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An electrochemical study oflead acid battery positive

electrodes

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• A Doctoral Thesis. Submitted in partial fulfilment of the requirementsfor the award of Doctor of Philosophy of Loughborough University.

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LOUGHBOROUGH UNIVERSITY OF TECHNOLOGY·

LIBRARY AUTHOR/FILING TITLE

__________ WE-f,S::(t~~_L_~_L _________________ _

------ -- --------------------- -- -- --- ---- - - - ------ -_..- I

ACCESSION/COPY NO.

C \ Vh"'l~"l.. ----------------- ---- --- --- --- ------------ - --- - - --

VOL. NO .

. 1 JUl 1988

3~989

.. 5 JUL '991 /

? ' I 199.

CLASS MARK

(

! 00'1 1927 02

. ~11@111111111111~lllllmllllllilllllllmW

'.

AN ELECTROCHEMICAL STUDY

OF

LEAD ACID BATTERY

POSITIVE ELECTRODES

by

SIMON WEBSTER

Supervisor: Professor N. A. Hampson

A Doctoral thesis submitted in

partial fulfilment of the requirement

for the award of Doctor of

Philosophy of the Loughborough

University of Technology,

September 1986

The work described in this thesis has not been submitted, in full

or in part, to this or any other institution for a higher degree .

.. ~

The thesis describes an electrochemical investigation into the

properties of various lead alloys used in the manufacture of lead­

acid battery positive electrodes. The electrochemical results have

been discussed in terms of current nucleation and growth theories.

The morphological aspects of the discharge reaction have been

investigated and theories are presented describing some of the

important influences of various alloying ingredients. It has been

found possible to suggest trends important in the optimisation of

alloy composition for modern lead-acid battery grids. This aspect

is especially relevant to the development of maintenance free

technology.

ACKNOWLEDGEMENTS

I wish to thank Professor Noel Hampson for his supervision and

encouragement over the last three years.

I am also grateful to all the members of the electrochemistry group

for their friendship. I wish to thank in particular Dr. P.J. Mitchell

for his advice and 'useful discussions' on electrocrystallisation

theory.

I would also like to thank Mr. J.1. Dyson for his personal interest

in the project and financial support is acknowledged from Oldham

Batteries Ltd. and S.E.R.C.

My thanks go to Miss A. Hurst for typing this thesis and also to

members of the department's technical staff for assistance during the

project.

Finally I would like to thank my wife Catherine for the support

she has given me throughout this study and especially for her patience

during the thesis 'write-up' period.

CONTENTS

CHAPTER

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

Introduction

Theoretical Principles

The Theory of the Experimental

Experimental Techniques

The Electrochemical Properties of Solid Lead After Alloying with Calcium, Tin and Antimony

Morphology of Planar Lead Dioxide Electrodes After Continued Potentiodynamic Cycling

The Corrosion of Various Lead Alloys in 5M H2S04

The Electrochemical Properties of Solid Lead-Bismuth Alloys in 5M H2S04

The Electroreduction Processes of Planar and Porous Lead Dioxide on Various Lead Alloy Supports

Final Discussions

References

Appendix

PAGE

1

8

26

48

54

74

79

87

97

111

114

124

A

ao' ar

C

* C

Co' CR

CD

CPixed

CDiffuse

Do

EEl e

E

Ep

E pzc

E!

F

LlG

LlGEl

h

i

io

I p or im

j

k

kb' kf

kO

L

LIST OF SYMBOLS

area of electrode

activity of oxidised and reduced species

capacitance

bulk concentration

concentration of oxidised or reduced species

double layer capacitance

capacitance of fixed layer

capacitance of diffuse layer

diffusion coefficient

equilibrium potential

electrode potential

peak potential

potential of zero charge

polargraphic halfwave potential

Faradays constant

Gibbs free energy

standard Gibbs free energy

height of nuclei

current density or current

exchange current density

peak current

complex number

potential dependent reaction rate constant

potential dependent rate constant for forward and reverse reaction.

standard or intrinsic rate constant

inductance

M

n, Z

N

No

0

q

R

RcT, Rn

Rn' Rsol

R

R

r

t

t m

T

u

V

V

W

x

X

Z

Z'

Z' ,

Cl

n

'" p

rh

molecular weight

number of electrons

number of nuclei

initial number of nuclei

oxidised species

charge on electrode or flux of diffusing species

resistance

charge transfer resistance

ohmic resistance of electrode and electrolyte

G as constant

reduced species

radius

time

time of maximum current

temperature

age of nucleus

volume

voltage

Warburg impedance

distance from electrode

reactance

cell impedance

real part of electrode impedance

imaginary part of electrode impedance

charge transfer coefficient

overpotential

sweep rate

density

potential at various point within double layer

y

------ -----------------------------------------------------------~

angular velocity, angular frequency

fraction of surface covered by growth centres

fraction of surface covered in the absence of overlap

CHAPTER 1

INTRODUCTION

The resistance of lead to corrosion in sulphuric acid solutions

[1] has resulted in it having a wide variety of applications in

electrochemical and metallurgical processes [2]. The three main

uses of lead are: the construction of equipment for the chemical

industry, the anode material in electroprocessing and as the support

grids in the lead acid battery. The manufacture of lead-acid

batteries is now the major consumer of both primary and secondary

lead supplies [2].

Although the lead-acid battery was introduced in the nineteenth

century by Plante [3], it still remains one of the most important

secondary power sources in use today. The historic details of its

discovery and development have been comprehensively described by

Vinal [4]. In terms of the number of units produced per year, the

usage of the lead-acid battery is approximately twenty times as

large as that of its nearest rival, the nickel-cadmium battery.

There are several contributory factors for the success of the lead­

acid battery:

It is very versatile providing on instant demand high

or low currents over a wide range of temperatures.

It has good storage characteristics and a long shelf

life, particularly in the dry charged state.

The basic material of construction, lead, is relatively

cheap when compared with nickel, cadmium and silver

- 1 -

which are used in other commercial storage systems.

The relatively low melting point of lead ~27°C) enables

the easy casting and joining of the various metallic

components e.g. grids and terminals.

The greatest disadvantage of the lead-acid battery is its energy

density (weight to capacity ratio) when compared to other secondary

power sources [5], as shown in Table 1.1.

Mass (wh/kg) Volume (wh/l) Cycle life Battery System Practical Theoretical Practical

Lead Acid: 161 . Pasted Plates 20-30 40-60 1200-1500

Tubular Plates 20-35 40-70 (Starter 300)

Nickel Cadmium: 236

Pocket Plates 15-25 25-50 1000-2000

Sintered Plates 25-33 35-65

Nickel Iron 304 20-25 40-70 2000

Nickel Zinc 373 60-80 90-110 200-250 (100% discharge)

Silver Zinc 460 55-120 90-250 10-200

Table 1.1: Average values for the energy density and cycle life of various

battery systems.

- 2 -

Today lead-acid batteries are marketed in a wide variety of

sizes and capacities, ranging from small batteries to units of

several tonnes. The main catagories of the lead-acid battery are:

Starting,lighting and ignition (S.L.I.) batteries, designed

for the internal combustion engine.

Industrial batteries for heavy duty applications e.g.

submarines, fork lift trucks, electric vehicles etc.

Standby power batteries which are maintained in a fully

charged state by the passage of a small charging or 'float'

current for use in telephone exchanges, emergency lighting

etc.

A more comprehensive survey of the lead-acid battery can be found in

a review by Burbank, Simon and Willihnganz [6].

The design of the lead acid battery varies considerably with

the application. However, the basic principles for each application

are the same: the battery consists of a positive electrode of porous

lead dioxide, a negative electrode of 'spongy lead' and an electrolyte

of aqueous sulphuric acid. The active material is supported on a

grid framework of metallic lead alloy (Pb-Sb, Pb-Ca or Pb-Ca-Sn).

In addition to supporting the active material, the grid serves as a

current conductor, the function of which is to maintain a uniform

current distribution throughout the active mass, thus minimising the

resistance of the battery.

The porous active materials are usually derived from a mixture

of lead oxide and lead powder produced from massive lead which has

been mixed into a paste with dilute sulphuric acid. This 'leady oxide'

- 3 -

mixture is pasted onto the metallic grids and then 'cured' and dried

under carefully controlled conditions to produce a mixture of lead

monoxide, lead sulphate and basic lead sulphates. The electrodes

are then formed in dilute sulphuric acid «2M H2S04) which reduces

the paste in the negative plates to 'spongy lead' and oxidises the

paste in the positive plate to lead dioxide. In assembly of the

battery, the positive and negative plates are isolated from each

other by thin sheets of porous insulators called separators, which

are good ionic conductors and excellent electronic insulators.

Many theories have been proposed to account for the reactions

taking place in the lead-acid battery [7-9]. The one which is now

generally accepted [10] is the 'double sulphate' theory' proposed

by Gladstone and Tribe in 1882 [11]. The double sulphate theory

has been confirmed thermodynamically by Craig and Vinal [12], Beck

andWynne-Jones [13] and Barrett [14]. A complete derivation is given

by Vinal [4]. The double sulphate theory states that lead sulphate

is formed at both positive and negative plates as part of the process

of discharge. Gladstone and Tribe [11] also found that the electrolyte

became more dilute during discharge,thus proving that sulphuric acid

acts both as an electrolyte and reactant. The charge and discharge

reactions are shown in Figs. 1.1 and 1.2 respectively. The overall

reaction of the lead-acid battery can be written as:

E=+2.04V

discharge ::;",===='" 2PbS04 + 2H20 charge

The behaviour of the positive plate of the contemporary lead-

acid battery is generally thought of as being the cycle lifetime limiting

- 4 -

: Negative Plate; , Electrolyte 'Positive Plate: , , , ---------------~-------------------------------,

, ' ,

Final Products of Discharge ~---------!1t~~~-------~11~-----~--:~i~~-------.: ; • • I

Ionization Process ,Pb++ SO -; 2H+ 40H- 2H+' SO -- Pb++ ,

p""" Prod.", by '.<reo, ~-~~-~ -:---,-;- --:--- -:--- : -'--:-}~-~;-i : I P.b++++ : :------ --------,- ----ZH20 ·~-------1-----·,

Original Materials Restored; Pb 'H SO H ~~O . PbO I , • 2 4 2:" 4: 2 I ------------------------------------------ ______ 1

FIG. 1.1. THE CHARGE REACTION OF THE LEAD-ACID BATTERY,

·~--~------------i---------------~---------------~ • I

, Negative Plate: Electrolyte' Positive Plate: I ,

·~---------------~---------------4-----__________ ~ I • j •

Original Materials Used: Pb :2H250,+ and 2HzO' Pb02 :

~-------- ------+-1i----------~-~--t-----------~ I l I

Ionization Process ,::-2--e--+--Pb-::---i,F~'-t~~lj,'--~~~~±pPb~+~+~~-~-2-~-: Current Producing Process L '~

D' h ~--------[Pb-5-0----riiii:-~:~~-:~~~~------ir ------:

Final Products of BC arge, 4 , • I~ , I ,2HZO; Pb504 . ------------------------------------------------_.

FIG. 1.2. THE DISCHARGE REACTION OF THE LEAD-ACID BATTERY,

component [6]. Much work has been carried out to improve character­

istics of this electrode within the framework of the need to improve

the battery in general [15]. Over the last 25 years or so, gains of

about 50% in energy and power density have been achieved with no

significant loss in cycle life. One of the most outstanding

developments in the last decade has been the reduction in the

antimony level from 14% and ultimately the replacement of antimony

as the main grid alloying ingredient. Modern non-antimonial alloys

employ calcium and tin as the added ingredients, whereas low antimonial

alloys generally contain less than 2% antimony.

Lead antimony alloys were introduced for use in battery grid

construction by Sellon in 1882 [16]. These additions of antimony,

have traditionally been used to improve .hardness, strength and

castability of battery alloys. It is widely known that antimony in

the positive grids extends the service life by improving the capability

to resist the effects of deep cycling [17]. This property is believed

to be due to the lead antimonial alloys promoting a corrosion layer

which has good adhesion to the active material and an active material

structure which imparts mechanical strength giving good cycle life

properties [17]. However, antimony does have a prime electrochemical

disadvantage [r8];this is shown schematically in Fig. 1.3. Under

anodic attack of the grid, during overcharge, antimony can pass into

solution (in the +5 oxidation state); it can then be either readsorbed

back onto the surface of the positive active mass or transferred via

the electrolyte to the negative grid. Ruetschi and Angstadt [19]

proposed the following mechanism for the dissolution of antimony

from the positive electrode:

- 5 -

SPb02 + 2Sb + SH2S04 + 2H+;;;",,===-- 2Sb02 + + SPbS04 + 6H20

The antimony which has been transferred from the positive grid is then

reduced (+3 oxidation state) and deposited on the negative electrode

surface. This deposited antimony has a lower hydrogen evolution

potential than lead and therefore gassing will occur more readily,

causing significant water loss from the battery. With the advent of

sealed 'maintenance free' batteries the problem of gassing and water

loss have had to be minimised. This has been achieved by replacing

antimony as the main grid alloy ingredient with various alloying

materials. The most successful ones have been based on lead alloys

containing calcium, tin, (aluminium and magnesium) [20]. These

modifications have overcome the hydrogen evolution problems and

proved satisfactory for use in 'float' 'service. However, for use in

batteries which need a deep cycling capacity the removal of antimony

has engendered poor cycle lives.

With these associated cycle life problems of the Pb-Ca system,it

was pertinent to investigate the so-called 'alloy effect' on the cycle

life of the positive electrode. This would give valuable information

on the beneficial properties of antimony and aid the discovery of

new and better grid alloying ingredients.

A substantial amount of work has been carried out on the effect

bismuth has on the performance of the lead acid battery [21]. This

is not surprising since bismuth is a major contaminant of many

sources of lead ores and at present is removed by the use of an

expensive process [1]. There is however, a conflict o.f opinion in the

literature over the effects bismuth has on the physical, mechanical

and cycle life properties of the alloys used in modern battery grids.

- 6 -

Posiltve plo le Stporotor Neoallvt plait

SbH) I \ ......

Corrolion DillulIon I" Sb Sb .. SI:> ( \l) - ... 5 b ('Ill - , \ / /

// \,' " _ / Grid allay

Grid alloy /' ' Charo_ " O •• rehoro·, /

'/ /' \ ' O/Cond°z / /...0' I corrosion

/ / I "harO' ' / / "" ,// 1/ ,

'" Adsorption Ml9,otion ----. \ Sb01T __ -------Sb(m)--------Sb([ln-~SbO .. Sb

Adsorbed Oeposiled

on Pb02

- - Malortly 01 dlnolvtd antimony

Anllmony pOlsonin9

FIG, 1,3, THE DISSOLUTION AND MIGRATION OFANTIMONY FROM THE POSITIVE ELECTRODE,

One group of workers has found it beneficial [22-24] whilst other

workers have found it to be detrimental, stating it should be removed

completely at all costs (25,26]. The battery industry has tended to

believe the latter, therefore lead alloys used in grid construction

are usually free from bismuth contamination. This difference of

opinion has led us to extend our investigation into the 'alloy effect'

on the positive electrode of the lead-acid battery to include bismuth

in order to clarify this situation.

In this thesis"work is described which was carried out in order

to investigate the electrochemistry of pure Pb (Koch-Light 99.999% pure)

and various pertinent ,lead alloys used in the manufacture of 'maintenance

free' batteries. A series of binary lead-bismuth alloys has also been

investigated. The results are discussed in terms of their relationship

to the cycle life of the positive plate of the lead acid battery.

- 7 -

CHAPTER 2

THEORETICAL PRINCIPLES

2.1 INTRODUCTION

Electrochemists are constantly concerned with the processes and

factors affecting the transport of charge across interfaces between

different chemical phases. In general, one of the two phases is the

electrolyte in which charge is usually carried by the movement of

ions, and the other is the electrode where charge is usually carried

by electronic movement. In this particular case the electrode is

lead dioxide and the electrolyte is dilute sulphuric' acid.

There is a three dimensional transition region between the two

phases where the properties have not yet reached the properties of

the bulk of either phase. This region is called the electrode/

electrolyte interphase and any entity which moves from the electrode

into the solution or vice ,versa, traverses this interphase [27].

2.2 THE STRUCTURE OF THE ELECTRODE/ELECTROLYTE INTERPHASE

The earliest model proposed to describe this interfacial region

was postulated by Helmholtz and Perrin [28] in 1879. It was a very

simple concept, where excess charge on the surface of the electrode

is neutralised by an equal number of opposite charged ions (Fig. 2.1).

This concept of two layers of opposite charge is the origin of the

term 'electrical double layer' and although the situation in reality

- 8 -

FIG. 2.1. HELMHOLTZ MODEL OF THE DOUBLE LAYER.

VARIATION OF POTENTIAL WITH DISTANCE THROUGH THE INTERFACE PREDICTED BY THE HELMHOLTZ MODEL.

is more complex,the original name still remains. The Helmholtz model

of the double layer is equivalent to a simple parallel plate capacitor,

and the following assumptions have to be made if the model is to be

valid:

a) The separated charges at the interphase are in electrostatic

equilibrium.

b) There is no transfer of charge in either directionocross

the interphase with changes in electrode potential.

c) The charge in the solution near to the electrode interphase

alters with variation in electrode potential.

These assumptions imply that the electrical behaviour of the

double layer should be purely capacitive and have no parallel resistive

components. Electrodes which obey the above model are known as

'ideally polarisably' electrodes. The classic example is the mercury

electrode in I mol dm- 3 KCl.

Gouy [29] and Chapman [30] modified the Helmholtz model by

realising that in an electrolyte, ions are free to move and are

subject to thermal motion. The Gouy-Chapman model predicts that the

greatest concentration of excess charge is adjacent to the electrode

where the electrostatic forces are most able to overcome the thermal

processes, and the concentrations decrease at greater distances, where

the electrostatic forces are weaker (Fig. 2.2). There is a serious

defect in the Gouy-Chapman model as it treats the ions as point

charges approaching to within very small distances of the electrode

surface. This leads to very high values for the charge concentration

in the immediate neighbourhood of the interphase. The theory does

predict that capacitance varies with potential, but it has been found

- 9 -

I

FIG. 2.2. GOUY - CHAPMAN MODEL OF THE DOUBLE LAYER.

VARIATION OF POTENTIAL WITH DISTANCE THROUGH THE INTERFACE PREDICTED BY THE GOUY - CHAPMAN MODEL.

E

COMPACT I

T DIFFUSE

FIG. 2.3. THE STERN MODEL. D IS THE DIELECTRIC CONSTANT OF THE COMPACT 'c' AND DIFFUSE 'n' LAYERS.

that there are significant deviations between the calculated and

experimental values for the double layer capacitance.

In 1924 Stern [31] proposed a theory of the double layer based on the

G/C model which, in majlY respects, has a high level of agreement with the

experimental results. This modified approach provides corrections in

the form of an adsorbed layer of ions which have finite sizes and approach

within a certain critical distance of the electrode surface

(Planar tayer orHelhomltz layer), while the remainder of the ions are

distributed in a diffuse layer which extends from the plane of

closest approach to the bulk of the solution. ('diffuse layer' or

'Gouy layer') (Fig. 2.3).

Grahame [32], in postulating a modified Stern model which takes into

account the presence of dipoles due to water molecules at the

electrode surface, stated that at least three layers must be

considered when describing the interphase. These were: the inner

Helmholtz plane, the outer Helmholtz plane and the diffuse layer.

The inner Helmholtz plane consists of specifically adsorbed ions

which have lost some of their water of hydration and so are closest

to the electrode surface; the outer Helmholtz plane contains normal

hydrated ions at their distance of closest approach to the surface

(Fig. 2.4). The diffuse layer is as previously described. The model

of the double layer can therefore be treated as two capacitors

connected in series:

1

CDiffuse

where CD = capacitance of Double layer

CFixed = capacitance of Fixed layer

C = capacitance of Diffuse layer. Diffuse

- 10 -

(2.1)

o o

FIG. 2.4. GRAHAME MODEL OF THE DOUBLE LAYER.

~,

VARIATION OF POTENTIAL WITH DISTANCE THROUGH THE INTERFACE PREDICTED BY THE GRAHAME MODEL.

FIG. 2.5. THE COMPLETE MODEL OF THE ELECTRICAL DOUBLE LAYER.

COMPACT LAYER

I I I I '~Solvent : I Molecules

.... I I

+

+

+ DIFFUSE LAYER

Inner /" Helmholtz Plane

~SolVated Cations

/

+

+

f-i-___ Specifically Adsorbed Anions

I I

~outer Helmholtz Plane

+

Equation 2.1 shows that as the concentration of the electrolyte

becomes more dilute, the value of the diffuse layer becomes

significantly larger than the capacitance associated with the fixed

layer. Hence CD becomes virtually independent of CFixed' At very

low concentrations a sharp minimum is obtained on a CD Vs. potential

plot. This minimum is associated with the point of zero charge

(P.Z.C.) for the electrode.

In 1963 this model was further improved by Devanathan, Bockris

and MUller [33] who considered the dielectric properties of the species

of the inner Helmholtz plane and outer Helmholtz plane. They proposed

that adsorbed solvated cations remained outside a layer of strongly

orientated solvent dipoles. The inner solvent layer is penetrated

by specifically adsorbed anions. The water molecules are thought to

be adsorbed with their negative poles pointing either towards or

away from the electrode surface, depending on the potential. This

is now the generally accepted model used to describe the double layer

and is shown in Fig. 2.5.

2.3 THE CHARGE TRANSFER PROCESS

Electrode processes are heterogeneous chemical reactions which occur

at the electrode.-electrolyte interphase and are accompanied by the

transfer of electric charge through this region. The reaction involves

the transfer of electrons from one substance to another and can be

represented ,by the general redox equation below:

o + ne :;;=:. R (2.2)

- 11 -

where 0 = oxidised species

R = reduced species

kf = rate of forward reaction

kb = rate of reverse reaction.

The dependence of this reaction on potential can be better

understood if transition state theory is considered. If the free energy

profile is as shown in Fig. 2.6 then at an electrode potential of

zero volts, ~Gt and ~Gi will correspond to the activation energies oc oa

of the forward and reverse processes. If the potential is shifted

to a new potential of value E, a change in the relative energy of the

electron resident on the electrode by -nFE will result. The '0 + ne'

curve will move up or down by that amount. The dashed line in Fig. 2.6

shows the effect for a positive potential shift. The change in

chemical energy of the system must equal the electrical energy

produced and therefore the change in Gibbs free energy is given by:

~G = -nFE (2.3)

and at equilibrium the standard Gibbs free energy change "ill be

given by:

= -nFEa e (2.4)

where Ea is the standard equilibrium potential. For the reaction e

taken to completion, the Gibbs free energy change for the process

left to right is given by the Vant Hoff isotherm

(2.5)

Now substituting for ~G and ~G9 gives:

- 12 -

11 - 0) of!! --r---------

o + ,,~

--- -/----- - --I

f.' • /;,/1

/ /

/ ---------I M;;',

R

RNCtK>n coordinate

FIG. 2.6. A DETAILED DIAGRAM OF THE EFFECTS OF A POTENTIAL CHANGE ON THE FREE ENERGIES OF ACTIVATION FOR OXIDATION AND REDUCTION.

Electrode of area A x=O

x

x+dx

FIG. 2.7. A SCHEMATIC DIAGRAM SHOWING PERPENDICULAR DIFFUSION NEAR AN ELECTRODE SURFACE.

RT E = E: + - In {a/aR}

nF (2.6)

which is the Nernst equation and predicts the potential of the electrode. e

E is a constant at a given temperature and pressure and is called· the e

standard equilibrium potential. e

E is defined by the magnitude of the e

potential when the activities of the reacting species are unity.

As with any chemical process, it is necessary to consider both the

thermodynamics and the kinetics of the electron transfer process.

Any theory of electrode kinetics must predict the Nernst equation for

corresponding conditions.

Returning to the free energy profile in Fig. 2.6. After. the

shift in potential from the equilibrium potential, the energy required

for the forward process is greater than that for the reverse process.

It is obvious that it is necessary to introduce a charge transfer

coefficient, a, to describe the way the energy is split between

the two processes. (a can range from zero to unity, typically it is

0.5 for a reversible reaction). For the forward reaction, in the

polarised state:

+ anFE

Similarly, for the backward reaction:

flGf - (l-a)nFE oa

(2.7)

(2.8)

Now, assuming that the rate constant kf and kb have an Arrhenius form,

then the forward and reverse reactions can be expressed as:

k = A exp 1- fiG I f f RT

(2.9)

- 13 -

- ---------------------------------------------------------------------------

and (2.10)

Expanding these equations in terms of the activation energies in

equation 2.7 and 2.8

kf = [-~G+ ) Af exp R;c exp [ -a:;E) (2.11)

and

kb [ -~Gta) [ (l-:~nFEJ = '\ exp exp

RT (2.12)

As can be seen, the above terms (Eqn. 2.11 and 2.12) have a potential

dependent and potential independent term. The potential independent

terms are equal to the rate constant at E=O and are designated by 9 9

kf and kb . Hence:

9 [ -a:;E) kf = kf

exp (2.13)

and

9 [(l-a)nFEl kb = kb exp

RT j (2.14)

* * In electrochemica1 kinetics, Co and CR

are used for bulk

concentrations and CR(x,t) Co(x,t) are used to denote concentrations

at distances, x, and times, t, away from the electrode surface. At

the standard equilibrium potential, when the electrode interface is at

equilibrium with a solution then both reactions occur at the same

rate.

- 14 -

Hence:

(2.15)

and the following must be true

* * kfCo = kbCR (2.16)

and

kf = kb = 9

k (2.17)

The rate constant k9

is known as the standard or intrinsic rate

constant. The potential independent term can therefore be removed

from equations 2.13 and 2.14. Hence:

kf = k9 exp [-anF~:-E:)j (2.18)

and

kb = k9 exp [(l-a)n::E-E:)j (2.19)

In electrochemistr~ a current is more meaningful than a rate constant

as it can be measured directly. Now:

i = nFkC (2.20)

but only the net current is measured:

(2.21)

- 15 -

I

Therefore equating equation C2.18) and C2.l9) in terms of current:.

i nFk9 - [-anpCE-E:)] C -

[Cl-ct)nFCE-E:) ) CRCo,t)] C2.22) = exp exp

RT o(o,t) RT - .

which is known as the Butler-Volmer equation. However, if the

solution is well stirred or the current density low, so that the surface

concentration does not differ appreciably from the bulk value, then

equation C2.22) can be simplified to:

[ r -anF (E -E:Jj

expl RT

exp [

(l-a)nFCE-E:)

RT ]1 (2.23)

Since also under these conditions E9 = E then overpotential is e eq

given by:

E - E = n ,eq

and the exchange current density by:

substituting for io in equation (2.23) gives:

. [ [-"oF"] [ Cl-Cl)nFnJ

1 i = 1 exp exp

o RT RT

which is known as the Erdey-Gruz and Volmer [34] equation.

C2.24)

C2.25)

C2.26)

Under equilibrium conditions, when the forward rate is equivalent

to the backward rate:

- 16 -

~ nFk Co(o,t)

9 nFk CR(o,t)

because no net current flows at equilibrium:

* Co(o,t) = C

0 (2.28)

* C R( 0, t) = CR (2.29)

substituting into equation (2.27) gives:

(2.30)

Taking logs of both sides of equation (2.30) and rearranging gives:

E e

* RT C = E9 + - In -..£

e * nF CR

(2.31)

(2.27)

Equation (2.31) is equivalent to equation (2.6) if the concentrations

* * Co and CR are replaced by activities. The kinetic treatment is shown

to be consistent with the thermodynamic treatment. By definition,

the exchange current density is given by the rates of the forward

and reverse process at equilibrium:

(2.32)

Under these conditions of balanced Faradaic activity

[ -cmFn~ exp RT

(2.33)

- 17 -

raising equation (2.31) to the power -a gives

[ -anFnJ _ [<j_a

exp - -. RT eR

(2.34)

which on substitution into equation (2.33) gives

(2.35)

The exchange current density is therefore proportional to k9 . k9

can be simply interpreted as a measure of the kinetic capacity of

a redox couple. A system having a large k9 will achieve equilibrium

quicklY whereas a smaller k9 will take longer.

For practical purposes, it is often convenient to consider the

limiting behaviour of the Erdey-Gruz and Volmer equation (2.26):

a) Large Overpotentials CTafel behaviour)

For overpotentia1s greater or equal to 100 mV the following

assumptions are true:

(2.36)

and if the electrode is sufficiently polarised then if » ib and

(2.37)

(2.38)

- 18 -

Taking logs of both sides of Equation (2.38):

anFn lni = lnio

RT

rearranging this equation gives the cathodic form:

RT RT n = -- lni - -- lni

cmF 0 anF

and for the anodic form:

RT RT n " lnio + lni

(l-a)nF (l-a)nF

(2.39)

(2.40)

(2.41)

The above equations (2.40) and (2.41) are known as the Tafel relation-

ship [35].

b) Low Overpotentials: (1nl ~ lOin mY)

x For small values of x, the exponent e , can be approximated as

1 + x; hence for sufficiently small overpotentials, n, (~lO/n mY)

equation (2.24) can be written:

i = i [fl - anFn~ fl + (lR~a)nFn~J

0 RT (2.42)

Hence:

nFn i " -i

o RT (2.43)

- 19 -

which shows that the current densit~ is linearly related to over­

potential near the equilibrium potential. Rearranging equation

(2.43) gives:

i o

-RT i = -- (2.44 )

nF n

The ratio n/i has the dimensions of resistance and is often called

the charge transfer resistance Rct

.

Rct = RT 1

nF i o

(2.45 )

This parameter can be evaluated directly in some experiments, and

it serves as a convenient index of kinetic facility. For a very a

large k , it clearly approaches zero.

2.3 MASS TRANSPORT PROCESSES

As stated in Chapter 2.2 a redox reaction occurring at an

electrode surface can be represented by:

o + ne (2.46)

and can be considered to consist of the following processes:

i)

H)

Hi}

o electrode

o - R . electrode+ne electrode

R ->-electrode ~ulk

- 20 -

(2.47)

(2.48)

(2.49)

The redox reaction can be controlled either by the rate of availability

of 0bulk arriving at the electrode surface (equation 2.47), or by the

rate of electron transfer (equation 2.48). These processes are

said to be mass transport controlled or charge transfer controlled

respectively. Sometimes neither of the above processes i~ as slow

as a chemical transformation involving the electroactive species, in

which case the chemical transformation is the rate determining process.

The three modes of mass transfer which are normally encountered

are migration, convection and diffusion.

i) Migration

Mass transfer by migration is the result of the forces exerted

on charged particles by an electric field. (This is negligible with

excess electrolyte).

ii) Convection

Natural or free convection will always occur spontaneously in

any solution undergoing electrolysis. This convection arises as a

result of density differences which develop near the electrode and

may also originate from thermal or mechanical disturbances. Forced

convection can be caused by stirring, rotating the electrode, bubbling

gas or pumping the electrolyte etc.

iii) Diffusion

Whenever concentration differences are established diffusion will

exist. A concentration gradient is formed as soon as electrolysis is

- 21 -

initiated; diffusion will occur to some extent in every electrode

reaction.

The investigation of the mechanism and kinetics of electrode

processes is normally undertaken with solutions containing a large

excess of base electrolyte where the migration of electroactive

species is unimportant and where the diffusion processes are well

defined i.e. using unstirred solutions or using forced convection which

may be described exactly. In both of the above examples the experi-

ment is carried out so that we may assume that mass transport in

only one direction, that ~s perpendicular to the electrode surface,

is important.

When considering a planar electrode immersed in an electrolyte

undergoing a redox reaction according to equation (2.46), the number,

N, of molecules of 0, which diffuse past a given area, A (cm2) in a

time dt, is proportional to the concentration gradient of the diffusing

species.

dN -= 0 Adt 0

de o

dX (2.50)

Equation (2.50) is known as Fick's first law and is a simple model that

describes diffusion to a plane electrode, assuming that the electrode

is perfectly flat and of infinite dimensions. The left hand side of

h . 1 dN. k h fl d· h b f t e equat10n, A dt 1S nown as t e ux, q an 1S t e num er 0

molecules diffusing through a unit area per unit time. 00 is the

diffusion coefficient. Rewriting Fick's law gives:

I dN - - = flux = q = A dt

o ae o o(x, t)

ax

- 22 -

(2.51)

However, during electrolysis the concentration of 0 in the volume

element, dx (Fig. 2.7) decreases.

d.C o (X, t)

at = [Onumbe: of moles _ numb~r of mOlesJ

enter1ng leav1ng

in time, t

dC q (x+dx) - qx o(x, t) =

at dx

C aq o(x,t) = as dx + OQ

at ax

From Fick's first law it is known that:

ae q = D o(x,t)

o ox

therefore differentiating with respect to x gives

dq -= dx

s· . and substituting for dx 1n equat10n (2.54) gives:

Co(x, t) =

at

(2.52)

(2.53)

(2.54)

(2.55)

(2.56)

(2.57)

This equation is known as Fick's second law and defines how Co varies

with time. A solution of this equation (2.54) under a given set of

- 23 _

boundary,conditions enables us to determine Co(x,t), and from this

determine the amount any'time after initiation of electrolysis.

The boundary conditions for the solution of (2.57) are:

a) Co(o,t) = 0 at t > 0 (2.58)

* b) Co(x,t) -> Co' as x ..... '"' (2.59)

* c) C o(o,t) = C at t < 0

0 (2.60)

* where Co is the concentration of 0 in the bulk and Co(o,t) is the

concentration at the electrode surface.

The solution of this equation is complicated [35] but leads to

the exact form of the i-t transient.

! * nFDo Co 1=_, __ _ (2.61)

This equation (2.61) is the Cottrell equation and states that the

diffusion limited current of a planar, stationary electrode is

inversely proportional to the square root of time.

2.4 POROUS ELECTRODE THEORY

When lead is placed in sulphuric acid solutions it corrodes to

form Pb2+ ions; these then combine with SO~- ions to form lead sulphate

[36-37]. Lead sUlphate is extremely insoluble and forms a non-conduct-

ing (impedance ~ 1010 Q. cm-I) surface film. This conversion involves

an increase in volume (~150%) giving a densely packed but thin film of

lead sulphate. When an anodic current is applied this equilibrium is

perturbed and as the potential increases, lead dioxide is formed

- 24 -

(charging process for positive plate). This is ·followed by a decrease in volume

(~50%) which leads to a porous structure. The performance of the

porous lead dioxide electrode is thought to be determined by the

following factors [38):

i) The amount of active material

ii) The thickness of the electrode

iii) The rate of discharge

iv) The temperature

v) The quantity and concentration of the electrolyte

vi) The porosity

vii) The design of the electrode

viii) The previous history of the electrode.

The task of modelling the porous electrode to account for all

these factors is enormous, and at best the model is a simplified

mathematical expression taking into account the kinetic and transport

phenomena occurring at the electrode. Work on such mathematical

modelling has been reviewed by a number of authors [39-42]. The

majority of models use a one dimensional approach where the pore

geometry is ignored. This representation is correct when the distances

over which there is a variation of concentration and potential is

large, compared with the dimensions of the pore system.

- 25 -

CHAPTER 3

THE THEORY OF THE EXPERIMENTAL TECHNIQUES

3.1 LINEAR POTENTIAL SWEEP TECHNIQUES AND CYCLIC VOLTAMMETRY

These techniques involve the application of a linear potential­

time waveform to an electrode, with the observed current being

recorded as a function of the applied potential. The simplest of

these techniques is linear sweep voltammetry (L.S.V.) and involves

sweeping the electrode potential between the limits El and E2 at a

known sweep rate, v, before halting the experiment, (Fig. 3.1). If

the sweeps are repeated continuously the technique is known as cyclic

voltammetry. In this case the waveform is initially the same as in

L.S.V., but on reaching, E2, the sweep is reversed rather than

terminated (switching potential). Cyclic voltammetry was first

introduced by Matheson and Nichols [43] and the fundamental equations

which describe linear sweep/cyclic voltammetry have been developed

by Delahay [44], Shain [45-46] and others [47-50]. These techniques are

used to elucidate data on reaction mechanisms, charge transfer processes

and other complicated electrode reactions.

During the potential sweep the current is recorded. The plot of

current as a function of potential is known as a voltammogram (Fig. 3.1).

The basic feature of a voltammogram is the formation of a current peak

at a potential characteristic of the electrode reaction taking place.

The position and shape of the current peak obtained depends on many

factors such as sweep rate, electrode material, temperature, solution

- 26 -

E

I I P

E

(

/ /

/

/ /

/ /

/

, / , / , / , / V

t

FIG. 3.1. POTENTIAL PROFILE AND CURRENT RESPONSE FOR A LINEAR POTENTIAL SWEEP.

E

composition and the concentration of the reactants. Slow sweep

rates are used to study steady state reaction whilst fast rates are

useful for detecting the existance of short lived intermediates.

Only the linear potential sweep technique can give accurate kinetic

parameters because the equation'derived applies only if there are'no

concentration gradients in solution before the commencement of the

sweep. Cyclic voltammetry causes complex concentration gradients to

appear near the electrode surface, hence this technique is best

suited for identifying steps in the overall reaction, and new species

which occur during electrolysis.

3.1.1. Reversible Reactions

Reversible reactions in electrochemistry are reactions where the

rate of electron transfer is significantly greater than the rate of

mass transport. Under these conditions the peak current density is

given by the Randles - Sevcik equation:

(3.1)

where n = number of electrons transferred in the overall process

D = diffusion coefficient (cm2s-1) o

v = sweep rate (Vs- 1)

* C = bulk solution concentration (mol cm- 3) o

Ip = peak current density (A cm-2)

Thus peak current density is proportional to the concentration of

electroactive species and to the square root of the sweep rate and

the diffusion coefficient. The criteria for reversibility have been

shown to be:

- 27 -

1 t.Ep = E A E C = 59/n mV p p

2 lE p Ep/21 = 59/n mV

3 IIA/ICI = 1 p P

4 Ip <X)

5 E is independent \) p

Table 3.1. Diagnostic test for the reversibility

of electrode processes.

3.1.2. Irreversible Processes

For an irreversible process the rate of electron transfer is

insufficient to maintain the surface equilibrium. The peak current

density is given by:'

I = -(2.99 x 105) n(CI n )! Co' D! ) at 25°C p a Cl 0 (3.2)

where: n is the number of electrons transferred up to and including Cl

the rate determining step.

For a reversible system E was independent of sweep rate but p

for the irreversible case Ep is found to vary with sweep rate as

shown below [45].

2.3 RT Ep = k + ---

2C1 n F a Cl

log \) (3.3)

- 28 -

where: RT

k = Ea + - __ e

~ n F a ~

(3.4)

i.e for each tenfold increase in v the peak potential shifts by

(30/~n ) mV at 25°C. It should also be noted that E occurs at a p

a higher potentia1s than E' by an activation overpotentia1 related to eq

ka

. The criteria for;~eversibi1ity have been shown to be:

1 No reverse peak

2 I " v ! p

3 E " log v P

4 IEp - Ep/21 = (48/~an~) mV

Table 3.2. Diagnostic test for the irreversibility

of electrode processes.

3.1.3 Quasi-Reversible Reactions

This phenomena occurs when the relative rate of electron transfer

with respect to that of mass transport is insufficient to maintain

equilibrium at the electrode surface. In the quasi-reversible region

both forward and backward reactions contribute to the observed current.

The criteria for quasi-reversibility have been shown to be:

- 29 -

1 I increases with vI but not proportional to it p

2 11 A/I Cl = 1 provided = p p ~c ~A = 0.5

3 6E is greater than 59/n mV and increases with increasing v p

4 a E shifts positive with increasing v

p

Table 3.3. Diagnostic tests for quasi-reversible electrode

processes.

3.2. A.C. IMPEDANCE METHOD

This method is used to evaluate kinetic parameters related to

the electrode undergoing study. With this technique it is possible

to examine simple charge transfer processes and more complex reactions

involving specific adsorption of reactants or products, as well as

chemical reactions preceeding or following the charge transfer process.

Electrochemical interphase, such as the surface of an oxidised

metal electrode can be viewed as combinations of passive electrical

circuit elements i.e. resistance, capacitance and inductance. For

these elements, Ohm's law will apply for an A.C. signal as long as the

resistance is replaced by appropriate expression for reactance, X, of

the passive element in question.

v = i X peak peak (3.5)

The reactance of a capacitor or an inductor can be expressed in several

forms, the most convenient 'are those using complex numbers:

- 30 -

XR

= R

1

Xc = jwC

XL = jwL

where: w = 211f

R = resistance

C = capacitance

L = inductance

(3.6)

(3.7)

(3.8)

This notation makes it possible to represent any reactance or

the impedance of a combination of reactances, as a vector in the real

and imaginary plane.

An impedance, Z, can be completely defined by specifying the

magnitude I Z I and the angle 4> its vector makes with the real posi ti ve

axis or alternatively, by specifying the magnitudes of its real,

ZI, and imaginary, Z11, components.

ZI = Z cos 4> (3.9)

.Zl1 = Z sin 4> (3.10)

or in complex number notation

Z=Zl+jZl1 (3.11)

Since the above reactance expressions contain, w the angular frequency

of the applied waveform, the magnitude and phase angle of the impedance

- 31 _

---------

I

COL

RSOL.

W

RE

"

FIG. 3.2. RANDLES TYPE EQUIVALENT CIRCUIT INCLUDING WARBURG COMPONENT.

N .., I

RSOL

L _____ . __ .. __ .

,

" . ~ , ,

, , , , ,

\ . RE + RSOL

z'

FIG. 3.3. THE COMPLEX PLANE (SLUYTERS PLOT) RESPONSE FOR FIG. 3.3.

vector representing the response of the circuit containing the

reactive ~lements will vary as lW' varies.

In order to appreciate the variation of the electrochemical

impedance with.frequency, it is convenient to consider a hypothetical

equivalent circuit; a combination of electrical circuit elements

that behave in a similar manner to the electrode. Randles [51]

proposed an equivalent circuit and this has been found to have a

wide application in many electrochemical systems. The equivalent

circuit is shown in Fig. 3.2 and the resultant behaviour is shown

in terms of a Nyquist diagram in Fig. 3;3. (Sluyters plot).

The resistance, R l' represents the solution and developed so

product on the electrode, the parallel combination of the resistor,

~, and the capacitor, Cdl , represent the reacting interphase. Cdl

is the electrochemical double layer capacitance (Chapter 2.1) resulting

from adsorbed ions and water molecules. RE is the charge transfer

resistance. In the Nyquist diagram in Fig. 3.3 the horizontal axis

represents the real part of the cell impedance i.e. the resistive

component, and the vertical axis the imaginary component, the

capacitive reactance. At high frequencies (>10 kHz) the capacitor

Cdl conducts easily, and effectively shorts out RE; only the effect

of the solution and film resistance R I remains. RIcan usually be so so

measured in aqueous medium by taking a measurement at 50 kHz [52].

As the frequency decreases, Cdl conducts less and less and the response

follows a semicircle. At low frequencies (as d.c. is approached) the

capacitor ceases to condu~t and the cell impedance becomes the sum of

Rsol + RE· This corresponds to the right-hand intercept on the diagram.

Most systems are not as simple as this and effects due to concentration

in solution are usually present. To account for these it is necessary

- 32 -

to include an additional circuit element, W in series with RE as

shown in Fig. 3.2. This additional element, the Warburg impedance,[53]

describes the impedance of the concentration and diffusion related

processes. This Warburg impedance is represented on a Nyquist diagram

or complex plane plot by a straight line at 45° to the axis. At high

frequencies the term is small, since the Warburg impedance describes

a mass transfer process involving ionic diffusion; consequently it

is observed only at low frequencies. The complete response of a

Randles type equivalent circuit including a Warburg component is shown

in Fig. 3.3.

3.3. POTENTIAL STEP ~ffiTHOD

In this method of perturbation, the potential of the working electrode

is changed instantaneously and the resulting current recorded as a

function of time as the system relaxes to the steady state. The rate

controlling mechanism can either be the diffusion of the electroactive

species to the surface or a solid state reaction involving the

incorporation of a species into the lattice.

3.3.1. Diffusion control

When the rate determining step is the diffusion of the electro­

active material to the electrode surface the current-time transient

appears as a sharp current response followed by a decay. This is

the result of the depletion of the electroactive species near the

electrode surface.

At high overpotentials, electron transfer is fast and the current

is always determined by the rate of diffusion. The whole transient

- 33 -

obeys the Cottrell equation and gives a linear i Vs t-! relationship

(Chapter 2.3).

At low overpotentials where electron transfer and diffusion

occur at similar rates, it is possible to show that at long times:

and at short times:

* i = nFk C co

3.2.2. Electrocrystallisation

(3.12)

(3.13)

As stated earlier, the potentiostatic step method can be used to

investigate nucleation and growth mechanisms which occur at the electrode

surface.

Electrocrystallisation is the process involving the formation of

nuclei and their subsequent growth into a crystal lattice with the

formation of another solid. Using nucleation and growth mechanisms,

studies on the formation of passivating layers have been extensively

studied.

Fleischmann, Thirsk [54] and Harrison [55] developed the

potentiostatic technique and the theory of the growth of such films

under potentiostatic conditions. Armstrong has however, extended

these equations to the more general problems of· layer by layer growth [56].

The nucleation and growth processes which are pertinent to the

charge and discharge of quasi porous lead dioxide which has been

electrochemically formed on solid lead supports has been discussed by

_ 34 _

Hameenoja et al. [57] and is dependent solely on the rate of charge

transfer (the current being independent of rotation speed). The

current-time relationship will depend on:

1) geometric factors, i.e. two dimensional (cylinders)

or three dimensional (hemispheres) growth,

2) rate of appearance of nuclei, i.e. instantaneous

or progressive nucleation.

In deriving any equation which predicts the current-time response

of a nucleation and growth process several assumptions have to be made:

1) the effect of the edge of the electrode have been

neglected,

2) after a suitable potential step has been applied the

nuclei form at discrete centres and grow [58]

3) the rate of growth of current is proportional to·the

area onto which growth occurs, i.e.

i « A (3.14)

The current can be written as:

i = nFkA (3.15)

- 35 -

where: n = number of electrons transferred

F = Faradays constant

k = rate constant of growth process

A = area of electrode

Faradays law can be applied as current proportional to the charge

passed with time and 'kA' as the number of charge carrying moles per

unit time.

p dV kA = (3.16)

M dt

where: p = density of deposit

M = molecular weight of deposit

V = volume

p dV dr and kA = (3.17)

M dr dt

p

[::) [::) nkFA = - nF (3.18) M

dV A and dt are known functions of geometry. Integration of equation (3.18)

gives r as a function of t and consequently current, i, at time t.

In order to mathematically model nucleation and growth processes

known geometries must be incorporated into equation (3.18). Equation (3.15)

only gives the current flowing into a centre which increases in size

in one dimension e.g. a needle. For centres increasing in size in two

or three dimensions other geometries must be considered. For the two

dimensional case cylindrical growth is usually considered and for the

three dimensional case hemispherical growth is considered.

- 36-

a) 2 Dimensional growth (cylinders)

A = 21Trh

where: h = height of the cylinder

r = radius of the cylinder

and the volume is given by:

differentiating with respect to r gives:

dV

dr

Therefore from equation (3.17)

dr M -= -k dt p

t

tk Mkt r = dt =

o p p

substituting into equation (3.19) and equation (3.15) gives:

Mkt i = nFk 21Th -­

p

- 37 _

(3.19)

(3.20)

(3.21)

(3.22)

(3.23)

(3.24)

Re-arranging gives the current for the cylindrical growth of a single

centre:

Mt i = 2nFrrhk2 -

p

b) 3-Dimensional growth (hemispheres)

The surface area of a hemisphere is given by:

The volume is given by:

v = 2/3T<r3

differentiating with respect to r gives:

dV -= dr

Therefore from equation (3.17)

dr Mk -= dt p

tfMk Mkt r = dt =

o p p

- 38 -

(3.25)

(3.26)

(3.27)

(3.28)

(3.29)

(3.30)

substituting into equation (3.19) and equation (3.15) gives:

i = nFkrr2 --- (3.31) p

re-arranging gives the current for the hemispherical growth of a

single centre:

i = 2nF (3.32)

For an electrocrystallisation process, in the initial stages of

the formation of a new phase , the individual centres can be assumed

to grow independently of each other without overlapping. The laws of

growth for a single centre such as 3.15, 3.25 and 3.32 can therefore

be combined with the appropriate law of nucleation to give the overall

current-time variation.

At a time, t, the overall current due to nuclei being formed at

a particular time t-u, in the interval du is given by:

(3.33)

where u = the age of the nucleus. It has also been shown that

discrete nuclei have been found to form at preferred sites [54].

If there is a uniform probability with time of converting sites into

nuclei, the nucleation law is first order:

N = No (1 - exp(-Zt)) (3.34)

where: No = total number of sites

Z = nucleation rate constant - .39 _

At short times two limiting forms can be approximated.

If Z is large, all the sites are converted to nuclei virtually

instantaneously:

while if Z is small the nuclei form with time:

N ~ N Zt o

(3.35)

(3.36)

Therefore substituting into equations (3.15), (3.25) and (3.32) will

give:

i) one dimensional growth - instantaneous nucleation

ii) one dimensional growth - progressive nucleation

t

i = JNoznFkA du o

i = nFkAN Zt o

iii) two dimensional growth - instantaneous nucleation

k2t i = 2nFnMhNo --­

p

- 40 -

(3.37)

(3.38)

(3.39)

(3.40)

iv) two dimensional growth - progressive nucleation

(3.41)

but (3.42) 2

o 0

i = nF1TMhZno (3.43) p

v) three dimensional growth - instantaneous nucleation

(3.44)

vi) three dimensional growth - progressive nucleation

t

=JNoZ2nF1TM2 k 3

i - u2du (3.45 ) p

t t

JU2

dU [~ u3J 1

but = = _ t 3 (3.46 ) 3

0

(3.47)

Considering equations (3.37), (3.39), (3.40), (3.43), (3.44) and (3.47)

for the current time responses it is obvious that a plot of i Vs t n will

not identify the surface process uniquely. Other techniques are

- 41 _

•

needed to confirm the nucleation and growth processes, the most

obvious being microscopic or electron microscopic counts of the

growth centres at different times after perturbation.

As time after perturbation increases, the current-time variation

cannot continue to follow the relationships stated earlier for two

reasons. Firstly the growth will be obstructed due to the centres

impinging on one another or on the crystal lites of the parent phase,and

secondly in the progressive nucleation there will be a change from the

linear law (Equation 3.36) to the first order law (Equation 3.34).

Bewick et al. [59] have adopted the theory of Avrami [60] to show

that if random overlap occurs between the nuclei then the fraction of

the surface covered by growth centres, y, is related to the fraction

that would be covered in the absence of overlap, y t' by: ex

-Yext Y = 1 - e

The volume of the cylinder will be given by:

v = yh

and the surface area, A, by

dV dy A=-=h-

dr dr

- 42 -

(3.48)

(3.49)

(3.50)

(3.51)

For instantaneous nucleation

Yext = N lIr2 (3.52) 0

A d [ -No lIr2)

(3.53) = h - 1 - e dr

A = h2N lIr exp(-N lIr2) (3.54) 0 0

substituting into equation (3.15) gives:

(3.55)

1 · f Mkt f . (3 23)· h rep aC1ng r or --- rom equat10n . g1ves t e current response p

for a 2-dimensional growth with instantaneous nucleation.

(3.56)

If the nucleation processes follow a progressive mechanism a similar

argument can be applied using the first order nucleation law

(Equation 3.34)

tj N Zk2

i = 2nFlIhM 0p

o

(3.57)

Therefore for a two dimensional growth with progressive nucleation

the current response will be given by:

- 43 -

i = nF1lhMN _Z_k_2

_t2_ exp [_1lM2N Z _k_

2t_

31 o p 0 3p2 ]

(3.58)

The derivation of a mathematical model to describe three dimensional

growth of hemispheres after overlap is limited because the integrals

cannot be solved in closed form. Armstrong [61] has overcome this

problem by considering the growth of right circular cones. This

approach simplified the mathematics and leads to a mathematical model

predicting the current-time transient.

Armstrong considered the cones to be cut into a series of thin

cylinders of height dx at a distance x from the electrode surface.

The growth of the cones continues with a velocity, V, perpendicular

to the plane of the electrode and with a rate constant, k, parallel to

the plane of the electrode. The derivation has been adequately covered

by Armstrong and only the results will be presented here.

i) three dimensional growth - instantaneous nucleation

(3.59)

ii) three dimensional growth - progressive nucleation

(3.60)

In the study of positive grids of the lead acid battery in this

laboratory,dimensionless curve fitting has proved to be the most

successful technique in the identification of the mechanism of

nucleation and growth [62].

- 44 -

The commonly occurring equations which represent both two and

three dimensional growth can be reduced to:

i) i = <XIt exp(SJt2) (3.61)

ii) i = <X2t2 exp(S2t3 ) (3.62)

iii) i = AIll exp(a3 t2)]exp(<X3t2 ) (3.63)

iv) i = 1.2 [1 - exp(a4 t3 )]exp(a4 t3) (3.64)

differentiating these equations with respect to time will give a single

maximum when ~! = 0 (im' t m) at which:

i m 0.5 <Xl = - e

t m

1 SI =--

2t 2 m

i -0.67 m <X2 =-e

t 2 m

2 S2 =-

3t3 m

A = 4i m

lnm <X3 =

t 2 m

(3.65)

(3.66)

(3.67)

(3.68)

(3.69)

(3.70)

- 45 -

A2 = 4i (3.71) m

1nl! ) OC 4 = (3.72)

t3 m

Substituting these values into the previous simplified equations, the

following is obtained:

For two-dimensional growth - instantaneous nucleation

i -= i m

For two-dimensional growth - progresstve nucleation

For three-dimensional growth - instantaneous nucleation

i -=

For three-dimensional growth - progressive nucleation

i -= i m

(3.73)

(3.74)

(3.75)

(3.76)

From the above equations (3.73) to (3.76) it is possible to

calculate the theoretical dimensionless values for the different

- 46 -

nucleation and growth mechanisms and compare them with the experimental

values in order to identify the type of surface process involved.

- 47 -

CHAPTER 4

EXPERIMENTAL TECHNIQUES

4.1 ELECTROLYTIC SYSTEMS

4.1.1 Electrolyte Solutions

The electrolyte solutions were prepared from 'Analar' grade

reagents and triply distilled water, obtained from deionised stock •

• The electrolyte was deoxygenated for several hours by the passage of

oxygen free nitrogen before commencement of each experiment. Fresh

electrolyte was used for each individual experiment. In the

experiments conducted, 2M H2S04 eSp.g. 1.12 kg/I) was used in the

formation of the porous electrodes and 5M H2S04 eSp.g. 1.288 kg/I)

for the electrochemical measurements.

4.1.2 Electrolytic Cells

All cells were manufactured from borosilicate glass (construction

shown in Fig. 4.1 and 4.2) and the fittings had lubrication-free

ground glass joints. The cell and all glassware was cleaned by

steeping in a 50:50 mixture of nitric and sulphuric acid for three

days. The glassware was then thoroughly washed with triplydistilled water

and soaked for 24 hours before use.

A conventional three limbed cell as shown in Fig. 4.1 was used

for all the electrochemical measurements. The working electrode was

- 48 -

- --- -----------------------

--

-7 ~-+--A

--~~------_+--~--B

~~r_-----r_---r_--~-- C

FIG, 4,1, THE THREE LIMBED CELL,

A = COUNTER B = WORKING C= REFERENCE D = LUGGIN CAPILLARY

)

FIG. 4.2. FORMATION CELL.

A = PROVISION FOR REFERENCE ELECTRODE B = COUNTER ELECTRODE C = WORKING ELECTRODE

A

B

c

----.---------------------------------------------------------------------------------

inserted through a loosly fitting teflon cap into the main compartment

of the cell (B). A counter electrode was placed in one side limb (A)

and the reference electrode in the other (C). The connection from

the reference compartment entered the main cell via a luggin

capillary (D) of 1 mm diameter, this was always placed 2 mm below the

centre of the working electrode. The formation ce~l, as depicted in

Fig. 4.2, was used to galvanostatically charge and/or cycle the

porous electrodes. The working electrode was inverted, to allow the

evolved oxygen to escape and the electrode was held securely in

position (C) by a 'teflon bung'. The counter electrode is shown in

position Band a reference electrode was incorporated so that the

potential could be monitored continually (A).

4.2 ELECTRODES

4.2.1 Planar Working Electrodes

These had the construction shown in Fig. 4.3. Their shape was

in accordance with hydrodynamic requirements. The lead and lead

alloys were machined from gravity fed cast lead rods which had been

allowed to age at room temperature for a minimum of 1 month. The

electrodes had a cross-sectional area of 0.2 cm2, and were set in a

teflon electrode shroud (63) . A stout steel spring was then

attached onto the back of the electrode ensuring good electrical

contact with the shaft of the rotating disc electrode (R.D.E.)

assembly. The electrode shroud was then screwed into a hollow

teflon holder. This construction allowed the simple removal of the

- 49 -

TEFLON ELECTRODE-I-­HOLDER

FIG, 4,3. PLANAR WORKING ELECTRODE.

TEFLON ELECTRODE SHROUD

working electrode for scanning electron microscopic (S.E.M.) examina­

tion. A Mercury pool provided the electrical contact between the

shaft and the external circuit.

Before commencement of the experiments a rigorous electrode

surface preparation regime was adhered to. This was as fo11ows:­

firstly the electrode was polished on fine silicon carbide paper

(600 and 1200 grit), roughened glass and finally tissue paper.

This was followed by a 5 sec. chemical etch in 10% nitric acid and

a thorough rinse in triply distilled water. The electrode surface

was then viewed through a binocular microscope to ensure that it

was free from embedded silicon carbide particles.

4.2.2 Porous Electrodes

The porous electrodes had the construction shown in Fig. 4.4.

This consisted of a 'shaped' solid support, constructed from the

lead alloy under investigation which was recessed beneath the level

of the tef10n shrouding. Positive battery paste was then forced into

the cavity forming a porous layer terminated by the lead alloy .e1ectrode.

The pasting and 'curing' was carried out by 01dham Batteries Ltd. to

the same standards as their industrial process.

The porous matrix was oxidised to lead dioxide by a ga1vanostatic

oxidation method in 2M HZS04' A constant charging current of 25 mA/cmZ

was used and continued to flow until the potential was steady and

gas evolution (oxygen) from the porous matrix had started to occur.

- 50 -

J

TEFLON ELECTRODE -----l­HOLDER

fl ---..s S~ID ~ METAL ------ TEFLON SUPPORT ~ ELECTRODE

_ SHROUD

LEAD DIOXIDE PASTE~

FIG. 4.4. POROUS WORKING ELECTRODE.

----.-! Ik..

(r- ...... ~<

I. 'I

., /' ,

I- r-~

;>

... . . . . . - JJ .t.-

, r------

'"

FIG, 4,5, REFERENCE ELECTRODE,

Cu wire

B 19

pyrex

solder

Hg:;q

Pt wire

Hg

4.2.3 Counter and Reference Electrodes

The counter electrode used in the formation and electrochemical

experiments was a pure lead rod (koch-Light 99.999%) of larger

surface area than the planar working electrode.

The reference electrode used in all the experiments was the

mercury-mercurous sulphate reference electrode, (Hg/HgzS04/H2S04).

The construction is shown in Fig. 4.5 and the sulphuric acid concentra­

tion was always the same as that used in the cell.

4.3 ELECTRICAL CIRCUITS

4.3.1 Linear Sweep/Cyclic Voltammetry and Potentiostatic Step

Experiments

Fig. 4.6 shows a schematic diagram of the experimental arrangement

used. Potentiostatic control was obtained using a potentiostat in

conjunction with a function generator. The resulting voltammograms

or current-time transients were recorded both graphically using an

x-y-t recorder and via a digital oscilloscope. The information

obtained from the transients and voltammograms was digitised and

stored on floppy disc for further analysis using a microcomputer.

4.3.2 Chronocoulometric Cycling Experiments

The experimental arrangement for the chronocoulometric cycling

experiments is shown in Fig. 4.7. Again potentiostatic control was

obtained by using a potentiostat in conjunction with a digital ramp

generator. However, in these experiments, the current response was

- SI -

Potentiostat XY Recorder

11 Function Generator

Multimeter \.. ~~ Lf

-

FIG 4.6. L.S.V. AND POTENTlOSTATlC PULSE CIRCUIT.

Potentiostat

WE RE CE

.... - .... Cell

Bufferl \ I Amplifier Y_ A

... --t D Microcomputer

Function Generator

C

Plotter

1

Printer

FIG. 4.7. CONTINUOUS POTENTIODYNAMIC CHRONOCOULOMETRIC CYCLING CIRCUIT.

V.D.U.

recorded via a 2-80 based microcomputer fitted with a 12 bit

analogue to digital converter (A.D.G). The anodic part of the

vOltammogram which represents the conversion of lead sulphate to

lead dioxide (charging reaction) was then numerically integrated

to obtain the charge contained in the oxidation peak. The values

were displayed against cycle number and stored on floppy disc.

4.3.3 Faradaic Impedance Measurements

The experimental set-up is based on a computer controlled

Solartron 1250 Frequency Response Analyser (F.R.A.) with a 1186

Solartron e1ectrochemical interface to control the potential. The

F.R.A. consists of a programmable generator which delivers the

perturbing signal, measures the system response, analyses the

results with the aid of a correlator, and then displays the results.

The computer controls the programming of the F.R.A. and stores the

resultant data. The generator can be programmed to choose a

frequency and measure the response at that frequency, or more often

to scan through a range of frequencies from the highest to the

lowest (10 kHz to 10mHz). At each frequency the response is

averaged over a number of cycles (10 in this case) and then displayed

in one of three possible ways: resultant impedance (R) and phase

angle 0, log Rand 0 or the real and imaginary parts of the impedance.

4.4.1 Optical Microscopy

Optical microscopy was carried out on polished and etched planar

electrodes. The preparation of the electrode was carried out by

microtoming l~ from the electrode surface with a freshly prepared

- 52 -

glass blade. This gave an equivalent finish to the traditional

polishing method but cut the preparation time down to about 10 min.

The electrode was then etched using a variety of etches depending

on the sample being examined. (See Appendix) .

4.4.2 Scanning Electron Microscopy

The potentiodynamically cycled electrodes were prepared for

microscopic examination after removal from the electrolyte. The

electrodes were washed in methanol, rinsed in acetone and stored

in a vacuum dessicator. The electrodes were then coated with a thin

layer of gold by diode sputtering to ensure conductivity before

examination under the electron microscope.

- 53 -

CHAPTER 5

The E1ectrochemica1 Properties of Solid Lead after Alloying with

Calcium, Tin and Antimony.

5.1 INTRODUCTION

The performance of the lead-acid battery depends to a large

extent on the type of lead alloy used in the battery grid construction.

As stated in Chapter 1, antimony has been employed in grig manufacture

for many years [16], mainly because it engenders desirable properties

such as good cycle life and improved castabi1ity. However, with the

advent of sealed 'maintenance free' batteries, alloys with low gassing

rates (high hydrogen evolution potential) have been required to replace

the lead-antimony alloys. This is because the lead-antimony alloys

contribute heavily to the hydrogen evolution problem. The 1ead-

calcium system has been employed for many years in 'float' service [64].

consequently development of new grids for 'maintenance free' applica­

tions has focussed on these lead-calcium and 1ead-ca1cium-tin alloys.

The non-antimonial alloys have overcome the hydrogen evolution problem

but the removal of antimony has resulted in rather inferior cycle lives.

This Chapter records and discusses the linear sweep vo1tammetry

measurements carried out on various lead alloys used in battery

production today. A continuous potentiodynamic chronocou1ometric study

~51has also been undertaken to investigate the 'alloy effect' on the

cycle life performance of the positive battery plate and the mechanism

-54 -

of passivation has been elucidated using A.C. Impedance. It should

also be noted that the industrial practice for battery cycle life

testing takes many years and employs a slow rate galvanostatic

technique. These cycle life experiments have been designed to

accelerate the testing regime time whilst still giving valuable

cycle life data.

5.2 Linear Sweep Voltammetry

5.2.1 Experimental

The linear sweep voltammetric studies were performed on working

electrodes prepared from cast lead alloys which had been allowed to

age at room temperature for a minimum of 1 month. These alloys were

thought to best represent industrial practice and their compositions

are shown in Table 5.1. The electrodes underwent the pretreatment

described in Chapter 4.

The oxidative sweep experiments were carried out at a stationary

electrode. The electrode was polarised to 2,000 mV* on the initial

cycle in order to initiate lead dioxide formation. This was followed

by a modified Plante type process but without the added agressive

ingredients.

5.2.2 Results and Discussion

(a) The non-antimonial alloys

The voltammograms in Figures 5.1 to 5.4 correspond to the various

non-antimonial alloys on the first potential excursion to 2,000 mV

* All potentials in this work are against Hg/Hg2S04 reference electrode.

- ss -

Analysis wt per cent Code

Se Sb Sn Ca Pb

A - - - - 99.999

B - - 0.3 0.095 remainder

C - - - 0.1 remainder

D - - 0.3 - remainder

E 0.02 1.8 - - remainder

F 0.03 2.75 - - remainder

G - 4.5 - - remainder

H - 10 - - remainder

Table 5.1. The composition of the alloys used in the

L.S.V. experiments.

- 56 -

I

s a: E

3

1

-1

-3

-s .6 .8

,

1 1.2 1.4 1.6 1.8 2

V

FIG 5.1. INITIAL L.S.V. FOR PURE LEAD: SWEEP RATE 50 MY/SEC.

s a: r E

3 I-

1 I-

-1 I- 7

-3 l-

-s •

.6 .8

I T I I

-,,,

.

, ,

1 1.2 1.4 1.6 1.8 2

V

FIG. 5.2. INITIAL L.S.V. FOR LEAD-CALCIUM-TIN: SWEEP RATE 50 MY/SEC.

Cl: e

s

3

1

-1

-3

-s

,

-

- I( -

I I

.6 .8 1

, , ,

-"

-

-

I I I I

1.2 1.4 1.6 1.8 2

V

FIG, 5.3. INITIAL L.S.V. FOR LEAD-CALCIUM:

Cl: e

s

3

1

-1

-3

-s

SWEEP RATE 50 MV/SEC.

,

-

C-

/'

V

f-

f-

I I

.6 .8 1

, ,

-~,

-

-

-

I I I ,

1.2 1.4 1.6 1.8 2

V

FIG. 5.4. INITIAL L.S.V. FOR LEAD-TIN: SWEEP RATE 50 MV/SEC.

and the return sweep to 600 mY. The sweep rate was fixed at 50 mY/so

The voltammograms are similar to those presented by Penesar [66],

Carr [67], Brennan [68], Sharpe [69] and Sunderland [70] in their redox

studies on lead alloys. In the anodic potential region (+1.6 mV VS.

Hg/Hg2S04) the current increases steeply owing to the electrode

undergoing an oxygen evolution reaction. During the return sweep

this current is larger than during the preceeding anodic oxidation

due to an apparent increase in catalytic activity of the electrode

surface. This change in surface properties is indicated by a small

reduction peak on the reverse sweep. The reduction peak in all of the

voltammograms is due to the conversion of lead dioxide to lead sulphate.

However, at a sweep rate of 0.1 mV/s (Fig. 5.5) an anodic peak

corresponding to lead dioxide formation was observed at 1.3 Von the

forward sweep. This observation agrees with the work of Visscher [71].

The lack of a peak in the anodic region at fast sweep rates is due to

the difficulty in separating the individual peaks because of the

simultaneous oxygen evolution reaction. The reverse sweep shows some

unusual, but characteristic behaviour, with an anodic peak being observed

as well as a cathodic reduction peak. The anodic peak is probably due

to desorption of oxygen, which exposes part of the lead surface, which

then reacts chemically with the sulphuric acid to produce lead

sulphate, this is immediately oxidised to lead dioxide giving rise

to an anodic peak.

The linear sweep experiments were continued between the potential

limits of 600 and 1350 mV and the sweep rate was kept constant at

50 mY/so A peak corresponding to lead dioxide formation became

apparent and increased initially with cycling. Figure 5.6 shows

- 57-

,--------------------------------------------------------------------------------------------

a: lE

3 I I ,

2 r

1 _

o

-1 r

-2 _

-3 I 1

600 800 1000 1200

FIG, 5,5, INITIAL L,S,V. FOR PURE LEAD: SWEEP RATE 0.1 MV/SEC.

,

1400

-

-

-

-

1600

mV

the corresponding voltammograms for the various lead alloys after

4 h continual cycling under these restricted potential limits. The

potential limits represent a typical potential excursion for a non-

antimonial positive battery plate under aggressive charge/discharge

cycling. The voltammograms in Fig. 5.6 are typical of many sited in

the literature [72, 73, 74], each voltammogram consists of a well

defined oxidation peak and a less well defined reduction peak. The

difference in the potential for lead dioxide formation is shown in

Figs. 5.1 to 5.4 and 5.6. This highlights the considerable nucleation

overpotential required for lead dioxide to form on a planar lead

surface. These results confirm the findings of Fleischmann et al.

[75] who first reported this phenomenon. The shape of the voltammograms

indicate that the reaction is electrochemically hindered in the cathodic

sweep. This is as expected because of the resistive layer of lead

sulphate formed at the metal-dioxide deposit interface during the

discharge process. This resistive layer of lead SUlphate slows down

the rate of electron transfer, giving the voltammogram a similar shape

to a diffusion controlled electrochemically irreversible reaction.

The anodic peak which represents the oxidation of lead sulphate

to lead dioxide does not return to zero above 1350 mV as a residual

current remains. This is a result of the electrode undergoing an

oxygen evolution reaction:

H20 +

--+ !02 + 2H + 2e (5.1)

This isof interest as the equilibrium potential for the decomposition

of water is 1.23 V [6], however, in these experiments oxygen evolution

- 58 -

N -S ()

"-a: s

3.5

2.5

1.5

.5

-:5

-1.5 600 750 900 1050 1200 1350

mV

FIG. 5.6. CONSTANT RESPONSE CURVES FOR THE NON-ANTIMONIAL ALLOYS OVER THE POTENTIAL RANGE 600-1350 MV AFTER CONTINUOUS CYCLING FOR 4H: SWEEP RATE 50 MV/SEC.

did not occur until 1.3 V, therefore there is a slight oxygen over-

voltage on porous lead dioxide. This leads to a higher charging

efficiency than would be theoretically expected. The charge

contained in the reduction peak was found to always be in the range

85-95% of the oxidation peak, indicating the electrode was always

fully charged after each cycle and that only a small amount of

charge contributes to oxygen evolution per cycle. The charge values

for the oxidation and reduction peaks are shown in Table 5.2.

Alloy Code ip Ep Charge of Charge of mA/cm2 mV anodic peak cathodic peak

/mC /mC

Pb A 3.5 1150 2.70 2.30

Pb-Ca-Sn B 3.4 1130 2.65 2.40

Pb-Ca C 2.6 1140 2.35 2.10

Pb-Sn D 2.4 1120 2.40 2.30

Table 5.2 The peak current, peak potential and the charge contained

in the anodic and cathodic peaks for the non-antimonial

alloys after 4 h cycling.

The broadening of the oxidation peak represents the increase in

porosity of the lead dioxide deposit formed as a result of continued

potentiodynamic cycling between the lead sulphate and lead dioxide

potential regions. The more extensive the porous deposit, the harder

the reaction has to be driven in order to convert lead sulphate to

lead dioxide. The oxidation peak will occur over a larger potential

- 59 -

range commensurate with the difficulty in driving the reaction deep

into the porous matrix. The voltammograms showed that initially

the lead-tin binary alloy had the most developed porous lead

dioxide deposit. With continued cycling, the porosity of the surface

layer for lead and the lead calcium alloy was shown to increase.

The effect of rotation speed on the voltammograms has also been

investigated and found to have no apparent effect. The rate of

oxidation of lead sulphate to lead dioxide in sulphuric acid is

not determined by a solution reaction under these conditions. It can

be concluded that even at a stationary electrode the diffusion layer

must be sufficiently thin for control of the current by mass transport

in solution to be absent .. TIle reaction proceeds via a solid state

mechanism.

The relationship between peak potential (Ep) in the oxidation

of lead sulphate to lead dioxide and sweep rate (v) in the form of

Ep Vs. log) 0 sweep rate (v) is displayed in Figure 5.7. This follows

the equation developed by Canagaratna et al. [76] for describing the

formation of lead dioxide at a constant thickness per cycle. As is

evident from the straight line plots in Figure 5.7 and the data in

table 5.2, the potential (Ep) of the oxidation peak (ip) for all of

the non-antimonial alloys occur at more negative potentials than

on the pure metal. This trend is in agreement with the work of

Bialacki [77] and Kelly [78]. The position of the peak current

(Ep) in relationship to the equilibrium potential (E9) is determined e

by the activation overpotential for that particular alloy, this is

9 inturn related to the intrinsic rate constant ~ (Eq. 3.3). A

small value for ~9 will indicate a sluggish reaction whilst a large

- 60 -

> "­

Q..

lLJ

1.3

1. 25

1.2

1. 15

1.1

1. 05

1 -1 -1.1 -1.2 -1.3 -1.4 -1.5 -1.6 -1.7

Log (SWEEP RATE)

FIG. 5.7. PLOT OF Ep VS LOG SWEEP RATE FOR THE NON-ANTIMONIAL ALLOYS.

value will indicate that the rate of reaction will be fast and

therefore the oxidation peak will occur at potentials close to the

equilibrium potentials. Comparing the non'-antimonial alloys

(B,C,D),with pure lead (A) it can be seen that the kinetic barrier

to the conversion of lead dioxide from lead sulphate is decreased

when lead is alloyed with calcium and/or tin.

The largest peak current (Table 5.2) was observed for pure

lead (A) and the lowest for the lead-tin binary system. This

indicates that lead undergoes the greatest anodic attack, whilst

the addition of calcium or tin exert a protective effect. It can

be seen that when calcium and tin are combined there is a synergistic

effect and the ternary alloy corrodes more readily. These results

are in agreement with Gonzalez U9] and McWhinnie [80] who independently

investigated the long term corrosion resistance of various non­

antimonial alloys.

(b) The antimonial alloys

The voltammograms in Figures 5.8 to 5.11 are similar to those

in Figures 5.1 to 5.4 and are for the various antimonial alloys.

Again there is no observed anodic peak at fast sweep rates for

lead dioxide formation and only a combined anodic peak for oxygen

evolution and dioxide formation is visible at high anodic potentials.

This is in agreement with Brennan et al. [81] and Danel et al. [82].

At slow sweep rates an anodic peak was visible similar to that for

the non-antimonial alloys (Fig. 5.12).

The linear sweep experiments were then continued between the potential

limits of 600 and 1250 mV and the sweep rate was kept constant at 50 mY/so

- 61 -

a: la

5

3

1

-1

-3

-5 .6 .8 1 1.2 1.4 1.6 1.8 2

V FIG. 5.8. INTITIAL L.S.V. FOR 1.8% ANTIMONY:

a: la

5

3

1

-1

-3

-5

SWEEP RATE 50 MV/SEC.

,

r-

r-

V r-

r-

I

.6 .8

, • , I I

-

} /'-

-

-

-

I I I I I

1 1.2 1.4 1.6 1.8 2

V

FIG. 5.9. INITIAL L.S.V. FOR 2.75% ANTIMONY: SWEEP RATE 50 MV/SEC.

a: e

5

3

1

-1

-3

-5

•

t-

I-

cV I-

.6 .8

I I I I I

-

~ ...

0

0

-

I I I I

1 1.2 1.4 1.6 1.8 2

V

FIG. 5.10. INITIAL L.S.V. FOR 5% ANTIMONY:

a: e

5

3

1

-1

-3

-5

SWEEP RATE 50 MV/SEC.

.6 .8 1 1.2 1.4 1.6 1.8 2

V

FIG. 5.11. INITIAL L,S,V, FOR 10% ANTIMONY: SWEEP RATE 50 MV/SEC.

ex: E

5

3 :-

1 f-

-1 I-

-3

-5 .6

I

I

. 8

I , ,

, I I

1 1.2 1.4

FIG. 5.12. INITIAL L.S.V. FOR 1.8% ANTIMONY: SWEEP RATE 0.1 MV/SEC.

I I

-

-

-

-

I

1;6 1.8 2

v

These potential limits compare favourably"to the potential limits set for

the non-antimonial alloys (600-1350 mY) because antimony has been shown by

Maja et al. [83] to lower the oxygen evolution potential. These

potential limits represent a typical potential excursion for a

positive battery plate constructed from a lead-antimony alloy.

The vol tammograms in Figure 5.13 correspond to the various

antimonial alloys and pure lead after 4 h continuous cycling at

50 mV/s under the restricted potential limits. Each voltammogram

consists of a well defined oxidation peak and a less well defined

reduction peak. The arguments applied for the non-antimonial

alloys in Chapter 5.2.2a also apply to these voltammograms. The

charge contained in the reduction peak was again found to always

be in the range 85-95% of the oxidation peak, indicating that the

electrode was fully charged after each cycle and that only a small

fraction of the anodic charge contributes towards oxygen evolution.

The charge contained in the anodic and cathodic peaks are given in

Table 5.3.

Alloy Code ip/mA Ep/V Charge of Charge of anodic peak cathodic peak

/mC /mC

Pb A 2.2 1.030 1.85 1.65

Pb-Sb(1. 8%) E 1.30 1.063 1.25 1.15

Pb-Sb(2.75%) F 0.73 1.054 0.55 0.50

Pb-Sb(5%) G 1.03 1.060 0.70 0.65

Pb-Sb(lO%) H 0.98 1.048 1.00 0.95

Table 5.3. The peak current, peak potential and charge contained in the

anodic and cathodic peaks for the various antimonial alloys.

- 62 -

N -e Cl

"-a: e

2.5

1.5

.5

-.5

-1.5 600

FIG, 5,13,

A

730 860 990 1120 1250

mV

CONSTANT RESPONSE CURVES FOR THE ANTIMONIAL ALLOYS OVER THE POTENTIAL RANGE 600-1250 MV AFTER CONTINUOUS CYCLING FOR 4H: SWEEP RATE 50 MV/SEC,

From the shape of the voltammograms in Figures 5.13 it can be

seen that the higher the antimony content, the broader the oxidation

peak. This indicates that the addition of antimony increases the

porosi ty of the developed lead dioxide film.

Figure 5.1'4 shows the relationship between the peak potential

(Ep) of the oxidation peak for the conversion of lead sulphate to

lead dioxide and sweep rate (v). This is in the form of a plot of

Ep Vs. logIO sweep rate. This, like the non-antimonial alloys,

follows the expected equation developed by Canagaratna [76], for

the development of a layer of lead dioxide at a constant thickness

per cycle. It is also clear from the straight line plots that the

formation of lead dioxide occured at a greater positive potential than

on the pure metal. This is in contrast to the work presented by

Kelly et al. [78] but in agreement with Bialacki et al. [77]. This

discrepancy could be due to the fact that the 'pure lead' alloy used

by Kelly (99.98%) contained traces of other metals which could help

resist anodic attack. The sweep rate employed was also slightly

different.

The largest peak current (ip) and anodic peak capacity was

observed for pure lead and the lowest for the 2.75% antimonial alloy

(Table 5.3). Again lead underwent the greatest anodic attack, with

antimony exerting a protective effect. Figure 5.15 shows a plot of

anodic peak capacity against antimony content. The addition of

antimony initially lowered the capacity of the anodic peak until it

reached a minimum at an antimony concentration of 2.75% antimony,

the capacity then continued to rise with increasing antimony content.

-63 -

> e "­Q.

LLJ

1. 15

1. 12

1.1

1. 07

1. 05

1. 02

1 -1 -1.1 -1.2 -1.3 -1.4 -1.5 -1.6 -1.7

Log(SWEEP RATE)

FIG. 5.14. PLOT OF Ep VS LOG SWEEP RATE FOR THE ANTIMONIAL ALLOYS.

This is in agreement with Brennan et al. [81] who concluded from their

differential double layer capacitance studies that antimony exerted

a protective effect with the 2% antimonial alloy having an anomalously

low value. The profile in Figure 5.15 indicates there are probably

two competing mechanisms. Ruetschi [84] and Lander [85] have shown

that under both potentiostatic and galvanostatic conditions, the

corrosion rates of antimonial alloys increase with increasing antimony

content. This can be explained by the fact that, in alloys containing

less than 6% antimony the mode of attack is largely intercrystalline

but with some additional sub grain attack. The grain boundries have

been shown to be corroded more deeply [86] than the channels traversing

the grains. As the antimony content increases corrosion attack is

more uniformly distributed along the interdendritic network and

antimony segregated areas. At the higher antimony concentrations

(9-10%), penetration of the antimony rich areas becomes prominent

leading to a higher corrosion rate which is less destructive. In low

antimonial alloys selenium is added as a grain refining reagent. The

grain refining works by allowing on solidification, grains to grow

around the added nucleating agent, resulting in a more uniform and

finer grain size. The addition of grain refiners becomes unnecessary

above 3-4% antimony because there is sufficient eutectic present to

fill any voids or cracks formed on solidification. Alloys with added

selenium have a finer and more uniform grain size, resulting in a

decrease in corrosion rate and depth of penetration [87]. The optimum

conditions for limited anodic corrosion over the range studied was

found to be 2.75% antimony.

- 64 -

u e

....... w c.!l 0:

1.5

Cl: ::c 1. 3 u

1.1

.9

. "/

.5 o 1 2 3 4 5 6 "/ 8 9 10

COMPOSITION Wt.!. Sh.

FIG. 5.15, PLOT OF CHARGE OF THE ANODIC PEAK VS ANTIMONY CONTENT AFTER 4H POTENTIODYNAMIC CYCLING,

5.3 CONTINUOUS POTENTIODYNAMIC CHRONOCOULOMETRY

5.3.1 Experimental

An identical experimental procedure was followed as in Chapter 5.2.1

but the potentiodynamic cycling was continued for up to 8,000 cycles.

The data was recorded via a microcomputer fitted with a 12 bit analogue

to digital convertor. This allowed for the online numerical integration

of the charge in the anodic peak (See Chapter 4). The charge of

the anodic peak was then displayed as a function of cycle number.

The results presented are the mean of ten separate experiments. This

number of experiments was required to eliminate surface effects

caused by the diffusion of the alloying ingredient to the electrode surface.

5.3.2 Results and Discussion

(a) The non-antimonial alloys

With continued potentiodynamic cycling the peak current and also

anodic peak capacity was found to vary with cycle number. Figure 5.16

shows the relationship between anodic peak capacity and cycle number.

As is evident, the alloys show a trend in which their anodic peak

capacity rises and reaches a maximum after 1,000 cycles and then

diminishes. These results indicate that initially an extensive lead

dioxide deposit is formed with continued cycling by the corrosion of

the planar lead electrode. This then reaches a maximum value where

further attack of the backing alloy is restricted and the capacity

then falls as the electrode passivates. Passivation is most likely to be

brought about by restriction of acid reaching the metal/porous lead

dioxide interface, which will lead to a resistive film of lead sulphate

- 65 -

w e

...... w (!1

a::: a: ::I:

3 I ,

Pb '0' 0,

"

, I

w 2.5 r- " '0' • " ." .

"

Pb-Ca.-Sn , ,

, , , , ,

, , Pb -Sn " " , ... ' :," ,Pb''':CO: ,,',:""'" "",''', .' • '0 • '. • •• '. 0' •• :

, "

: • • ' :' " '" .' • 0, " . '. .

2 " " : r- ," , : '

" .. ' . " ' , ,

'to • :. .

.:. : ", .. . . . .

1. 5 ~, : " "

, , , ,

" , ,

" .. "

, ,

" '. " . '. . , , ' ... ' : .. '" , ,

-

-

-

. , . ...

1 I I I I

o 1000 2000 3000 4000 5000

CYCLE No.

FIG, 5,16, VARIATION OF CHARGE OF ANODIC PEAK WITH CYCLE NUMBER FOR THE' NON-ANTIMONIAL ALLOYS,

forming at the interface, causing subsequent passivation. There is a

marked difference between the alloys containing calcium and/or tin on

one hand and pure lead on the other. These observations could be due

to the fact that after a deep discharge, passivation can be brought

about by a layer of lead sulphate and additionally, in the case of the

calcium containing alloys, a layer of calcium sulphate [86]. The

presence of this binary film in the latter situation will lower the

charge required to passivate the binary alloy. In the case of the ternary

lead calcium-tin alloys, an intermetallic compound of composition

Sn3Ca has been shown by Prengaman [88] to exist at room temperature.

This intermetallic compqund has been shown to be resistant to sulpha-

tion and/or oxidation [89] and so helps reduce the effect of passiva-

tion by the build up of a sulphate layer [88]. Within the restricted

potential limits of the experiment (600 - 1350 mV) any tin present at

the electrode surface would be oxidised to tin dioxide [90] and this

could then contribute to the matrix conductor via a semi-conductor

effect, so again resisting complete passivation.

(b) The antimonial alloys

The antimonial alloys showed a different characteristic to the non­

antimonial alloys. The distinctive characteristic of the antimonial

alloys is shown in Figure 5.17. Again the anodic peak capacity is shown

as a function of cycle number. As is evident (unlike the non-antimonial

alloys in Figure 5.16), the antimonial alloys show a trend in which

their charge capacity continues to rise with cycling during the whole

experiment. A similar trend was seen when peak current (ip):was plotted

against cycle number. Theprofi1e in Figure 5.17 indicates that a

- 66 -

c.J e

2.6

~ 2.4 r C!I 0:::

~ 2.2 r c.J

1.8 - :

1.6 -t · · · 1.4 ~ i

1.2 i

~

Pb .' .

I

. . " ... .' . '. ..

, ,

.. ' .' . ". .. ....... ... . .. .

" . .. . .

-

. .' --

-51. Sb _

. . . :

. . . .. . .. ". .. • • • • .... .. • • • ••• I. • " • •

1 r- • :

8 . . . '-.: : . · . .

• 6 r~ .. : . .' . . .

• 4 o

.. .. L

1000

. . .

. . . . . . . . . . . . . . .' .... " .. . . . ...

101. Sb-

-2.75i. Sb . . . . . . . . ". :'." .. .. .. . ... :. . ",. . " '.

I I

2000 3000 4000 5000

CYCLE No.

FIG, 5,17, VARIATION OF CHARGE OF ANODIC PEAK WITH CYCLE NUMBER FOR THE ANTIMONIAL ALLOYS,

I

. I

I

I

I

passivating layer of lead sulphate is unlikely to be formed between

the base metal and the formed lead dioxide deposit. The trends for

the antimonial and non-antimonial alloys are very similar to those

published by Burbank [91] in her studies on the capacity change with

cycling of the anodic coatings on pure and antimonial lead. Burbank

noted that the capacity of the antimonial alloys continued to rise

whilst that for pure lead reached a maximum and did not increase

significantly with continued cycling. Our results agree with those

findings.

Burbank [92] and Swets [93] have studied the crystal structure of

a and S lead dioxide, the two polymorphs most commonly encountered in

the lead acid battery. They have also studied other compounds which

are probably formed on battery cycling which include AB206 type

compounds such as PbSbzOs. This work was undertaken to elucidate the

role these compounds play in the nucleation or passivation of lead

dioxide and so explain the beneficial effect of antimony on the cycle

life performance of the lead acid battery. Burbank [92] suggested

the size of the ion plays an important role, and that ions more compact

than tetravalent lead will lead to the oxygen octehedra surrounding

the antimony ion becoming more compact, thus resulting in an increase

in lattice energy and so a more stable crystal mass. The use of ionic

radius ratios to predict structure once the stoichiometry is known, is

not a new idea [94] and could prove useful in selecting possible guest

ions for the lead dioxide lattice. Table 5.4 shows a list of cation/anion

radius ratios based on the widely accepted ionic radii of Pauling [95]. For

MX type compounds with large radius ratios it has been shown that they

favour the fluorite structure and those with the smaller ratio will

favour the rutile structure [94]. The radius ratio data in Table 5.4

- 67 -

indicates that a cation/anion radius ratio of between 0.4 and 0.7 will

help nucleate new lead dioxide whilst higher ratios might disrupt the

crystal lattice and passivate the electrode by the formation of lead

sulphate. The results expressed in Figures 5.16 and 5.17 agree with

these postulations. Ritchie [96] has also suggested that Sb5+ ions

4+ dissolved from the lattice may occupy vacant Pb octahedral sites in

the lead dioxide lattice and nucleate new a lead dioxide on subsequent

charging. This argument could also apply to other metals with a

smaller or equivalent ionic radii such as tin or selenium.

ion Valence Cation Cation/anion radius (A) radius ratio

Ca +1 1.18 0.90 +2 0.99 0.75

Pb +2 1.20 0.91 +4 0.84 0.63

Sb +5 0.62 0.47

Sn +4 0.71 0.54

Se +6 0.50 0.38

Table 5.4. Cation/anion radius ratios based

on Pauling's values [95].

5.4 A.C. IMPEDANCE

5.4.1 Experimental

Again a similar experimental procedure was followed as for

Chapter 5.2.1. After varying cycle times (1,000, 2,000 and 5,000 cyles)

- 68 -

the cycling was halted and the potential held constant at 1200 mV

(Vs. Hg/Hg2S04' 5M H2S04). This potential was maintained until the

current had fallen to a negligible value, then an impedance scan

was commenced (10 kHz to 10 mHz). A fresh electrode was used for each

experiment and the results presented are the mean of five separate

runs.

5.4.2 Results and Discussion

The A.C. Impedance measurements for all of the alloys were taken

at a fixed potential of 1200 mV (Vs. Hg/Hg2S04)' This potential was

chosen because it maintained the electrode in the fully charged state

whilst minimising the effect of oxygen evolution which would distort

the impedance spectra. This procedure was found to be satisfactory for

the comparison of the impedance spectra.

Figures 5 .18- 5.25 show the Sluyters plots for pure lead and the

various lead alloys after 4h, l2h and 24h continuous potentiodynamic

cycling. Each plot consists of a rising curve which is part of

a semi-circle of very large diameter, indicating a large charge

transfer resistance,Rct ' The Sluyters plot neither exhibit a well

defined high frequency shape nor a typical Warburg line for a diffusion

process. The reason for lack of low frequency data is because the oxygen

evolution reaction occurring on the porous lead dioxide deposit interferes

with the impedance spectra after a whil~ leading to excessive scatter in

the data. The results are typical for a planar lead electrode under

corresponding conditions ~7,~Gl and other workers ~8l have accounted

for this behaviour by the fact the reaction occurs completely in the

adsorbed state without a solution diffusive species. Such a mechanism

- 69 -

e ..c Cl '-

10

c; 8 '--

6

4

2

o o 2

• 4h

•

• • • • • • • •

•

4

• 12h 24~

• •

• • • •

• • • • • • ,:

6 8 10

R/Ohm FIG. 5.18. THE COMPLEX-PLANE PLOT (SLUYTERS PLOT) FOR A PURE LEAD

ELECTRODE AT 1200 MV AFTER 4, 12 AND 24H CONTINUOUS POTENTIODYNAMIC CYCLING.

10 e , • • •

..c • Cl 4h 12h 24h· '-u 8 • • ~ - -'- • - •

• • • 6 l- • • -

• • .4O

• • • 4 l- • . • • • • • • • • • •

2 • • l- • • 1 • . • • i t I

0 J I, .~ , I

0 2 4 6 8 10

R/Ohm I

FIG. 5.19. THE COMPLEX-PLANE PLOT (SLUYTERS PLOT) FOR LEAD-CALCIUM-TIN AT 1200 MV AFTER 4, 12 AND 24H CONTINUOUS POTENTIODYNAMIC CYCLING.

- - - - - ----~~~~~~~~~~~------------

e ..&! o "-

10

'i 8 "-...

6

4

2

o o

FIG. 5.20.

e ..c o

10

"­(j

~ 8 t­"-...

6 t-

4 t-

2 t-

o o

• •

4h

•

•

• • • .12h 24h

• •

• •

.. . .. • • •

.. • • • • • • • • • • • •

2 4

.. • ..

•

6 8 10

R/Ohm THE COMPLEX-PLAI~E PLOT (SLUYTERS PLOT) FOR LEAD­CALCIUM AT 1200 MV AFTER 4, 12 AND 24H CONTINUOUS POTENTIODYNAMIC CYCLING.

I • . . ,

• • • • • • • • :

•

. ..

• .12h 24h

• .. • • • • ..

• .. • .. ..

• • ..

• • • • • .. . .~ I

• I

j 1~ I

2 4 6 '-

8

-

-

-

-

10

R/Ohm FIG. 5.21. THE COMPLEX-PLANE PLOT (SLUYTERS PLOT) FOR LEAD­

TIN AT 1200 MV AFTER 4, 12 AND 24H CONTINUOUS POTENTIODYNAMIC CYCLING.

e ..c Cl "-

10

c.; 8 "--

6

4

2

o o

•

4h •• 12h

• • • • • • • • • • • :! . : •• •

4

• • • •

• •

6

·65h

•

8 10

R/Ohm FIG. 5.22. THE COMPLEX-PLANE PLOT (SLUYTERS PLOT) FOR 1.8%

ANTIMONY AT 1200 MV AFTER 4, 12 AND 65H CONTINUOUS POTENTIODYNAMIC CYCLING.

e ..c Cl "-

10

c.; 8 "--

6

4

2

o o

FI.G. 5.23.

••

4h • • 12h

• • • • • • • •

• • • •• • •• • • • t • .I .+

4

• • • •

•

• •

6

• 65h •

8 10

R/Ohm THE COMPLEX-PLANE PLOT (SLUYTERS PLOT) FOR 2.75% ANTIMONY AT 1200 MV AFTER 4, 12 AND 65H CONTINUOUS POTENTIODYNAMIC CYCLING.

10 s • .t:

Cl • "- • u 8 4h • 12h 65h :. • "- • .... • •

• • 6 ••

• • • • • • 4 • • • • • • •• •

2

o o 6 8 10

R/Ohm

FIG. 5.24. THE COMPLEX-PLANE PLOT (SLUYTERS PLOT) FOR 5% ANTIMONY AT 1200 MY AFTER 4, 12 AND 65H CONTINUOUS POTENTIODYNAMIC CYCLING.

S .t: Cl "-

10

'i 8 "-....

6

4

2

o o

• • 4h 12h

• • • • •

• • • • • • •

• • • • • •

6

• •

• 65h

•

8 10

R/Ohm FIG. 5.25. THE COMPLEX-PLANE PLOT (SLUYTERS PLOT) FOR 10%

ANTIMONY AT 1200 MY AFTER 4, 12 AND 65H CONTINUOUS POTENTIODYNAMIC CYCLING.

agrees with the known adsorptive properties of lead dioxide (99] and

with the linear sweep experiments in Chapter 5.2.2.

At high frequencies the impedance data shows considerable differences

between the antimonial alloys on one hand and the non-antimonial

alloys on the other. The antimonial allays show a well defined" high

frequency inductive loop. None of the other alloys exhibit this property.

Keddam ~~ has reported this type of behaviour for pasted porous lead

dioxide electrodes in lead acid batteries. The occurrence of the

high frequency inductive loop can be accounted for by the porosity of

the developed deposit. The vOltammograms in Figures 5.13 give further

evidence to support the idea that there is an increase in porosity of

the deposit on the antimonial alloys when compared tothe non-antimonial

alloys. With a porous electrode the electrochemistry will occur over

a distributed region of the electrode as discussed by Darby [l0l].

At sufficiently high frequencies the phase angle of the Faradaic

impedance will become negative, this arises physically because of the

changes in concentration which occur in pores. Therefore as this

cannot occur with a planar electrode no inductive loop will be seen.

The antimonial alloys give a well defined inductive loop indicating

that the pores are semi-infinite. It can also be seen that the curve

for the antimonial alloys rises less steeply than for the non-

antimonial alloys, again indicating an increase in porosity of the

electrode surface for the alloys.

The results on pure lead and the non-antimonial alloys agree with

the impedance spectra for electrodeposited lead dioxide as reported

by Cas son (97]. It can be concluded from this that in the oxidation

region the deposit on the non-antimonial electrodes resembles electrodeposited

- 70 -

; , Ohmic resistance of electrode and solution after varying cycle times

Alloy 4h l2h 24h

A 3(l 4(l 6(l

B 1.9(l 3.0(l 4.4(l

C 1. 8(l 2.7(l 4.0(l

D 2.0(l 2.8(l 3.7(l

E 1.8(l 1.8(l 2.5(l

F 1. 8(l 1.9(l 2.6(l . G 1. 9(l 2.0(l 2.8(l

H 1. 8(l 2.0(l 2.8(l

Table 5.5. The mean value of five separate

experiments for the ohmic resistance

of the various lead alloys after 4h,

l2h and 24h cycling (50 kHz)

~ 71 -

lead dioxide whilst for the antimonial alloys the formation of lead

dioxide involves the formation of a porous structure sufficient to

cause an inductive loop.

Considering the change in the impedance spectra with continued

potentiodynamic cycling, it is clearly seen that the intercept on the

real axis increases with cycle number for the non-antimonial allOYS,

whilst there is little variation with cycle number for the antimonial

alloys. Table 5.5 shows the mean values of five separate experiments

for the ohmic resistance, Rn for the various lead electrodes. The

measurement of the ohmic resistance was taken at 50 kHz on a freshly

cycled electrode. The ohmic resistance increases with cycling for

the non-antimonial alloys. This suggests an increase in the thickness

and soundness of the insulating layer of lead sulphate, which blocks

,the active sites of the electrode and limits the current flow, leading

to passivation of the electrode. The antimonial alloys on the other

hand, indicate that even after extensive cycling the ohmic resistance

does not alter significantly. This can be attributed to the increase

in porosity of the developed lead dioxide deposit which will promote

the continued performance of the electrode

5.5 CONCLUSIONS

1) The L.S.V. curves for the non-antimonial alloys show considerable

differences to those of antimonial alloys.

2) The antimonial alloys showed the greatest initial resistance to

anodic attack.

- 72 -

3) The shape of the vOltamrnograms and the A.C. impedance data shows

that the antimonial alloys have a surface layer of highest

porosity. The porosity increasing with antimony content.

4) The porosity of the non-antimonial alloys increased with potentio­

dynamic cycling.

5) The continuous potentiodynamic cycling curves and the A.C. impedance

data show that the antimonial alloys posses.s the greatest resistance

to passivation by lead sulphate, passivation by both calcium

sulphate and lead sulphate occurring with the non-antimonial

calcium containing alloys.

6) Of the alloys examined, lead sulphate shows the greatest reluctance

to nucleate on antimonial lead.

- 73 -

CHAPTER 6

ruE MORPHOLOGY OF PLANAR LEAD DIOXIDE ELECTRODES AFTER CONTINUED

POTENTIODYNAMIC CYCLING

6.1 INTRODUCTION

In Chapter Five the electrochemical behaviour of pure lead and

various pertinent lead alloys in 5M H2S04 have been investigated.

The results from the 1inea~ sweep vo1tammetry and A.C. impedance

studies concluded that the antimonial alloys develop a more porous

surface deposit than the non-antimonial alloys. This difference in

surface structure is thought to account for the difference in the

cycle life of the alloys. This Chapter investigates the morphology

of the various alloys and presents micro graphical evidence in support

of the e1ectrochemica1 data.

6.2 EXPERIMENTAL

The experimental procedure and electrode preparation was

similar to that described in Chapter 5 and Chapter 4 respectively

with the alloys having the composition shown in Table 5.1. The

electrodes were potentiodynamica11y cycled between the lead sulphate

and lead dioxide potential regions (600 ~ 1350 mV Vs. Hg/Hg2S04) .for

various cycle times. After a fixed cycle time the electrode was

removed, in the discharged state, and immediately washed with

methanol. Washing with methanol avoided creating a concentration cell,

- 74 -

which leads to artifacts in the morphology. After a thorough

wash in methanol the electrode was rinsed in acetone and dried

and stored in a vacuum desiccator. For the microscopic study the

electrodes were coated in a thin layer of gold by diode sputtering.

This increases the conductivity of the surface and avoids the

problems of charging associated with nonconductors. The microscopic

examination was carried out using an I.S.I. Alpha 9 scanning electron

microscope.

6.3 RESULTS AND DISCUSSION

Microscopic examination of the electrode surface of the various

lead alloys after ~ h continuous potentiodynamic cycling indicated

that on all of the alloys only a small amount of corrosion product

was present. The extent of corrosion was found to increase with

continued cycling. After 4 h cycling the electrodes were covered in

a thick layer of corrosion product. The micrographs in Figures 6.1

to 6.8 correspond to the various lead alloys after 12 h continuous

cycling. The electrodes are covered in an extensive layer of lead

sulphate. These results are in agreement with the electrochemical

data presented in Chapter 5. The anodic peak capacity of the electrodes

increased with cycle number (Figs. 5.16 and 5.17) over the first

1,000 cycles, this is commensurate with the build up of an extensive

layer of lead dioxide.

Considering the micrographs in more detail, it is obvious

there are morphological differences between the lead sulphate layer

on the non-antimonial alloys and the lead sulphate layer on the

antimonial alloys. The non-antimonial alloys (Figs. 6.1 to 6.4)

- 75 -

•

FIG. 6.1. S.E.M. MICROGRAPH OF PURE LEAD AFTER 12H CONTINUOUS POTENTIODYNAMIC CYCLING. MAGNIFICATION X 10,000

FIG. 6.2. S.E.M. MICROGRAPH OF LEAD-CALCIUM-TIN AFTER 12H CONTINUOUS POTENTIODYNAMIC CYCLING. MAGNIFICATION X 10,000

FIG. 6.3. S.E.M. MICROGRAPH OF LEAD-CALCIUM AFTER 12H CONTINUOUS POTENTIODYNAMIC CYCLING. MAGNIFICATION X 10,000

FIG. 6.4. S.E.M. MICROGRAPH OF LEAD-TIN AFTER 12H CONTINUOUS POTENTIODYNAMIC CYCLING. MAGNIFICATION X 10,000

•

FIG, 6,5, S,E,M, MICROGRAPH OF 1,8% ANTIMONY AFTER 12H CONT­INUOUS POTENTIODYNAMIC CYCLING, MAGNIFICATION X 10,000

FIG, 6,6, S,E,M, MICROGRAPH OF 2,75% ANTIMONY AFTER 12H CONT­INUOUS POTENTIODYNAMIC CYCLING, MAGNIFICATION X 10,000

•

FIG, 6,7, S,E,M, MICROGRAPH OF 5% ANTIMONY AFTER 12H CONTINUOUS POTENTIODYNAMIC CYCLING, MAGNIFICATION X 10,000

FIG, 6,8, S,E,M, MICROGRAPH OF 10% ANTIMONY AFTER 12H CONTINUOUS POTENTIODYNAMIC CYCLING, MAGNIFICATION X 10,000

exhibit a ?urface layer consisting of fine and uniformly shaped

lead sulphate crystals. This layer is mechanically sound and with

an average crystal diameter of about O.l~m This layer of lead

sulphate will be very effective in blocking (passivating) the

electrode for further reaction and so preventing re-oxidation of lead

sulphate to lead dioxide. Reutschi [102] has shown that. when

individual lead sulphate crystals in the outer corrosion layer are

very small (0.1 - 10 ~m) and uniform the outer corrosion layer becomes

impermeable to sulphate and bisulphate ions. (The pores of the

electrode become practically closed). A similar type of reaction has

been reported by Huber [103] on silver electrodes coated with silver

chloride. The sulphuric acid within the pores of the electrode will

simultaneously become depleted and diluted as discharge occurs,

this will lead to more alkaline conditions « pH 9) in the interior

of the lead dioxide deposit.

The Pourbaix diagram for lead has been modified by Delahay [104]

to take into account the presence of sulphate ions. Further modifica­

tion by Barnes and Mathieson [105] and Reutschi and Angstandt [106]

include the basic sulphates: PbO.PbS04, 3PbO.PbS04.H20, and 4PbO.PbS04

and typical E/ph plo'ts are shown in Figure 6.9 arid 6.10. These thermodynamic

diagrams are based on equilibrium conditions and predict spontaneous

reactions occurring on lead at different pH conditions. The

Pourbaix diagrams do not, however, contain any kinetic data and so

cannot be used to predict corrosion rates.

In the interior of the non-antimonial alloys, relatively high

pH conditions will prevail « pH 9) due to the blocking effect of the

fine lead sulphate crystals. Further corrosion of lead, will occur

- 76 -

-1. 2 o 2 4 6 8 10 12 14

FIG, 6,9, POTENTIAL/pH DIAGRAM OF THE LEAD/SULPHURIC ACID SYSTEM AT 25·C,

16

pH

E/V vs. Hg/H92S04 +1.5,..--___ ........ _---------------,

Il-Pb02 ---P

+1.0

+0.5

o

-0.5

-1.0

-1.5

S-Pb02 --I.' 'l--Ar--- Pb02/PbSO 4 (pH -0.48)

PbS04

Pb

mf-Hf--- Pb02/PbO.PbS04 (pH 6.35)

~oH+H--- Pb02/PbO (pH 9.34)

M11+t.1C.--- PbO/Pb (pH 9.34)

HtlIf----- PbO.PbS04/Pb (pH 6.35) --J+I

1-____ PbS04/Pb (p~ -0.48)

o 2 3 4 5

Distance/lJm

FIG. 6.10. SCHEMATIC REPRESENTATION OF THE MULTI-PHASE CORROSION LAYER AT DIFFERENT ELECTRODE POTENTIALS.~02]

by the dissociation of water, underneath the blocking sulphate layer.

This further corrosion will lead to the precipitation of lead oxide

and basic lead sulphates in the interior porous matrix [19,107-113]. The

mixed sulphate layer will be thermodynamically stable at these

relatively high pH values and this is in agreement with the Pourbaix

diagram presented in Figure 6.9. Lead oxide and basic lead SUlphates

formed during the discharge reaction have been shown to resist re­

oxidation to some extent [114] and to favour the formation of alpha

lead dioxide. Alpha lead dioxide, has different properties [10] to

the other polymorph Beta lead dioxide. Ruetschi [l14]has also shown

that alpha lead dioxide discharges at a higher rate per unit area and

that it also shows a tendency to passivate, limiting the electrode's

performance. This explanation agrees with the electrochemical data

in Chapter 5, where the non-antimonial alloys were shown to produce

a less porous surface coating, which eventually led to the passivation

of the electrode. Buchannan [115] in his recent photocurrent spectroscopy

studies on cycled lead alloys found the corrosion product on pure le~d

was of mixed oxide format, consisting of the semiconductor, lead oxide,

and basic lead sulphates. Buchannan also found that the corrosion

layer on pure lead was more extensive than on antimonial lead, infact

it was up to five times thicker. These results are also in agreement

with our electrochemical and morphological results.

Returning to the micrographs for the antimonial alloys

(Fig. 6.5 to 6.8). The antimonial alloys exhibit a surface morphology

which is consistent with the presence of prismatic block like crystals

of lead sulphate. This type of morphology leads to a more open

structure and has been shown by Ruetschi[102] in his study on ion

- 77 -

permeability through sulphate membranes not to restrict the free

flow of acid (sulphate and bisulphate ions) through the outer

corrosion layer. This will lead to similar pH conditions inside

the porous matrix as exist in the e'lectrolyte « pH 1) which is in

contrast to the conditions in the non-antimonial corrosion product.

The Pourbaix diagram in Figure 6.9 predicts that only lead sulphate

will be thermodynamically stable and that the conditions will be

unfavourable for the formation of lead oxide and basic lead sulphates.

Bagshaw and Wilson [116] have shown that due to the acidic conditions,

beta lead dioxide will be the favoured polymorph on recharge.

Ruetschi U14] has shown that this polymorph enhances the capacity

of the electrode and so prolongs cycle life. These observations

are again in agreement with the electrochemical results from

Chapter 5. The A.C. impedance data also indicated an increase in

porosity for the antimonial alloys and that a resistive sulphate film

is not formed at the metal-dioxide interface. The microscopic

evidence presented here gives support to this theory.

6 .4 CONCLUSIONS

1 ) The non-antimonial alloys and pure lead show a surface

morphology which is non porous and uniform.

2)', The antimonial alloys show the greatest reluctance to nucleate

lead sulphate.

3) The antimonial alloys have a surface film of highest porosity.

- 78 -

CHAPTER 7

THE CORROSION OF VARIOUS LEAD ALLOYS IN 5M HZS04

7.1 INTRODUCTION

A considerable amount of work has been undertaken

the corrosion rates of various lead alloys [117-121].

to investigate

The morphology

of the corrosion product has also received considerable interest [122].

In Chapter 5 the electrochemical properties of several pertinent

lead alloys used in battery grid construction have been reported. The

results were interpreted in terms of corrosion rates and cycle life

performance. These factors are very important in assessing new and

better alloys for grid construction,however, the mode of destruction

of the grid has yet to be considered. The grid corrosion plays an

important role in determining the life of the battery plate.

The battery grid serves not only as a frame work for the lead

dioxide paste retention, but as an electron carrier. The corrosion

of the grid will lead to surface oxidation and a reduction in the

cross-sectional area of the battery grid and consequently to a drop

in conductivity. If the mode of corrosion attack is localised

(i.e. at grain boundaries), then although the rate of corrosion will be

low, the results can be dramatic with the eventual severing of the

grid network.

This Chapter records and discusses the mode of corrosion attack

in comparison to the alloy microstructure on various antimonial and

non-antimonial alloys used in battery grid manufacture. In this

experiment a potentiodynamic cycling regime was adhered to, as it

was felt that this would more accurately imitate actual battery

cycling. The results have been elucidated using optical and scanning

electron microscopy.

7.2 EXPERIMENTAL

The potentiodynamic cycling was carried out between the potential

limits of 1350 mV and 1100 mV (Vs. Hg/Hg2S04). The descending sweep

was at a rate of 1 mY/sec which represents a slow rate discharge,

this was then followed by an ascending sweep at SO mY/sec to recharge

the electrode. The electrode was then held at 1350 mV (top of charge

potential) for twenty hours after each cycle in order to emulate

typical float service. The composition of the lead alloys is shown in

Table 7.1.

Analysis weight per cent !

i Code Sb Se Sn Ca Pb

, I i

I A - - - - 99.999 I B - - 0.3 0.1 remainder I

I C 0.1 remainder - - -I D 1.8 0.04 - - remainder

E 5 - - - remainder

F 10 - - - remainder

Table 7.1. The composition of the alloys used in the corrosion

experiments

- 80 -

All of the working electrodes were prepared as previously stated

from aged and cast alloys and the electrodes underwent the pretreat­

ment discussed in Chapter 4.

On completion of four weeks continuous potentiodynamic cycling,

the working electrodes were removed from the electrolyte and discharged

in a controlled manner across a I kn resistance against a charged

negative battery plate. The charge dissipated during this process

was monitored to ensure full discharge of the electrode.

The corrosion layer was then removed by immersing the electrode

in a solution of SM ammonium acetate for 24 hours. The surface

condition of the alloy backing was then examined using scanning

electron microscopy. The results were then compared with the micro­

structure of the microtomed lead alloy.

7.3 RESULTS AND DISCUSSION

7 .3. 1 Pure Lead

Figure 7.1 shows the microstructure of a microtomed section of

a cast pure lead sample (99.999%). The microstructure is consistent

with the presence of columnar type crystals which are formed by the

. cooling process within the mould.

The grain size is large (~O.07 mm grain diameter) and Young [87]

has shown that this type of structure will promote uniform corrosion

rather than attack at the grain boundary. This type of corrosion

attack was observed (Figure 7.2) after four weeks cycling. The

micrograph in Figure 7.2 indicates that the corrosion is very uniform

- 81 -

•

FIG. 7.1. MICROTOMED SECTION OF PURE LEAD. MAGNIFICATION X 50.

FIG. 7.2. S.E.M. MICROGRAPH SHOWING THE MODE OF CORROSION ATTACK FOR PURE LEAD AFTER FOUR WEEKS CYCLING. MAGNIFICATION X 750.

over the whole alloy surface and it should also be noted that the alloy

shows no preference for grain boundary attack.

7.3.2 The Antimonial Alloys

Antimonial alloys have traditionally been used in battery grid

manufacture for nearly a century [16]. The phase diagram for

antimony according to Raynor [123] is shown in Figure 7.3.

u o

~~------------~,

wt ~ Sb

, , , ,

Figure 7.3. Equilibrium diagram for antimony [123]

An alloy with an antimony content of around 10 wt.% has a low

melting point and freezes very rapidly over a narrow temperature

range. The alloy is also very rigid due to the formation of a

segregated dendritic network of eutectic, this can readily be seen in

Figure 7.4. As the antimony content decreases then the amount of

eutectic decreases proportionally leading to a softer alloy (Figure

7.5). The micrograph shows the 5% antimony alloy to have a fairly

fine and uniform grain structure. At low antimony levels, the

- 82 -

•

FIG. 7.4. MICROTOMED SECTION OF 10% ANTIMONY. MAGNIFICATION X 50.

FIG. 7.5. MICROTOMED SECTION OF 5% ANTIMONY. MAGNIFICATION X 50.

•

FIG, 7,6, MICROTOMED SECTION OF 1,8% ANTIMONY, MAGNIFICATION X 50,

FIG, 7,7, S,E,M, MICROGRAPH SHOWING THE MODE OF CORROSION ATTACK FOR 10% ANTIMONY AFTER FOUR WEEKS CYCLING, MAGNIFICATION

X 750,

•

FIG. 7.g. S.E.M. MICROGRAPH SHOWING THE MODE OF CORROSION ATTACK FOR 5% ANTIMONY AFTER FOUR WEEKS CYCLING. MAGNIFICATION

X 750.

FIG. 7.9. S.E.M. MICROGRAPH SHOWING THE MODE OF CORROSION ATTACK FOR 1.g% ANTIMONY AFTER FOUR WEEKS CYCLING. MAGNIFICATION

X 750.

alloys tend to crack and promote shrinkage porosity due to the increase

in the temperature range over which it freezes. These problems have

been overcome to some extent by the addition of grain refiners to the

alloy. Typical grain refiners in use are Selenium [124-126], Copper

[127], Sulphur [128] and Arsenic [1]. The addition of these grain

refining elements act to form a more uniform microstructure by

providing nuclei on which the solidifying alloy can nucleate and

grow. These effects can be seen in Figure 7.6 for the 1.8 wt.%

antimony alloy.

After four weeks corrosion, the antimonial alloys showed marked

differences in the mode of attack. Figure 7.7 shows the alloy

surface for the 10% antimonial alloy after four weeks corrosion.

The micrograph shows that the segregated eutectic region has been

preferentially eroded away. This leads to widespread corrosion

which is fairly uniform over the whole electrode surface. This type

of corrosion will consequently be less detrimental to grid life. As

the antimony content decreases the mode of attack changes. The

micrographs in Figures 7.8 and 7.9 show the mode of attack for the

5% and 1.8% antimony alloys respectively. As these micrographs

illustrate, the corrosion occurs mainly at the grain boundaries. The

grain boundary penetration is more extensive in the 5% alloy (Figure

7 . .8) as a result of more eutectic present. Hondros and Seah [129] have

investigated the segregation of various alloys during solidification.

They have shown that the grain boundaries in an antimony containing

alloy will be nearly 100% antimony and will thicken with increasing

antimony content. This explains the micrographical evidence

presented here.

- 83 -

At the top of charge potential (1350 mV Vs. Hg/HgzS04) antimony

will pass into solution (in the +5 oxidation state) where it can be

reduced at the negative electrode or be readsorbed back onto the

positive paste (Figure 1.3). Thus corrosion will occur preferentially

at the antimony rich regions which as Hondros et al. [129] stated.

occurs at the grain boundaries in low antimony alloys. In the

higher antimony content alloy. attack will occur in the antimony

rich dendritic network. The corrosion rate of the low antimonial

alloys will be less than for the 10%·antimony alloy. yet the corrosion

is more likely to be detrimental due to its localised nature.

7.3.3 Lead-Calcium Alloys

The lead-calcium based alloys have in recent years become

established alternatives to the lead-antimony system for battery

grids. The lead-calcium system has been shown to be age hardened by

grain refinement and precipitation of Pb3Ca. The existence of the

intermetallic compound Pb 3Ca has been confirmed by Hansen [130] and

the phase diagram is shown in Figure 7.10.

w 0:

" '< "' ~ 150 :>: w -

a

OL-~O~2--~G---'~O--~;'--~'8' CALCIUM lw' '-)

Fig. 7.10. Equilibrium diagram for lead-calcium [130]

- 84 -

•

FIG, 7,11, MICROTOMED SECTION OF LEAD-CALCIUM, MAGNIFICATION X 50,

FIG, 7,12, S,E,M, MICROGRAPH SHOWING THE MODE OF CORROSION ATTACK FOR LEAD-CALCIUM AFTER FOUR WEEKS CYCLING, MAGNIFICATION

X 750,

FIG. 7.l3.

FIG. 7.15.

•

MICROTOMED SECTION OF LEAD-CALCIUM-TIN. MAGNI F I CATION X 50.

S.E.M. MICROGRAPH SHOWING THE MODE OF CORROSION ATTACK FOR LEAD-CALCIUM-TIN AFTER FOUR WEEKS CYCLING. MAGNIFICATION X 750.

The microstructure of the lead calcium alloy is shown in Figure 7.11.

This is consistent with the presence of a large grained structure

(0.08 mm diameter) with segregated particles of Pb 3Ca. After the

four weeks corrosion, the alloy has undergone uniform attack but

with preferential dissolution of the segregated particles of Pb 3Ca

(Figure 7.12). The dissolution of Pb 3Ca has led to a series of

uniform voids over the electrode surface.

7.3.4 Lead-Calcium-Tin Alloy

The micrograph in Figure 7.13 shows a large grain structure

(0.08 mm diameter) with segregated intermetallic particles.

Prengaman [89] has recently published a phase diagram for the 1ead-

calcium-tin system (Figure 7.14) which indicates the intermetallics

are of the composition Sn3Ca.

2.4 5n

~12.2'LL __ ----­i'" 2. 0

• a 1. 8

~ 1. 6

Il. 1.. ~ 1.2 .. • (PbxsnyC.! .. Sn)C<l.) o i:i 1. 0 , ..

. .

. . • 2 ~~::::;::=~========

:'J .01 ,02 .0) .04 .05 .06 ,01 .08 ,09 .10.11 wr.tGHT PERCEflT C",LCIU"I

Fig. 7.14. Lead-ca1cium-tin phase diagram, lead rich region at room temperature. Prengaman [89]

- 85 -

He also reports that these intermetallics resist anodic attack. After

four weeks corrosion,in our study, the alloy surface showed uniform

corrosion with the precipitates undergoing corrosion at a different

rate (Figure 7.15). This is consistent with the findings of

Prengaman .

7.4 CONCLUSIONS

1) The non-antimonial alloys, particularly the pure lead and the lead­

calcium-tin alloys underwent the most uniform corrosion.

2) The non-antimonial alloys are the most suitable for long term

float service.

3) If gassing rates (hydrogen evolution) are unimportant, the

higher antimony content alloys will suffice.

- 86 -

CHAPTER 8

THE ELECTROCHEMICAL PROPERTIES OF SOLID LEAD-BISMUTH

ALLOYS IN SM HZS04

8.1 INTRODUCTION

Bismuth constitutes a major contaminant of primary lead as

it is found concurrent with lead naturally. It is usually removed

from lead supplies by the Kroll-Betterson process which reduces the

bismuth content to 0.1 wt. %. This purification process is carried

out by treating molten lead with calcium and magnesium; the bismuth

forms a variety of intermetallic compounds with these addi ti ves ,

which then float to the surface of the vessel and are removed as

dross. If further purification of lead is desired either electrolytic

refining or the Jollivet process is employed. The Jollivet process

is similar to the Kro1l-Betterson but the drossing agent used is a

more expensive platinum-magnesium alloy. Davey V3l] has stated

that bismuth levels below 1 x 10- 3 wt. % are achievable by the above

mentioned methods. The manufacturers of 'maintenance free' battery

grids usually stipulate removal of bismuth to the lower level

« 1 x 10- 3 wt. %) thus increasing the cost of production. Many

workers have investigated the mechanical and electrochemical properties I

I

evaluate I I

of simple binary and ternary lead-bismuth alloys V,78,128,132-13S] to

the necessity of the expensive removal procedures for bismuth. A

recent review by Ellis and Hampson [21] gives a comprehensive resum~

of this work.

- 87 -

The heightened interest in the bismuth content of lead calcium

alloy for 'maintenance free' applications has led to a controversy

in the necessity to remove bismuth from the base lead alloy.

Ritchie [25,26] carried out casting trials on alloys containing

bismuth and concluded that bismuth has detrimental effects on the

physical properties of lead calcium alloys and should be removed at all

costs. This contradicts previously published work by Dr Cupua [136]

and Morgen [137] who found that bismuth « 12 wt. %) had very little

effect on the physical properties of pure lead. Myers et al. [22-24]

have also investigated the effect of bismuth on lead calcium alloys.

The first two papers [22,23] concern themselves with the mechanical

and physical properties of the bismuth containing alloys and postulate

that bismuth has beneficial effects on ultimate alloy strength and rate

of hardening after quenching. Later Myers [24]concentrated on the

electrochemical properties of bismuth additions to lead calcium alloys

and stated that bismuth additions to the alloy show no adverse

corrosion effects or excessive gassing rates. This is in agreement

with the work of Kilimnik and Rotinyan [138]and Drotschmann [139]who

independently found that bismuth increased the hydrogen overvoltage on

the negative plate of the battery. (This property is very important to

'Maintenance free' battery performance).

This conflict of opinion in the literature concerning tolerable

levels of bismuth led us to carry out our own investigations on binary

lead-bismuth alloys over a wide range of bismuth levels « 3 wt. %) using

linear sweep voltammetry, A.C. impedance and optical/electron

microscopy.

8.2 EXPERIMENTAL

A similar experimental regime to that described in Chapter 5 was

performed on the cast binary lead-bismuth alloys [140]. In an attempt

to simulate industrial practice the working electrodes were prepared

from cast lead alloys which had been allowed to age at room temperature

for a minimum of one month. The composition of the alloys is shown in

Table 8.1. All the electrodes underwent the pretreatment described in

Chapter 4.

Analysis wt. per cent. Code

Si Pb

A - 99.999

S 0.04 remainder

C 0.09 remainder

D 0.3 remainder

E 0.5 remainder

F 1 remainder

G 2 remainder

H 3 remainder

Table 8.1. The composition of the binary

Pb-Si alloys used in the

electrochemical investigation.

- 89 -

8.3 RESULTS AND DISCUSSION

The vo1tammograms in Figures 8.1 to 8.7 correspond to the various

binary lead-bismuth alloys on the first potential excursion to

2,000 mV and the return sweep to 600 mV (Vs. Hg/Hg2S04 in 5M H2S04)

at a constant sweep rate of 50 mY/so The vo1tammograms are similar

to those presented in Chapter 5 for pure lead and the various lead

alloys, hence similar arguments can be applied to explain the

pertinent features of the vo1tammograms. It should, however, be

stressed that the large nucleation overpotentia1 for the formation of

lead dioxide is apparent on the first cycle. The linear sweep

experiments were then continued between the potential limits of

600 mV and 1350 mV and the sweep rate was again kept constant at

50 mY/so The vo1tammograms in Figure 8.8 correspond to the various

lead-bismuth alloys over this restricted potential range after 4 h

continuous potentiodynamic cycling. Each vo1tammogram consists of

a well defined oxidation peak and a less well defined reduction

peak. The anodic current which represents the oxidation of lead

sulphate to lead dioxide does not return to zero at potentia1s greater

than 1350 mV,but starts to increase due to the electrode undergoing

oxygen evolution. These results are very similar to the vo1tammograms

presented for the antimonial and non-antimonial systems in Chapter 5.

The charge contained in the reduction peak is always in the range

85-95% of the oxidation peak, signifying that only a small amount

of current contributes to oxygen evolution per cycle and that the

electrode is fully charged after each cycle. The values for the

anodic'and cathodic peak capacities after 4 h cycling are given in

Table 8.2.

- 90 -

a: e

8

4

o

-4

-8

,

f-

I -

(V

I

.6 .8

, I

I , ,

/ " -

-

I I I , , 1 1.2 1.4 1.6 1.8 2

V FIG, 8,1, INITIAL L,S,V, FOR 3% BISMUTH: SWEEP RATE 50 MV/SEC,

a: e

8

4

o

-4

-8 .6 .8 1 1.2 1.4 1.6 1.8 2

V

F [G, 8,2, INITIAL L,S,V, FOR 2% BISMUTH: SWEEP RATE 50 MV/SEC,

8 a: Si

4 "

0-h===:;;::===========----I

-4

-8 .6 .8 1 1.2 1.4 1.6 1.8 2

V FIG. 8.3. INITIAL L.S.V. FOR 1% BISMUTH: SWEEP RATE 50 MY/SEC.

8 a: Si

4

-4

-8 .6 .8 1 1.2 1.4 1.6 1.8 2

V

FIG. 8.4. INITIAL L.S.V. FOR 0.5% BISMUTH: SWEEP RATE 50 MY/SEC.

a: s

6

2

-2

-6 .6 .8 1 1.2 1.4 1.6 1.8 2

V FIG. 8.5. INITIAL L.S.V. FOR 0.3% BISMUTH: SWEEP RATE 50 MV/SEC.

a: s

6

2

-2

-6 .6 .8 1 1.2 1.4 1.6 1.8 2

V

FIG. 8.6. INITIAL L.S.V. FOR 0.1% BISMUTH: SWEEP RATE 50 MV/SEC.

a: e

6

2

-2

-6 .6 . 8 1 1.2 1.~ 1.6 1.8 2

V

FIG. 8.7. INITIAL L.S.V. FOR 0.05% BISMUTH: SWEEP RATE 50 MV/SEC.

N I 0 -* N -" 0 ..... a:

.35

.25

. 15

.05

-.05

-. 15 600

f

A H

750 900 1050 1200 1350

FIG, g,g, CONSTANT RESPONSE CURVES FOR THE LEAD-BISMUTH ALLOYS OVER THE POTENTIAL RANGE 600-1350 MY AFTER CONTINUOUS CYCLING FOR 4H: SWEEP RATE 50 MY/SEC,

Code i I Charge of anodic Charge of cathode p mA/cm2

Ep/v peak/mC peak/mC

A

B

C

D

E

F

G

H

Table 8.2.

3.5 1.145 2.70 2.30

3.3 1.150 2.50 2.13

2.5 1.160 1.60 1.36

2.9 1.175 1.83 1.68

3.1 1.20 1.92 1. 73

3.4 1.250 2.05 1.84

3.38 1.260 2.35 2.14

3.3 1.280 2.54 2.13

A comparison of i p ' Ep ' charge of anodic peak and cathodic

peak for pure lead CA) and the alloys CB-H) at 50 mV/s in

5M H2S0"

The relationship between peak potential CEp) for the oxidation

peak representing the conversion of lead sulphate to lead dioxide and

sweep rate (v) in the form of an Ep Vs. loglO sweep rate is displayed

in Figure 8.9. This follows the equation developed by Canagaratna

et al. ~~ for describing the formation of lead dioxide at constant

thickness per cycle. The results for the lead-bismuth alloys is in

agreement with the data presented for the various lead alloys in

Chapter 5. As is evident from the straight line plots and the data in

Table 8.2, the potential of the oxidation peak (Ep) shifts positive

with increasing bismuth content. This indicates that the kinetic

barrier required to convert lead sulphate to lead dioxide increases

- 91 -

> "-

0>­W

1.3

1. 25

1.2

1. 15

1.1

1. 05

-1 - 1 • 1 -1.2 -1.3 -1.4 -1.5 -1.6 -1.7

Log rSIIEEP RRTE)

FIG. 8.9. PLOT OF Ep VS LOG SWEEP RATE FOR THE LEAD-BISMUTH ALLOYS.

with bismuth content. This is in conflict with the work of Kelly [141]

who states that bismuth has little effect on peak potential. However,

the alloys used in her electrochemical study were prepared from a

low purity lead base in contrast to the high purity lead base used

in this study. The difference ,in impurity levels could explain this

discrepancy.

From Table 8.2, it can be seen that lead undergoes the greatest

anodic attack with bismuth exerting an overall protective effect.

Figure 8.10 shows a plot of anodic peak capacity against bismuth

content. The trend is very similar to that seen for the antimonial

system; the addition of bismuth initially lowers the peak capacity

until it reaches a position of maximum stability at a level of

0.1 wt. '% bismuth. The capacity of the electrodes then continues to

increase with increasing bismuth content. This trend supports the

work of Brynsteva et al. [142] who showed that the resistance to anodic

attack decreases to a minimum at 3.5 wt. % bismuth. Gonzales et al.

[143] Mashouets and Lyandres [144,145] have also shown independently

that bismuth increases the rate of corrosion of various lead alloys.

The observed initial drop in capacity (Figure 8.10) can be explained

in terms of grain refinement caused by the incorporation of bismuth

into the lead lattice. Young [87] has shown that the extent of

corrosion is related to grain size, with the degree of penetration

decreasing with diminishing grain size.

Bismuth has been shown to exhibit some grain refining properties:

Emmerich and Beckmann [1] have studied the effect of bismuth on

lead cable extrusion and found that above 0.02 wt. % bismuth grain

refinement is unmistakable. Myers et al. [24] as a result of their

studies on the effect of bismuth additions to lead calcium alloys

- 92 -

U G

3

2.5

2

1.5 o .5 1.5 2 2.5

COMPOSITION ~t % Bt

FIG. 8.10. PlOT OF CHARGE OF ANODIC PEAK VS BISMUTH CONTENT AFTER 4H CONTINUOUS CYCLING.

3

« 0.1 wt. % Bi), stated that bismuth improves grain refinement and

leads to increased rates of age hardening.

The grain refinement effect of this study is supported by the

micrographs presented in Figures 8.11 to 8.14. The micrographs are

of cast lead alloys which are unetched and microtomed to reveal the

grain structure. Pure lead (Figure 8.11) has the largest grain size

with visible grain boundaries. On addition of bismuth the grain size

decreases (Figures 8.12 to 8.14) resulting in small grain structure

at high bismuth content. This grain refinement causes depletion of

lead at the surface which is available for anodic attack. However, as

the level of bismuth increases, bismuth becomes more available for

dissolution and the effect of grain refinement is outweighed by the

increase in corrodability of the alloy U42]. From our observations

the optimum level for limited anodic corrosion of planar lead-bismuth

alloys is at about 0.1 wt % bismuth.

With continued potentiodynamic cycling,the variation of anodic

peak capacity with cycle number follows a similar trend to that

presented for pure lead and the lead calcium binary alloy (Chapter 5)

The lead bismuth profiles are displayed in Figure 8.15. After about

8,000 cycles the capacity of all the bismuth alloys reaches a constant

value of about 0.8 mC. This profile can be explained in terms of a

sulphation - passivation theory: Initially an extensive, lead dioxide

deposit is formed with continued cycling, this then reaches a

maximum thickness where further attack of the substrate is restricted

and the capacity then deminishes as the electrode passivates.

Passivation is brought about by the restriction of acid reaching the

interior of the porous deposit, this results in a restrictive film of

~. 93 ".

•

'I ...... \

i J J j

" - 1 I ,"" . ~

-' I .• L,,':',i ..... ~ __ •. ..'. _ .cc·

FI0, 8,11, MICROTOMED SECTION OF PURE LEAD, MAGNIFICATION X 50,

FIG, 8,12, MICROTOMED SECTION OF 3% BISMUTH, MAGNIFICATION X 50,

•

FIG, 8,13, MICROTOMED SECTION OF 0,5% BISMUTH, MAGNIFICATION X 50,

FIG, 8,14, MICROTOMED SECTION OF 0,1% BISMUTH, MAGNIFICATION X 50,

3 u

" ..... w '-" R '" a: x: u

oH 2.5

G

F 2

" ... ,' , 0

" .... ' '0 0 , 1.5 .' .' .,'

" .' ,,'

" ,',.'

o· . ,',,'

..... , ,

o 1000 2000 3000 4000 5000

CYCLE NUMBER

FIG, 8,15, VARIATION OF CHARGE OF THE ANODIC PEAK WITH CYCLE NUMBER FOR THE LEAD-BISMUTH ALLOYS.

lead sulphate forming at the metal/lead dioxide interface. Further

evidence is provided by the measurement of the ohmic resistance of

the electrodes after varying cycle times. Table 8.3 displays the

ohmic resistance of the electrode after 4 h, 12 hand 24 h cycling, the

ohmic resistance is obtained by an impedance measurement at 50 kHz.

Alloy

Pb

Pb-Bi (0.04%)

Pb-Bi(0.09%)

pb-Bi (0.3%)

. Pb-Bi(0.5%)

Pb-Bi (1 %)

Pb-Bi (2%)

pb-Bi (3%)

Table 8.3.

Ohmic resistance of the electrode and solu-

tion after varying cycle times

4 h 12 h 24 h

3 il 4 il 6il

2.7 il 3.4 n 5.5 n

2.6 n 3.8 n 5.9 n

2.8 n 3.5 n 6 n

2.8 n 4.1 n 5.2 n

2.7 n 3.9 n 5.4 n

2.8 n 3.6 n 4.9 n

2.7 n 3.9 n 5.1 n

,S,\-"",l.C>"v.. "'''-:0. -±. oD'l..,..5Z., .

The mean value of five separate experiments for

the ohmic resistance of the various lead alloys

after 4 h, 12 hand 24 h cycling (50 kHz)

It is evident from Table 8.3 that there is a formation of a

resistive layer.

Further evidence for the depletion of acid within the porous

matrix which is needed to promote a sulphate barrier is provided by

- 94 -

.

•

FIG. 8.16. S.E.M. MICROGRAPH FOR 3% BISMUTH AFTER 12H CONT-INUOUS POTENTIODYNAMIC CYCLING. MAGNIFICATION X 10,000

FIG. 8.17. S.E.M. MICROGRAPH FOR 2% BISMUTH AFTER 12H CONTINUOUS POTENTIODYNAMIC CYCLING. MAGNIFICATION X 10,000

•

fIG, 8,18, S,E,M, MICROGRAPH FOR 1% BISMUTH AFTER 12H CONTINUOUS POTENTIODYNAMIC CYCLING, MAGNIFICATION X 10,000

FIG, 8,19, S,E,M, MICROGRAPH FOR 0,5% BISMUTH AFTER 12H CONT­INUOUS POTENTIODYNAMIC CYCLING, MAGNIFICATION X 10,000

•

FIG. 8.20. S.E.M. MICROGRAPH FOR 0.3% BISMUTH AFTER 12H CONT­INUOUS POTENTIODYNAMIC CYCLING. MAGNIFICATION X 10,000

FIG. 8.21. S.E.M. MICROGRAPH FOR 0.1% BISMUTH AFTER 12H CONT­INUOUS POTENTIODYNAMIC CYCLING. MAGNIFICATION X 10,000

FIG, 8,22, S,E,M, MICROGRAPH FOR 0,04% BISMUTH AFTER 12H CONT­INUOUS POTENTIODYNAMIC CYCLING, MAGNIFICATION X 10,000

the micrographs in Figures 8.16 to 8.22. The micrographs show a surface

morphology which is consistent with the presence of a tight compact

film of lead sulphate. This film, as stressed in Chapter 6, acts as

a semipermeable membrane and blocks the free passage of sUlphate and

bisulphate ion promoting higher pH conditions within the deposit.

This promotes the formation of basic lead sulphates and lead oxides.

The mixed sulphate layer will favour the formation of a lead

dioxide on recharge and lead to the eventual drop in capacity.

Clearly, the lead-bismuth alloys behave in a similar way to both

lead and the lead calcium alloy. However, from the position of

bismuth in the periodic table, it might be expected to behave like

antimony. The use of ionic radius ratios to predict the cycle life

behaviour of bismuth produces a more accurate analysis of its

observed behaviour. Latimer [146] has shown that in strong acids

bismuth is present as BiO+:

2H+ + BiO+ + 3e = Bi + H20

a E "+0.32V

The presence of BiO+ gives a radius ratio value of 0.9 which does

not fall into the range of 0.4 to 0.7 which Burbank [92] stated will

lead to extended cycle life behaviour. This therefore gives further

evidence to support the idea that ionic radius ratio values are

useful in predicting new guest ions for future 'maintenance free'

battery grids.

- 95-

o

8.4 CONCLUSIONS

1) Small additions of bismuth exert a protective effect on pure

lead.

2), Theanodic corrosion of planar lead-bismuth alloys increases

with bismuth content.

3) Low level additions (~ 0.1 wt. %) may be beneficial to lead

alloys. These findings agree with the previous work of

Myers [22-24] and contradicts the conclusions of Ritchie [25,26].

4) The use of ionic radius ratios to predict cycle life has

proved successful for bismuth.

- 96 ~

CHAPTER 9

THE ELECTROREDUCTION PROCESSES OF PLANAR AND POROUS LEAD

DIOXIDE ON VARIOUS LEAD ALLOY SUPPORTS

9.1 INTRODUCTION

The discharge reaction at the positive electrode of the lead­

acid battery involves the development of a new phase which results

in totally different electrical properties to those of the underlying

phase. This concept of phase formation is typical of many other

reactions occurring in corrosion and battery technology.

In recent years there has been a renewed interest in electrocrystall­

isation reactions. This has resulted in a reconsideration of the

mathematical approaches to the subject, in particular the nucleation

and growth models. The continuous geometric models presented by

Harrison and Thirsk [55], Fleischmann and Thirsk [54] and Armstrong

et al. [56] have been extended and the production of new complimentary

ideas developed. However, the treatment of nucleation theory has remained

essentially the same since the adaptation of the instantaneous and

progressive models developed in the early sixties [58,147]. These models

do not necessarily consider the mechanism of nucleation but rather

depend on the geometry of the growing nuclei. Nuclei can be produced

simultaneously (instantaneous nucleation), or form linearly with

time (progressive nucleation). Once the form of nucleation has been

established, it is the crystal growth patterns which determine the

- 97 -

electrochemical response of the system to a perturbation. The deriva­

tion of the equations representing current-time relationship requires

the calculation of the area of the growing centres at any time, t.

At the start of the nucleation and growth process, intercrystal

collision presents no problem, however, when the growing centres

coalesce the mathematical models break down and the overlap problem

must be included in the model. Initially, an approach based on the

theory of Avrami [60] or the related "modified Evans" approach [148],

was adopted to tackle this problem and the derivation has been

discussed in Chapter 3.

The nucleation and growth theories have been extended by

Armstrong and Harrison to account for three dimensional growth. [56,149] •

Recently, a new model has been presented by Fletcher and Matthews,

[150] which attempts to solve the volume transformations for a number

of nucleation and growth processes in what is known as a "2'>D system".

The 2'>D nucleation and growth pattern is so called because the crystals

forming on an electrode surface only extend into one half of the third

dimension as growth into the substrate is forbidden.

Other transient techniques have been used to formulate rate

equations and to study the potential dependence of the rate constant

for nucleation and growth under various conditions. Carslaw and

Jaeger [151] and Frank [152] have also investigated the rate of mass

transport in electrocrystallisation processes in unstirred SOlutions.

Astley et al. [153] and Hills et al. [154] have derived equations to

describe the resulting current-time transients under diffusion control.

Other, non-continuous methods of interpreting nucleation and

growth have been published and calculations of the Monte-Carlo type [155]

~ 98 ~

have been applied to test the validity of the theory of two dimensional

nucleation as derived by the continuous models [156]. New methods

of data analysis are regularly presented in the scientific literature

[157-162] and many of these recent publications contribute significantly

to the overall understanding of nucleation and growth theory.

Recent investigation into the discharge behaviour of lead

dioxide [163] have postulated that the alloy substrate will influence

the nucleation and growth mechanism of the discharge product, lead

sulphate. In this Chapter the electrocrystallisation process of

planar and porous lead dioxide on various pertinent lead alloy

substrates in 5M H2S04 have been investigated and discussed with a

view to identifying new and better alloys for maintenance free

battery applications. In this present study of the discharge

characteristics of lead dioxide, only a limited number of (1"''''.'~),

patterns have bee found to be applicable. Nevertheless, many

t · ent to the system different models hare been applied and those per m

under study are ;omprehensively detailed in Chapter 3. The results

d 'f' t' ns are required presented here, indicate that certain mo 1 1ca 10

to these equations in order to describe real porous systems.

9.2 QUASI-POROUS LEAD DIOXIDE

9.2.1 Experimental

The planar working electrodes were prepared as described in

Chapter 4 from cast and aged alloys as these were felt to best

represent conventional industrial practice: their compositions are

shown in Table 9.1.

- 99 -

Alloy composition in weight per cent

~~ Sb Se Sn Ca Pb

A - - - . - 99.999

B - - 0.3 0.1 remainder

C - - - 0.1 remainder

D 4.5 - - - remainder

E 1.8 0.04 - - remainder

Table 9.1. The composition of the various lead alloy

backings used in the electrochemical

investigation.

The electrode pretreatment and potentiodynamic cycling was similar to

that described previously in Chapter 5. The potentiodynamic cycling

was continued for 1,400 cycles (~10 h) to produce a thick layer of

quasi-porous lead dioxide. This Plant~ type process for lead dioxide

formation was adopted in order to highlight the alloy effect. After

an initial potential hold period of 10 minutes at 1250 mV (Vs. Hg/Hg2S04

reference electrode in 5M H2S04), the residual current fell to a

stable and negligible value. The electrode was then stepped

instantaneously to 600 mV and the resultant current-time transient

recorded. This potential step (1250 mV ~ 600 mY) represents a very ,

vigorous discharge regime. It was felt necessary to adopt this approach

to investigate the alloy effect on the nucleation and growth of lead

sulphate because in practice lead-acid batteries with non-antimonial

grids tend to passivate more readily after deep cycling.

- 100 _

9.2;2 Results and Discussion

Figure 9.1 displays the resultant current-time transients

obtained as a result of a 650 mY potential step on the various lead

alloys after 1,400 potentiodynamic cycles between the lead sulphate

and lead dioxide potential regions. The current-time behaviour is

typical of all the results obtained for the various lead alloy

supports and is indicative of a solid state nucleation and growth

process.

In all of the potential step experiments a current spike was

observed at the front of the rising and falling current transient.

This current spike was attributed to double layer charging due to

its short life (microseconds). The current spike fell to zero before

the rising transient was observed. The subsequent nucleation and

growth transient showed no rotation speed dependence indicating that

the electrode reaction is not under diffusion control. This gives

further evidence that lead ions do not leave the electrode during the

discharge reaction and that the processes is "solid state".

The distinctive shape of the transient can be explained by the

following:

The current initially rises as the lead sulphate nuclei form and

grow. This shape occurs when the transport of material to the

growing centres is not rate determining and the rate of growth

depends solely on geometric factors. Eventually, the size of

the growing nuclei will become limited in all directions as

the centres coalesce and the rate of increase in the current

response will diminish and the transient reaches a maximum.

- 101 -

« g

-3

-2

-1

b

0-2 0-4 06 t Is)

FIG. 9.1. CURRENT - TIME RESPONSE FOR THE CATHQD1C R~DUCTION OF LEAD­DIOXIDE <1250 MY) ,0 LEAD SULPHATE (bWMV) ON THE VARIOUS LEAD ALLOYS.

« 1.8 r---------.-----~--_.----------r_----~ __ ~ • .....

1.6

1.4

1.2

I

.8

.6

.4

.2

B

o .4 . B 1.2 1.6

512*10- 2

FIG. 9.2. A LINEAR VS t2

PLOT FOR THE VARIOUS NON-ANTIMONIAL ALLOYS.

Finally the current falls to zero when the growing lead sulphate

crystals overlap completely and block the transport of charge

and material to the active sites.

It is shown in Fig. 9.1 that the shape of the transients are

consistent with a progressive nucleation mechanism, that is, the

active nuclei form linearly with time [54]. It can be concluded that

the developed quasi porous lead dioxide deposit does not contain

sufficient nuclei for the reaction to proceed via an instantaneous

mechanism and that the slower progressive nucleation mechanism prevails.

The dimensionality of the growing process can be identified by fitting

the various nucleation and growth equations (Eq. 3.56 to Eq. 3.60) to

the rise and fall of the current-time transients. Dimensionless

curve fitting (i/im Vs. t/tm) has also proved to be the most

satisfactory method for testing the congruence of the results.

To the rising part of the transient various relationships

describing both two and three dimensional growth have been investigated.

A plot of log i Vs. log t gave a slope of 2 indicating the appropriate

power of t. Figures 9.2 and 9.3 show the theoretical i Vs. t 2 plots

for the equation:

(3.43)

p

where: M is the molecular mass of the growing phase.

p is the density of the growing phase.

N is the number of nucleation sites. 0

Z is the nucleation coefficient.

and k is the nucleation rate constant.

- 102-

a: • "--1.6

1.6

1.4

1.2

1

.6

.6

. 4

.2 L-______ ~ ________ ~ ________ ~ ______ ~

o

FIG. 9.3. A LINEAR

N

0-..... -:z: ...J

4

3.5

:5

2.5

2 .5

• 4- • B 1.2

2 i VS t PLOT FOR ANTIMONIAL ALLOYS.

R

1.5 2 2.5 3 3.5

FIG. 9.4. A LINEAR Lni/t2

VS t' PLOT FOR THE NON- ANTIMONIAL _________________________ ALLOYS.

1.8

512*10-2

These straight line plots indicate that the growth of lead sulphate

on lead dioxide follows two dimensional growth kinetics characterised

by equation (3.43) which is derived for the growth of cylinders.

From the linear plots in Figures 9.2 and 9.3 it is possible to extract

kinetic information corresponding to the rate of formation of lead

sulphate. Table 9.2 displays the rate constants for pure lead and the

various lead alloys under study.

Alloy Nucleation rate constant kN x 10-16/moI 2 cm-6sec-1

0

A 7.9

B 20

C 8.6

D 10

E 9.9

Table 9.2. The nucleation rate constants for the

various alloys under electrochemical

investigation.

It is evident that the nucleation of lead sulphate on quasi porous

lead dioxide occurs at a comparable rate on the various antimonial and

non-antimonial alloys; the binary lead calcium alloy is analogous

with a larger rate constant.

To the falling transient, again various relationships have been

fitted and equation (3.58) was found to have the best fit.

- 103 -

-------N~~'r======~======~======~~======r=======,_------t­

" -z: ...J

:5

o

E

2 ~ ____ -...l ______ ~ ______ ~ ______ ~ ____ ~

.02 .03 .04

St3 FIG. 9.5. A LINEAR Lni It' VS t' PLOT FOR THE ANTIMONIAL ALLOYS.

• lr-------~------~~------+-------; -" -• B

.6

.4

.2

x

o~------~------_+--------~------~ .5 I 1.5 2 o

FIG. 9.6. DIMENSIONLESS 2-D PROGRESSIVE CURVE FITTING FOR PURE TIT. LEAD. X = EXPT. VALUES, -- = THEORETICAL VALUES.

1. nF1fhMk2ZNot2

= exp

p [

-1fM2ZNok2t 31 3p2 j

(The symbols are as previously described)

(3.58)

This equation represents two dimensional growth with subsequent over-

lap of the growing centres. The theoretical fits of lni/t2 Vs. t 3

are displayed in Figures 9.4 and 9.5. At long times the model was

found to breakdown and the current decay for the experimental data

was slower than that predicted by the geometrical model of Fleischmann

and Thirsk [54]. This is because the theoretical model does not

account for the problems associated with the growing phase as

coverage nears completion.

As previously stated, the congruence of the results can be

further tested by comparing dimensionless plots of the theoretical

equations with those for the experimental data [164]. The theoretical

values can be readily obtained by differentiating the nucleation and

growth equations with respect to time and setting d'i/dt to zero at

the turning point. At this point the current is a maximum (im) and

the time is known (tm). This has been adequately covered in

Chapter 3. Figures 9.6 to 9.10 show the dimensionless fits for the

non-antimonial alloys (A.B. and C.) and the antimonial alloys (D. and

E.) It is shown that the theoretical values obtained for a two

dimensional growth process with progressive nucleation gives a very

good fit over the majority of the transient. However, at long times

the model deviates from the experimental results.

- 104 -

• -..... -•

.8

.8

.4

.2

x O~ ______ ~ ______ ~ ________ +-______ -4

o .S 1 1.5 2

TIT. FIG. 9.7. DIMENSIONLESS 2-D PROGRESSIVE CURVE FITTING FOR LEAD-CALCIUM­

TIN. X = EXPT. VALUES, -- = THEORETICAL VALUES.

FIG. 9.8.

• -..... -1~-------+------~~-------+--------T

.8 .

• 8

x

.4

X

.2

X

0 0 .S I.S 2

TlTa DIMENSIONLESS 2-D PROGRESSIVE CURVE FITTING FOR LEAD-CALCIUM, X = EXPT. VALUES, -- = THEORETICAL VALUES.

• -.... -

FIG. 9.9.

• -..... -

0+-___ _+_-----+----_------1-o .5 1 1.5 2

~. TIT. DIMENSIONLESS 2-D PROGRESSIVE CURVE FInING FOR 5% ANTIMONY, X ± EXPT. VALUES. -- = THEORETICAL VALUES.

1~--------+-------~~--------~--------~

.8

.8

.4

x .2

x

O~---~----+_------__ --------I-o .5 1 1.5 2

TIT. FIG. 9.10. DIMENSIONLESS 2-D PROGRESSIVE CURVE FInING FOR 1.8% ANTIMONY,

X = EXPT. VALUES, -- = THEORETICAL VALUES.

9.3 PASTED POROUS LEAD-DIOXIDE

9.3.1 Experimental

The porous pasted working electrodes were of the design

described in Chapter 4. The automotive battery paste was pressed

into a teflon cavity terminated with a shaped lead alloy support.

The alloy backing acting as a current collector. The pasted

electrodes were cured in order to limit the free lead content. The

oxidation of the lead powder was catalysed by the water present,

hence the curing process took place in 100% humidity at 50oC. The

humidity also limits the shrinkage of the paste due to water loss.

Finally the electrodes were dried at about 100"C before formation to

lead dioxide. The pasted electrodes were then galvanostatically

oxidised in 2M H2S04 until the electrode reached a constant and

stable potential and oxygen was freely evolved from the electrode

surface (about 24 h). The porous working electrodes were then transferred

to a standard three limbed cell containing 5M H2S04 and potentiostatically

held at 1200 mV (Vs. Hg/Hg2S04 reference electrode) for 1 hr to

allow the acid to equilibrate deep within the pores of the electrode.

After this potential hold,the electrode was potentiostatically stepped

to a new potential and the current-time transient recorded. The size

of the potential step was varied on the pure lead electrode to

investigate the effect of overpotential on the rate and mechanism of the

electrocrystallisation processes occurring. The effect of the backing

alloy was also investigated.

- 105 -

9.3.2 Results and Discussion

Figures 9.11 to 9.17 present representative current-time transients

for the discharge reactions of a lead dioxide electrode on a pure lead

backing at different overpotentials. A freshly prepared and charged

electrode was used for each potentiostatic pulse experiment. The

different overpotentials represent typical discharge characteristics of

the positive plate of the lead acid battery under normal operating conditions.

Each transient shows an initial fall followed by a current peak (Figure

9.11- 9.17). The initial falling transient cannot be assigned to

double layer charging as in the quasi-porous system due to the extent

of the time scale (seconds), and therefore must be accounted for in

the reaction mechanism. The current peak is typical for a solid state

nucleation and growth process as described by the geometric models

originally developed by Fleischmann and Thirsk [54]. Further evidence

for a solid state mechanism is that the transients are rotation speed

independent, hence the reaction does not proceed via a soluble solution

species. The overall shape of the transient is typical of many electro­

crystallisation reactions involving the formation of a passivating film

under potentiostatic conditions [77,78,132]. A satisfactory description

of the mechanism for these types of transients is often difficult due to

the problems in modelling the formation of an insulating film on the

electrode, where the surface eventually becomes blocked and therefore

inactive.

Dawson [165] attempted to model the discharge reaction of electro­

deposited lead dioxide at low overpotentials using a dissolution

precipitation mechanism. Rotating ring disc studies have failed to

- 106 -

5

2

1

o o

n=50mV

1000 2000 3000 TIME/S

FIG. 9.11. THE CURRENT-TIME RESPONSE FOR THE REDUCTION OF POROUS LEAD DIOXIDE TO LEAD SULPHATE ON A PURE LEAD BACKING. POTENTIAL STEP 50 MV (1200-1150 MV).

Cl: e

"­I-

15

~ 12 0:: 0:: :;:) U

9

6

3

o

n=90mV

o 400 800 1200 1600 2000 2400 TIME/S

FIG. 9.12. THE CURRENT-TIME RESPONSE FOR THE REDUCTION OF POROUS LEAD DIOXIDE TO LEAD SULPHATE ON A PURE LEAD BACKING. POTENTIAL STEP 90 MV (1200-1110).

a: e

...... I-

15

~ 12 a::: a::: ::J u

9

6

3

o

n=100mV

o 400 800 1200 1600 2000 2400 TIME/S

FIG, 9,13, THE CURRENT-TIME RESPONSE FOR THE REDUCTION OF POROUS LEAD DIOXIDE TO LEAD SULPHATE ON A PURE LEAD BACKING, POTENTIAL STEP100MV (1200-1100 MV),

25 a: e

...... I-

~ 20 a::: a::: ::J u

15

10

5

o

n=120mV

o 200 400 600 800 1000 1200 TIME/S

FIG, 9,14, THE CURRENT-TIME RESPONSE FOR THE REDUCTION OF POROUS LEAD DIOXIDE TO LEAD SULPHATE ON A PURE LEAD BACKING, POTENTIAL STEP 120 MV (1200-1080 MV),

Cl: e , I-

30

~ 24 et: et: ;:)

U

18

12

6

o

n=130mY

o 100 200 300 400 500 600

TIME/S FIG. 9.15. THE CURRENT-TIME RESPONSE FOR THE REDUCTION OF

POROUS LEAD DIOXIDE TO LEAD SULPHATE ON A PURE

. 30 Cl: e , I-

~ 24 et: et: ;:) U

18

12

6

o

LEAD BACKING. POTENTIAL STEP 130 MV (1200-1170 MV) •

n=160mY

o 100 200 300 400 500 600

TI ME/S FIG. 9.16. THE CURRENT-TIME RESPONSE FOR THE REDUCTION OF

POROUS LEAD DIOXIDE TO LEAD SULPHATE ON A PURE LEAD BACKING. POTENTIAL STEP 160 MV (1200-1140 MV).

30 cc & "-I-

~ 24 0:: 0:: ::::l U

18

12

6

o o

n=200mV

100 200 300 400 500 600 ~

TIMElS FIG. 9.17. THE CURRENT-TIME RESPONSE FOR THE REDUCTION OF

POROUS LEAD DIOXIDE TO LEAD SULPHATE ON A PURE LEAD BACKING. POTENTIAL STEP 200 MV (1200-1000 MV) •

cc e

"­I­:z: lIJ

• 8

~ .75 ::::l u

.7

.65

.6 2.5 3

n=50mV

3.5 4 4.5 5 5.5 *1015/S12

FIG. 9.18. A LI NEAR i VS t 2 PLOT FOR THE 50MV POTENT! AL STEP.

identify any soluble Pb 2+ species formed during the discharge reaction

in sulphuric acid [169J. Also the solubility of Pb 2+ is at a minimum in

5M H2S0 4 [5], therefore Dawson's hypothesis is highly improbable. A more

likely mechanism to account for the current-time response is suggested

by Harman et al. [166]. The suggested mechanism proposed to account

for the results presented here (Figures 9.11 to 9.17) takes place via

a two stage process involving an adsorbed Pb 2+ intermediate on the

porous lead dioxide surface. The existence of an adsorbed intermediate

is highly probable on lead dioxide as it has been shown to have

extensive adsorbitive properties [99]. Initially, after the potentio-

static pulse has been applied to the electrode, the current response

will be at a maximum. This is a result of the large rate of formation

of the adsorbed Pb 2+ species. As time progresses, the rate of formation

of the adsorbed species decreases and the current response of the system

correspondingly decreases as the available surface area of the electrode

diminishes. The concentration of the intermediate Pb 2+ species in the

close vicinity of the electrode surface then reaches a maximum. This

reaction can be represented by equation (9.1).

kf + Pb4+ < ) PbS04 d - 2e a s

kb (9.1)

Once the concentration of adsorbed species has reached an equilibrium

value, the rate determining reaction will be the incorporation of lead

sulphate into the lattice, equation (9.2).

kl PbS04ads --+ PbS04lat (9.2)

- 107 -

As this stage is rate determining, the current response of the system will

follow the typical geometric models as described previously in Chapter 3.

From the rising transients in Figure 9.11-9.17, it is possible to

identify the nucleation and growth process. However, only tentative

suggestions can be made as the initial current spike influences the

response of the system in the latter stages. As stated previously, the

dimensionality of the growth process can be identified by fitting the

various nucleation and growth equations (Equations 3.56 to 3.60) to the

rising part of the current peak. Various relationships describing both

two and three dimensional growth have been investigated and the equation

giving the best fit was found to be equation (3.43) and indicates that

i = (3.43)

p

(the symbols are as discussed previously) .

the growth of lead sulphate on porous lead dioxide follows a two dimensional

growth process with progressive nucleation which is similar to that

obtained on the quasi-porous lead dioxide electrodes. Figures 9.18 to

9.20 show the theoretical i Vs. t 2 plots for the rising part of the transient.

To the falling transient no appropriate theoretical equation gave an

acceptable fit, this is most likely due to the limitations of the nucleation

and growth equations to planar electrodes [54,55].

From the slope of the rising transient it is possible to extract

kinetic data. However, due to the influence of the initial falling transient

on the subsequent solid state growth process, only comparative figures

are given rather than absolute values. The slope of the plots in Figures

9.18 to 9.20 have been used to calculate the nucleation rate constant

- 108-

10 a: & ..... .....

:z: 9 lJJ

0::: 0::: ~ u

8 n=100mV x

7

6 n=90mV

5 1 2.8 4.6 6.4 8.2 10

*1013/S12

FIG. 9.19. A LINEAR i VS t' PLOT FOR THE 90 MY AND 100 MY POTENTIAL STEP.

a: &

..... ..... :z: lJJ 0::: 0:::

30

B 25

20

15 2 4

n=160mV

n=130mV

n=120mV

6 8 10 *10f2lSf2

FIG. 9.20. A LINEAR ~ VS t' PLOT FOR THE 120 MY, 130 MY, 160 MY AND 200 MY POTENTIAL STEP.

using equation 3.43. The rate constants were found to vary with over-

potential (Table 9.4).

, n/mV Nucleation rate constant kZN

0 x 10-17/molZcm-6sec-l I

50 3.1 X 10-4

90 0.22

100 0.51

120 3.7

130 4.6

160 14

200 15

Table 9.4. The potential dependence of the nucleation rate constant

for the formation of lead sulphate in 5M HzS04

The increase in the rate constant explains the shift of the current peak

to shorter times with increasing overpotential. When equation (3.43) is

differentiated and di/dt is set to zero, the time of the current maxima

(tm) can be related to the nucleation constant, No and the rate constant,

k.

t 3 = m (9.3)

Therefore, as the rate constant increases with overpotential, tm will

decrease. A plot of log kZN Vs. n is presented in Figure 9.21 and gives o

- 109 -

N -::.::: o

:z Cl

-10

j -12

-14

-16

-18

-20

I!J

I!J

o 20 40 60 80 100 120 140 160 180 200

'9 /mV

FIG. 9.21. A LINEAR PLOT OF LOG K2 Nb VS OVERPOTENTIAL.

a: e

10

8

6

4

2

o o 10

Pb-Ce.

20 30 40 50 •

M In

FIG. 9.22. THE CURRENT-TIME RESPONSE FOR THE REDUCTION OF POROUS LEAD DIOXIDE TO LEAD SULPHATE ON A LEAD-

a: e

10

8

6

4

2

o o

CALC IUM BACK I NG • POTENT! AL STEP 100 MV (1200-1100 MV),

Pb-Ce.-Sn

10 20 30 40 50

Mln

FIG. 9.23. THE CURRENT-TIME RESPONSE FOR THE REDUCTION OF POROUS LEAD DIOXIDE TO LEAD SULPHATE ON A LEAD­CALCIUM-TIN BACKING. POTENTIAL STEP 100 MV (1200-1100MV).

Cl: &

10

8

6

4

2

o o 10

SI. Sb

20 30 40 so Mln

FIG. 9.24. THE CURRENT-TIME RESPONSE FOR THE REDUCTION OF POROUS LEAD DIOXIDE TO LEAD SULPHATE ON A 5% ANTIMONY BACKING. POTENTIAL STEP 100 MV (1200-1100 MV).

Cl: &

10

8

6

4

2

o o 10

1. 81. Sb

20 30 40 SO

Mln FIG. 9.25. THE CURRENT-TIME RESPONSE FOR THE REDUCTION OF

POROUS LEAD DIOXIDE TO LEAD SULPHATE ON A 1.8% ANTIMONY BACKING. POTENTIAL STEP 100 MV (1200-1100 MV).

a s lope of 130 mY per decade. However, KNo' not .K2NO is proportional

to current and hence the slope is equivalent to a tafel type slope of

65 mY per decade. This indicates that the discharge of lead dioxide

takes place via a two electron transfer. This provides further evidence

that the discharge reaction occurs via a two dimensional progressive

nucleation and growth process.

Figures 9.22 to 9.25 present typical current-time transients

for the various lead alloys. The overpotential was fixed at 100 mY

which is typical potential drop for a normal discharge curve. The

transients are very similar to those presented for pure lead and again

a similar progressive two dimensional nucleation and growth model can

be applied to the data. It can therefore be concluded

that the alloy substrate has no visible effect on the mechanism of

discharge for lead dioxide.

9.4 CONCLUSIONS

1) The data presented indicates that the discharge reaction of lead

dioxide occurs via a two dimensional growth process with

progressive nucleation.

2) The alloy substrate was also shown to have little, if any, effect

on the current-time response of the reaction. It must be stressed

that there is difficulty in analysing and interpreting the data

because the presently developed nucleation and growth models do

not take into account the porosity and complexity of the reaction

under discussion. However, it was felt that the present models

are satisfactory for comparative results to be discussed.

-110 -

CHAPTER 10

FINAL DISCUSSION

The cyclic voltammetric studies in Chapter 5 showed that pure lead

undergoes greater anodic attack than the antimonial and non-antimonial

alloys which exert some overall protective effect. The shape of the

voltammograms and A.C. impedance studies also indicated that the

electrochemically formed lead dioxide exhibits a higher degree of

porosity on the antimonial alloys than on the other alloys. This

was supported by evidence obtained by scanning electron microscopy.

(Chapter 6)

The corrosion studies on the various lead alloys in Chapter 7

revealed a difference in the mode of anodic attack, a factor important

in developing better alloys for maintenance free applications, as

localised corrosion is far more destructive than uniform corrosion.

The non-antimonial alloys all exhibit uniform corrosion with the lead­

calcium binary alloy showing clearly the dissolution of the intermetallic

particles of Pb3Ca. It was demonstrated that for the antimonial

alloys the mode of attack depended on antimony content. At low

antimony concentrations «5% Sb), anodic attack was generally

confined to the grain boundaries. As the antimony concentration

increased, anodic attack occurred at the inter-dendritic network of

eutectic. Hence, at higher antimony content (>5% Sb), the corrosion

attack was greater but less destructive due to its uniform nature.

- 111 -

This work could be extended to include a comprehensive X-ray diffraction

study on the corrosion product to identify a and 8 lead dioxide ratios.

It would also be of interest to ascertain grain boundary pentration and

corrosion depth using photo current spectroscopy.

On continuous potentiodynamic cycling the non-antimonial alloys

were found to passivate more readily than those containing antimony

(Chapter 5). This was attributed to a non-conducting film of lead

sulphate forming at the electrode/lead dioxide interface. A.C. impedance

studies also showed the formation of a resistive film with continued

cycling.

The reasons for the difference in behaviour of the alloys was

attributed to morphological differences in the formed lead dioxide

layer (Chapter 6). The porous lead dioxide film which forms on

the antimonial alloys allows the free diffusion of acid deep into

the pores of the electrode. Under these conditions, the polymorph,

8 lead dioxide, is thermodynamically stable, and has been shown to

promote long cycle life [10]. The hon-antimonial alloys develop a

tight compact film which effectively blocks the penetration of acid

to the Pb02/Pb interface. An increase in pH develOps in the porous

mass where the formation of a lead dioxide will be thermodynamically

favourable along with lead monoxide and basic lead sulphates depending

on potential. These compounds have been shown to resist re-oxidation

[10] and so limit cycle life. In calcium containing alloys, it was

postulated that the passivation is brought about by a binary film of

calcium SUlphate and lead SUlphate (Chapter 5).

Further work could be carried out to identify calcium sulphate,

tin dioxide and other alloy corrosion products in the lead dioxide

- U2- -

film using advanced analytical techniques such as electron probe

analysis, neutron diffraction and energy dispersive techniques (EDAX).

The results in Chapters 5 and 6 also suggest that if the

morphology of the surface film on the non-antimonial alloys could be

disturbed to allow the free passage of acid, then the cycle life

performance of the alloys may be prolonged. This hyphothesis could

be tested by the study of alloy additions such as magnesium and

aluminium which are known to increase the corrosion rate of the non­

antimonial alloys [80]. The dissolution of the ions from the electrode

surface may be sufficient to disrupt the lead dioxide film and allow

the free passage of acid.

The potentiostatic pulse experiments in Chapter 9 were used to

elucidate the discharge mechanism of planar and porous lead dioxide.

They have indicated that the reaction proceeds via a 2- dimensional

progressive nucleation and growth process. At present the nucleation

and growth theory is not sufficiently advanced to take into account

real porous systems and needs to be developed further if the

differences the alloy substrate imparts are to be identified. At

present,work is underway at Loughborough University to develop the

nucleation and growth theory to this level [166].

In Chapter 5 it was suggested that ionic radius ratios could

be used to predict new alloys for maintenance free applications. This

has proved successful in the electrochemical study of bismuth

additions to lead (Chapter 8). In this study it was found that small

additions of bismuth «3%) had little effect on the electrochemistry

and cycle life performance of pure lead. It would however, be beneficial

to test the ionic radius ratio theory on a larger selection of alloy

additives.

- 113-

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- 12.3-

APPENDIX

Preparation of lead microsections for examination of structure.

Lead is a very soft and ductile metal with a low melting

point of 327.3°C [1]. These physical properties cause considerable

problems when preparing specimens and finishing microsections for

microscopy. On polishin&the sample can easily become deformed even

under low pressure, giving rise to deformation which in turn changes

the structure of the alloy under investigation. Consequently, it is

essential to avoid all unnecessary polishing, excessive friction and

heating. This can be achieved by hand polishing on silicon carbide

paper (600 and 1200 grit) under a continuous flow of water. The

running water removes any dust formed and so helps limit deformation.

This is followed by polishing on a wool cloth with distilled water,

a few drops of dilute nitric acid and No. 1 alumina as the polishing

medium. Finally the sample is etched with 10% nitric acid or Vilella

solution [167] to remove any oxide film formed on polishing. For

microscopic observation of the alloy surface, the sample is rinsed

in distilled water to remove any adhering alumina, dipped in absOlute

alcohol and dried in hot air. It is important that the finished section

is not handled to avoid the formation of scratches. Photomicrographs

are taken as soon as possible, as samples tarnish readily in air.

A faster and more simple sample preparation technique is the microtome

method. This involves using a freshly 'broken' glass microtome blade

to remove the surface layer of the specimen. The first shavings of

- 124 -

10~m are removed, decreasing to l~M in thickness. Again the surface

oxide layer can be removed by etching in Vilella's solution or 10%

nitric acid. This technique has many advantages over the other

sample preparation techniques; it is quicker and it also limits

contamination of the sample by silicon carbide or alumina which is

very important if electrochemical measurements are to be carried out' on the

prepared sample.

In order to emphasise grain boundaries it may be necessary to

further etch the sample after polishing or microtoming. The most

important etching medium for lead and lead alloys were compiled by

Schrader in her etching manual, "Atzheft" [168] and some of the

important etches are summarised below:

Macroscopic etching of grain surfaces.

Development of microstructure and

grain boundaries.

Macroetch of pure lead and lead­

bismuth alloy

Lead antimony alloys up to 2% Sb

- 125 -

Normal Vilella etching

medium: 16 cm3 nitric acid,

16 cm3 glacial acetic acid,

68 cm3 glycerol, etch for a

few minutes.

As above, etch for a few

seconds.

100 cm3 H20, 25 cm3 glacial acetic

acid, 20 cm3 H202(30%), 20 cm3

HN0 3, etch for 2 to 10 minutes.

3 parts glacial acetic acid, 1 part

of H2D.2 (9%), etch for 10 to 30

minutes depending on depth of

deformed layer. If necessary subse­

quent treatment in conc. nitric acid.

Lead antimony alloys.

Unalloyed lead and lead calcium

alloy.

For lead-antimony above 2% Sb, lead­

tin up to 3% Sn, unalloyed lead.

- 126-

3 part glacial acetic acid, 1 part

H202 (30%), etch 6 to 15 sec.

2 parts glacial acetic acid, 1 part

H202 (30%) etch 8 to 15 sec.

Electrolytic etching in 60 cm3 pure

perchloric acid and 40 cm3 water.

The specimen is the cathode a Pt.

spiral the anode,etch 0.75 to

1.5 min.

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