PB84-229707
Seattle Distribution Systea
Corrosion Control Study. Volume 6
Use of a Rotating Disc Electrode to
Assess Copper Corrosion
Washington Univ., Seattle
Prepared for
Municipal Environsontal Research
Cincinnati, OH,
Aug 84
I
I
bKCZK'xm
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1, REPORT NO.
EPA-600/2-84-130
4. TITLE AND SUBTITLE
SEATTLE DISTRIBUTION SYSTEM CORROSION CONTROL STUDY
VOLUME VI - USE OF A ROTATING DISC ELECTRODE TO ASSESS
COPPER CORROSION
3. RECIPIENT'S ACCESSION NO.
PBS A 2 29?Q?
5. REPORT DATE
1 <
S. PERFORMING ORGANIZATION CODE
'. AUTHOR(S)
Ronald D. Hilburn
8. PERFORMING ORGANIZATION REPORT NO.
9. rERFORMING ORGANIZATION NAME AND ADDRESS
Department of Civil Engineering
University of Washington
Seattle, Washington 98195
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
R806686010
12. SPONSORING AGENCY NAME AMD ADDRESS
Municipal Environmental Research Laboratory-Cinti., OH
Office of Research and Development
U.S. Environmental Protection Agency
Cincinnati, OH 45268
13. TYPE OF REPORT AND PERIOD COVERED
14. SPONSORING AGENCY CODE
EPA/600/14
tS. SUPPLEMENTARY NOTES
Project Officer: Marvin. C. Gardels (513684-7236
16. ABSTRACT
, The UBii'oFB corrceion of coppar tubing used for transport of Tolt River water IB
characterised in this study as a heterogeneous rate procesa coapoeiai of ostal oxidation
ao/i ozide fila growth, Interred si cheaic.il reactions, and cssss transport in the liquid
phnee. Quantitative rate expressions were developed to characterize eecb of these rate
processes. Exr^ric^ttte derignefi to sesaure the temperature snd pi: •Uepc^deiice of corrosion
under rete control by each process vere conducted using steady-BCate electrochemical
f.cchfjiq-jus. T&e persistent and unexpected influence of solution transport of a reaction
produce, preaueed to be OH~, complicated characterisation end identification of undtr-
lylng rate procesa. burfoce pH could be characterized enplrically as a function of
(solution temperature, pH, nnd diffusion layer thickness.
this euplrical correlation for surface pH along with solution BS.BS trsn»r-ort taodels
developed for turbultnt and laainar pipe flou vere combined to form a steady-stnte pipe
flow ssodel for uniform copper corrosion. Predictions nade using the raoiel under stagnant
sincl low flow rate conditions show a stable ond lou corrosion rate of 0.2 ails per year
(MPY) In uster of pH > 6.0. At loaer pK, ptcilicted rates ore substantially increased
us llie pK id reduced one! teusperature is Increased. At hJjh flov rates, treoer-doua
acceleration of corrosion rate occurs, which a^aiu lacraaaeb with increasing ceisperature
and decreasing pH. Only »t pH > 8.0 sre the
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EPA-600/2-84-130
August 1984
SEATTLE DISTRIBUTION SYSTEM CORROSION CONTROL STUDY
Volume VI, Use of a Rotating Disc Electrode
to Assess Copper Corrosion
by
Ronald D. Hilburn
Department of Civil Engineering
University of Washington
Seattle, Washington 98195
Cooperative Agreement No. R 806686 010
Project Officer
Marvin C. Gardels
Drinking Water Research Division
Municipal Environmental Research Laboratory
Cincinnati, Ohio 45253
MUNICIPAL ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROJECTION AGENCY
CINCINNATI, OHIO 45268
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DISCLAIMER
Although the information described in this article has been funded
wholly or in part by the United States tnvironmental Protection Agency
through assistance agreement number R 806686 010 to Seattle Water Department,
it has not been subjected to the Agency's required peer and administrative
review and therefore does not necessarily reflect the views of the Agency and
no official endorsement should be inferred.
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FOREWORD
The U.S. Environmental Protection Agency was created because of
increasing public and government concern about the dangers of pollution to
the health and welfare of the American people. Noxious air, foul water, and
spoiled land are tragic testimonies to the deterioration of our natural
environment. The complexity of that environment and the interplay of its
components require a concentrated and integrated attack on the problem.
Research and development is that necessary first step in problem solu-
tion, and it involves defining the problem, measuring its impact, and search-
ing for solutions. The Municipal Environmental Research Laboratory develops
new and improved technology and systems to prevent, treat, and manage waste-
water and solid and hazardous waste pollutant discharges from municipal and
community sources, to preserve and treat public drinking water supplies, and
to minimize the adverse economic, social, health, and aesthetic effects of
pollution. This publication is one of the products of that research and is a
most vital communications link between the researcher and the user community.
This report presents the results and conclusions from studies dealing
with the effects of flow, temperature, and chemical composition of Tolt River
water on copper corrosion. The data support the conclusion that substantial
corrosion reduction can be achieved by raising the pH to a value above 8.0.
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ABSTRACT
The uniform corrosion of copper tubing used for cold water transport has
been characterized as a heterogeneous rate process composed of metal oxida-
tion and oxide film growth, '.nterfacial chemical reactions, and mass trans-
port in the liquid phase. Quantitative rate expressions were developed to
characterize each of these rate processes. Experiments designed to measure
the temperature and pH-dependence of corrosion under rate control by each
process were conducted using steady-state electrochemical techniques. The
persistent and unexpected influence of solution mass transport of a reaction
product (presumed to be OH") complicated characterization and identification
of underlying rate processes. .Surface pH could be empirically characterized
as a function of solution temperature, pH, and diffusion-layer thickness.
This empirical correlation for surface pH along with solution mass
transport models developed for turbulent and laminar pipe flow were combined
to form a steady-state pipe flow model for uniform copper corrosion. Predic-
tions made using the model under stagnant and low-flowrate conditions show a
stable and low corrosion rate of 0.2 mils per year in water of pK > 6.0. At
lower pH, predicted rates are substantially increased as pH is reduced and
temperature is increased. At high flowrates, tremendous acceleration of cor-
rosion rate occurs which again increases with increasing temperature and
decreasing pH. Only at pH > 8.0 are the dramatic pH and temperature effects
dissipated so that the rate is stabilized at a minimum value of approximately
0.2 mils per year.
Steady-state electrochemical techniques have been shown to give rapid,
reliable, and reproducible corrosion rate measurements and to provide the
versatility necessary for quantitative characterization of a heterogeneous
rate process such as aqueous copper corrosion.
This report was submited in the fulfillment of Contract No. R 806686 010
by the Seattle Water Department under the sponsorship of the U.S. Environ-
mental Protection Agency. This report covers the period June, 1979 to March,
1983, and work was completed as of March, 1983.
TV
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CONTENTS
Page
Foreword Ill
Abstract , i v
Figures vi
Tables x
Abbreviations and Symbols xii
1. Introduction 1
2. Conclusions 5
3. Recommendations 7
4. Uniform Copper Corrosion: A Heterogeneous Rate Process 8
5. Experimental Procedures , 61
6. Experimental Results and Analysis 100
7. Proposed Steady-State Pipe Flow Model for Uniform
Copper Corrosion 168
References 184
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FIGURES
Number i Page
1 Duplex Oxide Film Formed in Aqueous Copper Corrosion 10
2 Simplified Copper/Oxide/Water System 14
3 Chemical Reactions Involved in Aqueous Copper Corrosion .... 14
4 Temperature and Film Thickness Dependence of Electron
Transport Mechanism .„ .- 29
5 Cylindrical Coordinate System » 56
6 Parabolic Velocity Distribution Characteristic of
Laminar Pipe Flow 56
7 Levich Model for Turbulent Pipe Flow 47
8 Surface Roughness, Velocity, and Concentration Profiles in
Turbulent Flow 53
9 Copper Corrosion Rate Versus Pipe Flow Reynolds Number
from Cornet et al. (37) 55
10 Mass Transport Dependence of Copper Corrosion in Nitric Acid
from Frank-Kamenetskeii et al. (38) 56
11 Mass Transport Dependence of Copper Corrosion in Neutral
Solutions from Roberts and Schemilt (39) 57
12 Corrosion Rate of Copper in H?SO. Versus Hydrogen Ion
Concentration Under Varied Conditions of Kate Control
from Zembura (40) 57
13 Metal/Solution System for Experiments Designed to be
Under Kinetic Rate Control ., 63
14 Metal/Oxide/Solution System for Experiments Designed to
'Be Under Solution Transport Rate Control 64
15 Metal/Solution System for Experiments Designed to Be
Under Solution Transport Rate Control 65
vi
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FIGURES - Continued
16 Polarization Curve , 69
17 Diffusion Controlled Cathodic Half-Cell 70
18 Diffusion Controlled Anodic Half-Cell 71
19 Three-Point Method for Calculating Corrosion Rate Under
Kinetic Rate Control 74
20 Three-Point Method for Calculating Corrosion Rate Under
Transport Control by Anodic Reaction 76
21 Three-Point Method for Calculating Corrosion Rate Under
Transport Control by Cathodic Reaction . 79
22 Basic Electrochemical Cell for Corrosion Rate Measurements ... 80
23 Experimental Apparatus Used in this Study 81
24 Electrochemical Cell Used in this Study 82
25 Rotator for Rotating Disc Electrode 84
26 Rotating Copper Disc Electrode 84
27 Solution IR Drop 87
28 Variability in Three-Point Method 94
29 Test Tube Containing Weight Loss Coupon 97
30 Weight Loss Test Apparatus 97
31 Weight Loss Test Results 99
32 Frank-Kamenetskii Plot for Data Taken in Heterogeneous
Systems 103
33 Frank-Kamenetskii Plot of Kinetic Data at 25°C 113
34 Frank-Kamenetskii Plot of Kinetic Data at 15°C 115
35 Frank-Kamenetskii Plot of Kinetic Data at 5°C 119
36 Kinetic Data of Region I at 25°C 120
37 Comparison of Region I Results with All Kinetic Data
at 25°C 124
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FIGURES - Continued
38 Kinetic Data of Region II at 25° C 126
39 Kinetic Data of Region III at 25° C 128
40 Kinetic Data of Region III at 15°C and 5° C 129
41 Electrode/solution Interface in Experiments Designed for
Oxide Film Growth Rate Control 133
42 Frank-Kamenetskii Plot of Oxide Film Growth Data at 25°C 42
43 Frank-Kamenetskii Plot of Oxide Film Growth Data at 15°C 138
44 Frank-Kamenetskii Plot of Oxide Film Growth Data at 5°C 139
45 Oxide Film Growth Data at 25°C 141
46 Oxide Film Growth Data at 15°C 142
47 Oxide Film Growth Data at 5°C 143
48 Electrode/solution Interface in Experiments Designed for
Stagnant Diffusion Rate Control 144
49 Frank-Kamenetskii Plot of Stagnant Diffusion Data at 25°C .... 151
50 Frank-Kamenetskii Plot t-f Stagnant Diffusion Data at 15°C .... 152
51 Frank-Kamenetskii Plot of Stagnant Diffusion Data at 5°C ..... 153
52 Stagnant Diffusion Data at 25°C ..t.... 156
53 Stagnant Diffusion Data at 15°C .., 157
54 Stagnant Diffusion Data at 5°C 158
55 Comparison of Corrosion Rates Measured with and Without
Oxide Film at 25°C 160
56 Comparison of Corrosion Rates Measured with and Without
Solution Mass Transport Effects at 25°C 161
57 Comparison of Surface pH Values Calculated from Data with
Those Predicted by Empirical Expression for Surface pH
at 25°C 164
58 Comparison of Surface pH Values Calculated from Data with
Those Predicted by Empirical Expression for Surface pH
at 15°C 165
vili
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FIGURES - Continued
59 Comparison of Surface pH Values Calculated from Data with
Those Predicted by Empirical Expression for Surface pH
at 5°C 166
60 Corrosion Rate Estimates for 1/2 inch Copper Tubing at
Varied Flowrate and 25°C 175
61 Corrosion Rate Estimates for 1/2 inch Copper Tubing at
Varied Flowrate and 15°C 176
62 Corrosion Rate Estimates for 1/2 Inch Copper Tubing at
Varied Flowrate and 5°C 177
63 pH Dependence of Corrosion Rates Estimated for Laminar
Flow Conditions '. 178
64 pH Dependence of Corrosion Rates Estimated for Turbulent
Flow Conditions 179
65 Comparison of Copper Corrosion Rates Predicted by Pipe Flow
Model with Rates Measured by Independent Sources 183
ix
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TABLES
umber
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
*
Summary of Rate Expressions for Interfacial Reaction Rate
Control
Summary of Rate Expressions for Oxide Film Growth and
Mass Transfer to Stationary Electrodes in Quiescent
Solutions . .«„ ... ..
Sumnary of Rate Expressions for Solution Mass Transport
Rate Control
Syntteetic Tolt Composition
Corrosion Rate of Copper in Synthetic Tolt River Water,
Electrochemical Measurements
Summary of Data Analysis Methodology
Kinetic Rate Control Data: 25CC
Kinetic Rate Control Data: 15°C <,....
Kinetic Rate Control Data: 5CC
Region I Dat*: 25°C ,
Region II Data: 25°C
Regie® III Data: 25"C, 15°C, and 5°C
Oxide Film Growth Rate Control Data: 25°C „
Oxide Film Growth Rate Control Data: 15°C .,
Oxide Film Growth Rate Control Data: 5°C .. .»
Regression Results for Oxloe Film Growth Data
Page
16
25
36
49
60
89
95
109
111
136
117
121
123
127
134
135
136
140
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TABLES - Continued
19 Parameter Estimates Calculated for Oxide Film Growth Data ... 140
20 Stagnant Diffusion Data: 25°C 146
21 Stagnant Diffusion Data: 15°C 147
22 Stagnant Diffusion Data: 5°C . 148
23 Regression Results for Stagnant Diffusion Data 149
24 Calculated Diagnostic Parameters for Diffusion Rate Control 149
25 Null Hypothesis Testing Results 154
26 Parameter Estimates Calculated for StagnantDiffusion Data ... 155
27 Pipe Flow Model Parameter Values 171
28 Oata for Verification of Pipe Flow Model Regression Results 181
XI
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SYMBOLS
o
a Lattice parameter (approx. 2A for Cu^O)
ba, be Anodic and cathodic Tafel slopes (mv)
c Concentration of point defects in oxide (cnf ), or of a chemical
species in solution (mole/ cm )
Cu [] Copper cation vacancy within oxide (ionic vacancy defect)
Cu(M) Metallic copper
D Diffusion coefficient (cm2/sec)
d Pipe diameter (cm)
E E'lectrode potential (mv vs. SCE)
E Corrosion potential (mv vs. SCE)
E Electrostatic field strength in oxide film
e" Electron
e Rough surface protrusion height (cm)
e Elementary electronic charge (1.60219 x 10 cone.)
F Faraday constant (96 „ 485 cone.)
h Plank constant (6.62618 x 10~34 J-sec)
•fa Plank constant divided by 2ir
o
h Electron hole in oxide (electronic vacancy defect)
2
i Current density (
J1 Ionic defect particle current within oxide film
Je Electronic defect particle current within oxide film
K Equilibrium constant
k Ion product of water
W
k(E) Potential dependent rate constant for electron transfer reaction
kf Rate- constant for forward reaction
kp Rate constant for reverse reaction
k Boltzmann constant (1.38066 x 10~23 J/°k)
o
L Thickness of oxide film (A)
L Distance down axial length of pipe from inlet (cm)
xi i
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SYMBOLS - Continued
^Cu Completely charged balanced copper atom within oxide
m Effective electron mass
P
N Molar flux (moles cm sec)
P Partial pressure of dissolved 02 in liquid phase
q.: Io;ic defect charge (Z-e)
qfi Electronic defect charge (e)
R Rate of reaction, in bulk (moles/cm, sec), on surface
2
(moles/cm sec)
R Molar gas constant (8.31441 J/mole °K)
r Radial distance variable in cylindrical coordinates
R Pipe radius (cm)
Re Reynolds number
Sc Schmidt number
T Absolute temperature (°K)
t Transport number
u Ionic mobility in electrostatic field
v Field velocity (cm/sec)
•J Zero field energy barrier within oxide (ev).
XQ Work function at metal/oxide interface (ev)
X, Work function at oxide/solution interface (ev.)
X Distance variable cartesian coordinates
Y Axial distance variable in cylindrical coordinate?
Z Integer charge on charged defects and solution species
A Ionic equivalent conductance
CM hydrodynamic boundary layer thickness (cm)
£D Diffusion layer thickness (cm)
^ Kinematic viscosity of solution (cm9/sec)
-1
Y/ Ionic defect jump frequency (sec )
v Viscosity (c )
0 Electrostatic potential (v)
j6 Angular distance variable cylindrical coordinates
Rotation speed of rotating disc electrode (rad./sec)
xi i i
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SYMBOLS - Continued
Many of the symbols used contain subscripts for descriptive purposes or to
refer to location. The following descriptive subscripts are used:
1 chemical species
cor corrosion
re reduction
ox oxidation '
The following location subscripts are used:
S oxide/solution interfacial region
B bulk solution
Other symbols used are defined in the text.
xiv
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ACKNOWLEDGMENTS
I wish to thank and acknowledge the efforts of my supervisory committee:
Professor John F. Ferguson, Chairman; Professor Brian Mar; Associate Professor
Dimitris SpyKdakis; Assistant Professor Mark Benjamin; and Professor James
Murray, Graduate Faculty Representative, who read and provided helpful com-
ments on the manuscript.
Special thanks to Karen Nakhjiri for her careful assistance in performing
many laboratory experiments. I gratefully acknowledge Marvin Gardels of the
U.S. Environmental Protection Agency, and Carlos Herrera and Brian Hoyt of the
Seattle Water Department Water Quality Lab for their continued interest and
support throughout the study. Thanks also to Jane Lybecker for her help in
the typing of this manuscript.
This research was partly funded by a grant from the U.S. Environmental
Protection Agency and supplemented by support from the Department of Civil
Engineering of the University of Washington for purchase of some needed equip-
ment.
xv
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SECTION I
INTRODUCTION
Corrosion of materials used to transport drinking water is both a public
health concern and an enormous economic problem. For decades, water utili-
ties, homeowners, and commercial building users h:ve observed and responded to
its adverse effects. Identifying the effects more clearly has led to
increased understanding of the adverse impacts and a greater appreciation of
the enormity of the problem.
A recent national survey conducted for the U.S. Congress by the National
Bureau of Standards (1) and Battelle Columbus Laboratories (2) attempted to
quantify the total economic impact of metallic corrosion in the United States.
The estimated total cost in 1975 for industrial, corrmercial, and public estab-
lishments was $82 billion. This figure included monies spent to replace
deteriorated parts and equipment, to maintain and repair, and to control
corrosion directly. In the drinking water field, costs as high as $375
million/year have been estimated (3) for replacement parts and repair of
distribution systems transmitting corrosive water, with an additional cost of
$27 million/year to treat water (3) for corrosion control. Current costs are
likely to be even higher. Furthermore, the Seattle Water Department has esti-
mated that repair costs for consumer plumbing systems are 10 to 20 times
higher than those associated with the distribution system. Annual expendi-
tures of 500,000 for corrosion control are estimated to reduce consumer costs
by $2 million.
The drinking water cycle (which includes the raw water source, treatment
processes, and water distribution system) is subject to contamination and
water quality degradation in any of its phases. The impact of corrosion is
especially important because it occurs in the distribution system — the part
of the cycle closest to the point of customer use. Water quality degradation
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and contamination occur because of the release of metal cations and other
corrosion products into the water.
Public health concerns include ingestion and bodily accumulation of metal
cations from drinking water. Maximum contaminant 'levels for many potentially
toxic chemical species have been set according to National Interim Primary
Drinking Water Regulations. Dissolved lead and cadmium are the two most
likely contaminants to be present in excess of standards because of aqueous
corrosion (3,5,7) in plumbing systems using galvanized steel or copper tubing
with lead/tin solder.
The aesthetic impacts (4,6,8) often occur because of the leachinj of
copper, iron, zinc, and manganese from corroding pipelines. Their effect is
to render the water undesirable for drinking because of unpleasant taste and
visual characteristics, and to promote staining of porcelain bathroom and
kitchen fixtures. The current National Secondary Drinking Water Regulations
suggest maximum concentration limits on chemical species that cause adverse
aesthetic effects.
All of these effects arise from a chemical reaction between the material
and a chemical component of the transported natural water. In this reaction,
the structural material (a metal) is oxidized and dissolved while some
component in solution is reduced. So the overall process is an oxidation-
reduction reaction between the metal and a component of the solution. As the
reaction proceeds, the metal is thinned, yielding a shortened useful lifetime,
the length of which depends on the rate of the overall reaction. Chemical
species produced by this reaction are principally dissolved metal cations,
some of which have maximum concentration limits for aesthetic and health
reasons. Reaction products may also promote precipitation of solids, which
accumulate on the metal surface and in some cases reduce water pressure and
pipeline carrying capacity (8). Corrosion control efforts are then aimed at
slowing down the reaction to an acceptable rate or stopping it completely
without creating further ecological or water quality problems.
Aqueous copper corrosion is a complex system of coupled chemical anu
physical processes that involve reactions between a solid and aqueous-phase
components producing reaction products that are both solid and aqueous
species. For the reaction to proceed, aqueous phase reactants must move
through solution to the solid/liquid interface, which is the reaction site.
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Here surface interactions occur involving adsorption of aqueous species,
electron transfer, and formation of reaction products. Solid phase reaction
products accumulate on the surface, and aqueous phase products are transported
to bulk solution.
The overall corrosion process involves the transport of reacting species
in solution, chemical reaction at the solid/solution interface, and transport
of aqueous phase reaction products ciway from the interface to bulk solution.
The rate at which each of these processes proceeds affects the overall
corrosion rate.
Rigorous study of a process as complex as aqueous copper corrosion is
indeed a multidisciplinary effort. Principles taken from solid-state,
electrochemical, and corrosion sciences must be combined with those of water
chemistry and environmental engineering to describe and understand adequately
the overall process as a composite of fundamental rate processes. Though
coupled together, each component rate process is influenced by a distinct set
of environmental variables that affects the rate at which it proceeds. The
overall corrosion rate depends at least partially on the rates of these
component processes. The main thrust of this work, then, is to present an
overview of copper corrosion in drinking water as a composite of several
fundamental rate processes and through laboratory experiments to determine
which rate processes exert the greatest rate controlling Influence on the
overall process. The environmental variables most important in influencing
the rate-controlling processes are also evaluated.
Standard steady-state electrochemical techniques, augumented with special
instrumentation necessary for measurement in natural waters of low conducti-
vity, were used to measure corrosion rate. Measurements were made under
differing conditions of rate control to evaluate the dependence of component
processes on temperature, fluid motion, and chemical composition of the
system.
Specifically, the goals of this sttrdy were as follows:
1. To characterize as comprehensively as possible aqueous
copper corrosion as a heterogeneous rate process by
bringing together principles from various disciplines to
develop quantitative rate expressions for each of the
component rate processes involved.
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2. To demonstrate the utility of steady-state electrochemical
techniques as a laboratory tool for the study of corrosion
in drinking water systems.
3. To determine experimentally which rate processes are most
important in controlling the overall rate of uniform copper
corrosion.
4. To determine which environmental variables exert the
greatest influence on the corrosion rate in natural waters
of composition similar to that of the Tolt River.
5. To demonstrate the applicability of experimental results in
the development of a steady-state model for copper cor-
rosion in pipe flow.
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SECTION II
CONCLUSIONS
INTRODUCTION
The results and major conclusions of the research are summarized and
reviewed in this chapter in light of the objectives listed in Section I.
Suggestions are presented for future studies to resolve some of the questions
raised by this work.
SUMMARY
Aqueous copper corrosion has been characterized as a heterogeneous rate
process composed of metal oxidation, oxide film growth, interfacial chemical
reactions, and mass transport in the liquid phase. Quantitative rate
expressions were developed in Section 4 to characterize each of these rate
processes. The experiments conducted were designed to measure the temperature
and pH dependence'of corrosion under rate control by each of these processes.
The persistent and unexpected influence of solution mass transport of a
reaction product, presumed to be OH", complicated characterization and identi-
fication of underlying rate processes. It was possible to empirically
characterize surface pH, pH , as a function of solution temperature, pH, and
diffusion-layer thickness.
This empirical correlation for pH , along with solution mass transport
models developed for turbulent and laminar pipe flow were combined to form a
steady-state pipe flow model for uniform copper corrosion. Predictions made
using the model under stagnant or low flowrate conditions show a stable and
low (0.20 MPY) corrosion rate in water of pHg > 6.0. For pH £ 6.0, predicted
rates are substantially increased as pHg is reduced and temperature is
increased. At high flowrates, tremendous acceleration of corrosion rate
occurs, which again increases with increasing temperature and decreasing pHR.
Only above a pHR of about 8.0 are the dramatic pHR and temperature effects
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dissipated so that the rate is stabilized at a minimum value of approximately
0.2 MPY.
CONCLUSIONS
Based on this work, the following conclusions were drawn:
1. Over the pH range 6.0 to 3.5, the rate of copper corrosion is
reduced as pH is increased.
2. Over the temperature range of 5°C to 25°C, the rate of copper
corrosion is reduced as temperature is reduced.
3. The presence of a Cu~0 film on the copper surface reduces the
corrosion rate at all pH and temperature values studied.
4. The transport of a reaction product (presumed to be OH~) away from
the oxide/solution interface is the principal process controlling
the overall corrosion rate. At low pH (6.0), rate control by mass
transport is nearly complete. At higher pH values (>8.0), the
influence of the underlying rate process exerts a greater influence
on the overall rate.
5. In pipe flow under stagnant or low flowrate (laminar flow)
conditions, the corrosion rate of copper is stabilized, for pHg >
6,0, at a value of 0.2 MPY. Only when the pH is reduced below 6.0
do the accelerating effects of low pH and high temperature manifest
themselves.
6. At high (turbulent) flowrates in pipe flow, corrosion rates are
accelerated dramatically with reduced pH and increased tenperature.
Under these conditions, only at pHg > 8.0 is the corrosion rate
stabilized to an acceptably low value of 0.2 MPY.
7. The use of steady-state electrochemical techniques have been shown
to give reliable and reproducible corrosion rate measurements even
in watsr of low conductivity. In addition, they provide the ver-
satility needed for experimental design of adequate sophistication
to produce data that can be used in mechanism determination and
model development. These qualities greatly enhance the research
capabilities of the experimenter.
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SECTION III
RECOMMENDATIONS
Based on the results of this study, recommendations regarding additional
research are presented in.the areas of aqueous corrosion science, aqueous
copper corrosion, and expanded use of electrochemical techniques.
The ability to characterize complex metal/oxide/solution systems as
heterogeneous rate processes seems to be an important step in determining the
dependence of the corrosion rate on system variables. Bringing together
appropriate multidiscipHnary information to develop quantitative rate
expressions for processes Involved in the general corrosion of metals other
than copper used in the transport of drinking water is suggested as crucial
to the development of aqueous corrosion science.
Extension and refinement of the model presented for aqueous copper cor-
rosion is also suggested. Extension to a broader range of aqueous species
and concentrations to include species Involved in water treatment processes
such as chlorination seems advisable. Further sophistication in mathematic-
ally modeling the oxide/solution interfacial interactions controlling the
solution pH just next to the interface is also in order, along with precipl-
2$
tation studies involving the injection of Cu and OH into a volume of water
of known chemical composition simulating the effect of the corrosion process
In the solution adjacent to the oxide/solution interface. The effect of
precipitated hydroxide end carbonate solids in altering the corrosion rate by
depositing on the metal surface could then be evaluated.
We reconwend that the steady-state methods used here be further applied
to the study of other matal/oxide/solution systems. Testing and development
1s recosmended for transient electrochemical techniques such as the A.C.
Impedance method, which because of Its possibility for Instantaneous measure-
ment can provide invaluable insight into understanding of the coupled rate
processes involved in aqueous corrosion.
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SECTION IV
UNIFORM COPPER CORROSION: A HETEROGENEOUS RATE PROCESS
INTRODUCTION
To quantitatively model a chemically reacting systen as complex as
copper corrosion in drinking water it is necessary to: 1) break down the
overall system into its fundamental component processes; 2) identify, evalu-
ate, and quantify mechanisms for each component process; anJ 3) combine the
rate expressions derived for each component process to formulate a rate
expression for the overall process. The result 1s an ability to r,how to what
extent variables affecting each of the component processes influence Ihe rate
of the overall process. Of interest in this study are the effects of chem-
ical composition of the water as well as physical variables Involved in p
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AQUEOUS COPPER CORROSION: A QUALITATIVE: OVERVIEW
In aqueous systems corrosion involves an oxidation-reduction reaction
between the nwtal and an oxidiring agent in solution. In the oxidation
half-cell the metal is oxidized from the zero to the +1, +2, or +3 oxidation
state. At near neutral pH values the reduction half-cell gcnarally involves
molecular oxygen reduction from the zero to the -2 cxidat
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COPPER
Cu
CUPROUS
OXIDE
Cu-,0
u
J±3
AQUEOUS SOLUTION
MIXED OXIDES
(Cu20,Cu(OH)2,CuO)
Figure 1. Metal/Oxide/Solution System for General Copper Corrosion in Aqueous
Media.
a) copper dissolution
b) cuprous oxide film growth
c) cuprous oxide dissolution
d) molecular oxygen reduction
The oxidation half-cell involves several steps, not all of which are electron
transfer reactions. In the first step, copper is oxidized at the metal/oxide
interface forming copper cations in the film and producing electrons:
Cu > Cu + e~ (Copper Dissolution) (1)
Cations, Cu • , created in this step are transported to the oxide/solution
interface where they react with water to form new cuprous oxide.
Cu*1 + 1/2 H20 > 1/2 Cu20 + H+ (Film Growth) (2)
The oxide film grows from its outer edge into solution until a steady state
thickness is reached. Oxide then begins to spawl and break up into solution,
and an outer porous layer of mixed oxides is formed. Cuprous oxide dissolves
by reacting with hydrogen ion in solution as follows:
1/2 Cu20 + H+ > Cu2+ + 1/2 H20 + e" (Film Dissolution) (3)
10
-------
Corrosion proceeds via a film growth mechanism since the underlying layer of
film is being continuously regenerated and maintained at roughly a constant
thickness despite dissolution and break up of its outer regions due to mech-
anical strains and chemical oxidation.
Molecular oxygen reduction is the principal reduction half-cell For
copper corrosion at near neutral pH values. This reaction has been widely
studied and comprehensive works by Hoare (5), Damjanovic (6, 7), and Yeager
(8) show that the reaction proceeds through intermediate formation of
hydrogen peroxide in acidic solutions.
02 + 2 H+ + 2 e~ > H202 (4)
H202 + 2 H+ + 2 e" > 2 H20 (5)
02 is adsorbed from solution onto the oxide surface, followed by disso-
ciation and acceptance of electrons forming two 0~. species for each (L
adsorbed. 0" . sites are then protonated, forming surface bound H,,0?. At
this point the H?0? may either desorb and go into solution as an aqueous
+
species, or be reduced by further reaction with H to form water. Both of
these pathways have been reported, although a recent treatment by Smyrl (9)
suggests that only reaction (4) is involved, and virtually all H202 enters
solution as an aqueous species. There it may react with other solution
components, but it no longer participates in the reduction half-cell for
copper corrosion.
In alkaline solution, a slightly different reaction occurs. It has been
characterized by the following stoichiornetry:
02 + 2 H20 + 4 e" > 4 OH" (6)
Here 02 still adsorbs to the oxide surface, accepts electrons, dissociates
forming two 0~d species. But due to the high pH or low H+ availability in
solution, protons are acquired from water molecules with the formation of
hydroxyl ions.
Regardless of the mechanism, CL reduction requires acceptance of elec-
trons donated by the oxide film. The source of available electrons are the
reactions composing the oxidation half-cell. At least half of these elec-
trons are generated at the metal/oxide interface by the copper dissolution
reaction. Since molecular oxygen is reduced at the oxide/solution interface
11
-------
electron transport across the film is required to keep the overall corrosion
process going.
In addition to providing a physical picture of the overall corrosion
process and an accounting of the principal chemical reactions involved, the
Ives/Rawson study included an evaluation of the effects of several solution
species common to natural waters that do not participate explicitly in the
reaction mechanism of copper corrosion. The effects of chloride, sulfate,
nitrate, and bicarbonate ion on corrosion rate were evaluated experimentally.
While a complete explanation as to how each of these anions affects the
corrosion process is lacking, they all are reported by Ives and Rawson (4) to
influence the corrosion process by adsorbing at the oxide/solution interface.
Chloride ion was found to have the most significant effect on copper
corrosion of all the anions evaluated. It was found to penetrate the porous
oxide layer and absorb strongly at the underlying Cu?0 solution interface
increasing the rates of the copper dissolution, CiuO film growth, and Cu20
dissolution reactions. The effect at 100 ppm chloride was to double the
corrosion rate over that measured in chloride free water. The presence of
chloride was also found to initiate a change from general corrosion to
localized corrosion by becoming incorporated into the Cu-O film and altering
its transport properties. Unlike chloride, the other anions tested (sulfate,
nitrate, and bicarbonate) all showed minimal influence on the corrosion rate.
Calcium bicarbonate was reported to induce a slight passivating effect,
reducing the corrosion rate.
The Duplex Film Model gives a complex picture of a corroding copper
system, that in appearance might be difficult to quantify. A physical
picture of the overall system that is easier to work with quantitatively is
accessible by making several reasonable assumptions:
1. The continuous film, underlying the broken up or porous outer film,
is composed solely of Cu^O and is of constant thickness.
2. The outermost, broken up and porous, film provides essentially no
corrosion protection since water flows into the pores and cracks
making direct contact with the underlying continuous film.
3. The pores and cracks in the outer film are large enough that diffu-
sing species in the liquid do not have a longer diffusional path due
to the presence of the outer portion of the film.
12
-------
With these assumptions one can view the corrosion process in terms of the
ti
simplified model shown -in Figure 2.
When each of the ch3mical reactions participating in the aqueous corro-
sion of copper is placed in its spatial context, as shown in Figure 3 below,
the rate processes required for corrosion to occur become apparent:
1) Kinetics of the interfacial reactions is one process involved.
2) Transport of CL and H+ through solution to react at the oxide/
o i yi
solution interface and of OH", Cu , and other Cu complexes away
from the interface are other participating rate process.
3) The transport of copper cations and electrons across the oxide film
is also a necessity for the overall reaction to continue.
Quantification of these rate processes requires knowledge of some of the
properties of the oxide film separating the fnetal and the aqueous phase.
Cuprous oxide exists in nonstoichiometric ionic crystalline form as a p-type
semiconductor. It is nonstoichiometric in that it contains a deficit of both
copper cations and electrons. These deficits are manifested as point defects
in the oxida. So cuprous oxide contains ionic defects (cation vacancies) and
electronic defects (electron holes). These defects are involved in the
interfacial reactions as well as in the transport of charge across the film.
Interfacial reactions involvin; transfer of copper cations are more
precisely written as either producing or destroying cation vacancies. When
copper dissolves, the oxidation reaction occurring at the metal/oxide inter-
face involves a singly charged copper cation leaving the metal lattice and
entering the oxide. This reaction is normally written as:
Cu > Cu*1 + e" (1)
The creation of a copper cation shown by equation (1) above can also be writ-
ten in the following form as a defect reaction in which a cation vacancy
within the oxid2 is destroyed:
Cu + Cu+[] > e" (7)
Here Cu+[] symbolizes a singly charged copper cation vacancy within the
oxide, which is written as a reactant since it is consumed in the reaction.
13
-------
COPPER
Cu
CUPROUS
OXIDE
Cu,0
AQUEOUS SOLUTION
H20, 02, H , etc.
Figure 2. Simplified Copper/Oxide/Water System.
COPPER
CUPROUS
OXIDE
Cu
e"+ Cu.,0-
AQUEOUS SOLUTION
H2°
u.,0 + H*
OH
H2°
H,0
H
Figure 3. Chemical Reactions Involved in Aqueous Copper Corrosion.
14
-------
The electron transfer in equation (7) above can be written in terms'of its
electronic defect:
Cu + Cu+[] + h > 0 (8)
o
Here h is an electron hole (electron vacancy) in the oxide. It is also writ-
ten as a reactant since it is consumed in the reaction. The symbol 0 stands
for a completely occupied and charge balanced lattice site within the oxide.
The electron produced, as the copper cation leaves the metal lattice, enters
the oxide by consuming an electron hole in the oxide. In this manner cation
vacancies and electron holes are consumed at the metal/oxide interface.
The three remaining reactions occur at the oxide/solution interface.
Each ones involves creation of cation vacancies or electron holes, or both
within the oxide. The general picture then is that point defects, cation
vacancies and electron holes, are created at the oxide/solution interface by
reactions between the oxide and solution, and are consumed at the metal/oxide
interface by the reaction occurring there. A net migration of cation vacan-
cies and electron holes from the oxide/solution interface to the metal/ oxide
interface is then required for the overall corrosion process to continue.
The details of defect formation and consumption will be discussed in the
upcoming section on interfacial reaction kinetics, while the mode of defect
transport across the film will be discussed in the section on oxide film
growth and transport.
INTERFACIAL REACTION KINETICS
Three of the four principal reactions involved in the corrosion process
could limit its overall rate. In this section rate expressions are developed
that show how the chemical composition of the solution affects the corrosion
rate when controlled by the kinetics of a particular reaction. A summary of
the reactions and equilibrium expressions necessary for development of appro-
priate rate expressions is provided in Table 1. Rate control by one parti-
cular reaction occurs when the velocity at which it proceeds is so much
slower than other rate processes that they are virtually at equilibrium.
Since detailed mechanisms for each of these reactions have not been devel-
oped, it is not possible to derive rate expressions in as rigorous a manner
as one would like. Rather, a more simplistic approach is taken here which
15
-------
Table 1
Sa-rrcary of Interfacial Reactions and Equilibria
I. Metal/Oxide Intertaca:
Cu i.. a Cu + e* (nwtal dissolution)
K.
• . I *
Cu * Cu + h —*0 {defect fora) "
11. Oxide/Solution Intorfaca:
*' ' - I *
Cu + — HO - TCu 0 + H (film growth) +
MCu * 2*2° -•—-—-- Cu2° * Cu*'' * H*
^.-•^=±^.1^,..- '»»£ ^ _ ,0401^
1 • * 2* I 3 ^"H>1
— Cu 0 + h * H „ Cu 11 +• Cu * — HO
22 22
'+-*.! 1/2 "
-0 -t-H * o ^—'-*• ~ n Q (0 Reduction) |H2°2' lhl
C'K-
T°, *"7H,° * Trrr?*0" (0 Reduction) "
42 22 ^ 2 I li I k
j02*^H205=±OH- + ;
Notation;
N " copper ntoa filling o lattice site «lthln the oxide, Cu,0.
Cu 2
h - an electron vacancy (holo) In tn@ oxide.
CuC}" o cation vacancy In tho OK Ida
P « partial pressure of oxygen In liquid phase
Assumptions: (&* 1-1.0 ,IH,OI « 1.0, »H ICu 0] - 1.0.
Cu 2 &•
16
-------
sometimes assumes that a reaction occurs in one step when in fact it may
occur 1n several. With this in mind, rate expressions are derived for three
of the four principal reactions.
Rate Control by Metal Dissolution
The metal dissolution reaction involves metal atoms leaving the metallic
soMd to fill cation and electron vacancies in the cuprous oxide. It occurs
at the metal/oxide interface and can be written as follows:
Cu(m) - > Of1"1 + e" (1)
or in defect form as:
Cu(m) + Cu+[] + h - > 0 (8)
The corrosion rate is the rate at which copper metal dissolves:
The metallic copper activity is presumed to be one in this derivation and
cation vacancies and electron hole concentrations are presumed to be small
enough that their concentrations approximately equal their activities. The
corrosion rate then depends on the magnitude of the rate constant, k~(E),
which is potential dependent as well as the metal/oxide intarfacial concen-
tration of cation vacancies and electron holes. Imposing the condition of
virtual equilibrium of other rate processes allows development of a rate
expression which connects the corrosion rate with the chemical composition of
the solution. Virtual equilibrum of all reactions occurring at the oxide/sol-
ution interface fixes the concentration of cation vacancies [Cu []] at the
oxide surface. Chemical equilibrium at the ox ickY solution interface requires
that reactions Ila, lib, and He of Table 1 be at equilibrium when the
solution pH is less than 7.0, and that reactions Ila, lib, and lid oe at
equilibrium when the solution pH is greater than 7.0. Expressions for
interfacial equilibrium are derived as fellows:
17
-------
a) at pH _< 7.0:
MCu + 1/2 H2° - > 1/2 Cu2°
+ (f11m growth)
1/2 02 + H+ - > 1/2 H202 + h (oxygen reduction)
1/2 Cu20 + H+ + h - > Cu+[] + Cu2+ + 1/2 H20 (film dissolution)
M + 1/2 0 + H+ - > 2Cu+[] + 1/2 H0 + Cu
V =
[Cu+[]]2 [HOJ1/2 [Cu2+]
l/2
-If
2 '
2+
CCu+[]] =
KP
1/2
1/2
(10)
b) at pH ,> 7.0:
M* . + 1/2 H^O
Cu
D2 + 1/2 H2 0
:u~0 + H+ + h
-> 1/2 Cu90 + Cu+[] + H+
-> OH" +
Cu
H°
OH
KII=V
C3]* [OH"] [Cu^T]
Dl/4 K2 * ^3
CCu+[]] =
1/4
[Cu2i"][OH']
1/2
1/4
1/2
+ 1/2
(11)
18
-------
The equilibrium expressions derived in (10) and (11) above establish the
necessary link between cation vacancy concentration at the oxide/solution
interface and certain chemical components of the solution. They show ex-
plicitly, that the interfacial concentration of cation vacancies depends upon
the partial pressure of dissolved oxygen, the concentration of cupn'c ion in
solution, and the hydrogen ion concentration as well as a temperature
dependence imbedded in the equilibrium constants.
At this point it is necessary to establish a relationship between the
cation vacancy concentration at the metal/oxide interface, which is directly
proportional to the rate of copper dissolution, and the cation vacancy con-
centration at the oxide/solution interface, which is in equilibrium with sev-
eral chemical species in solution. For rate control by interfacial reaction
kinetics, transport of cation vacancies and electron holes across the oxide
film must occur at a much more rapid rate than the reaction controlling the
overall rate. This situation is likely to occur during the initial stages of
formation of the filrn, that is, when the metal surface is covered with oxide
but the film is of insufficient thickness to allow a concentration gradient
of cation vacancies to build up. Under these conditions:
[Cu+[]]m/0 = [Cu*[]]0/s (12)
When the oxide film grows to a greater thickness a gradient of cstion vacan-
cies across the film is established even at virtual transport equilibrium due
to the presence of an electrostatic field within the oxide film. Under these
conditions:
[Cu+U^o = a [Cu+[]]0/s (13)
where a is a constant, with a value less than 1.0, that depends on the magni-
tude of the electric field in the oxide. When the absolute value of the
charge on copper cation vacancies is given as ze, Freehold (10) has shown
that:
. - e-(zeLE/kT> (14)
Thus, at a given temperature, T, film thickness, L, and electrostatic field
strength, E, the ratio of cation vacancy concentrations at the t#o interfaces
is fixed. As variations in the solution composition occur, which cause
changes in cation vacancy concentration at the oxide/solution interface, the
19
-------
cation vacancy concentration at the metal/oxide interface must adjust to
maintain a. As it changes the rate of copper dissolution changes proportion-
ately. This sequence of events is expressed in the following functional
form:
a) at pH < 7.0:
R = ME)'
K
/2
[H202]1/2 [Cu2+]
1/2
(15)
and b) at pH _> 7.0:
R = k(E)
KnP
1/4
[Cu2+] K.
1/2
ll/2
(16)
Equations (15) and (16) are derived for the initial filrr. growth situation,
where a = 1.0. Analogous expressions, for conditions in which a fully devel-
oped oxide filrr. is present, can be derived by multiplying the right hand side
of equations (15) and (16) by a. These expressions can be simplified into a
form quite suitable for comparison with measured data. Equation (15) can be
rewritten as a function of solution pH as follows:
(17)
log1QR =
where: a. = k(E)
s - 0.5 pH
K,P
1/2
L'H202]
1/2
1/2
Note that all temperature dependence is consolidated into the a. tenr. and
'*+
that [Cu ] and [H?0?] are assumed constant with respect to solution pH,
which is at best an approximation. Equation (16) can be rewritten in a
similar fashion-(for pH _> 7.0):
log,Q R =
- 0.5 pH
(18)
20
-------
= k(E)
Again all temperature dependence resides in the a- term. The slope of
log R with respect to pH should be independent of temperature at pH < 7.0 and
pH _> 7.0. The corrosion rate under conditions of rate control by copper
dissolution is therefore shown to depend upon cupric ion concentration in
solution, oxygen partial pressure, solution pH, and temperature.
Rate Control by Cu20 Formation
The CupO formation reaction involves a copper atom within the oxide,
MP , reacting with water to form more oxide and produce cation vacancies in
the film. It occurs at the oxide/solution interface and can be written as
fol1ows:
M£U + 1/2 H20 > 1/2 Cu20 + Cu+[] + H* (19)
When this reaction controls the rate of the overall corrosion process the
following rate expression pertains:
jrt»X -i
R -— = kf [Mju][H20]1/2 - kr [Cu20]1/2[Cu+[]][H+] (2C)
When the activities of M£U, H20, and Cu20 are presisned to be unity the rate
expression becomes:
R - kf - kr[Cu+[]] [H+] (21)
Note that this rate expression presumes tne reaction to occur as a one step
process, which is at best an approximation. The cation vacancy concentration
at the oxide/solution interface is fixed by the virtual equilibrium of other
reactions occurring there. Separate rate expressions are necessary to des-
cribe the corrosion rate at pH values below and above 7.0. At pH <^ 7.0 the
concentration of cation vacancies at the oxide/solution interface is derived
as follows:
21
-------
1/2 Cu20 + r + H+ - > Cu+[] + Cu2* + 1/2 H2
1/2 C2 + H* - > 1/2 H202
1/2 ':u
1/2 02 + 2H1
Cu+[]
1/2H202 + 1/2H20 KIH = k3.k4
l/2
therefore: [Cu+[]] = (-
l/2
[H202]
l/2;
(pH £ 7.0)
(22)
Solving equations (21) and (22) simultaneously produces the following rate
expression:
fkr
pl/2,
T T T
[Cu2+][H20
]1/2
2J
CH+]3
(23)
This relationship can be rewritten in a general form suitable for coiiiparison
Oj.
with measured data wtien [Cu ] and [HCLj are presieried not a function of pH:
R = a - b 10
-3pH
(24)
Here both a and b are ter.perature dependent.
At pH >^ 7.0 the concentration of cation vacancies at the oxide/solution
interface is derived as follows:
1/2 Cu20 <• h + H* - > Cu+[] + Cu2"*" H- 1/2 H20 k-j
1/4 02 + 1/2 H20 - > OH" + h k&
1/2 Cu20
1/4
Cu+[] + Cu2+ + OH"
-------
Pl/4KIV[H*] F1/4K.,[H+]2
therefore: [Cu []] = ^ l^L (pH > 7.0) (25)
'
Solving equations (21) and (25) simultaneously produces the following rate
expression appropriate at pH _> 7.0:
,1/4
(26)
R - kf - kr
L1
When rewritten in a general fonr, suitable for comparison with daia the
following relationship 1s obtained:
R - a - bj 10"3pH (27)
where both a and b. are terperature dependent. Here a has the saire value
below and above pH « 7.0, while b takes on different values in the two pH
ranges. The general fonr. of the rate expression for rate control by Cu00
formation is thus established as a function of cupric ion concentration,
oxygen partial pressure, solution pH, and temperature.
Rate Control by 0? Reduction
The rrolecular oxygen reduction reaction involves the reaction of aqueous
dissolved caygen at the oxide/solution Interface. 0- adsorbs and accepts
electrons (produces electron holes) at the oxide surface providing the reduc-
tion half-cell for the overall redox process. This reaction occurs by a
sequence of steps which are different at pH values below seven than for pM
values above seven.
At pH < 7.0, 0, is reduced through intermediate fonr>at1on of H^0?.
C. i- £-
There sre differing opinions as to whether the reaction steps at FLO^ °r
proceeds Beyond to H?0 fonr.ation. Both reaction possibilities will be
presented, with reduction to H-O^ presun^d to be the favored pathway. The
overall reaction can be written in two steps as follows:
23
-------
2H+ > 2h + H902 (i)
H2
2H+ > 2h + H«0 (ii)
02 + 4H+ > 4h + H20
Vetter (11) has reported a composite of experimental evidence from many
investigators for 02 reduction en metal surfaces in acidic solutions and has
presented the following rate expression:
R = k(E) P (28)
This expression apparently holds no matter whether the reduction goes just to
H202 or all the way to H?0. On oxide covered surfaces the reduction rate is
reported by Yeager (8) to be slower than on metal surfaces with intermediate
formation of H^O^ also being the predominant pathway.
When the solution pH is equal to or greater than 7.0 the mechanism is
slightly different. The reaction is irreversible and has the following
stoichiometry:
02 + 2H20 > 4h + 40H"
Vetter (11) has proposed the following rate expression for 0? reduction on
metal surfaces which is in accord with the mechanism proposed by Yeager (8)
for oxide covered surfaces:
R = kf(E) P [H+] (29)
It is interesting to note that only above pH = 7.0 does the reaction rate
become pH dependent.
Rate expressions have been presented for conditions of rate control by
02 reduction at pH values below and above 7.0. Unlike rate control by other
reactions, there is no dependence on defect concentrations within the oxide;
in fact, only the potential drop across the Helmholtz layer at the oxide/
solution interface, pH, and P affect the corrosion rate under these condi-
tions.
Mechanisms and rate expressions have been presented here for the princi-
pal reactions involved in the corrosion process. By looking at the rate
expression one can identify the variables that affect the corrosion rate when
24
-------
rate limited by a particular reaction. In this way the effect of solution
composition on the overall rate becomes apparent provided the Ives/Rawson
ir.echanism is qualitatively accurate in describing the corroding system.
Table 2 contains a sumr.ary of appropriate rate expressions.
OXIDE FILM GROWTH AND TRANSPORT
Transport of charge across a continuous oxide film growing on a corrod-
ing copper surface is one of the fundamental rate processes composing the
corrosion process. As such, it could limit the rate of the overall process.
In this section rate expressions are developed that show how the chemical
composition of the solution affects the corrosion rate when controlled by
oxide film growth and transport. Initially, physical and chemical properties
of the oxide that affect the rate and mechanism of charge transport are
discussed. This is followed by an explanation of how solid state transport
models are put together using the coupled currents approach. The electron
tunneling model is then presented to show explicitly the effect of solution
composition on the rate of charge transport, as well as the overall corrosion
rate when rate limited by oxide film growth and transport.
The rate and mechanism of charge transport through a continuous oxide
film depends on several physical properties of the film. First of all, film
structure is important, that is, whether the oxide has an amorphous or
crystalline form under the snvironmental conditions present. Crystalline
solids tend to have spatially uniform transport rates, while rates in an
amorphous solid are spatially irregular containing preferential diffusion
paths. Near room temperature cuprous oxide has a crystalline structure that
is a body centered cubic lattice. Consequently a film growth and charge
transport model is developed for oxide films that are both continuous and
crystalline in structure.
The rate and mechanism of charge transport across the film are affected
by temperature, film thickness, nature of defect species being transported,
and nature of the.electrostatic field developed witH-n the film. For oxides
like cuprous oxide which grow by transport of charged vacancy defects a vari-
ety of growth mechanisms are available and a growing film may switch from one
mechanism to another depending principally on film thickness, but also on
temperature. For a given mechanism the rate at which charged defects are
25
-------
Table 2
Surnnary of Rate Expressions for Interfacial Reaction Rate Control
I. Rate Control By >*ata.l Dissolution
R-.IHV2
•hare: a •
K(E)
k(E)
K,P
1/2
1/2
£-1
1/2
11. Rata Control by Oxida Formation
R » a - b(H*l
whoro;
and
a « k 6 all pM
J/2
pH < 7.0
« pH 2. 7.0
K,vP
1/4 1
tCu2*lK
6 pH < 7.0
8 pH 2.7-0
III. Rsts Control by 0 Reduction
R - e
R - 8lH I
share: 8 * k CE)P
fi pH < 7.0
9 pH > 7.0
26
-------
transported across the film depends in some way on the magnitude of the
electrostatic field. Some mechanisms are more rate sensitive to field
strength and temperature than others.
Charge transport is presented here from the point of view of the coupled
currents approach, a conceptual framework developed by Fromhold (10) in his
treatise entitled "Theory of Metal Oxidation" to codify and provide a unified
basis for the variety of oxide film growth models that developed indepen-
dently during the years 1940 to 1975. Most of these models were developed
for a specific set of growth conditions, so no general overview of metal
oxidation and film growth existed. It took Fromhold's insight to character-
ize with such clarity and rigor the common threads running through the
different models.
For oxides growing by transport of charged elecronic and ionic defects
different mechanisms are generally used to transport each type of defect.
Each type of defect then has its own flux across the film called a particle
current. Overall charge transport and oxide film growth rate depend on the
coupling of the electronic defect particle current with the ionic defect
paticle current. The magnitude of the electrostatic field within the oxide
and steady state film thickness adjust to balance the two defect particle
currents within the oxide. This is the coupled currents approach. Transport
models based on this approach are composed of:
a. ionic defect transport rate expression
b. electronic defect transport rate expression
c. expression for electrostatic field in oxide
When one defect particle current is sufficiently larger than the other,
at steady-state film thickness and electric field strength, the overall
transport or film growth rate may be completely controlled by the smaller
particle current, but the magnitude of electrostatic potential developed
depends on the faster defect particle. This is the case for the electron
tunneling model presented next. At early stages of film growth, ionic defect
o o
transport limits film growth, but for film thicknesses over 20 A to 30 A,
electronic defect transport begins to limit overall rate of film growth (10).
27
-------
Electron Tunneling Model
The electron tunneling model was developed by Fromho'ld and Cook (12) by
bringing together the pioneering work of Mott (13) and Cabrera and Mott (14)
on low temperature growth kinetics of thin oxide films with later quantita-
tive developments by Simmons (15) on electron tunneling through potential
barriers. The result is a quantitative model which predicts the rate of
4
growth and steady-state transport rate of charge through the very thin oxide
films growing on metal surfaces at temperatures near 2b°C. The electronic
defect transport mechanisms for this model involves quantum mechanical tun-
neling of electrons from the metal through the potential barrier of the oxide
film to ultimately fill vacant energy levels in molecular oxygen adsorbed at
the oxide/solution interface. It is a mechanism that is appropriate only at
low temperature and for very thin films. As temperature and film thickness
are increased the likelihood of other electron transport mechanisms, such as
thermal emissions of electrons or electron holes over the potential barrier
in the oxide is increased. Figure 4 shows how the film growth mechanism is
affected by film thickness, temperature, and metal-oxide work function. The
Cu-Cu~0 work function has the value X0 = 1.024 ev at 300°K (12) so the
c. 0 o
limiting thickness for electron tunneling is about 39 A for a Cu-0 film.
Above this thickness, thermal emission of electrons or holes should predomin-
ate as the electronic defect transport mechanism.
The electron tunneling particle current is presented by Fromhold to be:
-2m1/2L
Je = (8u2f.L)"1[(2X0 + eE0L) exp [— -- (2XQ + eE0L)1/2l -
71
-2m1'2.. 1/2
(2X - eEL) exp[ — - - (2X - eE)1'^] (30)
L - eE0L) exp[ — -
The rate of electronic tunneling across the film is seen to depend upon tne
film thickness, L, electric field strength, E , metal-oxide work function,
X0, oxide-oxygen work function, X, , and effective electron mass, m, and h
which is Plank's constant (li) divided by 2*. For the electron tunneling
mechanism to be complete, relationships for the ionic defect particle current
and the electrostatic field strength must also be presented.
28
-------
Transition
Thickness
(A)
50
40
30
20
10
Thermionic
Emission
Electron
Tunneling
200 400 600 800
T (*K)
Figure 4. Temperature and Film Thickness Dependence of Electron
Transport Mechanism.
Ionic defect transport through the Cu^O film is by diffusion due to a
concentration gradient of cation vacancies across the film and a large
presumably homogeneous electric field within the oxide. The cation vacancy
diffusion particle current as developed by Fromhold for steady-state condi-
tions is as follows:
.
J1 = 4a*exp{-W/kT)sinh(ZieE0a/kT)[-!
- C^O) exp(Zte£0LAT)
(31)
Here a is the lattice parameter which equals approximately 2A for Cu«0.
Vis the jump frequency (sec"1) for ionic defects attempting to exceed a zero
field energy barrier of height, W in ev. kT represents the thermal energy of
ionic defects in ev, Z-e is the charge per cation vacancy* EQ is the
electrostatic field strength (V/cin) in the oxide. 0^(1} is the concentration
"-t
of ionic defects at the oxide-solution interface (no. of defects/on") while
-------
C.j(0) is the concentration of ionic defects in the oxide near the metal/oxide
interface (no. of defects/cm3). L is .the thickness of the film in A.
When the two defect particle currents are subjected to the coupled cur-
rents condition, s relationship for the electric field strength, E , can be
developed. The coopled currents condition is:
i a
= 0 (32)
Where q^ is the charge on each ionic defect, Z-e, and q is the charge
on each electronic defect, e. By substituting the relationshios for each
particle current into equation (32) one may in principle solve for E . For
o
this model and others analytically solving for E is not possible so the
model is evaluated under special limiting conditions. There are two limiting
conditions amenable to solution for the electron tunneling model. The first
condition arises Khen the film is just thick enough for rate control by
defect transport. This ir called the early growth stage, and for the
electron tunneling model the growth rate is limited during this stage by
ionic defect diffusion and the electric field strength is dictated by the
virtual equilibrium of electronic defects. The early growth stage model can
be represented as follows:
J1 = 4a\)exp(-w/kT) sinhU^eE,, a/kT)
* U i / ~r _ r- i /t.-r\ / *3 1 ^
- XL)/Le (33)
Equation (31) can be simplified by noting that for L = 5A, T = 298°K,
f
•,-8
and E = 10 v/cm the value of the exponential term is much smaller than one:
so the term:
10
) exp (Z.je E0L/kT)
1 - exp (Zje EQ L/kT)
Substituting this back into equation (31) above yields the following expres
sion for the ionic defect particle current:
30
-------
J1 = 4 aVexp(-w/kT) sinh(ZieEQ a/kT) C
(34)
Since the field strength, E , is not affected by defect concentrations
the only place solution composition can affect the rate of early stage growth
is through the oxide/solution interfacial concentration of cation vacancies,
C^L). For virtual equilibrium of interfacial reactions at the oxide/solution
interface two relationships derived earlier in evaluating interfacial reaction
kinetic rate control are appropriate. At pH < 7.0, recognizing that
[Cu n]Qx^HS surff -e = ^j^). t^ie interfacial cation vacancy concentration is
related to species concentrations in solution by the following relationship.
1/2
or:
ML)
[H202]1/2[Cu2+]
" v nl/2
[H202]1/2[Cu2+]
1/2
1/2
1Q-0.5 pH
(10)
(35)
At pH < 7.0, a similar relationship exists. It was derived earlier
to be:
,1/4
1/2
(11)
or:
,1/4
w.
1/2
10
-0.5
(36)
So the relationship hetween pH, P, [Cu+2], and J1 is explicitly shown for
pH < 7 as well as for pH >^ 7 for early stage growth. The pH dependence of
the rate of film growth can be summarized as follows:
a) At pH < 7.0: J » d 10~°*5 pH (37)
K
where d » 4 aV exp(-w/kT)sinh(ZieriEa/kT) [
1 °
and: log J = log d - 0.5 pH
I/?
[H202][Cu]
(38)
31
-------
b) at pH > 7.0: J = d 10'°'5 pH
where: d = 4a exp(-w/kT)sinh(ZieEQa/kT)
(39)
,1/4
[Cu2+] K
1/2
and:
log J - log d - 0.5 pH
(40)
The temperature dependence is contained in the values of the constant b for
both equations. Log J versus pH then plots as a straight line with a slope
of -0.5.
o
When the oxide film gets thicker, approximately 20 to 30A, the electron
tunnel particle current becomes rate limiting with the field strength deter-
mined by the virtual ionic defect equilibrium. When this situation arises
the transport rate is:
(8
(2XL - eEQL) exp[-
2m
eEQL) exp[-2m
1/2
1/2 "
EoeL)1/2] -
- eEQL)1/2]]
with:
Z1 e L
IC
(30)
(41)
Here the electric field strength, EQ, is dependent upon the cation vacancy
concentration at the oxide/solution interface, but is the only term in the
transport rate expression with such a defect concentration dependence. E is
therefore the only term that responds to solution composition through C^(L).
The relationships, equations (35) and (36), shown before which connect C,(L)
+?
with solution pH, P, and [Cu ] still apply under later growth stage condi-
tions.
Equation (30) can be simplified by evaluating the magnitude of the two
o c
exponential terms for T = 298°K, L = 30 A, and EQ - 10 v/cm. The first term
inside the brackets of equation (30) is found to be much larger than the
second:
(2X
eEQL) exp[-2m1/2 V1 L(2XQ
eEL)1/2]
(2XL - eEQL) exp[-2
1/2
L(2XL - eEQL)]
500
32
-------
The second term may then be omitted from equation (30) as being negligible
when subtracted from the first. The simplified rate expression becomes:
J = [8iA L2r1(2XQ + eEQL)
o + eV-)1/2l
(42)
As pointed out by Gibbs (16), a further simplification o-f equation (42) is
possible for cuprous oxide films in aqueous electrolytes, provided the
potential drop across the film is small. When the potential drop across the
film 1s on the order of tens of millivolts, the electron tunneling rate
expression has been reduced by Simmons (17) to the following ohmic form:
J = bV (43)
where: V = EQL
kT C,(L)
— In [-! ]
Z,e C,(0)
1 1
(44)
b » a positive constant (temp, independent)
Solving equations (43) and (44) simultaneously the following expression is
obtained:
(45)
Since C.(L) is related to solution composition by equilibrium expressions
derived earlier:
a) At pH < 7.0:
,1/2
[H202]1/2
10
-0.5 pH
(35)
and b) At pH >_ 7.0:
,1/4
w
1/2
10
-0.5 pH
(36)
Equation (45) may be rewritten as follows for pH < 7.0:
33
-------
,„
[Cu2+]
1/2
10
-0.5 pH
(46)
Rearranging and separating out the pH dependence the following form
evolves:
J =
+ C2 pH)
(47)
C = b In
1 Z.e
2 ~TTF~
KjP1'2
1 /p oj.
ru n l1'^ rrn*- 1
LH2U2J LLU J
CjtO)
1/2
where:
and
At pH < 7.0 tne rate is shown to be a linear function of solution pH, with
the slope, kTC2, of the J versus pH plot a linear function of temperature.
The intercept, kTC,, is a nonlinear function of temperature since both K, and
P are temperature dependent components of C,. Its temperature dependence
then should be slightly greater than linear.
For pH 2. 7.0, equation (45) may be rearranged in a similar fashion with
the following result:
pH) (48)
,1/4 1 1/2
J =
C2
where:
and
Note that both parameters C, and C? have the same temperature dependencies as
those derived earlier at pH <_ 7.0, with C,, having identically the same magni-
tude at pH < 7.0, that it does at pH < 7.0.
Rate expressions have been derived in this section that show explicitly
the manner in which P, cupric ion concentration, hydrogen peroxide concen-
tration, solution pH, and temperature affect the rate of copper corrosion
34
-------
when under rate control by oxide film growth *nd transport. A su.mary of
these relationships is provided in Table 3.
SOLUTION MASS TRANSPORT
Mass transport in aqueous solution refers to the individual movement of
Ions and molecules through solution due to the presence of sane driving
force. This driving force may be a concentration gradient in the case of
diffusion, a potential gradient in the case of migration, or a component of
solution velocity in the case of convection. The rate of mass transport is
P
measured as a flux (moles/cm sec) and is normally the phenomenon of interest
1n chemically reacting systems. This could be the flux of e reactant from
bulk solution moving toward the interface or the flux of a reaction product
moving away from the interface into bulk solution. In aqueous corrosion,
molecular oxygen and hydrogen 1on are solution species that act as reactants
1n the reduction half-cell, while hydroxyl ion is a product of the reduction
half-cell. If the reaction rate is fast enough, the transport of molecular
oxygen, hydrcxyl ion, or hydrogen ion through solution may be the rate
controlling step in the reduction half-cell or even the entire corrosion
process. The possibility of rate control makes solution transport phenomena
an Important subject of consideration. In this section the basic equations
of solution transport will be presented along with some development of their
chemical and hydrod;/namic aspects. Existing models for majs transport in
pipe flow will be presented which can be used as a basis for estimating
limiting fluxes of hydrogen ion, hydroxyl ion and molecular oxygen at varied
temperature, pipe size, pH, and flow velocity.
Principal Transport liquations
Two principal equations (18) that characterize the mass transport of a
species In solution to and from the solid/solution interface ore the overall
mass flux equation and the material balance equation. Each of these can be
uniquely derived for a particular species in solution. The overall mass flux
of species it may be represented as follows:
JNj « -DiVCi - ZjUjFCjVi? + V[Ct (49)
Equation (49) is written here in vector fora appropriate for ? variety of
35
-------
Table 3
Sunmary of Rate Expressions for Oxide Film Growth and Transport Control
I. Early Stage Mia Grcwth (ZA < L < 15 A)
R - «
•her»:
e£a/hT)
K|P
1/7
1/2
(-«/kT>»lnh(2
K P
II
2*
ICu .l_JC
«J
1/2
< r.o
e J»H > 7.0
11. Later Stogo Flls Sroafh (15 A < L < 3?
R • kT(C * C
whera:
a PM > 7.0
(ell
and b » a (voa!Tlw* constant
. So* (t?)
36
-------
flow geometries. The mass flux, _N^ » of species 1 1s the rate of movement of
species 1 across an area perpendicular to Us path (moles/sec cm2}. This
rate depends on the magnitude of the concentration gradient, 7C^ , in the
direction of movement and the diffusion coefficient, D-. They compose the
diffusional component of flux. An electrostatic potential gradient, vJ< , in
the direction of movement may also contribute to the mass flux provided
species i has a net charge. This effect is called t..e raigrational component
of flux. The component of fluid velocity, V, directed normal to the mass
flux can exert an enormous Influence on the rate of mass transport. This is
the convective component of mass flux. The combined effects of diffusion,
migration, and convection then determine the nagnitude of mass flux 1n any
particular direction.
The second principal equation characterizing mass transport of species
1n solutions is the material balance (18). It can be formulated for each
solution species as follows:
dCj
R, (50)
As a statement of the conservation of mass it describes the change in concen-
tration of species 1 with respect to time at a fixed point in space resulting
from the move?-
-------
N, = -
(51)
This form of the mass flux equation is appropriate for situations where
potential gradients do not exist within the solution and migrational effects
are negligible. It may be used where migrational effects are present by
replacing the ionic diffusion coefficient for species i, D-, with an effec-
tive diffusion coefficient, Dgf , given by Pickett (19) to be:
1
Def ' Di
I
(52)
Here (n/S^) is the number of electrons consumed per mole of species i reacted
or produced, Z^ is the charge on species i, and t- is the transport number of
1:
i m
DJCJZJ
(53)
for a solution containing m ionic species. Equation (51) then becomes:
When species i reacts only at the suiid/soluticn interface and not in the
bulk solution, the bulk reaction term, R^, in the material balance equation
is zero. So the material balance can be written as:
= -V- NI <55)
Solving equations (51) and (55) simultaneously the following relationship
results:
(56)
This relationship describes the concentration of species i as a function of
time and location as influenced by molecular or ionic diffusion and bulk
fluid motion, and is called the convective diffusion equation. Analytical
38.
-------
solutions to this equation for various hydrodynami c flow regimes comprise the
theoretical approach to solution transport problems (21).
Most analytical solutions are to the steady- state problem where:
Equation (56) then becomes:
V .VCj = D^2C. (57)
At low concentrations, where D- is not a function of C- , equation (57)
is analogous to the Fourier-Poisson equation for steady-state heat conduc-
tion, a problem that has been worked on for nearly one-hundred and fifty
years. Analytical solutions exist for a variety of flow regimes (see Crank
(20)) and many solutions to the steady-state convective diffusion equation
were originally derived for heat conduction.
The principal convective diffusion problem important in corroding drink-
ing water systems involves the transport of species in solution (hydroxyl
ion, molecular oxygen, and hydrogen ion) to and from the inner wall of a
circular tube under conditions of laminar and turbulent flow. Also, the
transport of solution species to the surface of a rotating disc electrode is
an important convective diffusion problem., since a rotating disc electrode
was used in the laboratory phase of this research.
The point in solving this problem is ultimately to be able to:
a. Estimate an upper bound on corrosion rates due to solution mass
transfer limitations.
b. Evaluate the effects of principal variables such as flow velo-
city, pipe size, and solution pH on the limiting flux.
Pipe Flow
The reynolds number, Re, is the appropriate dimension! ess parameter to
characterize pipe flow (22,23). Its value depends on several system proper-
ties:
d
(58)
39
-------
where d is the inside pipe diameter (cm), is the mean solution velocity
down the axial length of the pipe (cm/sec), and ^ is the kinematic viscosity
o
of the solution (cm /sec). Pipe flow at Re _< 2100 is generally laminar, for
2100 <. RE £ 4000 a transition region occurs, and at Re > 4000 flow is turbu-
lent. Due to the physical differences in the flow patterns and the differ-
t
ence'£ in velocity profile, separate solutions to the convective diffusion
equation exist for turbulent and laminar flow (24). Solutions under both
conditions will be discussed for pipe flow.
Solutions of the steady state convective diffusion equation for pipe
Flow, involves first a transformation of the vector form of the equation:
V .VCj = D^2 C1 (59)
into cylindrical coordinates, a geometry more appropriate for pipe flow.
Figure 5 shows the cylindrical coordinates r, y and (j) to he the radial,
longitudinal, and angular directions respectively.
Written in these coordinates there is angular symmetry, so the CA>depend-
ence drops out. Making other appropriate assumptions, the form of the steady-
state convective diffusion equation becomes:
= D.
^(ry
L
(60)
Determination of v as a function of radial distance, r. reduces the problem
to only three variables C^, r, and y. Then with appropriate boundary values
for Cj, this problem can be solved for the radial component of flux, N-, at
the surface of the pipe.
Laminar Flow
Several noteworthy solutions to the steady state convective diffusion
equation have been developed for laminar pipe flow. Solutions by Graetz
(25), Leveque (26), and Levich (21) are presented here. All presume fully
developed Poiseuille flow, which means the longitudinal component of velo-
city, v , is distributed parabolicly over the diameter as shown in the figure
below.
40
-------
f
f-
\
\
\
I
1 /
^
,* I
^ ^ '
y
^
\ (^ / r
\y* /
Figure 5. Cylindrical Coordinate System.
Figure 6. Parabolic Velocity Distribution Characteristic of Laminar Pipe
Flow.
41
-------
This velocity distribution is described as:
vy = 2(l - r2/R2) (61)
All other components of velocity are presumed zero and the pipe surface is
presumed smooth. Let's look now at specific solutions.
Graetz Solution
This solution was originally developed by Graetz (25) for heat conduc-
tion as a solution to the Fourier-Poisson problem. It was later applied to
analogo'.j mass transfer problems. Graetz used the method of separation of
variables to derive the following series solution:
Di(CR ~ c«) a i ? y Di
Ni = 2R E J \ \ e*& H) (62)
1 M k=l i k k 2 R2
The eigenvalues, \k, and coefficients, Mk, have numerical values worked out
in the literature for k=l, .,., 10. All other parameters are physical and
geometric properties of the system. With this solution one can predict the
mass flux of species i to or from the inside wall of a pipe of radius, R,
when i is traveling in a fluid moving down the pipe with mean velocity, .
Note that the radial flux, N., changes with distance down the pipe from the
inlet (at y=0) and the solution is applicable for all values of y.
Leveque Solution
The Leveque (26) solution treats the region where y values are small,
close to the pipe inlet, and where r values are large, very near the wall of
the pipe. The velocity distribution in this region was approximated by
Leveque to be:
Vy = 4(l - r/R) (51)
Like Graetz solution, Leveque1s work was initially presented as a steady-
state solution of the Fourier-Poisson equation of heat conduction then later
extended to the analogous mass transfer situation. The solution is as
fol1ows:
42
-------
Di(CB - Co) y°i i
Ni = ~ 2R El.3566( V) - 1-2 - 0.296919(—-±
2r 2IT
yD, 2/3
+ 0( !—=) ] (64)
2IT
It is considered appropriate only for short distances down the tube:
0.02R2
y < ——
Note that this solution depends on the same physical and geometric parameters
as the Graetz solution.
Levich Solution
This solution (21) parallels that of Leveque in that it considers only
the region very close to the pipe wall where the parabolic velocity profile
can be approximated as a linear function of radial distance, r. Unlike the
Leveque case this solution is not derived solely for the inlet region, small
values of ys so its applicability is similar to that of the Graetz solution.
Ths solution is as follows:
N1 = 0.6884 DjtCg - CQ)
(66)
Once again the same physical and geometric parameters determine the magnitude
of the mass flux.
Each of these solutions has been corroborated experimentally and exten-
sive literature exists on the subject. While these solutions are useful in
preoicting transport limited mass fluxes under conditions of laminar flow,
oftentimes fluid flow in pipes is not laminar. These models alone are not
adequate to predict limiting fluxes in water supply and household plumbing
systems over the entire range of flow velocities normally encountered. Mass
transport in turbulent pipe flow must also be considered.
43
-------
Turbulent Flow
Turbulent flow is characterized by rapid and random velocity fluctuations
about some time-averaged value at a fixed point in space. In addition to the
longitudinal component of velocity, eddies continually form and mix the water,
so transport takes place by both molecular motion (diffusion) and by turbulent
mixing. The notion of a diffusion layer across which molecular or ionic
species must diffuse is maintained in turbulent flow although its thickness is
greatly reduced from that of laminar flow due to the turbulent mixing of
forming and dissipating eddies. At present there is no single conceptual
picture of turbulent flow that is universally accepted, although many models
are presently being evaluated. Because of the ill-defined fluid dynamics,
first principles approaches to turbulent transport have not been completely
successful in explaining experimental results. Several empirical models that
correlate measured mass flux with flow properties have been developed and will
be presented along with solutions to the turbulent convective diffusion
equation.
The convective-diffusion equation for turbulent pipe flow can be devel-
oped from its original vector form:
<>ci ?
—!•= D,9 Ci - V .yc, (56)
<>t
by replacing the concentration terms, C., with instantaneous turbulent
concentration:
C1 = C1 + C! (67)
i
where C. is the time averaged concentration at a point and C. is the instant-
aneous fluctuation in concentration from its time averaged value, C^. The
velocity vector, ^, must also be replaced with an instantaneous velocity
vector:
V = tf + V* (68)
I
where ^ is the time averaged fluid velocity vector at a point and V^ is the
instantaneous fluctuation velocity vector from the time averaged value, ^_.
When these time averaged values are inserted into eouation (56) above, the
turbulent convective-diffusion equation can be written as follows:
44
-------
2 (69)
where DtQt is the total diffusion coefficient incorporating ionic (molecular)
and eddy diffusion.
°tot = Di + De (7°)
Here De is the eddy diffusion coefficient, which may be considerably larger
than the ionic (molecular) diffusion coefficient of species i.
Equation (69) above can now be converted into cylindrical coordinators:
(71)
and solved in a manner similar to that for laminar flow, provided the time
averaged longitudinal velocity component, v , is knosn as a function of
radial distance, r. Several empirical correlations exist relating v and r
for pipe flow. Commonly used correlations are v = const,, v is a linear
function of r or v is a logarithmic function of r. The value of the eddy
diffusivity, D , is also a function of r close to the wall. Empirical
correlations relating D and r exist, so at least in principle the convective
diffusion equation is solvable for turbulent pipe flow. Solutions developed
by Linton and Sherwood (27) and by Van Shaw et al. (28) are representative of
the deterministic approach, which is still evolving, and will be presented.
Stochastic methods (29) are also being developed hut will not be discussed
here. Another theoretical approach developed by Levich and extended by
Davies (30), that does not make use of the convective diffusion equation will
also be presented.
Solutions of Linton and Sherwood and Van Shaw et al.
Van Shaw et al. solved the turbulent convective diffusion problem in a
manner identical.to an earlier solution by Linton and Sherwood (27). By use
of cartesian coordinates (neglecting curvature) and assuming a linear
velocity profile:
45
-------
(72)
Here x is the distance variable normal to the, presumed flat, pipe surface
and takes the place of cylindrical coordinate, r. y is still the direction
down the longitudinal axis of the tube. Disregarding the dependence of 0 on
x the following solution was developed:
^ = 0.276 (CB - C0)Re'°'42 Sc'2/3 (L/d)'173 (73)
The time averaged mass flux in the x direction, R. is given as a function of
the radial ir.ean of the instantaneous time averaged velocities, , the
Reynolds number, Re, the Schmidt number, Sc, and the distance down the pipe
from the inlet, L. The Schmidt number is defined here as:
Sc = N;/D1 (74)
where V* is the kinematic viscosity of the bulk solution (cnr/sec) and D- is
the molecular (ionic) diffusion coefficient. This solution differs only
slightly from the earliar solution of Linton and Sherwood:
Hi = 0.232(CB - C0)Re-°'4 Sc'2/3 (L/d)'1''3 (75)
Data presented by Van Shaw et al . and Linton and Sherwood both show an
increasing tendency for the data to follow their theoretical predictions as
pipe diameters are reduced to one inch or less and at Reynolds numbers
between 104 and 105.
Levich Solution
The Levich model for mass transfer in turbulent pipe flow was not
derived as a solution to the turbulent convective diffusion equation.
Rather, it presumes the conceptual model of the liquid/solid interface as
shown in Figure 7 below. The turbulent boundary layer, of thickness yb, is
divided up into three sections with differing resistances to mass transfer.
Mass transfer across each of the three sections occurs by a different
mechanism and is evaluated separately. At steady state the mass flux across
each of the three zones is equal. The steady- state flux is then derived by
46
-------
Solution
Concentration C
Diffusion
Sublayer
b Turbulent
Boundary
Layer
Main Turbulent
Stream
Figure 7. Levich Model for Turbulent Pipe Flow.
equating the fluxes and supplying appropriate boundary conditions. In the
outermost zone, o j< y £ y. , transport takes place by turbulent mixing, a
convective action. In the middle zone, <5_ £ y £<£., the eddy diffusion
coefficient, De is presumed much larger than 0.= so that transport occurs by
eddy diffusion at a flux equal to D times the concentration gradient across
the zone. In the inner zone, 0 _< y _<_ transport is based solely on
molecular diffusion at a flux equal to D. times the concentration gradient
across the zone. Based on this analysis by Levich which was extended by
Davies (30) the following relationship for the mass flux developed.
Re
R
(76)
This solution appears to be more closely in line with published data.
Empirical correlations based solely on experimental data will be presented
next.
47
-------
Empirical Correlations
Two empirical correlations are commonly used to characterize mass trans-
port in turbulent pipe flow. The Chi 1 ton-Col burn (31) correlation arose in
1934 out of an effort to correlate heat transfer data in turbulent pipe flow
with available mass transfer data. It remains a useful correlation and is
given as follows:
.0115 D.(CR - C ) n o ,n
-i-5 2_ ReO-8 Scl/3 (77)
Another commonly cited correlation is that of Harriott and Hamilton (32):
.0048 D.(CB - C ) Q 913 Q.346 ,7fls
Ni(avg) = IT Re Sc (78)
Both relationships express the mass flux in terms of a value that is
averaged over distance down the pipe in a region of fully developed turbulent
flow. Note that the functional form of these correlations is similar to the
solutions of the convective diffusion equation. While similar in form, the
two approaches, theoretical and empirical, represent different points of
view. The theoretical approach has its roots in some conceptual model of the
phenomenon which may be a highly idealized (or naive) representation of what
is actually going on. Empirical correlations, on the other hand, make no
pretenses at phenomenological explanations, they simply reflect the actual
tendencies that exist in measured data. Clearly both have merit as well as
limitations.
Mass transport through a stagnant liquid can be viewed as a special case
of the convective-diffusion problem where all components of solution velocity
are zero. In this case the velocity term of equation (56) vanishes and the
following relationship results:
= D,
JT ~ ui v "1
For the one-dimensional case in cartesian coordinates, the relation is a
statement of Pick's Second Law:
43
-------
c)CH
5T = Di
with the following boundary conditions:
at: t = 0: Cc = CR — cone, at electrode equals that of the
S Bbulk
t > 0: C(- = 0 -- completely diffusion controlled
and as x —> «», C(x,t) > Cg
the standard solution, C(x,t), to this differential equation is given
(33) as:
.1
C(x.t) • CB erf
^1727172
(81)
i
where erf (z) is short for the error function of ZB a standard function with
values given in Table 4 below.
Table 4
Mass Transfer to Stationary Electrodes in Quiet Solutions
from Adams p. 48
I erfj
0 0,0000
0.2 0.2227
C.4 0.4284
0.8 0.7421
1.0 0.8427
1.2 0.9103
1.6 0.9764
2.0 0.9953
2.5 O.S996
3.0 0.999
1.000
Of interest, in corroding systems is not so mudt the concentration
profile but the rate of mass transport through solution to the sol id/solution
Interface where the reaction occurs.
?
This rate is given as a flux, N9 in (moles/cur sec) to the surrace as
follows:
-------
l/2 CR
(82)
So, the surface flux is a function of both time and bulk concentration for a
species being transported from the bulk to the surface to participate as a
reactant in a reaction at the solid/solution interface. Adams (33) reports
that conditions required for semi-infinite linear diffusion are difficult to
maintain for periods longer than about 30 to 45 seconds. Natural convection
due to thermal gradients and environmental vibrations tend to mix the
solution and limit the time of stagnation.
The flux given above is an instantaneous value which changes with time.
A more appropriate value for a corroding system with stagnant water would be
a time-averaged value of the mass flux. Such a value can be determined by
Integrating the Instantaneous flux, N^ , over a stagnation time penod, t, and
then dividing by t (34):
dt
which turns out to be the following:
D
CB
This relationship is applicable only when the solid surface is acting like a
shielded electrode (35, 36), that is, when the solid surface completely
surrounds the liquid in the directions normal to that of ma$s transport. So
the actual surface of a corroding pipe does act as a shielded electrode, but
a rotating disc electrode inserted into solution for corrosion rate measure-
ment does not.
The correction factor for conditions where the electrode is not shielded
has been derived by Soos and Lingane (35) and l.ingane (36) to be:
[1 + a(Dt/r2)1/2]
where: a « 2.12 (a constant)
r = electrode radius (an) for disc electrode
50
-------
The average flux to an unshielded electrode over time period t Is then:
v 1/2
Navg ' T/rTT/2 tl - a( J (85)
n
For solution species that are products of the corrosion reaction which must
diffuse away from the electrode surface to the bulk the average flux over
time period t is given (34) as:
Nayg - 2(CS - CB)(DM)1/2 (86)
where C<- is the surface concentration of the diffusing species and Cg is its
concentration in bulk solution. Applying the correction factor for an
unshielded electrode, the average flux becomes:
Navg * 2
-------
- (9.K X
y Viscosity of Water
5°C
15°C
25°C
1.5188 cp
1.1404 cp
0.8937 cp
A reduction of nearly 50% for a temperature change of only 20°C. From the
Levich equation for turbulent transport one can see that:
n ,-Ml 2/3
Di(25°C)
Using this relationship:
Ni(5°C) = 0.670 Ni(25°C)
Other factors remaining constant, a change in temperature from 25°C down to
5°C reduces the mass transport rate to roughly two-thirds its former value.
Pipe size effects enter directly through the R term in Levich's equa-
tion:
-1/3
NfU/2 in)
N.;(l in)
R(l/2 in)
R(l in)
}n this case, with other factors being equal:
N^l/2 in) = 1.26 N.(l in)
The effect of a reduced pipe diameter from 1 in to 1/2 in is to increase the
mass flux by roughly one-fourth when both pipes have the same flow rate. For
tubulent flow the ratio of pipe radii shown above is raised to the -0.12
power.
52
-------
In corroding systems, where oxide films or other corrosion products form
on the surface of a metal, initially smooth metal surfaces become quite
rough. Figure 8 shows what a corroded metal surface may look like at high
magnification. All mass transfer relationships presented so far have been
derived for flow through smooth pipes. This is a condition that seldom
Velocity Concentration
Profile Profile
Fluid Flow
Figure 8. Surface Roughness, Velocity, and concentration
Profiles in Turbulent Pipe Flow.
exists for pipes carrying natural waters in the near neutral pH range, since
solid phase corrosion products are almost always observed. The presence of
corrosion products invariably roughens the solid surface which in turn influ-
ences the fluid flow. Close to the solid surface small eddies are created
which reduce the thickness of the laminar diffusion layer (£* in Levich's
(21) model). The mass flux to the surface is increased as S~ is reduced.
Davies (30) has presented the following relationship which describes the
effect of surface roughness:
Re0'1 Sc°'5 (e/d)0'15 (89)
11 i " const.
Here e is the height of surface protrusions and d is the diameter of the
pipe. Generally, (e/d) values range from 0.0001 for relatively smooth
surfaces to values near 0.05 for relatively rough surfaces. Using the
relationship above, one can estimate the impact of surface roughness on the
mass flux:
53
-------
Ni (rough) = (e/
Ni(smooth) (e/d)°'15
Using (e/d)r = 0.0£ and (e/d)s = 0.0001, and calculating the ratio of
mass fluxes:
Ni(rough) = 2>54 Ni(smooth)
So the mass flux to the surface may be more than doubled as the surface
becomes roughened by buildup of corrosion products. This is an important
aspect of solution phase mass transport that is not very well characterized
at present and makes precise quantitative estimation of mass fluxes in real
world corroding systems difficult.
Thus, it is shown that each factor considered:
pipe size
PH
flow velocity
temperature
surface roughness
can significantly influence tha rate of mass transport of reacting species to
from the pipe surface,
Applications of Mass Transfer Analysis To Aqueous Copper Corrosion
Estimating the effects of solution mass transport on corrosion rates,
has received mi/ch attention in the literature. Studies have focused princi-
pally on transport of molecular oxygen to the reacting surface under condi-
tions of laminar or turbulent flow. Results of a few of these studies will
be presented here.
The corrosion of copper tubing under solution mass transport control has
been studied by several authors. Cornet et al. (37) have presented experi-
mental results for copper corrosion by 2.1 N H?SO. at 30°C. Experiments were
done for 1/2, 3/4, and 1 inch diameter pipes over a range of flow velocities
(300 1 Re £ 10 ) that included laminar and turbulent flow regimes. Under
these conditions the rate imiting flux was that of molecular oxygen which was
54
-------
shown to vary greatly with flow velocity and be virtually independent of pipe
diameter. A sharp increase in mass flux was observed as the flow transi-
tioned from laminar to turbulent flow (Re >^ 4000). At Re >_ 104 the corrosion
rate shows the effects of mixed control, that of reaction kinetics and solu-
tion mass transport, which greatly reduces the dependence of corrosion rate
on fluid velocity, Re. Figure 9 shows these trends:
Frank-Kamenetskeii et al. (38) have studied copper corrosion in nitric
acid under conditions of rate control by molecular oxygen transport. Their
data, presented in Figure 10 below, covers both laminar and turbulent flow
conditions and shows a sharp increase in mass flux as the flow becomes turbu-
lent. Here the Peclet number, Pe, is defined as:
2R
Pe = ReSc =
(90)
1000
Corrosion
Rate (HDD) 100
20
2xl02 103
1CT
Reynolds Number
10=
Figure 9. Copper Corrosion Rate Versus Pipe Flow Reynolds
Number fromCornetet al. (37)
The Nusselt number, Nu, for mass transport, also called the Sherwood number,
Sh, is defined as a dimensionless mass flux:
2R
Nu «
N1
(91)
55
-------
So, Figure 10 is essentially a plot of mass flux versus flow velocity.
Nu
80
60
40
20
8 12 16 20 24
Pe (x 10"5)
Figure 10. Mass Transport Dependence of Copper Corrosion in Nitric Acid
Acid from Frank-Kamenetskeii et al. (38).
Roberts and Shemilt (39) have presented results of mass transport controlled
copper corrosion in near neutral pH solution. Their study was aimed at
assessing the effect:; of strain on oxide film rupture and repair under
laminar flow conditions. Their results show, at least qualitatively, the
expected increase in rate of mass transport with increasing flow velocity.
The modified Sherwood number used in Figure 11 is just the Sherwood number
multiplied by a constant that relates it to oxide film strain, and as such,
it is still a qualitative indicator of mass flux. The effect of oxygen
concentration variations on the mass flux is difficult to explain and raises
the possibility that molecular oxygen may not be the rate limiting reactant
in this system.
Zembura (40) investigated the rate of copper corrosion in a mixed
electrolyte of 0.1 M Na^SO. and H^SO^ at pK values that were varied roughly
from 0.5 to 4.5. Using a rotating disc electrode, he was able to measure
both the kinetic rate of copper dissolution and solution mass transfer rates.
The experimental results, shown in Figure 12, indicate that the kinetics of
copper dissolution were rate controlling from 0.5 _< pH _< 3.8. Above this pH
range mass transport of H became rate limiting. At no time was the
56
-------
61
'05
&1I
I , . 1 , t
ISO
500 1000
REWOtOS NUMBER
4000
Figure 11. Mass Transport Dependence of Copper Corrosion in Neutral
Solutions from Roberts and Schemilt (39).
-3.0
LOG I
(a/cm2)
-5.0
-7.0
\
\
0, Transport
Limitation
H Transport
\ Limitation
, Reaction Rate
Control
\
\
PH
Figure 12. Corrosion Rate of Copper in H2SO, Versus Hydrogen Ion
Concentration Under Varied Conditions of R^te Control from
Zembura (40).
57.
-------
corrosion rate high enough to be rate limited by Op mass transport, oven
though 02 reduction was shown to be the reduction half cell reaction. As
indicated by Zembura and Fulinski (41) both (L and H+ are involved In the
02 reduction half-cell reaction. As the solution pH is raised to 4 or above
the mass flux of H becomes less than the mass flux of 00 due to the small
molar concentration of H+ at these higher pH values.
This work has interesting implications for copper corrosion in slightly
acidic natural waters. Here hydrogen ion concentrations range from 10 K to
10" M indicating that hydrogen ion mass fluxes could be even more limiting
than in Zanbura's work.
Mass Transport Summary
Rate expressions for convective-diffusion of solution species under
conditions of stagnant, laminar, and turbulent flow are all important for
modeling real corroding systems. The rate expression for steady-state solu-
tion mass transport to or from the solid/solution interface can be formulated
in the following general form:
nFD(C, - C-)
This form is appropriate for species being transported to or from the inter-
face under cond^Lions of stagnant, laminar, and turbulant flew. For the case
of a reacting soecies diffusing toward the interfdce, such as On and H :
C? 0 surface concentration - > 0 for complete diffusion control
C, - bulk concentration of reacting species
For the case of a reaction product, such as OH", diffusing away
from the interface:
C, = the steady state concentration of the reaction product at
the interface
C- - concentration of diffusing reaction product in bulk
solution
58
-------
Differing flow conditions are accounted for by defining
-------
Table 5
Sunroary of Rate Expressions for Solution Mass Transport Rate Control
&D
(Cg (bulk cone.): for diffusion toward interface (H*^)
r (interfacie1. cone.): for diffusion away from interface
v •*
(OH")
( 0: for diffusion toward interface (H+, 02)
b) C2 » <
1 Co: for diffusion away from interface (OH )
1 /?
0.5 («Dt) ' stagnant diffusion
. . -0.333
c) OD « \ 1'453^y~DR-' laminar diffusion
133.3R Re"°°88 sc"°*333 turbulent diffusion
60
-------
SECTION 5
EXPERIMENTAL PROCEDURE
INTRODUCTION
The approach taken in this study was to identify physical and chemical
properties of the copper/cuprous oxide/Tolt River water system that exert an
influence on the overall rate of uniform corrosion of copper tubing used for
cold water plumbing. Then by varying the magnitudes of these influential
parameters, conditions favorable to a minimized rate of copper corrosion could
be determined. This was felt to be an important step in developing a rational
and economic control strategy for copper corrosion in Tolt River water. It
would also serve as a denonstration of tne utility of electrochemical methods
for corrosion rate measurements in low conductivity drinking water-
Identification of parameter;, exerting an influence on the overall process
evolved cut of the development of rate expressions for each of the component
processes, derived in Section 4, which show explicitly the dependence of the
rate of that process on the chemical and physical properties of the systei.u
Solution pH and temperature were found to be two parameters strongly
influencing the rate of each process modeled in Section 4 and »ere therefore
pinpointed as useful indicator variables to fit mechanistic models to measured
data. Experiments designed to measure corrosion rates under rate control hy
each of the component rate processes were then performed at. varied pH end
temperature.
The principal measurement made in this study was the electrochemical
determination of corrosion rate. This measurement was repeated many times
under varied conditions of solution composition, temperature, and type of rate
control. Experimental design consisted of systematic variation of these
61
-------
conditions in such a way that measured corrosion rates could be compared
directly with rate expressions developed in Section 4 for each of the
component rate processes. Appropriate mechanisms for each component rate
process could then be evaluated and a mathematical model for the overall
corrosion process developed. This chapter contains a description of the type
of data as well as the manner in which it was measured. The logic and details
of the experimental approach used are developed first. A section on electro-
chemical methods which includes general background information on how the
methods work, what they measure, and a brief accounting of the basic equipment
necessary to measure corrosion rates electrochemically, is next. This is
followed by an explanation of the experimental apparatus actually used in this
research along with a complete account of the laboratory setup and procedure
used in corrosion rate determinations. The laboratory setup and procedure
used to conduct weight loss testing is described in the final section of the
chapter.
LABORATORY PHASE OF THE STUDY
As stated earlier, all data taking in this study involved measurement of
corrosion rate under varied conditions of rate control, chemical composition
of the solution, and temperature. The entire measurement effort can be
divided up into the following four distinct sets of corrosion rate measure-
ments:
1) Interfacial Reaction Rate Conv.ro 1,, measured electrochemical!}';
2) Oxide-Film Growth and Transport Rate Control, measured electro-
chemical ly;
3) Stagnant Diffusion in Solution Rdte Control, measured electro-
chemical ly; and
4) Stagnant Diffusion in Solution Rate Control, measured by weight
loss.
The first three of these sets of measurements correspond to the component
rate processes modeled 1n Section 4. The final set was used for quantitative
comparison of corrosion rate measurement by weight loss and electrochemical
tests.
62
-------
Data under kinetic rate control were taken by designing experiments in
which possible rate limitations by oxide film transport was eliminated and
the possibility of rate control by solution mass transport reduced. This was
done by running polarization curves on freshly polished copper electrodes '
rotated at 3000 RPM. Any oxide film was effectively removed from the elec-
trode surface by polishing. Rotation of the rotating disc electrode at 3000
RPM reduces the diffusion layer thickness in the solution to such a small
value that the concentration gradient increases greatly and solution mass
transport for most species is capable of proceeding at rates much greater
than those determined experimentally. Figure 13 shows a schematic of the
metal/solution system in which corrosion rates under kinetic rate control are
measured. These rates correspond to the kinetics of the process at the
metal/solution interface that is rate controlling. This could be ratal dis-
solution, early stage oxide film growth, or molecular oxygen reduction.
Rate expreslons, derived in Section 4, were presented for each of these reac-
tions as a function of pH and temperature. Comparison of the pH and tempera-
ture dependence of the rates with that of measured data will provide a basis
for selection of a rate controlling process under these experimental condi-
tions.
COPPER
1 SYNTHETIC TOLT
• RIVER WATER
OH" |
.f^"1"
Figure 13. Metal/solution system for Experiments Designed to be Under
Kinetic Rate Control.
Data under rate control by cxide film growth and solid state tranc-port
ware taken by designing experiments in MTch possible rcte 1'lmitdticns by
63
-------
interfacial reaction kinetics and solution mass transport were til initiated.
This was done by running polarization curves on an electrochemically aged
copper electrode rotated at 3000 RPM. The electrochemical aging process
consisted of passing a 10 ua anodic current across the electrode/solution
interface for a period of two hours, promoting oxide film growth. Oxide
films were grown at a variety of cell currents and over a range of time
periods. Those grown at 10 uA for two hours gave the lowest cell current
values, indicating that they most nearly represented complete film transport
control. Rotation of the rotating disc electrode at 3000 RPM, as explained
earlier, insures that solution mass transport processes are capable of
proceeding at high rates and thereby reducing the possibility of rate control
by solution mass transport. Figure 14 shows a schematic of the metal/oxide/
solution system in which these corrosion rates are measured. Measured rates
then correspond to the rate of oxide film growth, which is limited by charge
transport across the film. Rate expressions, devaloped Section 4, for early
and late stage growth of oxide films by the electron tunneling mechanism were
presented as as function of pH and tenperature. A comparison of these rate
expressions with measured data provide a basis for determining which film
growth model is appropriate. Or.ce the appropriate model is identified the
dependence of its rate on chemical species in solution other than pH can be
noted in addition to its pH dependence.
COPPER
CUPROUS
OXIDE
aa™ & ii IIIIITI.
**^J51""" w 1 i
«*— CutD-——
I
as—— 6d — — i* SYNTHETIC TOLT
1 RIVER WATER
<^S— — H+ ^
^m»__«. 0 1
1
«__»-^. OH" '
1
Figure 14. Metal/Oxide/Solution System for Experiments Designed to be Under
Fi1m Growth Rate Control.
64
-------
Data under rate control by solution mass t; ansport were taken by deign-
ing experiments in which possible rate limitations by interfecial reaction
kinetics and oxide film growth were eliminated. This was dont by running
polarization curves on freshly polished copper electrodes th*t A-ere not
rotated. Under these experimental conditions mass transport in solution was
expected to be the slowest step in the corrosion process. Figure 15 shows a
schematic diagram of the metal/solution system from which corrosion rate ddta
presented in this section were measured. Measured rates, then, correspond to
the rate of mass transport of H* or CL to the electrode surface through
stagnant media, or the ra^e of stagnant diffusion of OH" away frcm the
electrode surface to the bulk solution. Rate expressions developed in Section
4, for H , OH", and 0? mass transport in stagnant solution were presented as a
function of pH and temperature and can be compared with .neasurr^ data. On
this basis the rate controlling diffusion process is identified. Experiments
to measure corrosion rates under rate control by each of the component rate
processes composing copper corrosion in drinking water were designed to be
carried out at varied pH (6.0 _< pH _< 8.3) and temperature (5°C 1 T _< 25°C).
This data could then be compared with rate expressions developed in Section 4,
and an overall process model developed by putting together quantitative models
of appropriate rate processes. Those efforts are describe; in Sections 6 and
7. This chapter continues with an explanation of the electrochemical
corrosion rate measurements used.
COPPER
SYNTHETIC TOLT
RIVER K'ATER
Figure 15. Metal/Solution System for Experiments ,-->$i'»e Under
Solution Transport Rate Control.
-------
ELECTROCHEMICAL METHODS
Electrochemical methods have been used in corrosion research for some
twenty- five years (1), in the past decade these methods have been developed
on a quantitative basis (2) for use in drinking water systems, especially for
waters of low conductivity (< 150 pmos/cm) (3). The principal advantage of
electrochemical methods is that a corrosion rate determination can be made
rapidly. This is advantageous from the point of view of error assessment,
since replicate runs can be readily made to assess the reproducibility of a
measurement. Another advantage is that an instantaneous rate of corrosion is
measured, as opposed to a rate averaged over a period of several months as in
a weight loss coupon test. Rapid and instantaneous corrosion rate measure-
ments are useful in observing the change in corrosion rate that occurs with
slight changes in solution composition, an important consideration in this
research. How electrochemical methods work and what they actually measure is
described in the upcoming section on fundamentals.
Fundamental's
Electrochemical methods can be used to measure corrosion rates in
aqueous systems because oxidation-reduction reactions are involved. Consider
the simple pair of redox half-cell reactions shown below:
l 1/2 H20 (2)
Since each half-cell reaction involves the transfer of electrons, the magni
tude of the kinetic rate constants, kQx(E) and kre(E), are functions of
electrode potential. They can be written in the following form:
o
k ' k
ox
kre(E) = k°e exp
-E + E
66
-------
Here, k°x and k" are the potential independent portions of the rate con-
stants and can be characterized by an Arrhenius type expression as a function
of temperature. The term E in both expressions represents the electrode
potential measured with respect to a reference potential, which in this case
is that of the Saturated Calome'l Reference Electrode. E° is the equilibrium
potential for the oxidation half-cell and can often be calculated from the
Ner.ist equation. E°g is the equilibrium potential for the reduction half-
cell and can be calculated from the appropriate Nernst equation. The con-
stants b and b are called the anodic- and cathodic Tafel slopes respectively
and nave numerical values characteristic of the particular half-cell reaction
they represent.
The velocity of each half-cell reaction can be written in the forms
shown below (omitting back reactions) when the corrosion potential is
sufficiently ":ar from either half-cell equilibrium potential that its forward
reaction term predominates over the back reaction term. This is normally the
case. The reaction velocities of the oxidation and reduction half-cells can
be expressed as follows:
V = kox
-------
tron equivalents per mole of reactant consumed (r, 1 for each half cell as
written), and F is the Faraday Constant (96,485 coul/equiv).
The half-cell current densities can be expressed in the following form:
E-E° E - E°
nP f\\? L ^,
,• _ llr rii_T i.o _ „ OX
I ~ "A—
cx -E
exp(- 5) (10)
This current densities oppose one another in direction so that the net cur-
rent density flowing in the cell is:
These current density equals zero when the electrode potential equals tho
corrosion potential, E , and t
the corrosion current density, i
corrosion potential, E , and the current densities of each half-cell equal
= ''
cor
'cor ' io* «P ' re
Simultaneous solution of equations (9) through (12) yields the Stern-Geary
(4) equation:
This equation relates the net current density, i, flowing in an electrochemi-
cal cell with values of electrode potential, E. Both of these parameters, i
and E, are measurable, arid if an experimental plot of i vs. E can. be obtained
the values of i , E , b . and b^ can be evaluated. This, of course, is
cor' cor a c
how corrosion rates are determined electrochemically.
As derived here the Stern-Geary equation describes the dependence of
cell current on electrode potential in a corroding system where both anodic
and cathodic half-cell reactions are proceeding under rate control by chemi-
68
-------
cal kinetics. Each half-cell current density then exhibits the following
exponential form:
E - E.
"cor*
ba
(14)
(15)
with the measured cell current density being the algebraic sum of these two
half-cell current densities. A plot of cell current density versus electrode
potential is called a polarization curve. Figure 16 shows a typical polari-
zation curve for a corroding system in which both half-cell reactions are
proceeding under rate control by chemical kinetics. The solid line is a
trace of the measured cell current density at corresponding values of elec-
trode potential, E. The broken lines refer to the half-cell current densi-
ties. The cathodic (reduction) half-coll current is shown here as negative
since it flows in a direction opposite to that of the anodic (oxidation)
half-cell which is positive by convention.
E (SCE)
Figure
Polarization Curve.
69
-------
The experiir.ental output of an electrochemical corrosion rate determina-
P
tion is this plot of net cell current density, i (pA/cm), versus electrode
potential, E (mv vs. SCE). The corrosion rate is then calculated from this
plot called a polarization curve. This curve can then be fit to the Stern-
Geary model and Icor, bft, and t>c calculated. Although derived solely for
reactions under kinetic rate control, the Stern-Geary model has practical use
in systems where one half-cell reaction is diffusion controlled, as well.
When the cathcdic half-cell reaction is diffusion controlled, the second
exponential term in the Stern-Geary equation is no longer potential dependent
and approaches 1,0 in value (b > - »). The Stern-Geary equation then
takes the following form:
I = I
cor
E - E
exp (—T—-
- 1
(16)
The characteristic shape of a polarization curve measured under these condi-
tions is shown in Figure 17. Once again the solid line refers to the cell
current density, and the broken lines to the component half-cell current den-
sities.
Figure 17- Diffusion Controlled Cathodic Half-Cell.
70
-------
An analogous situation exists when the anodic reaction is diffusion con-
trolled. The first exponential term in the Stern-Geary equation now is inde-
pendent of potential and approaches 1.0 (b > ») in value. The Stern-
a
Geary equation then becomes:
I = I
cor
1 - exp - (-
E - E
(17)
The characteristic shape of a polarization curve measured under these condi-
tions is shown in Figure 18, with solid and broken lines having the same
meaning as above.
I
0
!a
cor
E (SCE)
Figure 18. Diffusion Controlled Arndic Half-Cell.
All three of these combinations of rate control were encountered in the
laboratory phas^ of this study, arid all three polarization curve shapes are
amenable to corrosion rate and tafel slope calculation. Methods for calcu-
lating these parameters from measured curves are discussed next.
Calculating Corrosion Rates from Polarizationi Curves
The most versatile and precise way of calculating corrosion rates from
polarization curves was found to be the three-point method, originally
71
-------
developed by Barnartt (5) for investigation of electrode reaction mechanisms,
is directly applicable to corroding systems (6). The method is versatile in
that it is applicable to electrode reactions where both half-cell reactions
are proceeding under rate control by chenical kinetics or where one half-cell
reaction is transport limited. Thus it provides a means of calculating
corrosion rates measured under the three conditions of rate control modeled
in this study. Algorithms are developed here for use in the calculations of
the corrosion rate, anodic tafel slope, and cathodic tafel slope. Derived
first for conditions of rate control by chemical kinetics, then for transport
control of anodic reaction, and finally transport control of the cathodic
reaction they are directly usable for data taken under rate control by
intert'acial reaction kinetics, oxide film growth and transport, and by
solution mass transport respectively.
Kinetic Control
Beginning ivith the Stern-Geary equation;
E-E_... E - E
I = I
cor
, v ,
exp ( — - ) - exp (
cor,,
I£—'
(18)
Note that in this form'b is a negative number. The following terms can be
defined (see Figure 19):
1) I = Ij, when (E - Ecop) = &E
2) I = I2, when (E - Ecop) = 2AE
3) 1 = I3, when (E - ECQr) = -2AE
4) u = exp(AE/ba)
5) v = exp (AE/bc)
6) rj = |I2/I3|
7) r = i
Based on these definitions the following relationships for 1^ I2, and I, can
be developed:
' - ' '
"'
72
-------
So that:
99 99
Multiplying through by (u'v'/u vc) allows a more concise expression for r, :
U2,2(u? - v2)
" 7 - 7
-
2 2, 2 2>
u v (u - v )
(v2 - u2)
-uV
2 2
1 1 W
U V
rl =
In a similar fashion it can be shown that:
I,
= u + v
To calculate the corrosion rate, I_-_, and values for the tafel slopes it is
\f -j i
necessary to solve the following three equations simultaneously:
'cor ' V
-------
So:
ba = AE/ln u = AE/(ln[
likewiss: be = AE/ln v = AE/ln[
- 4 I r
(20)
(21)
In order to calculate values for these parameters from an experimental
curve three data points are needed, two of them selected at potentials posi-
tive with respect to E and one negative with respect to E . The first
\f\) I \^U I
data point is arbitrarily selected to be (E,,!.) where (E, - E ) = AE. Data
point number two, (E,,,!,), is then selected so that (E, - E } = 2AE and
C. C, £ \r\Jl
data point number three, (E,I0), so that (E, - Ernr,} = 2AE. Figure 19 shows
o \j
-------
cor
cor
A
(22)
o
Where A is the surface area of the working electrode in cm. This
method has been used to calculate corrosion rates for polarization curves
taken under kinetic rate control.
Transport Control of Anodic Reaction
The method to calculate corrosion rate derived in this section is aporo-
priate for a corroding systen in which the anodic (oxidation) reaction is
transport controlled but the cathodic reaction is rate controlled by chemical
kinetics. The form of the Stern-Geary equation that describes this situation
1s as follows:
cor
1 - exp (-
E - E
cor
be
(23)
Development of the method for corrosion rate calculation requires definition
of the following terms:
1)
2)
3)
4)
5)
1
I ...when
- Ecor> = ^
I - I«, when (£ -
1=1,, when (E -
v = exp(&E/bc)
I«
•-• - Ac
= -2AE
I
I
Based on these definitions the following expressions can be developed for
I
and r:
- l/v
and 13 - ICQr (1 - I//-)
75
-------
so that:
r =
= (1 - 1/v)
(1 - 1/v2) - (1 - 1/v)
The corrosion rate can then be calculated from:
= '
cor
Since L, and r are of known value:
I,
I
cor (1 - r)
(24)
The value of the cathodic tafel slope, b , can also be calculated in a
straightforward manner as fellows:
.
In r
(25)
Data taken under rate control by oxide film growth and transport corres-
pond to a situation where the anodic half-cell reaction is rate controlled by
solid-state diffusion, but the cathodic half-cell is not. Figure 20 shows a
polarization curve measured under conditions of transport control for the
anodic ha-lf-cell along with the appropriate data points necessary to calcu-
late the corrosion rate and cathodic tafel slope.
Figure 20. 3-Point Method for Calculating Rate Under Transport Control
by Anodic Reaction.
-------
The first data point (E,,L) is arbitrarily selected above E so that
- E
) = AE. Data point number two (E?)!?) is chosen so that
:cor) = -AE. The third dita point, (E.,VI3) is then chosen so that
J =
relationship:
- ECQr) = -2AE. The corrosion rate is then calculated from the following
I
cor
I
1
cor
(26)
and the corresponding cat'.iodic tafel slope:
b ._4L_
(27)
This method has been used to calculate corrosion rates from polarization
curves measured under oxide film growth and transport control.
Transport Control of Cathodic Reaction
The method derived next is appropriate for calculation of corrosion rate
and anodic tafel slope for a corroding system in which the cathodic reaction
1s transport controlled but the anodic reaction is rate controlled by
chemical kinetics. The form of the Stern-Geary equation thct describes this
situation is:
I E-E.
I - Icor j exp(-
'cor.
(28)
The following terms require definition for development of the method for cor-
rosion rate calculation:
1) I = Ij, when (E - Ecor) » AE
2) I = I2» W(ien (E " ECor'
3) I » I3, w-hen (E - ECQJ = -2iE
4) u = exp(AE/ba)
arid
5) r -
77
-------
Based on these definitions, the following expressions can be developed
for I., !„, U, and r:
1)
and
r »
'3 -
The corrosion rate and anodic tafel slope can then be calculated from:
I,
and
'1
b » AE/ln r
&
(29)
(30)
When the corrosion rate is controlled by transport through solution it
1s the cathodic half-cell that is diffusion controlled. This 1s observed
visually by the shape of the polarization curve. Figure 21 shows the
characteristic shape of a polarisation curve with a diffusion controlled
cathodic half-eel! reaction.
The first data point, (E,,!,), is arbitrarily selected above E so
A 1 CO)
that (E, - £„„.) •= vfiE, The second data point, (E-.lJ la selected below
1 CO! t. L
so that (£• - E " "AE* The third data P°1r'^ (^-3^0). 'S ehocen
below E_ , so that (E7 - E ) D ~2£.E. The corrosion rate and anodic tafel
•S' \f\ft
slope are calculated from:
[
and
(32)
78
-------
Figure 21. 3-Point Ftethod for Calculating Corrosion Rate Under
Transport Control by Cathodic Reaction.
Corrosion rates were calculated from polarization curves measured under
rate control by solution mass transport in this fashion. In fact, all corro-
sion rate values presented in Section 5 involve electrochemical measurement
and have been calculated by one of die three methods described here,
Instrument at jj3_n
The basic equipment required to generate a polarization curve consists
of an electrochemical cell, s device to control electroda potential, a ml 111-
voltnseter to measure eJectrcde potential, and a mlcroaifneter to measure4 eel!
current. The basic electrochemical cell is composed of three electrodes, the
working electrode where the reaction v-#hose rate is being measured occurs, s
reference electrode which along with a lugoin capillary allows rrieasurement of
electrode potential of the working electrode, arid a counter electrode which
1s used to provide a reaction site for the hslf-cell reaction not being
measured. The ce'l current which flows between the working and counter
electrodes is neasu^ed with a micro£..T?r.i>ter. Electrode potential is i^aeuced
with a roll 11 voltmeter as the potential drop batween the working as;ij reference
electrode^. A sirr-ple experirr^ntal syctor utich c;n bo used to ^--"-eraiv
polarlzaticn curves has been ^ublislied in a:s A5TH St.'s.KiTd (7) •'•"vl is p-h
79
-------
in Figure 22 below. By manually changing the electrode potential of the
working electrode with the potentiostat and recording the cell current that
flows at ea~h electrode potential value, one can generate a polarization
curve. This simple setup is not the actual experimental apparatus used on
this project. It is presented here solely for the purpose of illustrating
the basic manner in which a polarization curve is generated.
MILLIVOLTMETER
POTENTIOSTAT
MICROAMMETER
REFERENCE
ELECTRODE
Figure 22. Basic Electrochemical Cell for Corrosion Rate Measurements.
The experimental apparatus used in this study is somewhat more elaborate
than that shown in Figure 22 but contains the same essential electrochemical
cell and potentiostat setup. Additional instrumentation includes a function
generator (to sweep electrode potential linearly with respect to time), and
X-Y recorder (to record the plot of cell current versus electrode potential),
an IR Compensator (which allows removal of solution resistance effects in low
conductivity water), and a rotating disc electrode (which allows measurements
to be made under conditions of either kinetic or transport rate control). A
schematic diagram of the instrumentation used is shown in Figure 23.
This setup allowed a somewhat automated polarization curve generation
which tended to eliminate differences in operating procedures between runs
and enhance reproducibility. Each component of this apparatus will now be
described in greater detail.
80
-------
Function
generator
Potentiostat
, IR compensator
Electrochemical
cell
X-Y recorder
Figure 23. Experimental Apparatus Used in this Study.
Electrochemical Cell
The electrochemical cell used in this study is shown iri Figure 24. The
cell itself is a 1-liter Pyrex reaction vessel (Pyrex Resin Reaction Kettle.
Corning 0947) into which 800 ml of test solution is placed. A 1/4-inch thick
plexiglass lid covers the cell with holes drilled to allow insertion of elec-
trodes, thermometer (not shown), and gas dispersion tube (not shown).
o
Two 1-cm platimien foil electrodes were used as counter electrodes. They
were held in place by use of rubber cement and Nalgene stoppers. A hole was
cut in the bottom of a hollow Nalgene stopper just large enough for the top
end of a platinum foil electrode to pass through. The Nalgene stopper was
then placed on the electrode and fixed in place by filling the hollow cavity
with rubber cement. The Nalgene stoppers were of appropriate size to fit
firmly into the holes drilled in the plexiglass lid. Both platinum foil
electrodes were mounted in this way. A saturated Calomel reference electrode
was used. It was mounted by placing it inside a salt bridge with a water
tight seal. The salt bridge (luggin capillary) was held in its proper place
in the cell by use of a Nalgene stopper assembly similar to that used for the
counter electrodes. The salt bridge is then filled vrith test solution end its
tip placed close to the face of the working electrode. The working electrode
81
-------
Immersion
thermostat
Platinum (oil
electrodes
Saturated calomel
electrode
Figure 24. Electrochemical Cell used in This Study.
used was a copper rotating disc electrode, an instrument of adequate sophis-
tication that it warrants the further discussion provided next.
By drilling holes in the plexiglass cell lid anci mounting the electrodes
and thermometer by use of Mai gene stoppers, the cell could be assembled and
disassembled over and over without changing the precise spatial arrangement
of electrodes, thus eliminating a possible reduction in reproducibility due
to changing cell geometry*
When measurements were being made, temperature control was important.
For tliat reason the entire reaction vessel was immersed in a 10-liter
constant temperature water bath controlled by a Thermomix circulator Model
1441 BKUo This allowed temperature control to ±1°C over the range used (5°C
to 25°C).
Rotating Disc Electrode
The rotating disc electrode is used to remove solution mass transport
limitations on corrosion rate measurements. By rotating the electrode the
rate of mass transport of reacting species in solution to the electrode
82
-------
surface (as well as the rate of mass transport of aqueous phase reaction
products away from the electrode surface) in increased. At some rotation
speed, the mass transport rate is fast enough that it no longer limits the
rate of reaction, thus making a kinetically controlled rate accessible to
measurement. The instrument used is a Pine Instruments ASR.Rotator with a
DDI 15 removable end disc electrode. The apparatus is shown in Figure 25,
along with a rotation speed control box (not shown) that allows precise
setting of electrode rotation speed up to 10,000 RPM. The electrode is
rotated about its vertical axis by the electric motor and drive belt assem-
bly. The electrode is composed of a fltt circular copper disc imbedded in a
cylindrical teflon housing which rotates at controlled angular speeds.
Figure 26 shows the copper disc.
When rotating in solution, a well-defined hydrodynamic flow regime is
established. The flow regime becomes radial near the disc, even at low
rotation speeds, and sets up a reproducible and laminar hydrodynamic boundary
layer of constant thickness across the face of the disc. A diffusion layer
is set up within the hydrodynamic boundary layer across which reacting
species from the bulk must diffuse to reach the surface of the disc. Mass
transport to and from the electrode surface may become limited by molecular
diffusion across the diffusion layer, which is normally less than one-tenth
the thickness of the hydrodynamic boundary layer. The relationship between
diffusion layer thickness, SQ, and rotating speed, oo, as originally derived
by Levich (8) is:
£D= 1.61D1/3V1/6
-------
IUCTRJC WT08
BUT
ROT ATI KG
STftftt
Figure 25. Rotator for Rotating Disc Electrode.
\
\
r
*D
\
Diffusion layer
\
Hydrodynsmic boundary layer
Figure 2S. RotaMr.g Copper Disc Electrode.
84
-------
Although turbulent diffusion layers are sometimes used, and are discussed at
length by Pleskov and Filinovskii (10), the upper limit on rotation speed set
for a reproducible hydrodynamic boundary layer effectively li.nits electrode
use for mass transport. The rate of solution mass transport is related to
the diffusion layer thickness as follows:
Oc D(C - C )
.) = D — = - -- i- (35)
Here CR is the bulk concentration of diffusing species (moles/cm ),
^ o
C is the surface concentration of diffusing species (moles/cm ), and J is
^ p
the mass transport rate (moles/cm sec). When equations (33) and (35) are
solved simultaneously, the explicit dependence of J on <^> is showi.
D2/3(CR - Cc)o
J= - - - £* - (36)
1.61 O176
As rotation speed, w. is increased the thickness of the diffusion layer, £_,
is reduced bringing the bulk concentration of diffusing species closer to the
surface of the rotating disc. This increases the concentration gradient and
therefore the mass transport rate. For reactions with slow kinetics, such as
molecular reduction, solution transport limitations may be eliminated at
rotation speeds of less than 10^0 RPM.
Potentiostat
The potentiostat is pernaps the most important piece of electronic
instrumentation necessary for electrochemical corrosion rate measurements. A
variety of conmercial instruments is- available. All of them provide a means
of controlling the electrode potential of the working electrode, sows have
other built-in conveniences such as a voltmeter for electrode potential
measurement and an anmeter for cell current measurement. An Aardvark Model V
Standard Laboratory Potentiostast, built by Floyd Bell Associates, Inc. was
used in this study. This potentiostat contains multiple scale electrode
potential and cell current measuring devices as well a? X-Y recorder jacks so
that electrode potential and cell current can be plotted directly. An exter-
nal voltage source input is included also which allows one the option of
85
-------
either setting and changing electrode potential manually or having the elec-
trode potential changed automatically by an attached external voltage source.
Finally, the potentiostat contains shielded inputs for connection to each of
the electrodes in the cell.
Function Generator
A function generator is used as an external voltage source to control
the time rate of change of electrode potential of the working electrode. The
instrument used in this study is an Aardvark Model Scan-3 Electronic Poten-
tial Scanner manufactured by Floyd Bell Associates, Inc. for use with the
Model V Potentiostat. The potential scanner produces an output voltage that
changes linearly with respect to time, at a controlled rate of change. This
output voltage is applied to the external voltage source input of the
potentiostat, which then applies the linear change in voltage with respect to
time to the working electrode/solution interface.
IR Compensator
Generation of a polarization curve requires measurement of electrode
potential of the working electrode while current is flowing through the cell.
As the current flows out of the working electrode (when it is an anode) and
passes through solution, a potential drop is generated between the electrode
surface and the tip of tne salt bridge (reference electrode) due to the
resistance of the solution to current flow. Figure 27 shows this situation.
This potential drop is sometimes small and of little consequence, but in
low conductivity solutions the solution resistance can be large enough that
the IR , term distorts the measurement of electrode potential even at low
sol n
cell current values. This extra voltage drop is called the IR drop and it
shows up as either a positive or negative error in electrode potential
measurement, depending on the direction of flow of cell current (that is
whether the working electrode is acting as an anode or a cathode). When IR
drop is present the measured potential between the working and reference
electrode is:
E = E + IR , (21)
rr.eas soln
86
-------
REFERENCE . *
ELECTRODE ~~
1
1
1
1 'J
AT: 1-0 ' I/
W^B^VBBl
WORKING
""ELECTRODE
E
AT: J«iO
1R
Olstsncs
Figure 27. Solution IR Drop.
Where Em is the measured voltage drop, E, ^s the working electrode poten-
tial, and IR , is the voltage drop due to solution resistance.
The effect of solution IR drop can be eliminated electronically by use
of an IR Compensator. An Aardvark Model IRX IR Compensator, manufactured by
Floyd Bell Associates v:as used in this study. This model is manufactured for
use with the Aardvark Model V Potentiostat and is easily inserted into the
system between the potentiosU.t and i.he cell electrodes. By dialing in &
compensating resistance approximately equal in value to the solution resis-
tance between the tip of the salt bridge and the working electrode surface
the solution resistance is effectively rernov3d from the measurement of
electrode potential. The Model IRX allows insertion of up to 100,000 ohms of
compensating resistance, which would handle even distilled water.
Analytical Procedure
In order co ensure reproducibility and be able to compare corrosion rate
measurements made at slightly differing solution composition it was necessary
to develop a uniform laboratory procedure that would ensure thst all experi-
87
-------
mental runs were conducted as nearly as possible in an identical fashion.
This included standard procedures for equipment preparation (electrodes,
cell, and test solution). pH and conductivity measurements, final setup of
instruments and actual measurement. The details of these standard procedures
are outlined in this section.
Equipment Preparation
Each morning it was necessary to turn on the pH meter, IR compensator,
and potential scanner one-half hour prior to use for warmup, after which it
would operate consistently all day. Other equipment such as electrodes,
glassware, and test solution required fresh preparation prior tc each experi-
mental run.
Three different copper disc electrodes were used on a rotating basis
throughout the study. Each was polished before an experimental run first
with Metadi Diamond Polish (5 micron)/deionized water rinse followed by
polishing with 0.05 micron-alumina (Buehler Micropolish)/deionized water
rinse, and finally cleaned for five minutes in a Branson B-220 Ultrasonic
cleaner filled with fresh distilled water/deionized water rinse. This was
followed by immediate inversion into test solution for corrosion rate
measurement.
Two platinum foil counter electrodes were used in each run. The sane
two were used each time but were cleaned between runs using a Bon Ami/water
solution and Q-tip cotton swabs. This was followed by rinsing three times
with distilled deionized water and immersion into the test solution.
The saturated calcoiel reference electrode required daily check of
solution level, uncapping, and insertion into the salt bridge for use
throughout the day. The salt bridge was filled with test solution once each
day and was merely rinsed with distilled dsionized water between runs. At
night it was dipped in Nitric Acid wash end stored in deionized rinse water.
Tha pyrex reaction vessels and plexiglass lid were immersed in the 6N
HN03 wash overnight, then removed and generously rinsed with distilled water
prior to contact with test solution. Normally two reaction vessels were used
each day. Between runs, the vessels were rinsed three tinas v^ith distilled
water followed by -3 final rinse with distilled deionized water. By using tvo
83
-------
vessels preparation for the next run could begin prior to completion of the
present one.
Test solution composition *as varied between runs. A standard mix of
synthetic Tolt River water was prepared, 10 liters at a time, using reagent
grade chemicals and glass distilled deionized water. The standard mix
contained the principal inorganic anions and cations found in Tolt River
water, without trace elements and organic constituents. All anions were
added as either acids or salts of sodium or calcium. The composition of
synthetic Tolt River water is shown in Table 6.
Prior to each run the synthetic Tolt River water had to be temperature
equilibrated in the constant temperature water bath to the temperature speci-
fied for that run and than the pH was adjusted to its desired level by addi-
tion of 0.1 M CaO using an eyedropper.
! Table 6
| Synthetic Tolt Composition
i
j Concentration Synthetic
! Species Range in Tolt River ToU Concentration
I „
I HCO" 1.4-4.5 mg/1 as CaC03 2.47
! d" 1.3-2.6 mg/1 2.49
I
j F" 0-1.01 mg/1 0,95
i SO! 1.95 1.94
Si02 4.20 4.20
ph 6.0-6.3 6.3
k 25 umhos/cm 18 ymhos/rm
pH And Tcmpe rat ure Mea s u reme nt
pH and conductivity measurements were made on the test solution prior to
and following each test run. On occasion pH was followed continuously
throughout a run. pH was measured with a Ketrohm/ Brinkman Model: p'H-104
89
-------
Digital pH meter using a Beckman glass pH electrode with a Beckman, Altex,
ceramic junction, Silver/Silver Chloride reference electrode. The pH meter
was normally calibrated at least once daily at the temperature at which
experimental runs were to be made. Calibration at pH = 6.86 was found to be
adequate since most measurements were made between 6.0 _< pH _< 9.0. The test
solution was stirred during pH measurement and a response time of roughly 10
minutas was four.d necessary for stabilization of pH in low conductivity
water.
Conductivity was measured with a Barnsted Conductivity Bridge Model
PM-70CB, using a Barnsted Model E3421 conductivity cell with a 0,1 cell
constant. This cell with its electrodes was directly immersible in the test
solution and completely self-contained. The instrument required little
calibration or maintenance, just a rinsing of the cell electrodes with dis-
tilled deionized water prior to and following each use. Between uses the
cell wa--; immersed in distilled deionized water which was changed daily. The
instrument response time was fairly rapid except at low conductivities (below
approximately 30 pmhos/cni) when 8-10 minutes was needed for stabilization.
Final Setup And Measurement
When preparation of the electrodes, cell, and test solution is complete
along with pH and conductivity measurements on the test solution, the
electrochemical cell is then assembled by placing the electrons in the test
solution and hooking up the shielded electronic leads that run betvjaen the
electrodes and the potentiostat. A reducing potential (approx. 200 mv below
E ) is placed on the working electrode to prevent any oxidation from
occurring. The X-Y recorder is zeroed and calibrated and appropriate IR
compensation is dialed in for the upcoming test run. The potential scanner,
set at the appropriate scan rate, is then turned on end the voltage scan
begins. The electrode potential of the working electrode is then followed.
as it changes with respect to time, on the X-Y recorder which keeps a plot of
electrode potential and the corresponding cell current. The potential
scanner sweeps the electrode potential of the working electrode in a positive
direction through E „ and on to a value approximately 150 mv positive of
E „. The magnitude cf the cell current starts off negative indicating that
a net reduction reaction is occuring at the working electrode. Gradually
-------
this current is reduced to zero as the potential is swept through the
corrosion potential. It then increases in the positive direction as the
oxidation half cell takes over at potential values more positive than E
From this plot, the corrosion rate is calculated which corresponds to the
composition of the test solution used in that run. By varying the concen-
tration of a desired solution parameter and making corrosion rate determina-
tions at each concentration one may determine quantitatively the effect of
that parameter on the corrosion rate.
Sources of Error in Corrosion Rate Measurement.
Each of the following effects could significantly impact the accuracy or
reproducibility of measured corrosion rates:
1} interfering reactions;
2) stability of environmental conditions;
3) calibration of instrumentation; and
4) appproximations involved in corrosion rate calculation
When corrosion rates are determined from polarization curves using the
method of Barnartt an assumption that the measured cell current contains
contributions from only the anodic and cathodic ha~lf-ce!lr of the corrosion
rate is implied. When other redox couples are present in solution and
reactive within the 200-400 MV range of swept electrode potential they may
contribute to the ove~a11 cell current causing the shape of the polarization
curve to depart somewhat from that predicted by the Stern-Geary model. Minor
interferences reduce the accuracy of the corrosion rate calculated from the
distorted polarization curve. Minor interferences can distort the shape of
the polarization curve to the extent that it is impossible to calculate a
corrosion rate estimate. This source of error is minimized by using solu-
tions of known composition and impurity level.
Variation of system properties during the course of a mt ..5uresent is
another possible source of error in corrosion rate determination. The
principal environmental variables in this research vvere temperatura, solution
pH, and diffusion layer thickness. Temperature was maintained at a constant
value by use of the inversion thermostat and water bsth configuration
described earlier. It was continuously monitored throughout each run and
. 91
-------
possible deviations due to heats of reaction were negligible. Temperature
was at all times maintained within ±1°C of its prescribed value.
Constant solution pH could be maintained throughout a run only when the
solution buffer capacity was adequate to neutralize the amount of hydroxyl
ion produced during the course of a measurement.
In general, pH variation throughout a run was less than approximatley
0.3 pH units, despite the low alkalinity level of synthetic Tolt River water.
Largest deviations occurred in runs taken under kinetic rate control at 25°C
in the range 7.0 _< pH <_ 8.5 where the variations sometimes exceeded 1.0 pH
unit. When this occurred, additional alkalinity in the form of bicarbonate
was added (approx. 10 rug/* as CaCO-j) and the measurement was remade.
Diffusion layer thickness was well-defined and stabilized in measure-
nents made under rate control by interfacial reaction kinetics and oxide film
growth by rotating the rotating disc electrode at 3000 RPM for each run.
Under conditions of stagnant diffusion, diffusion layer thickness was less
well defined but data shown later was very reproducible.
Improper calibrations of electronic instrumentation is an obvious source
of error. During the course of this study it was found that the critical
calibration was that of the zero point of current on the X-Y recorder. Even
a small offset between an i = 0 reading on the microamseter (in the potentio-
stat) and that on the X-Y recorder can cause a large distortion in the shape
of the polarization curve. Similar offsets in measurement of the zero of
electrode potential are not nearly so critical in effecting corrosion rate
values. These errors were minimized by offset calibration of the X-Y
recorder before each run.
The final source of error discussed here involves the corrosion rate
calculation itself. Using the method of Barnartt a measured polarization
curve is evaluated as through it conformed exactly to the exponential
of the Stern-Geary model. Although this model represents a simplified
version of the corrosion process, for most polarization curves it adequately
defines the shape of the curve. The numerical method developed by Barnartt
then gives a precise and accurate value. Under these conditions the calcu-
lated corrosion rate is in theory independent of the size of AE used in the
calculation. Problems with this method arise when the polarization curva,
92
-------
for whatever reason, doesn't quite fit the Stern-Geary form. Under kinetic
control, ICO|_ can be calculated from the following expression:
'l
h
2
- 4.0
12
h
1/2-
1/2
cor
J
where the values of l^t l^t and I3 depend on the size of AE chosen. When the
measured curve fits the model well the same I value is calculated over a
wide range of choices of AE. When the curve does not fit the model well, it
may still be possible to calculate reasonable corrosion rate values but care
must be taken in the choice of AE. A value too large or too small may cause
the denominator in the above relationship to approach zero, thereby causing
the calculated corrosion rate to approach infinity. Figure 28 shows a plot
of I values calculated from the same polarization curve but using differ-
ing AE values. A choice of AE < 20 MV drives the corrosion rate value
calculated from the mod°1 toward infinity. Likewise a choice of AE > 32 does
the same thing. Reasonable values must be chosen from within tK; range 20 _<
AE £ 32. Calculated cOTCsion rates reported in the following chanter were
made largely using a AE = 30 MV since I was approximately constant with
respect to AE at that value.
The overall reproducibility of these measurements was quite good when
the four possible sources of error mentioned above were accounted for. Table
7 shows the results of six runs under identical conditions of temperature,
pH, and
-------
VD
ill
1.0 -
z °
O o 0.8
O ^
££
O
0.6
16
24
32
40
44
Figure 28. Variability in Three-Point Method.
-------
Table 7
Corrosion Rate of Copper in Synthetic Tolt River Water
Electrochemical Measurements
Corrosion Rate Corrosion Rate
Run No. (pA/cm2) (MPY)
1
2
3
4
5
6
MEAN
STD. DEV.
0.51
0.55
0.56
0.48
0.55
0.48
0.52
± 0.04
0.23
0.25
0.26
0.22
0.25
0.24
0.24
± 0.02
with the method used for calculating corrosion rates will be discussed in
this section.
Laboratory Setup and Procedure
Detailed guidelines are available for conducting weight loss coupon
tests. The laboratory setup and procedures used in this research are similar
to those outlined in RACE Standard TM-01-69 (1976 Revision) entitled "Labora-
tory Corrosion Testing of Metals for the Process Industries" (11) and
ANSI/ASTM Gl-72 (Reapproved 1979) entitled "Standard Recorcnended Practice for
Preparing, Cleaning, and Evaluating Corrosion Test Specimens" (12). The
tests consisted of preparing and weighing copper test specimens, immersing
them in synthetic Tolt River water for a controlled time period, removing the
corrosion products and reweighing. The corrosion rate was then calculated
from the difference in mass due to formation of corrosion products during the
immersion period.
Copper specimens v.
-------
mentioned earlier by segmenting the rod into discs. Hole were drilled in the
center of each disc for purposes of suspending the specimen in tne water.
Each specimen was individually suspended in a test tube filled with synthetic
Tolt River water. Figure 29 shows the details of how this was done. In all,
nine specimens were used. Test tubes containing the specimens were placed in
a test tube rack and lowered into a constant temperature water bath which ran
continuously throughout the testing period, keeping the temperature of the
test solution at 25°C. Figure 30 shows how this was done.
The teflon string suspending the copper specimens was tied to the
Nalgene stoppers through small holes in the.- bottom of the stoppers. The
holes were small enough to effectively keep the water in the constant
temperature bath from splashing into the test tubes and contaminating the
test water. Although small, the holes did allow air flow in and out of the
test tube so that reduced levels of 0? in the test water were avoided. The
test watiir was changed daily by filling a clean test tube with fresh water
and then transferring the coupon, which was still attached to the nalgene
stopper by the teflon string, to the new test tube. This was a simple
process which did :-ot require touching the corroding copper specimens, since
transfer from one test tube tc another was made by holding the nalgene
stopper, and involved less than a 10-second contact time between the copper
coupon and the ambient air. Synthetic To'lt water used for replacement was
prepared, as described earlier, in 10-liter volumes from reagent grade
chemicals and distilled deionized water. New batches were made up ds needed
which turned out to be roughly every 3 to 5 days. Each specimen was identi-
fied by a number on its attached nalgene stopper and its date of immersion
was recorded. At least. 2 and normally 3 specimens were immersed for the same
test period as replicates.
Prior to immersion each specimen was abraded with No. 240 and then No.
600 grade silicon carbide sand paper which removed a substantial layer of
outer metal. This was done to reduce surface roughness as well as to elimin-
ate variations in metallic surface conditions between specimens at the time
of initial immersion. Specimen dimensions were measured with a micrometer
caliper frcsn which surface area calculations were made. This v/as followed by
scrubbing the specimens with Bon Ami (a nonchlorinated and mild scouring
powder) and a firm bristled tooth brush, rinsing with distilled water, air
96
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SYNTHETIC TOLT
RIVER WATER
COPPER
SPECIMEN
\
TEST
TUBE
Figure 29. Test Tube Containing Weight Loss Coupon
CONSTANT TEMPERATURE
WATER BATH
COPPER SPECIMEN SYNTHETIC TOLT
ItfllERSIOH
THERMOSTAT
Figure 30. Weight Loss Test Apparatus.
97
-------
drying, and weighing on a Metier Analytical Balance (Type K6). Specimen
number, weight (to nearest 0.1 mg), surface area, and date/time of immersion
were then recorded for later use.
When a specimen had been immersed for the desired time period it was
removed from the test solution and scrubbed to remove corrosion products
(using cold water, Bon Ami, and a strong bristled brush). The corrosion
products formed on the copper specimens were principally a dull rust color,
which corresponds to hydrated cuprous oxide (13). Occasionally, patches of
black cupric oxide are observed. As the oxide films are removed from the
copper, its surface becomes very bright. This brilliance was used as an
indication that corrosion products had been successfully removed. Specimens
are then rinsed, air dried, and weighed on an analytical balance.
Calculating Corrosion Rate from Weight Loss Data
The rate of uniform corrosion can be calculated from weight loss data
for each coupon by use of the following relationship:
o - . . 534
(MPY) ~ TArea) (Time) (Metal Density)
Here RMv is the corrosion rate in mils/year, 534 is a unit conversion
factor, weight loss is in milligrams, area is in square centimeters, imner-
2
sion time is in hours, and metal density is in grams/ on . The density of
copper is 8.91 gm/cm . .
Since coupons were immersed for varying time periods, the corrosion rate
was determined by plotting weight loss versus time for all coupons, the slope
of which is the corrosion rate. A weight loss parameter, B, was calculated
for each coupon as follows:
B = (Mt. Loss) 534 ,^
(Area) (8. 91 gm/cnf)
U'hen B is plotted versus immersion time (hours) and a straight line is
regressed between the data points, the slope of that line is the corrosion
rate in mils/year.
Results of the weight loss tests are plotted in Figure 31 in the fashion
described above. Data shown run from an immersion tiir.2 of one to four
98
-------
months. The slope of the regression line is shown to be 0.23 MPY, a value
that compares quite favorably to the electrochemical corrosion rate measure-
ments of Table 7. Those measurements were made under identical conditions
and produced a value of 0.24 MPY. Based on this comparison it was concluded
that the rate of the corrosion reaction was being measured correctly by the
electrochemical system. Coupons immersed for periods longer than four months
showed signs of localized corrosion, pitting, and were not very reproducible.
Measured rates were slightly higher ranging from 0,23 MPY to just above 0.30
MPY for immersion times of seven months.
1000 1
500
SLOPE-0.23 f
R-0.91
1000 2000
TIME (HRS.)
3000
figure 31. Weight Loss Test Results.
99
-------
SECTION 6
EXPERIMENTAL RESULTS AND ANALYSIS
INTRODUCTION
The results of experiments designed to be under rate control by each of
the component rate processes are presented in this chapter. Whenever pos-
sible these results are compared to theoretical models developed in Section 4
which describe the variations of each component process with respect to pH
and temperature. This chapter begins with an explanation of methods of ana-
lysis developed for use in heterogeneous systems. A presentation and ana-
lysis of data taken under rate control by interfacial reaction kinetics fol-
lows with development of quantitative- rate expressions. Presentation and
analysis of data taken under rate control by oxide film growth and under rate
control by solution mass transport follow. Appropriate rate expressions and
possible mechanisms are developed. The chapter closes with a summary of
findings and conclusions.
Many of the experiments reported on in this chapter were designed to
completely eliminate the effects of solution mass transport and allow inde-
pendent quantification of the underlying rate control1 ing process which could
be either an interfacial reaction or oxide film growth depending on the con-
ditions at thf. electrode surface. Design of these experiments was based on
the assumption that the rate controlling diffusing species was molecu'iar oxy-
gen, whose mass transport rate is increased significantly even at low RPM.
It was later determined, as is described below, ti.et the rate controlling
diffusing species is not 0, but a reaction product which must diffuse away
- ?+
from the electrode surface. In theory, that species could be OH , Cu , some
Cu(OH) 2~n complex, or a combination of some or all of those species. Since
the stagnant diffusion data, presented later on, were fit quite well using
OH" as the diffusing species, the analysis that follows presumes that OH~ is
the rate controlling diffusing species.
100
-------
Experimental elimination of solution mass transport effects is more com-
plicated when the diffusion species is a reaction product. Under' such condi-
tions the effect of diffusion on the overall rate may persist, f.ven at high
RPM making it more difficult to quantify the pH and temperature dependence of
the underlying rate process. Special analytical ratthods are r2cessary to
evaluate such data.
A method of analysis is presented here that allows quantification of
rate data under conditions where an underlying rate process and solution mass
transport both affect the overall rate. For the data presented here, both
the rate of the underlying process and the rate of mass transport are
dependent upon the interfacial OH" concentration.
The rate of hydroxyl ion, [OH~], diffusing away from the electrode into
bulk solution. It can be written as follows:
Dnn
RMT - Tjj (D
Here C and CD are the surface and bulk hydroxyl ion concentrations in
1 2
(moles/cm ), DrH is the hydroxyl ion diffusion coefficient (cm /sec),
-------
R = Rmt - pk
Equating the rate expressions produces the following:
8 cs '
U = n - CR (4
DOH B
which yields the expression:
,jC*b - (C* -1) (5)
In logarithmic form this becomes a linear1 relationship
log v + b log C* = log (C* -1) (6)
with slcpe b and intercept, leg u. Figure 32 shows a plot of log C* versus
log (C* -1). The three regions of constant slops (I, II, and III) are of
physical significance in that they correspond to conditions of complete
kinetic rate control, mixed kinetic and mass transport rate control, and
complete diffusion control.
In Region I, log C*sO so C & I and:
The process therefore proceeds at a rate defined by the rate of the under-
lying rate process with a rats expression ot the form:
102
-------
o
CO
3.00
2.00
LOG C
1.00
0.00
-2.00 -1.00 0.00 1.00 2.00
LOG( C*-l )
Figure 32, Frank-Kamenetskii plot for data taken in heterogeneous systems.
-------
R - a Cb .a CBb
Data points that fall in this region are then analyzed by plotting log 1
v. pHp, since:
'B
R - Kio'6)
R --L—L
-3 pHb
and: CB = 10 ° KW 10
then: I = [(HEl_)(i0-3 KJb] + 10
10"b w
• og I = log[(10"3 Kjbl + b PHR
10"
Regression of log I values on their corresponding pH0 values allows deter-
o
mination of b, as the slope and
Kw)b]
w
as the intercept. From this value of the intercept, a can be calculated.
When the underlying rate controlling process is an interfacial reaction the
regression parameter, a, is an Arrhenius type rate constant which is tempera-
ture dependent:
a = A exp(- /T)
KG i
E, is the activation energy for the rate controlling step of the surface
a
reaction in (calories/mole °K), A is called the frequency factor, and RG is
the universal gas constant. When values of a are knwn at several tempera-
tures, In a can be plotted versus 1/T (°K"1) since:
In e = In A -(^) j
G
Regression yields the value of In A as an intercept and -EA/Rg as the slope.
.104 .
-------
In region II, the rate of the overall process is jointly controlled by
the rate of the underlying process and solution mass transport. That is, log
C > 0 but not large enough to .Tiake any simplifying approximations. Deter-
mination of a and b is therefore accomplished in a different fashion than in
region I. Here both rate processes are at work at rates of equal magnitude:
R - D- (r r \
RMT - ?„ (CS - V
so
Substituting this relationship for C<. into the rate expression for the
underlying rate process we get:
Since the overall rate, R, is equal to R., and R^y. we can write:
* - .(Ca + V >"
d UOH
This rate expression is now in a form suitable for determining coefficients,
a and b, for the underlying process rate expression from data measured under
joint kinetic/mass transport rate control. Taking logarithms, base 10, of
both sides of the expression above we get:
log R = log a + b log(Cp + -?i — )
D UOH
Defining new variables Y and X, and coefficient a1 wa have:
Y = log R
-------
and the following linear relationship:
Y = a' + bX
By transforming each data point into the form of Y and X, we can by
linear regression find values for a' and b. From a1 we can determine a.
The measured corrosion rate, Icor(iJA/i;m ) > can De converted into a Y
value by noting that:
and:
Y = log R = log
Here n is the number of electrons transferred per mole of OH" produced, n
1. F is the farraday constant, 96,485 coul/eq, and I is the measured
p
corrosion rate in (u./cnr ).
t\
X can be determined for each data point by noting that:
3
= (10 J) Kw 10
pH
9.08 x 10"2 D1/3
n c
0.5
(for RDE at 3000 RPM)
(for Stagnant Dlffu-
and
X = log [Cg + ~
OH
The values of K , Dn,,, and \J are all temperature dependent but knov/n, so
W Un
that for 9 given data point:
cor'
> T
corresponding values of X and Y can be calculated. Vlhen Y is plotted versus
X the slupe of the regression line will be constant over a range of data
where a single reaction mechanism is operating.
In range III, C* » 1, so that C$ » C3 and
(cs-cB)scs
105
-------
This corresponds to a situation where the overall rate is completely con-
trolled by diffusion in solution. The appropriate rate expression is then:
Under these conditions GS generally increases to some steady-state or satura-
tion value (2), which may or may not be related to the value of Cg. Cs
becomes independent of CR when its magnitude is controlled by some other
reaction going on in solution, such as precipitation. Under these circum-
stances the overall rate may be represented as:
D Ce
where C is a concentration in equilibrium with other species in solution.
It may be temperature dependent. A plot of I versus pH3 for data taken under
these conditions is a straight line with slope of zero and intercept at:
T
For the case where C<- is dependent upon Cg, a general form relating their
values is:
cs - peg
so that the overall rate expression becomes:
DPCB
p = 2.
A plot of log I v. pHQ is now a straight line of the form:
nFDn,, p(10"3 K )b
log I = log[ ^ —»L_] + b PHR
10"b
-------
,„
io-
can be determined by linear regression. The value of p can be determined
from the slope and intercept values. The general form of the. rate expression
for reactions completely diffusion controlled is then:
io-6 cT0
Data falling into region III are then analyzed by plotting log I vs. pHR and
regressing to find b and p. As b - > 0, p - > C a limiting case where
C_ is independent of CR.
A recapitulation of the methods necessary for analysis of data falling
Into regions I, II, and III is given in Table 8. It shows explicitly that
analysis of data falling into regions I and III is much simpler thsn in
region II, requiring only a plot of log I versus pHn, linear regression, and
direct calculation of appropriate parameter values. While analysis of data
In region II requires calculation of transformed variables X and Y first and
then regression. Calculation of appropriate parameter values is complicated
in this region when the temperature dependence of data taken under these
conditions reflects the joint effects of a changing rate of surface reaction
and a changing rate of diffusion in solution.
Initial experimental design was then an attempt to generate data only in
regions I end III. Experiments designed to be under rate control by inter-
facial reaction kinetics should give data in region I, completely free of
solution mass transport effects. Experiments designed for rate control by
oxide film growth and transport should also give data in region I, free of
solution mass transport effects. Experiments designed to be under rate
control by stagnant diffusion in solution should then give data in Region
III. The extent to which this was successful becomes apparent as the dsta
taken under each type of rate control are examined.
108
-------
Table 8. Summary of Data Analysis Methodology
REGION I; COMPLETE KINETIC CONTROL
a) Rate Expression: I = c 10
where: c = (-^-A-MIO'3 Kjb , I =* uA/cm? a =• A exp(-
10°° w "G
b) Form for Regression: (Determine a and b)
log I = log co + b PI-L
REGION II; MIXED KINETIC/MASS TRANSPORT CONTROL
a) Rate Expression: I * (~^) C^
where C is determined frosn rb _OK ,r r .
numericll solution of: aLS = ^~ ILS " ^'
b) Form for Regression: y a a' * bX (determine a and b)
-6
where: y « log (•=—^-~p—i-)
,3 pHB I(10-6)6
x » log DO K.. 10 + —mi—"-]• a< a Io9 a
w ni- UOH
REGION III; CO??LETt DIFFUSI_OJj_CQfiTROL
a) Rate Expression: I » (——-—-^-r~—^—) i0
io"b6D
b) Form for Regression: (determine a and b)
nF 0OH P (10~3 K )b
log I « log [—• -—£-,——~~ ^ + b PHB
10"° 0D
109
-------
RATE CONTROL BY INTERFACIAL REACTIONS KINETICS
Data presented in this section resulted from experiments designed to
measure corrosion rates under the conditions of rate control by interfacial
reaction kinetics. It was assumed that by minimizing the influence of the
other component rate processes that the dependency of the rate of the con-
trolling interfacial reaction on solution pH and temperature could be deter-
mined quantitatively. Experimentally this meant running polarization curves
on freshly polished copper electrodes rotated at 3000 RPM. Any oxide film
present on the copper surface was effectively removed by polishing the sur-
face, eliminating the influence of solid-state transport through an oxide
film on the overall measured rate of corrosion. Rotation of the rotating
disc electrode at 3000 RPM substantially decreases the thickness of the
diffusion layer for OH", H+, Cu2+ and 02 and thereby reduces the influence of
their respective rates of mass transport on the overall rate of the process.
So the measured corrosion rate was intended to correspond to the rate at
which the rate limiting interfacial reaction is taking place. This could be
the metal dissolution, early stage oxide film growth, oxide film dissolution,
or molecular oxygen reduction reaction. Rate variations with respect to pH
and temperature are then used to compare measured data with theoretical rate
expressions.
Data taken in this fashion at 25°C are shown in Table 9. Standard mix
synthetic Tolt River water with pH adjustments made by CaO addition was used
in each run. Details of the composition of this solution were shown earlier
in Section 5. Values of pH and conductivity recorded in Table 9 are an a
average of those measured at the start and completion of each run. Corrosion
rate values have been calculated from polarization curves by the method of
Barnartt. R is the amount of resistance necessary to compensate for the
voltage drop due to solution resistance between the working and reference
electrodes. The recorded temperature is that of the solution which was
maintained at a constant, value throughout each run by use of an immersion
thermostat and water bath.
*
Figure 33, shows a plot of the data in the form of log C versus log
(C -1). Here C was calculated in the following fashion:
110
-------
Table 9. Kinetic Rate Control Data: 25°C
Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
10
16
17
18
19
20
21
22
23
T
(t)
^
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
2S
25
25
25
25
25
25
1*
7.88
7.63
9.22
8.37
8.63
6.25
6.57
6.71
6.35
6.51
6.65
6.24
6.90
6.05
6.54
6.59
7.02
7.10
7.33
7.64
7.63
7.66
7.68
I
0.53
0.99
0.63
0.89
O.ES
2 JO
• oo
1.84
1.44
2.99
1.S8
. 1.64
2.62
1.52
3.35
1.61
O.SO
0.96
0.55
0.74
0.70
1.06
1.26
0.66
2) RPM
3000
3000
3000
3000
3000
3v/00
3000
3000
3000
3000
3000
3000
3000
3000
3000
3000
3000
3000
3000
3000
3000
3000
3C03
X
16.2
16.3
18.6
19.0
20.8
15.8
14.7
15.2
14.3
14.7
15.0
13.9
15.5
-
••
-
-
-
-
-
-
-
-
"Q
22.000
21,000
19,000
18,000
-
21,000
21.000
21,000
23,000
22,000
22.000
23,000
21,000
27.000
25.0CO
20,000
21.000
26.000
18.000
19.CQO
16.000
17, CM
16.000
log C*
0.06
0.23
0.05
0.05
0.02
1.69
1.21
0.96
1.62
1.28
0.83
1.67
0.83
1.9S
1.18
0.58
O.SP
0.37
0.31
0.170
0.24
0.26
0.26
PHS
7.%
7.87
8.27
8.41
8 64
7.95
7.77
7.69
7.97
7.80
7.73
7.91
7.73
8.01
7.72
7.57
7. £9
7.47
7.64
7.81
7.67
7.S7
7.58
111
-------
Table 9 - Continued
Run
24
25
26
27
28
29
30
31
32
33
34
35
35
37
38
T
(t)
25
25
25
25
25
25
2S
25
25
25
25
25
25
25
25
PH
7.76
7.80
7.75
7.89
7.92
8.00
9.19
9.25
9.37
9.87
9.91
O.S5
7.76
8.80
9.15
1 •>
(uA/cmZ)
1.41
0.64
0.71
1.17
0.78
1.04
0.42
0.51
0.55
0.3S
0.23
0.29
1.11
O.S8
0.43
RPM X
3000
3000
3000
3000
3000
3000
3000
3000
3000
3000
3000
3000
3000
3000 20.9
3000 20.7
RD
24,000
22,000
17.700
10,500
19,000
23.000
14,000
12,000
11,000
7,700
8.100
7,000
21,000
16,000
16.000
log C*
0.24
0.010
0.14
0.16
0.11
0.12
0.00
0.00
0.00
0.00
0.00
0.00
0.2S
0.01
0.01
PHS
8.00
7.92
7.89
8.05
8.03
G.13
9.19
9.25
9.37
9.87
9.91
9.96
3.00
0.80
9.15
112
-------
2.0 J
1.0
0.5
-2.0
-1.0 0.0
LOQCcf-1)
1.0
Figure 33. Frank-Kamenetskii plot of kinetic data at 25 C.
2.0
-------
? nF D
I(yA/cmZ) = - p- (C .. CR)
-6 ' s B
- -pHD
c^ 10 "3cTn i 10 B
so that: C =(—) = (!+ - D— - }
CB nF DOH Kw
Each data point, (I, pHg) , has been determined under conditions of controlled
tempc-rature and diffusion layer thickness, so that C* may be calculated and
the plot of Figure 33 produced.
The plot of data points in Figure 33 is quite different than that
expected based on the experimental design. That is, these data were expected
to be either completely or nearly completely controlled by the rates of
interfacial reaction which means that all- data points should fall along or
close to the log C =0 axis with log (C -1)1 -0.8. In fact, only a few
of the data points actually conformed to this expectation. Most fall into
reaions JI and III indicating mixed kinetic/solution mass transport rate
control and complete solution mass transport rate control respectively. It
is interesting to note that each of these regions corresponds to a bulk
solution pH range:
Region I: 8.63 < PHg < 9.95
Region II: 7.02 < pHB < 8.63
Region III: 6.05 < pHg < 7.02
indicating that as the solution pH is increased from an initial value of 6.05
to a value greater then 7.02 rate control of the overall process changes from
complete diffusion control (Region I) to mixed rate control. When the pH is
raised above pH = 8.63 the overall process is controlled by the rate of the
underlying rate process. Each data point must then be evaluated in terms of
whether it falls into regions I, II, or III and then subjected to the type of
dfita analysis appropriate for that region.
Data taken at 15°C are shown in Table 10. The plot of Figure 34 shows
that most data taken at this temperature fall into -.'eg ion III, with a few
data points in region II but none in region I. Here the region of rate
-------
2.5
2.0
1.5 -
O
1.0
0.5 i
T-16"C
-1.0
0.0 1.0
LOGCCf-1)
2.0
Figure 34. Frank-Kamenetskii plot of kinetic data at 15 C.
-------
Table 10. Kinetic Control Data:
Run
I
2
3
4
5
6
7
0
9
10
11
12
13
14
15
16
17
T
CO
15
15
15
15
15
15
15
15
15
IS
IS
15
15
IS
15
IS
15
pH
6.22
6.27
6.52
6.86
6.93
7.4Z
6.65
7.54
6. SO
6.04
7.52
8.00
8.10
7.52
7.45
8.19
6.05
2
3
2
2
1
1
1
(uA/on2)
.27
.37
.37
.49
.81
.69
.33
1.61
1
2
1
1
0
0
0
0
1
.59
.23
.43
.62
.87
.95
.37
.92
.54
RPM
3000
3000
3000
3000
3000
3000
3000
3000
3000
3000
3000
3000
3000
3000
3000
3000
3000
fc
10.1
12.1
13.6
13.4
12.0
14.3
12.7
13.3
11.6
11.7
11.8
12.9
13.6
13.0
12.5
15.4
10.0
33
25
22
24
27
2S
27
25
26
26
28
25
20
25
23
20
33
Ro
.000
.000
.000
.000
.000
.000
,000
.000-
,000
.000
,000
.000
,000
.000
.000
,000
,000
log
2.07
2.19
1.79
1.48
1.28
0.81
1.42
0.69
1.64
2.24
0.67
0.33
0.20
0.54
0.59
0.18
2.07
C*
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
P"S
.19
.22
.31
.34
.21
.23
.07
.23
.14
.28
.19
.38
.30
.06
.04
8.37
8
.12
116
-------
Table 11. Kinetic Rate Control Data: 5°C.
Run T I ? R
(°C) pH (pA/cnr) RPH K 0 log C* pHs
1
2
3
4
5
6
7
8
9
10
5
5
5
5
5
5
5
5
5
5
7.85
6.30
6.32
6.37
7.83
8.19
8.27
7.14
7.18
6.79
1.28
1.40
3.71
2.58
1.09
0.63
0.75
0.84
1.04
1.17
3000
3000
3000
3000
3000
3000
3000
'3000
3000
3COO
12.2
10.0
10.7
10.8
12.3
14.3
12,8
12.1
10.5
10. 5
25,003
34,000
32,000
31,000
27,000
21,000
24,000
25,000
28tOOC
28,000
0.77
2.29
2.69
2.48
0.74
0.33
0.33
1.25
1.30
1.73
8.63
8.59
9.01
8.85
8.57
8.52
8.60
8.39
8.48
3.52
-------
control by solution mass transport encompacses a pHg range rf 5.0 to roughly
> 7.6, extending diffusion rate control to higher pH values than at ?5°C.
Data taken at 5°C are presented in Table 11 and are plotted in Figure 35
in the form of log C versus log (C -1). This plot shows that nearly every
data point at this temperature falls in region III, the region of complete
rate control by diffusion in solution. The upper limit on pHg for diffusion
control is roughly 8.0 at this temperature, a change that corresponds to the
trend noted in comparing data at 25°C and 15°C.
Analysis of Data in Region I
So, despite the initial intention to have all the data fall into region
I, experimental results show that only a few data points, measured at 25°C
and at solution pH values greater than 8.6, actually correspond to conditions
of complete rate control by interfacial reaction kinetics. &•• will be shown
later on in this chapter, this is presumed due to the persistent and unex-
pected influence of diffusion of hydroxyl ion, OH", away from the corroding
metal surface, as a reaction product of the molecular oxygen reduction reac-
tion. This mass transport effect is especially pronounced in poorly buffered
solutions where the bulk concentration of OH" is low (pHR < 8.0) and only
starts *D die out at higher pH values where the amount of OH" produced by the
corrosion reaction is negligibly small in comparison to the OK" concentration
in solution. Region I data, therefore only exist at high pH. Corrosion
rates measured at pH values high enough to be included here were only
measured at 25°C.
Region I data are analyzed by plotting log I versus pH& with the slopa
and intercept determined by linear regression. Data points in region I are
shown in Table 12 and plotted in Figure 36. The solid line on the plot
corresponds to the regressed linear relationship between log I and pHg.
Regression of log I on p!^ gives the fol lowing rate expression:
log I = -3.600 - 0.300 pHB
with: r2 = 0.907
which can be written in the form:
118
-------
2.5
2.0 -
€5 1.5 •
O
1.0
0.5
T- 5*C
-0.5 0.0 -1.0
LOGCC-1)
-2.0
-3.0
Figure 35. Frarik-Kamenetskii plot of kinetic data at 5 C.
-------
-6.200 4
T-25°G
O
-6.400
-6.600
8.6
9.0
PH
9.4
9.8
Figure 36. Kinetic data of region I at ?5°C.
-------
Table 12. Region I Data: 25°C
T(°C)
25
25
25
25
25
25
25
I (uA/cm2)
0.59
0.57
0.47
0.41
0.51
0.23
0.27
PHB
8.62
8.79
9.15
9.19
9.25
9.91
9.95
log I
-6.229
-6.244
-6.328
-6.387
-6.292
-6.638
-6.569
I - (2.509 x 10"4) 1Q-0'30 P B
o
for I in units of A/on . The Arrhenius factor, a, can be calculated since:
Co - ()K^ (!Cf3)b - 2.509 x 10'4
1Q-6 w
or a = 3.26 x 10"10
Since no region I data were taken at temperatures other than 25°C it is not
possible to determine the value of the activation energy, E., of the rate
limiting step or the frequency factor, A.
Figure 37 shows a plot of data collected over the pH range of 6.0 to
10.0 at 25°C along with the regressed kinetic rate expression determined
above. The regressed rate expression predicts a kinetic rate that is higher
than that actually measured at pK < 8.5, which is in accord with the earlier
realization that below pH = 8.5 the effects of solution mass transport tend
to slow down the overall rate of the corrosion process. Whether or not the
quantitative kinetic rate expression developed at high pH is appropriate for
.121
-------
data taken at pH < 8.5 can only be determined by evaluation of the data which
fall into regions II and III.
Analysis of Data in Region II
Data that fall in the region of mixed kinetic/mass transport rate
control are analyzed by first transforming variables (I, pHg, T) into (X, Y,
T) for each data point. Then by linearly regressing the values of Y on X at
each temperature kinetic parameters a and b can be found frc,7! the intercept
and slope of the regression line respectively. The regression variables X
and Y are calculated from raw data values as follows:
pH I(10-6)cT
X=log -
and
and tabulated in Table 13.
Only data taken at 25°C are analyzed in this fashion since approximately
all lower temperature data fell into region III. A plot of Y versus X for
data points in this region is shown in Figure 38. The solid Tina on the plot
corresponds to the regressed linear relationship between X and Y, which can
be expressed as follows:
Y = -6.814 + 0,461 X
with: r2 = 0.848
which leads to the following rate expression for data in this region:
I = (1.482 x 104) Cs°'461
where Cc- is found by solving the following non-linear algebraic equation:
O
njj
CS0<461 - (2.205 x 105) Cs +• (2.227 x 10"12) 10 B = 0
Analysis of Data in Region III
In region III, the corrosion process is under rate control by diffusion
through solution. The rate expression appropriate for this condition was
derived earlier on to be:
122
-------
Table 13. Region II Data: 25°C
T(°C) I (yA/cro2) pHR Added DiCO,~]
25
25
25
25
25
25
25
25
25
0.56
0.74
1.17
0.74
0.85
0.74
0.94
0.84
0.9?.
7.10
7.33
7.89
7.35
7.37
7.60
7.82
7.60
7.58
0
0
0
10
10
10
10
10
10
-11.236
-11.115
-10.916
-11.115
-11.055
-11.115
-11.011
-11.060
-11.021
-9.528
-9.357
-8.344
-9.339
-9.304
-9.202
-9.020
-9.181
-9.177
123
-------
*—I
ro
UJ
O
c:
O
o
4.0
3.0
2.0
1.0 J
6.0
7.0
PH
8.0
• i
9.0
—i
10.0
Fiaure 37. Comparison of region I results with all kinetic data at 25 C.
-------
I . (
nF D p(10'3 K )b bpH
OH
io
-6
* ) 10 B
which can be reduced to the linear form of:
log I = c + b pH,
o " r"B
nFDOH
where: c = log
Data points in the form of (log I, pHn) can be regressed at each temperature
to find values of p and b. Data points in region III are shown in Table 14
and plotted in Figures 39 and 40 for 25°C, 15°C and 5°C respectively. The
solid line on each plot corresponds to the regressed linear relationship
between log I and pH.
At 25°C regression results in. the following linear relationship:
log I = -1.842 - 0.597 pHg
with: r2 - 0.975
which leads to the following rate expression:
I = (1.440 x 10'2) 10-°'597 pHB
from this, the value of p can bt calculated which is independent of tempera-
ture:
nF D P(10"3K )b
x 10
K
D
So: p = 3.15 x 10~"
This leads to the following general rate expression:
I = (-
1.876 x 10"9 D
' „ 0.597
OH •. 1Q-0.597pHB
125
-------
ro
CT)
-n.ooo •
Y
-1K100
-11.200
T-25'
-9.500
-9.300
-9.100
x
-8.900
Figure 38. Kinetic data of region II at 25 C.
-------
Table 14. Region III Data: 25°C, 15°C, and 5°C
T (°C)
25
25
25
25
25
25
25
25
25
25
15
15
15
15
15
15
5
5
5
5
DH,,
• D
6.05
6.24
6.25
6.51
6.54
6.57
6.73
6.65
6.99
7.02
6.22
6.27
6.65
6.50
6.93
6.52
6.32
6.37
7.18
6.79
I (wA/cmd)
3.35
2.62
2.88
1.78
1.61
1.84
1.44
1.64
0.90
0.96
2.27
3.37
1.33
1.59
1.81
2.37
3.71
2.58
1.04
1.17
log I
-5.475
-5.582
-5.541
-5.703
-5.793
-5.735
-5.842
-5.785
-6.056
-6.018
-5.644
-5.472
-5.87S
-5.799
-5.743
-5.625
-5.431
-5.588
-5.S83
-5.932
127
-------
ro
CO
-5.400
—-5.
-5.800
-6.000
T-gS'C
6.0 6.2 6.4 6.6 6.8
PH
7.0
Figure 39. Kinetic data of region III at 25 C.
-------
ro
-5.400 -
-5.600 -
©-5.800
-J
-6.000
6.0 6.2
6.4
6.6
6.8
7.0
7.2
Figure 40. Kinetic data of region III at 15 C. and 5 C.
-------
Where the temperature dependence is imbedded in Dn. .,<£,. and K .
UH' U W
At temperatures of 15 and 5°C the data points were of fewer number and a
plot of log I versus pHg values indicated that data at both temperatures
could effectively not be distinguished. These data were then regressed
together to give the following rate expression:
I = (3.074 x 1C)"3) icf0'486 pHB
with: r2 = 0.647.
frorrt which p can be calculated at 15 and 5°C.
At T = 15°C: p = 4.35 X 10"21
At T = 5°C: p = 3.63 X 10"21
The following general rate expressions then pertain:
1.21 x IP"8 DOH -0.486PHB flt ^
I=-7—1086- 10
D w
dr'd 1.00 x 10"8 Dnu -0.486oHp
1 ' -7-7^486-^ 10 at 5°C
D Kw
As noted before the temperature dependence is imbedded in DQM,
-------
effects of other component rate processes that the dependency of the rate of
oxide film growth on pH anc temperature could be determined quantitatively.
Experimentally this meant running polarization curves on electrocheriically
aged copper electrodes rotated at 3000 RPM. The electrochemical aging
process consisted of passing a 10 uA anodic current across the electrode
solution interface for a period of two hours at the appropriate temperature
and pH. These conditions promote oxide film growth in great excess of that
needed to attain a steady-state thickness of Cu,C. At 20 yA hr film thick-
o L
ness greater than 2000 A could be attained if all copper oxidized went into
forming the film, film dissolution was zero, and the film didn't break up.
But the film is dissolving and breaking up so the 20 pA hr age time repre-
sents the shortest preparation time that gave cell current density values
consistently as low as those measured at longer age times, indicating that
the oxide film was exerting its maximum influence on the overall rate of the
corrosion process. Rotation of the disc electrode at 3000 RPM, as explained
earlier increases the rate of all solution mass transport processes minimiz-
ing their influence on t^.a rate of the overall process. So the measured
corrosion rate was intended to correspond to the rate of oxide film growth or
solid-state transport through the oxide film. Rate variations with respect
to pH and temperature are used to compare data with theoretical models
developed in Section 6 for early and late stage film growth by quantum
mechanical tunnelling.
A schematic diagram of the metal/oxide/solution system in which corro-
sion rate data presented in this section were taken is shown in Figure 41
below.
By minimizing the effects of mass transport in solution,, the rate of
o
oxide film growth which corresponds to the rate at which electron holes, h,
and copper cation vacancies, Cu+[], are transported across the film,, can be
measured. A plot of log c' versus log (C -1} was then expected to give data
points falling into Region I, the region in which the overall rate is
completely controlled by the underlying rate process, free of solution mass
transport influences. As it turns out, these data reflect an influence of
solution mass transport of a reaction product away from the oxide/solution
interface similar to that found for the data under interfacial reaction rate
131
-------
control. So these experimental conditions turn out to give data that reflect
the joint influence of:
1) Mass transport in solution (presumably OH")
2) Oxide film growth
The methods of Frank-Kamenetskii are then called upon once again to quantity
the pH and temperature dependence of the coupled rate process of oxide film
growth in the presence of OH" diffusion. A rate expression that expresses
the joint effects of these two processes can be developed from the data.
Data taken are shown in Tables 15, 16, and 17 for 25°C, I5°C and 5°C
respectively. Plots of log C versus log (C -1) shown in Figures 42, 43 and
44 indicate that many of the data points fall into region III, the region of
diffusion in solution control. Not enough data fell into region II to be
able to characterize the underlying rate process so all data were evaluated
in the forni (log I, pHg), as per region III. Estimates of the slope, b, and
intercept, a, can be calculated for the relationship:
log I = a + b pHg
These values are presented in Table 18 along with 95% confidence interval
values for each estimate and calculated values of p at each temperature.
The following rate expression appropriate for coupled oxide film growth
and solution mass transport of OH" can be used to predict rates of copper
corrosion at 25, 15, and 5°C:
"F POH
lO'6
Values of parameters necessary for corrosion rate calculation are given in
Table 19 below. Figures 45, 46 and 47 show the precision with which the
quantitative rate expression fits the data at all three temperatures.
132
-------
COPPER
CUPROUS
OXIDE
*— CiTfa
SYNTHETIC T'-LT
RIVER WAT-_«
- — -> o;
Figure 41. Electrode/solution -interface in experiments designed Tor oxide
film growth rate control.
133
-------
Table 15. Oxide Film Growth Rate Control Data: 25rc.
CO
-p.
Run .
No.
1
2
3
4
5
6
7
8
9
10
T
25
25
25
25
25
25
25
25
25
25
pH
6.24
8.40
6.31
8.09
7.18
7.38
7.19
7.90
6.22
6.43
(pA/cra )
0.96
0.51
0.87
0.49
0.58
0.62
0.72
0.66
0.98
0.68
RPM
3000
3006
30CO
3000
3000
3000
3000
3000
3000
3000
F*
' cm '
13.5
16.7
12.7
18.5
16.6
16.6
16.6
17.0
13.4
15.1
RQ
20,000
16,000
26,000
16,000
21,000
21,000
21,000
19,000
25,000
23,000
Growth
Tl.iie
(pA-hr)
20
20
20
20
20
20
20
20
20
20
log C*
1.25
0.03
1.14
0.05
0.34
0.25
0.38
0.10
1.28
0.94
PHS
7.49
8.43
7.45
8.14
7.52
7.63
7.57
8.00
7.50
7.37
-------
Table 16. Oxide Film Growth and Rate Control Data: 15 C.
CO
01
Run
No.
1
2
3
4
5
6
7
8
9
T
15
15
15
15
15
15
15
15
15
pH
6.66
7.97
6.21
7.06
6.88
6.87
8.33
6.04
7.59
!COR,
(liA/cnf)
0.71
0.56
0.62
0.71
0.49
0.50
0.43
0.78
0.54
RPM
30CO
3000
3000
3000
3000
3000
3000
3000
3000
K
* era '
12.6
15.4
11.8
15.9
14.9
15,4
18.1
11.5
14.0
".
24,000
18,000
27,000
21,000
26,000
21,000
13,000
24,000
27,000
Growth
Time
(uA-hr)
20
20
20
20
20
20
20
20
20
log C*
1.15
0.18
1.52
0.80
0.81
0.83
0.07
1.79
0.34
PHS
7,81
8.15
7.73
7.86
7.69
7.70
8.40
7.83
7.93
-------
Table 17. Oxide Film Growth Rate Control Data: 5°C.
o-i
Run
No.
1
2
3
4
5
6
7
8
9
10
re,
5
5
5
5
5
5
5
5
5
5
T
pH
7.50
7.40
8.47
8.16
7.28
6.86
0.77
7,99
6.43
6.25
(yA/ClT!2)
Oc53
0,38
0.47
0.48
0.37
0.49
0.56
0.43
0.57
0,54
RPM
3000
3000
3000
3000
3000
3000
3000
3000
3000
3000
K.
(kLcir)
11.0
11.0
14.0
13.3
11.6
10.4
9.4
11.7
10.6
9.8
RQ
29,000
28,000
19,000
23,000
27,000
28,000
32,000
23,000
24,000
27 ,000
Growth
T1ma
(yA-hr)
20
20
20
20
20
20
20
20
20
20
log C*
0.81
0.71
0.16
0.28
0.80
1.29
1.48
1.35
1.73
1.92
PHS
8.31
8.11
8.63
8.44
8.08
8.15
8.21
8.34
8.21
8.18
-------
2.0
b 1.5
1.0
0.5
-1.0
0.0 1.0
LOG(C*-1>
2.0
Figure 42. Frank-Kamenetskii plot of oxide film growth data at 25 C.
-------
CO
CO
2.0
1.0
0.5
-1.0
0.0 1.0
LOG(C*-1)
2.0
Figure 43. Frank-Kamenetskii plot of oxide film groth data at 15 C.
-------
CO
10
2.0
l> 1.5
1.0
0.5
-1.0
0.0 1.0
LOQCC^D
2.0
Figure 44. Frank-Kamenets.kii plot of oxide film growth data at 5 C,
-------
T°C
Table 18. Regression Results for Oxide Film Growth Data
± a
(95)
± b
(95)
25
15
5
- 4. 845
- 5.608
-6.023
±
±
±
.428
.444
.257
- 0.
- 0.
- 0.
183
085
038
±
±
t
.060
.062
.035
- 0
- 0
- 0
.929
.847
.790
3.393
3.151
9.971
x ID'18
x 10-17
x 10'17
Table 19. Parameter Estimates Calculated for oxide Film Growth Data.
JOH
RDE
>D(at 3000 RPM)
25
15
5
-0.183
-0.085
-0.038
3.39X10"18
3.15X10"17
9.97xlO"17
5.26xlO"5
3. 98x1 O"5
2.89xlO"5
l.OlxlO"14
0.45xlO"14
O.lSxlO"14
1.553xlC"3
1.463xlO"3
1.385xlO"3
RATE CONTROL BY SOLUTION MASS TRANSPORT
Data under rate control by solution mass transport were taken by design-
ing experiments in which the influence of interfacial reaction kinetics and
oxide film growth were minimized. This was done by running polarization
curves on freshly polished copper electrodes that were not rotated. Under
these conditions mass transport through stagnant solution was expected to be
the slowest step in the overall corrosion process. A comparison of rates
measured under conditions of kinetic or oxide film growth rate control with
solution mass transport data taken at the same pH and temperature indicate
that in all cases measured rates were significantly reduced K'hen the working
electrode was not rotated. This is an indication that solution mass trans-
port rate processes are going on and do influence the overall corrosion rate
140
-------
Bf'
yj
2
0.80
0.60
tt
£E 0.40
0.20
T-25°C
6.0
I »
7.0 8.0
PH
Figure 45. Oxide film growth data at 25 C.
9.0
-------
INi
1.20
1.00
yj
5 °-80
IE §
2 °
6 O 0.60
« 5
O <
O
O
0.40 ^
0.20
T»16*C
6.0
7.0
8.0
9.0
Figure 46. Oxide film growth data at 15°C.
-------
-Pi.
CO
1.00
JU 0.80
0.60
O
O
°"40
0.20
T-6°C
6.0
7.0 8.0
PH
9.0
Figure 47. Oxide film growth data at 5 C.
-------
especially 1n stagnant solution. These data then were taken under conditions
most likely to produce complete rate control by solution mass transport.
Rate variations in the data with respect to pH and temperature should then
correspond to the pH and temperature dependence of the rate controlling
diffusion process. This could be the rate of mass transport of H+ or 0? to
the electrode surface to act as reactants in the cathodic half-cell reaction
or mass transport of OH" or Cu away from the electrode surface as reaction
products of the cathodic half-cell or oxide film dissolution reaction
respectively. A schematic diagram representing the metal/oxide/solution
system from which data presented in this section were measured is shown in
Figure 48.
COPPER
I
SYNTHETIC TOLT
| RIVER WATER
I
Cu'
Figure
Electrode/solution interface in experiments designed for stagnant
diffusion rate control.
Since the diffusion layer thickness,^, is time dependent and of different
magnitude for each diffusing species time-averaged mass transport rates are
necessary for each diffusing species. Appropriate rate expressions were
developed in Section 4 and are presented here as follows:
1. For diffusion of H4" from bulk solution to interface:
I =
-t- a(-
1/2 .1/2
IT L
when: [H+3B » [H+]s
144
-------
n = 1 mole a~/mole
2. For diffusion of 0- from bulk solution to interface:
3 f'V a/2-
onrr\ Mn*Mri i T » *- ' *
cnrUn ^ iu )\_i < a r.
°2 r2
1/2 tl/2
IT L
[o2J
I =
when: [023B » [02]$
n = 4 moles e"/mole 0?
3. For diffusion of OH" from interface to bulk solution:
T "•
2nF
(103)
l/2
[OH']S - [OH"]B
n = 1 mole e"/rnole OH"
2+
4. For diffusion of Cu from interface to bulk solution:
I =
when:
2nF
u-
7 ur,, r
DOft-Mn^ri -^ n ^
P £.! IIU JL-l + al o
^ r
1/2 .1/2
n If
Js » [Cu2+]B and [Cu2+
} 1
KsPC
;U(OH)
£
^ [OH"]2
2+
n = 1 mole e/mole Cu'
2 ?
In all of these expressions, a = 2.12, r = 0.2270 cm , and the stagna-
tion time, t, is taken as 40 sec. Experimental results are presented next
and ultimately compared with these rate expressions for determination of
which diffusing species is rate controlling.
Data taken are shown in Table 20, 21 and 22 for 25°C, 15°C and 5°C
respectively. A plot of log C versus log (C^-l), in Figures 49, 50 end 51
will be siiOv/n later, indicates that a great majority of data points at all
145
-------
Table 20. Stagnant Diffusion Data: 25°C
Run
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
T
CO
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
pH
6.39
6.38
6.39
7.39
8.84
7.33
7.0$
8.45
8.56
6.85
7.70
8.82
8.22
7.85
6.02
9.37
!COR2
0.55
0.48
0.48
0.36
0.16
0.42
0.43
0.21
0.31
0.45
0.39
0.16
0.31
0.33
0.53
0.16
RPN
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
(^
14.0
14.3
14.1
15.2
16.2
15.1
14.9
16.1
15.8
16.9
16.6
17.7
16.0
15.2
13.1
18.5
R°
23,OCj
23.000
23.000
18.000
17.00C
17.000
18.000
17,000
17,000
16,000
16,000
15.000
16.000
19.000
23.000
14,000
106 C*
2.17
2.12
2.11
1.03
0.05
1.14
1.41
0.17
0.19
1.63
0.79
0.06
0.35
0.61
2.52
0.02
PH,
£.56
8.50
8.50
8.42
8.90
8.47
8.47
8.62
8.75
8.49
f.49
8.68
8.57
3.46
8.54
9.39
145
-------
Table 21. Stagnant Diffusion Data: 15 C.
Run T
Ho. (°C)
1 16
2 15
3 15
4 15
5 16
6 16
7 16
8 16
9 15
pH
6,44
8.31
6.73
? i9
6,05
6.97
7. SO
7.31
7.62
!COR2
i i ( fs / f Ui \
\ fi
-------
Table 22. Stagnant Diffusion Data: 5°C.
00
Run
No.
1
2
3
4
5
6
7
8
9
10
11
T
(°C)
5
5
5
5
5
5
5
5
r
5
5
pH
7.08
7.25
7.26
8.36
6.05
6.36
6.30
6.36
8.39
8.81
8.71
^OR,
(pA/cnf)
0.23
0.22
0.22
0.13
0.35
0.26
0.40
0.31
0.25
0.12
0.18
RPM
0
0
0
0
0
0
0
0
0
0
0
/pmhos>
( cm '
12.1
13.0
11.4
11.5
10.2
12.2
11.4
12.7
11.0
12.2
13.6
RQ
25,000
23,000
26,000
26,000
30,000
25,000
30,000
27,000
28,000
26,000
24,000
log C*
2.00
1.82
1.81
0.60
3.21
2.77
3.02
2.85
0.80
0.29
0.45
PHS
9.08
9.07
9.07
8.96
9.26
9.13
9.32
9.21
9.19
9.10
9.16
-------
three temperatures lie in Region III, the region sf rate control by diffusion
in solution. Data are then analyzed in the form (log I, pKj. Estimates of
the slope, b, and intercept, a, for the relationship:
log I = a + b pH
are presented in Table 23, along with 95% confidence interval values. The
correlation coefficient, r, for each data set is also presented.
The log I versus pHB plot can be used to determine which of the possible
diffusing species is actually rate limiting. The possible species, as men-
tioned earlier, are H+, Op, OH", and Cu2"1". Considering the general expres-
sion:
log I = a0 4 b0 PHB
The values of an and bn appropriate for rate control by diffusion of H or
2+
0? to the electrode surface and diffusion of Cu sway from the electrode
surface are given in Table 24 below. The values of afl and bn predicted for
each of the diffusing species above are then compared to values of a and b
determined by regression of the data points.
By Null hypothesis testing (5) one can determine whether the regressed
values of a and b differ significantly from the tSvesretical values of a and
bQ for each diffusing species. If the (aQ, bQ) values of one diffusing
species do not differ significantly from the regressed (a,b) values that
species can be selected as the rate controlling diffusing species. In Table
25 below the results of these tests are described by a (+) for acceptance of
the Null hypothesis and a (-) for rejection of the Kull hypothesis. The Null
hypothesis in each case is that a = a. or b = b. A (+) therefore means that
there is no significant difference between a and a- or b and b^. A (-) means
that there is a significant difference. All comparisons are made at 25°C.
On the basis of these tests none of the species above can be se1ected to
explain the data at 25°C under conditions of diffusion in solution rate
control.
The diffusion of OH" was not considered in the table above since it
involves coupling of an underlying process that is dependent upon the surface
hydroxide concentration with that of mass transport in solution. The method
149
-------
Table 23. Regression Results for Stagnant Diffusion Data
± a(95)
± b(95)
25 - 5.6051
15 - 5.1866
5 - 5.8132
* .1913
t .5499
i .5765
- 0.109
- 0.196
- 0.111
± .027 - 0.950
* .076 - 0.932
± .071 - 0.793
Table 24. Calculated Diagnostic Parameters for Diffusion Rate Control
ao
Species (Functional Form)
ao
(T - 25°C)
H* log
0 log
2
Cu log
"lQ*3 nF D +1
.. " r ,,,<- . n
t 13 . JiJ "i .U
4V j
n ^*
103 nF D [0, ]B 1
_ 4 A, i o^n n
_ _,^,...-^.— ....... „. T x.^jy |j
L °^
D «J
K» «n
10 RF Dr,,2+ KSp Cu(OH),
„ ,., . V*J ,, - ill cpn 5. r.
o , 'ij.U^U "t.U
V &D^
a «d
150
-------
-J
3.0
2.5
2.0 H
1.5 1
.0
0.5
A »»
-1.0
0.0
1.0
2.0
3.0
LOG(C-I)
Figure 49. Frank-Kamenetskii plot of stagnant diffusion data at 25 C.
-------
en
ro
3.0
2.5
2.0 J
1.5 J
1.0 J
0.5
3.0
LOQ(C-I)
Figure 50. Frank-Kamenetskii plot of stagnant diffusion data at 15 C.
-------
3.0 1
2.5 4
2.0
1.5
1.0
0.5
2.0
LQG(C*-1)
Fiqure 51. Frank-Kamenetskii plot of stagnant diffusion Jata at 5 C.
3.0
-------
Table 25. Null Hypothesis Testing Results.
Species a/aQ b/bQ
°2
H+
Cu2+
of Frank-Kamenetskii , described at the outset of this chapter, provides the
basis for comparing the data with a theoretical model.
This analysis suggests that diffusion of OH" away from the surface of
the electrode may be the rate controlling diffusion process in solution. It
further suggests that the underlying rate process is also dependent on the
surface concentration of OH" , or surface pK, a result shown to be the case
for both, oxide free and oxide covered electrodes earlier in Section 4.
The rate expression appropriate for region III is once again:
io"6 cTD
From the regressed values of a and b at 25, 15, and 5°C the temperature
dependence of b and p can be evaluated and a general rate expression deve-
loped which closely models the measured rtata at all three temperatures.
Table 26 shows the numerical values of p and b at all three temperatures,
along with their 95% confidence interval variations.
Figures 52, 53 and 54 show the precision with which the quantitative
rate expressions fit the data for all three temperatures.
Data presented in this section were found to be largely under rate
control by solution mass transport, in accord with experimental design. The
rate limiting diffusing species has not been determined, although the field
of possibilities has been reduced. The pH and temperature dependence of the
data were characterized quite well by the diffusion of OH" away from the
electrode surface c:nd it may very well be the rate limiting diffusing
.154
-------
Table 26. Parameter Estimates Calculated for Stagnant
Diffusion Data
T b ± Ab p ± Ap
25 -0.109 ± .027 2.313 x 10"16 ± 1.280 x 10"16
15 -0.106 ± .076 2.026 x 10"17 ± 1.523 x 10"17
5 -0.111 ± .071 1.547 x 10"16 ± 1.135 x 10"16
species. To characterize this with more certainty will require a more
rigorous accounting of all the reactions occurring at the oxide/solution
interface. This should include the effects of copper cation complexation,
Cu(OH)2 precipitation, along with the effects of surface and solution buffer
capacity.
DATA ANALYSIS SUMMARY
Several general observations can be made concerning the likelihood and
importance of rate control by each of the component rate processes. First of
all, a comparison of the magnitude of the three types of data as a function
of pH, shown in Figures 55 and 56 at 25°C, show the following:
a) Corrosion rates measured at pH < 7.0 on electrodes without
oxide films were much larger than those measured on oxide
covered electrodes.
b) Corrosion rates measured in stagnant solution were
considerably lower than those made at 3000 RPM.
These observations are significant in that they demonstrate both the influ-
ence of oxide fi^m growth and solution mass transport on the overall rate and
suggest that a model of the overall process include the coupled effects of
these two rate processes. Kinetic data may be important but only at sites
where the oxide film has been damaged or removed. The fact that solution
mass transport control data were of smaller magnitude than the other two sets
of data at corresponding pH and temperature values indicates tht there is
155
-------
0.60 j
0.50 J
OC 5 0.40
O
0.30
O 0.20
0.10
T-gg'C
6.0
7.0
8.0
9.0
Figure 52. Stagnant diffusion data at 25 C.
-------
Ul
H
<
O
0.60
0.50
0.40
0-30
0.20
U.10
6.0
PH
9.0
Figure 53. Stagnant diffusion data at 15 C.
-------
en
CO
0.60 -
0.50
0.40
2
O
O 0.30
J£ <
0.20
0.10 .
6.0
7.0
8.0
PH
9.0
Figure 54. Stagnant diffusion data at 5 C.
-------
some species in solution whose rate or diffusion effects the rate of the
overall corrosion process.
The rate of the process therefore is dependent upon not only the chemi-
cal reactions involved and the growth of oxide film but also on the hydro-
dynamic flow regime of the corroding system, since it inevitably influences
the rate of solution mass transport. There is a definite solution mass
transport influence and the species exerting that influence may very well be
OH" diffusing away from the surface into bulk solution. This situation where
a reaction product must diffuse away from the reaction site is characterized
by a persistent influence on the overall rate of the process even at very
high Reynolds Numbers to the point of masking the effects of the underlying
process. The effect of a slow diffusion of OH" away from the surface is to
increase the pH of the solution adjacent to the oxide surface reducing the
oxide film growth rate. As the diffusion rate is increased, at higher Re,
the surface pH can drop allowing a faster rate of oxide film growth and
greater corrosion rate. The high pH values that arise at the oxide surface
may promote precipitation of such solids as Cu(OH)- which have low solu-
bilities. This may even suggest that actual rate control of the corrosion
process occurs in the solution adjacent to the oxide surface-, not within or
on the oxide itself. In addition a variety of Cu(OH) ~n complexes may form
in the solution adjacent to the oxide surface reducing the "free OH""
concentration, lowering the surface pH.
Empirical Cha^cton:Cation o^ pH
Data ;\jned to be under oxide film growth rate control and solution
mass transit rate control were both, in reality, principally under rate
control by diffusion of a reaction product away from the electrode surface.
Assuming that the diffusing species to be OH" it is possible to calculate the
surface pH, pH-, for each data point as follows:
pHs = leg
where: I =
159
-------
en
o
1.5
c >» '-o
O Q-
'S E
o
t,
;•„
O
O
o.s
W/O OXiDE
w;
T-25"C
6-0 6-5 7.0 7.5 8.0 S.'s
Figure 55. Comparison of Corrosion Rates Measured with and without
Oxide Film at 25°C.
-------
01
T-26 C
OXIDE FILM ©ROWTH
6.0 6.5 7.0
Figure 56. Comparison of Corrosion Races Measured v/ith and without
Solution Mass Transport Effects at 25 C.
-------
C = 103 r.F DQH
These va'iues were calculated and included in Tcbles 15, 16, 17, 20, 21 and
22, for oxide film growth and solution mass transport data sets. These
calculated values shew that pH is dependent upon temperature, pHg, and
diffusion layer thickness, as one might expect. Since it wasn't possible to
completely characterize mechanistically or quantitatively the underlying rate
process accompanying OH~ mass transport in solution, the following empirical
formulation was decided upon:
PHB - f(T, pHB, j
sed was:
log pHs = leg K -*• ct log 0 -*• 0 log T + |log
-------
When all 58 data points were regressed in this form the following values for
K, a, e, and y were found:
r = 0.948
K = 7.962 x 103
a = 0.333
3 = -1.075
^ = .0328
Using these regressed values the following quantitative form for
pHs results:
PHS = (7.962X103) 0°'333 r1'075^'0328
where: 0 = 1.0 - 0.32 pHp 4 0.039 pH 2 - 0.0015 pH 3
L' IJ D
T = absolute temperature (°K)
In this form variations in the data with respect to all three principal
system variables are captured.
The goodness of fit of this function is shown in Figures 57, 58 and 59
for comparison with data at 25, 15 and 5°C respectively.
This regression equation, which incorporates solution pH, T, and <£"„,
to predict the variations in pHo, which must be estimated based on some of
the same parameters, is an unsatisfactory modeling result. The importance of
the pH at the interface is significant and is expected to have a controlling
effect on the rate of th« cathodic reaction, on Cu+ oxidation and on precipi-
tation of Cu(QH)?, as well as determining the soluble copper hydroxide
species. The regression equation does catalog the data in a form that
predicts the estimated parameter, pHs, within reasonable limits. The task of
understanding and mechanistically modelng the interfacial reactions remains
for future studies.
CONCLUSIONS
The finding that uniform copper corrosion in synthetic Tolt River water
proceeds under rate control by solution mass transport of a reaction product,
likely to be OH", is significant in providing direction for further research
163
-------
9,0 -
PH
3
8.0
7.0
6.0
7.0
PH
B
STAGNANT DIFFUSION
OXIDE HLM
8.0
9.0
Figure 57. Comparison of surface pH values calculated from data with those
predicted by empirical expression for surface pH at 25 C.
-------
9.0 .
8.0
7.0
6.0
7.0
STAGNANT DIFFUSIOM
OX6DE FILI
—r ——i i
8.0 9.0
Figure 53. Comparison of surface pK values calculated from data with those
predicted by empirical expression for surface pH at 15 C.
-------
01
9.0 \
8
8.0
7.0
STAGI^ANTXDJFFUSIOI
OXIDE F9LM
6.0
7.0
8.0
9.0
B
Figure 59. Comparison of surface pH values calculated from data with those
predicted by empirical expression for surface pH at 5 C.
-------
in copper corrosion in drinking water. The study of precipitation and
complexation of dissolved copper species may prove to be the key to further
understanding of the complexity of processes making up aqueous corrosion of
copper. This finding has implications for other metals as well. Since
OH" is a product of the CL reduction reaction, a cathodic half-cell for
almost all metal corrosion in aqueous solution of near neutral pH, its mass
transport, complexation, and precipitation by metal cations present m^y be
controlling the rate of other corroding systems.
167
-------
SECTION 7
PROPOSED STEADY-STATE PIPE FLOW MODEL FOR UNIFORM COPPER CORROSION
INTRODUCTION
The use of copper tubing for cold water transport in households and
commercial buildings is widespread. Problems arising from its accelerated
corrosion have been outlined earlier. The principal value of corrosion
research performed in the laboratory lies in its application to real life
corroding systems, such as copper tubing used for cold water plumbing. In
this chapter a simulation model is presented that allows one to predict the
rate at which copper tubing will corrode under a given set of environmental
conditions. It is developed based on the presumption that mass transport of
OH" is the rate controlling process and combined results of laboratory
studies presented in Section 6 with quantitative models for mass transport in
laminar and turbulent pipe flow presented in Section 4. The result is an
ability to predict the rate of uniform copper corrosion in cold water
plumbing systems under varied conditions of flow, te?aperature and pH of the
water. Such a model can provide valuable insight, into identification of
principal variables affecting the overall processv the extent to which each
variable exerts an influence, and the range of magnitude in which the maximum
effect is manifested. Possible strategies for corrosion controls, or at least
corrosion rate reduction are also suggested.
RATE EXPRESSION DEVELOPMENT
To develop a mathematical model that predicts the changes in corrosion
rate of copper due to variations in flcw5 temperature, and chemical composi-
tion of the water, the coupled effects of several rate processes need to be
considered. As discussed earlier it is presumed that the cuprous oxide film
covering the copper grows to sane steady-state thickness wSiere the rate of
168
-------
film growth and the rate of film dissolution are equal. The following stoi-
chiometric relationships were given for film growth and dissolution:
CU+1 + 1/2 H20 > 1/2 Cu20 + H+ (film growth)
1/2 Cu20 + H+ > Cu2+ + 1/2 H20 + e" (film dissolution)
Both of these reactions occur at the oxide/solution interface and involve
either the production or consumption of protons. When the rate of production
of Cu20 by the film growth reaction equals the rate of dissolution, or Cu?0
consumption, by the film dissolution reaction the net rate of proton produc-
tion by these two reactions is zero. That is, the rate of H* produced in
film growth is exactly offset by the rate of H+ consumed in film dissolution.
The other reaction occurring at the oxide/solution interface is the
molecular oxygen reduction reaction which has differing stoichiometry in
acidic and alkaline solutions:
02 + 2H* + 2e~ > H202 at pH < 7.0
and 02 + 2H20 + 4e~ > 40H~ at pH _> 7.0
Obviously there is net consumption of H (or production of OH~) involved in
this reaction in both acidic and alkaline solutions. Therefore, it can be
noted, that at the oxide/solution interface where film growth, film dissolu-
tion, and CL reduction all take place simultaneously an overall consumption
of protons occurs regardless of the solution pH. The effect then of the
corrosion reactions is a tendency to increase the pH of the solution adjacent
to the oxide surface. How large the pH change is depends on the overall rate
of 0? reduction, the buffer capacity of the solution and oxide surface, and
the rate of mass transport of OH" away from the surface into bulk solution.
For a corroding copper system at steady-stats film thickness, rate con-
trol was shown to be due principally to the persistent effect of mass trans-
port in solution of a reaction product presumably OH". It was also invlu-
enced by the underlying rate process through its effect on pH^. This overall
169
-------
ettect was captured by the empirical relationship derived for pH as a
function of T, pHg, and <5"n in Section 6:
pHs = (7.9616 x 103)0°'33J (273.0 + T)"1'075^ D'°328
where: 0 = 1.0 - 0.32pHR + 0.039 pHg - 0.0015 pHg
This expression for pH was found to best fit the 53 data points
regressed and serves as an expression that catalogs the temperature, pH, and
P dependence of the chemical process occurring at the interface. When used
in conjunction wich laminar and turbulent mass transport pipe flow models,
uniform copper corrosion in those systems can be characterized. The rate
expression used in the model here is that presented earlier in Table 4-5:
? nF Dnn
I (pa/cm2) = - £*- [C, - CR]
10~b
I 453[___JL ] Laminar Diffusion
y DOH r (^ 1 2800)
133 3r Re"0'88 Sc"°'333 turbulent diffusion
• ' (Re > 2800)
170
-------
pHs - (7.9616 x 103) 0°'333 (273.0 + I)'1'075 V°328
0 = 1.0 - 0.32 pHB + 0.039 pH^ - 0.0015 pH3
These relationships constitute the proposed steady-state pipe flow model for
uniform copper corrosion. As mentioned earlier they are a combination of
results of this research with results presented in the literature for solu-
tion mass transport in pipe flow. These equations are easily programmed on a
digital computer. Corrosion rate estimates, computed in this fashion, are
presented for flow in a circular pipe of one-half inch diameter. Numerical
values for C, Kw, and D are provided in Table 27 at 5, 15, ar.d 25°C.
Table 27. Pipeflow Model Parameter Values
T = 25°C T = 15°C T = 5°C
C
Kw
Sc
^D (Lam.)
^D (Turb.)
5.076 x 103
1.01 x 10"14
171.1
2.146 Re"0-333
84.646 Re"0'88
3.841 x 103
0.45 x 10"14
276.4
Sc-°<333
r)C-0.333
2.798 x
0.18 x
519.
103
io-14
0
The diffusion layer thickness, c>"D, depends on the Reynolds number, Re, and
the Schmidt Number, S , the pipe radius, r, and for laminar flow the distance
down the axial length of the pipe from its inlet, y. Results presented
below are calculated using a pipe radius of 1/2 inch and an axial distance of
4.0 cm from the pipe inlet. The Reynolds Number for pipe flow is defined as:
d
where d is the inside pipe diameter (cm), the mean solution velocity ir,
the direction parallel to the corroding surface ( = A/Q cm2/sec) , andv is
o J
the kinematic viscosity of the solution in (cm/sec). The Schmidt Number is
defined as follows:
171
-------
OH
with both \) and D^ being temperature dependent. For known conditions of T,
pHg, and £^ values of pH and corrosion rate ess be calculated.
RANGE OF APPLICATION OF PIPE FLOW MODEL
The range of application of the pipe flow model is limited in two
respects. First, for the model to be valid the corrosion process must be
completely or at least partly controlled by tha rate of solution mass
transport of OH". The rate expression used in the model presumes this.
Second, the corroding system must be operating within the range of values of
pHg, T, and ^ over which data was taken and used in determination of the
empirical relationship for pH . Each of these constraints exerts some
influence on the overall spectrum of usage but neither turn out to oe overly
limiting. The only data found not to be at least partly under rate control
by solution mass transport (Region I), occurred at very high pH (pH > 8.5).
Under these circumstances, the underlying rate process be it oxide film
growth or an interfacial reaction, completely controls the rate of corrosion.
At pH values of 8.5 and below the data showed a persistent influence of
solution mass transport of OH".
The second constraint places limits on pH, T and / due to the range of
variation of these parameters exhibited by the data used ta generate the
empirical relationship for pH . The regressed relationship for pH$ is not a
good fit to the data at T = 25°C, 3000 RPM (oxide film data), and pHB > 7.5
and underestimates pHP by as much as 0.5 pH units at pH^ = 8.5. At 15°C and
3000 RPM the regressed relationship for pHg once agalr. underestimates pHs et
pHB > 8.0. Overall the regressed relationship for pHs fits the data reason-
ably well for pHR < 7.5 at all temperatures and values of diffusion layer-
thickness tested. Data taken was limited to the following range in parameter
values:
6.C 1 pH <_ 8.5
5 < T < 25° C
172
-------
1.385 x 10-J 1 <*"D <. 3.375 x 10'^ cm
Since the first constraint was mot, universally at pH < 8.5 the limitations
set by the second constraint are in general the controlling conditions.
These limitations being the range of parameter values shown above modified to
exclude regions of poor goodness of fit of the regressed relationship for
pH$. Care should be taken in interpretation of corrosion rate predictions
under conditions near or beyond these limits. Extrapclation to pH values
less than 6.0 seems justified since the first constraint is met, but extra-
polation beyond pH = 8.5 is not justified.
RESULTS OF PIPE FLOW MODEL
Corrosion rate estimates have been calculated using the pipe flow model
for a wide range of temperature, p(-L, and flowrate values. Some presented
values correspond tn areas outside the range of safe application outlined in
the last section. Of note, are conditions at high flowrate (Re > 10000) and
high pHg (pH > 8.0). Here the model predicts corrosion rates that rapidly
approach zero as either pHn or Re is increased, a tendency that is not in
accord with experimental results. This occurs when the regressed expression
for pH underestimates its actual value, causing the term:
PHS pHQ
[10 - 10 ]
to be substantially reduced in value and approach zero. This same effect
occurs when the overall rate is either being significantly influenced by or
completely controlled by the rate of the underlying rate process. As Re is
increased the transition from solution mass transport rate control to rate
control by the underlying rate process occurs at a lower pHg. The diffusion
layer thickness produced by a rotating disc electrode at 3000 RPH corresponds
to diffusion layer thicknesses produced in turbulent pipe flow at the follow-
ing Reynolds Numbers:
Re « 34,500 at T » 25 °C
Re * 30,750 at T = 15°C
Re • 25,800 at T • 5°C
173
-------
nu myner- Keynuiub numoers tne transition in rate control oegins to occur at
7.5 _< pHB 1 8.5.
In calculating rates for presentation in Figures 60 through 64 the pro-
posed model gave some estimates that rapidly approached zero at high Reynolds
Numbers. When this occurred the values presented are those predicted at the
same pHg and T, but at a lower Re. These estimates are drawn with broken
lines. This is a reasonable approximation since an increase in solution mass
transport rate, as signified by an increase in Re, should not decrease the
overall rate but at a minimum allow it to ranain unchanged in the limit where
the rate of the underlying rate process completely controls the overall rate.
In Figure 60 corrosion rate, in mils per year, is plotted verus Log Re at
25°C over a range in flowrate that includes both laminar and turbulent flow.
Corrosion rates estimated at low flowrates (laminar flow regime) range
between 0.50 and 0.20 MPY with' the major rate changes occurring between pH -
5.0 and pi) = 6.0. At high flow rate (turbulent flow regioie) corrosion rate
estimates range between values greater than 1.0 and 0.2 MPY with significant
rate reductions occurring as pH is increased above 7.5.
A plot similar to that described above is given in Figure 61 for pipe
flow at 15°C. Corrosion rate estimate at lew flowrate varied between 0.4 and
0.20 MPY with the major changes occurring between pH = 5.0 and 5.5. At high
flowrate, corrosion rate estimates range from 0.8 MPY at pH 5-0 to 0.2 MPY st
pH _> 8.0 down slightly from the corresponding rate estimates at 25°C.
The combined effects of pH and flowrate on the rate cf copper corrosion
at 5°C are shown in Figure 62. Corrosion rate estimates at low flowrates
range from 0.28 to 0.20 MPY at pH < 5.5 but at higher pHg are effectively
independent of pHD at a value of 0.16 MPY, a slightly lower value than hi en
u
pH estimates at 15 and 25°C. At high flowrate, corrosion rate estimates vary
from 0.80 MPY at pH 5.0 down to 0.20 MPY at pH 3.5. Once again showing
slightly lower values than corresponding estimates at higher temperatures.
Looking at these three plots cf corrosion rate estimates it is obvious, as
was mentioned above, that the effects of pH and temperature on corrosion rate
are considerably different at low flow rates than at high flowrates. At low
flowrate (RE < 1000) as shown in Figure 63, there is only a dependence on
pHp at pH < 5.0, and only a minimal temperature dependence. Above pH = 6.0
174
-------
; en
1.00
0.£
tit
8-
e «c O-frO
<
s w
© >
«!?
~fl
fS
G
S.40
0.20
3.000
3.500
LOQ RE
4.000
4.500
Figure 60, Corrosion rate estimates for 1/2 inch copper tubino at varied
flowrate and 25 c.
-------
1 en
2.500
3.000
3.500
4.000
4.500
LOG RE
Figure 61. Corrosion rate estimates for 1/2 inch copper tubing at
varied flowrate and 15 C.
-------
2.500
3.000
3.SCO
4.COO
4.500
LOG RE
Figure 62. Corrosion rateQestimates for 1/2 inch copper tubing at varied
flowrate and 5 c.
-------
CO
UJ
0.60
0.50 -
0.40
0.30
0.20
0.10
5'G
5.0
6.0
7.0
Figure 63. _E>'H dependence of corrosion rates estimated for laminar flow conditions.
-------
1.00
0.80
* m °-60
2 >
o «
oc i
CE 3;
O 0.40
O
0.20
5.0
6.0
PH
7.0
8.0
Figure 64. pH dependence of corrosion rates estimated for turbulent flow
conditions.
-------
corrosion rate estimates are consistently less than 0.25 MPY, ntiere 0.3 MPY
is sometimes considered the maximum desirable corrosion rate for copper in
drinking water. At Mtjh flcwrates (Re = 50,000) corrosion ratss can increase
dramaticaTy. Figure 64 is a plot of corrosion rate versus pHB at 5, 15, and
25°C and Re = 50,000. It shows some interesting results. At low pHB (pHn <
7.0) both flowrate and temperature exert significant influence on predicted
rates. The combination of low pKg end high temperature give the most unfav-
orable situation with rates increased as much as 500% over rates predicted
under comparable conditions at low flowrate. This effect is lessened greatly
as pHg is increased to a value above 7.0. In fact, for pHg > 8.0 the accel-
erating effects of temperature, flowrate, and pHg are essentially eliminated.
MODEL VERIFICATION
The accuracy with which the proposed model predicts corrosion rates
under specified environmental conditions can only be tested by comparison
with independently measured field data. Ideally, field data would be avail-
able over the entire range of pKp, temperature, and flowrate desired and the
model could be tested over its entire range of desired use. Although much
field data exists on copper corrosion in Tolt River Water, most of it was
taken in the presence of a chlorine residual. Since chlorination has a big
impact on corrosion rate (3, 4) but was not considered in the development of
this model, data taken 3t a nonzero chlorine residual is not considered. A
small amount of field data is available, at present for limited model veri-
fication. Data taken in studies conducted by the Seattle Water Department
(1, 2) are presented here and compared with model predictions. Corrosion
rates were measured by weight loss of copper coupons mounted in a pipe flow
test loop. Since data presented v.-ere taken at different flot/rates and tem-
perature,some standardization was required for comparison. For each field
datum presented a model prediction corresponding to the same environmental
conditions was calculated. The ratio of measured rate to predicted rate is
then used as a goodness of fit criteria. When this ratio equals 1.0 the
model perfectly fits the data. Deviations from 1.0 are a measure of the
inability of the model to predict measured values. Data values along with
predicted model values are presented in Table 28. Over the range of pH- ccrn-
180
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Table 28. Data for Verification of Pipe Flow Model.
Pipe diem.
T(°C) (in)
Flow
Re
Corrosion Corrosion
Rate Rate
Measured Predicted
(KPY) (MPY) a/b Reference
6.7
6.55
6.7
6.6
6.7
6.7
6.0
6.0
9
9
9
12
12
12
12
12
1.0
1.0
1.0
1.0
i.O
1.0
1.0
1.0
0.45
0.45
0.45
0.25
0.25
0,25
0.25
0.2S
gal /ml si
gal /rain
gal /ml n
ft/sec
ft/ sec
ft/sec
ft/ sec
ft/sec
6927
6927
6927
1760
1760
1760
1760
1760
0.
0.
0.
0.
0.
0.
0.
0.
14
18
18
15
15
14
29
35
0
0
.18
.18
0-18
0
0
0
0
0
.20
.20
.20
.27
.27
0180
1.00
1.00
0.85
0.75
0.70
1.07
1.29
1
1
1
2
2
2
2
1
-------
pared (6.0 _<. PHg _< 6.7) Figure 65 shows the reasonably good predictions
afforded by the pipe flow model. Thorough verification of this model, how-
ever, must wait until adequate field data is available for comparison over
the full range of pHg, temperature and flowrates desired.
CONCLUSIONS
A steady-state pipe flow model for uniform copper corrosion in Tolt
River water has been developed in this chapter. It is proposed for use in
determining optimum environmental conditions favorable to a reduced rate of
corrosion of copper tubing used for cold water transport of Tolt River water.
The model is developed based on the presumption that mass transport of OH"
away from the corroding surface controls the rate of the overall process, a
presumption that seems well founded in light of results reported in Section
6. Predicted values compared favorably with field data and show explicitly
individual effects of pH, temperature and flowrate on the overall rate of
corrosion.
182
-------
1.50
H
CO
l.CO
CE
0.50
6.0
6.5
7.0
7.5
Figure 65. Comparison of copper corrosion rates predicted by pipe flow
model with rates measured by independent sources.
-------
REFERENCES
SECTION I
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Special Publication 511-1, L.H. Bennett et a1., eds. May, 1978.
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Special Publication 551-2, J.H. Payer et al., eds. May, 1978.
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SECTION II
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35. Soos, 2.G. Lingane, P.J. KDerivation of the Chrcnoamperornetric Constant
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Current Using ths Rotating Disc Method," Corrosion Science, 8, p. 703,
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SECTION JIJ
1. Skold, R»V. Larsent T.E.D "Measurement of the Instantaneous Corrosion
Rate by Means of Polarization Data;i, Corrosion, _1_3_, 69, 1957.
2. Uaboian, R. "Electrochemical Techniques for Corrosion," Nat. See, for
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Currents", Advances in Corrosion Science and Technology, Vol. 6, 1976
Plenum Press.
4. Stern, M, Geary, A.L. "Electrochemical Polarization I. A Theoretics!
Analysis of the Shape of Polarization Curves*, J_.. n_ectrocheff!. Soe., 104,
p. 56. 1957.
5. Barnartt, S. "T«o-Point end Three Point Hethcds for the Investigation of
Electrode Reaction Mechanisms," Electrochlniica Actjt _15_e p. 1313, 1970.
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Techniques for Corrosion, NACE, 1977. p.l.
7. ASTK 65-71, Standard Reference Method in Making Poterstiostatlc and
potentiodynamic Anodic Polarization Heafurerents. Part 31, p. 1047, 1971.
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187
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9. SchUchting, H. Boundary Layer Theory. 6th Ed. McGraw-Hill 1968
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11. "Laboratory Corrosion Testing of Metals for The Process Industries", MACE
Standard TM-01-69 (1976 Revision) National Association of Corrosion
Engineers 1976.
12. "Standard Recoroiended Practice for Preparing, Cleaning, and Evaluating
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for Testing of Materials, 1979.
13. "Identification of Corrosion Products on Copper and Copper Alloys", RACE
Publication 36159, Nat. Assoc. of Corrosion Engrs., 1962.
SECTION IV
1. D.A. Frank-Kamenetskii, Diffusion and Heat Transfer in Chenical Kiretics,
2nd Ed. Plenum Press, 1969.
2. Y.G. Letiich, Physicoc_hCTiicaJ[ Hydrodynamics,, Prentice-Hall, 1962.
3. Y.V. Pleskov and V.Y, Filir.ovskii, The Rotating Disc F.lectrode, Plenum
Press (Consultants' Bureau), 1976.
4. Bondart, Michel. Kinetics of Chemical Processes, Prentice-Hall, 1968.
Englewood Cliffs, MJ.
5. Kennedy, J.8. and Neville, A.M. Basic Statistical Methods for Engineer.;
and Scientists, 2nd Ed., IEP New York, 1976.
SECHON V
1. Hoyt, Brian P. "SWD Field Corrosion Tasting 1972-1973 Data Summary"
Seattle Water Department Memorandum June 8, 1977.
2. Hoyt, Brian P. and Chapman, James D. "Corrosion Characteristics of
Seattle Water and Evaluation of Treatment by Lime"; Seattle Water-
Departments Quality Control Division, Nov. 1972, Revised Hay 1975.
3. Nakhjiri, K.S., Herrera, C.E., and Hilburn, R.D. "Counteractive Effects
of Disinfection and Corrosion Control" Seattle Pistnb:;tpon Svstc-i
Corrosion Control Study, Volume V., A report to the njnicTpTTTnviron-
mental Research Laboratory Cincinatci, Ohio 1982.
4. Larson, T.E. "Corrosion by Domestic Waters" Illinois Stats Water
Survey, Bulletin 59, 1975.
188
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