.1.3 Electrochemical Cell 3.1.4 Dry box 3.1.5 Vacuum and gas supply systems 3.2 Chemicals 105 3.2.1 Lithium chloride - potassium chloride 3.2.2 Sodium nitrate - potassium nitrate 3.2.3 Aqueous solvent 3.2.4 Sodium sulphide 3.2.5 Polysulphides 3.2.6 Lithium oxide 3.3 Electrodes 108 3.3.1 Micro- and counter- electrodes 3.3.2 Reference electrodes 3.4 Experimental Procedures 111 3.4.1 Apparatus preparation 3.4.2 Electrochemical measurements
SECTION 4 : RESULTS AND DISCUSSION 115
•
4.1
4.1.1 4.1.2 4.1.2.1 4.1.2.2 4.1.3 4.1.3.1 4.1.3.2.1 4.1.3.2.2 4.1.3.3 4.1.3.3.1 4.1.3.3.2 4.1.4 4.1.4.1 4.1.4.2 4.1.4.2.1 4.1.4.2.2 4.1.4.2.3 4.1.4.3 4.1.4.3.1 4.1.4.3.2 4.1.4.3.3
4.1.5 4.2
4.2.1
The sulphide-sulphur electrode on inert electrodes in lithium chloride - potassium chloride eutectic 115 General introduction Reversible potentials - potentiometry Results Discussion Chronopotentiometry Introduction Results Discussion Cathodic chronopotentiometry Results Discussion The application of other electrochemical techniques Introduction Results Steady-state voltammetry Cathodic galvanostatic charging Open-circuit decay and galvanostatic potential build-up Discussion curves Steady-state voltammetry Cathodic galvanostatic charging Open-circuit decay and galvanostatic potential build-up curves Comparisons with previous work The sulphide-sulphur electrode on inert electrodes in sodium nitrate - potassium nitrate eutectic 158 Introduction
4.2.2 4.2.3 4.3
PAGE
Results Discussion Platinum sulphide films formed in fused lithium chloride - potassium chloride eutectic 165
4.3.1 Introduction 4.3.2 Results 4.3.3 Discussion 4.3.3.1 Film formation kinetics 4.3.3.2 Film reduction kinetics 4.4 Formation of sulphur films on a liquid bismuth electrode
in lithium chloride-potassium chloride eutectic .• 179 4.4.1 Introduction 4.4.2 Results 4.4.3 Discussion 4.5 The oxide-oxygen electrode in lithium chloride -
potassium chloride eutectic 181 4.5.1 Introduction and potentiometry 4.5.2 Chronopotentiometry and steady-state polarization 4.5.2.1 Results 4.5.2.2 Discussion 4.5.3 Studies of the anodic oxide film on platinum electrodes 4.5.3.1 Results 4.5.3.2 Discussion 4.5.3.2.1 Film formation kinetics 4.5.3.2.2 Film reduction kinetics 4.5.3.3 Comparison with aqueous systems 4.5.3.4 Incorporation of chemisorbed species 4.6 The sulphide-sulphur electrode at inert electrodes
in alkaline aqueous solutions 201 4.6.1 Introduction 4.6.2 Results 4.6.2.1 Steady-state polarization 4.6.2.2 Non-steady state galvanostatic studies 4.6.3 General discussion 4.7 Anodic behaviour of iodide and bromide ions in 216
lithium chloride - potassium chloride eutectic
SECTION 5 : SUMMARY, CONCLUSIONS AND CONJECTURES 219
5.1 Sulphur electrodes 219 5.2 Metal oxide and sulphide surface films 222 5.3 Iodine and bromine electrodes 224 5.4 Elovich kinetics 225
Photographs Index to photographs Symbols used References Acknowledgements
-1-
•
SECTION I - INTRODUCTION
1.1 General
Electrochemistry, the study of the behaviour of chemical species
with a net charge, is conveniently divided into two parts, ionics and
electrodics (1). The former concerns the study of ions in solution and is
therefore a discipline involving bulk phases, whereas the latter is
concerned with the rather special situation existing at the interface
between an electronic and an ionic conductor, including the transfer of
electric charge across it. This description of electrodics immediately
suggests a pre-occupatipn with a rather narrow and therefore unimportant
area of nature, but this feeling is perhaps somewhat illusory. The subject
is able to say a great deal concerning surface phenomena. However, the
true key to its fundamental value is the essential involvement of electrons
in the systems, both in the study of energies of species via potential
measurements, and the measurement of reaction rates via the flow of
electrons around an external circuit. As a very high degree of control is
available in the electrochemical potential of electrons in an electronic
conductor, considerable influence of these variables can be achieved. This
should lead to greater understanding of the nature of interacting matter.
These studies should also help to suggest ways of controlling
nature, that is technology. It is certainly true that the use of
electrochemical systems can be of great value to technology. However,
perhaps a relevant point is that the value of fundamental studies of
simple systems, concerned particularly with "fine detail" in nature, can
be easily overstressed in relation to their worth in technological
application.
•
-2-
1.2 Charge transfer reactions involving non-metals
Most elements have some metallic properties; therefore they form
simple cationic rather than anionic charged species. The small number
of elements definitely classed as non-metals lie around the top right-
hand corner of the Periodic Table. These are Groups VIIB, VIB down
to tellurium, and Group VB, nitrogen. Also hydrogen can readily lose
its electron to form a proton. This is classified with the other
non-metals, although electrochemical liberation of hydrogen involves a
reduction, in contrast to the remainder which are liberated from their
anions by oxidation. Also polyatomic anionic species, such as the
pseudohalide" ions can be oxidized at electrodes.
Almost all electrode kinetic studies have been performed in aqueous
media, and therefore it is not surprising that by far the most studied
non-metal electrochemical reactions have been those involving hydrogen
and oxygen (e.g. 2).
As the ionic species concerned also constitute the solvent, transport
of the ions to the electrode surface is unlikely to be the rate-determining
step and indeed these reactions are completely surface rate-controlled.
However, these reactions involve a considerable degree of complexity, and
although forming model systems around which much of the subject of elec-
trode kinetics developed, theoretical advances concerning the charge-
transfer process now mainly involve the simple metal ion redox systems as
models.
Apart from this, a considerable intrinsic interest remains in the
electrochemistry of non-metals. Unfortunately, work on this topic has
been very fragmented, possibly lacking a common motive is the case in the
electrodeposition of metals for example. Most work, apart from the H2 and
02 electrodes, has been concerned with the halogen electrodes.
-3-
•
•
1.2.1 Electrode MechanisMs
Anodic oxidation of simple anions in solution usually produces the
neutral elemental species as a first step. These species can (1) be
evolved as a gas, (2) redissolve in solution, or (3) be deposited on
the electrode surface. Also a combination of these possibilities may
occur. It is reasonable to expect (1) to occur when the temperature is
above the boiling point of the species concerned, i.e., when its vapour
pressure is above the external pressure. This is borne out in practice,
e.g., the evolution of oxygen from water, and chlorine from hydrochloric
acid. (2) is expected to occur particularly when complex ions can be
formed between the anion and its parent element, e.g. tri-iodide ion from
iodide ion and iodine. (3) is of course the type of process occurring
during metal electrodeposition. A crucial difference with non-metal
deposition is that it involves the formation of a non-conducting layer on
the electrode surface, which can have the effect of blocking the path
for electrons and inhibiting the process. Also, with liquid metal electro-
des, a further possibility arises of product dissolution into the bulk
of the metal. This is perhaps,a limited effect as non-metal solubilities
in metals are low except at high temperatures.
A crucial aspect of this field concerns the physical state of this
adsorbed intermediate. A number of non-metals, e.g. hydrogen, are
capable of being chemisorbed on the metal surface. This considerably effects
the energy state of the adsorbate, and hence its activity. Interactions
between species can also be important and should depend markedly on coverage.
There exists a whole field of study concerned with the behaviour of
chemisorbed species at electrodes which is analogous to that of the
gas-metal interface. These species are sufficiently stable to exist as
•
-4-
products, rather than as intermediates, e.g. oxygen on platinum.
The reverse (reduction) reactions are more difficult to classify.
Sometimes, as in the case of platinum-oxygen, the energy-state of the
intermediate may markedly alter the course of reduction back to the original
anion.
The effect of the electrolyte media in the case of dissolved anions
is difficult to assess. It can, of course, be described thermodynamically
by means of activity coefficients, but no direct analog of complex ions
formed between a metal ion solute and surrounding ligands is expected.
Specific chemical interactions can take place, e.g. S2- + H30+
HS + H20, but more subtle "solvent effect" treatments belong to
future investigations.
The above summarises the main characteristics of simple non-metal
electrode processes. One of the central aims of this thesis is in fact to
treat the subject in as unified a way as possible.
1.3 Fused Salts
These fall into three main categories: (a) simple ionic salts such
as alkali metal halides; (b) simple oxy-anion melts such as alkali metal
nitrates or sulphates; (c) complex polymeric melts, for example silicates.
In this study, melts of type (a) and (b) were used. These two types
are, in principle, almost ideal electrolytes for ionic species. Solubili-
ties are high, with Henry's Law applicable to high solute concentrations.
The systems show good thermal stability, thermal and electrical conduc-
tivities are high, and viscosities of types (a) and (b) are similar to
"normal" liquids. Interest in fused salts has grown steadily. A number
-5-
of reviews on the chemical (3-7) and electrochemical (8-11) aspects
have been published.
Further relevant aspects of molten salts will be discussed in
following sections.
1.4 Present Work
The major portion of the experimental work outlined in this thesis
is concerned with the kinetics of the (nominally) sulphide-sulphur electro-
de in fused lithium-potassium chloride eutectic at inert electrodes.
Some results are also reported for the fused sodium-potassium nitrate
eutectic, and also aqueous solution.
The choice of system arose in a rather indirect way. The original
aim was to investigate a sulphur electrode formed at a fluoride slag-
liquid lead interface, as a model for the electroslag-remelting process
for removing sulphur from ion. As a result of a change of emphasis in
the project, the sulphur electrode aspect was retained, but the corrosive
slag and surrounding electrode system was replaced by chloride melts and
gold, platinum, and carbon electrodes. The chloride melt provides a
good inert electrolyte system for the sulphide ion, and at least gold
appears to be unattacked by this media. The system as now studied (as
well as perhaps the original slag system) is considered to be irrelevant
to the electroslag process and this will not be discussed further.
However, the sulphur electrode in melts is considered to be a rather
novel one. Some work has been performed on the oxygen electrode in
fused chlorides, but no other anion systems have been extensively studied
in these media. One clear advantage of the melts over more complex solvents
-6-
such as water is that the solution chemistry, particularly for elementary
anions is expected to be very simple. Any mechanistic complexities
occuring at the electrode should then be more easily elucidated.
It also became clear during the course of the work that the
sulphide-sulphur electrode had in fact received very little attention in
any electrochemical media. One reasonable study had been published in
alkaline aqueous solution( 12) using steady-state techniques and potentiome-
try. The results were considered to be interesting, particularly regarding
the effect of dissolved sulphur on the anodic reaction. This work was
therefore extended by performing some experiments at lower sulphikr concen-
trations and under galvanostatic pulse conditions. These separate
investigations have resulted in an attempt to unify sulphur electrode
behaviour under these varying conditions.
Some experiments were also performed on the oxide-oxygen electrode
in fused chlorides. This work is concerned with the build-up 'of a
chemisorbed oxygen layer on platinum. The system shows some interesting
similarities to the well-known aqueous solution. The electrochemical
properties of a"platinum sulphide" film were also investigated, along
with a sulphur film on a liquid bismuth electrode. Finally, some other
simple anion systems in fused chlorides were briefly studied.
The technique used for much of the work was the galvanostatic
technique in various forms. Situations involving diffusion to or from the
electrode surface under galvanostatic conditions were encountered, as the
solutes were present in fairly low (--,10-2.M) concentrations. This techni-
que is termed chronopotentiometry. Although currently unfashionable among
many electrochemists, the method is a very useful one for arriving at
basic mechanisms, as the theory is very simple. However, accuracy is not
high. A galvanostatic approach was also used in the study of adsorbed
-7-
intermediates. This will be termed galvanostatic charging, reserving the
term chronopotentiometry for cases involving diffusion.Potentiometry
and steady-state voltammetry were also used.
Due to the non-availability of a good potentiostat, current-time
transients were not recorded under these conditions. The often-quoted
• advantage of potentiostatic conditions is the resulting condition of
constant reaction affinity for the charge-transfer process. However,
most of the systems investigated were not "irreversible" in the accepted
sense, i.e. the charge-transfer process is sufficiently fast to be
at quasi-equilibrium at the electrode surface. Also, in the case of the
sulphur electrode in.melts, the galvanostatic condition happened to
describe a particularly simple electrode condition, for reasons to be dis-
cussed later.
•
-8-
SECTION 2 - THEORY AND LITERATURE SURVEY
2.1 Interfaces - general
The study of electrode processes is involved essentially with the
physics and chemistry of surfaces. Most surfaces studied are not
electrochemical, but nevertheless all these investigations have a good
deal of common interest. This is particularly true of chemisorption
and physical adsorption of gases on solids and on the corresponding elec-
trodes. In view of this, some emphasis will be laid on gas-solid
phenomena and the value of this to interfacial electrochemistry.
Two limiting types of electrode reaction may be distinguished(20)
These are when reactant species form either (a) weak or (b) strong
bonds with the electrode surface. Types (a) and (b) may often be identi-
fied with (a) physical adsorption, and (b) chemisorption with the
electrode. In the case of (a) however, solvent interactions with the
electrode may well be the dominant effect. Using this classification,
specific electrode effects, e.g. electrocatalysis, are only expected
with (b); it was considered primarily for this purpose. A slightly
more general classification is proposed in which type (b) is broadened
to include systems which exhibit strong interactions between surface species.
As demonstrated later, this type of system may not involve large interac-
tions with the electrode itself, although the two effects are often seen
together, particularly in the chemisorption case.
At equilibrium, these effects may be considered in two ways(21)
(a) by the use of adsorption isotherms, relating bulk activity and
surface concentration (more precisely, surface excess) for a given species,
or (b) using the concept of a two-dimensional equation of state.
-9-
These two approaches can be thermodynamically related via the Gibbs'
adsorption equation, and both have been used extensively. Approach (b)
focusses attention completely on the state of the adsorbate itself,
whereas (a) directly relates surface state with the corresponding bulk
activity term in the Nernst equation and is therefore more useful in
• electrochemical equilibria. The two approaches will be discussed in
more detail later.
However, non-equilibrium surface states are often encountered,
particularly with electrode processes, and attention switches to a
description of energy states involved in an activated process.
Usually the rate process is associated with a slow charge-transfer
step, and hence one is involved with the effect of potential on this
process rather than the electrode potential effect on the electrochemical
potential of bulk species as in the equilibrium case. This is in addi-
tion to any purely chemical effects on the energy of the activated com-
plex, and therefore the net observed phenomena is likely to be complex.
Consequently, purely electrochemical theory will be developed in
the next section, followed by a discussion of physical interactions
at surfaces. These will subsequently be combined to consider problems
relevant to the electrochemical formation of chemisorbed and other
• interacting species at electrodes. In conjunction with this, experimental
contributions to the subject will be reviewed.
2.2 Thermodynamics of electrochemical interfaces - charge transfer
equilibria
The thermodynamic aspects treated in this section refer to non-
• polarizable electrochemical interfaces, i.e. where potentials are defined
-10-
in terms of a redox equilibria. Double-layer structure is only
incidental to this problem. The well-known Nernst equation
ac d
E = Eo RT
In Ini F
r a: aB aA
(Eqn.2.1)
• for the generalized cell reaction aA + bB g cC + dD, describes
the position of equilibrium in electrochemical systems. It may be
derived from simple thermodynamic reasoning by the equilization of
electrochemical potentials throughout the system (e.g. 22), or by kinetic
reasoning (see 2.3.7).
It may be noted that the activities referred to in equation 2.1
are bulk activities. Its simplest application is when the activities may
be equated with concentrations, i.e. when activity coefficients may
be taken as unity. This is very often the case with dilute ((1C71 M)
solutions of simple non-complexing ions in ionic fused salts;; ideal
mixing is achieved and Henry's law is obeyed. A more complex case arises -e
with, for example, the equilibrium X g Xads. where Xads represents
a neutral atom stabilized by adsorption on the metal electrode, and may
only be present in the surface region. A solution to this problem
• involves a description of the adsorption isotherm relating the (perhaps
hypothetical) bulk and surface activities of species X. In this way
potential-surface coverage relations determined in electrochemical measu-
rements can be compared to purely chemical interfacial situations.
On passage of a net current across an electrochemical interface,
disturbance of the equilibrium embodied in equation 2.1 is inevitable.
This equilibrium involves (1) diffusion and perhaps convection to the
electrode surface, (2) adsorption of reactants at surface, (3) electron
•
transfer at the surface, with perhaps also purely chemical transformations,
(1+) desorption of products from surface, (5) diffusion and perhaps
convection of products away from surface. In most cases, one or more
of these steps will be markedly more activated than the rest, and these
will control the rate. The remaining steps may then be considered to
• be in "quasi-equilibrium", i.e., the frequency of activated "jumps"
for the reverse step is almost equal to that of the forward step. Often
the rate-controlling steps are (1) and (5), and (2) and (4) are
usually non-activated. In this case the potential under passage of net
current is defined by the activities of reactant and product very close
to the electrode surface (just outside the double layer) via the Nernst
equation. Thus a "concentration overpotential" may be defined as the
potential difference between the potential under net current involving
depletion of reactants.and build-up of products, and the zero current
rest potential. In the event of a slow chemical change a reaction
overpotential may be similarly defined.
Often however, the electron-transfer act itself is sufficiently
activated to limit the overall rate. In this case the potential-rate
(current) relation involves an analysis of the potential of this
activated process, and is the central problem of electrochemical kinetics.
• Generally, systems where concentration overpotential, or activation
or chemical overpotential are dominant are often known as "reversible"
"irreversible" IrreversibleIT systems respectibly, as the former case describes
electron-transfer quasi-equilibrium at the interface.
-12-
•
2.3 Electrochemical Kinetics
2.3.1 Absolute Reaction Rate Theor/..
Like other microscopic rate processes the theory of electron trans-
fer at electrode surfaces has been treated using absolute reaction rate
theory (23). This considers that, for example, for a bimolecular reaction
, t ,t A + B [ AB J -> products, the activated complex [ AB' can
be considered to be in equilibrium with the reactants
n t an equilibrium constant K = [ AB J / [A] [ B]. ,t
of reaction is - d [A] /dt = [ AB' x (rate of
giving rise to
Further, the rate
passage over barrier).
The rate of passage over the barrier is equal to the frequency (v) with
which the complex dissociates into the products and has the value
v = -kT/h. Hence the reaction rate - d [A] /dt = k2 [A] [B3
where k2 is the rate constant (Eqn. 2.2)
The crucial aspect of the theory concerns the evaluation of K . It
may be related to a standard free energy of activation by AGot
-RT1nKc
, taking the standard state as one of unit concentration. The
effect of potential on this parameter for electron-transfer reactions
forms the central theoretical problem of electrode kinetics.
2.3.2 Basic factors in ion discharge
Consider the reaction X + M -4 Xads M + e(in metal), where
X- represents an ion close to an electrode metal surface M so that
electron transfer is possible (the so-called "pre-electrode state").
The electrochemical standard free energy of activation for this reaction
is AG , and can be considered to be between X and M. Hence the
•
„ K LA J LB JkT/h
•
-13-
electrochemical rate may be written
of kT r AG
i = nPv = L -- h exp (- RT )1 nF [X-] [1-6] (Eqn.2.3)
where i is current passed, and the varying activity (available area)
of the electrode is considered by including a(1-6) term, where
is the coverage by Xads.
2.3.3 The effect of potential on the activation energy
This problem has no obvious solution, as for a given change in
overall potential difference across a single interphase, the fraction
which is available in altering the electrochemical free energy of
—* activation AG
o is not known xsE,rae . The measured potential refers
of course to the potential difference between two wires of the same
composition connected through two electrochemical interfaces (e.g. 21+) -
the working electrode and reference electrode interfaces. It is arranged
to hold the potential drop at the reference electrode constant and there-
fore any variation in potential observed will occur at the single working
electrode interface. Assuming that negligible bulk "IR" potential drop
is present, this drop occurs between just outside the double layer and
the bulk metal. Also, because of the nature of metallic conductors,
the potential in the metal will be sensibly constant at all points right
up to the surface layer of atoms.
Using transition-state theory, there are three main modifications
required to this total potential to provide a description of its effect
on the electron transfer reaction rate.
These involve a knowledge of
(i) the fraction of potential between the reactant (pre-electrode
state) and the product state effective in promoting or hindering
electron transfer
(ii) the potential drop between the outside edge of the double layer and
the pre-electrode layer
" (iii) the difference in species concentration between the two states
mentioned in (ii).
Factors (ii) and (iii) require knowledge of the double-layer structure
and its variation with potential, and have been described for systems
obeying the Gouy-Chapman-Stern model (25). No satisfactory correspon-
ding treatment exists for melts.
The primary problem, however, is factor (i). This is generally
surmounted by considering that a constant fraction a (the "transfer
coefficient") of the total potential drop between reactant and product
states is active in promoting electron transfer and the same fraction
is available of any change in potential. The effect of potential on
the electrochemical free energy for the reaction is given by
tGo Go nY,Pm (Eqn.2.4)
where p is the Galvani (inner) metal-solution potential difference.
The relation follows from the concept of electrochemical potential (26).
Thus;.
o * AG = A Go - riFfflm (Eqn.2.5)
(a is the anodic transfer coefficient) - and equation 2.3 now becomes
oS i - kT.
hnF pc] (i_c).e
xp [ - RT AG ]
exp [ anF
ET .A4 ] (Eqn.2.6)
A fuller description of the above is given elsewhere (e.g. 22, 27).
-15-
2.3.4 Effect of reverse reaction
The above considers only the forward rate of the electron transfer
process; experimentally the net rate is measured. Thus an analogous
relation to eqn. 2.6 can be written for the reverse (cathodic) reaction,
but with the rate dependence on potential in the opposite sense.
o*
exP [- exP [ - ibm ][r] Thus i
•
=
kT 4G° and i = of exp [- r (1-u)nF ir RT ] exP L Rt L
(Eqn.2.7a)
(Eqn.2.7b)
(neglecting coverage effects by species X).
By equating 2.7a and 2.7b, the corresponding Nernst equation
may be obtained. The potential at this point will be an equilibrium
potential and be associated with an exchange current density i0, i.e.
where
•
= i . It is useful to define an electron transfer over-
voltage 1, where q = 0 at the equilibrium potential.
Thus 1 = E - Ee
L . clinF (CY -1)nF and L
▪
(net) = io exp —1,71-F- 1 - RT
a where i0
= nFko [r] [X] derived by inserting the appropriate
Nernst relation. ko
is the standard electrochemical rate constant
kT AG° * a nF e ko
= . exp ( - ) exp (- TT- - lam )
kT A o (1.4Y)nF e = IT . exP ( G
) exp
( RT ) (Enq.2.8a)
-16-
With varying overvoltage two simple limiting relationships
immediately follow
(1) Large 1 - Here the second experimental term can be neglected,
and the form
nE 14- = i0 exp( -TT .
results, known as the "Tafel Relationship"
(Eqn.2.9)
(2) Low 1 - Here the exponentials can be linearized, and the form
3-o• T.T • 11 . nF
(Eqn.2.10)
results.
Electrochemical Reaction Orders
The above theory has been derived assuming first order kinetics
forthe species X-. Often, however, the experimental order is other than
unity. This may be associated with a non-unity molecularity, but in
electrode kinetics is usually associated with a chemical step in quasi-
equilibrium next to the electron transfer step (e.g. 2).
Generally, one may write
Z i+ = nFk (FT C.°'j r nE
o ) exP ex RT • PM (Eqn.2.11)
forthepartialanodicreactionofspeciesS.3 with reaction order
ZSpecies S. is considered to be in equilibrium via a chemical o,j
step with another species So
actually undergoing electron transfer so Z 4
that Co = Ko j II C.°" . So
is a species considered to undergo -a
simple unimolecular electron transfer at the electrode surface.
In the Tafel region the partial current i+ becomes also the
net current. Thus from eqn. 2.11, at constant & for species Sk
-17-
a log i+ =
slog C k C
Zo,k .
J
(Eqn.2.12)
Thus by varying the concentration of a given species, keeping all
other concentrations constant, the reaction order for this species may
be determined by variation of the observed current with concentration,
providing the reaction is electron transfer controlled and the reverse
reaction rate can be neglected.
It is perhaps useful to note that with simple one-step electroche-
mical reactions, the partial forward current must be independent of
product activities providing no chemical effects on the activation
energy are present as a result of product adsorption energy (see later).
2.3.6 The transfer coefficient
This quantity (cy) is essentially a means of circumventing the
lack of knowledge of the effect of potential on the activation free
energy by correlating the latter with the charge in reaction free energy.
Its validity may be justified by the use of Morse curves for energy
versus reaction co-ordinate (28) but it is essentially a correlation
between a kinetic and a thermodynamic change and cannot be derived from
any fundamental law. It is an example of a "linear free energy relation-
ship" (c.f. the BrBnsted acidity function). However, the exponential
linearity of many Tafel relationships testifies to constancy of a .
with potential. The use of a has been reviewed (29). Often its value
has been taken to be 0.5 implying symmetry in the form of the energy
barriers. It may be experimentally obtained either from the slope of
the Tafel relation assuming fi, or be obtained from equation 2.8a by
-18-
the variation of the exchange current with reactant or product activity.
Often the experimental values of a are about 0.5, but many
instances exist where this is not the case, and the coefficient can
vary widely between the limits zero and unity (30). However, it
must be noted that most experimental values are not corrected for double-
layer effects, and the exchange currents greater than cm. 10 3 amp. cm-2
are obtained by relaxation techniques with a necessarily greater number
of assumptions. Probably many measurements made in the past using these
techniques are questionable due to insufficient attention to experimental
detail. Also statements such as "the transfer coefficients for gas
electrode reactions are usually one half" sometimes made in the litera-
ture have no proven basis; in fact direct determinations of / for
these systems are by no means common. In summary, the transfer coefficient
is apparently usually invariant with potential and often can be around 0.5,
but this is by no means general.
Usually it is assumed that the transfer coefficients for the forward
(a) and reverse (3) processes must equal unity. This is assumed in the
derived equations, and must follow at the equilibrium potential where the
Nernst equation results as a consequence of a + 5 = 1. However, under
conditions of net current flow, anodic and cathodic processes may take
place on different sites, and are expected to do so where either reactant
or product is strongly chemisorbed. This was first noted by Audubert (31)
and incorporated into the "differential site theory" of the hydrogen
electrode (32).
Surprisingly, the temperature dependence of the apparent transfer
coefficient has been little studied. Early Tafel measurements (e.g. 12,
33) indicated a Tafel slope. (ET/xnF) independent of temperature. This
also has been found recently under certain conditions for the bromine and
-19-
hydrogen electrodes(198). The latter case has been explained by proton
tunnelling effects, but explanation of the bromine results by the varying
effect of potential on anion specific adsorption with temperature is
not completely convincing. Similar temperature dependence of the transfer
coefficient has been seen with systems involving high-field ion
conduction as the rate-limitation, Ref. (34). •
2.3.7 Derivation of the Nernst equation with varying intermediate
adsorption enera.
It is valuable to note that the Nernst equation involving two
species present in the bulk phase is invariant to changes in energy of
an intermediate which may be directly involved in electron transfer.
This is clearly seen using a kinetic argument (32) as follows.
Consider, for example, a hydrogen electrode at equilibrium with
a fixed concentration of hydrogen ions in solution and a fixed pressure
of hydrogen gas. Assume that the electron transfer process is H -4
soln.
+ +e-
Hads. with the additional equilibrium H
ads g H2 (gas).
Suppose that the adsorption energy is increased by AX. This
will decrease the discharge activation energy by 7AX where a is the
• cathodic transfer coefficient. Also the activation energy for ionization
will be increased by (1-a)AX. These alter the electrochemical rate
constants by factors exp(a AX/RT) and exp (- (1-4x)AX/RT) respectively.
As the concentration of hydrogen ions is fixed, the rate of discharge
will also be increased by exp(ci AX/RT). But the surface concentration
of adsorbed hydrogen atoms has been increased by exp (AX/RT) via the
equilibrium with hydrogen gas. Hence the net rate of ionization has been
•
-20-
increased by exp(u AX/RT), the same as the discharge rate, and the
same potential is maintained. A similar argument may be used to allow
for the effect of the double layer on the energies and concentrations
of adsorbed ions and it is thus seen that under net zero current flow,
the Nernst equation must reflect only bulk activities providing time-
equilibrium is maintained to the surface. These activities however, may
only have a hypothetical existence, e.g. for electrochemical hydrogen
adsorption prior to hydrogen evolution.
2.3.8 High-field ion transport processes
2.3.8.1 General
The above theory relating to electron transfer between ions and
electrodes is an example of the movement of charge under the influence
of an electrical potential gradient, i.e. a field. The movement of
other charged species, for example simple ions, can also be influenced
by fields in an analogous way. A common example is seen in the concept
of ionic mobility in bulk solutions. Here the rate of ion movement in
a given direction is linearly dependent on the potential gradient (field
strength) applied. This is analogous to the low overpotential region of
the general electrochemical rate equation (eqn. 2.10) and corresponds
physically to the situation where the number of succesful "jumps" in the
reverse direction are comparable to those in the forward direction. In
contrast, the Tafel relationship (eqn. 2.9) embodies the physical
concept of a negligible number of reverse to forward jumps and represents
complete irreversibility, i.e. extreme disturbance from a two-way dynamic
equilibrium. This is known as the "High-Field Approximation".
-21-
In bulk liquids and solids, the field strengths required for the
exponential high-field relation to apply cause complete dielectric break-
. down due to tremendous Joulean heating. However, with very thin films
of components forming ionic lattices on a metallic subtrate, these field
strengths can be applied as heat dissipation is much easier. The films
studied have been generally of a metal oxide on the parent metal grown
by anodic oxidation from aqueous solutions. In the past, the phenomenon
of high-field ion transport in thin oxide films has only been considered
in relation to growth on the "valve" metals (34) and on passive iron (2).
Recent evidence suggests, however, that a similar step may be rate-
controlling for the electrochemical growth of noble metal oxides (35,36)
as opposed to a classical slow ion discharge path.
2.3.8.2 The ion-transport mechanism
Conceptually, the process is very similar to electron transfer consi-
dered above. However, greater emphasis is given to the idea of physical
movement of charge; this results in a close association of reaction
co-ordinate with the position of the ion within the lattice structure and
leads to a description in terms of "jump distances" and fields.
The charged particle is regarded as passing down the field Ef
by a distance 8 from the initial to the activated state with a
gain of energy Ef
nF, where 8 is some fraction y of the total
transfer distance 8 between the initial and final states. For a
symmetrical lattice y 0.5, thus 8 is sometimes called the "half-
jump distance" ]. Equations analogous to eqns. 2.4 - 2.10 may therefore
be derived. However, it should be noted that the two derivations refer
-22-
to separate mechanisms. The electron transfer mechanism suggests that
the activation energy is modified by the effect of the electrode potential
on the electron energy levels (37), whereas the ion-transport model
clearly involves an effect of the potential on the energy-position
profile of the ion concerned.
As with the electron transfer mechanism, a central problem is the
estimation of the proportion of the total potential drop across the in-
terface (or film) available for accelerating or hindering the process.
This is partly embodied in the transfer coefficient y, but also with
varying film thickness the proportion of available potential will
proportionately fall (assuming a linear field through the film), and
give rise to an increasing apparent Tafel slope.
A particular problem is the assignment of an electric charge to
the moving particle. An assumption has obviously first to be made
concerning the species involved in the rate-determining step. Often in
metal-oxide films, it is assumed this is the metal ion. However, it is
unknown whether it can be assigned its complete formal charge in a
partly covalent lattice. For noble metal oxide films, it has been
suggested that simultaneous rearrangement of the metal and oxide ions
take place (36); no justification for this exists except a fit to
experimental Tafel slopes.
Film growth experiments, as with simple redox equilbria involving
exclusively surface reactants or products, cannot be studied under
steady-state conditions as passage of current must lead to a build-up
or removal of a surface species. This behaviour under transient conditions
will be fully discussed in detail later.
-23-
2.4 Surface Chemistry Aspects
2.4.1 General thermodynamics
As all chemical systems must involve surfaces, i.e. regions between
different phases ("interphases"), the range of phenomena encountered
coming under the general title of surface chemistry or physics must be
large indeed. A fundamental characteristic of intelphases is the presence
of asymmetric force fields inevitably resulting from the juxtaposition of
two phases of differing chemical composition. This has a marked effect
on the quantity and therefore free energy (assuming thermodynamic
equilibrium with the bulk regions) of adsorbed species present. The
concept of adsorption at interfaces represents the equivalent of the solute,
solvent distinction in bulk phases; thus adsorption relates to the addi-
tional presence of an adsorbate in an interfacial region conceptually
regarded as having an independent existence.
As mentioned earlier, descriptions of interphases are generally of
two types (i) by the adsorption isotherms or (ii) by a two-dimensional
equation of state, both relating to a given adsorbate. The Gibbs
adsorption equation provides a link between these and constitutes the
fundamental relation describing equilibrium between bulk and surface
regions. It has the form
d y = - r RT d In a (Eqn. 2.13)
where y is the surface tension, ri the surface excess per unit area,
and a is the bulk activity (For a derivation see e.g. (21)).
Also 7 = - ,r dy, where n is the "surface pressure" exerted by
the absorlaing species, and has the dimensions of force per unit length.
-24-
•
= PT ji d In a (Eqn.2.14)
It is important to note that 'this can be derived from purely
thermodynamic reasoning, and is therefore not dependent on a model of
the microstate.
2.4.2 Nature of Surface Forces
Due to the inevitable fields of force around each elementary
particle or species at surfaces, interactions will occur resulting in
adsorption of foreign species if available. As the interactions are
necessarily mutual, it is not always possible to categorize the types of
resulting phenomena. However, the principal types of forces operating
are discussed below.
(i) Weak attractive (".physical")_tzpes
These are rather weak by comparison with "chemical" forces, involving
energies of a few k.cals.mole at the most, and are relatively non-
specific. Types include permanent and induced dipole interactions,
disperSion, and short range repulsive effects. They are only conveniently
studied at gas-solid interfaces, as with condensed fluid types, solvent
interactions complicate the situation enormously.
(ii) Electrostatic forces
These arise from the interactions between ions, and therefore such
fields can be expected to be set up at interfaces with a high ionic con-
centration, such as an ionic solid or liquid. These fields can act on
permanent or induced dipoles to give forces similar to types (i) or of
•
-25-
course with adsorbed ions. This is essentially the problem of ionic
liquid-metal interfacial electrochemistry.
(iii) Image forces
These operate when a polar species is adsorbed on a conducting
material. The interaction can be considered between the dipole and its
induced "image" in the conductor. The energy contribution is usually less
than 1 kcal. mol .
(iv) "Chemical" forces
These involve a transfer of electrons between species. When these
are an adsorbed atom and the substrate, chemisorption occurs. It usually
- involves fairly high energies, i.e. > 10 k.cals.mol
1 . Also bonding
can occur between adsorbed atoms, eventually leading to an adsorbed
polymer in some cases. Chemisorption may be studied in condensed as well
as gas-liquid or -solid interfaces, as, due to the bond energies involved,
it usually swamps any forces considered as types (i)-(iii). Thus
it is in principle possible to compare results between electrochemical
interfaces (usually solid-metal types) and similar gas-solid systems.
2.4.2 Adsorption Models
As with purely bulk phases, equilibria between bulk and surface
regions are often usefully considered in terms of a simple, widely applica-
ble, idealized model. The behaviour of real systems can then be described
in terms of deviations due to the existence of further energetic factors.
A model commonly used for this purpose is embodied in the Langmuir
-26-
Isotherm. This takes the form
e kP
(Eqn. 2.15)
where 0 is the fractional coverage of an adsorbate, k is a constant,
and P is the partial pressure of the adsorbate in a gas phase, or the
corresponding concentration in a condensed phase. It may be derived
(e.g. 39) by a consideration of adsorption and desorption rates on a
plane surface assuming (i) all adsorbate atoms and adsorption sites are
energetically equivalent, (ii) adsorption is localized, and (iii) only
monolayer adsorption is possible. A statistical derivation gives essen-
tially the same result. With most real systems, at least one of the
above assumptions does not hold. Attraction (for physical adsorption)
or repulsion (for chemisorption) between adsorbed atoms commonly leads
to a non-equivalence of the energetic state with increasing coverage,
and often non-localized adsorption takes place.
However, for completely mobile species, an isotherm very similar
to Langmuir's may be obtained by a consideration of the two-dimensional
equation of state
u(A-A0) = RT (Eqn.2.16)
whose u is the surface pressure, A the total area per molecule,
and Ao the area occupied by the adsorbed particles. This is a two-
dimensional analogue of Boyles' Law modified by considering the co-volume.
By applying Gibbs Adsorption Equation (eqn. 2.14),
kP = exp (76)
(Eqn. 2.17)
(considering that A/Ao =
-27-
Clearly (except at high coverages), this equation approximates well to
the standard Langmuirian form (eqn. 2.15).
It should be noted that the two expressions were derived using
different models and therefore are not equivalent. This incidentally
raises a general problem of distinguishing between separate models
purely on the basis of experimental isotherms or equations of state.
Often similar algebraic expressions are obtained which make comparison
very difficult, especially with data of limited accuracy (40).
The equation of state approach is probably useful when adsorption
is completely non-localized and the species are free to move over the
surface. A careful distinction must be drawn between this and the case
of mobile adsorption which refers to activated movement over the surface.
This surface mobility is often seen with chemisorbing systems [directly,
using the field emission microscope (39)].
Many isotherm and equation of state models have been derived to
explain the varied phenomena observed. Particular examples considered
relevant to the theme of this thesis will be considered in following
sections.
2.4.4 Surface Kinetics
So far only systems in equilibrium have been considered. Often
adsorbing systems will reach equilibrium so rapidly that kinetic measu-
rements are not feasible, e.g. physical adsorption, which usually appears
to be completely non-activated. A notable exception to this is chemi-
sorption, which is frequently sufficiently activated so that rate measu-
rements are easily made. Also very slow polymer adsorption and rearrangement
processes have been observed (41).
-.28-
Chemisorption-equilibria
The following sections will consider only chemisorption on solid
metals from gases (39). Electrochemical chemisorbing systems will be
considered later.
Isotherms - the Temkin model
Experimental equilibrium data are generally in the form of isotherms
i.e. bulk gas pressure versus surface coverage at constant temperature.
Calorimetric methods of obtaining adsorption heats are used extensively,
along with more sophisticated measurements, such as surface potentials.
Because of the relatively strong adsorption bond present, the
fundamental adsorption model used is that of Langmuir (eqn. 2.15),
derived for localized adsorption rather than a 2d gas. However, this
equation is seldom obeyed in chemisorbing systems. A reason for this is
seen by referring to calorimetric resultS. These often show a marked
decrease in the heat of adsorption with adsorbate coverage (reaction
becoming less exothermic), the decrease frequently being approximately
- linear, at least up to fairly high coverages (6)", 0.8). This is considered
in the Temkin isotherm (39). It is assumed that the adsorption heat (q)
varies as q = q0 (1-b0), where q0 is the adsorption heat at 0 = 0
and b is a constant. Thus the Langmuir isotherm (Eqn. 2.15) becomes
1-0 RT 0 q0(1-b0)
= k0P exp (-2- ) = k0P exp ( RT
Taking logarithms,
qob0 1nP = - 1nK0 + RT in (176)
(Eqn.2.18)
where K0 = k0 exp ( q° ) RT
For chemisorption qob>>RT. Thus in the middle range of coverage (say
0.25 < 0 > the dominant term is q0b8/RT
-29-
RT b
0 ). lnKoP (Eqn. 2.19) qo
This is known as the logarithmic Temkin isotherm. The same approximate
form may be obtained by considering ,a heat fall with coverage due to a
non-uniform-surface.
Good fits to experimental data are often found for the adsorption
of simple gases (eg. H2, 02, N2 ) on metals such as tungsten, iron,
etc. Also there is reasonable evidence (e.g. 42) of quantitative
agreement between falls in calorimetric adsorption heats and the qo
and b factors in the Temkin isotherm.
2.4.5.2 Explanations of adsorption heat fall with coverage
Three types of explanation have been proposed; (i) intrinsic
surface heterogeneity, (ii) direct lateral interaction effects,
(iii) induced heterogeneity - electron transfer effects.
Theory (i) considers a solid surface consisting of sites of varying
adsorption energy due to the existence of edges, corners, and boundaries
along with lattice defects. It is closely associated with the concept
of active sites in heterogeneous catalysis (1+3) and support comes from
the finding that very small (much less than monolayer) quantities of
catalytic poisons are required to completely inhibit surface reactions.
However, it would be highly fortuitous if the effect gave rise to a linear
heat fall with coverage.
Lateral repulsive effects (ii) are probably important particularly
for large adsorbates (44). Mostly only nearest neighbour interactions
have been considered. Usually, however, the magnitude of the heat falls
are too large to be reasonably explained by this effect alone, particularly
for small particles such as hydrogen atoms.
Electron transfer to or from the'adsorbate (iii) will create an
-30-
array of dipoles which increases the work function of the metal so that
bond formation will be hindered and the bond energy lowered (45).
This explanation has been criticised (46) as the dipoles formed will
be discrete and will not form a uniform double layer of charge across the
surface. Therefore the effect may only be small. However, dipole-dipole
interactions similar to type (ii) could be important.
Other isotherms have been devised, such as the Freundlich Isotherm
(39). This early model,originally proposed empirically, has the form
= cpi/n (Eqn.2.20)
where C and n are isotherm constants, but dependent on temperature.
It may be derived by assuming an exponential variation of site energies
with coverage. Thus in the low coverage region it is similar to the
Langmuir form, whereas at 0 = 1 the form is meaningless. It is fair
to say that the Temkin isotherm is more applicable to real systems than
the Freudlich, although considering the accuracy and reproducibility
of much of the data, it may be simply have become less fashionable !
2.4.2.3. Surface Potentials
A commonly measured property is the surface potential change on
adsorption AV (46). This is related to the change in the electronic
work function of the metal, and may be expressed as AV = 4rrns0µD
(Eqn. 2.21), where ns is the number of surface sites per cm2 and p,D
the dipole moment of the adsorbed species, derived by assuming the dipole
layer acts as a parallel plate condenser. Sometimes AV is proportional
to the coverage 0, but often marked curvature is seen. This is often
attributed to deviations from a simple localized adsorption model. On
non-uniform surfaces, such as evaporated metal films, large deviations
-31-
are observed as the orientation of dipoles becomes rather haphazard
except for the outermost edge of the film. The sign and magnitude
of the surface dipole potential can give valuable information on the
bonding involved (47). Thus chemisorbed films generally have dipoles
with the negative pole outwards, whereas physical (van der Waals)
adsorption has the opposite polarity. Chemisorbed films frequently
involve potentials of the order of a volt. Surface potential measurements
are extremely valuable in providing information on the structure of the
film, such as changes occurring during incorporation of chemisorbed
oxygen into metal lattices (48).
2.4.6 Chemisorption Kinetics
2.4.6.1 General the Elovich equation
Often the rate of build-up or removal of adsorbate in chemisorbing
systems is low. This is commonly attributed to an appreciable activation
barrier for the adsorption and desorption processes. Occasionally a
low probability of forming the activated state (entropy effects) will
effect the rate markedly; usually however, the phenomena is discussed
in terms of the activation enthalpy involved, and the kinetics followed
a rather more extended time course than would be expected on the basis
of a constant activation barrier.
The most ubiquitous kinetic relationship to date has been the
Elovich equation. This has the form for adsorption
-(22 = a exp. ( dt (Eqn.2.22)
-32-
where q is the quantity adsorbed (in simple cases directly related to
coverage 6), and a and b are constants. It is consistently found to
fit a large range of kinetic data, tending to fail towards the end of the
process when the rate becomes excessively slow.
Extensive reviews have appeared (49, 50). Originally stated
empirically, theoretical models accounting for its widespread applicabi- •
lity have proliferated in the literature. Usually, the integrated
form of eqn. 2.22 is used for ease of data fitting. Assuming that
q = 0 at t = 0, Eqn. 2.22 becomes
q = 2.3 b log (t + to) -.2.3 b log to (Eqn. 2.23)
where to = b/a.
If at t = 0 an instantaneous quantity of gas qo is adsorbed,
then
q = 2.3 b log (t + k) - 2.3 b log to (Eqn. 2.24)
go where k = to exp. .
For to or k values such that experimental t >> to,k;
linear plots of q versus log t are obtained, otherwise they are
• convex towards the log t axis and can be linearized by provision of
the suitable parameter to. or k.
2.4.6.2 Experimental applicabilitz
Often on clean metal surfaces, chemisorption is apparently non-activa-
ted, but for many systems, particularly on evaporated films and oxide
substrates, the processes are slow. Sometimes the Elovich (b) slope
changes during adsorption, i.e. breaks are observed. Normally b and
-33-
1/ln a are proportional to the absolute temperature. Also lna
usually increases with applied gas pressure, whereas b either remains
constant or is proportional to the pressure, (c.f. Ft0 electrochemical
case, section 2.6.3.3).
2.4.6. Models for the Elovich equation
The general kinetic equation for adsorption can be written
E* = K (P)n exp (-
dt RT ) (Eqn. 2.25)
where K(P) is a pressure dependent constant incorporating the collision
frequency per unit area and a "condensation coefficient", n is the
number of sites available for adsorption, and E* is the activation
energy. (A similar equation may be written for the desorption case).
A common approach is to regard the site number n as being
approximately constant and consider the activation energy increasing
linearly with coverage. It is tempting to regard this as the kinetic
analogue of the Temkin isotherm via a linear free energy relationship
(c.f. the use of the coefficient in electrochemical kinetics). The
Elovich equation follows from both intrinsic and induced heterogeneity
models. In the former case it is interesting to note (50) that for
three sets of sites, each of constant energy with rate constants
k1 : k2 : k3 = 1 : 30 : 1,000, the logarithmic plot is linear over
at least a 104 variation in time. As the required difference of
activation energy for an order of magnitude change in rate constant is
ti 1.2 kcals. mol at room temperature, it can be seen that a set of
only three different crystal planes can give the required effect.
A difficulty of this model is that it predicts that the b slope
-34-
should remain constant for a given system and temperature. Sometimes,
however, .under varying gas pressure and thermal cycling conditions (51),
this "constant" can vary widely. It has been considered in these cases
that the surface consists of high ,(A) and low (B) adsorption activation
energy regions. On admittance of gas the region B adsorbs gas quickly,
the adsorbed atoms migrating from B to A in the rate determining
step. A modification of the model (52) introduced an intermediate
chemisorbed state as a necessary precursor to the final chemisorbed state
of lowest potential energy. Thus an energetic transformation is involved
not requiring the concept of the non-uniform surface.
Similar discussions to the above can be made with desorption.
However, the activation energy here is the heat of adsorption plus the
adsorption activation energy for that coverage. To derive an Elovich
equation, it is necessary to assume that the adsorption heat increases with
decrease of coverage (a Temkin-type relation), and this variation is
larger than the decrease of adsorption activation energy with decrease
of coverage.
An alternative approach is to assume that changes in the site number
n in equation 2.25 are dominant. To derive the Elovich equation it is
necessary to assume that n = no exp (- q/b), where no is the initial
number of sites. It can be shown that this involves a rate of site
incapacitation proportional to the square of the number of sites occupied
(49). This has lead to theories suggesting an initial creation of a
number of sites on the introduction of gas which subsequently decay by
a second order mechanism. The approach is in harmony with the common
experimental result of good Elovich fits even when the gas pressure is
varying markedly during the adsorption; thus perhaps it is the mass action
-35-
of the solid rather than the gas which controls the kinetics. It can
also provide an explanation of the b slope variation with gas pressure,
but the physical reason for such kinetics is, however, rather obscure.
Active radicals have been suggested (49); also the case where an adsorbing
molecule inactivates a greater area than it occupies itself leads to a
similar result (53).
2.4.6.4 Other applications
Eley (54) has considered (initially for polymer viscoelasticity) a
general first order kinetic equation modified by a free energy barrier
which increases during the progress of the reaction (Eqn. 2.27). For
a unimolecular reaction in a dilute fluid medium, if the concentration of
reactant at time t is C(t), and at equilibrium C(00), define x = C(t)-
C(00). Then
dx dt kx (Eqn. 2.26)
where from absolute rate theory
All*
kT -R
k = ( h exp ( ) exp (- —RT )
If also AG* = AG2 - yx, i.e. the free energy of activation rises
linearly with the conversion of reactants to products.
Eqn. 2.26 now becomes dx _ kT ( Gd3 - yx) dt
exp L RT
= x A exp( 14) (Eqn.2.27)
2 The integral is lnx- Y---x + 2 12! RT Y-2-c \ RT . • ' = -At + const.,
-36-
which for yx < RT becomes
login x - 2.3RT -A't + const
(Eqn.2.28)
Eqn. 2.28 can be tested by plotting logiox against t and should give
a straight line at high t (corresponding to dominance of the pre-
exponential term in equation 2.27). y may be obtained by taking a value
G of the extrapolated portion of the above plot at a given (small) t
and plotting logio x- G against x, which should be a straight line of
slope Y/2.3 RT. Thus .a complete test of the equation may be sought
by plotting together both sides of eqn. 2.28.
Other models for the viscoelastic behaviour of polymers have however
been much more widely considered, usually at constant strain to minimise
the viscous (non-elastic) component. A very common approach (56) is
to assume a series of unimolecular processes having a distribution of
relaxation times. Various forms of relaxation distribution give rise to
the logarithmic relationship in time often observed (the "Elovich form").
It is to be noted that an analysis of the complete relaxation curves on this
basis involves the inevitable use of semi-empirical parameters which
must reduce the value of the approach.
The concept of the relaxation spectrum for polymer movement is easily
considered to be due to a Gaussian-like distribution of segment lengths
causing a distribution of retardation forces, whereas the activation
barrier approach is more intuitively satisfying when the kinetic properties
of atoms and simple molecules are involved. It does emphasise, however,
the problems associated with the distinction between different molecular
models for rate processes on the basis of kinetic data alone. (Also see
Section 4.1.4.3.3)-
-37-
2.4.7 Other adsorption types
- 2.4.7.1 Physical adsorption
A variety of adsorbing systems have been studied where the adsorbate
only forms weak bonds with the substrate surfaces. On gas-solid inter-
faces physical ("van der Waals") adsorption has been studied with inert
systems where chemisorption is absent. It is necessary to often consider
multilayer adsorption and the existence of attractive van der Waals
forces between co-adsorbed species (21). As the adsorption is non-
localized, the imperfect gas equation of state approach has been much used.
2.4.7.2 "Insoluble monolayer" films
A rather special form of interface concerns the case of slightly
soluble organic chain molecules at the liquid-air interface. Usually
the liquid is water and the chain contains a hydrophilic - OH group,
creating a highly orientated type of adsorption with the - OH group
being attracted into the water and the chains held normal to the surface.
The films are best described by 2d-equations of state as film pressures
can be readily obtained by surface tension measurements, and bulk activities
are very low. The systems are of particular interest as the resulting
equations of state indicate strong analogies with three-dimensional
matter in that "gas", "liquid", and "solid" types may be distinguished.
Thus films are found to follow a modification of Boyle's Law at low
coverages, but as this increases various types of condensed matter appear
as evidenced by the surface pressure - surface area per molecule plots.
Regions of clustered molecules ("micelles") have been postulated to explain
some results (38).
A similar type of system concerns spread films of polymers and
-38-
proteins at the air-water interface. Plots of surface pressure versus area
per molecule usually do not have clear transitions between the different
two-dimensional "states" of matter, but rather have smooth curves asymtotic
to the close-packed density of the solid film (21, 41). Theoretical
interpretations of these results have considered pure entropy (57) and
mixed entropy and enthalpy effects (58) with increasing surface coverage.
• Some progress has been made, but the molecular complexity of these
systems remains somewhat daunting The topic has some relevance here,
as interpretations in the discussion section on the nature of sulphur
films at electrodes studied in this thesis consider the consequences of
polymer formationy(Section 4.1.4.3).
2.5 Electrochemical Adsorption
2..1 Introduction
Only adsorption of species directly concerned in electron transfer
reactions at electrodes will be considered. These will largely be of the
• neutral chemisorbed type outlined in section 2.4. A large quantity of
work has been concerned with adsorption at ideally polarizable interfaces,
usually at liquid electrodes. This has considered mainly adsorption of
simple ions and neutral organic species from aqueous solutions; here the
'potential determines the charge on the double layer rather than the rate
of an electrochemical reaction or the position of redox equilibria. Of
course, these "double layer' effects are always present, but the forces
involved in chemisorption generally swamp these. The general subject has
• been reviewed (59).
-39-
2..2 Concepts and equations
As discussed above, the concentration of adsorbed species at
an electrochemical interface involved in a redox equilibrium depends on
the electrochemical potential p rather than the chemical potential which
is the relevant parameter for purely chemical systems such as with gas
phase adsorption. Thus a similar equation to eqn. 2.1+ can be written
. for species 1, p
i = p
i + nF$. The electrochemical standard free
energy of adsorption will be a linear function of potential and the
equilibrium constant for the adsorption-desorption process will depend
exponentially on p.
For a redox reaction with a constant number of electrons transfered,
the fractional surface coverage (0) can be related to the charge ,q by
q = k0 (Eqn.2.29)
As the coverage is dependent on the metal-solution potential
difference, a differential "capacity" may be defined by
_ aa _ kdO Cads - dp
-
dfb
(Eqn.2.30) dffl/ dt
where i is current density and t is time. Cads
is known as the
adsorption pseudocapacitance. It must be noted that the origin of this
quantity is quite different from the ionic double layer capacitance.
Thus the former arises from actual transfer of charge ("leakage") across
an interface, rather than the accumulation of charge on one side, and
the resulting induction of an opposite charge, on the other side of the
ionic double layer.
The ionic double layer capacitance is always present, but generally,
adsorption pseudocapacitance, if present, will swamp this term. Thus
double-layer capacitances are normally 20 µ F cm-2 , whereas adsorption
pseudocapacitances, particularly where a Langmuir-type isotherm is
-40-
involved are at least five to ten times that value. Hence it may often
be neglected.
Experimental Methods
General
The methods used all involve the application of non-steady state
current or potential pulse programmes and the recording of a potential
or current - time profile as response. These measurements have a two-
fold purpose; to record the quantity formed on the surface i.e. the
surface concentration from the current-time integral, and the potential
and hence the electrochemical potential corresponding to such a concentra-
tion. Thus potential-coverage, pseudocapacitance-potential, or coverage-
pseudocapacitance relationships may be derived.
A simple case arises when, in the potential region studied,
only chemisorbed species are formed. This is often the case for appre-
ciable ranges of potential as the free energy of the chemisorbed species
is markedly lowered by the bond formation with the electrode. Often,
however, the surface species is an intermediate in an overall (usually)
anodic reaction involving subsequent evolution of gas or dissolution as
outlined in section 1.2.1; charge measurements to determine the species
concentration may then involve production or depletion of a diffusing
bulk species. This problem will be discussed later.
Common experimental methods are the following.
2..3.2 Galvanostatic charging
This method, historically the first to be used, consists of the
application of a constant current pulse and the measurement of the
-41-
resulting potential-time behaviour. Both formation and removal of
chemisorbed species can be studied in this way. The technique includes
both "slow" and "fast" variants. The former involves low charging
currents such that the transients last a few secondsor more; instrumen-
tation is eased and the system is more likely to be in quasi-equilibrium.
However, when stripping adsorbates in chemical equilibrium with similar
bulk species (as in hydrogen evolution) significant re-adsorption may
occur and lead to false coverage values. The latter technique surmounts
this difficulty as with currents of around one amp. cm 2 , the pulse
duration can be lowered to 1074 sec. and re-adsorption effects minimised
or eliminated. Similar considerations apply to the electrochemical
formation of intermediates.
As the rate of passage of charge is constant in the galvanostatic
method, charging time for a given current can be directly related to
coverage change. The slopes of the potential-time plots (dt/dp) are thus
proportional to the differential adsorption pseudocapacitance which may
be obtained by electric or manual differentiation of the signals.
An explicit case involving the galvanostatic technique involves
irreversible electrochemical desorption of a surface species. If all
surface species are energetically equivalent (i.e. a kinetic equivalent
of the Langmuir isotherm holds, rather than an Elovich equation), then
Desorption rate ip =!kD q, . exp.
vnF — RT B)
(Eqn.2.30a)
where q is the surface charge (concentration), m the reaction order,
kD the desorption rate constant.
Thus, at constant iD,
-42-
E = - mRT
. lnq + constant. anF
As qa(T - t), where T is a transition time for a potential time
stripping arrest, then
E = Constant - 2.3nF . log (T - t) (Eqn.2.30b). umRT
This equation has, however, been rarely used (e.g. 171), but is very much
simpler than the corresponding relationship for linear sweep voltammetry
(65). Similar equations can be derived for other galvanostatic reduction
models, (see section 4.3.3.2.2).
2,2.3 3 Potentiostatic techniques
The integral pseudocapacitance between two potentials may be obtained
by observing the current-time transient obtained when potentiostating
between the two potential . The same limitations apply as above, and
as it requires more complex equipment is seldom used.
2..3.4 Linear Potential sweep
This technique, widely used recently, consists of the application
of a linear potential time ramp and the measurement of the resulting
current-time response. The method is often extended to a cyclic form.
As dP/dt = constant, the measured current-time response is directly
proportional to Cads from eqn. 2.30.
_A.C._bridge method
The classical bridge method for the determination of ionic double-
layer capacitances by low-amplitude A.C. impedence measurements can be
applied to the pseudocapacitance case. Strongly frequency-dependent
results are usually obtained however, even at very low frequencies
cycles sec-1 )(59).
Open-circuit decay
A very useful method involves the observation of the potential-time
decay curves resulting from the cessation of (usually) a steady-state
current. The method has usually been applied to regions where an overall
production of bulk species is occuring, and where only activation
overpotential is involved.
If the capacitance is pure double layer, on breaking the circuit it
is assumed that self-discharge will take place in order to discharge the
double-layer capacity and lower the potential to an equilibrium open-
circuit value. For the pseudocapacitance case the process is more compli-
- - cated; thus for the system X e X (1), X + X X2 (2),
ads ads
the discharge of the Xads
species (the pseudocapacitance) must take
place by continued occurrence of the second step with electrons for this
being supplied by a reverse of the first step. Two types of analysis
are involved.
(a) From initial values of the decay slopes. This involves the assumption
that the reaction continues at a rate momentarily the same as before.
Thus eqn. 2.30 can be written
initial Cads
'dtit = 0
Thus the capacitance corresponding to a range of potentials may be deter-
mined by varying the initial decay potential.
-144-
(b) By complete analysis of the decay curve. This is applicable if the
external current-potential curve is known experimentally in the same
_ potential range, and then equating these currents with that for self-
discharge during decay (22, 59, 60). Thus, for Tafel behaviour
( C = i i nitial =
i exp (Eqn.2.31)
where T is the activation overpotential, and b is the Naperian Tafel
slope. After integrating and taking logarithms,
11 io Cb
In + (t + J) (Eqn.2.31a) b
where J is an integration constant . Cb / .
Thus when t >> J, a plot of 1 versus lnt will give b, and
thus from J, the capacitance C may be calculated. The above assumes
that the capacitance is constant over the potential range for decay.
Treatments for more general cases have been given (22, 61). Decay
transients have also been recorded from initial non-steady conditions in
connection with high-field ion conduction studies (e.g. 35, 63).
The case of galvanostatic build-up to a steady-state potential in
a Tafel region has been treated (60) but experimentally little used.
The case of decay under conditions of a slow surface chemical
reaction will be considered in Section 4.1.4.3. 3.The involvement of
concentration overpotential in decay phenomena has been considered (62)
but is highly complex. The decay does not have the simple exponential
potential form as in the cases considered above.
2.2.3.7 General limitations of the methods
The above methods, as generally used, refer to the (usually anodic)
formation or removal of a neutral chemisorbed intermediate species
Xads
from an ionic species X in solution. If changes in potential
are to be directly relatable to either the activity of Xads
(quasi-
equilibrium or "reversible" case) or to the electrochemical reaction rate
("irreversible" case) then the surface activity of X must remain
approximately constant i.e. there must be a constant chemical potential
of X right up to the electrode surface. This will always be the case
for species forming the solvent, such as hydroxyl and hydroxonium ions
in water (here proton-jump mechanism will maintain equilibrium). However,
for X ions forming a dilute solution, finite transport rates to and from
the electrode surface will create chemical potential gradients at high
enough imposed currents which can eventually lead to exhaustion of the
ionic species at the electrode surface. In fact, techniques employing this
mass transport phenomena ('electroanalytical" techniques) can give valuable
information on the kinetics and mechanism of electrode reactions and will
be discussed later on.
All techniques will give equivalent coverage, and hence pseudocapaci-
tance-potential plots provided that electrochemical quasi-equilibrium is
maintained. However, anodic formation and cathodic reduction of chemisor-
bed layers are often slow processes; thus if a current is passed compa-
rable with the exchange current density for the redox step, then an
activation overpotential term will be included in the potential measurement
.and the resulting pseudocapacitance will only be an apparent one.
These two cases will be discussed in turn, along with common isotherms
or rate equations, and their application.
2.2.4 Electrochemical Adsorption Equilibria
2.2.4.1 General
When Nernstian equilibria with respect to the chemisorbed species
and its parent anion (or cation H30 ) is maintained, the situation is
formally analogous to equilibrium in gas phase chemisorbing systems
discussed in section 2.4.5. Here, however, the electrochemical equili-
brium Xsolvated
== Xads
replaces the gas-solid equilibria
Xgas
== Xads. Therefore for equilibrium, equality of electrochemical,
rather than chemical potential is required; thus changes in the interfacial
potential difference with [X-solvated ] held constant are equivalent
to a variation of gas phase partial pressure of Xgas. This may be
expressed as
nF P = exp e--• 0 14') RT • ' (Eqn.2.32)
where P is the (hypothetical) partial pressure of Xads.
2.2.4.2 The Langmuir isotherm
This isotherm, expressed as
e kP (Eqn.2.15)
1 -
was discussed in section 2.4.1. The constant k is related to the
AG° standard free energy of adsorption AGo by k = exp (- ). RT '•
Combining eqns. 2.15 and 2.32, we obtain
nF - exp (— ) RT • M 1 - 0 (Eqn.2.33)
A plot of coverage versus potential for this model is shown in fig. 2.1.
As for other interfaces, the Langmuir adsorption isotherm is seldom obeyed
-46-
in electrodics; however, it does provide a useful starting point for more
realistic models.
2..4.3 The Temkin isotherm
As for gas phase chemisorption, this isotherm has found wide
applicability in electrochemical adsorption studies.
Recalling the logarithmic Temkin isotherm derived above
0 = RT In K
o P
gob
Replacing qob by fRT so that generally
A Go8
= A Go - fRT8
(Eqn.2.19)
- (Eqn. 2.34)
where f is known as the "heterogenity parameter", and combining with
eqn. 2.32, we obtain
fRT 5314 + K1 (Eqn.2.35)
Thus in the middle range of coverage, a linear relationship of
coverage with potential is observed with the slope depending on the factor
fRT. Some plots with varying fRT values are given in fig. 2.1. It may
be seen that for larger fRT values a correspondingly greater potential
span is required to reach a given coverage. A detailed description of
various Temkin isotherms is given in (59).
Electrochemical Adsorption Kinetics
When using external current techniques (sections 2.5.3.2 - 2.5.3.6)
the situation may arise where the surface charge transfer reaction for the
FIG% Z.I. — VACATtoN OF CoVElcf4E WITH
roTENTIAL- FOR LANG-r1U(6. (fer----0) ANID
LANP4Olft + TVIKIN CoOrrionIS .
+8
04 CoIRA'A&E
e 047
of
LINEAR ® - Om REG4mS CogRcSroaD ro APIIIMBILITY OF ECM. 2.351 Setnon) 2.5.41--3.
fR-1-=20
(Nor To scALe) .
0/ 0-1- 04 0.8 io
psi err V VOLTS
-4-9-
forNation or removal of a chemisorbed species completely controls the
rate. This is the classical slow discharge case studied for bulk product
species by steady-state techniques and the application of the Tafel
relationship. Of course, this technique may be used when the chemisorbed
species acts as an intermediate in an overall gas evolution or soluble
product system as here the adsorbate coverage is time-independent.
Overall kinetic equations have been derived for this case for various
isotherm types (59).
However, the case considered here is when the chemisorbed species
either represents the final product (or initial reactant) or is produced
in an overall steady-state reaction but does not form a step in the overall
process (as perhaps Pt0 in 02 evolution); here non-steady techniques
are obligatory.
A number of treatments of this kinetically controlled case have
been given, usually for galvanostatic or linear potential sweep transients
(e.e. 64, 65, 66) both for the Langmuir and also a general Temkin
case, by the introduction of a heterogeneity parameter f. For the totally
irreversible case a constant shift of the coverage-potential along the
potential axis is seen with increases of the logarithm of the charging rate
parameter - current in the galvanostatic case and sweep rate in the linear
sweep case. This shift is a measure of the Tafel slope for the formation
or removal of the adsorbed species, and the apparent a,n value for the
reaction may be calculated. The treatments predict that the shape of
the transients will remain completely unaltered; this necessarily assumes
that no time relaxation effects resulting in a rearrangement of the
layer are involved. As will be seen shortly this is often unrealistic.
A point not often considered is the meaning of the heterogeneity
parameter f in this case. It must be noted that f cannot have the
-50-
same significance here as in the Temkin isotherm model, as it refers
to a rate process i.e. the relevant term is the adsorption free energy
of the activated state for the charge transfer reaction rather than
the free energy of the chemisorbed species itself. Assuming therefore
that the electron transfer and atom adsorption processes occur in a
converted single step, the relevant "heterogeneity parameter" will be
that involved in the Elovich rate equation discussed in section 2.1+.6.
The relationship between Temkin and Elovich heterogeneity parameters
(gas phase or electrochemical) does not appear to have been explicitly
studied; this would be fairly difficult as the systems in which chemi-
sorption or desorption kinetics can be investigated are consequently
difficult to attain at true equilibrium. A common error with electroche-
mical systems in the past has been to ascribe thermodynamic meaning to
given potential-coverage relationships for irreversibly adsorbing systems
(e.g. 67). Application. of the linear sweep method in particular has been
rather uncritical, often deducing the existence of species types from
the presence of current-time peaks by analogy with the diffusion-controlled
case.
The existence of electron transfer accompanying the adsorption or
desorption step does provide a complication over the gas-solid case,
although in the latter the necessary dissociation of most gases upon
chemisorption provides a factor not present in formation of the adsorbate
from a simple ion. Thus a description of the resulting electron transfer
act involves not only the effect of chemisorption on the activation
energy, but of the local electric fields on the electrochemical transfer
coefficient. However, as adsorption free energy changes fundamentally
arise from a redistribution of electric fields, the two factors may arise
from a common source.
-51-
In summary, a number of doubtful and incomplete conclusions have
been reached, particularly for irreversible systems such as noble metal
oxides formed from aqueous solution, which have served to complicate and
confuse the present state of the field.
2.6 Electrochemical Adsorption - Previous Results and Discussion
2.6.1 General
A brief review of some published electrochemical adsorption data will
now be presented, with some critical discussion of possible mechanistic
and structural models suggested by the results. Aqueous inorganic systems
will be discus6ed chiefly as analogies may be drawn with gas-solid
phenomena; organic adsorption tends to be more complex and therefore it
is more difficult to deduce the underlying phenomena.
2.6.2 Hydrogen Adsorption
This has been chiefly studied on platinum-group metals, usually
platinum itself in aqueous solution by cathodic deposition. Reviews
have appeared (e.g. 59, 68, 79). The chemisorption process can be studied
without concomitant H2 evolution as the former commencies 0.5 v below
the latter. The process is reversible under most conditions, and thus
the coverage by hydrogen atoms should be completely determined by the
potential and not the charging rate. This seems to be borne out by
careful experiments, even for A.C. bridge determinations at low frequencies
-1 (< 100 cycles sec ). The coverage-potential behaviour does appear to
-52-
indicate Temkin-like behaviour on platinum, although two pseudocapacitance
peaks are often found, depending on conditions, which may be explained
by two different kinds of adsorption site, possibly different crystal
planes.
Thermodynamic energies of adsorption have been determined (69), and
appear to be somewhat less than for the gas phase values, indicating a
competitive effect of the solvent for surface sites. Also heterogeneity
parameters tend to be much lower than gas phase values; at least f = 10
for the latter compared with f = 4-5 for the former (ref. 59, p. 390).
However, much more accurate work is required for an extensive discussion.
2.6. _Oxygen Adsorption and Oxide Formation
2.6.3.1 Introduction
Extensive build-up of what appears-to be a dense layer of adsorbed
oxygen is commonly observed for anodic oxidation of all metals in aqueous
solution. On some less noble metals such as iron, this is preceded by
anodic dissolution of the metal, the resulting oxygen (or oxide) layer
markedly inhibiting this process and giving rise to passivation phenomena
(see later). Also on the valve metals, such as tantalum, a thick metal
oxide film is formed, which grows by high-field ionic condition (34). On
noble metals such as platinum and gold, an oxygen film of around a monolayer
thick appears to be formed prior to the anodic evolution of oxygen and
no significant metal dissolution seems to occur (but see (75)).
The literature on this topic, although very extensive, is rather
fragmentary and confusing, and thus a short review of the fundamental aspects
will now be given. Reviews on various aspects have previously been
-53-
published (e.g. 59, 68, 70, 71). Nearly all the data refers to aqueous
solutions, although a short study of platinum film growth from an oxide
solution in fused lithium-potassium chloride will be presented later,
together with some results for platinum sulphide films.
2.6.3.2 General behaviour
Most of the discussion will concern the platinum system, partly as
this has been experimentally studied in this work, and also as most work
has centred on this system.
In marked constant to the hydrogen case, the formation and reduction
of oxygen films are highly irreversible processes, and considerable kinetic
hystell&sis is involved; thus the concept of adsorption pseudocapacitance
is very limited. Also films of thickness appreciably greater than one
monolayer (calculated for Pt 0 or Au CO are found. These and other
factors have lead to considerable controversy as to whether the film is
simply a chemisorbed oxygen layer or has at least the element of an ordered
oxide lattice. Most of the evidence has come from anodic film formation,
and this will be discussed first.
Film formation
The evidence from the various techniques used will be discussed in
turn, indicating especially areas where the simple chemisorption theory
appears to be inadequate.
(1) Anodic galvanostatic charging
Many investigations have used this technique; the form of the poten-
tial time curves is commonly a linear "ramp" starting at around + 1.0 v
(v. N.H.E.) (depending on current density) to the potential of oxygen
-54--
evolution ("J +1.5 v). The charge involved for Pt and Ao generally
indicates the formation of at least two equivalent monolayers; however
the charging curve is usually smooth except at very low current densi-
ties, and shows no breaks corresponding to a monalayer. The potential
span involved ("J 0.6 v) suggests an Elovich-type system with a substantial
f value for a chemisorbed model. Plots compared on a potential-charge
scale at varying current densities do not coincide, the slope increasing
with current. This has been attributed to increasing penetration of
oxygen ("denrasorption") into the metallic surface layers at decreasing
charging rate, (72). This implies that only chemisorbed oxygen is effec-
ting the kinetics. In fact most discussion has either suggested (or
assumed) that the film is either randomly chemisorbed or perhaps in
patches which have a distinct co-operative ("lattice") structure. To
accommodate the observed coverages with the simple chemisorption model,
a ratio of 0:Pt greater than one has been postulated (73). The oxide
model allows for this by the formation of further lattice layers.
By plotting the current-potential relationships at a given coverage,
linear Tafel plots are obtained. The slope at zero coverage has been
considered as the slope increases with coverage due to the possible oxygen
penetration effect; it has a low value (1.; RT/2F) which is difficult
to explain on a simple ion discharge theory with a reasonable transfer
coefficient. This result however, has been largely ignored.
(ii) Potentiostatic charging
A few investigations on platinum (71+, 75, 77) and gold (76) have
concerned the build-up of films under potentiostatic conditions. Generally,
the growth is linear in logarithmic time, i.e. & = b1 log t + K -
(Eqn. 2.36), where b1 and K are constants, holds well. However, the
-55-
constant b1 tends to increase with potential and ref. (74) indicates
non-linear plots (curving towards the t-axis) at times < 10 seconds.
The above appears to be consistent with the chemisorption model
assuming slow Elovich-type kinetics (section 2.4.6). Thus eqn. 2.36
corresponds to the integrated Elovich equation (Eqn. 2.24). Conway (74)
has criticized this approach by stating the need for (a) a site occupancy
term (1 - 8), and (b) a term for the back reaction. However, factor
(a) is negligible except at high coverages, and the existence of an
appreciable reverse reaction rate is unlikely as considerable hysteresis
is involved between the formation and reduction of these films. ,-11 any
event, these criticisms could also be levelled at the use of the Elovich
equation generally, but much data, particularly in gas phase work, are
evidence for its wide applicability.
(iii) Open-circuit decay
Galvanostatic oxidation and subsequent open-circuit decay at platinum
has been studied (78). The decay occurs across a capacitance at a
(virtually) constant coverage formed in the preceding galvanostatic case.
The capacitance was assumed to be approximately constant over the potential
range studied which involves effective Tafel slope measurements over a
few seconds. The Tafel slopes were found to linearly increase with coverage
by three-fold between zero and two equivalent monolayer coverages. This
is incompatable with the chemisorption model which predicts a constant
slope. These results are consistent with the galvanostatic pulse measure-
ments considered above, and thus throws doubt on the occurrence of
oxygen absorption to explain the change of these potential-charge slopes
at varying currents. The capacitance values are between 100-200 p,F cm-2
which indicates some adsorption pseudocapacitance. The values agreed with
those from an A.C. bridge technique.
-56-
(iv) Capacity measurements
Values of "capacitance" at platinum have been obtained by a number
of workers, using potential-step (77, 80) A.C. impedance (78, 81)
open-circuit decay (78), and linear potential sweep (82). The earlier
results have been sumarized by Gilman (68). The results are widely
scattered, but it does appear that the (possibly double-layer) capaci-
tance decreases with potential above + 1.0 v., even at constant oxygen
coverage. However, the fairly high values often obtained (> 100 F. cm 2)
suggest the occurrence of pseudocapacitance probably arising from some
reversibly bound oxygen (68).
2.6.3.4 Film reduction
(i) Hysteresis
A major characteristic of the oxygen film on platinum and gold
(and on other metals where the film can be reduced) is the considerable
hysteresis between the formation and reduction of the layers, the removal
process taking place at markedly more cathodic potentials than the
formation, with a rather different coverage-potential profile more
characteristic of a simple redox process under Langmuirian conditions.
This has been discussed in terms of a permanent hysteresis effect (83)
by Conway (66, 74), assuming that originally chemisorbed oxygen
undergoes a totally irreversible place exchange reaction to form a surface
oxide. This mechanism may well be correct, but the concept of permanent
hysteresis is hardly considered relevant to the systems as thermodynamic
equilibrium is unlikely to be attained. Thus under potentiostatic
conditions, the layer growth continues linearly in logarithmic time for
as long as has been studied hours); of course it would appear to
-57- •
have virtually equilibrated in linear time. Kinetic hysteresis appears
a much more satisfactory way of considering the problem. Thus
exchange currents for the process may be obtained by extrapolation of
anodic and cathodic Tafel plots which decrease with coverage (75).
(ii) Reduction kinetics •
This has mainly been studied from previously potentiostatic electrodes
by galvanostatic linear potential sweep pulses (e.g. 66, 74, 75, 84) .
Fairly irreversible waves are obtained, with Tafel slopes for both pla-
tinum and gold of about 2RT/3F. This is fairly constant with coverage,
and thus the waves describe similar potential-coverage relationships.
Film "ageing" effects are apparent which increase the hysteresis,
depending on coverage and formation time (66, 75, 85). The hysteresis
appears (on Pt) to be a function of the total quantity of surface oxide
rather than one of the potential and rate at which it is formed.
As for the anodic process, no agreement on the mechanism has
been reached. Two interesting approaches for platinum have been in
terms of Elovich-type desorption kinetics with a variable heterogeneity
parameter (66), and by means of a variable reaction order model (84).
• The Elovich-type treatment
This approach, for linear sweep reduction transients on platinum (66)
considers desorption kinetics determined by a simple coverage function
with activation energies modified by a desorption heterogeneity parameter
f. Film ageing tends to lower the f value, along with a cathodic
shift of the wave. The former indicates a more homogeneous film; the
latter is explained by a concomitant increase of the adsorption free
-58-
energy as the layer rearranges. A similar approach for galvanostatic
reduction transients does not seem (to have been specifically applied.
It may be noted that the shape of these transients on platinum is
of an inflected symmetrical arrest,which is unlikely to fit the above
treatment, at least in the initial part of the wave (see experimental
discuSsion later). On gold, the arrests are very sharp which suggests
f e= 0, along with little dependence of reduction rate on.coverage
(no simple 8 term in the kinetic equation)
The reaction-order treatment
Ohashi et al. (84) assumed an empirical equation for platinum
oxide reduction
i = nF kc q exp (- um
RTF.E +kcq)
(Eqn.2.37)
where q is the surface change (concentration), m is the cathodic
reaction order, Xc is a heterogeneity parameter, and kc is a
cathodic rate constant. This equation is based on a similar model to the
above, except that the possibility of a non-unity reaction order is con-
sidered. For the galvanostatic case,
dE RT [ m c (dt
)t = t nF T c
-t nF _ (Eqn.2.38 )
where Tc
is the cathodic transition time, and t the time at
which (dE/dT)t,t is taken. By taking the midpoint of a series of
transitions at constant current with varying initial coverage from an
anodic galvanostatic pulse, X.c was found to be negligible (constant
desorption activation energy) and m = 2 if n = 2 and a = 0.26.
-59-
A similar result was obtained from linear sweep and potential step
reduction transients. However, this approach can be criticized. The
reaction order requires a series of arrests at different total coverages
for its determination, also no evidence is presented to demonstrate the
same relation at other than the transition midpoint. For single
transitions, the second-order reaction can be transposed to a appreciable
heterogeneity parameter anyway (see later). The suggested reaction
was
2 Pt° + 2H+ +2 4. 2Pt + H202
(Pt + H202 Pt 0 + H2O )
No consideration was taken of potential-current dependence. This cannot
be explained by the suggested model which predicts a Tafel slope of about
2RT/F rather than the 2RT/3F slope observed.
2.6.3.E The high-field _growth model
From the above, it is clear that the simple chemisorption model
(involving perhaps incorporated "oxide") appears rather inadequate.
The main discrepancies are
(i) dependence of the potential-charge slope on current for anodic
galvanostatic transients and associated coverage dependence of the
decay Tafel slope;
(ii) uniform growth of oxygen coverage to two or three equivalent monolayers;
(iii) low Tafel slopes for oxidation and reduction;
(iv) decrease of capacitance with coverage.
Very recently, a model for oxide formation and removal in terms of
a rate-determining ion movement process under the influence of a "high field"
formed within the oxide layer and the solution-oxide interface has been
FIG. 2.2.
(a.). 190TENT1AL eeof (LE 14111-11t4 PIEThG - S&LUMW livTtgeilASE Win °XIX. not
0
Ct)
NOMENCLATURE For goVE
OX 0)-S
LAYEt
\\\\
\\
\\
-61-
suggested (75, 78). A simplified model of the interface is shown in
figure 2.2. The rate-determining step, due to Vetter and Schultze (75)
is considered to be an simultaneous place exchange of Pt2+ and 02-
between the inner Helmholtz plane and the oxide layer under the influence
of the imposed field (see section 2.38). Only a fraction of the measu-
rable potential drop (Pm - pi) is available for this process; thus
available potential = ce(Pf - ad) ( Eqn. 2.38), where ta, is a transfer
coefficient. At zero coverage pm = pi., but as oxide is deposited,
a finite (Pm - pf) is developed as a potential drop across the film
similar to that occurring in passive and"valve" metals films. This is
all "unavailable" potential and thus does not contribute to assisting the
rate-determining step. This may be expressed as
[ anF
Pate ianodic = AF ka . exp L (0 (Eqn.2.39) TM ffll) Bqi
where ka
is a rate constant, n is the equivalent electron number, q is
the quantity of oxide deposited, and B is a proportionality constant
dependent on (gif - pi) i.e. B is f(Of - pi).
It may be noted that eqn. 2.39 has the form of an Elovich equation
for adsorption, but the "heterogeneity parameter" is a function of
reaction rate, defined by ce(pf - Pads). Here the reaction rate is lowered
for a given total (pm - pi) by a build-up of dipoles which arise from
the oxide presence giving a potential drop (pm - pf) linearly dependent
on the dipole concentration, the magnitude of the dipoles being dffected
in turn by the surrounding field strength by an induction effect.
The model is very similar to that employed with thicker anodic films
(34) but as it concerns a very few oxide layers (one to three), the
effect of incomplete layers must be considered. This crucial aspect of
-62-
tree model is open to some doubt, but experimental evidence for the direct
proportionality between surface dipole concentration and generated surface
potential exists from gas-phase chemisorption studies (46). In summary,
the oxide film is capable of creating a potential difference (Pm - Pf)
unavailable to the electrochemical rate-controlling step, and its magnitu-
de is directly proportional both to surface oxide concentration q
and double-layer potential drop (Pf -
This model provides some explanation of the phenomena noted above to
be unaccountable by the chemisorption theory. These points are now con-
sidered in turn.
(i) By this model, the imposed current density defines a potential
difference (Of - ad' )' this being proportional to the logarithm of the
'
current density by a Tafel relation. Therefore, when a given anodic
current is imposed on the system the potential rise seen as the coverage
increases is completely due to the term (gm - Pf ), the size of which is
proportional both to the coverage and the term (Of - fad).Thus the
(dE/dq) slope is proportional to log i as found experimentally. As
explained above, this effect can also be accounted for by the "dermasorp-
tion" concept. However, the variation of Tafel slope with current
at constant coverage rules out this possibility, at least as the dominant
factor.
(ii) Uniform kinetics are expected on this model for coverages much
greater than an equivalent monolayer as penetration of oxygen into the
metal is the essential rate-determining step.
(iii) Vetter (75) has considered a number of possible rate-deteriining steps
depending whether this involves metal ion movement, oxide ion movement
or both in a concerted slow step. For the platinum case it was considered
that the concerted step is most likely, where the apparent transfer
-63-
coefficient is determined as a* = a (Z++ I ZI ) = 4 a (Eqn.2.40)
where Z+ and Z are the positive and negative ion charges (both two
in this case). Eqn. 2.40 leads to a = 0.42 from the experimental slope
- a reasonable value. It must be noted, however, that Eqn. 2.40 is
based on the idealized model of pure charge movement. Extensive covalency
would tend to lower the effective charges (34). Also no a priori
determination of a was made.
The cathodic Tafel slope was found to be practically independent
of coverage. This was explained (75) in terms of reduction at the edges
of oxide "islands" with a constant "local" capacitance and field.
This raises the Tafel slope to RT/a*F where ce = 1 throughout most
of the reduction process, c.f. gold (86).
(iv) The decrease of double-layer capacitance with coverage may be explained
by considering the oxide layer as generating a capacity in series with
the solution double-layer (75). However, the chemisorption model can
also lead to this result, for example, by "blocking" of surface sites
similar to that observed with organic adsorbates.
Finally, oxygen evolution is considered to take place via an electron
tunnelling current through the film once formed (75, 78). This process
becomes dominant on platinum at coverages > 1.5 equivalent monolayers.
2.6.3.6 Limitations of the models
The high-field model, although undoubtedly oversimplified, appears
to be an improvement over the rate-controlling chemisorption model with
subsequent oxide incorporation considered previously. However, it is
not completely satisfactory particularly under potentiostatic anodic
growth conditions.
-64-
It is recalled that a good fit to a direct to growth law
is generally obtained. This appears to be incompatible with the high-
field model-, in spite of comments made to the contrary (ref. 75, p. 137).
This may be seen by reference to eqn. 2.39. The growth law may be
transposed to the differential Elovich form i = K. exp [-kq], where
K and k are constants. However, although this is comparable with
eqn, 2.39 for the potentiostatic case (i.e. pm -!l constant) with a
B value invariant with coverage, B must here be a function of
coverage as it is proportional to (Df
- pads)
which defines the current
and thus is varying. The only condition for which the logarithmic growth
law will hold is when (Pm - pf) << (Of - pl) which is unlikely. Thus
(75) log. current-potential plots for a series of coverages derived
potentiostatically and galvanostatically do not coincide, and the former
are markedly non-linear. Admittedly, the slopes roughly co-incide at
low currents ("., 10 6 amps. cm2) which correspond to long observance
times (102 sec.) but the potentiostatic plots are shifted considerably
to more positive potentials. Obviously the kinetic and therefore structural
"condition" of the film is quite different in the two cases. Also the
deviations from the logarithmic growth law at small times (< 10 sec)
observed in (74) indicate an even more pronounced effect than apparent
in (75).
However, the logarithmic growth constant k is seen (74, 75) to
decrease with constant potential applied which is qualitatively in
agreement with the high-field model as the constant B is dependent on the
field strength, and is not in agreement with a site energy variation
model leading to the Elovich equation which predicts a constant growth
slope. (similar dependance of the growth parameter is seen for solid-gas
chemisorption with varying initial pressure (section 2.4.6)). Also see
Section 5.4 .
-65-
te,
Assuming that the discrepancy between the high-field model and
experiment under potentiostatic conditions does not mark a complete break-
down of the model, it is interesting to speculate on the persistence
of the Elovich rate form. Elovich data is usually (but not neccesarily
for electrochemical cases) obtained directly from the experimental cove-
rage-time plots. Thus a time relaxation process may be involved which
is an essential part of the occurrence of the rate form, perhaps a
spontaneous film relaxation process following the initial (almost instan-
taneous) deposition of adsorbate; layer "ageing" effects for example
as describedty a progressive decrease of the heterogeneity parameter
for oxide reduction (see above, ref. 66) are often logarithmic in time.
If the existence of incorporated oxide is accepted, there remains
the question of the quantity of oxygen remaining in the chemisorbed state
(outside the platinum lattice). Indeed, the increase of the Tafel decay
slope with coverage can be explained by a surface dipole model involving
only the chemisorbed species in a similar fashion to the incorporated
oxide. From capacitance data, Vetter concludes (75) that adsorbed oxygen
has a coverage e <0.1 at 1.5 v.
Ellipsometry (137) indicates that a film thickness greater than a
monolayer is present at high (A- 2.0 v) potentials, and although a break
in the charge-potential plot is seen, the optical film growth appears
to be uniform.
2.6.3.7 Mechanism involving_a quasi-equilibrium intermediate
There is a difficulty in explaining the Tafel slopes at low coverages.
The high-field mechanism does provide an explanation, but involves the
assumption of a large ionic character to the bonds and also the dominating
-66-
involvement of this step at low coverages. Intuitively one would expect
chemisorption, at least as an initial step. These layers may then induce
ionic motion by the electric field formed by the surface dipoles, leading
to oxide incorporation and generating new sites for further chemisorption.
Thus the two mechanisms may aid each other (53).
Indeed, if the process involving concerted movement of 02 and
M2 + ions is considered, it is implicit in the model that there will be
a previous step forming a chemisorbed species 6-0 - M5+ which will
for a well-polarized bond (evidence from gas-phase surface potential
measurements, section 2:4.3.3 ) approach the form 02- - In any
event, a formal two-electron electrochemical equilibrium exists between
this species and solute oxide species. If a Langmuir isotherm holds
(for low coverages), then this "oxide" intermediate has a ten-fold coverage
change every 2.3RT/2F volts. Combining this with the Tafel slope for
ion movement (PT/2F) yields a net apparent RT/4F slope, i.e. 15 mv.
per log unit at 25 °C. The idea of an electrochemical adsorbed intermedi-
ate with the essential activity variation with potential has been noted
(74, 85, 138). The approach can accommodate the observed ^J 30 mv.
slope for Pt0 formation (75) assuming incomplete bond ionicity.
The decay slope lowest value of 19 my (78) is somewhat lower, but it is
not clear which logarithm base was used I. It is recalled that evidence
for reversibly chemisorbed oxygen exists from capacitance measurements,
which may be a "non-incorporated" surface layer.
2.6.3.8 Comparison with gas-solid systems
Oxygen is not known to chemisorb on to gold from the gas phase
(except slowly on to powders), but high adsorption heats are not expected.
-67-
The existence of thick films formed electrochemically from aqueous solution
is perhaps surprising, and may be due to involvement of an "Au0H"
intermediate (see section 4.5.3.3). Oxygen adsorption on platinum is
usually limited to around a monolayer at room temperature (87), although
some incorporation may be involved (126). Films formed from the gas
phase seem to be reduced in aqueous solution similarly to those formed
electrochemically (88).
2.6.3.9 Other oxide films on platinum
By anodic oxidation even at room temperature for prolonged periods
at high potentials (into the 02 evolution region), thicker oxides than
normal can be formed on platinum as seen by the reductive stripping tech-
nique. Above'2.1 v in H2SO4 solutions, two types of oxides are formed
(89, 90). The type I oxide is found at all potentials, but the type II
oxide (reduced at more cathodic potentials) only appears under strongly
oxidizing conditions above 22 °C (91). However, the growth rate of the
type II oxide passes through a sharp maxima at ^' 2.15 v (90), considered
to be a passivation potential arising from a protective oxide film
(90). A parabolic growth law was derived, indicating rate-controlling
diffusion (89). Very thick oxide films appear to be built up in fused
alkali nitrate media (92).
2.6.3.10 Miscellaneous anodic films
Two main areas of interest have concerned oxide films built up on
"passive" and "valve" metals (34). The former concerns films which
appear to inhibit metal dissolution, such as on iron; and the latter
concerns the fairly thick rectifying films formed on tantalum or
-68-
aluminium for example. It is interesting to note that the formation
kinetics of these films (particularly under galvanostatic and open-
circuit decay conditions) show a considerable similarity with the noble
metal films considered above. The behaviour appears to be generally one
of rate-determining high-field ion conduction through, or at the surface
of, the forming oxide lattice (e.g. 35, 93).
Film growth kinetics have also been reported on a platinum anode in •
molten potassium thiocyanate (138). Under constant current or potential
conditions a constant charge is required to passivate the electrode,
probably resulting from a Pt SCN film formed from a polymeric surface
(SCN)x
species. Open-circuit decay curves from various film coverages
yield a slope linearly dependent on coverage similar to the oxide cases
discussed above. A constant low Tafel slope is recorded of value RT/F.
This is discussed in terms of quasi-equilibrium electrochemical adsorption
of SCN, and subsequent rate-determining rearrangement by a chemical step.
However, it is not clear how this is compatible with the Tafel slope
coverage relationships, explained by a decreasing transfer coefficient
for an irreversible process as the film thickens.
Electrochemisorption of organic species has also been investigated
at noble metal electrodes (e.g. 139) Elovichian adsorption kinetics
are usually observed.
2.7 Other Electrochemical Techniques
In this section some experimental techniqes available for the study
. -69-
of electrode process involving reactants and products both having a
bulk existence will be discussed. Attention will be mainly restricted
to those cases applied in the experimental part of this thesis.
Techniques may be usefully divided into (i) steady-state, and
(ii) non-steady state types. General reviews are now widespread (e.g.
1, 2, 94, 95).
2.7.1 Stead-state techniEues
These techniques essentially consider the time independent measure-
ment of current andpotential approached either galvanostatically or
potentiostatically.. As expected from the discussion in section 2.3
electrode kinetic information is only obtainable for the irreversible case
by these methods; i.e. where a surface electrochemical or chemical reac-
tion is rate-controlling and there is a negligible gradient of chemical
potential between the bulk and interfacial regions for a given electro-
active species. For reversible systems, the current-potential
relationships are a function of mass transport processes to and from the
electrode surface; i.e. stirring the electrolyte or the use of a non-
stationary electrode will effect the rate.
2.7.1.1 The irreversible case
Here direct application of the theoretical equations considered in
section 2.3 can be made provided that a true steady-state can be maintained
with constant activity of reactants, intermediates, products and electrode
surface state. Generally systems with exchange currents of <1073 amp.
CM2 (for about 10
2 M bulk concentration) may be studied using
stationary electrodes, as above this slow diffusion and convection processes
-70-
become appreciable for reasonable overpotentials. Moderately faster
systems may be studied using forced convection or rotating disk electrode
techniques, thus increasing the mass transport rate.
2.7.1.2 The reversible case
If a solution containing an electroactive species X (and an inert
supporting electrolyte to minimise bulk migration effects) is polarized
e- at an inert electrode in a region of net current flow so that X — + Y--*
occurs, eventually a limiting current condition is obtained for electro-
chemical reaction for the species independent of the Plectron transfer
rate, provided that the potential is below that for solvent or supporting
electrolyte decomposition. This limiting rate depends on the mass-
transfer of the species X to the electrode surface. At a stationary
electrode this is by a mixed diffusion-convection process, but may be
approximated by the Nernst diffusion-layer concept where the concentra-
tion gradient occurs within a certain distance 8 of the electrode
surface. By the application of Fick's Law, this leads to the limiting
current density it
nFD C i1
= x x (Eqn.2.41)
where Dx is the diffusion coefficient, C
x the concentration of X.
The effective film thickness 8 decreases with stirring, and is often about
1073cm. for unstirred solutions. Usually uncertainties in 8 reduce the
practical value of this relation.
However, the current-potential relation below this plateau is
dependent on the type of overpotential present. For a reversible reaction,
e each potential is defined by a Nernstian equilibrium. Thus for X Y
-71-
E = Ec(,y - FT In [ X
Y_.]] (Eqn.2.42)
By noting that eqn. 2.41 may be generalized to any concentration
bulk gradient (Cx - C
Xsolution), the concentration terms in eqn. 2.42
may be eliminated to yield (94)
11 - RT E = El + In (
2
where i is the current density at potential E, and
El EX,Y+ RT In ( Y DX
(Eqn.2.43) .
(Eqn.2.43a)
El is known as the "half-wavy' potential. 2
Of course, eqn. 2.43 was derived by equating thermodynamic solution
activities with concentrations. The potential-current form will therefore
be altered when this assumption does not hold. Also it is assumed that
the bulk concentration of species Y is zero. For irreversible
reactions, the current-potential curves are generally elongated and
displaced along the potential axis (94).
2.7.2 Transient techniques - chrono.potentiometry
2.7.2.1 Introduction
The inherent difficulty with the steady-state approach for reversible
systems is that the mass transport process does not lend itself to accurate
theoretical description due to the involvement of convective processes.
For many electrocatalytic or metal deposition reactions, a true steady-
state is never reached; thus time-independent techniques involving
-72-
diffusion-controlled depletion of the reactant have considerable value
in the study of electrode processes.
These approaches involve the application of an electrochemical
perturbation (commonly constant current, potential, or linear potential
sweep), and the measurement of the resulting time-dependent response
(e.g. potential-time in the galvanostatic case). Conditions are
arranged so that the perturbation leads to a given variation of reactant
surface concentration with time, so that the experimental electrochemical
response may be compared with theoretical models describing particular
reaction schemes. Such techniques (often grouped with steady-state
voltammetry as "electroanalytical" methods) are members of a larger class
of relaxation techniques. These include a range of methods used to
obtain electron transfer rates of fast reactions by means of small
perturbations for short times (< 10 6 secs) The electroanalytical techniques
whilst using the same perturbating waveforms involve larger perturbations
for sufficient times so as to create diffusion depletion at the electrode.
The upper time limit is the appreciable onset of convection effects
( > few seconds).
The technique chiefly used in this study was chronopotentiometry.
This will now be described in detail.
2.7.2.2 Chronopotentiometry - general
As this has been extensively reviewed ( e.g. 94-98), the approach will
be a critical rather than exhaustive one.
The technique essentially involves the application of a controlled
(usually constant) current pulse to an electrode in contact with a solution
of the electroactive species 0 (containing sufficient supporting electrolyte
C
73
na-. 2.3 . Cf!Mao PaEarlo MET tcY — WAVE SHAPES ANC) CoNsTROcTioni S .
1
ir ------A 11
-74-
to suppress migration effects). The resulting potential-time arrest
consists of three regions shown in fig. 2.3a
(i) Rapid rise AB from the rest potential Erest
to E1
at which point
the species 0 commences reaction 0 + net R. In this region only double
layer charging ideally occurs.
(ii) Gradual potential rise BC during which the surface concentration
of 0 falls to zero (at C).
(iii) Rapid rise CDduring which the reaction-continues, resulting eventually
in another plateau corresponding to solvent decomposition. The time
required T for the exhaustion of 0 at the electrode surface is referred
to as the transition time. By a solution of Fick's Law for the relevant
boundary conditions at constant electrode reaction rate, and considering
only linear diffusion to a plane surface,the following relation (the
Sand equation) is derived
1 1 T2 = 172 nFCo D 2 / 2i
0 0 (Eqn.2.44)
where Co
is the surface concentration of species, 0, Do
its diffusion
coefficient, and i the current density. Thus a plot of T2 versus
1/i should be a straight line with zero intercept, also i T2 = constant
( = u2nFC°0D0 2 / 2).
It should be noted that eqn. 2.44 is independent of the rate of
the electrode process itself, but only defines the time dependence of
Co at a given imposed reaction rate. Thus deviatiors from eqn. 2.44
are only concerned with variations of Co
or to surface concentrations
of species related to 0 via chemical equilibria, and provide information - -
on phenomena occurring before the electron-transfer step.
-73-
2.7.2.3 Deviations from the Sand equation
(i) Slow preceding chemical reaction
kf - Consider a reaction Y 0, followed by 0
+ neR. Y is
kb electroinactive in the considered potential range. Two limiting cases
are apparent when (a) the imposed rate is so slow that Y is completely
converted to 0, and (b) the imposed rate is so fast that the quantity
of Y converted during T is negligible. Thus two current regions may
I be encountered where eqn. 2.44 is obeyed but with different i T2
I products. For intermediate current values, it may be shown that i T2
decreases linearly with current density (96).
(ii) Adsorption of electroactive species
In the presence of adsorption of an electroactive species, current
will not only originate from species arriving at the electrode by diffu-
sion, but will also occur by reaction of the adsorbed species. Thus
i = iadsidiff" and the qualitative existence of the effect is detec-
ted by an increase of iT2 with current density as the adsorbate contribu-
tion increases. As reaction of the adsorbate does not require an initial
transport process fads
T = constant. Thus by extrapolating the charge
iT obtained to infinite current, the iads T contribution (fads
T =
nF where is the surface excess) can be obtained. However, the nature
of this extrapolation depends on a model for the division of the faradaic
current between diffusing and adsorbed contributions.
Four such limiting models have been commonly used (98); the first
three refer to a slow adsorption equilibrium such that no interconversion
of diffusing and adsorbed species occurs during the current pulse.
-76-
(a) AR, SR model; where all the adsorbed species reacts before the
diffusing species starts to react. This should involve two separate
or almost separate potential-time arrests. If not, the adsorbed charge
may be determined from iTads = nFil+ (nFC)2 irD / 4i - (Eqn. 2.45)
by extrapolating the linear plot iTads versus l/i to zero l/i,
where C is the initial bulk concentation.
(b) SR, AR model, i.e. the solution reactant is completely depleted
before the adsorbed species reacts. An approximate treatment leads to
the same algebraic form as for (a).
(c) SAR model, i.e. simultaneous reaction. Here a plot of versus
I T2 should lead to a straight line with intercept nFr.
(d) For a rapid and constant equilibrium between adsorbed and diffusing
species, it is necessary to postulate an isotherm for the equilibrium.
I If a linear isotherm is postulated a linear plot of C/T2 versus C2/i
should be obtained with the intercept (n/D)2 1./2
Thus, in principle, the reaction model for adsorption along with the
surface excess can be obtained by application of the above trial plots.
Further distinction between fast and slow adsorption equilibria may be
obtained by variation of the starting potential, where the latter case
may show a variation of surface excess with initial potential, whereas the
former case is not expected to vary, as adsorption equilibria are maintained
as the potential changes. Distinction has been achieved for certain
favourable cases (99). However, the value of the two approaches has been
criticized (100) as accurate values of T are difficult to obtain (see
later), double-layer charging is difficult to allow for as the potential
is not controlled, and the models are oversimplified and tend to "merge"
into one another in practice.
-.77-
In summary, it is undoubtedly true that adsorption itself is much
better studied by controlled potential techniques, particularly double-
step chronocoulometry (101), as double-layer charging effects may be
determined, and adsorbed and diffusing contributions may be separated
on a time basis. However, at least useful semi-quantitative data is
obtainable from chronopotentiometric studies which may regard adsorption
effects as a sideline to the outline determination of the electrode
mechanism.
(iii) Other deviations
Care must be taken to recognise factors other than the above in
leading to deviations from equation 2.44.
(a) Double-layer charging... This distorting effect on chronopotentiograrns
I has been widely considered (e.g. 102). It acts to increase the iT2
product with current density as for an adsorbed species, and also make
the waves less distinct. However, compared to adsorbed charges, the values
are small (e.g. for Cd, = 50 11F cm-2 over 0.2 v, charge = 10 p.coulombs.cm-2)
(b) The influence of convection at long times ( > few seconds for an
unshielded electrode) raises the transition time above the expected value.
(e) Electrode surface roughness effects also lead to an increase of I
iT2 with i as the diffusion layer occupies more area leading to a
lowering of the real compared to apparent current density.
(d) Electrode blocking_effects. If the electrochemical reaction involves
a deposition of material which can "block" the electrode surface with an
insulating layer, the real current density can rise during the transition
and thus lower the transition time below the expected value. The effect
would be more pronounced at lower current densities which involve the passa-
I ge of a greater charge during the transition; thus a rise of iT2 with
-78-
i is expected, perhaps eventually leading to a plateau where the effect
is negligible. This has been observed experimentally (103). An extreme
case is complete "blocking" or inhibition of the electrode reaction.
This will be considered later.
2.7.2.4 Current reversal
If during the constant current pulse at some point prior to the
transition time for the system 0 np the current is reversed to the
opposite polarity, a reverse transition corresponding to re-oxidation of
R back to 0 will be obtained (C1 El Fi in fig. 2.3b). Thi' variant,
known as cyclic chronopotentiometry has considerable value in elucidating
the nature of the product R, as shown in the various reaction schemes
now discussed.
(a) Soluble product. The diffusion equations corresponding to the case
where R is soluble in the electrolyte or (liquid) electrode when solved
1 (96) give rise to the relation T
1 = 3 'r, providing the current is reversed
at or before the forward transition time. The potential ranges of these
transitions also provide evidence of the reversibility of the process.
Thus, if complete reversibility exists, the quarter-time potential ET/4
for the forward process should co-incide with the "ET/4" for the reverse
(ilvi4il accurately 0.215 T1 ). An increasing activation overpotential
component creates a difference between these two potentials which can
be related to the electrochemical rate constant for electron-transfer (104).
1 A value of T
1 < 3 ---•T may indicate a following chemical transforma-
tion to aneleciroinactive species (105), or an electron number for the
reverse smaller than for the forward process (106).
(b) Insoluble product. Here all the product is retained at the interface
and the reverse and forward transition times should beEqual, i.e. T. T.
-79--
1 Relations of the type — 3 — T < Ti < T indicate partial insolubility
(or adsorption) of the product.
2.7.2.2 Potential-time curves
The potential-time relation during the transition time T provides
information onlhe electrochemical response to the surface concentration-
time relaxationcurve for reactants and products and thus providesinforma- •
tion on mechanisms. The chronopotentiometric technique is well suited
for this, as the mathematical relationships lack the complexity of other
methods (e.g. linear sweep voltammetry).
(a) Reversible cases
Here Nernstian equilibrium at the interface is assumed, and thus
the potential at any time is given by the ratio of oxidized 0 to reduce R
species present. Thus the experimental relationship depends on the state
of the reaction product. Concentration-time relations for various cases
have been derived (96), and some results are given below for the
reaction 0 + ne
R with zero bulk concentration of R.
(i) Soluble product case
If the product R is soluble in the electrolyte or liquid electrode
phase, '1
RT t2 E = + ln ( ) E_
1 / 4 nF t2 (Eqn.2.45)
where t is the time after the start of the transition. It may be
noted that eqn. 2.45 has a marked similarity to eqn. 2.43 for the steady-
state voltammetric case; Et/4 is in fact equivalent to El here. 2 1 I 1
From Eqn. 2.45 a plot of log (T2 - t2 /t2) versus E should yield
a straight line of slope 2.3 RTC nF. Thus a good fit with an integral
-8o-
n-value for the slope is evidence for the model suggested above; also
from equation 2.45 no dependence of Et/4 on current density or
concentration 0 is predicted. These relations, i.e. logarithmic
fit and slope, current density or concentration dependence of Et/4
and the ratio of reverse: forward transition times provide the normal
diagnostic criteria for the fit of potential-time curves to various mecha-
nistic models (for details see reviews cited). Similar models to the above
involving various mechanistic complications have been considered (107).
(ii) Insoluble (constant activity product case
If the reversibly-formed product is deposited on an electrode of the
same material, or coats an inert electrode so that a pure product phase
is produced, the product activity is constant with quantity of deposit.
Thus the potential-time curve only concerns the variation of the reactant
activity with time; this leads (96) to the relation
E = E + RT
In ( T2 - t2) + const. TA nF
(Eqn. 2.46)
A general equation for the insoluble case is not possible if no
a priori activity-coverage relation is known. Generally, initial
deposits will have an increasing activity with coverage, and this acts
to "draw-out" the potential-time relation over a larger range of
potentials. This phenomenon may be seen for the case of soluble deposition
into thin liquid metal films on solid substrates (108).
(b) Irreversible cases
If the electron-transfer rate is sufficiently slow, the currents
Co(t) = Co(t = o) - 2x D2 • t2
o where X 1 nFDo
(Eqn.2.48) I 1T 2
RT 2k
a,nF ZRT
. In o
•
anF In (T2 - t2) E • D
o 2
(Eqn.2.49)
-81-
normally applied in chronopotentiometry (10-5 -10 amp. cm
2) will
correspond to complete irreversibility (i,e, at least tenfold the exchange
current), and the relation between potential, current, and concentration
derived in section 2.4 will be applicable. As the equation for the
general reaction order model has not been derived in the literature,
this will now be done. For a process of reaction order Z in reactant 0
slow for the reaction 0
• ne R, eqn. 2.11 may be put in the form
r nF nFk o o C
z a exp L — RT E (Eqn.2-47)
(CY here is the cathodic transfer coefficient) and Co
is the surface
concentration of 0. From diffusion theory (96)
Eqn. 2.47 can be rewritten
1
-anF (nF.k )
= C0(t) • exp ( ZRT E) (Eqn.2.47a)
o
Combining eqns. 2.47(a)and 2.48, it follows that
Thus a plot of E versus log (T2 - t2) should yield a straight line
of slope ZRT/YnF. The potential-time curve thus describes a reaction
order plot at constant current (rather than conventionally at constant
potential).
-82-
EXtrapolation of the curve to t = 0 permits estimation of the
electrochemical standard rate constant ko. A plot of any given point
during the transition against In i will also give the slope RT/yriF;
thus comparison with the potential-time slope will give the reaction order
Z and the ,xn value.
• 2.7.2.6 . Measurement of the transition time
A central problem in chronopotentiometry is the accurate estimation
of the true transition time T. Due to the logarithmic functions invol-
ved, the ends of the transitions have rather large curvatures, making
it difficult to estimate accurate transition times purely by inspection
(Note at t = T y the term inside the logarithm is zero and therefore
the corresponding potential is not defined). Various graphical methods
have thus been used (109-113) but all are semi-empirical. Two methods
were used in this study, illustrated in fig. 2.3(c.) and (d) for the
reversible and irreversible cases respectively. The former is the
"three tangents method", probably most useful for fairly sharp inflected
waves; the latter is constructed by selecting a point at which the curve
becomes straight after the arrest (112). Neither of these methods have
• theoretical justification, but appear to give consistent results in a
variety of cases. It should be noted that this problem marks one of the
• main drawbacks of chronopotentiometry as a quantitative tool. Error in
the transition time is particularly serious for the irreversible case (112).
In many cases, particularly for relatively impure systems such as melts,
concomitant impurity reactions will distort the curves to an extent which
makes the application of the diagnostic criteria very difficult and uncertain.
Even generally, it would be unwise to claim an error of less than 5-10% in T
-83-
although this error has a resulting 2.5 - 5% uncertainty in the factor
1- T2 in the Sand equation. However, the technique has the considerable
advantage of experimental and, theoretical simplicity, in welcome contrast
to perhaps the more fashionable computer curve-fitting methods of others,
particularly linear sweep voltammetry.
2.8 Passivation and Inhibition
2.8.1 General
Commonly with anodic processes (usually metal dissolution), a film
may be formed on the electrode which inhibits and eventually completely
stops the process taking place. This phenomena is often known as passi-
vation. The mechanism of formation and resulting structure of the
passivating film has been a source of controversy for many years.
Information on this has come from two distinct sources; studies on liquid
metals under rather idealized conditions, particularly of the initial
phases of film growth (e,g, 114, 115), and perhaps less precise studies
on the overall passivation process, often using solid metals of practi-
cal importance (e.g. 2, 116, 117). Consideration will be given mainly
to studies of the latter type.
Some confusion has centred around the use of the term "passivity".
It usually refers to the case where the inhibition effect persists after
the pre-treatment has ended (118), and is well known with metals such
as iron in aqueous solutions (2) where it appears that the film required
is of a three-dimensional type (117, 118). With liquid electrodes it
-84-
also seems that a three-dimensional ordered film is required to markedly
hinder metal dissolution (119). Experimentally, either potentiostatic
or galvanostatic pulse techniques have been used to study passivity.
The folmer corresponds to a simpler theoretical situation for the initial
film nuclei growth studies (i.e. constant reaction affinity), whilst the
latter has ch(fly been used for information concerning the overall process
• by means of the resulting potential-time arrests.
2.8.2 Galvanostatic studies of passivity
The potential-time behaviour for current pulses above the critical
value required to passivate (i.e. the current density immediately prece-
ding the "Flade" potential) is naturally dependent on the solubility of
the oxide or other film produced.
(i) If the film is completely insoluble, the relationship is T =
constant - (Eqn. 2.50) will apply, where is is the anodic
current density, and T the time required for passivation
(given by a sharp arrest on the potential-time curve).
(ii) If there is simultaneous dissolution of the layer at a constant
rate, by a corrosion current ik, then (ia - ik)7 = const. -
(Eqn. 2.51), giving a linear relationship between ia and 1/T with
intercept ik, the "Franck Model". •
(iii) If the anodic product is freely soluble, passivation will eventually
occur when the surface concentration of dissolving film reaches a criti-
cal value. Such a situation is analogous to the chronopotentiometric case
considered above, where diffusion to the electrode is considered for the
boundary conditions Cx(t=0) = C
X(bulk); C
X(t = T) = zero; where C X
is the surface concentration of electroactive species X. Here the
-85-
conditions are Cx(t = 0) = zero, Cx(t = T) = Cx (critical for passivation),
involving a diffusion - away process. Thus a similar relation applies
where jaT2 = constant - (Eqn. 2.52), neglecting the charge required
to form the eventual film, which will appear as an adsorption iT
contribution (see above). This relation has been seen for a number of
anodic passivation processes (e.g. 120). Analyses concerning the current
variation of iaT2 have been made with these systems (121) but uncertainty
exists in the validity of the approach, e.g. Cx(t = T) may vary with
applied current density.
2.8.3 Inhibition mechanisms
Lowering of diffusion or charge-transfer currents upon adsorption of
organic surface-active species is commonly seen (122). The effects are not
only dependent on the nature and coverage of the adsorbate, but also on
the nature of the electroactive species. At low coverage of adsorbate, the
molecules are expected to form a two-dimenSional gas and thus electon-transfer
is not markedly hindered. In high coverages, however, a definite structure
can arise by Van der Waals interactions, this hindering transfer of charge.
This can occur by (a) inhibited penetration of the electroactive species to
the surface (the "sieve" theory), or by a deceleration of electron-transfer
caused by changes in the double-layer structure.
Under galvanostatic conditions complete inhibition or passivation may
be considered in two ways.
(i) For electron-transfer controlled systems a rise in potential to maintain
the rate caused by factors (a) and (b) alone.
(ii) For reversible systems a blocking of the electrode surface by the film
followed by a rise in current density per active electrode area, leading
to local diffusion-depletion of reactant and a sharp potential rise.
-86-
Inhibition effects of anodic films for anodic deposition or redox
reactions have also been seen, e.g. the inhibition of the hydrogen ioni-
zation reaction by oxide or halide films (79) and limiting currents for
the anodic oxidation of sulphide ion by a sulphur film (123). These effects
are usually seen only under net current flow and disappear on open-
circuit, i.e. they are not persistent as for metal film passivation.
2.9 Electrode processes involving simple anions
The aim of this section is a critical description of some
previous work on the anodic oxidation kinetics of simple anions relevant
to the experimental part of the thesis and cathodic reductions forming
anions as products, apart from the surface chemistry of adsorbed species
considered earlier. The classification of these systems was considered
in section 1.
2.9.1 Electrode reaction rates
These vary widely with the system. Theoretical understanding of
electrochemical rate constants generally is at an early stage, and is
associated with a knowledge of single electrode potentials. However,
reasonable estimates of hydrogen and oxygen electrode rate constants
have been made (124). For systems involving chemisorbed intermediates,
a strong dependence of rate on electrode metal has been found (e.g. 20),
indicating the importance of electrocatalytic effects by analogy with gas-
phase catalysis. Temperature effects on rates have been little studied,
-87-
but the existing data suggests an activation energy of about 10 k.cal
mole 1 to be common. Electrode reaction rates in melts are usually
considerably faster than for the corresponding aqueous systems, obviously
due to the higher temperatures. However, considerations of "correspon-
ding states" are important in comparing rates in different solvents,
it perhaps being necessary to consider, for example, "isoentropic" states
as in some transport phenomena (125). Various systems studied will now
be discussed in turn, omitting the hydrogen and oxygen electrodes in
aqueous media as these have been extensively discussed elsewhere (e.g.
1, 2, 22, 24, 27). Where feasible the discussion will attempt to unify
the various phenomena.
2.9.2 Sulphur electrodes
In contrast to the oxygen and other electrode systems,very little
published work exists on the kinetics and mechanisms of the sulphur
electrode in any media.
2.9.2.1 Aqueous media
Early work on the discharge of sulphide ions at an inert platinum
electrode (123) indicated formation of polysulphides in solution except
at high current, where a passivation process, presumably due to a sulphur
film,caused considerable rise in potential. Hickling (12) later performed
potentiometric and steady-state overpotential studies at various inert solid
metal electrodes in an alkaline aqueous mixture of sulphide and sulphur.
By varying the bulk concentrations of both sulphide and sulphur in
1M-NaOH, good Nernst relationships were found corresponding to the equation
-88-
E = RT E s
Eo + 2F in pa29 2 (Eqn.2.53)
which suggests (neglecting activity coefficients) the potential-determining
equilibrium 2S2- e S22- assuming that the dissolved sulphur
forms the polysulphide S22- ion with negligible loss of S2-. With
higher ratios of [E] [S21, higher polysulphide equilibria may be
written, but if the standard electrode potential for these systems is
similar [as expected (127)] closely convergent Nernst relations result,
which explains the experimentally-found reliability of equation 2.53
up to high sulphur concentrations. Reasonable agreement of calculated
(0.49 v) (127) and experimental (-0.52 v) standard (molar) potentials
was also found, and were reasonably independent of electrode material as
expected for true redox solution equilibria (see section 2.3.7).
On steady-state anodic polarization, Tafel regions are obtained.
The overpotentials appeared to be reasonably reproducible even on the
addition of notorious catalytic poisons, such as arsenious oxide, and
were unaffected by stirring. The overpotentials also were largely
independent of the nature of the electrode, which is strong evidence against
the electron-transfer to a chemisorbed species being the rate-determining
step (c.f. hydrogen electrodes). At low sulphur concentrations, the
Tafel slopes corresponded to around RTAYF or more, (where = 4), but
at higher concentrations ( > 1M) a constant RT/2xF slope was obtained.
Replotting the published curves on a fixed reference potential scale
indicated no effect of change of sulphur concentration on the partial anodic
rates for the higher sulphur contents. As discussed (12), the data
is consistent with the following anodic mechanism
(1) Sx2- M M.... SX
2-
(M represents the metal surface)
S 2- 4. s 2- x x
-2e M... s s2-
x-1 x + 1
-89-
(iii) Sx - 1
S2- -> M S X2-
whith (ii) the rate-determining step. The reaction thus occurs on a
constantly renewed sulphur or polysulphide surface, which explains the
reproducibility and the independence of electrode material, along with
the passivation effects at high current. Experimental work at lower
sulphur contents will be described later, where a marked change in the
anodic mechanism is seen along with a dependence on electrode material.
Some work has recently been performed involving anodic sulphide
behaviour at a liquid mercury electrode (128). However, this metal is
2- not inert to sulphide oxidation, dissolving as the complex Hg S2
and at higher potentials passivating theclectrode for metal dissolution
by the formation of a two dimensional HgS film.
The effect of adsorbed sulphur on the rate of organic oxidations
at a platinum electrode has been studied (e.g. 169). For some systems
e.g. formic acid, the presence of sulphur appears to accelerate the reac-
tion. This has been attributed to removal of surface oxides by the sulphur.
2.9.2.2 Other room temperature systems
Cathodic reduction of sulphur dissolved in dimethylsulphoxide at
a gold electrode has been studied using cyclic chronopotentiometry and
linear sweep voltammetry (129). The ring molecule S8 appears to be
the electroactive species with the initial product S87 which can further 2-
reduce to S82- or dimerize to (S8)2 . All reduction and subsequent
oxidation steps are irreversible. The S8 species seems to be quite
-90-
stable in this media (^' several weeks), but it is not certain whether
the S8 species is only formed at the electrode by adsorption or
exists in the bulk of the solution.
Sulphur has also been cathodically reduced in liquid ammonia by
exhaustive electrolysis yielding two electrons per sulphur atom indicating
eventual monosulphide formation (130). Linear sweep transient information
is somewhat ambiguous, but appears to indicate a certain dependence of
the reduction and oxidation potentials on electrode material. Chemisorbed
sulphur species were considered.
2.9.2.3 Fused salts
Not surprisingly, data for sulphur electrodes in fused salts is
very scarce indeed. Early work in equimolar sodium-potassium nitrate
established oxidation potentials at graphite for anions in the series
OH < NO3- < S2- < S042- < Cl (131). Voltammetric curves for sulphide
oxidation at platinum were also obtained in lithium-potassium chloride melt
at almost - 0.45 v versus PVPt2-1- (1M) (132), although this result has
not been confirmed (134). Potentiometry with a sulphur vapour electrode
in contact with graphite and a fused silver chloride electrolyte indicated
Nernstian behaviour with a two electron slope for both sulphide and sulphur
activity variation (133).
A potentiometric, voltammetric, and chronopotentiometric study of
the sulphur-sulphide electrode in fused lithium-potassium chloride at
420 °C has recently been published (134). The potentiometric system consis-
ted of a liquid sulphur pool (below the b.pt. of sulphur, 445 °C) floating
on the melt in an isolation compartment. Sulphide was formed by
coulometric dissolution from this pool using a graphite electrical
-91-
connection. Nernst plots were recorded with varying sulphide activity,
giving a slope corresponding to about two electrons (1.86 + 0.04 )
and a standard potential of -1.008 v (on the molar scale versus Pt/Pt2 +
(1M)). Presumably this refers to the interface S xIl 2-/S,.
q, C, with
the semiconducting sulphur pool providing electrical connection. However,
the electron number is somewhat below two, which indicates a contribution
from 2S2- •-2i S22-, i.e. redox polysulphide equilibria in solution.
Voltammetric curves were obtained "with only sulphur present"
(134) [presumably with the sulphur pool electrode, as elsewhere it is
stated that sulphur is insoluble in pure li/KC1 melt]. A cathodic wave
at about - 0.9 v. was obtained, along with an anodic wave at 0.0 v.
probably due to 2S + 2C1 S2C12 + 2e-. With sulphide also present,
under stirred conditions, linear potential-current plots were obtained
giving a cell resistance of 10-15 ohms, probably an IR drop through
the sulphur pool.
Anodic chronopotentiometric curves were recorded in these (polysul-
phide) solutions on gold and rhenium electrodes. Reasonable adherence
to the Sand equation was found with the single transitions obtained. The
-1 diffusion coefficient obtained (3.12 x 10 6 cm2 sec ) was calculated
on the basis of a two-electron oxidation. If however, the reaction
2S2- •e-- S22' is assumed, this corresponds to a one electron reac-
tion in sulphide which gives a diffusion coefficient of 1.32 x 10-5 cm2 at 420°C
- , sec
1 x/ a more reasonable value compared with other fused salt systems.
Unfortunately, the potential-time curves are not available, so any
check on the mechanism is not possible, (see Section 4.1.5).
The discharge of sulphide ions in various melts containing lead
ions in the temperature range 450 °- 700 CC has been studied (157).
-92-
Generally the discharge process on graphite was inhibited by formation
of a lead polysulphide film which became very thick (microscopically
observable ) at the high concentrations 4% MS) and current densities
0.1 amp. cm 2 )used. Tafel behaviour was usually seen, the slopes of
about 2RT/3F can be explained by rate-determining discharge of a
complex lead chlorosulphide species. However, only Langmuir conditions
were considered and the complexity of the system is somewhat daunting
The chronopotentiometric discharge of sulphide ions on a gold anode
in fused calcium chloride at 900 °C has been studied (158). For con-
centrations in the deciMolar range, sharp transitions were obtained I
with an (apparently) constant iT2. Assuming diffusion depletion of
sulphide ion and a two-electron reaction, a diffusion coefficient of t 945°C
2.1 x 10 cm2 sec-. was calculated. However, potential oscillations
at the end of the transition wave were seen, which indicates a possible
passivation process limited by diffusion away from the surface (c.f.
a liquid bismuth electrode system discussed later). This is supported
by some steady-state overpotential results which give a straight line of
overpotential versus log i with a slope of RT/2F. No explanation of
this result was given, but is consistent with a model of the potential
rise being entirely due to an accumulation of sulphur product by
-2e S2- --* Sads'
Sads
-0 Sgas , the adsorbed sulphur following a
Langmuir isotherm.
2.9.2.4 Sulphur species
The ability of sulphur to catenate in chains and rings is well
known; rings with six or more atoms have about the same bond energy per
-93--
and thus little "strain" from bond angle variation appears to be present (159).
However, the S8 form appears to be very common as evidenced for
example by the conversion from S6 to S8 under thermal conditions or
in the presence of free radicals (ref. 159,p107).
Liquid sulphur appears to involve an equilibrium between S8 rings
and linear-chain polymers, on the basis of which successful predictions
of viscosity and heat capacity data were made (160). This was confirmed
by paramagnetic measurements (161), the linear species having two
unpaired electrons per molecule. A rapid radical displacement reaction
- S. + -S-S -S*S + .S-
was required to explain all the spectral details, along with an S-S
bond energy of < 35 k.cals.mole 1 for a long chain compared with values
of 51 k.cal.mole 1 for S2 and 63 k.cals.mole 1 for an S8 ring
(162). Direct comparison of these results is uncertain as the latter has
been determined directly from thermochemical data and the former from
paramagnetic reasonance spectra. The decrease in bond energy with linear
polymerization has been attributed to delocalization of the odd electrons
at the chain ends with possible formation of a three-electron bond with
the adjacent sulphur atom (163). Polymer formation in liquid sulphur
commences sharply above 150 °C.
Dissolved sulphide ions combine with sulphur in many types of liquid
media to form polysulphide ions Sx2- of varying size having the characte-
ristic yellow or reddish colour. In some aprotic solvents, including fused
salts (e.g. liquid alkali halides above 400 °C), the nominally polysulphi-
de solutions often have a deep blue colour (135). This was originally
attributed in fused salts to S2 molecules (164), but it was subsequently
-94-
shown that sulphur itself is insoluble, at least in lithium-potassium
chloride, and the colour was suggested to be due to a polysulphide
species (165). However, combined evidence from U.V. and I.R. spectra
strongly suggests the presence of S2- (135) or S3 (136) ions,
analogous to the superoxide ion 02 .
2.9.3 Oxygen electrodes in aprotic solvents
2.9.3.1 General
Most careful work involving oxides as solutes has concerned either
fused alkali nitrates or chlorides as solvents. Some work has also been
performed in alkali carbonates and room temperature organic solvents.
2.9.3.2 Fused alkali nitrates
Much controversy has surrounded the question of stable oxide species
in fused alkali nitrates. Early work assumed that the oxide ion itself
was by far the most stable (e.g. 140), and (presumably) as the relevant
salts are difficult to obtain and preserve, carbonate or oxalate was
often used as solute, decomposition to oxide being assumed. Potentiometry
at an inert electrode using oxygen gas gave two-electron Nernst slopes.
However, one-electron Nernst slopes have also been obtained (141).
(These slopes all apply to oxide activity changes at one atmosphere 02 gas).
Subsequently, on the basis of rotating disk voltammetry involving oxide
solutes in fused sodium-potassium nitrate at a platinum electrode, Jordan
and Zambonin (142) have suggested that initially-added oxide is almost
wholly converted to peroxide and some superoxide by reaction with nitrate
ions. In the presence of oxygen most of the peroxide is converted to
-95-
superoxide. On the basis of the voltammetric work, this argument is quite
convincing, and also explains the one-electron Nernst slope sometimes
le obtained as being due to the equilibria 02 02(gas) (143). The
two-electron slopes are explained by stability of the species (e.g.
carbonate) added, thus dealing with a different redox system.
However, Kust and Duke (140) have obtained two-electron slopes
with "oxide" formed by coulometric dissolution of oxygen at a platinized
platinum electrode. Also, the use of the rotating disk technique is
not entirely unambiguous, as evolution of oxygen at the surface may effect
local equilibria markedly. The checking of these results using other
techniques, e.g. chronopotentiometry, where small quantities of charge
are passed during the measurement, has not yet been done; also no
careful potentiometric results with either a gas or an oxide-film electrode
involving unambiguous oxide solutes have yet been reported. Thus judge-
ment on these questions must be reserved.
2.9.3.3 Fused alkali chlorides
Potentiometric, steady-state overpotential, and chronopotentiometric
studies have been performed in lithium-potassium chloride eutectic using
oxide solutes (14, 144). With lithium oxide solute, a one-electron
Nernst slope was obtained at one atmosphere oxygen pressure, identical
potentials being observed at gold and platinum electrodes. This was
2e- suggested to be due to the equilibrium 2 02- 022- (144) or
n e w2 02 (143). No satisfactory potential response to oxygen
partial pressure variation was noted, which suggests the former equilibrium
2- involving peroxide generated by 2 02- + 02 -* 202 . A two-electron
Nernst slope at a platinum-oxide film electrode has been obtained,
although in an argon atmosphere (145).
-96-
Steady-state overpotential measurements were made using calcium and
lithium oxide solutes at gold and platinum electrodes in an inert
atmosphere.(14). Unfortunately only Ifoverpotentials" were recorded and
not potentials6gainst an external reference. Linear Tafel plots were
usually obtained with slopes RT/F, although reproducibility was a problem,
particularly on platinum (c.f. the aqueous systems). The overall
reaction 202- 45. 02 was assumed (although perhaps the
potentiometry indicates (near the rest potential) 2 02- -2e 022- ).
From an analysis of low overpotential-current relationships at a "bubbling"
oxygen electrode, the factor n/v.=---. 2.0 (where V is the stoichiometric
number - i.e. the number of times the rate-determining step appears
in the overall reaction). This, along with the Tafel slope, suggested
the rate-determining discharge of an oxide ion to give an adsorbed oxygen
atom, and is further evidence against the equilibrium involving superoxide
ions as in (143). The conclusion would stand unchanged if peroxide was
the overall product.
The chronopotentiometry also was recorded without an external
reference electrode (14). Reversible waves were obtained both in nitrogen
and oxygen atmospheres which fitted the soluble product model [i.e.
E = RT/nF.log [T2 - t2/ T2 ], with the slope Rly2F at higher (> 0.025 M)
lithium oxide concentrations. However, these waves appeared to be displa-
ced to a considerably more positive potential (-•' 0.6 v) than the rest
potential in nitrogen or oxygen atmospheres, suggesting that this equilibria
was not responsible for the potentiometric potentials. The potential-
time analysis suggests the reaction 02- -2e 0...M (-3 -a. 02 ) and
the diffusion coefficient of oxide ion was estimated to be-, 9 x10 5 cm2
1 at 450°C _ sec/ This value is rather larger than most metal ion values, and suggests
that the small uncomplexed oxide ion moves around easily in this melt,
( see section 4.5.2.2.)
-97-
2.9.3.4 Other aprotic solvents
Some work has been performed in room temperature organic solvents,
such as dimethylsulphide. Reduction of oxygen in this solvent occurs
in two one-electron steps to superoxide and peroxide (146). This has
been suggested (146) to be formally the case for all solvents, but in
protic solvents such as water, the initially produced superoxide ion
disproportionates to oxygen and hydrogen peroxide. No work on possible
formation and removal of oxide films has apparently been published in
these media.
2.9.4 Iodine electrodes
A considerable literature on the kinetics and mechanisms of the
iodide-iodide redox system at inert electrodes, chiefly platinum, exists.
By impedance (147), and rotating disk (148) techniques a rate determining
step of Iads for the anodic process was determined. This contrasts
with adsorption data from chronopotentiometry, thin-layer voltammetric,
and radiotracer experiments (149) which detect strong adsorption of iodide
but none in an apparently elect active state. However, it may be noted
that the adsorbed iodide would not be detected by the electrochemical
techniques if, at the end of the transient (chronopotentiometric or linear
sweep voltammetric), the resulting product tri-iodide (I3 ) ion was adsorbed
to an equal extent as the original iodide. This could be formed from the
iodide and the adsorbed iodine found to be present on anodically polarized
electrodes (149). These results can be further reconciled (167, 170) by
considering that electron-transfer from the iodide ion occurs in a second
layer, with the first iodide layer acting as a bridging agent similar
to halide-ion bridging from cationic redox systems, (see section 4.7).
-98-
SECTION 3 : EXPERIMENTAL ASPECTS
3.1 Apparatus
3.1.1 Electronic equipment
The basic electronic signals required to be supplied to the cell
were of galvanostatic orpotentiostatic type.
The constant current supply unit used throughout this study was
based on an original design by A.D. Graves, fully described for example
in ref. (13). This was a simple passive circuit consisting of a constant
D.C. voltage supply from units supplied by Benridge Lev. Ltd., fed through
a bank of high wattage resistors. The potential supply ranged from 15 v
to 80 v. By also varying the number and value of resistors in the bank
the resulting current ranged from 15 p amps to 30 ma, and was constant
within 0.2 milliseconds to at least 2%. Switching was facilitated by
fast mercury-wetted relays triggered from a 30 v. D.C. supply. Current
reversal was achieved by means of a second relay which switched between
two equipotential Benridge units with opposite polarity. The forward
pulse time was varied from one millisecond to ten seconds by means of
a capacitive circuit giving a time-delayed trigger to the second relay.
Potentiostatic control was available if required when a time galvanostatic
circuit was open by connection to the same ("make-after-break") relay.
Also, by separately opening the galvanostatic or potentiostatic circuits,
switching between these and an open-circuit condition via the relay was
achieved. Thus, a variety of transients could be supplied to the cell.
The potentiostatic circuits mostly used were either a simple
potentiometric battery-operated bias unit, or a Weir Minireg Type 401.1
power supply operated in the constant voltage mode. This unit has a rise-
-99-
time of a few milliseconds, which was judged sufficient for its purpose.
Faster potentiostatic control was available by means of a waveform
generator used in the square-wave mode. This had a rise-time of 1/10 th
millisecond for currents of <0.25 amps. This waveform generator,
loaned by Dr. P.F. Blackman of Electrical Engineering Department, also
supplied linear potential sweep transients.
These signals were fed between the micro-and counter-electrodes. As
in practice the counter-electrode incurred negligible polarization due
to its very large area and the presence usually of a very reversible rest
potential, no potential feedback arrangements were made from the
reference electrode. However, all potentials were measured against either
a quasi-reference, or a silver ion reference bulb.
Potential-time transients were recorded using a Tetronix Type
RM 564 storage oscilloscope, with a 2B67 time base and a 3A8
' operational amplifier unit. One of the two amplifiers in this unit was
used as a unity gain amplifier, with a very high impedence input and a
low impedence output. Signals from the electrodes were fed to the
oscilloscope via this unit to ensure that the current drawn from the
cell was negligible. The second unit was used to amplify the potential
scale to provide settings of down to 1 mV per cm. on the screen.
Steady or slowly-changing potentials were measured using a
Dynamco Type DM 200/MR.2 digital voltmeter. The entire electronic
assembly was earthed to a common source and mounted on a "handy-angle"
portable framework construction.
3.1.2 Furnace and temperature control
A vertical wire-wound furnace was used. The tube was made of alumina
-100-
and was 3" internal diameter and 17" long. It was wound logarithmi-
cally symmetrically from the centre with 16 S.W.G. Kanthal Al wire,
and the wire coated with alumina cement. The winding resistance was
about 20 ohms. The tube was lagged with a layer of "Triton" ceramic
fibre and placed in a box constructed with "Syndanyo" of dimensions
(19"x 19"x 20"). This was packed tightly with firebricks (Morgan Ltd).
The box was mounted on a "Dexion" frame and arranged to slide vertically •
by means of runners and pulleys at each corner together with counter-
weights at each side. This way the furnace tube was made to slide a
distance of 12" in the frame, which allowed it to be moved up slowly
to enclose the experimental cell contained in a pyrex jacket, fitting
closely into the furnace tube. The cell itself was supported by a water
cooled brass ring bolted to the top of the framing. This arrangement
enabled conditions of the cell to be easily checked when desired, and
also facilitated its slow heating and cooling. An earthed shield of
Nimonic 75 alloy lined the inside of the furnace tube to minimise electri-
cal noise. The furnace temperature was controlled by a Eurotherm P.I.D.10
controller. This is a variable proportional type. The controlling
thermocouple, of Pt/Pt, 13% Rh, was sheathed in alumina and inserted
near the centre of the furnace. A good constant temperature zone of
length about 7 ins. was obtained, in the centre of which rested the
fused salt inside the electrochemical cell. This could be controlled
to + 1 oC.
3.1.3 Electrochemical Cell
The cell is shown diagrmmatically in fig. 5.1. It consisted of
an outer pyrex envelope (A), of external diameter 70 mm. and length 14 in.
FIG-. 3. 1.
rELECT6OCRENICAL CELL
S
NoT 1$ 'AWES
TD S CASE
A
101
-102--
capped by a water cooled brass head (B). The pyrex pot (C) containing
the electrolyte rested on a pad of silica wool (G) at the bottom of
the envelope, For some experiments, in lithium /potassium chloride,
the electrolyte was contained in a vitreous carbon pot as the melt con-
taining sulphide was found to slowly attack the glass.
The cell head (B) fitted on the top of the outer envelope and
was sealed to it by clamping an "0" ring between a chamfered groove
and a brass ring (D) screwed up to it. Electrode leads, etc. were
contained in 6 mm outside diameter pyrex tubes (E) pushed through
holes in the cell head. There were six of these arranged in a circle
with an additional central hole. These holes, 7 mm. in diameter, were
countersunk at the top at 45 o to accommodate small (Wilson) "CV rings,
which were all pressed between the brass head and the tubes by means of
a circular keeper plate (F). This plate was screwed to the main body of
the head, which was also hollowed inside through which water flowed to
provide cooling. With the "0" rings tightly pressed a vacuum of at
least 1072 torr could be obtained. Movement of the tubes was facili-
tated by loosening the keeper plate. The six surrounding holes were
generally used for micro-, counter, or reference electrode leads, along
with a tube containing a thermocouple, and one for gas outlet, whereas
the central hole was used for solute addition and also a gas inlet. The
arrangement for this is shown in fig. 5.1. The B10 joint normally
contained a plug. When it was desired to add solute this plug was
momentarily removed and replaced with the arrangement (H) shown. The
joints were only very lightly greased on the top half of the ground glass
to avoid contact with the solute. Immediately afterwards, the cell was
evacuated and flushed with argon twice to remove any traces of air. The
solute was then introduced into the melt by carefully rotating the bent
-103-
tube upwards. This simple arrangement involving a direct fall of solute
particles into the melt was found to be necessary for the sodium
sulphide samples used, which were of loosely granular form.
For the aqueous work, the same basic cell arrangement was used,
except for a shorter outer envelope. A saturated calomel electrode via
an Agar salt bridge and Luggin capillary was connected to the cell
through the cell head, all these being clamped in retort stands. All
the aqueous experiments were performed at room temperature, 23 + 1 0C
under an atmosphere of argon.
3.1.4 Dry box
All loading of the electrochemical cell with solidified melt,
reference bulb solution, etc. was performed in a dry box under atmosphere
Pressure of nitrogen. This assembly consisted of a large mild steel
bos, with perspex windows and flexible rubber gloves for handling purposes,
as usual. The dry atmosphere inside the box was maintained by continuously
circulating it through a molecular sieve drying train. The pressure
inside the box was controlled by two electromagnetically operated valves
via a diaphragm pressure switch. The cell was introduced into the box
-1 through a vertical pressure port, which was evacuated to about 10 torr
and re-filled with dry nitrogen at least twice before the cell was placed
in the box.
Batches of purified melt were also stored in desiccators over mole-
cular sieve in the box, and these and some solutes were weighed out on
a Sartorious 2432 balance of sensitivity 2-200 gm.
-104—
Vacuum and as supply systems
Three separate rotary pumps were used for electrochemical cell,
melt purification, and dry box systems respectively. The types of
pumps used depended partly on their availability.
For the melt purification, a single stage rotary pump with a pumping
speed of 150 litres min 1 and an ultimate vacuum of 5 x 10 3 torr
was used (Edwards ES 150). For the main vacuum lines, one inch diameter
glass was used to maximise pumping speeds. These were fed directly via
precision-ground isolation taps (greased with Apiezon "N" grease) directly
to the purification cell (described later). Volatile compounds were
removed from the vacuum system by a liquid nitrogen cooled trap. The
vacuum was measured by an Edwards MA-5 Pirani head and a Model
7-2A Pirani gauge.
Side tubes controlled the entry or argon (H.P. grade) into the cell.
This was first dried by magnesium perchlorate and residual oxygen removed
by passing through calcium turnings at 500 °C. The pressure in the gas
line was recorded with a mercury manometer.
The vacuum and argon supply lines to the electrochemical cell were
similar. Here a double stage pump of speed 50 litres min 1 was used.
The ultimate vacuum was 5 x 1074 torr. (Edwards ED50). The outlet from
the cell was connected to a bubbler containing dibutyl pthalate to indicate
gas flow rates, and to avoid "sucking back" of air into the cell.
The dry box pump was connected directly to the pressure port. Here
an Edwards ES150 pump was used.
Generally, double-stage pumps were used where a good vacuum was
essential, provided that pumping speed was not also an important factor.
The melt purification required a good pumping speed to avoid appreciable
build-up of pressure in the cell upon melting and subsequent electrolysis.
-105-
3.2 Chemicals
3.2.1 Lithium Chloride - potassium chloride
To minimise working temperatures the eutectic mixture was used
(58.8 mole % LiC1 + 41.2% KC1). The lithium chloride used was Hopkin
and Williams G.P.R. grade and the potassium chloride was Hopkin and
Williams A.R. grade. Purification of this melt is necessary as the li-
thium chloride is very hygroscopic and contains heavy metal ions as
impurities. Attempts to remove the water by heat alone lead to hydroly-
sis of the salt. A number of different purification processes have
been used in the past, discussed for example by Wrench(14). The method
used in this study involved the vacuum pre-electrolysis of the molten
eutectic using a carbon anode and a stainless steel cathode.
The ball-milled mixture was melted in a pyrex container supported
in an outer jacket evacuated to about 1072 torr and heated by a coil of
nichrome wire. The electrolysis was performed using a potential of 2.5 v
and was continued until the current passed fell to about 1 ma. (for
about 25 cm2 of electrode surface area). When the current became
constant (this generally took about 4-5 hours), the melt was filtered
through a sintered glass disc by piercing the base of the vessel with the
steel cathode sliding in a precision glass joint. This process was
facilitated by applying a small pressure of argon to the jacket above the
filter, which was mounted above a cone which fitted into a socket, forming
part of the outer jacket. A full description and diagram of the apparatus
is given in (14). The apparatus used here was built on a larger scale then
described there, and was capable of producing up to 340 gm.of melt in
a single run. This was found to be a considerable advantage as less
time was spent on this procedure than if only 100 gm. of melt was
produced as previously. The purified melt was usually used within a
-106-
couple of days as'a number of workers were constantly requiring it. It
also gave a "breathing space" to allow for purification failures
caused, for example, by breakage of apparatus by thermal strain.
3.2.2 Sodium nitrate - potassium nitrate
Ibre again the eutectic mixture was used (45 mole % NaNO3 + 55
mole % KNO3). Both components were Hopkins and Williams A.R. grade.
This melt is fairly easily purified to acceptable electrochemical
standards by melting under vacuum. This was performed in the same
apparatus as used for the chlorides, but just allowed to melt overnight
under 1072 torr. vacuum, filtered to remove any solid particles and
stored in the dry box.
3.2.3 Aqueous solvent
Water doubly distilled from alkaline potassium permanganate solution
was used. The supporting electrolyte was Hopkins and Williams A.R.
grade sodium hydroxide, used directly.
3.2.4 Sodium Sulphide
Due to the availability of the sodium salt, this was used for all
experiments involving alkali metal sulphide solutions. Hopkins and
Williams M.A.R. or A.R. grade Nat S.9H20 was purified by a procedure
due to (15).
The hydrated salt was allowed to stand for a few weeks in a vacuum
desiccator over concentrated sulphuric acid in a warm place, e.g. near
-107-
a furnace. This procedure removed most of the water. The last traces of
water were removed by heating the salt to 700 °C in a silica tube in
a fast stream of hydrogen gas ("white-spot" grade, dried by passing
through magnesium Perchlorate). The resulting salt was of white, granular
form (estimated assay 99.5 - 99.8 %). Originally, pellets of this
material produced by a hand press were added to the chloride melt.
However, the salt was found to take a very long time to dissolve in this
folm, and subsequently the small granules formed in the purification
process were used directly. As these were porous, dissolution was much
faster. The solutions in the melts were always slightly yellow in
appearance, which suggested the presence of small quantities of sulphur
forming the characteristic polysulphide colour in solution. Some of this
sulphur undoubtedly arose by oxidation of sulphide species by impurities
in the melt although some also probably arose by self-hydrolysis by
traces of water left in the salt. The impurity could be detected
electrochemically by a small cathodic arrest on the galvanostatic charging
curves (see later) For the aqueous work, the dry hydrated crystals were
weighed as Na2S.9H20.
Polysulphides
Samples of sodium and potassium polysulphides ranging in composition
from M2S2 to M2S6 were kindly supplied by Dr. B. Cleaver's group
at Southampton University. These were prepared by heating together
alkali metal and sulphur in the appropriate proportions in an autoclave.
They were used without further purification.
-1o8-
3.2.6 Lithium oxide
This was supplied by Alpha Inorganics Ltd., U.S.A., and stored
under nitrogen until use. It was used in pellet form, the pellets
prepared with a hand press in the dry box.
3.3 Electrodes
3..1 Micro- and counter-electrodes
Electrode materials used were gold, platinum, vitreous carbon,
and liquid bismuth. The electrodes are reproduced in Fig. 5.2.
Initially a number of different sealing methods were used in order to
define a known exposed area, particularly for the gold. These included
sealing of wires in pyrex and other borosilicate glasses, and alumina.
The latter type was prepared by taking a hollow alumina tube of internal
diameter about 1 mm. and pushing a thin gold wire through it and
towards one end whilst holding this in an oxy-gas flame. This way a
hemispherical gold bead was formed at the end of the tube, giving a
good seal. However, on cooling the alumina tubes often cracked
and were also prone to cracking under conditions of an experiment. The
seals in pyrex were found to be even less satisfactory. Eventually,
it was decided to use electrodes of a small"Flag" type. These were
prepared for both gold and platinum cases by taking a thin ("J 0.010 in.
thick) sheet of metal, and cutting a square of about 3 mm. side. This
was then carefully spot-welded to a very thin wire about 2 cm. in length
at one corner, which in turn fused to a length of lmm. diameter silver
wire in a pyrex tube with an "Araldite" seal at the top. This type
lo9
ALL siteer sHerr
CO LL.
wiRe
lei Lictfrof htitAvo)/Kmos
flGr. 3-2 .
B($ MUM
WALKitsier nu<
age-V.9e
(a) Att, P-6 rile& - ELe ago? *
(&) 414. CotinfrEK e Le caop
)VIV 6003 eatgsdni eLce-rgoe
Si. (e)
erekNICs 0C13
-110-
of electrode, although lacking the precise area definition of a good
seal was found to have a reproducible area within at least + 5% by
dipping it into the melt so that the flag was only just below the surface.
By observing the length of wire also immersed, the area could be calculated.
This type of electrode avoids uncertainties in area associated with see-
page of electrolyte inside electrode seals. This can also lead to
spurious effects associated, for example, with the presence of a large
IR drop in this electrolyte film.
The vitreous carbon used was of cylindrical rod form 1/16th
diameter. (Vitreous Carbon Ltd.) Satisfactory seals of this material
were made in pyrex, although the end exposed was not ground flat as this
would probably have cracked the seal. Electrical connection was made
with a tungsten rod by means of carbon powder. The assembly was contained
in a single pyrex tube and "Araldited" at the top as before. The
liquid bismuth electrode was of an inverted "walking stick" type (see
diagram 5.2). The bismuth metal was purified by melting Analar bismuth
metal and filtering under argon to remove any solid particles. Small
pieces of this were dropped beforehand in the tube so as to form a liquid
resting in the "U" of the tube when molten. Some more pieces were
then added so that the meniscus of the metal just protruded above the
tip of the tube. This was then lowered into the melt. The surface area
was estimated from the diameter of the tube and the curvature of the
interface.
A large ("J40 cm2) gold sheet, spot welded as in the case of the
solid micro-electrodes was used as the counter electrode.
3.3.2 Reference electrodes
For both the chloride and nitrate melts, a silver-silver ion refe-
rence solUtion in the appropriate melt contained in a pyrex bulb as
membrane was used. This type of reference was originally developed by
Inman (16). At melt temperature the pyrex is sufficiently conducting
with a high impedance instrument such as a digital voltmeter to act as
a good membrane, presumably through alkali metal ions. The silver ion
solution was prepared by anodic dissolution of a large silver flag
electrode, using a bismuth pool electrode in a separate compartment as a
counter. The concentration was about 10-2 M, well inside the Nernstian
concentration region.
For the aqueous studies'a saturated calomel electrode was used as
reference, using an Agar-KC1 salt bridge via a separate IN-NaOH solution
and Luggin capillary.
It should be noted that Luggin capillary arrangements were unnece-
ssary for the melt work as IR drops are very low in these systems.
Any IR drop appearing at higher currents in the galvanostatic work was
allowed for by measurement of the potential gap occuring at the
beginning or end of the transients.
3.4 Experimental Procedures
3.4.1 _Apparatus preparation
All glassware in contact with melt, etc. was cleaned by prolonged
soaking in 1:1 nitric-sulphuric acid mixture, followed by thorough
washing with distilled water and acetone, and drying in an oven at
about 200°6.
_112-
The metal electrodes were prepared new each time, and cleaned by
boiling in concentrated hydrochloric acid, followed by washing with
water and- acetone. The gold, but not the platinum, was heated to
redness in a flame. Heating of the platinum was avoided as it tends
to oxidize at elevated temperatures.
The cell was assembled by first cleaning the brass cell head with
fine emery paper, and inserting the electrodes, etc. through the rubber
Wilson seals. This was then screwed down tightly on to the outer envelope
containing the reaction pot and reference bulb. This assembly was then
transferred to the dry box via the pressure port to dry out overnight.
Just before commencing an experiment, the melt used as solvent was weighed
out (usually about 80 gm.). Also the silver ion reference solution was
added to the reference bulb, and connected to the silver wire acting
as the reference electrode metal by means of platinum wire tied around
lugs on the outside of the bulb and tube above it. A number of the bent
tubes for solute addition were also weighed with sodium sulphide or other
solute. The cell assembly was re-assembled, removed from the dry box,
and connected to the vacuum and gas lines by means of ball-and-socket
joints. After evacuating and flushing with purified argon three times,
a vacuum of 10 2 torr was obtained, the furnace was raised to enclose
the furnace slowly, and the cooling water was turned on. On melting,
the electrodes and thermocouple tube were lowered into the melt in their
final positions.
2.4.2 Electrochemical Measurements
The standard "three electrode" arrangement was used. Current was
-113-
passed between the micro and counter electrodes and the potential measured
between the micro and reference electrodes.
On equilibrating a melt at the correct temperature with the electrodes
in position, it was first checked for (electrochemical) purity by passing
a series of anodic and cathodic galvanostatic pulses. These were
recorded on the oscilloscope. An absence of potential time alests up to
the cathodic and anodic limits was regarded as a reasonable criterion of
purity. (These limits are,for the chlorides,lithium deposition on the
cathodic side and metal electrode dissolution or chlorine - evolution on
the anodic side). Also the apparent electrode capacitance was measured
by taking the potential-time slopes at varying currents. This capaci-
tance was seen to vary with the melt sample and was usually around 100-
150 pF. cm2
for platinum and gold electrodes. As this is somewhat
higher than normal double layer capacitance values (17), these oeing
about 40-50 pF. cm-2
, some faradaic reaction must be assumed to be
taking place. This could be reaction of small amounts of impurities
or perhaps dissolution of the electrodes. It is interesting to note that
similar values were obtained using the "fast charging" galvanostatic
technique (18) for platinum electrodes at least for potentials < -1v
versus Pt/Pt2+ reference electrode and ascribed to an oxide film build
up. This is possible with traces of oxide and water in the system
The capacitance, however is fairly constant over the whole potential range.
It is probably very difficult if not impossible, to set up a completely
polarizable electrode system comparable with analogous aqueous systems
in these very hygroscopic melts. In the sodium-potassium nitrate melt,
however, apparent capacitances of double-layer value, 20-30 F. cm 2
were usually obtained with platinum and gold electrodes.
For the experiments in fused chlorides, sulphide was studied at
concentrations above 1073 M. This was because, below that level, the
chronopotentiograms tended to decrease in length with time, probably
due to oxidation of the sulphide ion by impurities in the melt. In
the nitrates, the waves steadily decreased with time at all concentrations,
indicating slow oxidation by the nitrate ion (19).
Steady-state current-voltage plots were recorded by applying a
series of potentials and recording the resulting steady-state current
by measuring the potential drop across a standard resistor. Measurements
were taken with both ascending and decreasing potential.
The chronopotentiometric potential-time.traces were taken with the
widest possible range of currents possible (generally 300 p amps - 150 ma.
CM 2 ), various currents being repeated from time to time to check the
stability of the system. After each trace, the system was allowed to
re-equilibrate for a couple of minutes before repeating. Most measurements
were checked this way for reproducibility.
The galvanostatic potential build-up and open-circuit decay curves
were also recorded on the oscilloscope using time bases tip to 5 sec.
per cm. screen distance.
Platinum sulphide and oxide films were built-up under constant
potential conditions recording the growth-time with a stop-watch before
stripping the film galvanostatically, recording on the oscilloscope.
All oscilloscope traces were recorded on Kodak FX-120 film using
Tetronix camera attachments. The negatives were printed and enlarged
to "enprint" (postcard) size for ease of data analysis. Measurements
-were taken from the prints using an accurate (4- 0.1 mm) ruler. A grid
pattern was present on the photographs to correct for any distortion of the
printing paper.
-115-
SECTION 4
4.1 The sulphide/sulphur electrode on inert electrodes in lithium
chloride-potassium chloride eutectic
4.1.1 General Introduction
The bulk of the experimental work was concerned with a predominantly.
kinetic investigation of the sulphide-sulphur redox system on inert electrodes
in fused lithium-potassium chloride in the temperature range 3600 - 550°C.
The following description has been separated into two parts. The initial
potentiometric and chronopotentiometric study (sections 4.1.2, 4.1.3)
provided an outline of the electrochemical mechanism. In particular, the
latter technique yielded strong evidence for the presence of an inhibiting
sulphur film formed on anodic polarization. This was further investigated
by means of other techniques described in section 4.1.4.
4.1.2 Reversible 2otentials- .potentiometrz
4.1.2.1 Results
On dissolving anhydrous sodium sulphide (purified as in section 3.2.2)
in purified LiCl-KC1 eutectic melt, open-circuit potentials on a variety
of electrodes (Au, Pt, vitreous carbon) were soon established which were
independent of the electrode material. The melt containing sulphide was
always found to be a very pale yellow colour, probably arising from the
presence of. small quantities of dissolved sulphur (as 522-) as an impurity
in the Na2S. At low (-J 10-3 M) sulphide concentrations, the potential
initially drifted slowly positive with time, although at higher concentrations
41.
$
■••
POTENTIOMETRY OF Nd.iS IN
Ti-I1UM CHLORIDE — POTASSIUM CHLORIDE
/yr 1-37t
—068 •
-0-57
—056
E VOLTS (v's. SAIC).
—0.55
O.54
-o.53
4 -0.51
-0.50
0 SLOPE =7f rev.
2.3.(01))fir 2F
M IS MOLARITY OF NO SOLUTION!
to 1.6 t.i 20
LOG„ (rt x (03).
-117-
it was rather more stable. Measurements were taken of rest potentials
(against the silver reference electrode) versus bulk sulphide concentra-
..1 tions in the range 5 x 10 10 M for various temperatures between
, 420 0C and 530 °C. Linear plots for potential against the logarithm
of the sulphide concentration were usually obtained, with a slope of RT/2F
(e.g. fig. 4.1.1).
Dissolution, particularly at the lower temperatures (<420 °C) was
slow, the sulphide often taking up to two hours to dissolve completely.
A solubility limit of l M at 440 ° e C appeared to be reached, as
no potential shift above that corresponding to this concentration occured
with additional solute present, even after ten hours.
...
4.1.2.2 Discussion
The most reasonable interpretation of the two-electron slope obtained
is to assume the redox equilibrium 2g - 7,4g 822- is operative. This
yields the Nernst equation •
RT r 2-] E = E° —7 In [ sr 2
(assuming activity coefficients are unity). Thus, on adding a constant
ratio of 1822-1' / S2- ], the resulting apparent Nernst slope of
RT/2F will be obtained. It will be seen later with cathodic voltammetry
(section 4.1.4.2.1) that the polysulphide concentration is indeed propor-
tional to the total added sulphide concentration.
4.1.3 Chronoptentiometry
4.1.3.1 Introduction
This technique was used to obtain at least a qualitative picture of
-118-
the mechanisms (and possibly kinetics) of the oxidation of sulphide ion
and the reduction of sulphur. Sulphur itself is known to be insoluble
in LiCl-KC1 eutectic (134), and vapourises from polysulphide solutions
of high sulphur content at the temperatures considered (3600 - 5500C).
Thus it was decided initially to study the anodic oxidation process
from nominally pure monosulphide solutions at a gold electrode, which
appeared to be inert under these conditions. However, some cathodic
chronopotentiometry using added polysulphide solute was also performed.
4.1.3.2 Anodic chronopotentiometry
4.1.3.2.1 Results
On adding low ("... 2 - 5 x 10 3 M) concentrations of sodium sulphide
in the temperature range 3600 - 4500C, unusually elongated but neverthe-
less distinct potential-time arrests were seen (e.g. photo 4.1.1). If the
anodic galvanostatic pulse was applied from the rest potential, no apprecia-
ble initial "double-layer charging "region was seen. However, if the
starting potential was made more negative by pre-biasing, a sharp initial
potential rise was seen, changing slope at the rest potential (photo 4.1.1).
With varying current densities, transitions recorded from a constant poten-
tial obeyed the Sand equation reasonably well (fig. 4.1.2), although an
intercept on this plot was obtained which, analyzed according to the SAR
model (section 2.7.2.3) yielded an approximate adsorption intercept of 700 p
coulombs. cm 2( fig. 4.1.3). However, with negative prebiasing, the waves leng-
thened markedly for a given applied current density (photo 4.1.2), until
• the starting potential reached the limiting current for polysulphide reduction
(see section 4.1.4.2.1).
With increasing sulphide concentration, the transition became sharper
-119-
and above "' 2 x 1072 M, particularly at lower current densities (< 1 ma
cm a ), it had the form of a potential-time "ramp" leading to a short pla-
teau near the end of the arrest (photo 4.1.3). The potential at the
end of the arrest remained constant with varying current density, however.
I The IT2/AC product was approximately independent of concentration C
and had the value 450 + 100 amp.cm.sec2 mole 2 at 430°C.
Current reversals from various points on the anodic potential-time
arrests were also taken. Typical results for the high concentration
(> 2 x10 2 M) waves are seen in photo 4.1.4. The potential regions for
both the waves seen remained constant with varying current density, indica-
ting reversibility. The ratio forward/reverse transition times for the
first reverse wave was about 6 - 8, increasing somewhat with sulphide concen-
tration. No similar simple relationship was found for the second (plateau)
arrest. (This was studied from the anodic steady-state, as discussed in
section 4.1.4.2.2).
If sulphide solutionS were used with some added polysulphide, similar
results were obtained, but with a smaller deposition potential region and
a smaller IT2/AC constant.
The observed behaviour was largely independent of electrode material.
However, results on platinum were less reproducible than.on gold, particularly
on samples having a thick PtS film (see section 4.3). The arrests on
vitreous carbon were somewhat less "sharp", particularly at the end of the
transition.
Above"' 450°C, the end of the transition became less distinct,
particularly at lower current densities; for temperatures> 500 °C,
measurements of T were only possible for currents above 30 ma. cm2
I With varying temperature, the iT2 products varied somewhat irreproducibly;
however, from an Arrhenius plot, an approximate activation energy of
-120-
—1 rsj 6 kcal. mole was deduced.
A second, ill-defined wave of irreproducible length was also
seen; it,had a quarter-time potential of + 0.60 v + 0.1 v (versus
S.M.S.E.). This has previously been observed (134), and attributed to
the formation of S2C12, presumably from chloride ions discharging on a
sulphur layer on the electrode surface.
Occasionally, with nominally pure sulphide solutions, radically
different anodic waves were seen. These were of two types. (i) A
reasonably sharp inflected wave (e.g. photo 4.1.5). This was originally
attributed to a change in mechanism due to the presence of adsorbed
sulphur as sulphur appears to be required in the solution to yield the
effect. However, further experiments showed that sulphur did not
necessarily induce the effect. The waves increased in length for a given
current density with increasing negative pre-bias, but generally were con-
siderably shorter than the "ramp" type for given concentration and current I
density conditions. Sand's behaviour was found (a constant iT2 product),
indicating no appreciable reactant adsorption; also an approximately
-1 constant iT-2./AC 4̂ 150 amp. cm. sect- mole was obtained. However,
the waves decreased in length with time.
The potential-time characteristic fitted a reversible one-electron
model (fig. 4.1.5). On current reversal, a small reverse wave
(T forward Treverse = 8 - 10) was obtained, whose "quarter-time" potential /
[ + 0.09 v at 430 °C (versus S.M.S.E.)] coincided with that for the
forward wave (i.e. reversible behaviour) (fig. 4.1.5). In addition, a
second reverse wave (rforward T reverse = 3-3.5) was obtained at similar /
potentials to the first reverse wave for the "normal" (ramp) type waves
described above.
(ii) Occasionally, on first adding monosulphide to the melt, a "splitting"
0
0/
01, 0.3 Ot 0-5 0.4 0.7 01
"71 T. - CURRENT PER ELECTISo'DE.
121
F1&.tLZ. SAN) nor - AWYPIC, CiftiONO fOTENT1OMETAY
OF Sz- IN uce-kce. .
1-53°C, Au ELEc.TRoToE , AREA 0-IS 6 cre
Ctiatzq =1.19 x , La- Me...
SEC
1-0
• ,T,Jf. L SLOE)
517 Atli°. crt
1.3.
121.0T OF SAR AliSogerioN MODEL-
TATA FR414 f lG. '11.2.
3.2
1. 6
1-2
!mean- a.. —750 jk.couottss.
12#2,
0.t 01 - 1.6 2.0 irk sEcis:
12+ (wo its)
FIG-. 41.'
•
CNeoNoroTENTIollTRIC WAVE ANALYSIS -
IEVERSIBLE " MOTEL
(moil PHOTO .
N a x S ce- Vet , 1-35°c,.
Au. EtetTROE
0 240 E MV. 2Z0
• 100
T-- 1-35°c. 2 3 RT MV.
0 SLoPE = it5 mv. \0
0
O
0.6
Lo irk LOG„ ty
-125-
of the "ramp"-type wave into at leasttwo longer waves was seen. The first
was usually very sharp (small potential range); also large potential
oscillations and maxima were seen (photo 4.1.6). However, this phenomena
usually disappeared with time (^' 15 minutes) resulting in stable ramp-
type waves. A similar "splitting" effect occured with high polysulphide
concentrations, or sometimes with high (^' 10 -1
M) sulphide concentrations.
4.1.3.2.2 Discussion
The form of the normal anodic potential-time curves (e.g. photo 4.1.3)
is rather unusual; the large ("J 0.6 v) potential range indicates a consi-
derable variation of reactant or product activity (or both) during the
diffusion-limited process. Initially it was considered that the waves were
formed by limiting diffusion-depletion of sulphide ion at the electrode
surface, i.e. the simple chronopotentiometric case (section 2.7.2). However,
the increase of the iT2 product with increasing negative pre-bias, along
with the eventual loss of the arrest at temperatures appreciably above the
boiling-point of sulphur (445 °C), are evidence against this model.
Moreover, the results can be explained on the basis of the soluble-product
passivation model (section 2.8.2), which predicts a constant iT2 product
at low current densities i, with an increasing iT contribution at
higher currents from the charge required to form the passivating (or inhi-
biting) film. Thus the model predicts an algebriacally similar result
to the chronopotentiometric reactant-adsorption model which is observed
here. The passivation model considers that the diffusion-depletion of the
reactant is not the limiting process. This requires that the actual
diffusion coefficient for sulphide ion is markedly higher than the derived
value ("J 3.4 x 105 cm2 sec 1 )on the basis of the Sand equation.
-126-
The value given is about the average value for complexed cations in fused al-
kali halides (4). However, there is some evidence that single anions
have markedly higher diffusion coefficients e.g. for S2- in fused CaC12
at 945 °C, D = 2 x 1074 cm2 sec-1 (158); for 02- in LiCl-KC1 at
450 °C, D > 1074
cm2 sec 1 (14). The passivation effect is considered
to be due to the formation of a very thin ("J few A° thick) solid film
of sulphur onthe electrode surface formed by anodic oxidation from
sulphide. This can dissolve as Sx2- (134) and diffuse away from the
surface. Eventually, the sulphur coverage (and polysulphide surface con-
centration) will reach such a value that large areas of the electrode
are "blocked" (i.e. unavailable for electron-transfer). The current
density will then rise sharply on uncovered areas, with the result that
local sulphide concentrations fall rapidly towards zero, causoing a rapid
potential rise. The charge determined for passivation 700 p coulombs
CM2, approximates to a close-packed sulphur monolayer (-J750 p.coulombs.
CM-2). Thus the effect of the potential pre-bias on the wave length is to
lower the initial sulphur (and polysulphide) surface concentration and
thus to require a greater increase of this to occur to reach the critical
0 passivating value. At temperatures above 450 C, sulphur (boiling pt. =
445 °C) can be released as gas bubbles from the electrode surface, thus
delaying and eventually preventing the high-coverage passivation effect,
at least for long observation times (low i) as observed.
It follows that most of the potential change during the transition
must be due to an increase in the product (sulphur) activity. Since a
deposition range of at least"' 0.6 v is encountered a large free energy
change in the sulphur layer with coverage must be involved (for a two-
electron reaction, 0.6 v E AG° of 27.5 kcal. mole 1 , neglecting pre-
exponential effects)(see section 2.5.4.3). The observed change in the
-127-
potential-time shape with varying current density indica_t es a complex time-
variation of the sulphur activity change, although passivation occurs at a
constant overpotential.
The weight of evidence strongly suggests that the sulphide-sulphur
redox couple exhibits reversible (Nernstian) behaviour under the conditions
encountered. Although the complex form of the anodic chronopotentiometric
transients do not permit the application of simple mechanistic models,
both the first and second reverse waves showed no potential-current density
dependence; also no current dependence of the forward arrest potentials were
seen.
The occasional departures from the small "ramp"-type waves Pi) and
(ii)] may be ascribed to changes in the form of the sulphur film on the
electrode surface. The reverse one-electron waves (i) are tentatively
ascribed to the separate equilibria
-le
S2- S...M ±S2 ...M 4 2S22-
thus involving the redox couple S2- / S2 . The wave analysis requires a
le
"dne ion 4==t one ion plot to yield a straight line of integral slope.
The small "reversible" reverse wave may be ascribed to S2 reduction,
most of which is converted in the following fast chemical step (large K)
to S22- species which explains the simple 3 : 1 = forward : reverse
transition-time ratio seen for the S22- reduction wave, required for a
reversible soluble product model (section 2.7.2.4). Qualitative evidence
exists for the S2 ion (section 2.9.2.4).
The lengthening of the transition time with negative pre-bias may here
be ascribed to either a decreasing electrode "blocking" effect by adsorbed
sulphur, or an increasing concentration of free sulphide ion, as opposed
-128--
to disulphide ion (S22-) in the diffusion layer. This will effect the
transition-time as diffusion-depletion of S2- ion is the limiting
process.
The wave "splitting" effect (ii) must be due to a distinctly
different activity-time relation for the formation of adsorbed sulphur at
constant current density. It is interesting to note that markedly longer
anodic transition times (photo 4.1.6) can be obtained for an electrode
behaving this way than with the "ramp"-type waves. This is further indica-
tion that the limiting process for these normally-obtained waves is
polysulphide diffusion away, rather than sulphide diffusion to the
electrode surface.
4.1.3.3 Cathodic chrono,potentiometry
4.1.3.3.1 Results
Very small cathodic chronopotentiograms close to the rest potential
could be obtained from high (> 2 x 10r3
M) concentrations of sodium
sulphide. This is undoubtedly due to the presence of some disulphide (S22-)
present in the melt as an impurity, as considered above. However, for a
more quantitative characterization of the cathodic reaction, potassium
polysulphide was added (as K2S6) to the melt at 420 °C. Deep blue solutions
(section 2.9.2.4) were formed and sulphur vapour was first rapidly, then
slowly evolved from the melt until, after a few hours, only a pale blue
colour remained. This it was only possible to roughly estimate the
concentration of "dissolved sulphur". However, reproducible cathodic
chronopotentiograms were obtained on gold electrodes (photo 4.1.7) which
obeyed the Sand equation well, and yielded a quarter-time potential
-0.570 v at 420 °C versus S.M.S.E.) independent of current density and
0.`C 9.Z "tz -17.1 0 ►
AZ "S9 Z
'')c,SN7
3 CoV_I:Jr13
1)9C-"6-17( ahi -?) NI 9-47 t)i
'CP LI+ 0101-id WChU) Stiol oml A- No 3NO ii) -14101W .318.1S93A3 „
- SI SKM\IV 3Vt" 01913140111\13.10dONOVI-1)
°A14 4,L=
0+
09
OZ1
741 - 0471
091
081
4%1
-130-
approximately, polysulphide concentration. Good fits were obtained to the ,
wave analysis plot E versus log [T2 - t2 / t], with n = 1.8 (fig. 4.1.6).
Other models yeilded non-linear plots and markedly non-integral slopes.
Reverse-current chronopotentiometry produced rather ill-defined anodic
transitions (photo 4.1.7), with Tforward / Treversec
3, as expected
• for the simple soluble product model. 1 _1
An approximately constant value of IT2/AC = 1900 amp. cm sect mole .
was obtained, although this value is probably too low due to sulphur
evaporation.
4.1.3.3.2 Discussion
Polysulphide reduction on inert electrodes was found to be a simple
reversible process unhindered by the presence of sulphur films, as
expected, since these are removed rather than formed during the reduction
reaction. The process observed experimentally when K2S6 was added
probably involved the S4.-5 ion as the potential-time analysis fits
4- 2e the mechanism S42- 47==± 2S22- reasonably well (fig. 4.1.6.). However,
it should be noted that the chronopotentiometric wave analysis assumes that
the initial product concentration is zero. In this case there are likely
to be some S22- ions present which can distort the first part of the wave,
where its logarithmic concentration is changing most rapidly (96).
Assuming a two-electron reaction, the Sand equation yields a value D>
_4 _1 1.2 x 10 cm2 sec for the polysulphide diffusion coefficient, whilst
a four-electron step yields > 3 x 10 5 cm2 sec . This may be taken as a
rough lower limit for this quantity.
-131-
4.1.4 The application of other electrochemical techniques
4.1.4.1 Introduction
The chronopotentiometric study described above indicated that the
formation of a sulphur "film" on the electrode surface region was
dominating the anodic behaviour of the system. Other forms of electroche-
mical perturbation were found to provide rather more insight into the
nature of this film. The results obtained using these techniques
are described below.
4.1.4.2 Results
4.1.4.2.1 Steady-state voltammetry
Steady-state current-voltage plots for a stationary micro-electrode
in an unstirred solution were recorded for monosulphide solutions in the
temperature range 370° - 540 °C, in both anodic and cathodic directions.
In the cathodic direction, inflected current-voltage curves leading
eventually to a limiting current (at about - 0.65 v at 430°C) were obtained.
This limiting current was approximately proportional to the sulphide
concentration such that ilim
[S2-1 n:f. 24.0 ampcm moles 1 .
In the anodic direction, surprisingly linear plots of current
density against overpotential were obtained (fig. 4.1.7). At low
("a 5 x 10-3 M) sulphide concentrations, the linear region extended to at
least 200 mv. from the reversible potential and passed through the origin.
The currents at a given potential were increased markedly with stirring.
At higher overpotentials, the currents fell increasingly below this line.
High overpotential data was difficult to obtain as considerable current
fluctuation at constant potential (and vice versa) was obtained. However,
there appeared to be a limiting(?) current at about T1 = 0.5 v. From
FIG-. +1.7. STEADY-STATE ANopic, Cm(3ENT-
PoTENT)AL. PLOT .
PE ELEcTfnE AREA = 0-169c-il l.
E-Nct2S] =731 x io3 M. T= 1-35°c.
0
too --
90
70 _ /LAMP. ELE'crRne .
60 -
50
tO
30--
len
0
0 20 0
0 - 0/ I 0
OVERNTENT(AL 1-)
40 8o I2A 160 Zoo 21-0 2 0
-133-
cathodic stripping (see section 4.1.4.2.2) this potential is identical
with the "plateau" potential formed on the chronopotentiograms. With
increasing sulphide concentration, the initial linear I/V region was
reduced in length (e.g. at 3 x 10-2 M, is only valid to 11 = + 100 mv);
but the current-voltage slope was roughly proportional to sulphide con-
centration. With increasing temperature, the linear I/V
slopes increased such that an Arrhenius plot could be drawn, giving
an activation enthalpy of 5.5 + 1 k.cal. mole 1 . For temperatures
> 450 °C, a decreasingly distinct current rise at + 0.5 v was obtained
(c.f. chronopotentiometric results) although, due to current fluctuation,
the measurements were rather inconclusive. No noticeable hysteresis
effects were observed, and identical results could be obtained using either
the galvanostatic or potentiostatic methods.
4.1.4.2.2 Cathodic galvanostatic charging
It was originally noted during the anodic chronopotentiometric studies
that the reverse (cathodic) pulses showed a considerable charging (coulombic)
process to be present, at least at potentials positive to the polysulphide
reduction wave, yielding pseudocapacitances (Cads) of at least 0.6 - 1.0
mF. CM-2 (see section 2.5.3.2).
A series of cathodic galvanostatic charging curves from steady-state
anodic polarizations were recorded; some typical results are summarized
in table 4.1.1, and photos 4.1.8, 9. It is seen that for the region below
= 150 my (at least for low S2- concentration), Cads typically has
the value rs, 4 mF. cm . Above that potential the capacitance decreases
somewhat. Measurements for overpotentials < 100 my were difficult, due to
a contribution from the polysulphide reduction wave. Generally, however,
Cads was fairly constant at low (< 200 mv) overpotentials, but gradually
Ti-1-11LE tr. I. A.7).5oRPrionl es 5uyoc Relict-wee F611
CA )(C aavitosiffrio TRAtiserliS — TAKE-Ai FROM
Elotpic sTr.faf STS .
11.= +160101V.
L MA. etc':
C Mr. all:
C Mr cfl. AT Vats] AT C ricti.s3 = 5.7x icr3t1 to-21.
11.3 1, 1-.5 20-5 /79 t.2 3t-5 5.35 4.55
AT It
t1.3 Z. 3.3 2o5 24 2.95
3(6.5 2-3. 2-7
Osogi/Ttem PsexpocApe,, 4Thwee C je vAt
EEC44. 2:36) secnal .
Aw e(,ecrifoE =4-.32°C. ANOIC, sit Aliy-srATE ovefearfoAt.
+25ortv. ()KA fog Ctldts3 = 5.7 x I/1MM
fRoti Rao. 4111') •
-135-
decreased up to the "plateau" overpotential regionl(Photo 4.1.9.).
Temperature effects were also studied. At low (< 200 mv) overpoten-
tials the pseudocapacitance appeared to be approximately (+ 5%) independent
of temperature (in the range 370° - 540 °C), but at higher overpotentials
increasing "curvature" of the transients was seen which led to decreasing
pseudocapacitances, with increasing temperature. This can only be a
rather tentative statement, however, as Cads was only decreasing by
rsj 10% over this range, which is comparable with the experimental reprodu-
cibility.
4.1.4.2.3 02en-circuit decay and galvanostatic potential build-up curves
As a complementary study to the anodic steady-state work, observations
were made of the open-circuit potential-time decay from, and the potential-
time galvanostatic build-up to steady-state anodic overpotentials. Decay
curves were initially recorded; some typical results are shown in photos
4.1.10, 11. In unstirred solutions, the transients were highly reproduci-
ble, although at low temperatures ("a 370 °C) some potential oscillations
during decay were sometimes present. The behaviour was essentially inde-
pendent of electrode material, but distorted curves were obtained for
platinum with thick Pt S films present.
Very good fits were obtained to a semi-logarithmic time dependence;
E = K + b log (t + e), where K and b are constants, and e is an
adjustable parameter (fig. 4.1.9). This behaviour algebraically corresponds
to ILovichian kinetics (section 2.4.6), as well as for decay under slow
charge-transfer conditions (section 2.5.3.6). This equation fails near the
end of the decay, but can be linearized by the use of the rate equation
suggested by Eley (ref. 54, see section 2.4.6.4). (fig. 4.1.10 ).
-136-
It was generally found at least for decay from overpotentials
< 100 mv. that the logarithmic decay slope b was directly proportional
to the starting overpotential, whilst e was a constant (fig. 4.1:11).
This proportionality held at least down to very low ("J 10 mv) starting
overpotentials. The potential where the linear I/V relationship for the
steady-state failed appeared to be similar to where the linear decay
slope/starting potential relationship also failed. In the latter case,
the decay slopes usually were lower than expected above this point, together
with a marked decrease of &, i.e. the initial (dE/dt)t.0 slope
increased. For decay from very high (>. 300 mv) overpotentials, markedly
non-logarithmic decay behaviour was observed.
At low overpotentials (< 100 mv) the decay phenomena (as a function
of overpotential) was independent of the bulk sulphide concentration.
At higher overpotentials, the decay rates increased and the decay slopes
decreased below direct proportionality with starting overpotential as the
sulphide concentration was increased. This is entirely analogous to the
steady-state behaviour.
Electrolyte stirring markedly hastened the decay process. Rather
irregular fluctuations were observed, but generally turbulent agitation
of the electrolyte (or electrode movement) produced a rapid fall to a low
overpotential.
Galvanostatic potential-time build-up curves to the anodic steady-state
were also recorded. Interestingly, the approach to steady-state low
overpotentials (< 100 mv) was exactly symmetrical with the corresponding
decay curve (photo 4.1.12). At higher overpotentials, the build-up log.
slope increased above that for the corresponding decay.
On close inspection of both the build-up and decay curves an initially
sharp potential change was seen for N 5% of the total potential change
-137-
with a slope (dE/dt) roughly increasing in proportion to the sulphide
concentration.
Some measurements were taken of build-up and subsequent decay curves
from various points on the build-up curve (and vice versa) (Fig. 4.1.12).
These curves were found to obey the Boltzmann Superposition Principle (see
following discussion). Potential-time curves following a step increase or
decrease of current density were found to be completely analogous to the
effects observed with open-circuit conditions described above, at least in
the low overpotential region.
High current galvanostatic stripping was applied during these various
transient conditions. Approximately similar E-t curves were obtained
compared with stripping from the corresponding steady-state potential.
Some decay curves were also taken from low cathodic overpotentials.
The curves for very low (< 50-100 mv) overpotentials were very similar to
the anodic results. However, for higher overpotentials distorted non-logarith-
mic curves were obtained, the initial decay rates being markedly faster.
The effect of temperature (in the range 360° - 550 °C) was also
studied for simple decay curves as for the other measurements described
reproducibility was no better than ± 5%, but reasonable Arrhenius plots
for decay rates for 1 < 100 my were obtained, with an activation
enthalpy of 6-8 kcal. mole-1 . The effect of temperature on the logarithmic
decay slopes was extensively studied. It was very difficult to reproduce
slope data for a given temperature to less than 5-10% after a temperature
cycle. However, in general, decay slopes taken from overpotentials
< 100 my were constant with temperature in this range, although some
slight (") 2 - 5%) downward trend with increasing temperature was often
seen. From higher overpotentials, particularly> 200 my., a marked slope
/0
0
NO
0
0
P.1
NO
0
0
M-. if: l.9. roi-EwriAL— LoG.TIME 'tor fall °FEN—
CIRCUIT 'DEW CURVE FRotl 111\101c.
STEAPY-STATE .
so
72
64-
56
fl
Au ELEcrgoTE
Li\laz.S3 =211- x10-211.
'DEM Fgort 1=100 MY.
/ WO
OK
_ E isiv.
FALL
no
0 A
In
8$ 0/
21-
40
32
4---
LINE fot
E --:1 •6- LoGio(k +80);
wiiege e ,-- O-53 SEC, .)
t- =--- 51- MV.
I . . 1 I _ I . I . I
0 o.2 o.4 0.6 as (.0 1.2. Lk 1.6 1.s 2.0
LoG-10-E, 1 (k,=01-tot sec).
MY. 16
+0 04zot SEC.
±,
F1G.1-.1.I Oa,.
ANALTS1S OF POTENTIAL—TIME' 1E.CAY CURVES —
RUA-1'100MM PUE TO ELEY, (SEE SECTION 2.4-.1/0.
ALSO SEE OVEJ
ELEcTRoVE
1ECV Friotof E LSOPIV. =t1, 0 Elqat.Si =1:3I X 163 t1.
T= 1-35 °G. o 0
0
Is,
0 0
EZ
— OvEgpoTENTIAL
(x IN SEenol
t_oPE. a" +6 sec-.1
O N
01 o
FIT To (2_ n
Lo-i - @- - nit co
4ST.
(EON. 2.2.) SECTION 2.9-.6.1). 0
14-0
0
o/
o/
go
eEorRock SLOPE =330 M.= er
23 BE
IN SEcnol 2.4.6"1-).
0
40 go 100 loo
t, 4-o
-6, a 0.420t seC.
A
16o
Ito
120
100
20
0
1G-.+. 1. 1 1 . fiELATI04 E:TWEEN LOGARIT4flie XECAY S1.0fE AACD
STEDY-STM STARTING- OVERF0TENTIOL
— AS 4- (51-Cotial), Lc: et -Kee 2 Tr--- 1-35t, . ft eLECTOPE
1+1
L.44,63;0E00 s Lae, riv, rimiriereg e
goIrki.E=-- '1,0G-,(t+0 +K.
7-31x16411 -Nays
21txtetti-t1eS
1
4-0 $ 0 120 I‘o Roo zit Iso E mv. STAKTIMer oVEkforEtirrIAL.
I
1
rTS. TAKEN 'Ff PLOTTING- LeNerlis G-I, (2c) - A aairiST CuVC Cl P'S -136LoW
YRS
At GliciiwosrATIC SviLD-Oe To flo-OrtV.=11
SDE — OPEN-NMI DEW 'Mut.% eguiLD— -
UP ASC ogn
c
1.4
LIZ. rt./. USTRA TIM Or THg Afatcool op SareflANN'S
S UPEReoS Man) eginteLE TO erOLVANOsThriG Oft- Ctgas ir Tea( TRAristarrS . NA= 0"m, ua-Kce.
T. +37°c.
1÷2._
2 see .3wisi641-1,
20 MV. piviste0-'
Co tieLETE CURVE AZC NoT fpwrIcAL. wrni C&j. (RELATiVELY ilia-I4 OvEAPoTeuttftt. (v-156 tiv) 059 3or s ourlmilaN 15 stILL VA*
fo *PbCrei'( tArpek OKYinf&- cosyrioNS.
6o
68
FIO tI.13. lierEo€Nice OF LoOARITIIMIC DECAY SLoPE oN eoTENTioSTATC
FORMATION 'TIME la AT vivo PoT6NitAL
STEAPY- STATE ANOIC OVCRedreNTIAL = 150 my
LowEli oVEANTENTIAL = 100 Fly .
ENdisi = 2.75 x10411 .
I.E..cTRol)C. r=- 411C.
0
Sca-GsiRN DECAY SLOPE MV.
0 LOG-tc:r SEC.
54,
50
aI oz O•3 01 05 o.6 o. al t.o
141i
increase with increasing temperature was often seen (typically 10-20%
over this range).
Some open-circuit decay curves were recorded after stripping
galvanostatically (e.g. photo 4.1.14) or potentiostatically to lower po-
tentials from steady-state anodic overpotentials. In the latter case, the
resulting decay slopes (b) depended on the time (t1) the potential was
held at the lower value. These slopes gave an approximately linear b =
K log t1 plot (fig. 4.1.13).
4.1.4.3 Discussion
The data outlined in the last three sub-sections, together with the
chronopotentiometric results, have resulted in a general, if in some aspects
tentative, model for the anodic behaviour of this system. The separate
pieces of evidence arising from the various results will now be discussed
in turn, followed by a discussion of the resulting model.
4.1.4.3.1 Steady-state voltammetry
(i) Cathodic polarization
The cathodic waves obtained under steady-state stationary electrode
conditions were certainly due to polysulphide reduction, as observed
chronopotentiometrically (section 4.1.3.3). The wave shape cannot be
analyzed theoretically by the simple reversible voltammetric equation 2.4.3
(section 2.7.1.2) as the sulphide bulk activity is not zero. However, the
more cathodic region can be approximately analyzed as here the variation
of reactant activity with potential is dominant; this yielded an approximate
2e two-electron slope in agreement with the mechanism S22_ RF=t 2S2-.
From equation 2.41 (section 2.7.1.2) for the limiting current of the
-145—
voltammetric wave, a very approximate polysulphide concentration may be
calculated. Thus, assuming 8 (diffusion layer thickness) 5-10
x 1073
cm.(184),D, 2_ ts, 5 x 10-5 cm2 sec _1;
from equation 2.41 it °2
is calculated that about 2 mole % of S22- impurity is present in the
added sulphide. However, this is only a rough estimate.
(ii) Anodic polarization
The linear current-potential plots seen (fig. 4.1.7) on anodic
polarization are very unusual (They were not due to simple resistive IR
drop as open-circuit decay was slow and continuous over the entire potential
range - see later). To the writer's knowledge, only two examples of this
linear behaviour, at least over a wide range of potentials (> 0.1 v), have
previously been reported (185, 186), both concerning the anodic oxidation
of hydrogen.
There is a theoretical difficulty in accounting for such plots. Thus
(186), the rate-determining step was considered to be a reaction between
adsorbed OH radicals and hydrogen. The OH radicals were considered to
obey a Temkin isotherm, yielding a linear dependence of potential on
coverage (for OH e Mads)( see section 2.5.4.3), thus apparently yielding
the desired kinetics. However, the Temkin isotherm is derived on the basis
of non-equivalence of adsorbate with change of coverage; hence the presence
of kinetically, but not thermodynamically, equivalent OH radicals has to
be assumed.
The observed dependence of the sulphide anodic ITV curve on stirring
is indicative (but not proof, see later) of a reversible fransport-controlled
reaction. Normally then, one would expect an inflected-type voltammetric
wave leading to a limiting current following equation 2.43 (section 2.7.1.2)
-11+6-
+ne [or a derivative of this for the general case mX ± nY, where
m / n ]. However, this is not obtained here; linear I/V plots being
obtained with current densities, even at high overpotentials much below
(4( 20 %) the expected sulphide limiting current density on the basis of
equation 2.41. This indicates that little of the marked concentration
overpotential observed for this system can be ascribed to changes in
sulphide surface activity.
A general difficulty exists, however, in the description of the
system in terms of a single, reversibly-formed polysulphide product (e.g.
S22-). It is reasonable to assume that the polysulphide ion activity is
directly proportional to the concentration (suggested by the potentiometric
results above). Assuming quasi-equilibrium at the interface, the potential
must be proportional to the logarithm of the polysulphide activity. Further,
by Fick's first law (e.g. ref. 12, p. 160), the current will be proportional
to the activity gradient in diffusing species across the diffusion layer
adjacent to the electrode. Hence assuming a simple transport-controlled
mechanism, the normal inflected-type waves will be obtained, and the linear
I/V plots observed cannot be explained. [It should be noted that any,
say sulphur, film formed on the electrode surface in electrochemical
equilibrium with the sulphide and diffusing polysulphide species, cannot
affect the potential independently of the ionic species, irrespective of
the isotherm followed by the film. This follows from a simple extension
of the argument given in section 2.3.7 ].
The thermodynaic impasse mentioned can be removed by assuming that
sulphur dissolution from the surface is the rate-controlling step, the
product of which (polysulphide species of varying rank) are not in
thermodynamic equilibrium with this surface species. Bodewig and Plambeck
(134) have shown that polysulphide, and not sulphur, is soluble in
-147-
LiCl-KC1 at 420°C. This reaction may be thought of as "dissolution"
occuring not only at the electrode, but also in regions some distance
from the surface as the sulphur chains initially attached to one sulphide
ion become redistributed between the excess of monosulphide present.
Thus the stirring dependence observed can be explained (also see section
4.1.4.3.3). The approximate direct proportionality between the linear
current/potential polarization slope and the bulk sulphide concentration
can be simply explained by considering that the sulphur dissolution rate
increases in proportion to the number of sulphide "acceptor" ions present
in the surface region. The reaction thus will be "Sx" (surface) + S2- -$
•
Sx 1
2-. No direct relation between the thermodynamic free energy of
sulphur polymer species and the effective dissolution rate is expected.
To account for the linear sulphur concentration (coverage) - potential
relation it is necessary to consider that the sulphur polymer species in
electrochemical equilibrium with monosulphide ions follow a Temkin isotherm
(section 2.5.4.3). Some thermochemical data for polymeric sulphur is
available (as mentioned in section 2.9.2.4) as evidence for the free energy
changes with coverage required. Thus the heat of scission of a polymeric
sulphur bond is < 35 kcal. mole , whereas diatomic sulphur requires
^J 65 kcal mole for dissociation (161). The former low value has been
ascribed to stabilization of the resulting (two) chain segments by resonance
involving the unpaired electrons to form "three-electron bonds" (163).
This argument implies that the bond dissociation energy for polymeric
sulphur (e.g. Sx
Sx -
S) does not undergo any reduction with increa-
sing chain length (i.e. both Sx, Sx - 1 exhibit this "three-electron
resonance stabilization" whereas S does not). This has yet to be
confirmed. However, an effective reduction in bond energy from, say
-148-
2 S2 S4 (2 x no resonance -0 1 x resonance) to 2S4 -0 S8 (2 x
resonance -> 1 x resonance) would result from this theory. This
qualitatively yields the required free energy increase (-AG ) with
increasing sulphur chain length. Entropy effects may also be invoked.
This will be considered in the next two sections, along with further
discussion of the sulphur surface model.
4.1.4.3.2 Cathodic Galvanostatic Charging.
The results indicate a considerable '" 3 - 4 mF. cm 2 )adsorption
pseudocapacitance Cads
for galvanostatic reduction, at least in the
anodic overpotential region 7] < 200 mv. Moreover, at least for the
region fi 100-200ravC ds is approximately constant, tending to a
decrease slightly with increasing overpotential. This suggests that a
Temkin isotherm (for the reducible material) was followed, and is in
agreement with the anodic steady-state results discussed above. The Cads
values decrease slightly with current density, indicating a small diffusion
contribution. This could arise from some re-adsorption, at longer
observation times (lower currents) of the preceding steady-state anodic
reaction. The potential-time profiles, however, did not appreciably
shift with respect to potential with varying current density, which is
further evidence of the reversibility of the sulphide-sulphur system in
this media (with respect to electron-transfer). The small potential shifts
observed can be ascribed to the increasing effect of higher sulphide
surface concentration formed during stripping pulses at higher current
densities, thus affecting the Nernstian activity ratio.
A problem does-arise in the interpretation of such "stripping curves"
in this case, as the product was not definitely identified. Thus,
complete reduction to S2-, or only partial reduction to soluble Sx2-
may occur. Moreover, a mixture of products may result, depending on the
potential and/or current density applied.
A charge of at least 1.5 m. coulombs cm-2
is estimated to be
stripped from the start of the "plateau" film region down to the rest
potential. This is at least twice the charge required to passivate the
electrode under chronopotentiometric conditions as described in section
4.1.3.2.2. However, the chronopotentiometric result does refer to the
condition of previous high-current anodic pulses, whereas the cathodic
stripping result is the reducible charge taken from a previous anodic
steady-state. As seen in table 4.1.1 reducible charges from previous
anodic chronopotentiometric pulses are considerably below those from the
corresponding anodic steady-state. This suggests that a "film relaxation
process" occurs so as to lower the free energy (and thus potential)for a
given coverage with time.
In principle, the temperature dependence of Cads
should distinguish
between enthalpy and entropy changes giving rise to the overall decrease
of the adsorption free energy with coverage (Temkin isotherm). Unfortunate-
ly, the accuracy of the results (> + 5%) coupled with the relatively small
temperature range available 12% in °K) do not allow a definite conclusion
to be reached. Very tentatively, the observed T dependence of Cads
at low overpotential (<200 mv) indicates that enthalpy changes are
dominant from equation 2.34, 2.35 (section 2.5.4.3)1. At higher
overpotentials, the decreasing Cads with temperature can be ascribed to
an entropy contribution [as MS = - AG, neglecting 6H].
The enthalpy changes are presumably associated with a decreasing
bond energy with increasing sulphur chain length (see previouS section).
Chemisorption to the electrode itself is unimportant, as seen by the
independence of the various phenomena on the electrode material.
-150-
The dominant effect is thus "self-chemisorption", involving chemical bonding
of the adsorbate to neighbouring molecules to form polymers, rather than
no rural chemisorption to the substrate itself. The decreasing entropy with
increasing coverage can be understood in terms of decreasing freedom of mo-
vement of the polymer segments. The system could, in principle be
quantitatively treated by the "two-dimensional imperfect gas" concept for
mobile adsorption (section 2.4.3). It is interesting that the smooth
Cads profile below the "plateau" is qualitatively similar to that observed
for the (analogous) surface pressure-area plots for polymer adsorption at
liquid-air interfaces. These lack the discontinuities attributed to 2d-
phase changes for other mobile adsorbing systems (see section 2.4.7.2).
The potential-time redUction arrests seen from potentials above the
"plateau"region (photo 4.1.9) were analyzed according to equation 2.30b
for the irreversible desorption model (section 2.5.3.2). Reasonably linear
plots of E versus login (T-t) particularly in the latter half of the
arrest were obtained with slope " RT/2F. In this(reversible) case, if
the product activity change can be neglected the model can apply, but (xn
is replaced by n in equation 2.30 b. This will most likely be towards
the end of the transition, as observed. The two-electron reaction could
be due to, e.g. (S8(ring) --> S82-, the reactant being adsorbed according
to an equivalent site (Langmuir) isotherm.
4.1.4.2.3 Open -Circuit decay and galvanostatic potential build-u2 curves
An observed dependence of the rate of an electrochemical reaction on
stirring is often used as conclusive evidence for the presence of a rate-
determining transport step to or from the electrode surface, as opposed to
a rate-determining chemical or electrochemical step occuring at the
-151-
electrode (e.g. ref. 2). The argument is partly based on the assumed
existence of a e'Nernst") diffusion layer whose thickness (commonly",10 3 cm)
depends on the stirring rate, within which no convective stirring takes
place. However, strong evidence exists,(184) to suggest that some convection
persists down to very small (",molecular distances) from the electrode
surface, and thus the diffusion layer concept is only useful in practice
because diffusion, rather than convection, becomes the dominant mode of
transport near the surface.
Thus, the stirring dependence for the open-circuit decay rates observed
above does not necessarily preclude the involvement of a rate-determining
surface reaction, providing that convection effects can effect the rate of
such a reaction, (e.g. dissipation of a structured film away from the
surface). Indeed, some of the results described above are very difficult
to explain on the basis of a transport-controlled reaction, as will now
be discussed.
(i) The decay rates observed were much slower than qualitatively expected
for a transport-controlled diffusion process away from the electrode surface.
(ii) The logarithmic time-dependence of the process is difficult to
reconcile with transport control particularly if an associated linear
relationship between potential and sulphur coverage is applicable (logarith-
mic Temkin isotherm), as suggested by the steady-state and galvanostatic
stripping results discussed above. Thus the E = b log (t + K) relation
can be transposed to q = bi log (t + K) (q is the coverage (surface
"charge") of sulphur). This represents Elovichian desorption kinetics
(section 2.4.6), which is compatible with the activation energy increasing
linearly with the progress of the reaction.
(iii) The complete symmetry between the galvanostatic build-up and open-
circuit decay curves at low overpotentials cannot be explained by rate-
-152-
diffusion controllingpradients. In both cases, the rates will be determined by the
diffusion gradient for the product which obviously will lead to non-
symmetry between net current and open-circuit conditions.
The effect of stirring can be explained as a convective disturbance
of the sulphur layer formed adjacent to the electrode surface, leading to
dispersion of the film in the surrounding electrolyte and the accelerated
dissolution of film. Thus potential decay rates are enhanced, asthe
potential is related to the sulphur activity at the surface.
The question now arises of the nature of the activated surface
process giving rise to the observed build-up and decay phenomena. A signi-
ficant experimental finding was that the logarithmic slope for decay and
build-up (in potential units) increased in proportion to the potential
difference between the initial and final states. This has been seen
(for potential decay transients) with systems exhibiting activated high-
field ion conduction through very thin films of varying thickness (see
section 2.3.8). [ In these cases decay phenomena refer to approximately
constant film conditions and to decreasing potential assistance for the
irreversible process (section 2.5.3.6.).However, such a mechanism cannot
be operative here, since the observed decay slope also decreases continu-
ously to zero as the starting overpotential falls to zero. For the high-
field case, a limiting low decay slope must be obtained, usually related
- to monolayer film conditions (but see discussion for oxide films, section
2.6.3).
A reasonable mechanism involves the concept of a number of%ites"
where film growth occurs, which are proportional to the imposed current
density (for a given S2- concentration). These are considered to be
"created" or "destroyed" very soon ((0.1 sec) after switching on the
current, or opening the circuit respectively, and "grow" to a fixed
-153-
equiibrium size, all such sites being kinetically eauivalent . Schemati-
cally, the mechanism is :
S2- 4-2xe
_ Sx
S(film)
Thus, the steady-state current-potential condition corresponds to equilibrium
for the film formation process from the "precursor" unit Sx.
Direct proportionality between the logarithmic slope and the overpoten-
tial difference eventually attained can thus be explained, as growth
to or from higher overpotentials involves a greater coverage (and hence
potential) change for a given fractional change in site size. The potential
will be directly proportional to the sulphur coverage if the Temkin isotherm
is obeyed (indicated by the voltammetric and cathodic stripping results
discussed above). The small, but sharp potential change (dE/dtalS2-1)
seen at the beginning of both build-up and decay transients could be
due to the formation or dissolution, respectively, of these sulphur
"precursors" required as site "foundations" from which film growth or
decay occurs.
A similar, but modified, model considers that each imposed current
density defines a given type, rather than number of sulphur precursor
units. In both cases the rate of film dissolution per sulphur atom will of
course be the same for a given current. However, the former model considers
that with a higher current, a larger number of identical units will
dissolve, whereas the latter considers the same number of units, but with
each unit consisting of a long polymer chain. In the light of the steady-
-154—
results (section 4.1.4.3.1), the latter model appears to be more reasonable.
These chain segments, acting as film precursors (as before) are considered
to form the film by a "relaxation" process (see below), the kinetics of
which could beindependent of chain length. As was previously discussed,
(section 4.1.4.3.1), the steady-state results indicate a similar departure
between thermodynamic (Temkin) and kinetic (film dissolution) properties
of the layer.
A significant finding is the good agreement of decay and build-up
curves from the non-steady state (i.e. during previous build-up or decay
curves respectively) with Boltzmann's Superposition Principle. This
phenomenological law was first stated for the delayed elasticity of solid
matter, and subsequently widely verified, particularly for polymer systems,
under small stresses and strains (187, 188). It states that the "stress"
(e.g. increase in length of a specimen) experienced by a system at a given
time is a function of the entire strain (e.g. loading) history, and that
each strain increment applied at a given time makes an independent contribu-
tion to the final strain. and thus such effects are additive.
Thus it is seen (fig. 4.1.12) that for a given build-
up with a subsequent decay curve from a non-steady state (i.e. along BDE),
the decay BDE is identical with decay CGH if allowance is made forthe poten-
tial change along BC. In this case, the "stress" imposed is equivalent
to the current density, whilst the analog of the "strain" is the potential
(or sulphur coverage). Further, the linear increase of the build-up or decay overpotential
slope with the eventualAdifference is in agreement with the principle,
along with the total symmetry of the build-up and decay curves. (It is
also interesting to note that the steady-state linear ITV plots on this
formation are a direct analog of Hookes' Law for steady-state elasticity.
-155-
i.e. stress at strain.)
However, the problem of a molecular interpretation still remains.
In the field of delayed elasticity ("viscoelasticity") of polymers,
molecular interpretations have been very scarce, which is not surprising
considering the extreme complexity of the molecular processes involved
in the concerted movement of polymer chain segments. The applicability
of the superposition principle, with its implication of a "memory" effect,
suggests the involvement of time-relaxation processes set in motion by the
initial perturbation (e.g. stress). This (often implicit) idea has led to
a description of the viscoelastic rate equations (often linear in log t)
in terms of a large number of "segments" having a distribution of relaxa-
tion times, each segment relaxing exponentially in time (i.e. a first-order
process) (187). (However, an infinite series of exponentialswith adjusta-
ble coefficients is hardly diagnostic of mechanism :). A mechanism which
involves "freezing" of material in new configurations as strain proceeds
(as for conventional fixed-site adsorption kinetics, section 2.4.6)
is obviously ruled out.
Thus it may be useful to describe the sulphur film as a two-dimensional
polymer undergoing (with build-up and decay transients) two-dimensional
perturbations analogous to three-dimensional bulk (volume) deformation.
[ Here it is increase in coverage at fixed surface area ], with an imposed
external pressure. Boltzmann's Superposition Principle usually holds for
such polymer systems at low stresses (187). However, this only suggests
that the phenomenological behaviour of the two types of system are similar,
and as the molecular processes are obscure for the 3d-case, little of mecha-
nistic value can be gained per se.
To investigate the temperature dependence of the kinetic parameters,
two effects need to be considered; (i) the isotherm coverage-potential
-156-
relation and (ii) the net observed T-dependence of the potential-time
transients.
(i) has been considered in the previous section - Cads was tentatively
found to be independent of temperature. Thus the observed T-independence(ii)
of the decay slopes at low overpotentials can very tentatively be
attributed to an increasing entropy of activation for the film relaxation
process, giving rise to the Elovichian kinetics (The T.-dependence of rates
is chiefly due to activation enthalpy). This suggests that the activated
complex for the film relaxation process has a decreasing probability as
the film growth proceeds, perhaps involving a decreasing number of relaxa-
tion "pathways" available for the polymer segments.
The very good fit obtained to the "Key" plot (fig. 4.1.10) (see
section 2.4.6.4) indicates that a first order process is in operation.
The existence of the first-order term can arise from a decreasing number
of available sites for further growth as the film grows, or (for film
removal) a decreasing number of polymer segments left to desorb as the
removal progresses.
A process having kinetics logarithmic in time was also observed for
partial potentiostatic reduction of the film, followed by subsequent decay
after various times (fig. 4.1.13). This provides further evidence of the
spontaneous time-relaxation effect mentioned above.
Comparisons with previous work
As discussed briefly in section 2.9.2.3, Bodewig and Plambeck (134)
have published a potentiometric, voltammetric, and chronopotentiometric
study of a sulphide-sulphur electrode formed by cathodic dissolution from
a liquid sulphur pool. The potentiometric data of this and the present
work cannot be directly compared, as the former work deals with various
-157-
polysulphide ions of unknown concentrations and chain length. Although
the "sulphur activity" in solution is formally defined as unity, if it is
in equilibrium with a pure sulphur phase as in (134), this state obviously
cannot be compared a priori with solution activities in the dilute (Henry
Law) region.
The extremely low diffusion coefficient determined for "Sx2- "
by anodic chronopotentiometry on gold and rhenium (-sJ 3 x 10 6 cm2 sec-1 at
420°C) (134) is very suspect; a more likely mechanism is limiting soluble
product passivation by sulphur (see section 4.1.3.2.2). The calculated
value of the diffusion coefficient (if a limiting diffusion-depletion of
sulphide occured) is dependent on the assumed electron number (see section
2.7.2.2). This cannot necessarily be assumed from the Nernst slope (as
done in ref. 134) as the product may not correspond to the other species
comprising the zero current redox equilibrium. For the general reaction
xS2- 2xe xS, xS + S2- S x
2 - 1 ; • the electron number n 1 +
(for x a 1) and n-0 2 (for high x values). For n = 1, the calculated
diffusion coefficient for "Sx2- " becomes 1.32 x 10-5 cm2 sec 1 .
However, even this (limiting) value is still somewhat lower than the lowest
"reasonable" value obtained for cathodic chronopotentiometry of x2-
(X 4), described in section 4.1.3.2.2 Pc 2- > 3 x 10 5 cm 2 sec 1 ).
This strongly suggests that another mechanism (i.e. passivation as mentioned
above ) is the limiting process in ref. 134. Unfortunately, the potential-
time plots were not published and therefore no check on the mechanism
is possible.
-158-
4.2 The sulphide-sulphur electrode on inert electrodes in sodium
nitrate-potassium nitrate eutectic
4.2.1 Introduction
Having obtained the rather unusual results described above for the
fused chloride electrolyte system, it was thought desirable to see if the
general behaviour could be reproduced in other solvents. The behaviour
in low-temperature solvents such as water (see section 4.6) indicated
complete irreversibility for the S2-/S redox couple. Therefore some
measurements were made in a low-melting fused salt system, sodium nitrate-
potassium nitrate eutectic, at about 250°C at gold and platinum electrodes.
4.2.2 Results
On adding "J 10-2 M of Na2S to a NaNO3-KNO3 eutectic melt at
250°C, very negative (NJ -1.1 -> 1.2 volts versus S.M.S.E.) rest potentials
were obtained. The values for gold tended to be somewhat (NJ50 mv) more
positive than for platinum, but no steady values were obtained. The
solutions were a very pale yellow colour. The measurements reported here
refer to 2-5 x 10-2
M solutions, above which sulphide dissolution became
extremely slow.
On the application of anodic galvanostatic pulses between 1-20 ma cm -2
complex, but reproducible, potential-time plots were seen (photo 4.2.1),
similar for both Pt and Au electrodes. The slope and potential regions
. for the complete arrest changed somewhat with current density. The initial
arrest plateau occured at about the same potential with varying current,
but the end of the arrest and the initial E-t'amp" became more positive
-159-
with increasing current density i such that a linear Tafel slope of ^'
RT/F was obtained. The 1ength of the waves slowly decreased with time
(") 10% per hour). Reasonable agreement with the Sand equation (section
2.7.2) was obtained (fig. 4.2.1). Diffusion coefficients calculated
from these plots were low (^' 5 x 107
cm2 sec ), but uncertainty existed
as to the precise sulphide concentration. No satisfactory reverse waves
could be obtained.
Occasionally, at low current densities (0.2 - 2 ma.cm-1 ), irrever-
sibly shaped waves were obtained on gold (photo 4.2.2). The waves were
shifted anodically with increasing current density with a Tafel slope of
RT/F. Linear plots of E versus logio ('r2 _ t2) were obtained, with a
slope of 2RT/F.
Steady-state anodic polarization yielded linear current-overpotential
plots similar to those observed in the fused chloride (fig. 4.2.2). Except
in the high ( T > 0.6 v) overpotential region, no hysteresis between
ascending and descending potential scans were obtained. The current at a
given potential was raised on turbulent stirring. The results were appro-
ximately independent of electrode material, although Au gave less stable
currents which tended to decrease with time. The electrode could be
"regenerated" with cathodic pulsing. No build-up of sulphide "phase" films
on platinum was seen (contrast section 4.3).
The open-circuit decay phenomena from steady-state overpotentials were
also very similar to that observed in the fused chlorides (photo 4.2.3).
Thus the curves fitted the equation E = b log (t K) (fig. 4.2.3),
with the b slope increasing in direct proportion to the starting overpoten-
tial, within the linear current-potential region. Above this, the decay
curves became increasingly distorted. However, the galvanostatic build-up
curves were not symmetrical with the corresponding decay curves (photo 4.2.4).
0
I. i14.SECji. Ct1 2
1.0 z.o 3.0 M
40 5,0
IS CUMENr PER ELECTRO,C
I6o
ANotc Cl-iroNCATENTiotlEifVf OF Sz- tom
tN MA,N01- KNo3 SAN, eLoT
Pk EL Cr A REA — 6.21-7 crtt
[Nhs] ". 3.5 x Le 11.
250°C.,
o -
(174- SL-0 Pe 74.
0A
0 o 6
161
fl . 1%2.2 . A
STEW —STATE N 01) IC
+0 CuMENT fo-rENTIOL ftzer A toN IN I\Ia 0
E EcrRoPE 0 A
T= 2,54}-t
Ate. 30 ROYE:i.
ELEZTRoDE 0 AREA
0 0 A A
0 ASCeM1)1N6- POTENTIAL
A j)ESCINJANCr POTENTIAL
0 A
0 0
0A
0 to
0A
0 0 a
-11 41 -0.1 -0.7 -0.6 E voLTs (vasus s.rts
0
00
A 0
o°
A
40
0
POTENTIAL— LOCr.T1t1E. PLOT FOR OPEN —
CitiGuIT PECAY CURVE rfforl ffNOPIC.
STE.Arr—STptTE (rAkem FRoti Niro .
320 ELeafo)E 1= 25` .0
1)ec41 Hort It= '366 my.
0 / 2110
E Mv. 0/
210 FALL. 0
162,
200
1 0
LINE Fog
[20 = LOG,, (.6 +X)
WHERE K = 0-05 SEC,
6 = 11-5 mv.
0
0
0.8 2.0 2:1- 3.Z
Loa-1;C( 57.54,1 :4 Ste-.
-163-
Cathodic galvanostatic stripping from the anodic steady-state
overpotentials (photo 4.2.5) yielded stripping profiles dependent on
the current density. The initial reduction pseudocapacitance (the higher
dE/dt slopes in photo 4.2.5) was about. 0.3 mF cm 2 leading to a much
higher pseudocapacitance ('s' 3 mF. cm72 ). The potential-time profile was
shifted negative, approximately linearly in log i, but with varying slopes.
The pure melt itself yklded capacitances < 100 pF cm 2 on
galvanostatic charging.
On adding sulphur pellets, the rest potential slowly drifted
positive (.' 200 mv) and sharp chronopotentiograms were formed close to the
rest potential. These gave a linear plot of E versus logi n (T2 - t2 )
but with slope 0.8 RT/F. On current reversal, co-incidence of IT E TA"
values were obtained, with Tforward
/ T reverse 2. These waves, however,
rapidly shortened with time, gas evolution occured and eventually (after
^' one hour) the melt became colourless, only a wave close to the anodic
limit being obtained.
4.2.3 Discussion
Unfortunately, the gradual loss of the sulphide by (presumably)
oxidation by the nitrate melt precluded any satisfactory quantitative
studies. Sulphide has been reported to be oxidized to , S032-,
5042- in molten NaNO3 at 3300C (189). Sulphur appears to accelerate
this process, as the residual wave which eventually remained after adding
sulphur to the solutions of sulphide in NaNO3 - KNO3 was probably a
e nitrite oxidation wave, N0-2 NO2 (190).
Sulphur has been reported to react with LiNO3-KNO3 eutectic,
N20 being evolved (191). This explains the gas evolution observed.
-164-
The electrode kinetic behaviour of sulphide in NaNO3 - KNO3 (at
"250oC) appears to be intermediate between the observed behaviour in
LiCl-KC1 and alkaline aqueous solutions• Thus "passivation" - type
chronopotentiograms were obtained, the limiting process probably being
inhibition by a (soluble) sulphur film as for the chloride melt (see
section 4.1.3.2.2) rather than limiting diffusion-depletion by sulphide
ion as suggested by the very low diffusion coefficient calculated on the
basis of the latter model. However, some irreversible aspects were noted.
'Thus, on anodic charging, a species was produced with an associated Tafel
slope of RT/F. This suggests an irreversible formation of sulphur
(n = 2, = i) under these conditions.
The irreversibly-shaped chronopotentiograms occasionally seen on
gold are rather similar in behaviour to the (more reproducible) oxidation
waves observed on gold in alkaline aqueous solutions (section 4.6.3). Thus
'the Tafel slope (potential-current dependence) is RT/F, half that
observed for the irreversible wave analysis plot, 2RT/F(potential-sulphide
activity dependence). The explanation offered here is similar to that
given in section 4.6.3, i.e. a rate-determining electron-transfer reac-
tion involving two sulphide ions (second-order kinetics), at least one
bonded to sulphur (to form a polysulphide ion). It is interesting to note
that these waves were only clearly formed on anodic pre-biasing, which
will continuously produce sulphur at the electrode surface.
However, the low current density results obtained for the steady-
state current-potential plots were very similar to those obtained for the
(reversible) chloride melt system. A similar explanation for the linear
anodic current-potential behaviour is suggested here (see section 4.1.4.3.1)
involving rate-determining dissolution of sulphur species having a linear
potential-coverage relationship (Temkin isotherm). The decay behaviour
-165-
is also similar, with decay slopes varying linearly with the steady
overpotential, ascribed to removal,of a polymeric sulphur film involving
a rate-determining film relaxation process (see section 4.1.4.3.3). The
decay kinetics are however rather faster in the nitrate system. The
lack of symmetry between the galvanostatic build-up and open-circuit
decay curves suggests that the film formation process in this melt is rather
different. Perhaps the application of a given current density does
not immediately ( < 0.1 sec) create a steady-state surface concentration
of a given sulphur "precursor" species required to give the logarithmic
film-formation kinetics.
It is considered that under these low current conditions (< 100 p amp.
cm -2 at ^' 4 x 1072
M - S2-), electrochemical reversibility was maintained
and the sulphur activity was therefore dictated by the potential via a
Nernst relationship. The irreversibility seen at overpotentials> 0.6 v.
may be associated with inhibition effects by the sulphur product. The
concept of a single exchange current density io (for a given sulphide
concentration) is not very useful here, as "reversibility" encountered at
a given current density i (i.e. i << io) may give way to "irreversibility"
(i.e. i » io) under different surface conditions.
4.3 Platinum sulphide films formed in fused lithium chloride-potassium
chloride eutectic
4.3.1 Introduction
During studies of the anodic oxidation of sulphide ion as a solute
in lithium chloride-potassium chloride eutectic, the formation of a
-166-
platinum sulphide film on a platinum electrode occured, as evidenced by
sharp cathodic galvanostatic arrests after keeping the electrode
at, or at potentials anodic to, the rest potential. A short study was
performed in order to elucidate the kinetic behaviour of this film,
particularly to compare it with apparently analogous films studied in this
work and elsewhere (e.g. 116). Quantitative studies of phase film forma-
tion at high temperatures are very scarce indeed, although they may have
considerable practical value in semiconductor devices, storage batteries, etc.
The anodic formation of the sulphide film cannot be studied using
anodic transient techniques, as comcomitant formation of soluble polysulphide
occurs, the work therefore basically consisted of the application of
cathodic galvanostatic transients subsequent to film formation, to
characterise the quantity and (hopefully) nature of the film present.
4.3.2 Results
On galvanostatic stripping of the film, three potential-time arrests
were seen, their separate occurence depending on the potential and time
of formation. At short formation times (< 20 secs), one cathodic arrest
was seen (photo 4.3.1) around - 0.45 v (versus S.M.S.E). Stripping
charges (obtained from the potential-time arrest length) were quite constant
(+ 5%) with current density except at low (< 2 ma. CM2
) currents,
where some increase was noted, probably due to a contribution from deeply
incorporated sulphur.
A dependence was noted of the reduction potential on the applied
current density, indicating irreversible behaviour. Linear Tafel plots
were obtained with approximate slope rs, RT/2F, although this value
-167-
tended to decrease somewhat with coverage.
At a given potential, the film growth rate was approximately linear,
following'an initial rapid rise, but leveled off (fig. 4.3.1). At
formation times >i minute, a second stripping wave formed about 0.15 v
cathodic to the original (photo 4.3.2). This gradually grew at the
expense of the first wave until eventually ( rNj 2 mins.) the first wave
disappeared entirely. This second wave continued to grow with time,
becoming "sharper", and at very long (>15 mins.) formation times developed
an "overshoot" at the commencement of the arrest (photo 4.3.3). The
growth-time relationship was initially linear in time but deviated below
this line at longer times and it can then be described by a parabolic rate
law, (charge)2 .= const. t. (fig. 4.3.2). Charges up to a least sixty
equivalent monolayers were grown. This second wave also exhibits irrever-
sible behaviour, with linear Tafel plots obtained as before. For short
(< 2 mins.) formation times the slopes vary markedly with coverage (fig.
4.3.3). With increasing formation times these slopes gradually decrease,
e.g. for 5 mins. formation the half-wave slope is 49 mv.
At formation times above two minutes, a third stripping wave was
sometimes seen, specially at high currents; it was very indistinct, how-
ever, and no quantitative analysis was attempted.
The charge for the reduction of the second wave tended to fall with
current density; however, there was considerable irreproducibility
(fig. 4.3.4).
• It was generally noted that the film-growing capability of a given
electrode sample increased with use; this made precise growth-time measure-
ments difficult. Usually an electrode "aged" for at least a few hours in
the molten electrolyte was used, enabling reasonably consistent results
to be obtained. After much used, the electrodes had a faint brown and
-168-
eventually pale blue colour. Under the microscope, these blue-coloured
samples had small "crystallite" patches of about four microns diameter;
and under high magnification these patches appeared to be conglomerates
of smaller growth areas. Each large patch was separated by at least
15 microns "background" growth.
Growth rates as a function of constant polarization potential were
also studied. At varying potentials (versus the rest potential, at which
most data were taken), growth rates varied as shown in fig. 4.3.5.
An attempt was made to observe the effect of increase of sulphide
and polysulphide concentrations; however, irreproducibility was such that
only a qualitative increase of growth rates was observed.
Some measurements were taken at a rather higher temperature, 525°C.
Film growth, as expected, was rather faster at this temperature. The
first stripping wave was entirely absent, and the second was very sharp and
linearly shaped (photo 4.3.4). The Tafel slopes were slightly (r''' 5-10%)
higher than at the lower temperature, although the values again fell with
increasing formation time.
As the film grew at constant potential, the start of the second strip-
ping arrest (for times< 2 mins.) become more positive; whereas the end
of the reduction arrest remained at constant potential;
no "ageing" effects were thus observed. Growth times
> 2 mins. produced an invariant reduction range.
The "IR" drops with the film present, determined galvanostatically,
were similar to the bulk (electrolyte) drops found (' 2-3 ohms. cm-2
).
so 30 40 fogitATIon) TitiE SECS.
0.i
rl .+3.1.
LAS eg aeowni ̂ foTeurioTrATIC FOlItticrioN) TIM ?La'
(fog IsT. "A S" atflutoosrfine STKiffigOrt
Czet- t(CC Et ecuox 7= 1-34f-ac
= x 10-2- M . o 0
fortt14-noN Ar gesr faT-eKTIAL .
lb,
o.
rSEZ. RA atILV/WognRC
srg(P044. covert'''. peNsiTy 325116.01-2,
az
0.
0.
170
i ria. t.s.2. .
LAYER G6314111 - PoTENTIo Wino Fog n nom
(CO 20 *as* GALVANOSTale Srelfe)fiCr
WS), Lct-kce , et ELeei-e0)E, p- i.31Pc,. Dra,,si =.- 2.18 x lo-21.1.
fig tiiMoM AT REST ferfEN TiAL, 0 / 0 /
'nee,. Fori GALtoriosroc
STRIFNA- I CIMENT 0.1 TeNsrff = 3K Hh.cri.1
/ . /
0
/ . /
0
0/
0/0
/ 2 - 3 4-
Fogmtinb4 -nnr 7 MINS. S
0
Eacreoe AREA= 10 CH t. -0.24
0 0.Z 0.6 0.$ 1. 0
LOG,0I AA. ElEcrizte,
171
FIG-.t.3 3 . RED via/ roTEwrIAL — LoG-. Cogetcr PLOTS FoR
aALY(140STATIC POTENTIAL -TIME STRVINCT OF 4P-CS"
LAYERS 2to. sTRieI Cr )A/AVE I AS -Cove0-0,
MIN Famlivflot4 AT 1QEST ecTetscriptL /v
o.36 tficti.s3= 1--x1C2M v F 0
E VOLTS . VEt5V5 REST foffivrIAL A
0 .5%0 v wts.E1
/A/
/ V o
A
SLOPE crEv: 6o MV. le C) = (iv.
Tsnigr, EF= 83 my. (id tS TRANSITIatS
-0.2%
Ar „ Rr 461°C. 1311V1
172.
116
F10. t:3 t. fELATiari 18ETWEEN ReootBLE. CHARGE Anti
GALAN° STRIPeilla FOR S6 LW eRS
ELECTOC ; AREA =.-0'142 cre. ) T= 1-5teC.
Uce-KCE Ea,s1 to-7-ri.
Mim. FORtiAllog PCT REST folENTI f1 I- ,
O 0 00
0
0
to 0
3.8
IT. neowLemzs.ELEcrgae.'
3.6
31-
3.2
3.o
4o.1 a .8 2*
1-1)&i.I Lis la- tad' et.ccgo)e!
ISEc. foK anwAworrtric sTele(iq. J comic 3)eNsrrY -_,.. +5.6
o n o
1-4
1.2.
1.0
0.S
qrtS 4 Lime GeowTH RATE AS S- (FoettA1ic4 PorecriAL
2 tilts(. toilworn , [Nat3..1 2 giett(
173
0.6 0
V ?W. AN01)1C, REST' Perrentnal-.
0.1-
o.2.
0
zo to lo So 16 - 12o Ito Ito Iro 2fi3
V I% CATIfolle., of ResT ferrArria_
Io
171-
1.3.‘ . GALVANosTATIC, foreWrIAL.—TIME WOE ANALYSIS Fog
gUsucTiol OF "Pk.S1 LAYEA (to .SrgieeirsfQ- WAVE). — 10evas13LE TESaRrnot4 MO E4- EON 2.30
SE-c.TIOM 2.5.3.2 Fog rbornoN or REST raregnAL, 1 Mill. FoRKITioN TitiE .
A AT 4-6*. 2*1 Si ---- 73 my' \ ) 2F — .
A sLeee = 56 iv. A
113 A
O
\A SLOPE \ o =34t1V.
103 KA.cht4 0
O
1.6
Loon (T-t)
.11
-175-
4.3.3 Discussion
4.3.3.1 Film formation kinetics
The very thick films of sulphur on platinum (compared to oxygen -
see later) in lithium-potassium chloride melt are obvious. Platinum
is known to form two thermally stable sulphides, PtS and PtS2, both
semiconductors, as are many transition metal sulphides (ref. 159, chapter
19). The growth of the film even at the rest potential and the linear
increase in growth rate with anodic overpotential (fig. 4.3.5) are
strong evidence for the reactant being sulphur, present in (nominally) pure
sulphide solutions as an impurity (see section 4.1.4). The reduction in
growth rate with increasing cathodic overpotential is also compatible
with this, although a quantitative fit of the potential dependence is not
possible as the corresponding sulphur surface concentration is not known
a priori. The initial linear film growth region ( < i min) (fig. 4.3.1)
probably involved diffusion depletion of the reacting polysulphide species,
as the formation rates are comparable to the known cathodic limiting
currents for polysulphide reduction. However, subsequent linear film
growth of the second film type ( > 1 min.) (fig. 4.3.2) is undoubtedly due
to slow film kinetics, as the formation rate is only <1/10th of the
initial rate. Growth kinetics, particularly at longer times, can be well
represented by the parabolic growth law (fig. 4.3.2) (However, a semiloga-
rithmic law might just be fitted). This linear-) parabolic transition has
often been seen (e.g. with CuS formation on copper (174)). The linear
growth region is associated with a constant reaction rate at a growing
surface, maintained by transport through an often porous (non-continuous)
film (ref. 175, p. 253). The parabolic law is expected where the diffusion
rate through the growing layer becomes rate-determining (as the electro-
chemical potential gradient within the film falls rather than the boundary
reaction, and is applicable at the low field strengths found for thick
-176-
(say > 500 A°) films (116). This model is reasonable in the light of
determined reduction charges of around 50 equivalent monolayers and above,
which can easily correspond to films of thickness"' 10-5 cm._ The blue
colour of thick films can be regarded as arising from interference pheno-
mena. Here the Bragg equation is applicable; for re-enforcing
interference n = 2d cos 6, where n is an integer, X is the wave-
length concerned, d the film thickness, and 0 the angle of incidence.
If cos 8 tr-' 1, n = 1, blue light wavelength "J 4700 A°, an approximate
film thickness of 2.3 x 10-5 cm is obtained. The electrodes maintained
this colour when reduced, indicating the formation of a rough "platinized-
platinum" surface.
4.3.3.2 Film reduction kinetics
The linear Tafel plots obtained under galvanostatic reduction conditi-
ons are good evidence for a high-field electrochemical mechanism (ion
movement or electron transfer) as a rate-determining step. The slopes
generally increase with film "thickness" for a given formation time.
This may be ascribed to an increasing proportion of the metal-solution
potential difference becoming "unavailable" for the rate-determining step.
However, film "relaxation" effects as removal proceeds, with change in
reduction rate (current density), could also account for the phenomenon;
also, this field effect, if present, must be limited to the film edges,
as the film thicknesses encountered would lead to very largelb„yer "resis-
tances" (under either "low" or "high" strengths) and thus to very high,
or non-linear, Tafel slopes, neither of which are observed.
Hence, a reasonable model for the film morphology is that of a
porous (platinized) platinum surface into which either PtS or PtS2 is
-177-
grown; it is considered that a sufficiently metallic character is
maintained so that the overall conductivity of the film is high. The first
stripping- wave may then correspond to the removal of a randomly constructed
sulphide film which gradually rearranges into a more regular, stable
lattice with lower free energy, therefore requiring a more negative potential
for reduction.
The typical value of the Tafel slope, r" RT/2F, is interesting in
that it is very similar to the value obtained for very thin Pt0 films
formed in lithium-potassium chloride (see below). A similar explanation is
applicable here, i.e. a concerted metal-sulphide ion movement under a high-
field asihe rate-determining step (see section 4.5.3.2.2 and 2.6.3.5).
Values < PT/2F, obtained at low film thicknesses and long formation time
can be accommodated by considering that the transfer coefficient (or frac-
tional jump distance) is >0.5, or by assuming that concerted activated
movement of both ions is replaced by activated movement of one ion, the
other being in quasi-equilibrium (75, 34). This leads to a modification
of eqn. 2.40,
a, = ( Z+ + a ) = 3 (if a, =
where the metal ion is considered to be mobile. It should be noted that
the uncertainty of the true charges carried by the "ions" remains (34).
Thus a Tafel slope of RT/3F (.7._ 48 my per log. unit at 450°C) is
predicted, and this value is actually approached.
Analysis of the galvanostatic reduction waves was performed for an
irreversible desorption model using equation 2.30b (outlined in section
2.5.3.2). For the first stripping wave, fits to the model were rather poor, "
but in the half-waVe region at low current densities a line of slope"'RT/F
could be obtained. This indicates a reaction order m = 2. For the second
-178-
stripping wave, reasonable fits to the model were obtained, particularly
for formation times > 2 minutes. As expected from the dependence of
the Tafel slope on film thickness, a decreasing slope (mv. per log
unit) for the plot E v's logi n (T - t) (from eqn. 2.30b) with
increasing current density was obtained (fig. 4.3.6). If this is due
to a high-field effect (as mentioned above), then reduction at low
current densities should minimise this. It is seen (fig. 4.3.6)
that the slopes approach RT/2F under these conditions, i.e. m 1.
This result may be interpreted in terms of a linearly progressive
reduction in the number of active "crystallite" sulphide film regions
as the film is stripped, yielding a desorption rate a "coverage"
[ or at constant imposed rate (i.e. galvanostatic conditions), desorp-
tion potential a log ("coverage") ]
Furthermore, the lowering of this "reaction-order" slope
paralleled the lowering of the Tafel slope (f [ current density ] )
with increasing formation time. This "ageing" effect is therefore
purely operative in the "an" term, and may be associated with lattice
rearrangement effects.
-179-
4.4 Formation of Sulphur films on a liquid Bismuth electrode in
lithium chloride - potassium chloride eutectic
4.4.1 Introduction,
A very brief study was made of the anodic oxidation of sulphide
ion at a liquid bismuth electrode at 425 °C. The initial object was to
attempt to observe the sulphide oxidation process on an electrode which
was capable of dissolving the sulphur product (176), so observing
chronopotentiometric waves not limited by passivation processes on the
electrode surface.
4.4.2 Results
It was found that the rest potential of the bismuth electrode in
contact with sulphide - containing electrolyte was considerably more nega-
tive than for inert solid metals (e.g. - 0.85 v more negative with
5.3 x 163 m - S2-). On galvanostatic anodic polarization, potential -
time arrests were seen close to the rest-potential. These were very
different from those seen on inert solid electrodes, consisting of
symmetrical inflected waves over about 100 mv., but they were very
irreproducible with respect to length and were often characterized by
markedly regular potential fluctuations at the end of the arrest (e.g.
photo 4.4.1). Moreover, the waves were lengthened by previous cathodic
pulsing and pre-biasing. Assuming diffusion - control with obedience to
Sands equation (not proved), the longest waves obtained corresponded to
a diffusion coefficient (assuming n = 2) of 1074 cm2 sec-1 .
On reversing the current from previous anodic chronopotentiometry
two types of results were obtained. When the reversal was performed
-180-
during the arrest region, a sharp reverse wave was obtained at a very
similar potential to the forward wave (photo 4.4.2) (after allowing for
IR drop). The ratio forward to backward transition times was approxima-
tely three to one. However, on reversing the pulse after the completion
of the anodic arrest, this "reversible" wave gradually disappeared
and was replaced by very irregular potential-time arrests at a considera-
bly more cathodic potential (photo 4.4.2). Quantitative analysis of
this phenomena was not attempted, however, as the currents required to
obtain well-defined reverse waves were higher than could be normally
supplied by the galvanostat in use.
4.4.3 Discussion
The considerably 0.45) more negative rest potentials suggest a
stabilization of sulphur species with the electrode, the species not being
in direct equilibrium with the bulk. Alternatively an electrode of the se-
cond kind could be in operation. The dependence of the anodic wave length
on the prebias potential, the marked potential-time oscillations, and the
general irreproducibility suggest that the process involved a passivation
of the electrode surface by the sulphur product. Regular potential
oscillations are often seen with passivating systems (2). Most of the
sulphur (if the product is dissolving in the bismuth) or polysulphide
product appears to be removed from the surface as evidencedby the forward-
reverse time ratio (see section 2.7.2.4). It is considered that some
diffusion-depletion of sulphide must have occured as the lower limit
of the sulphide diffusion coefficient 1 x 1074 cm2 sec
is rather high
(assuming n = 2) [c.f. value for S2- in CaC12 at 945 oC
2 x 104 cm2 sec i (158)]
-181-
The change in the reduction process occuring after the anodic
arrest region is rather interesting. Although quantitative studies were
not performed, it is possible that much of the cathodic overpotential
for the post-anodic arrest reduction transients is kinetic. It probably
involves reduction of a Bi2S3 phase film [- AG7 at 25 °C = 39.4
kcals mole 1 (Circular 500) ]. This contrasts with the simple reversible
behaviour of the pre-arrest reverse wave which probably involved a random-
ly chemisorbed sulphur layer.
4.5 The oxide/oxygen electrode in lithium chloride-potassium chloride melt
4..1 Introduction and potentiometry
A short study was made of the electrochemistry of lithium oxide
solute in lithium-potassium chloride in an argon atmosphere at 450°C,
with the initial aim of checking the potentiometric behaviour of a metal-
oxide electrode prepared by forming the film anodically on both platinum
and gold electrodes. Previously, a two-electron Nernst slope for variable
oxide concentration had been obtained with a platinum electrode(145)
Stable rest potentials were difficult to achieve in the "J 1072 M oxide
concentration range, particularly with gold, polarized anodically to
(hopefully) form the oxygen. film. However, a qualitative dependence of
potential on oxide concentration, at least for platinum, was found. This is
similar to the results cited in ref. 145. Rest potentials were usually
around - 0.25 v (versus S.M.S.E.).
Subsequently, anodic chronopotentiometry and steady-state polarization
-182-
was performed to compare the behaviour with that reported by Wrench (14).
During this study, a process probably involving the formation of a
chemisorbed oxygen film on platinum (but not on gold) was observed by
the galvanostatic technique. The results are considered to be interesting
as very similar bahviour was observed to the much-studied (but probably
more complex) aqueous system.
4.5.2 Chronopotentiometry and Steady-State Polarization
4-5.2.1 Results
A well-defined anodic chronopotentiometric arrest was seen, on both
platinum and gold electrodes, from solutions of lithium oxide in the
concentration range 102 .* 2 x 1071 M (photo 4.5.1) . The potential-
time curve fitted the simple soluble product model E versus T2 t2
login ( ) with slope 2.3 RT/2F. Reasonable agreement with the t2
Sand equation with respect to current density variation was obtained;
also the quarter-time potential was independent of current density and oxide
concentration and had the value + 0.175 v (versus S.M.S.E.). However,
the equation was not obeyed in a simple manner with respect to concentra-
tion, and below 5 x 102 M - oxide the waves were irregular and decrea-
sed in length with time. Current reversal during the forward transition
(photo 4.5.1) produced reverse waves with quarter-time potential co-
incident to the forward value. The ratio forward to reverse transition
times was variable, but usually about four to one. Diffusion coefficients
calculated on the basis of the stoichiometric oxide concentration were 1
very low, about 2 x 107 cm2 sec , at ^1450°C.
-183-
A steady-state overpotential plot was also recorded at potentials
negative to the reversible anodic wave. Stable potentials were difficult
to achieve with increasing anodic potentials, but scanning downwards from
the reversible wave produced a reasonable Tafel plot of slope
^-IRT/F. Admission of air into the system under argon caused the rest
potential to drift positive to around - 0.05 v (versus S.M. S.E.), and
reduced somewhat the length of the reversible anodic wave.
4.5.2.2 Discussion
Similar results were obtained by Wrench (14), but here reference
potentials were not explicitly stated; also current reversal was not
performed. However, the behaviour of platinum electrodes in (14) was found
to be very different to that of gold, with complex passivation-type waves
in the concentration range 1072 - 10-1 M. This contrasts with the behaviour
found in the present work, (near-identical behaviour for both platinum
and gold electrodes). This discrepancy may be associated with a poor
platinum-glass seal used in (14), along with excessive oxidation
of the metal surface occuring during this sealing process.
Wrench suggested that the reversible wave was due to the reaction
-2e 02- + MO T.:=7± MO....0, where MO is the metal surface concerned
with a layer of oxygen.
In view of the very. low diffusion coefficients obtained here, the
scheme 0 2- 02 is preferred, the peroxide ion being a minor
component of the solute; about 5-10% of the total oxide added is
required to give a "reasonable" diffusion coefficient (ry 2 - 5 x 10-5 -1
cm sec sec ).
-181+-
Wrench noted (14) a diffusion coefficient of ' 10 cm2 sec
obtained for anodic waves under both nitrogen and oxygen atmospheres
(see section 2.9.3.3). However, the waves obtained under nitrogen
atmospheres were reported to be very irreproducible with respect to length.
The longest waves obtained in (14) could arise from some electroactivity
of 02- ions via the formation of 022- with the oxygen produced in
the anodic process.
Forward to reverse transition time ratios greater than three can
be explained by loss of oxygen bubbles from the surface. The plot for 2
the alternative scheme 202- 022- E versus logio L(T2- - t2) 1----2 e
1 1,
gave a non-linear plot with a non-integral slope.
The steady-state result is in agreement with (14). No incompatibility
of this irreversible kinetic result with the reversible chronopotentiome-
tric waves exists as the effects occur in different potential regions and
thus relate to different electrochemical reactions. Hence the slow dis-.
charge of oxide ion to give adsorbed oxygen, suggested by Wrench to be
rate-determing from the Tafel measurements, does not necessarily give rise
to the reversible chronopotentiometric wave. The discharge of the peroxide
ion is the most likely event in this potential region.
4..2.3 Studies of the anodic oxide film on platinum electrodes
4..2.3.1 Results
During the chronopotentiometry study above, it was noted that on
platinum a definite small charging "ramp" prior to the reversible wave
occured for oxide concentrations around 10-1 M, and above. This process,
which was absent on gold, commenced at about - 0.150 v (versus S.M.S.E.),
-185-
and continued with an approximately constant adsorption pseudocapacitance
of about 3.5 mF cm 2 until the commencement of the reversible process
at about -0.10 v (versus S.M.S.E.). An ill-defined charging ramp from
0.25 v to -0.15 v was also present with pseudocapacitance 1 mF cm 2.
Interest in this process was heightened when it was found that
galvanostatic reduction of the (presumed) oxygen film involved hysteresis
in a similar fashion to that of the oxide film on platinum and gold
electrodes in aqueous solution (photo 4.5.2)( see section 2.6.3). Repro-
ducibility was fair (+ 10% for charging from sample to sample) but for
the reduction (stripping) transients, variations in definition were seen
with various electrode samples, and thus one typical sample was used for
the bulk of this work. However, more work is required on a number of
samples prepared in different ways to increase confidence in the general
behaviour observed. Various kinetic parameters of the film were studied
and are discussed below.
(1) Anodic galvanostatic charging
In contrast to the aqueous case, no distinct dependence of the
initial potential for oxide formation on current density was seen. The
potential-time plots were fairly linear at high currents (>10 ma cm 2)
but tended to non-linearity at lower currents (photo 4.5.3)(c.f. gold
in aqueous solution, ref 86). Adsorption pseudocapacitances were around
3.5 mF cm 2 , and tended to increase with lower currents.
(ii) Potentiostatic growth-time curves
These were recorded by forming the film for given times (0.5 seconds
to 30 minutes) at a series of constant potentials, and determining the
-186-
quantity of film present by measuring the transition time for the cathodic
stripping arrest. Some results for varying fixed potentials are given in
fig. 4.5.1. Two growth regions were found at a given potential with
different growth constants. At least the first region was linear in
logarithmic time. The rate of growth of the second region was also proba-
bly linear in log. t, but sufficient data was not obtained. The results
were found to be reproducible on re-recording data for short formation
times after growing the film for long times.
(iii) Galvanostatic reduction transients
As mentioned above, a clear cathodic potentia;-time arrest was seen
which was similar to that observed from aqueous solutions. For current
reversal conditions (photo 4.5.2), the wave had an inflected form with
reduction charge Q0 somewhat less than anodic charge QA; however,
considerable charge was passed in regions other than that of the arrest,
so that an inequality such as total Qc < QA (commonly seen for aqueous
systems) cannot be confirmed. At all charging rates employed (50 p, amp. -
100 ma cm72
), the potential of the cathodic arrest was negative to that
of the anodic build-up curve.
For quantitative study of the reduction phenomena the film was formed
potentiostatically, reduction then being observed at varying current
densities under constant formation conditions. The resulting arrests
yielded a constant i T product, indicating reduction of a surface, rather
than a diffusing species, as expected. The potential at a given coverage
was dependent on the cathodic current density, linear plots of E versus
log i (Tafel plots) being obtained for constant coverage (i.e. at a given
point in the cathodic arrest region). A slope of approximately PT/2F
-187-
was obtained, although this increased somewhat with decreasing coverage
(fig. 4.5.2).
With increasing formation time (> a few seconds) at a constant
potential, the reduction arrest shape was virtually unaltered, but the
arrest region was shifted more cathodic; this shift was linear in logarith-
mic time (fig. 4.5.3). Reduction potentials as a function of formation
potential for a given time were also examined. Generally, for more posi-
tive formation potentials, the reduction arrest also occured at more
positive potentials. In the formation potential range (-0.190v to -0.090 v).
the shape of the reduction transients were unaltered, i.e. the potential
range for reduction remained constant. At higher formation potentials,
however, this reduction range was increased with increasing (more positive)
formation potential so that the start of film reduction occured at incre-
asingly positive potentials, whereas the end of the wave stayed at
approximately the same potential, (Photo 4.5.6).
At long formation times, in the region where the growth rate versus
the logarithm of time slope increases (fig. 4.5.1), the reduction arrest
shape altered and became more linear during the transition (photo 4.5.4).
Comparison was made between films formed for a given time by
(a) partial potentiostatic oxidation, and partial open-circuit conditions,
and (b) continuous potentiostatic oxidation (photo 4.5.5). It is seen
that the potential arrest regions for the two pre-treatments are very
similar, and the film formed partly on open-circuit has "aged" considerably
from the same film examined just after the potentiostatic period of the
anodic pre-treatMent.
0
e
4-0
30
Va.
0 tgg
65
40
0 G-ROWT11 - Lai-. TIME PLOTS Fori
L194.0" f INS As f (fottfriosTfmC
f oR MATO N pOTENTI A o 0
cifiviGe uNtr5 50 - I ctifteGE uN
35.4 . . coutznES I
0 0
0 0 x
0 foArlillionl AT
70riv.(v. S. rts.E). 0
10
0
x
0
o X X
Z 0 EP,
0 X
x
(57 *
° A
roT6NTiosTATIC fOrighTtoM AT
X V — ISOMV. (v. 511.S..).
11 a V
0 in — 50 Fly. .1
0 — 148"014lt ti
X — 30 MV
LOCrio-t secs. f. I FoRtiliTiok1 TIME.
1-0 2 c 3.0
V
V 0
A 0
0
E VOLTS 6/Mos
Slur OF ME 0
—0.50
-o•14
[ AT zi-1-3°C 21
ft 71 MV.
E VOLTS
ALF -WAVE er. -o.fo
00
-049-
- 0.40
-0-tZ
-0-37
-o%
FIG. . Loa-. cueRENT REDoenal PoiEJmft1 FOR GALvmosTer-ric,
51120114q- wekves OF (N La—gee Arr ff3°C.
P& ELEcrgo'DE Pt ge4 = 0.261 cril".
foRtIA-nom eoTFATIAL ---= +• 0.03ov. (Vs. SASE). -0.52
foCt14-noil TIME = 15secs,
-032
-0.38
o.36
-0.3o
0.7 lz t-i 2-o 21
0.4 LoCribi (Me. X loc. L.E..ci-Rose-1.
1,0
FIG-. 11:5.3. RENC,Ttal forEiNrnal_ Vtgsus Loa-. rarenmoswric,
FoiVIATiea TitlE FoR GALVANosi-Pmc
REDoeTioN Of 4Pe04 IN uct-kee , T= 1-15°C.
/
-4)42
E mrs STARr of ham.
(v. S.t(.s.).
-010
-OS
Pt ELEctimE . , -2. 0 REPUCTI014 cuRRENT PENsiir = 1-41 MA.cti. /
roRMirrioN PoiamilL ----- -0.0Z0v. o O/ (vis S.M.s.E).
-o3C
--0.32
-03o
-0.2Z
-05 ci 1.0 Z0 • 3.0 Lotrie-E secs.
O
171
foTENTIAL —1•015 AriALYSis FOR GALVA-NosrA--ne ffEPueTioN OF ``ISO' FlUIS IN LiCe- kee. ,
E v•LTs ,irreKerice 3eiwEeri cuxvss
AC I be. servgem oBscoe), Pt' CALcotSire) V SIN Cr MilwALtNa. S ITS 3ZSag trial
moel.
-010
/ 1—, E-t coRve FOK GALVAwo STATIC.
0 R E:Doczion] dESERvE)) r. L i. = .frof no. ati:,1* foglifinor4
eoretTriAL --:'. - 0 .TO r1v., T.-z-lif3t . sk ELEcios.
CR ARCre STRWP6) --zo.66 ri.couLott8s.Crftl.
0 C
A
A 5*--- E-t c4gArE / CALCULArej Moll
6.---__„,a ' EGA]. 2.30& (section!
2.5.34 w ht ::. i
io 20 So to 50 Co 7o TO 90 Les
, of r . '1' is TKAintridnr TIME Foq E-t TRANI SmsT,
-049 - E uotzs (vegsug
-0.50
O
-192-
On admitting air into the system, the rest potential drifted slowly
positive (e.g. to about 4- 0.040 v for rs'' 0.1 N oxide solution, after
one hour). Thisis consistent with the observation of Wrench (14).
Cathodic reduction from this rest potential yielded cathodic stripping waves
similar to those obtained following anodic polarization in inert atmospheres.
Discussion
4.2.3.2.1 Film forMation kinetics
The apparent independence of the lowest potential for oxide formation
with current density for the anodic galvanostatic transients indicates
'electrochemical reversibility for the growth process, at least for low
coverages.However, potentiostatic formation for periods >0.5 seconds
produced logarithmic oxide growth curves which is indicative of a slow
activated rate process. This latter process was probably the incorporation
of the initially adsorbed oxygen in the metal substrate whereas with the
anodic galvanostatic measurements it was probably the reversible formation
of initally chemisorbed oxygen, perhaps in a "precursor" state (172),
whichwas being observed. Certainly, the adsorption pseudocapacitance
obtained galvanostatically increases with decreasing current density,
particularly at lower potentials. This is consistent with increasing
incorporation of adsorbed oxygen as the observation time during the pulse
increases. Marked hysteresis occurred, however, even at high current
densities (--,100 ma.cm 2 ) with current reversal (observation time 5 msec),
indicating extensive incorporation even on this time scale.
-193-
The two logarithmic growth regions for the potentiostatic growth of
oxide appear to be due to two different forms of incorporated oxide;
the second form (type b) associated with a higher growth rate, requiring
the presence of an initial quantity of type a to form. This may be
associated with a higher valency oxide. The changeover in formation
kinetics is also indicative of a second type of oxide. It occurs at a
surface charge of around 1.5 m coulombs cm 2 , equivalent to about three
Pt° monolayers; it is unlikely that all this charge is being held in a
simple chemisorbed layer, and thus the postulate of incorporated oxide is
reasonable on this basis alone.
Direct logarithmic growth kinetics are common both for chemisorption
and film thickening processes (53). Discussions of the applicability of
the rate law in gas phase chemisorption f section 2.4.6) and electro-
chamisorption cases (section 2.6.3.3) have been given earlier. In the
present case, it may be useful to assume that the thermodynamic activity
of initially formed adsorbed "oxygen" (or oxide bonded to a metal cation,
i.e. a strongly dipolar bond) is defined by the potential applied (analo-
gous to a given gas pressure in gas-metal chemisorption), and that
subsequent incorporation involves Elovich-type kinetics with an increasing
activation barrier as the more active incorporation sites are progressi-
vely filled, (this is discussed in section 2.6.3.7).
As seen in fig. 4.5.1, potentiostatic film growth as a function of
potential can be divided into two regions, (i) - 0.18 v to -0.08 v.,
where the growth plots are almost co-incident, and (ii) above - 0.08 v.,
where the growth plots are associated with increasing values of charge for
increasingly positive potentials. This phenomenon may be associated with
the dependence of hysteresis on the formation potential. Thus, in the
-194-
potential range -0.18 v. to -0.08 v., the incorporation rate may be
primarily a function of the number of metal sites available. Greater
hysteresis at the lower potentials may be caused by initial adsorption
and incorporation at a smaller number of more labile sites, which leads
to a greater rate per site, with an associated lower free energy of the
activated and final states; thus preferential incorporation at these
"deep" sites can lead to greater hysteresis than seen with higher poten-
tial formation, although the quantities of oxide involved could be similar,
(formation at higher potentials could create alarger,
but less selectively adsorbed initial layer).
Supporting evidence for the existence of these "active" sites is seen
from the anodic galvanostatic transients; here at low charging rates
much larger pseudocapacitances may be seen in the potential region - 0.18 v
to - 0.08 v., indicating more extensive incorporation provided the imposed
rate was not high. Physically, these active sites could correspond to
surface grain boundaries, etc. (183). At potentials > - 0.08 v., the
increasing adsorbed oxygen activity may be considered to become sufficiently
high to fill most of the available incorporation sites anyway and lead to
faster and more extensive incorporation. potential of
The linear increase of hysteresis in logarithmic time from the X
reduction transients at constant formation potential can be understood by
considering that a subsequent rearrangement process occurs after initial
incorporation, by a related ion movement process. Hence analogous kinetics
to the growth process are involved. The occurence of this "ageing" process
even on open circuit is evidence for the spontaneity of the process.
-195-
4.5.3.2.2 Film reduction kinetics
The Tafel slope for film reduction,"'RTAV, is rather low. As for
the aqueous Pt0 case an explanation in terms of concerted ion movement
is reasonable (75)(see section 2.6.3). Thus, in the case of concerted
ion place exchange under the influence of a high field,
a* = a ( Z = a (Eqn.2.40)
when Pte +' and 02- ions are involved.
Thus, for the real transfer coefficient cx = i, the apparent coefficient
= 2, and the Tafel slope RT/x*F becomes RT/2F, in agreement
with experiment.
For the reduction process, the Tafel slope appears to be almost
independent of coverage (c.f. aqueous case). For high-field processes
(section 2.3.8), this slope should change with coverage as. the local field
conditions vary. This would be expected for a random removal process;
however, non-random reduction, e.g. from the edges of oxide patches
("islands") (75), can yield the required constant local field conditions
during the reduction.
It should be noted that the above assertion that of = 2 in eqn.
2.40 involves the assumption of only a small "unavailable" potential
across the oxide layer [ (Pm - pf) in fig. 2.2; section 2.6.3.5], in
this case, Vetter (ref. 75, p. 156) deduces (partly from the anodic
kinetics) that (pm - pi.) is comparable with (pf - , a0,1s) under these
conditions. This has the effect of rasing the Tafel slope for reduction.
However, no corresponding deduction can be made for the melt case as the
anodic kinetic data is less clearcut. If an appreciable local (0 ) f
term does exist, the observed Tafel slope for the melt case can be
-196-
accommodated by considering rate-determining oxide ion movement with
metal ion movement in quasi-equilibrium (see section 4.3.3.2).
The complete potential-time relationship for reduction (in the
initial growth slope region), was analyzed according to the irreversible
equivalent-site desorption model (section 2.5.3.2) and gave reasonably
linear plots of E against login (T - t) (Eqn. 2.30b), with slopes
'NJ 380 my (Nd 2.3 . 2.6RT/F ). This relation is based on a simple model
of the electrochemical desorption rate involving a pre-exponential factor
including q'', where q is the surface charge, and m the reaction or-
der in q. Here m r.:,5 (as the expression m RTAnF from current
dependence at constant q becomes RT/2F). This value is obviously
very unlikely, and thus some alternative reason must be sought for the large
potential range of this reduction process. The required effect can be
obtained by assuming that there is a finite distribution of site energies,
either arising from a non-uniform surface lattice, or by site-site repul-
sions which vary with "coverage" (surface occupation), thereby increasing
the activation energies for desorption with decreasing coverage. As
discussed earlier for chemisorbing systems (section 2.4.6), the resulting
free energy variation is often a linear function of coverage. The result
of this combined site energy/site number approach for a typical reduction
arrest is shown in fig. 4.5.4 for m = 2; it can be seen that a fairly
linear relation between potential E and surface charge q, except at low
q, is obtained. The assumption of m = 1 yields a markedly curved E-q
plot; hence it is very tentatively suggested that a second order desorp-
tion process is involved.
One drawback of this combined model should be noted. Experimentally,
it is found that the reduction yields geometrically similar waves
-197-
(although shifted cathodic - the "ageing" effect) as the total surface
charge increases. Thus the "heterogeneity parameter" f is constant
per total reduction charge rather than per fixed (coulombic) charge.
However, this reduction of the f value (defined conventionally,
section 2.4.5.1) can be ascribed to the film becoming more "homogeneous",
linearly in logarithmic time, concurrently with the transition to "deeper"
sites, as embodied in the general "ageing" effect mentioned above.
It remains to accountfor the existence of the charge-dependent
rate term and the associated (but more tentative) second-order desorption
kinetics. A simple way to explain second-order desorption in oxygen is to
postulate the rate-determining formation of a dinuclear oxygen species
(e.g. 022-) but this is difficult to reconcile with the concerted metal
ion-oxide ion movement required by the Tafel slope. A possible model consi-
ders that this concerted ion movement occurs when an oxide ion is next to
an oxide lattice defect (vacancy), producing the..apparent second-order
kinetics if the number of defects decrease in proportion to the oxide
removal and hence lattice breakdown.
Simple random desorption is precluded on the basis of the approxi-
mately constant Tafel slope for reduction with coverage which led to the
oxide "island" model considered above. However, the approximate rate-relation
coverage/required can be obtained by considering that the "islands" are
reduced such that their numbers, as well as their size, are progressively
lowered as desorption proceeds.
4.2.3.3 Comparison with aqueous systems_
As extensively discussed in section 2.6.3, apparently analogous
-198-
chemisorbed" oxygen films to those just described are build up on the
platinum-group metals and gold from aqueous solutions. It is therefore of
interest to make comparisons between these systems involving'a very diffe-
rent electrolyte and temperature range.
A build-up of an oxide film on gold analogous to that seen with
aqueous systems is not seen with the melt system; in aqueous solution
these films in fact grow rather more extensively than the corresponding
platinum films. In contrast, no significant anodic filmS on gold was
seen to form in the fused salt media, even at very high anodic potentials.
(Some sub-monolayer layer formation on gold in an inert atmosphere as seen
from galvanostatic reduction transients was noted by Wrench (14). However,
these were very ill-defined). Also, no unambiguous evidence exists for
oxygen chemisorption onEpld from the gas phase (section 2.6.3.8). Thus,
the existence of the aqueous films is perhaps due to the essential invol-
vement of the hydroxyl ion in this media.
A "platinum oxide" film, however, is formed in the melt which in
some aspects behaves very similarly to the corresponding film in
aqueous solution. Thus the galvanostatic oxidation-reduction profiles
appear to have a similar form in the two media. However, a difference
apparent in the anodic charging is the reversible discharge of oxygen
in the melt case, at least at low coverages. In the aqueous case also,
this phenomenon probably occurs for the initial build-up as seen by careful
inspection of the galvanostatic potential-time curves (e.g. ref. 75
p. 142), and is possibly oxygen in a "precursor" adsorbed state as mentioned
above. Galvanostatic anodic pseudocapacitances are higher in the melt
case (") .3.8 mF.cm 2 compared to 1 mF. cm-2
for the aqueous case);
this is probably a temperature effect. Potentiostatic anodic
-199-
growth kinetics are linear in logarithmic time in both cases. However,
for the aqueous systems a continuous increase in the growth constants a
and b in the relation charge q = a 4- b log t are seen, which
is not completely reproduced in the melt system; no completely satis-
factory explanation of this phenomenon can be offered (see section
2.6.3.6). However, the rates of spontaneous relaxation processes appear
to be logarithmically dependent on time [e.g. "ageing" effects discu-
ssed above and in (66) I.
The galvanostatic reduction aqests observed for both systems involve
irreversible kinetics with low associated Tafel slopes at constant coverage.
It is primarily this phenomenon, explained by a concerted ion movement
process under a high field, which strongly suggests incorporation of oxygen
species on a metal oxide "lattice" (The supporting evidence is the
hysteresis between film formation and removal, and uniform kinetics
involving coverages increasing considerably beyond a nominal monolayer).
Significantly, the low Tafel slope for reduction for the melt system
throws considerable doubt on the explanation put forward for the aqueous
reduction in terms of intermediate quasi-equilbrium formation of Pt0H
(74); obviously such a mechanism ruled out in aprotic solvents.
The potential change during reduction is large for platinum oxide
in both systems; however with aqueous solutions symmetrical inflected-
type waves are obtained which will not fit the type of model proposed
for coverage-dependent desorption rates used in section 4.5.3.2.2 above,
(equation 2.30b). This point was apparently not appreciated by Ohashi
et al. (84), who used the derived model only at the half-wave point.
In aqueous solution, gold oxide reduction occurs galvanostatically
over a very narrow range of potentials (e.g. 85, 86); this indicates that
the "active" coverage stays almost constant during reduction and suggests
-200-
the presence of large oxide "islands" not decreasing greatly in number
until towards the end of the arrest. Perhaps more continuous oxide
lattices are formed with gold compared to platinum.
Some differences are apparent in the film "ageing" effects observed
in the melt and aqueous cases. At constant potential, both systems show
a logarithmic change of reduction potential with time, perhaps due to a
place exchange of incorporated species (66). However, for the aqueous case
increasing anodic formation produces reduction profiles commencing at more
negative, rather than the more positive potentials observed for the melt
system. This increasing hysteresis for the aqueous system has been found
to be due to the increasing charge, rather than the rate of charge
formation (66), i.e. the "thicker" the layer, the relatively more stable
it becomes. This also may be so for the melt case, but this effect is
possibly overshadowed by the increased formation rate which leads to less
selective and hence less stable incorporation at higher potentials.
Incorporation of chemisorbed species
Having concluded that extensive incorporation of oxygen into the metal
lattice occurs with electrochemically-formed oxide films on noble metals,
it is interesting to speculate on possible reasons for this. The subject
of the incorporation of chemisorbed species formed from the gas phase
has been recently reviewed (173); this has commonly been studied either
by surface potential changes or by direct observation techniques such as
field emission microscopy.
Incorporation of oxygen into platinum from the gas phase has been
observed by titration of the layer with hydrogen (126). Thus at 393°K
there were nearly two oxygen adatoms associated with every platinum surface
-201-
atom, but rapid reaction with H2 gas was confined to about half this
amount.
The incorporation of oxygen into nickel has been extensively
studied (e.g. 48). Logarithmic (Elovichian) kinetics are commonly found
which are ascribed (48) to decreasing field assistance from the surface
dipole layer as incorporation proceeds, along with field hindrance from
the incorporated product. The studies usually involve intial "dosage"
of the metal with the chemisorbed layer. However, in electrochemical
cases, continuous re-adsorption is expected to occur. Direct logarithmic
kinetics cannot be obtained for constant total potential conditions,
as discussed in section 2.5.3.7.
A marked difference between the gas phase and electrochemical results
appears to be a much greater proportion of at least loosely incorporated
atoms in the latter case (at least if the conclusions of the above discu-
ssions and refs. 75 and 86 are accepted). A possible reason for this
is the reduction in bond energy (and even elimination of adsorption sites)
by competitive adsorption of solvent particles, thus making the incorpo-
rated state (free from these interactions) relatively more stable (see
section 2.6.2).
4.6 The sulphide/sulphur electrode at inert electrodes in alkaline
aqueous solutions
4.6.1 Introduction
It was desired to briefly extend the investigation of the alkaline
aqueous sulphide-polysulphide system studied by Allen and Hickling (12),
-202-
particularly with regard to the effect observed by these authors of the
increase of the anodic Tafel slope with decrease of the sulphur content to
low values. It was felt that this may involve a specific "catalytic"
involvement of sulphur in the sulphide oxidation mechanism. The phenome-
non of anodic "passivation" for the sulphide oxidation process noted
previously (12, 123) was also briefly investigated, and compared to
analogous phenomena oberserved in the melt systems.
4.6.2 Results
4.6.2.1 Steady-state polarization
Some of the results reported (12) for anodic polarization of an
aqueous 1M - NkS, 1M-S, 1M-NaOH solution on gold and platinum electrodes
were first checked. Very reasonable agreement was obtained with both the
reversible potential (-0.518 v. versus N.H.E.) and the kinetic parameters.
Thus, good linear Tafel regions were obtained of slightly lower slope than
in (12); 63 mv. per logio unit for Pt, 51 my. for Au (compare 67 mv,
58 mv. respectively obtained in (12)). Exchange current comparison was
very satisfactory; 5.3 p.amp cm 2 for Pt, 2.7 p.amp cm-2 for Au
(compare 5 p.amp cm-2 , 2 p.amp cm 2 respectively (12)).
Open-circuit decay transients were recorded on platinum and gold
anodes from steady-state overpotentials. For both metals, decay curves
with slopes constant in logarithmic time, even with a varying starting over-
potential, were obtained. These slopes were 55 mv. for platinum and
39 mv. for gold. The capacitances (calculated from the decay rate is dis-
cussed in section 2.5.3.6) were calculated to be ^J30 pF cm for both
electrodes. The overpotential parameters were found to be extremely
reproducible with respect to time and varying polarization conditions,
-203-
in agreement with (12).
Some cathodic overpotential data was assembled in the same systems.
With platinum a linear Tafel region of slope 116 my was obtained with an
extrapolated exchange current in agreement with the anodic data, but for
overpotentials above rsj 220 my an increasing (but non-constant slope
was obtained. With gold, a short Tafel region of slope 70 my was obtained
but here curvature was even more marked.
Overpotential data was also obtained for (i), a similar system
to the above but containing only 0.1 M-sulphur, and (ii), for
sulphur-free sulphide solutions of varying concentration as described
below.
(i) The system studied was 1M-Na2S, 0.1M-S, M-NaOH(aq) again on
platinum and gold electrodes. Here a marked difference in behaviour for
anodic polarization was noted on the two electrodes. Thus gold yielded
a good anodic Tafel plot of slope rs-' 65 mv. (fig. 4.6.1), and an extrapo-
lated exchange current density io of 0.75 p amp cm-2 , whereas
platinum gave a Tafel slope of 110 mv. with io = 8.6 p amp cm 2 .
(This is to be compared with a slope of 122 mv. and io of 9 p amp cm2
for platinum determined in (12)). Cathodic polarization yielded no
satisfactory linear Tafel plots for both metals; gold at low overpotentials
yielded a slope of 114 mv, changing to 75 my at higher overpotentials,
whilst platinum gave an approximately ^, 230 my slope. Reproducible
results were usually only obtained whilst scanning the potential downwards.
Low overpotential-current data C91 = 2 - 30 my) was also obtained.
Although the results were somewhat irreproducible, some typical results
for gold and platinum are given in fig . It is seen that close to
the rest potential, the anodic and cathodic current-potential slopes
indicate that the electron number is n = 1 for platinum on both sides of
7204-
of the rest potential; but for gold the slopes indicate that n = 2
in he anodic, and n = 1 in the cathodic direction. Analogous results
were also obtained for both metals in a solution of 1M-Na2S, 10-2 M-S,
R-Na0B(aqueous).
In view of the lower reproducibility of the polarization curves at
these low sulphur concentrations, some Tafel plots were recorded by
measuring the initial potential plateau obtained under galvanostatic pulse
conditions. Generally, similar results were obtained, although the
extrapolated exchange current densities were somewhat higher.
(ii) The systems studied were 10 3 1M-Na2S, M-NaOH(aqueous). No
sulphur was added, although traces were undoubtedly present as an
impurity, as evidenced by a very pale yellow colour at high sulphide
concentrations. Generally, good linear Tafel plots of slope 120-130 my
were obtained on gold and also on platinum, although results on the
latter metal were less reproducible, tending to give much higher slopes
200 mv) at higher overpotentials. Electrodes were slowly "deactivated"
with time and were reactivated by brief heating in an oxy-gas flame. By
taking the various polarizing currents at a fixed potential (versus the ca- .
lbmel reference electrode) for sulphide concentrations in the range
1073 - 1M, a "reaction order" plot was constructed (fig. 4.6.3) (see
section 2.3.5), which yielded a slope corresponding to a first-order process.
Open-circuit decay curves, from various steady-state anodic overpoten-
tials in the linear Tafel regions, were also recorded. For gold, decay
slopes of about 60 mv. were obtained, with capacitances 15 pF cm 2.
For platinum, varying decay slopes between 80 my and 120 mv. increasing
with the starting overpotential, were obtained. The corresponding capa-
citances were between 10 and 15 i.LF cm-2.
-205-
4.6.2.2 Non-steady state galvanostatic studies
Anodic constant current pulseS of sufficient magnitude to induce
chronopotentiometric behaviour (section 2.7.2) were also applied to the
sulphur-free systems.. No satisfactory waves were obtained for platinum;
however on gold, particularly at low (< 1 ma cm2) current densities,
sharp potential-time arrests were obtained (e.g. photo 4.6.1). Below about
5 x 107' M-Na2S, very good obediance the Sand equation was seen,except
at very high ( > 30 ma cc 2 ) current densities, where an increase of the 1
iT2 product was obtained. At 10 3M, a diffusion coefficient of
4.1 x 10-5 cm2 sec 1 (assuming n = 1) was calculated. However, the
waves were qualitatively observed to lengthen with increasing pH, indica-
tingthat the S2- ion only is electroactive, rather than the HS ion.
- K [Published values for HS + OH ir.rk S2- + H20, K^J 1014 + 20%
(182) ]. A similar pH dependence was noted also for the steady-state
results. The potential-time analysis yielded reasonably linear plots of
E versus log10 ( T2 - t2) with slopes of about 135 my (fig. 4.6.4).
With increasing log10 (current density) the waves were shifted linearly
anodic with a slope of 60 my + 5 my. It is interesting to note that
this resulting Tafel plot could only be observed under transient galvanos,-
tatic pulse conditions. In the steady state, much lower currents were obtai-
ned at the corresponding potentials and the Tafel slopes observed were
about twice this value (i.e. 120-130 mv., as stated above).
At high sulphide concentrations (>^J 5 x 10-3 M-Na2S) and current
densities ( > 5 ma cm-2 ), the iT2 product increased markedly with
current density i. Good linear plots were obtained for l/i against
T with a reproducible intercept representing the dissolution ("corrosion")
current on the Franck model (e.g. fig. 4.6.5) (see section 2.8). Typical
pulse given in photo 4.6.2.
zo /
0 i 2. 3 LoGio I ?AMP. E LECIRole
-0
206
r1 cr . I-. g . 1 .
A NOlC s-rE 0Y- STATE TAFEL PLOT .
Ito- Na,S ,0 1111- S , M-Na 014 (A61) .
II Lt 6 LE a g ON ) RHEA .r":" 0 .255 Ctii.
T 1= 23°C .
o
E VOLTS
VERSUS
SATURA1V
CALOMEL.
0
0 SLOE / --:--- 65tiv.
0
0 / 2'3.5 AT 2Vc r=-51fiv] / F
0
o few- ciRCOlT POTEXT(AL
0
SLOPE = 52X /04voLTS. AMPS
0
0 ExClifikUE CURRENT (Feel TAFEL Purr)
O opletr. eEcneol,E-!
+.6.2ot..
LOW OVEN EN-rift - GWENT PLaT
I 1 0-IM (1161).
tt. ELEaRnE, ARC= O.255 ti (ALso SEE ovErii-Enf).
Id?
-0775 0.1 0.Z 0.3 6.5
-0:11
-0.76 E votn-S, veRsos
sArociare-9 ckortEl...
icArVaLecTeo)C!
-0.78 o EL.EcrRal NOM A 91, Rr
-o.
- 0 -80
F zoilf
(F./NI EON. 2..0 7 SECTION Z'S 1").
FRO AN0INC I/ kJ SLOFE
=2•0
FROM amoDic 'EA/ SLOPE
= Ito .
.O\
0 0
SLOPE 0 \ = 1.05 x 105 \
0
-0.11
LOW OVEriroTENTIAL—CUMENT PLoTI IM-1\laIS 1 0M-5 I1-1•t0ii (Asa). P-1 ELEc1li0E , AREA = 0161 cti2
0 -075
SLOE
I. 10+ voLT5
-076
E VOLTS,
VFRS05
SATURATE)
CALotIEL
-018
EXCHANGE CoRREArr frtion TAFEL (tors)
2-3AMR ELEcr-R4E-1
Itt.Atilf.ELEcrRoDE-.1
0.5
1 .5 • 2, 2.5 0
oco ELECTRON NUMBEfj n,
SLOPE D rfiort An1010 SLOP.) i-o: 1-2 x 104VOLTS IRV! CATHODIC It „ ) 11,= 0'95
0 -0.10
3.0
FIt 1-.63 .
fiEncriokl Of0Efl PLOT — ANo)te
eoLARIZATIoN (TA-FEL 6EG-1W) 1o" 3-)111-1\ra z.S ti-Nita (AO).
eizaeo)E PrIMA =0255012.
'7= 23°c.
LoCr.l. tow. ELE-crizope.? V&. t's
scrruRATEI) CALAMEL-
SLOPE = 1.0
REficrioni Of■Defc.
0
201
0.6 -o.% -0+ 0 1.2,
Lo 0 [mot.ARtry of tjettS x lot
ORONO foraNnotic1-11 WIVE ANALYs1S —
"letiEVERSIBLE MODEL 7..ao
(fRoN 19140TO +.4.1) .
E.1441.S.1 = I-75x lo-3111 ) M- Na011 (0). eLecrime , rec.
SOFE = 13f riv.
[ FOR T= 23°C, • 2.3.2Ar g
F
to
160
M V. 140
120
0 oz 0+ 0.6 LOG„fre i-)
210
30
Zo
10
I MA. ELECTRODE
2. 6 '3
Igisficerr (Zit) a 3.11/lull:I
Ahlo)ie, GALVANo ST AT1C futSlrgr,
Sawing 19KOucT "PR ssivAnohl" Pio EL — cow si-Parr [AYER I) ssoLuTial RATE
(sec sEcnom 24-21 ENatS1 =-- ri-Nitoi (A61).
Au ELEcrgoTE AMA ct12.
70 ( r -(n114 2-51).
(FgOM SLOPE) 1-g5tt.COULOISS .Ce) 1 - SEC = 3-1 tia.ce
211
50
-212-
Finally, it was noted that cathodic galvanostatic pulsing on gold
produced a short ( rs-'50 p.coulombs. cm 2 )"stripping" plateau
probably due to the reductive desorption of some sulphur adsorbed on
the surface. The current density dependence of the plateau potential
produced a linear Tafel plot of slope '',60 mv. Platinum did not yield
well-defined arrests, but some charging process was noted, probably
electrochemical hydrogen adsorption and eventual gas evolution; in fact
the gold results suggested that this occurred above the stripping plateau.
The potential regions concerned (rest potentials -0.5v. versus N.H.E.)
suggest that appreciable cathodic hydrogen formation could possibly occur
leading to mixed potential phenomena. This indeed probably occurs for mar-
ked cathodic polarization, but the existence of the simple anodic Tafel
behaviour and the straightforward potentiometric results given in (12)
are evidence against this at least for the experimental conditions
encountered here. However, more work is intended in the near future to
more firmly establish this and other experimental points covered.in the
brief experimental survey described above.
4.6.3 General Discussion
The remarkable reproducibility and approximate independence on electro- with S present
de material of the anodic polarization data as suggested in (12) must be
due to a surface state involving coverage by sulphur-containing species
which act as sites for a rate-determining electron transfer reaction.
The similar exchange current values obtained for Pt, Au, W and graphite
electrodes are evidence against any strong or specific chemisorption of
this sulphur species to the electrode surface. [ The results of (12) are
briefly reviewed in section 2.9.2.1 1.
-213-
The most interesting and significant findings of the present investi-
gation are the apparently marked change of anodic mechanism when the sulphur
content was lowered, and the differences seen for sulphur-free systems
under galvanostatic pulse and steady-state conditions. The ", 60 mv. anodic
Tafel slope for most electrodes with solutions of high sulphur content
is indicative of a two-electron transfer step (12) (assuming a = 2 ).
However, the anodic slopes of 120-130 mv. obtained for gold and platinum
electrodes in sulphur-free media, and for platinum in solutions of low
sulphur content, along with the unity reaction order and pH dependence
are indicative of a one-electron anodic reaction involving one S2-
particle in the activatedcomplex (assuming a = A possible mechanism
involves the formation of an S ion as the product of the anodic rate-
determining step. Such an ion has not, at least chemically, been shown to
exist in bulk media, although only a transient existence of such a species
is required to yield the derived one-electron slope. It is interesting
that other ostensibly two-electron reactions have been shown to probably
occur in two distinct one-electron steps [e.g. Cd2+ -' Cd° (180)].
Furthermore, the electron affinity (energy released) for the process
- S S - = 24 k.cals. gm. atom
1 ; whereas for S a S2- -80 k.cal.
gm atom
-
(181), indicating that considerable intrinsic stability surrounds
the monovalent anion state. Moreover, S2 (or S3 ) species are now
well established as stable entities, at least in aprotic solvents
(section 2.9.2.4).
A similar explanation is envisaged to account for the low overpoten-
tial results for solutions of low sulphur content. In the case of gold,
however, the one-electron slope was obtained in the cathodic direction
only. This infers a change of mechanism very close to the reversible
-214-
potential. A possible explanation is that at these low sulphur contents,
the sulphur atoms (or polysulphide ions) produced in the anodic reaction
itself are required to catalyze the process according to the'normal
two-electron mechanism suggested in (12) (see section 2.9.2.1). On the
passage of a net cathodic current, however, these species are in short
supply, and a step involving reduction of the polysulphide species to form
Sx becomes rate-determining for both cathodic and anodic partial currents.
Hence the simple one-electron reaction can be obtained even in a potential
region where the reverse (anodic) reaction is important. On platinum at
low sulphur contents, the one-electron mechanism appears to persist even
at marked anodic overpotentials (see above).
Analysis of the cathodic Tafel regions are not very straightforward;
however the 114 mv. slope obtained on gold agrees with the suggested
one-electron process on the cathodic side.
The above behaviour with gold electrodes is compatible with the obser-
ved differences between the anodic chronopotentiometric open-circuit decay
and steady-state results on gold obtained with sulphur-free sulphide
solutions.
Thus effective Tafel slopes of 60 mv. were obtained for the first
two cases, whilst 120-130 mv. was obtained for the latter case with the
same electrolyte composition. Moreover, the chronopotentiometric wave
analysis plot yielded a slope of about 130 mv. for the irreversible model,
which combined with the observed current dependence for the wave potential
(Tafel slope) leads to a second-order reaction in sulphide for this two-
electron step. (see section 2.7.2.5). This is in agreement with the propo-
sed rate-determining step for polysulphide-catalyzed electron-transfer (12);
x2- S2- -2e,
--r- M....S S2 2- X-i
-215-
It confirms that a polysulphide ion, rather than a sulphur atom
acts as the agent for the electron-bridging process, and suggests the
mechanism
Q 2-
-2e M- Sx_ . S2-
. \ S•
S2-
2
( X)
The polysulphide necessary for this process to occur must have been
produced initially. This suggests that an autocatalytic process will
occur, provided that the current is high or the observation time is suffi-
ciently low so that the polysulphide is not markedly removed by diffusion
and convection from the surface. Again,platinum is ineffective for this
process, which suggests a specific catalytic effect obtainable with gold.
The pH dependence of the chronopotentiogram length indicates not only
that the S2- ion is the electroactive species, but also that the reaction
HS + 0H- 4 H2O + S2- is slow under these conditions, as no "chemi-
I cal" effect was observed (i.e. no decrease of iT2 with current density
i, see section 2.7.2.3). This effect is analogous to that seen with the
aqueous HCN CN + H+ system for cyanide oxidation, where again
CN was electroactive rather than the protonated species (152).
The reasonable fit to the "Franck" model (section 2.8) obtained for
chronopotentiograms on gold at high (>5 ma cm2) current densities suggests
that a passivation process is controlling the potential-time phenomena. The
derived charge required to passivate, ••' 460 p.coulombs. cm 2 , is
approximately (assuming a two-electron formation) equivalent to one sulphur
atom per surface gold atom, and is markedly less than that corresponding
to a close-packed sulphur monolayer, 740 p.coulombs cm-2 [assuming S
covalent radius = 1.04 A° (183)]. Thus, this passivation phenomenon,
involving at least a marked hindrance for the anodic catalysis for
-216-
sulphide oxidation by adsorbed polysulphide, occurs at a suprisingly low
coverage. This is possibly due to a preferred geometrical orientation of
the species in the activation complex for reaction (X) which becomes
more difficult to attain as neighbouring sulphur atoms or adsorbed
polysulphide ions provide increasing stereochemical hindrance at high
coverage.
The cathodic stripping process observed on gold electrodes from
unbiased potentials suggests n = 2, oi = 2 for the reduction process
(Tafel slope = PT/F). This indicates a simple irreversible stripping
of sulphur atoms.
Generally, the conclusions reached are somewhat tentative, being
based on a brief experimental investigation. However, some fundamentally
interesting points arise which would fully justify a more detailed
investigation in the future.
4.7 Anodic behaviour of iodide and bromide ions in lithium chloride-
potassium chloride eutectic
During the early anodic chronopotentiometric studies of sulphide ions
in LiCl-KC1, the intercept seen on the Sand. plot (T2 versus t2 )
(section 4.1.3) was originally ascribed to sulphide adsorption. Some
iodide was then added to determine if this ion could "displace" the
supposedly adsorbed S2- from the interphase. Previous potentiometry
(192) had shown the 1.712 couple to be rather more positive (standard
molar potential = + 0.536 v. versus S.M.S.E. at 450°C) than the
S2-/S couple (standard molar potential = 0.265 v. versus S.M.S.E. at
450°C) (134). However, no effect of the iodide was seen on the sulphide
-217-
oxidation wave, and furthermore blank experiments performed with only
iodide solute in LiCl-KC1 (10 3 1M-KI, ^' 450°C) yielded no anodic
-chronopotentiograms at all on gold or platinum electrodes. A similar
experiment with bromide ions also failed to detect any anodic waves
[here Br/Br2 standard molar potential = +0.920 v versus S.M.S.E.
at 450°C (192)].
Thus it appears that at least iodide is not electroactive at all
in LiCl-KC1 melt. (Any bromide wave may be obscured as it would be very
close to the chlorine evolution potential, + 1.065 v versus S.M.S.E.).
Previous mention of the lack of a clear anodic voltammetric wave for I
in LiCl-KC1 on a graphite electrode has been given (193). This contrasts
with the simple reversible chronopotentiograms obtained for iodide ions
in NaNO3 - KNO3 eutectic (151).
There is no evidence to suggest instability of iodide in chloride
melts, and double-layer capacitance measurements (193) indicate that it
is extensively adsorbed on a liquid lead electrode in this media (194).
However, in aqueous solution with added Cl ions, the iodide wave is
distorted and shifted to more positive potentials (195). On the basis of
this and other evidence it has been suggested that the tri-iodide ion
(I3 ), rather than the iodide ion (I-) is electroactive in this media
(196), as added Cl- ions will form the complex 12C1 ion in competi-
tion with 13 . Furthermore, in anhydrous trifluoroacetic acid, iodide
ion is completely electroinactive (197). This has been correlated with the
instability of the 13 ion in this media. The reaction
2 213 e- 312
3- 31
▪
- -1
--
- 313
-218-
has been postulated (197), the 13- ion acting as a catalyst for the
iodide oxidation. The electroinactivity of the iodide ion in the
chloride melt can be understood by considering that the large excess of
Cl ions present preferentially co-ordinates to any 12 molecules
produced to form 12C1 which "blocks" the required mechanism. This
finding is in agreement with the idea of electron-transfer occurring
from iodide ions adsorbed in a "second" layer across a iodide "bridge"
as discussed in section 2.9.4.
When the system contains a large activity of iodine, as in the
potentiometry (192), this presumably creates sufficient 13 for
electrochemical equilibrium to be established and a normal one-electron
Nernst slope with respect to iodide activity to b e obtained,
as observed.
-219-
SECTION ,5 : SUMMARY, CONCLUSIONS AND CONJECTURES
5.1 Sulphur electrodes
The mechanisms and kinetics of sulphide-sulphur redox electrodes were
studied in three solvents; fused lithium chloride-potassium chloride
eutectic, fused sodium nitrate-potassium nitrate eutectic, and alkaline
aqueous solutions. Gold electrodes appeared to be inert substrates for
all three sulphide-containing media under the polarization conditions
studied. Due to the volatility of sulphur in the fused media, solutions
of monosulphide were used which contained small quantities (^J 2%) of
polysulphide as an impurity.
In the fused chloride media, the existence of the redox equilibrium
2S2- S22- was determined potentiometrically for the sulphide
concentration range 10 3 - 1M. On anodic polarization under chronopo-
tentiometric conditions, potential-time arrests were obtained which appro-
ximately obeyed the Sand equation with respect to current density and con-
centration. On the basis of the arrest length (i.e. calculated diffusion
coefficient), and the effect of pre-bias and temperature on the arrest
length and shape, a model involving inhibition of the sulphide oxidation
reaction by a soluble sulphur film was considered be most likely.
Cathodic chronopotentiometry of polysulphide solutions S42-)
produced reversible chronopotentiograms involving the probable quasi-
equilibrium S42- 2S22-. A rough estimate of the polysulphide
diffusion coefficient, 'NJ 1 x 10 4 cm.2 sec , was obtained.
Steady-state voltammetry of monosulphide solutions on stationary
' inert electrodes produced inflected anodic waves leading to a limiting current
proportional to the added sulphide concentration, ascribed to reduction
-220-
of the polysulphide impurity in the added Na2S. Anodic polarization
yielded linear current-potential plots over a wide (> 0.1 v) potential
range, attributed to a slow surface dissolution reaction of the anodically
produced sulphur to form soluble polysulphide species. The surface
concentration of sulphur, presumably polymeric, was considered to be a
linear function of overpotential (logarithmic Temkin isotherm). Cathodic
galvanostatic charging curves from steady-state anodic overpotentials
also suggested an approximate Temkin isotherm for reducible material.
The sulphide-sulphur redox couple appeared to be reversible under all
conditions studied in this media.
The kinetics of formation and decay of the (assumed) polymeric sulphur
film were studied with potential-time galvanostatic build-up and open-
circuit decay curves respectively. These processes generally obeyed the
Boltzmann Superposition Principle, at least for small overpotentials
(<, 100 mv), and the kinetics essentially followed an Elovich rate equation.
Possible kinetic models involving relaxation of sulphur polymer segements
on the electrode surface during film formation and removal were considered.
Although a detailed mechanistic model could not be obtained, the film
appeared to be formed from, and removed via, polymer "precursor" units,
the number and type present depending on the imposed current density. A
schematic mechanism is thus
- 2 e
S S S 2- P 11-- polymer film
S 2 2 S2-
where S is the precursor polymer unit. All behaviour was essentially
independent of inert electrode material.
The behaviour in the fused nitrate system was in some respects
-221-
similar to the chloride system. Thus linear current-overpotential plots
were obtained for the sulphide concentrations studied (1072 -> 5 x 1C72 14).
Open-circuit decay behaviour was also very similar, with Elovichian decay
kinetics. However, galvanostatic build-up curves were not symmetrical
with these, explained by the imposed current density not immediately
"defining" a steady-state polymer "precursor" concentration during the
build-up curves.
Chronopotentiograms for sulphide oxidation were probably limited by
a soluble sulphur passivation model as for the chloride media. although
less evidence was assembled. A slow reaction of sulphide ian occurred
with the melt, making quantitative studied difficult. A kinetic overpoten-
tial was present under these high current conditions (> 1 ma. cm-2 ), the
potential shift suggesting irreversible formation of sulphur from sulphide.
However, for the steady-state current densities reversibility was likely,
the sulphur formed altering the Nernstian activity ratio as for the
fused chloride case.
For the corresponding alkaline aqueous system, the kinetics were
completely irreversible (electron-transfer controlled), and conventional
steady-state Tafel plots were obtained. The anodic Tafel slopes depended
on the bulk sulphur concentration in that the two-electron (for a= 2) slope
observed for sulphur concentrations comparable with sulphide, changed to
a one-electron slope at low sulphur contents. This has been interpreted as
a change from the two-electron reaction
N.... s2 - X-1
+ S2- gems M....S + S 2- X-1 2
catalyzed by polysulphide, to a one-electron transfer to form "S-",
which subsequently dimerized to S22-. A similar change in mechanism was
-222-
considered to account for the difference between anodic steady state and
chronopotentiometric pulse conditions with sulphur-free dilute (",10 3 M)
sulphide solutions on gold. Thus the steady state Tafel plots yielded
one-electron (CY = slopes, whereas analysis of the chronopotentiograms
yielded a two-electron, second-order reaction in sulphide. This is
consistent with the mechanism given above for sulphur-containing systems,
and suggested that the pulse experiments provided a large build-up of
sulphur at the interface. Similar chronopotentiograms were occasionally
produced in the fused nitrate media, but were not reproducible.
For added sulphide concentration >5 x 1073 M, passivation-limited
"chronopotentiograms" were obtained; sulphur dissolution was not the
dominant factor here as the Sand equation was not obeyed.
Thus, in all three systems, sulphur played a dominant role in the
anodic process, either in providing and alternative mechanistic pathway
as in the aqueous system; or by accumulating as a polymer network at
the interface and altering the Nernst activity ratio and hence the
potential, as for the melt system.
5.2 Metal oxide and sulphide surface films
Thenchemisorbed" oxygen films observed to form on platinum by anodic
polarization from an oxide solution in LiCl-KC1 eutectic, had some simila-
rities with the much-studied aqueous films. Thus the galvanostatic
potential-time profiles were linear for film formation, with an arrest
for reduction involving a marked hysteresis. The film formation kinetics
were studied potentiostatically, film growth being measured by the length
-223-
of subsequent galvanostatic stripping arrests. Two logarithmic growth-
time regions were found, attributed to different types of oxide film;
also the kinetics depended on the formation potential. At least three
equivalent Pt° layers could be grown, and the film properties could
most easily be described in terms of dominant rate-determining incorpo-
ration of oxygen to form a "phase oxide", under the high local fields
present at the interface. In particular, the low Tafel slopes ("JET/2F)
obtained for film reduction at constant coverage could (as for the aqueous
case) only be satisfactorily explained by postulating a rate-determining
concerted metal ion-oxide ion rearrangement step under a high field. The
approximately constant Tafel slope with varying coverage was explained by
considering reduction to take place from oxide "islands" (patches) at a
constant local field. Film "ageing" effects, observed as a logarithmic
time dependence of the potential and shape of the galvanostatic reduction
arrest were attributed to rearrangement of the incorporated oxide film.
Much thicker (", 103 A° ) films were formed on platinum from sulphide
solutions in LiCl-KC1 eutectic. The film growth kinetics were initially
linear, then parabolic in time, attributed to a rate-determining surface
reaction (Pt S --> PtS) giving way to activated ion transport through th
growing film at low field strengths. The galvanostatic reduction arrests,
used for determining film thicknesses, were composed of two main waves,
the first wave for short film formation times being replaced by a second
more cathodic wave at longer times (> 1 min.). This was attributed to
an initially random sulphide layer rearranging into a more regular
stable lattice.
The Tafel slopes for galvanostatic reduction at constant coverage
were low ("' RT/2F). A similar explanation to the oxide case is proposed.
An analysis of the reduction wave slopes indicated (for the second
-224--
stripping wave) a first order reaction in reducible sulphide with no
appreciable site energy distribution. This was attributed to reduction
from a progressively decreasing number of similar "crystallite film
regions.
The large differences in film growth between the platinum oxide and
sulphide systems may be partly ascribed to free energy effects,
4500C for Ft S 2 = 6.0 k.cal. mole" ( 177 ) , - A G45
°°C [ - AG
formation formation
for Pt° = 2.6 kcals. mole 1 (14)] although other, kinetic factors
are doubtless in operation.
The anodic oxidation of sulphide in LiCl-KC1 on a liquid bismuth
electrode produced irreproducible chronopotentiometric waves probably due to
passivation by a chemisorbed sulphur film (Bi2S3?). The longest waves
produced a diffusion coefficient for sulphide ion of "J 1C r4 cm2 sec 1 .
The surface film as seen by cathodic stripping, reversibly removed up to
the anodic passivation time, appeared to attain "phase" properties after
this point, as seen by irregular stripping arrests at high cathodic poten-
tials.
L._5 Iodine and bromine electrodes
At least iodide, and probably bromide ions, were found to be electro-
inactive at platinum and gold anodes in LiCl-KC1 eutectic. This was
attributed to the necessary formation of 13 being prevented by preferen-
tial co-ordination of any iodine produced to form 12C1. This lends
support to a general model of iodide (and probably bromide) oxidation
occuring by "bridging" across adsorbed 12 molecules (produced by any
-225-
previous I oxidation), by an autocatalytic mechanism involving 13 ions.
5.4 Elovich Kinetics
The Elovich rate equation (section 2.4.6) was found to be applicable at
least in outline, to both the sulphur film data and some aspects of the Pt0
films. The wide applicability of the equation to interfacial kinetic pheno-
mena has previously been discussed (e.g. 49, 53, 54). However, it should be
noted that the logarithmic rate form involved is a relatively insensitive
function, particularly if the rate changes involved are not large. Thus the
1-5 x 102 changes in rate for the sulphur film kinetics could be fitted by
other similar models, particularly as here uncertainty exists of the associ-
ated isotherm form. The good logarithmic fit for potentiostatic formation of
aqueous Pt0 layers with rate changes of ^'l05 (75) is rather more impressive.
As discussed in section 2.6.3.6, the potentiostatic film formation kine-
tics of Pt0 cannot be completely accounted for by the high-field conduction
model. However, the varying logarithmic slope with formation potential
obtained in aqueous solutions also cannot be explained by simple adsorption
model involving a constant activation energy change per given coverage change.
Interestingly, this result is rather similar to the varying decay and build-
up log. slopes with overpotential seen for the sulphur film kinetics. In
outline both these results can be derived by considering a constant activation
energy change for a given fraction of the eventual coverage change, and are
in accord with the Boltzmann Superposition Principle. A spontaneous time-
relaxation effect (required by the principle) appears to exist during Pt0
film formation, as evidenced by the dependance of the layer properties on
the formation history (75).
Finally, this author has recently accumulated data suggesting that an
Elovich rate form involving an increasing activation energy is also applicable
to thesis preparation.
p140T0.4.I.1 .
FOTO. t 13 .
22
--3
Qs
4
:01
Iva, .11.9.
?MT°. 1-..I.I0 ,
2O
FOTO . 4-. 1. 11 .
PHoTo .1-.1.1Z
M • RH MINIM
MIME= ••••• MENNE 11111
•• ••••• MN
WM MN IMO •• ••
mr.... n.. um
!tor
• 1' 0-1911d
47114' olotid
ZS
233
toltaro.1-:2.
P Rao . +23 ,
••■■■•••+.4.■ Wiii■ii W-MN OM MN MIll •• •• Ell •••
NOME
231-
Pltoro.t2.4f.
23E.
floilLtS.1 .
ilitsro.1-3.2..
NE
E
P
iii INF ism=
.. ...............
=a.m..... • ....m
om..
'Z'ci,.. alow
. I • s4vipici
2SZ
PRro,t5.3.
Pliera.175.4-.
23,
' 9 .9:437-1-oild
' .5.94.0-10fid
047
Piro.44 .1.
241
-21+2-
INDEX TO PHOTOGRAPHS
-1 -1 -2 4.1.1 x = 0.5 sec. cm ; y = 0.2 v cm ; i = 1.99 ma. cm
Au electrode T = 429°C. [Na2S ] = 5 x 10-3 M. top
wave unbiased, lower wave -200 my prebiased.
4.1.3 - - x = 1 sec cm
1 ; y = 0.2 v cm
1 ; i = 5.19 ma cm
-2
Au electrode T = 410°C. [Na2S] = 3.53 x 107' M.
4.1.4 x = 1 sec cm-1 ; y = 0.2 v cm-1
i = 1.46 ma cm-2.
Au electrode. T = 443°C. [Na2S = 1.17 x 10 2 M .
-100 my prebiased.
4.1.5
4.1.7a
- - x = 0.5 sec cm
1 ; y = 0.2 v cm 1 ; i = 1.92 ma cm-2 .
Au electrode. T = 1+35°C. [Na2S = 2.27 x 1072 M.
x = 0.5 sec. cm-1 ; y = 0.2 v cm-1 ; i = 11.5 ma cm-2
Au electrode T = 427°C. [Na2S] = 1.5 x 10 2 M. Various
anodic pulses (read upwards).
- x = 0.5 sec.cm
1 ; y = 0.1 v cm-1 ; i = 20.2 ma cm
-2
Au electrode. T = 423°C. [ IK2S611] "J 2 x 10-2 M. (Cathodic upwards).
1+.1.7b x = 0.2 sec. cm-1 ; y = 0.1 v cm-1 ; i = 15.9 ma cm-2
Au electrode T = 423°C. ["K2S4"] ", 6 x 10 3 M (Cathodic upwards).
4.1.8 x = 5 msec. cm-1 ; y = 0.05 v cm.1 ; i = 11.3, 20.5, 38.5 ma cm-2 .
Au electrode. T = 432°C. [Na2S] = 5.7 x 10 3 M. + 250 my prebiased.
Cathodic downwards - read downwards.
- - 1 4.1.9 x = 0.05 sec. cm
1 ; y = 0.1 c cm ; y = 20.3, 34.7, 49.8 ma cm-2
Au electrode. T = 420°C + 450 my prebiased. Cathodic downwards -
read downwards.
x 0.5, 5 sec. cm1 ; y = 5 my cm-1 ; Pt electrode.
T = 435°C. Decay from + 30 mv.
4.1.10 -
-243-
4.1.12
4.1.14
x = 0.5, 5 sec cm ; y = 20 mv. cm . Pt electrode.
T = 435°C. Decay from + 100 mv.
- - x = 2 sec. cm
1 ; y = 0.02 v cm
1 . Au electrode T = 427▪ C.
Galvanostatic build-up, open-circuit decay (Anodic upwards).
- x = 0.2, 2 sec cm ; y = 20 mv cm
1 . Cathodic i = 6.34 ma cm2
followed by open-circuit decay.
4.1.11
-
4.2.1 x = 0.2 sec cm ; y = 0.2 v cm1 ; i = 2.24 ma cm-2. 1
Pt electrode. T = 252°C. [Na2S] 3.5 x 1072 M.
4.2.2 x = 0.5 sec cm1 ; y = 0.1 v cm ; i = 0.57 ma cm 2.
Au electrode. T = 229°C. [Na2S] r`d 9 x 1073 M.
4.2.3 x = 0.02, 0.2, 2 sec cm1 ; y = 50 my cm1 . Pt electrode.
T = 254°C. Decay from +350 mv.
-1
4.2.4 x = 0.5 sec cm
-
; y = 50 my cm . Pt electrode. T = 251 C.
Galvanostatic build-up (i = 73.5 p amp cm-2 ) open-circuit
decay (Anodic upwards).
-1 -1
4.2.5 x = 10 msec cm ; y = 0.2 v cm ; y = 2.79, 5.44, 7.10,
13.1, 19.6 ma cm-2 . Pt electrode T = 251 °C. Cathodic
(downwards) from - 45 my (v's S.M.S.E.).
4.3.1 x = 50 msec cm-1 ; y = 0.1 v cm-1 ; i = 42.4 ma cm2 .
T = 430°C. Unbiased formation times 1/3, 1 min.
4.3.2 x = 0.2 sec cm-1 ; y = 0.1 v cm-1 ; i = 23.2 ma cm2 .
T = -4!54°C. Unbiased formation for 2 mins.
4.3.3 - -
x = 0.5 sec. cm1 ; y = 0.1 v cm 1 ; i = 44.3 ma cm-2.
T = 454cC. Unbiased formation for 23 mins.
4.3.4 - -
X = 0.2 sec cm1 ; y = 0.1 v cm 1 i ; = 81.5 ma cm
-2
° T = 540C. Unbiased formation for 3 mins.
-244--
4.4.1 x= 0.2 sec cm-1 ; y= 0.1 v cm-1 ; i = 10.5 ma cm-2
from -0.315 v (v's S.M.S.E.) T = 425°C.[Na 2 .= 5 . 2 x 10 3 M
-
4.4.2 x = 0.1 sec cm-1 ; y = 0.2 v cm 1 . ; = 78 ma cm-2 . from
-0.456 v (v's S.M.S.E.) T = 425°C. [Na2S] = 2.82 x 10-2 M.
4.5.1 _ x = 50 msec. cm ; y = 0.1 v cm
1 ; i = 25.1 ma cm-2.
Pt electrode. T = 425°C. [L120] = 0.185 M.
_1 4.5.2 x= 50 msec. cm-1 ; y = 0.1 y cm ; i = 5.67 ma cm-2 .
T = 425°C. [1.,i20]= 0.185 M.(Horizontal trace at -0.50v.v's S.M.S.E.)
4.5.3
4.5.4
4.5.5
-1 -1 x = 0.2 sec cm ; y = 0.1 v cm ; i = 0.56, 1.18, 2.29, 4.05 ma
cm-2. T = 425°C. [Li20] = 0.185 M. (Anodic upwards -
from -0.545 v. v's S.M.S.E.).
-1 x = 0.1 sec cm
-
; y = 0.2 v cm . Cathodic i = 4.011ma cm -2 .
T = 443°C. [Li20] = 0.20 M. 1, 3, 8, 15 mins. formation at
-0.085 v (v's S.M.S.E.).
_1 x = 50 msec. cm 1 ; y = 0.2 v cm Cathodic i = 4.01 ma cm
-2
T = 443°C [L120] = 0.20 M. 1st wave 15 sec. at - 0.035 v.,
2nd wave 15 sec at -0.035 v, open-circuit for 30 sec;
3rd 45 sec. at -0.035 v. (v's S.M S.E.).
4.5.6 x = 50 msec. cm 1; y = 0.2 v cm 1 . Cathodic i = 5.61 ma. cm .
for 30 sec formation as f(forrnation potential) - 115 my -) + 35 my.
[Li20] = 0.20 M, T = 443°C.
4.6.1 - -
x = 1 sec cm1 ; y = 0.1 v cm1 . ; = 0.440 ma. cm
-2 .
Au electrode. T = 23°C. [Na2S] = 1.75 x 10 3 M, M-NaOH.
(base of photo - 0.600 v. v's sat calomel).
4.6.2 x = 0.2 sec cm-1 ; y = 0.1 v cm1 ; i = 1.93 ma. cm-2 .
Au electrode. T = 23°C. [Na2S] = 2.37 x 10-2 M, M-NaOH.
-245-
SYMBOLS USED
E measured electrode potential
overpotential
e E equilibrium potential
ax activity of species x
[X] concentration of species x
f m Galvani (inner) potential difference
I current
current density
_a i partial forward current density
Ar partial backward current density
io exchange current density
ko standard electrochemical rate constant
n number of electrons transferred
electrochemical potential
chemical potential
T temperature in °K
k Boltzmann Constant
h Planck Constant
Fix surface excess of species x
S.M.S.E. Standard Molar Silver Electrode
S.M.P.E. Standard Molar Platinum Electrode
N.H.E. Normal Hydrogen Electrode
D diffusion coefficient of species x x-
E° Standard electrode potential
-246-
RhkERENCES
1. J.01 14. Bockris, A.K.N. Reddy; "Modern Electrochemistry" Vols I and II.
2. K.J. Vetter; "'Electrochemical Kinetics" Academic Press (1967).
3. D Inman, S.H. White; Ann. Reports. Chem. Soc. 62, 106 (1965).
4. G.J. Janz; "Molten Salts Handbook" Academic Press (1967).
5. H. Bloom; "Chemistry of Molten Salts". Benhamin (1967).
6. B.R. Sundheim (Ed); "Fused Salts" McGraw-Hill (1964)..
7. M. Blander (ed); "Molten Salt Chemistry" Interscience (1964). 8. Yu. K. Delimarskii, B.F. Markov; "Electrochemistry of fused Salts"
Sigma Press (1961).
9. A.D. Graves, G.J. Hills, D. Inman; in "Advances in Electrochemistry and
Electrochemical Engineering" Vol. IV p. Delahay (Ed) Interscience (1966).
10. D. Inman, A.D. Graves, B.S. Sethi; "Electrochemistry Vol I - A
Specialist Periodical Report" The Chemical Society (1971).
11. D. Inman, A.D. Graves, A.A. Nobile, As Ref. 10, Vol II (1972).
12. P.L. Allen, A. Hickling; Trans. Far. Soc. 53, 1626 (1957).
Chem. and Ind., 1558, (1954).
13. R. Spencer, Ph.D. Thesis, London University (1967).
14. N.S. Wrench; Ph.D. Thesis, London University (1967).
15. G. Brauer (Ed);"Handbook of preparative inorganic chemistry" p.358-60.
16. D. Inman; Ph.D. Thesis, London University (1957).
17. A.D. Graves, D. Inman; J. Electroanal. Chem. 22, 357 (1970). 18. A.D. Graves, D. Inman; Nature 208, 481 (1965). 19. T.R. Kozlowski; R.F. Bartholomew, H.M. Farfinkel, J. Inorg. Nucl.
Chem. 32, 401 (1970).
20. R. Parsons; Surface Science 2, 418 (1964). (1967). 21. A.W. Adamson; "Physical Chemistry of Surfaces" 2nd Edn. Interscience
22. B.E. Conway; "Electrode Processes" Ronald (1965).
23. S. Glasstone, L.J. Laidler, H. Eyring; "Theory of Rate Processes"
McGraw-Hill (1940).
24. D.J.G. Ives, G.J. Janz (Eds); "Reference Electrodes" Academic Press
(1961) Chapter I.
25. R. Parsons; "Adv. Electrochem. and Electrochem.Eng." P. Delahay (Ed)
Chapter I, Vol I, Itterscience (1961).
26. E.A. Guggenheim, J. Phys. Chem. 33, 842 (1929). 27. P. Delahay; "Double Layer and Electrode Kinetics" Interscience (1965).
28. J. Horiuti, M. Polanyi; Acta. Physicochim. U.R.S.S. 2, 505 (1935).
29. H.H. Bauer; J. Electroanal. Chem. 16, 419 (1968).
-247-
30. N. Tanaka, R. Tamamushi; Electrochim. Acta. 9, 963 (1964).
31. R. Audubert; Disc. Far. Soc. 1, 72 (1947)-
32. Ref. 24, Chapter II..
33. H.P. Stout, Trans. Far. Soc. 41, 64 (1945).
34. L. Young; "Anodic Oxide films" Academic Press (1961).
35. J.L. Ord, F.C. Ho; J. Electrochem. Soc., 118, 46 (1971).
36. K.J. Vetter, J.W. Schultze, J. Electroanal. Chem. 34, 131, 141 (1972).
37. R.W. Gurney, Proc. Roy. Soc. (Loud.), A134, 137 (1932).
38. I. Langmuir; J. Chem. Phys. 1, 756 (1933). (1964). 39. D.O. Hayward, B.M.W. Trapnell; "Chemisorption" 2nd Edn. Butterworths
40. R. Parsons; J. Electroanal. Chem. 7, 136 (1964).
41. G.L. Gaines, Jr; "Insoluble Monolayers at Liquid-Gas Interfaces"
Interscience (1966).
42. T.W. Hickmott; J. Chem. Phys., 32, 810 (1960).
43. H.S. Taylor, Proc. Roy. Soc. A108, 105 (1925).
44. J.K. Roberts; Proc. Roy.Soc. A152, 445 (1935). 45. M. Boudart. J. Am. Chem. Soc., 72, 1531, 3556 (1952).
46. F.C. Tompkins, "The Solid-Gas Interface" Vol II, p. 765 E.A. Flood
(Ed), M. Dekker (1967).
47. J.C.P. Mignolet, Disc. Far. Soc. 8, 105 (1950).
48. T.A. Delchar, F.C. Tompkins; Proc. Roy. Soc. A300, 141 (1967).
49. M.J.D. Low, Chem. Reviews, 60, 267 (1960).
50. C. Aharoni, F.C. Tompkins; Adv. in Catalysis, 21, 1 (1970).
51. P.M. Gundry, F.C. Tompkin6; Trans. Far. Soc. .5.2, 1609 (1956).
52. P.M. Gundry, F.C. Tompkins; "Chemisorption" W.E. Garner (Ed),
p. 152, Butterworths (1957).
53. P.T. Landsberg; J. Chem. Phys. 23, 1079 (1955). 54. D.D. Eley; Trans. Far. Soc. 49, 643 (1953).
55. D.D. Eley; D.C. Pepper; Trans. Far. Soc. 2, 568 (1947). 56. A.V. Tobolsky; "Properties and Structure of Polymers" J. Wiley (1960).
57. S.J. Singer; J. Chem. Phys. 16, 872 (1948).
58. K. Motomura, R. Matuura; J. Colloid. Sci. 18, 52 (1963).
59. E. Gileadi, B.E. Conway; "Modern Aspects of Electrochemistry"
Vol. III, p 347 Butterworths (1964).
60. H.B. Morley, F.E.W.-Whetmore; Can. J. Chem. 24, 359 (1956).
61. P. Javet, L. Nanis; Electrochim. Acta. 1785 (1968).
62. W.T. Scott; J. Chem. Phys. 23, 1936 (1955).
63. J.L. Ord; J. Electrochem. Soc. 112, 46 (1965).
64. B.E. Conway, E. Gileadi, H.A. Kozlowska, J. Electrochem.Soc.112,342(1965).
-248-
65. S. Srinivasan, E. Gileadi; Electrochim. Acta. 11, 321 (1966). (1969).
66. P. Stonehart, H.A. Kozlowska, B.E. Conway. Proc. Roy. Soc. A310, 541
67. S.E.S. El Wakkad, S.H. Emara. J. Chem. Soc., 461 (1952).
68. S. Gilman; "Electroanal. Chem. - A Series of Advances" 2, 111 (1967).
69. W. Boeld, M. Breiter; Electrochim. Acta 5, 145, 169 (1961).
70. J.P. Hoare; "Electrochemistry of Oxygen".
71. M.A. Genshaw. Chapter TV-in "Electrosorpton" E. Gileadi (Ed) Plenum (1967)
72. S. Schuldiner, T. Warner; J. Phys. Chem. 69, 4048 (1965).
73. T. Biegler, D.A.J. Rand, R. Woods. J. Electroanal. Chem. 29, 269 (1971).
74. D. Gilroy, B.E. Conway; Can. J. Chem. 46, 875 (1968).
75. K.J. Vetter, J.W. Schultze; J. Electroanal. Chem. 34, 131, 141 (1972).
76. A.C. Makrides; J. Electrochem. Soc. 113, 1158 (1966).
77. S. Gilman; Electrochim. Acta. 9, 1025 (1964).
78. J.L. Ord, F.C. Ho; S. Electrochem. Soc. 118, 46 (1971).
79. A.N. Frumkin. "Adv. in Electrochem & Electrochem Eng."
Vol. 111 P.287. Interscience (1963).
80. H.A. Laitinen, C.G. Enke; J. Electrochem Soc. 107, 773 (1960).
81. M.W. Breiter; Electrochim. Acta. 7, 533 (1962);
J. Electroanal. Chem. 7, 38 (1964).
82. M.W. Breiter; J. Electrochem. Soc. 109, 42 (1962).
83. D.H. Everett; Chapter 36 in "The Solid - Gas Interface".
E.A. Flood (ED). M. Dekker (1967).
84. K. Ohashi, K. Sasaki, S. Nagaura; Bull. Chem. Soc. Japan. 39, 2066 (1966).
85. S.B.Brummer, A.C. Makrides; J. Electrochem. Soc. 111, 1122 (1964).
86. J.W. Schultze, K.J. Vetter. Ber Bursenges. Phys. Chem. 75, 470 (1971).
87. D. Brennan, D.O. Hayward, B.M.W. Trapnell; Proc. Roy. Soc. A256, 81 (1960)
88. K. Sasaki, Y. Nishigakiuchi; Electrochim. Acta. 16, 1099 (1971).
89. J. Balej, O. Spalek; Coll. Czech. Chem. Comets. 37, 499 (1972). 90. S. Khibata, M.P. Sumino; Electrochim. Acta. 16, 1089 (1967).
91 S. Shibata; Bull. Chem. Soc. Japan. 40, 696 (1967).
92. R.L. Every, R.L. Grimsley; J. Electroanal. Chem. 9, 167 (1965).
93. J.L. Ord; J. Electrochem. Soc. 112, 46 (1965).
94. R.W. Murray, C.N. Reilley; "Electroanalytical Principes" Inter Scigg3)
95. E. Yeager, J. Kuta; Chapter 4 in "Physical Chemistry - an Advanced Treatise" Vol 1X A. H. Eyring. (ED). Academic Press (1970)
96. P. Delahay; "New Instrumental Methods in Electrochemistry" Inter Sci2g4)
97. D.G. Davis; "Electroanal. Chem. 14, 447 (1967).
98. M.Paunovic; J. Electroanal. Chem. 14, 447 (1967).
99. R.AMurray, D.J. Gross; Anal Chem. 38, 392 (1966).
-249-
100. CAl.J. Lingane; Anal. Chem. 39, 485 (1967).
101. F.C. Anson; Anal Chem. 38, 54 (1966).
102. R.W. Laity, J.D.E. McIntyre; J. Am. Chem. Soc. 87, 3806 (1965). 103. B. Burrows, S. Kirkland; J. Electrochem. Soc. 115, 1164 (1968).
104. F.H. Beyerlein, R.S. Nicholson; Anal. Chem. 40, 286 (1968).
105. H.B. Herman, A.J. Bard; J. Electrochem. Soc. 115, 1028 (1968).
106. C. Furlani, G. Morpurgo; J. Electroanal. Chem. 1, 351 (1959/60).
107. W.H. Reinmuth; Anal. Chem. 32, 1514 (1960).
108. P. Bos, E. Van Dalen; J. Electroanal. Chem. 17, 21 (1968).
109. P. Delahay, T. Berzins; J. am. Chem. Soc. 75, 2486 (1953). 110. W.H. Reinmuth; Anal. Chem. 33, 485 (1961).
111. J.D. Voorhies, N.H. Furman; Anal. Chem. 30, 1656 (1958).
112. C.D. Russell, J.M. Peterson; J. Electroanal. Chem. 5, 467 (1963).
113. D.C. Noonan; Thesis. Columbia University (1961).
114. M. Fleischmann, H.R. Thirsk; "Adv in Electrochem & Electrochem Eng.
Vol 111, Chapter 3. P. Delahay (Ed), Inter Sci24)1
115. R.D. Armstrong, J.A. Harrison, H.R. Thirsk; Corr. Sci., 10, 679 (1970).
116. D.A. Vermilyea; As Ref. 114. Chapter 4.
117. T.P. Hoar; "Modern Aspects of Electrochemistry" Vol 11 P. 262.
J. O'M. Bockris (Ed). Academic Press (1959).
118. U.R. Evans; Electrochim. Acta. 16, 1825 (1971).
119. R.D. Armstrong, H.R. Thirsk; Electrochim. Acta. 17, 171 (1972).
120. N.A. Hampson, N.J. Tarbox; J. Electrochem. Soc. 110, 95 (1963). 121. J.P. Elder; J. Electrochem, Soc. 116, 757 (1969).
122. 0.14 Reilley, W. Stumm; "Progress in Polarography" Vol 1 P. 81. P. Zuman; I.M. Kolthoff (Eds). Inter Science (1962).
123. H. Gerischer; Z. Elektrochem. 54, 540 (1950).
124. N. Salomon; J. Electrochem. Soc. 113, 940 (1966).
125. C.A. Angell, C.T. Moynihan; "Molten Salts" P 315 G. Mamantov (Ed),
M. Dekker (1969).
126. M. Akhtar, F.C. Tompkins; Trans. Far. Soc. 67, 2454 (1971).
127. W. Latimer "The Oxidation States of the Elements and Their Potentials
in Aqueous Solutions". 2nd End. (1952). p. 70. 128. R.D. Armstrong, D.F. Porter, H.R. Thirsk;;J. Phys. Chem. 72, 2300 (1968
129. M.V. Merritt, D.T. Sawyer; Inorg. Chem. 9, 211 (1970).
130. M.H. Miles, W.S. Harris; J. Electrochem. Soc. 117, 1225 (1970).
131. S.I. Rempel, E.N. Malkova; J. Applied Chem. V.S.S.R. 25, 631 (1952).
132. G. Delarue; Bull. Soc. Chim. France, 906 (1960).
133. W.T. Thompson, S.N. Flengas; Can. J. Chem. 46, 1611 (1968).
-250-
134. F.G. Bodewig, J.A. Plambeck; J. Electrochem. Soc. 116, 607 (1969);
F.G. Bodewig. Thesis, University of Alberta (1970).
135. W. Oiggenbacht J. Inorg, Nucl. Chem. 30, 3189 (1968);
Inorg. Chem. 10, 1306 (1971).
136. D.M. Gruen, R.L. McBeth, A.J. Zielen; J. Am. Chem. Soc. 93, 6691 (1971).
137. R. Parsons, W.H.M. Visscher; J. Electroanal. Chem. 36, 329 (1972). (1971).
138. A.J. Calandra, M.E. Martins, A.J. Arvia; Electrochim. Acta. 16, 2057.
139. V.S. Bagotzky, Yu. B. Vassiliev; Electrochim. Acta. 11, 1439 (1966).
140. R.N. Kust, F.R. Duke; J. Am. Chem. Soc; 85, 3338 (1963).
141. A.M. Shams El Din, A.A. Gerges; "Electrochemistry - Proc. 1st. Aust.
Conference, 1963" Pergamon (1964).
142. P.G. Zambonin, J.Jordan; J. Am. Chem. Soc. 91, 2225 (1969).
143. P.G. Zambonin; J. Electroanal. Chem. 24, App 25 (1970). 144. N.S. Wrench, D. Inman; J. Electroanal. Chem. 17, 319 (1968).
145. A.M. Arthur; Unpublished Results.
146. D.T. Sawyer, J.L. Roberts. J. Electroanal. Chem. 12, 90 (1966).
147. K.J. Vetter; Z. Physik. Chem; 199, 285 (1952).
148. J.D. Newson. A. C. Riddiford; J. Electrochem. Soc. 108, 699 (1961).
149. R.A. Osteryoung, F.C. Anson; Anal. Chem. 36, 975 (1964).
A.T. Hubbard, R.A. Osteryoung, F.C. Anson; Anal. Chem. 38, 692 (1966)
150. J. Badoz-Lambling, C. Dutruc-Rosset; Anal. Chim. Acta. 19, 43 (1958).
151. R.B. Fulton, H.S. Swofford; Anal. Chem. 40, 1373 (1968).
152. D.T. Sawyer, R.J. Day; J. Electroanal. Chem. 5, 195 (1963).
153. L.I. Krishtalik, G.E. Titova; Sov. Electrochem. 4, 249 (1968).
157. P.L. King. Ph.D. Thesis. University of New South Wales (1971). 158. P.A. Tichauer. Ph.D. Thesis M.I.T. (1971).
159. G. Nickless (Ed); "Inorganic Sulphur Chemistry" Elesevier (1968).
160. G. Gee; Trans. Far. Soc. 48, 515 (1952).
161. D.M. Gardner, G.K. Fraenkel; J. Am. Chem. Soc. 78, 3279 (1956).
162. J. Berkowitz, J.B. Marquart; J. Chem. Phys. 39, 275 (1963). 163. F. Fairbrother, G. Gee, G.T. I1errall, J. Polymer Sci. 16, 459 (1955).
164. J. Greenberg, B.R. Sundhem, D.M. druen, J. Chem. Phys. 29, 461 (1958).
165. F.G. Bodewig, J.A. Plambeck; J. Electrochem. Soc. 117, 904 (1970).
166. A.C. Makrides; J. Electrochem. Soc. 113, 1158 (1966).
167. W.D. Cooper, R. Parsons; Trans. Far. Soc. 66, 1698 (1970).
169. T. Loucka;J. Electroanal. Chem; 36, 355 (1972).
170. A.B. Thomas, R.J. Brodd; J. Phys. Chem. 68, 3363 (1964).
171. J.S. Mayen; J. Electrochem. Soc. 113, 385 (1966).
172. As Ref. 52.
-251-
173. M.W. Roberts; "Recent Progress in Surface Science"
Vol. 111 J.F. Danielli Et Al. (Eds). Academic Press (1970).
174. T.P. Hoar, A.J.P. Tucker; J. Inst. Metals. 81, 665 (1952/3).
175. K. Hauffe; "Oxidation of Metals" Plenum (1965).
176. J.V. Happ, T.R.A. Davey; Trans. A.I.M.E. 80, C190 (1971).
177. O. Kubaschewski, E.L. Evans, C.B. Alcock;
"Metallurgical Thermochemistry" 4th Edn. Pergamon (1967).
178. B.W. Burrows, G.J. Hills. Electrochim. Acta. 15, 445 (1970).
179. J.J. MacDonald, B.E. Conway; Proc. Roy. Soc. A269, 419 (1962). (1970). 180. A.R. Despic, D.R. Jovanovic, S.P. Bingulac; Electrochim. Acta; 15, 459
181. H.O. Pritchard; Chem. Revs. 52, 529 (1953).
182. A.J. Ellis, R.M. Golding; J. Chem. Soo, 127 (1959).
183, H.S. Taylor, Proc. Roy. Soc. A108, 105 (1925).
184. L.L. Bircumshaw, A.C. Riddiford; Quart. Revs. 6, 157 (1952). 185. A.N. Frumkin, E. Aikasjan; Izvest. Akad. Nauk, 202 (1959).
186. Z. Nikolaveva, A. Krasilshchikov; Zhur. Fiz. Khim. 32, 1545 (1958).
187. J.D. Ferry; "Viscoelastic Properties of Polymers"
2nd Edn J. Wiley (1970).
188. I.M. Ward; "Mechanical Properties of Solid Polymers" J. Wiley (1971).
189. As Ref. 19.
190. P.G. McCormick, H.S. Swofford; Anal. Chem. 41, 146 (1969).
191. B.J. Brought D.H. Kerridge; Inorg. Chem. 4, 1353 (1965).
192. H.A. Laitinen, J.W. Pankey; J. Am. Chem. Soc. 81, 1053 (1959).
193. M. Leroy; Mem. Pres Soc. Chim, 968 (1962).
194. A.A. Nobile; Unpublished Work.
195. I.M. Koithoff, J. Jordan; J. Am. Chem. Soc; 76, 3843 (1954).
196. J. Badoz-Lambling; Anal. Chim. Acta. 19, 43 (1958). 197. G. Petit, J. Bessiere. J. Electroanal. Chem. 25, 317 (1970).
198. B.E. Conway, D.J. MacKinnon, B.V. Tilak. Trans. Faraday Soc., 66, 1203 (1970).
-252--
ACKNOWLEDGEMENTS
I thank Associated Lead Manufacturers Ltd. for providing a College
Bursary for the major portion of this work, and also the British Iron
and Steel Research Association for financial support during the initial
stages.
I would like to express my sincere appreciation to my supervisor,
Dr. D. Inman, for his tolerance and understanding during my introduction
to the art of fundamental research.
I also thank the following people for much assistance during the
course of this work :
M.A. Arthur
Liz Bowling
The late Tony Graves
Gordon Hicks
Miss P.R. Martins et alia
Miss Maria Serrano
Percy Worner et alia
and many other helpful friends.