ELECTROCHEMICAL IMPEDANCE SPECTROSCOPY FOR THE
CHARACTERIZATION OF CORROSION AND CATHODIC PROTECTION OF
BURIED PIPELINES
By
KENNETH E. JEFFERS
A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
UNIVERSITY OF FLORIDA
1999
ACKNOWLEDGMENTS
Sincere thanks and appreciation go to Professor Mark Orazem for accepting me
into his research group and giving me the chance to learn about electrochemical
engineering. His technical and professional advisement were integral to the success of
this work. Thanks also to supervisory committee members Professor Ranganathan
Narayanan and Professor John Ambrose for their contributions to the completion of this
work. I would also like to thank Peter Zory for hearing my defense after very short notice.
I wish to acknowledge and express appreciation to the Pipeline Research
Committee International and the Gas Research Institute whose funding supported this
work.
Thanks to colleagues Steve Carson, Doug Riemer, Mike Membrino, and Kerry
Allahar for knowing more than me and sharing their experience and skills with me.
Thanks for allowing me to pick your brains. Additional thanks to Doug Riemer for
maintaining the group's computing power.
Finally, and most importantly, special thanks to my wonderful wife, Beth, who
was willing to delay settling down into family life while I pursued this opportunity to
complete an advanced degree. None of this could have been possible without her
encouragement and support. She is truly a blessing, and I would be lost without her.
TABLE OF CONTENTS
page
ACKN OW LED GM EN TS ................................................. ii
LIST OF TABLES ................................................. v
LIST OF FIGURES ......... ....................................... vi
ABSTRACT ........... ........................................ xx
CHAPTERS
1 INTRODUCTION ......... ................................... 1
2 THEORY .......... ................................ ........ 4
2.1 Steel Corrosion ....... ..... ............................. 4
2.2 CurrentPotential Behavior of Steel ......................... ..... 5
2.3 Surface Films .......... ................................. 10
2.4 P principles of E IS . . ...... ................................. .. 10
2.5 Statistical EIS D ata Analysis . ........ ........................ .. 14
2.6 Process M odel Developm ent . . ....... ........................ .. 16
2.6.1 R action K inetics . . ....... ............................ .. 17
2.6.2 Transport.......... ................................ 21
2.7 Application.......... ................................... 26
3 EXPERIMENTAL METHODS . . ....... .......................... 27
3.1 Summary ....... ... ................................. 27
3.2 Experim ental Apparatus ................................ 28
3.2.1 Electrodes ......... ......................... ........ 28
3.2.2 Current D distribution ............................... 30
3.2.3 C ell E lectrolyte . . ...... ............................... 33
3.2.4 Corrosion Cell D esign ............................. . . 33
3.2.5 Instrumentation and Data Collection ................... 36
3.3 Experim ental Procedures . . ...... ........................... .. 39
3.3.1 Applied DC Bias and Frequency Range ................. . 39
3.3.2 Variable Amplitude Galvanostatic Modulation ............. . 41
3.3.3 Initial Preparation . . ...... ............................. 43
4 EXPERIMENTAL RESULTS ....................................... 58
4.1 C orrected Cell Potential . ........ ........................... .. 58
4.2 Cylinder Electrode Experiments .......................... 59
4.2.1 Experiment 1 Modulation About the Corrosion Potential ......... 59
4.2.2 Experiment 2 Modulation About 1.6 pA/cm2 ............. . 61
4.2.3 Experiment 3 Modulation about 2.5 pA/cm2 .. . . . . . . 62
4.2.4 Experiment 4 Modulation about 4.0 pA/cm2 .. . . . . . . 63
4.3 Discrete Holiday Experiments ............................ 70
4.3.1 Holiday Experiment 1 Modulation About the Corrosion Potential . 70
4.3.2 Holiday Experiment 2 Modulation About 5.0 pA/cm2 ........... 71
5 DATA ANALYSIS.......................................... 74
5.1 Overview ........... ....................................... 74
5.2 Process M odel Regression Analysis ........................ 75
5.2.1 M odel Param eters . . ...... ............................. 75
5.2.2 Quality of R egression . . ....... .......................... 78
5.2.3 Regression Parameter Results ........................ 84
5.2.4 Parameter Values as a Function of Applied Current Density ....... 101
5.3 Estimation of Polarization Resistance ...................... 107
5.4 Link to Polarization Parameters .......................... 119
6 CONCLUSIONS ........................................... 124
7 SUGGESTIONS FOR FUTURE WORK .............................. 128
APPENDICES
A FORTRAN CODE FOR BEM SIMULATIONS ........................ 130
B LABVIEW CONTROL OF EXPERIMENTS .......................... 141
C MEASUREMENT MODEL APPROACH ............................ 150
D REGRESSION PARAMETER RESULTS ............................ 164
R E FE R E N C E S ........................................................ 202
BIOGRAPHICAL SKETCH . . ...... ................................. 206
LIST OF TABLES
Table page
21. Parameter values used to calculate the polarization curve for steel in neutral
to slightly basic, oxygenated soil electrolytes. Potentials were
referenced to the coppercopper sulfate (Cu/CuSO4) electrode. . . . . . . ... 8
31. Chemical analysis of the supplied pipeline grade, 5LX52, steel coupons. ....... 46
32. Results for the total current integrated on the electrode surface determined
from the current distribution resulting from the BEM simulations. Also
included is the calculated electrolyte resistance for both electrode types
while accounting for the porosity of the solid matrix. The porosity or void
fraction assumed for the calculation was 0.40. Also included are the
results from impedance measurements and from using the anode
resistance formula, equation (37), for the cylinder electrode........... . .. 46
33. Calculated concentrations of ionic species included in simulated soil
electrolyte. Molarity units are in moles/liter. The calculated
conductivity is also included . ......... .......................... .. 47
34. Masses of salts in g/L added to water to prepare simulated soil electrolyte.
The solution pH is included ............. ........................... .. 47
35. Experimental outline including electrode type and applied current density. ...... 48
51. Process model parameter values, at selected times, used to extrapolate the
impedance response of the cylinder electrode maintained at the
corrosion potential ............. ................................... 111
52. Parameter values, at selected times, used to extrapolate the impedance
response of the cylinder electrode at an applied cathodic current density
of 1.6 pA/cm2 ................................................... 111
53. Process model parameter values, at selected times, used to extrapolate the
impedance response of the holiday electrode maintained at the corrosion
potential. ................................................ 112
54. Extrapolated values for Re, Z(0), and Rp from regression of the process model
and measurement models to the impedance data presented in Figure 543..... 112
LIST OF FIGURES
Figure page
21. Calculated polarization curve of steel with the potential as a function of the
applied current density. Currentpotential curves are included for each
reaction contributing to the total current density .................. ...... 9
22. Schematic diagram of a circuit containing a resistor in series with a Voigt
circuit......... ................................... ........ 13
23. Nyquist plot for the circuit in Figure 22 with the parameter values
Re = 10 Q, Cd= 10 F, andRt= 250 Q ................................ 13
24. Geometry for the diffusion model .............................. 26
31. Schematic of the simulated holiday electrode .............................. 49
32. Axisymmetric plane, including boundary conditions, of the 1/8" holiday
electrode for BEM sim ulation.. . ......... .......................... 50
33. Current density and potential distributions, generated from BEM
simulation, as a function of axial position on the 1/8" holiday electrode.
The center of the holiday or conductive metal band was located 3" from
the end of the bottom acrylic insulating piece ........................... 51
34. Current density and potential distributions, generated from BEM
simulation, as a function of axial position on the cylinder electrode. ......... 52
35. Schematic of corrosion cell body showing position of electrodes ......... . ... 53
36. Schematic of corrosion cell top cover piece .............................. 54
37. Corrosion cell flow diagram including instrumentation .. . . . . . . 55
38. Preliminary experimental polarization curve for pipeline grade steel,
generated from a galvanodynamic sweep from anodic to cathodic
current densities at a rate of 0.3 pA/cm2 per minute. The closed circles
correspond to the applied conditions listed in Table 35 for the cylinder
electrode experim ents . ......... ................................ 56
39. Preliminary impedance spectrum in Nyquist form to identify high
frequency instrumental artifacts. The response is from the cylinder
electrode in liquid electrolyte only, with K = 0.00122 Q1cm1, to
variable amplitude galvanostatic modulation about the corrosion
potential. The tested frequency range was 1000 Hz to 0.01 Hz. The
calculated spectrum was generated from measurement model regression
parameters........... ............................. ........ 57
41. The corrosion potential, measured with respect to a calomel reference
electrode, as a function of time for the cylinder electrode ............. . 64
42. Nyquist plots at selected times for the impedance response of the cylinder
electrode to variable amplitude galvanostatic modulation about zero
applied current . . ....... ...................................... .. 64
43. Bode plots of the negative imaginary component as a function of
frequency, at selected times, for the cylinder electrode in response to
variable amplitude galvanostatic modulation about zero applied current. ...... 65
44. The cell potential, measured with respect to a calomel reference electrode,
as a function of time for the cylinder electrode maintained at an applied
cathodic current density of 1.6 tA/cm2 ................................. 66
45. Nyquist plots at selected times for the impedance response of the cylinder
electrode to variable amplitude galvanostatic modulation about an
applied cathodic DC current density bias of 1.6 tA/cm2 ............. . .... 66
46. The cell potential, measured with respect to a calomel reference electrode,
as a function of time for the cylinder electrode maintained at an applied
cathodic current density of 2.5 tA/cm2 ................................ 67
47. Nyquist plots at selected times for the impedance response of the cylinder
electrode to variable amplitude galvanostatic modulation about an
applied cathodic DC current density bias of 2.5 tA/cm2 ............. . .... 68
48. The cell potential, measured with respect to a calomel reference electrode,
as a function of time for the cylinder electrode maintained at an applied
cathodic current density of 4.0 tA/cm2 ................................. 69
49. Nyquist plots at selected times for the impedance response of the cylinder
electrode to variable amplitude galvanostatic modulation about an
applied cathodic DC current density bias of 4.0 tA/cm2 ............. . .... 69
410. The corrosion potential, measured with respect to a calomel reference
electrode, as a function of time for the holiday electrode ............ . 72
411. Nyquist plots at selected times for the impedance response of the holiday
electrode to variable amplitude galvanostatic modulation about zero
applied current .......... ........................................ 72
412. The cell potential, measured with respect to a calomel reference
electrode, as a function of time for the holiday electrode maintained at
an applied cathodic current density of 5 pA/cm2. The increase in the
potential at the end of the trace occurred after resetting the applied
current to 0......... ....................................... 73
413. Nyquist plots at selected times for the impedance response of the holiday
electrode to variable amplitude galvanostatic modulation about an
applied cathodic DC current density bias of 5.0 pA/cm .............. . ... 73
51. The impedance response in Nyquist form of the cylinder electrode to
variable amplitude galvanostatic modulation about the corrosion
potential, including the results for the process model regression using
modulus weighting. The error bars represent the 95.4% confidence
intervals for the model estimation for both the real and imaginary
components. The data were generated 24 hours after the WE was
exposed to the electrolytic environment ........................ . 80
52. Both the normalized real and imaginary component residual errors, as a
function of frequency, resulting from process model regression to the
data of Figure 51....... ................................... 80
53. The normalized real component residual errors, as a function of frequency,
resulting from process model regression to the data of Figure 51. The
estimated stochastic noise limits are included ........................... 81
54. The normalized imaginary component residual errors, as a function of
frequency, resulting from process model regression to the data of Figure
51. The estimated stochastic noise limits are included............. 81
55. The normalized real component residual errors, as a function of frequency,
resulting from process model regression to data generated from
modulation about an applied DC current density bias of 1.6 pA/cm2.
The impedance response was measured from the cylinder electrode after
24 hours of exposure. The estimated stochastic noise limits are included
with the 95.4% confidence intervals............. ...................... 82
56. The normalized imaginary component residual errors, as a function of
frequency, resulting from process model regression to data generated
from modulation about an applied DC current density bias of 1.6 pA/
cm2. The impedance response was measured from the cylinder
electrode after 24 hours of exposure. The estimated stochastic error
structure limits are included with the 95.4% confidence intervals............ 83
57. The diffusion time constant for the film and cell potential as functions of
time for the cylinder electrode with the applied current equal to zero......... 90
58. The bulk layer diffusion time constant and WE potential as functions of
time for the cylinder electrode with the applied current equal to zero......... 90
59. The ratio of the diffusivities of oxygen in the bulk to the film and WE
potential as functions of time for the cylinder electrode with the applied
current equal to zero........ ................................. 91
510. The calculated film thickness in microns and WE potential as functions
of time for the cylinder electrode with the applied current equal to zero....... 92
511. The calculated bulk diffusion layer thickness in microns and WE
potential as functions of time for the cylinder electrode with the applied
current equal to zero . ......... ................................ .. 92
512. The calculated film thickness in microns as a function of potential for the
cylinder electrode with the applied current equal to zero ............ . 93
513. The calculated bulk diffusion layer thickness in microns as a function of
potential for the cylinder electrode with the applied current equal to zero ..... 93
514. The effective charge transfer resistance and WE potential as functions of
time for the cylinder electrode with the applied current equal to zero......... 94
515. The effective charge transfer resistance as a function of potential for the
cylinder electrode with the applied current equal to zero ............ . 94
516. The charge transfer resistance for oxygen reduction and WE potential as
functions of time for the cylinder electrode with the applied current
equal to zero.......... ..................................... 95
517. The charge transfer resistance for oxygen reduction as a function of
potential for the cylinder electrode with the applied current equal to zero ..... 95
518. The diffusion impedance coefficient and WE potential as functions of
time for the cylinder electrode with the applied current equal to zero......... 96
519. The diffusion impedance coefficient as a function of potential for the
cylinder electrode with the applied current equal to zero ............. . 96
520. The cell capacitance and WE potential as functions of time for the
cylinder electrode with the applied current equal to zero ............ . 97
521. The cell capacitance as a function of potential for the cylinder electrode
with the applied current equal to zero......................... . ...... 97
522. The electrolyte resistance as a function of time for the cylinder electrode
with the applied current equal to zero......................... . ...... 98
523. The diffusion time constant for the film and WE potential as functions of
time for the cylinder electrode with an applied DC current density bias
of 1.6 iA /cm 2 .. . . . . . . . . . . .. . . . . . . . . . . . . . 9 9
524. The diffusion time constant for the film as a function of potential for the
cylinder electrode with an applied DC current density bias of 1.6 pA/cm2 ..... 99
525. The effective charge transfer resistance and WE potential as functions of
time for the cylinder electrode with an applied DC current density bias
of 4 .0 iA /cm 2 ................................................... 100
526. The effective charge transfer resistance as a function of potential for the
cylinder electrode with an applied DC current density bias of 4.0 pA/cm2.. . 100
527. The diffusion time constant for the film after 4 days of exposure plotted
as a function of applied current density for the cylinder electrode........... 102
528. The bulk layer diffusion time constant after 4 days of exposure plotted as
a function of applied current density for the cylinder electrode......... ... 102
529. The ratio of the diffusivities of oxygen in the bulk to the film after 4 days
of exposure plotted as a function of applied current density for the
cylinder electrode ......... .................................. 103
530. The calculated film thickness in microns after 4 days of exposure plotted
as a function of applied current density for the cylinder electrode........... 103
531. The calculated bulk diffusion layer thickness in microns after 4 days of
exposure plotted as a function of applied current density for the cylinder
electrode ............ .......................................... 104
532. The effective charge transfer resistance after 4 days of exposure plotted
as a function of applied current density for the cylinder electrode........... 104
533. The diffusion impedance coefficient after 4 days of exposure plotted as a
function of applied current density for the cylinder electrode .......... ... 105
534. The cell capacitance after 4 days of exposure plotted as a function of
applied current density for the cylinder electrode ................ . 105
535. The electrolyte resistance after 4 days of exposure plotted as a function
of applied current density for the cylinder electrode ............... . 106
536. Nyquist plots at selected times, including experimental data and process
model extrapolations, for the impedance response of the cylinder
electrode to variable amplitude galvanostatic modulation about zero
applied current .......... ....................................... 113
537. Nyquist plots at selected times, including experimental data and process
model extrapolations, for the impedance response of the cylinder
electrode to variable amplitude galvanostatic modulation about an
applied cathodic DC current density bias of 1.6 tA/cm ............. . 113
538. Nyquist plots at selected times, including experimental data and process
model extrapolations, for the impedance response of the cylinder
electrode to variable amplitude galvanostatic modulation about an
applied cathodic DC current density bias of 2.5 tA/cm ............. . 114
539. Nyquist plots at selected times, including experimental data and process
model extrapolations, for the impedance response of the cylinder
electrode to variable amplitude galvanostatic modulation about an
applied cathodic DC current density bias of 4.0 A/cm2 ............. . 114
540. Nyquist plots at selected times, including experimental data and process
model extrapolations, for the impedance response of the holiday
electrode to variable amplitude galvanostatic modulation about zero
applied current .......... ....................................... 115
541. The cell potential, measured with respect to the calomel reference
electrode, and the applied current density as functions of time for the
holiday electrode ............. .................................... 116
542. Cathodic polarization curve, generated from a galvanodynamic sweep
performed using the holiday electrode. The sweep rate was 0.33 tA/
cm2 per minute. The measured cell potential is plotted as a function of
the applied current density including the experimental points
corresponding to the step changes in Figure 541 ................. . 116
543. Nyquist plots for the impedance response of the holiday electrode to
variable amplitude galvanostatic modulation about several applied
current densities. The collected data and extrapolated spectra using the
process m odel are included ............. .......................... .. 117
544. The slope of the polarization curve, calculated from the data presented in
Figure 542, as a function of applied current density for the holiday
electrode. Extrapolated polarization resistance values, using both the
process model and the measurement model approach, are included for
the experim ents in Figure 543 ............. ....................... .. 118
545. The natural logarithm of the effective charge transfer resistance plotted
as a function of potential including the equation for the fitted line.
Values were obtained from process model regression to impedance
response data collected for the cylinder electrode maintained at the
corrosion potential . ........ ................................... . 122
546. The corrosion current as a function of time calculated from the Tafel
slope for iron dissolution determined for the cylinder electrode
maintained at the corrosion potential ................................. 122
547. The natural logarithm of the effective charge transfer resistance plotted
as a function of potential, including the equation for the fitted line.
Values were obtained from process model regression to impedance
response data collected for the cylinder electrode with an applied
cathodic DC current density of 4.0 pA/cm2. . . . . . 123
548. The hydrogen evolution current density as a function of time calculated
from the Tafel slope determined from the cylinder electrode with an
applied cathodic DC current density of 4.0 A/cm2.. . . . . . 123
A1. The holiday electrode cell boundary including the x and y coordinates for
each vertex. The edges are numbered for a total of 8.. . . . . . . 131
B1. Flow chart for operation of main control, '1260/273_main_8/98.vi'........... 146
B2. Flow chart for operation of 'I_V monitor.vi'. ........................... 147
B3. Flow chart for operation of 'run impedance scan.vi'................ . 148
B4. Flow chart for operation of 'poll 1260 for data.vi'. ................ 149
C1. The impedance response and the measurement model prediction, in
Nyquist form, from a preliminary scan conducted on the cylinder
electrode using variable amplitude galvanostatic modulation about the
corrosion potential. ............................... . ..... . 154
C2. The normalized real component residual errors with confidence intervals,
as a function of frequency, resulting from measurement model
regression, using modulus weighting, to the real component of the data
in Figure C1. ........ ..................................... 155
C3. The normalized residual errors with confidence intervals, as a function of
frequency, between the imaginary data of Figure C1 and the predicted
imaginary component resulting from measurement model regression to
the real com ponent of the data ............. ........................ .. 155
C4. The data of Figure Cl, in Nyquist form, including the full set of replicate
scans, after rejecting the high frequency artifacts ................. . 156
C5. The residual errors, as a function of frequency, for the real component of
the impedance resulting from measurement model regression of 5 line
shapes, using modulus weighting, to the complex data of each individual
scan of Figure C 4 . . ........ ................................. .. 157
C6. The residual errors, as a function of frequency, for the imaginary
component of the impedance resulting from measurement model
regression of 5 line shapes, using modulus weighting, to the complex
data of each individual scan of Figure C4 ............................. 157
C7. The standard deviation, as a function of frequency, of the real and
imaginary stochastic errors calculated from the real and imaginary
residual errors of Figure C5 and Figure C6, respectively. The model
for the standard deviation includes the parameters, with values,
P = 0.0017792 and 8 = 0.021916 ............. ..................... ... 158
C8. The normalized residual errors, as a function of frequency, between the
imaginary data of scan 1, shown in Figure C4, and the predicted values
resulting from measurement model regression of 3 line shapes, using
error structure weighting, to the real component of the data. Error
structure weighting was used. The plot includes the confidence intervals
and the limits of the stochastic error structure model ................ . 159
C9. The normalized residual errors, as a function of frequency, between the
real data of scan 1, shown in Figure C4, and the predicted values
resulting from measurement model regression of 2 line shapes, using
error structure weighting, to the imaginary component of the data. The
plot includes the confidence intervals and the limits of the stochastic
error structure m odel . ......... ................................ 160
C10. The normalized residual errors, as a function of frequency, for the
imaginary component of scan 1, shown in Figure C4, resulting from
measurement model regression of 2 line shapes, using error structure
weighting, to the imaginary component of the data. The plot includes
confidence intervals and the limits of the stochastic error structure model.... 161
C11. The normalized real component residual errors, as a function of
frequency, resulting from a complex fit of 5 line shapes, using error
structure weighting, after rejecting inconsistent high and low frequency
points from the data shown in Figure C1. The confidence intervals and
stochastic error structure limits are included .................... 162
C12. The normalized imaginary component residual errors, as a function of
frequency, resulting from a complex fit of 5 line shapes, using error
structure weighting, after rejecting inconsistent high and low frequency
points from the data presented in Figure C1. The confidence intervals
and stochastic error structure limits are included ............... ..... 163
D1. The electrolyte resistance as a function of time for the cylinder electrode
with the applied current equal to zero ........................ . ...... 165
D2. The diffusion time constant for the film and cell potential as functions of
time for the cylinder electrode with the applied current equal to zero. ....... 166
D3. The diffusion time constant for the film as a function of potential for the
cylinder electrode with the applied current equal to zero ............ . .... 166
D4. The bulk layer diffusion time constant and cell potential as functions of
time for the cylinder electrode with the applied current equal to zero. ....... 167
D5. The bulk layer diffusion time constant as a function of potential for the
cylinder electrode with the applied current equal to zero ............ . .... 167
D6. The ratio of the diffusivities of oxygen in the bulk to the film and cell
potential as functions of time for the cylinder electrode with the applied
current equal to zero ........... ................................. 168
D7. The ratio of the diffusivities of oxygen in the bulk to the film as a function
of potential for the cylinder electrode with the applied current equal to zero.. 168
D8. The calculated film thickness in microns and cell potential as functions of
time for the cylinder electrode with the applied current equal to zero. ....... 169
D9. The calculated film thickness in microns as a function of potential for the
cylinder electrode with the applied current equal to zero ............ . .... 169
D10. The calculated bulk diffusion layer thickness in microns and cell
potential as functions of time for the cylinder electrode with the applied
current equal to zero .......... ................................... 170
D1 1. The calculated bulk diffusion layer thickness in microns, as a function of
potential for the cylinder electrode with the applied current equal to zero. . 170
D12. The effective charge transfer resistance and cell potential as functions of
time for the cylinder electrode with the applied current equal to zero. ....... 171
D13. The effective charge transfer resistance as a function of potential for the
cylinder electrode with the applied current equal to zero ............. . 171
D14. The charge transfer resistance for oxygen reduction and cell potential as
functions of time for the cylinder electrode with the applied current
equal to zero.............................................. 172
D15. The charge transfer resistance for oxygen reduction as a function of
potential for the cylinder electrode with the applied current equal to zero ..... 172
D16. The diffusion impedance coefficient and cell potential as functions of
time for the cylinder electrode with the applied current equal to zero. ....... 173
D17. The diffusion impedance coefficient as a function of potential for the
cylinder electrode with the applied current equal to zero ............. . 173
D18. The cell capacitance and cell potential as functions of time for the
cylinder electrode with the applied current equal to zero ............. . 174
D19. The cell capacitance as a function of potential for the cylinder electrode
with the applied current equal to zero ......................... 174
D20. The electrolyte resistance as a function of time for the cylinder electrode
with an applied DC current density bias of 1.6 tA/cm2 .. . . . . . . 175
D21. The diffusion time constant for the film and cell potential as functions of
time for the cylinder electrode with an applied DC current density bias
of 1.6 A /cm 2 .................................................. 176
D22. The diffusion time constant for the film as a function of potential for the
cylinder electrode with an applied DC current density bias of 1.6 tA/cm2 . 176
D23. The bulk layer diffusion time constant and cell potential as functions of
time for the cylinder electrode with an applied DC current density bias
of 1.6 1A /cm 2 .................................................. 177
D24. The bulk layer diffusion time constant as a function of potential for the
cylinder electrode with an applied DC current density bias of 1.6 pA/cm2 . 177
D25. The ratio of the diffusivities of oxygen in the bulk to the film and the cell
potential as functions of time for the cylinder electrode with an applied
DC current density bias of 1.6 pA/cm ............................... 178
D26. The ratio of the diffusivities of oxygen in the bulk to the film as a
function of potential for the cylinder electrode with an applied DC
current density bias of 1.6 tA/cm 2 ................................... 178
D27. The calculated film thickness and cell potential as functions of time for
the cylinder electrode with an applied DC current density bias of
1.6 tA/cm2. .............................................. 179
D28. The calculated film thickness as a function of potential for the cylinder
electrode with an applied DC current density bias of 1.6 tA/cm2 ........... 179
D29. The calculated bulk diffusion layer thickness and cell potential as
functions of time for the cylinder electrode with an applied DC current
density bias of 1.6 tA /cm ........................................ 180
D30. The calculated bulk diffusion layer thickness as a function of potential
for the cylinder electrode with an applied DC current density bias of
1.6 tA /cm 2 .. . . . . . . . . . . . . . . . . . . . . . . . . . . 18 0
D31. The effective charge transfer resistance and cell potential as functions of
time for the cylinder electrode with an applied DC current density bias
of 1.6 p A /cm 2. .................................................. 18 1
D32. The effective charge transfer resistance as a function of potential for the
cylinder electrode with an applied DC current density bias of 1.6 tA/cm2 .... 181
D33. The diffusion impedance coefficient and cell potential as functions of
time for the cylinder electrode with an applied DC current density bias
of 1.6 tA /cm 2 .................................................. 182
D34. The diffusion impedance coefficient as a function of potential for the
cylinder electrode with an applied DC current density bias of 1.6 tA/cm2. .... 182
D35. The cell capacitance and cell potential as functions of time for the
cylinder electrode with an applied DC current density bias of 1.6 pA/cm2 .... 183
D36. The cell capacitance as a function of potential for the cylinder electrode
with an applied DC current density bias of 1.6 pA/cm2 ............. . 183
D37. The electrolyte resistance as a function of time for the cylinder electrode
with an applied DC current density bias of 2.5 tA/cm2 ............. . 184
D38. The diffusion time constant for the film and cell potential as functions of
time for the cylinder electrode with an applied DC current density bias
of 2 .5 [ A /cm 2 .................................................. 185
D39. The diffusion time constant for the film as a function of potential for the
cylinder electrode with an applied DC current density bias of 2.5 pA/cm2. .... 185
D40. The bulk layer diffusion time constant and cell potential as functions of
time for the cylinder electrode with an applied DC current density bias
of 2 .5 [ A /cm 2 .................................................. 186
D41. The bulk layer diffusion time constant as a function of potential for the
cylinder electrode with an applied DC current density bias of 2.5 pA/cm2. .... 186
D42. The ratio of the diffusivities of oxygen in the bulk to the film and the cell
potential as functions of time for the cylinder electrode with an applied
DC current density bias of 2.5 pA/cm2 .............................. 187
D43. The ratio of the diffusivities of oxygen in the bulk to the film as a
function of potential for the cylinder electrode with an applied DC
current density bias of 2.5 pA/cm2 ................................... 187
D44. The calculated film thickness and cell potential as functions of time for
the cylinder electrode with an applied DC current density bias of
2.5 [A /cm 2 .......... .......................................... 188
D45. The calculated film thickness as a function of potential for the cylinder
electrode with an applied DC current density bias of 2.5 pA/cm2. ........... 188
D46. The calculated bulk diffusion layer thickness and cell potential as
functions of time for the cylinder electrode with an applied DC current
density bias of 2.5 pA /cm 2. ......................................... 189
D47. The calculated bulk diffusion layer thickness as a function of potential
for the cylinder electrode with an applied DC current density bias of
2 .5 IA /cm 2 . . . . . .. . . . . . . . . . . . . . . . . . . . . 18 9
D48. The effective charge transfer resistance and cell potential as functions of
time for the cylinder electrode with an applied DC current density bias
of 2 .5 IA /cm 2 ................................................ .. 190
xvii
D49. The effective charge transfer resistance as a function of potential for the
cylinder electrode with an applied DC current density bias of 2.5 pA/cm2. . 190
D50. The diffusion impedance coefficient and cell potential as functions of
time for the cylinder electrode with an applied DC current density bias
of 2 .5 [lA /cm 2 .................................................. 19 1
D51. The diffusion impedance coefficient as a function of potential for the
cylinder electrode with an applied DC current density bias of 2.5 pA/cm2. . 191
D52. The cell capacitance and cell potential as functions of time for the
cylinder electrode with an applied DC current density bias of 2.5 pA/cm2 ... 192
D53. The cell capacitance as a function of potential for the cylinder electrode
with an applied DC current density bias of 2.5 pA/cm2 .. . . . . . . 192
D54. The electrolyte resistance as a function of time for the cylinder electrode
with an applied DC current density bias of 4.0 pA/cm2 .. . . . . . . 193
D55. The diffusion time constant for the film and cell potential as functions of
time for the cylinder electrode with an applied DC current density bias
of 4 .0 [ A /cm 2 .................................................. 194
D56. The diffusion time constant for the film as a function of potential for the
cylinder electrode with an applied DC current density bias of 4.0 pA/cm2 . 194
D57. The bulk layer diffusion time constant and cell potential as functions of
time for the cylinder electrode with an applied DC current density bias
of 4 .0 p A /cm 2 .................................................. 195
D58. The bulk layer diffusion time constant as a function of potential for the
cylinder electrode with an applied DC current density bias of 4.0 pA/cm2. . 195
D59. The ratio of the diffusivities of oxygen in the bulk to the film and the cell
potential as functions of time for the cylinder electrode with an applied
DC current density bias of 4.0 pA/cm .............................. 196
D60. The ratio of the diffusivities of oxygen in the bulk to the film as a
function of potential for the cylinder electrode with an applied DC
current density bias of 4.0 pA/cm2 ................................... 196
D61. The calculated film thickness and cell potential as functions of time for
the cylinder electrode with an applied DC current density bias of
4.0 pA/cm2. .............................................. 197
xviii
D62. The calculated film thickness as a function of potential for the cylinder
electrode with an applied DC current density bias of 4.0 tA/cm2........... 197
D63. The calculated bulk diffusion layer thickness and cell potential as
functions of time for the cylinder electrode with an applied DC current
density bias of 4.0 tA /cm ........................................ 198
D64. The calculated bulk diffusion layer thickness as a function of potential
for the cylinder electrode with an applied DC current density bias of
4 .0 ptA /cm 2. . . . . . . . . . . . . . . . . . . .. . . . . . . . 19 8
D65. The effective charge transfer resistance and cell potential as functions of
time for the cylinder electrode with an applied DC current density bias
of 4 .0 p A /cm 2. .................................................. 199
D66. The effective charge transfer resistance as a function of potential for the
cylinder electrode with an applied DC current density bias of 4.0 tA/cm2. . 199
D67. The diffusion impedance coefficient and cell potential as functions of
time for the cylinder electrode with an applied DC current density bias
of 4 .0 tA /cm 2 .................................................. 200
D68. The diffusion impedance coefficient as a function of potential for the
cylinder electrode with an applied DC current density bias of 4.0 tA/cm2 . 200
D69. The cell capacitance and cell potential as functions of time for the
cylinder electrode with an applied DC current density bias of 4.0 tA/cm2. . 201
D70. The cell capacitance as a function of potential for the cylinder electrode
with an applied DC current density bias of 4.0 tA/cm2 ............. . 201
Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science
ELECTROCHEMICAL IMPEDANCE SPECTROSCOPY FOR THE
CHARACTERIZATION OF CORROSION AND CATHODIC PROTECTION OF
BURIED PIPELINES
By
Kenneth E. Jeffers
August 1999
Chairman: Mark E. Orazem
Major Department: Chemical Engineering
An electrochemical cell was constructed to simulate a steel pipeline buried in low
ionic strength soil and connected to a cathodic protection system for corrosion prevention.
Electrochemical impedance spectroscopy measurements were performed to monitor
surface film formation and changes in charge transfer reaction kinetics. Statistical models
were regressed to impedance data to identify nonstationary behavior and to estimate the
stochastic error structure of the measurements. A process model for the impedance
response was developed by considering contributions to the total current flow within the
cell and diffusion of reacting species. Regression of the process model to data yielded
parameter values changing with time. The regression parameters were used to extrapolate
asymptotic resistances and were linked to the polarization behavior of steel. The
experimental and analytical methods developed were useful for monitoring the time
dependent electrochemical behavior of steel at different levels of cathodic protection.
XX
CHAPTER 1
INTRODUCTION
The motivation for this work stems from the need to gain insight into the design
and operation of cathodic protection (CP) systems for networks of buried pipelines in
service for the transmission of petroleum. Currently, sophisticated boundary element
models are being developed to characterize CP systems to determine if they provide an
adequate level of corrosion prevention for given environmental conditions. Such models
can account for the influence of discrete coating holidays, multiple pipelines in a rightof
way with single or multiple CP systems, the use of mixed anodes, and variations in
coating properties along a length of pipe [1, 2].
The complications associated with the modeling efforts arise from the need to
employ nonlinear boundary conditions for determining the current and potential
distributions along a given length of pipe and at points within the surrounding soil [1 5].
The boundary conditions are often characterized by curve fits of experimental data. Thus,
it is important to generate representative data from welldesigned experiments which
consider general field conditions. Important physical effects include the role of soil
chemistry and the formation of films on exposed metal surfaces, oxygen diffusion through
porous media including coatings and films, and charge transfer reaction kinetics.
In previous work, the role of film formation and the time dependent polarization
behavior of steel have been investigated. Mathematical models and experimental
procedures were developed and based on real time, current and potential measuring
methods [6, 7]. Kinetic and transport parameters were regressed from potentialtime data
and related to the polarization behavior of steel. The results gave insight into the time
scales necessary to polarize metal structures to assure a desired level of cathodic
protection has been achieved.
The objective of the present work was to develop an experimental method using
electrochemical impedance spectroscopy (EIS) to measure the frequency response of
pipeline grade steel subjected to soil environments and cathodic protection. EIS has been
shown to be a sensitive technique for monitoring nonstationary behavior, which proved to
be ideal for exploring corrosion systems where film formation contributes to influence
reaction kinetics and transport properties over time.
In previous work EIS has been used to monitor corrosion processes and has been
used extensively for characterizing the performance of protective polymer coatings [8].
However, the difficulty associated with EIS is data interpretation. Typically, EIS spectra
are analyzed by fitting equivalent electrical circuits, containing elements such as resistors
and capacitors, to the data [8, 9, 12]. This allows determination of trends in diffusion time
constants and changes in high and low frequency resistance limits. However, it may be
possible to fit several different circuit models to the data, which may or may not explain
the physical phenomena occurring within an electrochemical cell. Others have
endeavored to analyze EIS spectra by fitting models developed from a knowledge of
faradaic and transport processes associated with charge transfer reactions and diffusion of
reacting species from the bulk electrolyte to the metal surface [911]. For this work, a
process model was developed by considering the anodic and cathodic electrochemical
reactions of pipeline grade carbon steel exposed to oxygenated electrolytic soils and by
solving the governing equations of diffusion for the reacting species.
Wellcontrolled experiments were designed to assure the generation of reliable
data suitable for regression of process models. To guarantee symmetric current and
potential distributions, an electrochemical cell was designed and constructed with a
cylindrical geometry. A stationary cylindrical coupon, machined from pipeline grade
steel, served as the working electrode. The coupon was embedded in a solid sand matrix,
saturated with low ionic strength electrolyte containing species present in typical soils,
and surrounded by a counter electrode consisting of a platinumrhodium alloy mesh
screen. Experiments were conducted by controlling the net current flow between the
working and counter electrodes. Appropriate current values were applied to simulate the
conditions of cathodic protection.
The impedance spectra generated for this work were analyzed by regressing
statistical and process models to the data. Application of statistical models allowed
estimation of the measurement error structure, which gave insight to the reliability of the
data. Application of the process model yielded time dependent parameters useful for
monitoring changes in reaction kinetics and diffusion properties with time as films formed
on the steel surface. The thicknesses of the film and bulk diffusion layers were estimated,
and asymptotic spectral values were calculated.
The results from the EIS work showed that the electrochemical system exhibited
nonstationary behavior long after the measured potential had reached a steady state. The
experimental method was useful for extracting parameters changing with time, and such
parameters could then be linked to the polarization behavior of steel.
CHAPTER 2
THEORY
2.1 Steel Corrosion
The present work considers pipelines buried in moist, oxygenated soils with
neutral to slightly basic pH. External corrosion of the pipeline surface occurs via chemical
attack from the surrounding medium. Electrons held by the metal are transferred to
electrolyte species during electrochemical oxidationreduction, halfcell reactions. Metal
dissolution is the anodic reaction as iron, the major component in the pipeline metal alloy,
is oxidized to ferrous ions according to
Fe Fe2+ + 2e (21)
Reduction of oxygen is the cathodic reaction according to
02 + 2H20 + 4e 40H (22)
The rate of oxygen reduction is limited to the rate at which oxygen diffuses to the steel
surface from the surroundings. As the pipeline is polarized to more cathodic potentials,
for example, when connected to a CP system, hydrogen evolution occurs at increasing
rates as water is reduced according to
2H20 + 2e H2 + 20H (23)
The current density of the metal surface can be related to the rate of the
electrochemical reactions according to Faraday's law
r (24)
nF
where n is the number of electrons transferred during the reaction, and F is the Faraday
constant. The total current density on the pipeline is the sum of the current contributions
from the anodic and cathodic reactions (21), (22), and (23) according to
iot = iFe + i + iH (25)
The sign convention for equation (25) is that anodic currents are positive and cathodic
currents are negative.
2.2 CurrentPotential Behavior of Steel
The currentpotential behavior of a metal in a given electrolyte is shown by the
polarization curve, which can be generated experimentally by performing dynamic sweeps
controlling one electrical quantity through a sequenced range of values and measuring the
other at each point in the sweep. Galvanodynamic sweeps are performed by ramping or
stepping the current and measuring potential; whereas, in potentiodynamic experiments
potential is controlled. The data are usually presented on a plot with potential on the
vertical axis and current density plotted on the horizontal axis on a logarithmic scale. The
polarization curve is often used as a boundary condition for cathodic protection modeling
[15], and is a tool for determining the corrosion potential, Tafel slopes, and corrosion
rates [12, 13]. Typical currentpotential behavior for steel is presented in Figure 21. The
curve was generated by calculating current density values at applied potentials using an
equation adapted by Orazem et al. [3, 4] from that developed by Nisancioglu [7]
according to
V V* (V V*2) (V V*H2)
itot = 10 PFe +10 02 10 PH2 (26)
lim, 02
The terms in equation (26) correspond to the current contributions from reactions (21),
(22), and (23), respectively, and Vis the potential of the steel measured with respect to a
reference electrode located in the soil electrolyte adjacent to the pipe. The parameters
PFe' 02 and PH2 are the Tafel slopes for each reaction, and ilm, o2 is the mass transfer
limited current density due to oxygen reduction. The parameters V*Fe, V*02, and V*H2
are effective equilibrium potentials that include the influence of exchange current
densities, temperature, and concentrations. For example,
V*Fe = EFe lOg(io, F) (27)
where iO, Fe is the exchange current density for iron dissolution [5]. The equilibrium
potential, EFe, can be determined from the Nernst equation according to
EFe = EOFe + log [Fe2+] (28)
where EOFe is the standard potential for iron dissolution and [Fe2+] is the concentration
of ferrous ions [12]. Figure 21 includes curves for the contribution of each separate
reaction as well as the net total current density. The values used for the calculation are
listed in Table 21. All potentials were referenced to the coppercopper sulfate
(Cu/CuSO4) electrode.
Because of limitations with placement of the reference electrode, the polarization
curve must be corrected for the ohmic drop due to current flow through the cell
electrolyte. Many available potentiostats are equipped with options for performing IR
compensation routines to correct the potential measurements. One such method is the
current interrupt technique [14, 15]. The current interrupt routine begins by measuring the
potential and abruptly turning off the cell current. Then, two or more offpotential
measurements are made separated by short time delays usually on the order of 50
milliseconds. A line is fit through the points, and a potential value is extrapolated back to
the point of the current interrupt initiation. The difference between the extrapolated value
and the potential before the interrupt is the ohmic drop. After the routine is finished, the
cell current is resumed to its previous setting or stepped to a new desired level.
Many factors lead to uncertainty in determination of the ohmic drop by use of the
current interrupt method. Errors arise because the time delay between the potential
measurements after the current interrupt is somewhat arbitrary. Increasing or decreasing
the time delay and number of potential measurements recorded can change the slope of the
line fit to the points, thus leading to uncertainty when extrapolating back to the start of the
interrupt. Also, as surface films begin to form, a sudden drastic change in the current can
disrupt the surface causing oscillations or spikes in the potential transient. To avoid
uncertainty in the determination of the cell ohmic resistance, electrochemical impedance
spectroscopy can be employed. As discussed in section 2.4, the ohmic resistance is the
high frequency limit of the impedance.
Table 21. Parameter values used to calculate the polarization curve for steel in neutral to
slightly basic, oxygenated soil electrolytes. Potentials were referenced to the copper
copper sulfate (Cu/CuSO4) electrode.
Parameter Value
V*Fe 526 mV
pV*2 104 mV
VH2 955 mV
3Fe 59 mV/decade
o32 59 mV/decade
3H2 118 mV/decade
ilim, 02 1.02 iA/cm2 (0.95 mA/ft2)
0.4 ,
0.5
0.6
0 Corrosion
S0.7 
0.8
c 0.9
t 09 .Total Current
o0 H2 Evolution .
1.0
02 Reduction
1.2 "" ' '' '"
0.01 0.1 1 10 100
Current Density, mA/ft2
Figure 21. Calculated polarization curve of steel with the potential as a function of the
applied current density. Currentpotential curves are included for each reaction
contributing to the total current density.
2.3 Surface Films
Surface films form due to the localized increase in alkalinity at the steel surface
resulting from the cathodic production of hydroxide ions. To maintain charge neutrality, a
concentration gradient of cations develops near the surface, and several precipitation
reactions can occur. Ferrous ions react with hydroxide ions to form ferrous hydroxide,
Fe(OH)2, which is then further oxidized to ferric hydroxide, Fe(OH)3, also known as rust.
Calcareous deposits have been observed to form as the applied potential becomes
more cathodic. For example, carbonate ions, present from mineral sources or dissolved
carbon dioxide, can react with calcium and magnesium cations to from carbonate
precipitates. At more significant cathodic potentials, the rate of hydroxide ion production
may be enough to increase the pH, near the surface, to levels high enough such that
magnesium hydroxide can also precipitate.
Calcareous deposits reduce corrosion rates by acting as resistive coatings which
inhibit transport of oxygen. Films have been reported to exhibit both blocking and porous
behavior [12]. Carson and Orazem calculated large Tafel slopes, approximately one order
of magnitude larger than literature values, for steel in saturated soils [6]. They attributed
the behavior to calcareous film formation, noting that a large potential shift was required
to reduce the corrosion current.
2.4 Principles of EIS
In situ analysis of an electrochemical system is often performed using electrical
methods, since the electrical response can be attributed to the kinetics of the surface
reactions. Electrochemical impedance spectroscopy is a frequency response technique
where a sinusoidal potential is applied to an electrochemical system, and the responding
sinusoidal current signal is measured. Typically, a spectrum is generated by sweeping a
range of frequencies and measuring the impedance at each point. Since the polarization of
electrochemical systems can exhibit highly nonlinear behavior (as shown in Figure 21),
impedance measurements are normally conducted using small amplitude perturbation
signals. This approach allows confinement to an approximately linear segment of the
polarization curve. In this pseudolinear system, the response will oscillate at the same
frequency as the input, will be phase shifted, and will be free of harmonics.
Analysis of the input and output signals leads to determination of the cell
impedance. The input potential signal can be expressed in cartesian and polar variables as
V(t)
Vo Cos (t)
Vo0expjot}
(29)
where V(t) is the oscillating potential at time t, Vo is the signal amplitude, and co is the
angular frequency. The responding current signal has amplitude I0 and phase shift p
according to
I(t) = I0cos(cot ) = I0exp{j(ot )}
(210)
where the imaginary number j = i. The complex impedance follows Ohm's law and
is found as the transfer function relating the potential and current signals according to
Z = (t = Z cos(ot) Zlexp(j) = IZ(cos4+jsin) = Zr+jZj (211)
I(t) cos(cot )
where Zr and Zj are the real and imaginary parts of the complex impedance, respectively.
Impedance data is typically presented in a Nyquist plot where the negative of the
imaginary component is plotted on the vertical axis, and the real component is plotted on
the horizontal axis.
Often, EIS data is interpreted using equivalent circuit models made up of resistors,
capacitors, and other elements. For example, Figure 22 presents a circuit with a resistor
in series with a Voigt circuit containing a resistor and capacitor in parallel. The circuit is a
simple model for the impedance response of an electrode process. It includes an
electrolyte resistance, Re, the double layer capacitance, Cd, and a charge transfer
resistance, Rt. The impedance for Randle's cell is calculated as
1 Rt
Z = Re+ = Re+ (212)
1 +jCd1 + jtOC
where t is the time constant associated with the RC circuit. The nyquist plot for the circuit
with an electrolyte resistance of 10 double layer capacitance of 10 jpF, and charge
transfer resistance of 250 Q is shown in Figure 23. At high frequency, the denominator of
the last term in equation (212) becomes very large making the whole term negligible
compared to the first term. Thus, the high frequency limit for the impedance is the
electrolyte resistance, Re, as shown in Figure 23 where the left end of the semicircle
intersects the real axis. At very low frequencies, jTco in equation (212) approaches zero,
and the result for the impedance is Re + Rt, shown in Figure 23 where the right end of the
semicircle intersects the real axis. The Voigt circuit is a starting point for developing more
complex equivalent circuit models. EIS data can also be interpreted using models
developed from a knowledge of physical processes occurring within the cell. Such a
modeling approach is developed in section 2.6.
Re
oMAr
Cd
Rt
HE
Figure 22. Schematic diagram of a circuit containing a resistor in series with a Voigt
circuit.
150
100
50
0
50 100 150 200 250
300
Figure 23. Nyquist plot for the circuit in Figure 22 with the parameter values Re = 10 Q,
Cd= 10 pF, andRt= 250 Q.
o
2.5 Statistical EIS Data Analysis
Electrochemical systems involving time dependent film formation usually exhibit
nonstationary behavior during the time required to generate an impedance spectrum.
Impedance data collected under nonstationary conditions will fail to satisfy the Kramers
Kronig relations. Since most process models applied to impedance spectra assume the
steadystate, it is important to determine whether the collection time was short enough to
model the system as stationary. A statistical technique of regressing measurement models
to impedance spectra has been developed for filtering out nonstationary behavior [1621].
The measurement model takes the form of the line shape based on the KramersKronig
consistent Voigt circuit (see Figure 22) with impedance given by
Z(co) = Zo + k (213)
where Zo represents the high frequency impedance or electrolyte resistance, Rk is a
resistance parameter, and Tk is an RC time constant. The technique follows an iterative
procedure of adding successive line shapes to the model followed by regression to the
data. The confidence intervals for the parameter estimates are calculated, and the number
of parameters, necessary to fit the spectra, is constrained by the requirement that the
95.4% confidence intervals for each parameter must not include zero.
The measurement model regression technique is also used to determine the nature
of the experimental errors. The residual errors between the data and the model consist of
systematic and stochastic contributions, ESyst and Estoch, respectively. The systematic
errors consist of lack of fit errors, 1of, due to inadequacies of the model, and bias errors,
Fbias, associated with nonstationary behavior, es, and instrumental artifacts, eins. Thus,
the experimental errors at any frequency can be expressed as
Z Z = lof+ (ns + ins) + stoch (214)
where Z is the model value for the complex impedance Z [19]. The approach is to collect
consecutive pseudoreplicate impedance spectra and to regress the measurement model to
each scan separately. By fitting the same number of line shapes to each replicate, the non
stationary error contribution is effectively filtered out as the regressed parameter values
are adjusted for each individual scan. The errors due to instrumental artifacts are assumed
to be constant from one experiment to another, and since one model was regressed to each
replicate data set, the lack of fit error contribution is also constant. Another assumption
stipulates that the stochastic errors, stoch = stoch, r +Jestoch j, are normally distributed
with mean e = 0. The standard deviations for the real and imaginary components of the
errors at each frequency can be estimated from the deviations of the residual errors from
the mean value by
N
^2 y 1(res, r, k res r)2
N
k=l (215)
N
'2 (F res,j, k~ res,j)2
k=
where ar and yj are the calculated variances for the real and imaginary components of
the residual errors, respectively, N is the number of data points at each frequency, and
eres = mean(lof + eins)
(216)
Since the standard deviations of the stochastic errors are functions of frequency, a model
for the error structure was developed assuming that the standard deviations of the real and
imaginary components are equal [19] according to
2
Cr = = a Z + 3 Zr + 7 + 8 (217)
Parameters ca, P3, y, and 8 are constants, and Rm represents the current measuring resistor.
In summary, the measurement model technique is used to estimate the noise level
associated with stochastic errors for individual measurements and to identify Kramers
Kronigconsistent data. Knowledge of the error structure can be utilized when regressing
nonlinear models to impedance data. Regression by a weighted least squares strategy,
including errors in the real and imaginary components of the data, is given by
minimization of
(Zr, k Zr, k)2 (Z, k Z (218)
k yr, k k 'j, k
where Zrk and Zj,k are the real and imaginary components, respectively, while ,2 k and
"2
j, k are the real and imaginary components of the variance at each frequency,
respectively. Variance weighting ensures emphasis and deemphasis of data with low
noise and highnoise contents, respectively, and increases the quality of information
obtained from impedance measurements [19, 22].
2.6 Process Model Development
This section outlines the development of a mathematical impedance model. The
model was developed for a pipeline grade steel electrode, covered by a thin porous film or
coating, immersed in dilute electrolytic solution. The contributions to the total current
flow and transport processes associated with oxygen diffusion from the electrolyte to the
electrode surface are explained in detail. The electrical quantities, current density and
potential, as well as concentration are written as sums of steady and oscillating terms:
X = X + Re[Xexp{jot}] (219)
where Xis the variable of interest, the overbar represents the steady value, the tilde
distinguishes the oscillating value, and co is the frequency of oscillation. The geometry
assumed for solving the transport equations is presented in Figure 24. The development
follows principles reported by previous authors [911, 23].
2.6.1 Reaction Kinetics
The total current density is given as the sum of the faradaic current and the current
associated with charging of the double layer:
C dV (220)
i i+ ddt
Substitution of Vfor Xin equation (219) yields the time derivative
V = joVexp{jct} (221)
dt
Substituting equation (221) into equation (220), writing the total current in the form of
equation (219), and cancelling the exponential term, yields an expression for the total
current density in terms of oscillating variables according to
if +jCoCdV (222)
The faradaic current density is expressed as a function of the potential and concentration
according to
if = f(V, ci) (223)
If the magnitude of the oscillating terms is sufficiently small, equation (223) can be
linearized according to
I cVf_ + (224)
The charge transfer resistance is expressed as
1
R, (225)
Combining equations (225) and (224) yields
f= (R +c c (226)
As previously stated by equation (25), the total faradaic current density is the sum
of the current contributions from the anodic and cathodic reactions. By assuming Tafel
kinetics, the current contribution from iron dissolution, reaction (21), is written in terms
of the potential measured with respect to a reference electrode, V, according to
Fe = nFeFkFeexp (V VFe) (227)
where VFe is the equilibrium potential for iron dissolution, kFe is the reaction rate constant,
and CJFe is the apparent transfer coefficient. Following the form of equation (224) where
the amplitude of the potential perturbation is small, equation (227) can be linearized:
FFeF 2 OXFeF _
Fe = nFe kFe RT exp RT(V VF) FV (228)
19
which can be expressed in terms of the charge transfer resistance as demonstrated by
equation (225):
Fe t (229)
t, Fe
Similarly, the current contribution from hydrogen evolution, reaction (23), is
H2 = Fkexp ( V VH) (230)
[RT H)
which can be linearized and expressed in terms of the charge transfer resistance to obtain
an expression for the oscillating current density given by
aHF2 [ H F V
H= n H kH RT exp RT VH2) tV = (231)
The contribution from the reduction of oxygen, reaction (22), can be expressed in terms
of potential and concentration according to
io= no FkoZ,o0 exp (V Vo) (232)
RT(V V02) (232)
which can be linearized with respect to potential and concentration given by
0oF2 [ aor0F ]1
io2 = no2ko co2, T exp (VVo)V
(233)
02oF RT2
Also, the flux of oxygen away from the electrode surface is
d 020
02= n02Fk D02, = n02Fk2 D02J 2' 0'(0) (234)
y = 0 0,f
where 6'(0) is the dimensionless flux at the surface. Equation (234) yields
10202f (235)
2,0 n02FD021f 6'(0) 2
The charge transfer resistance is expressed according to
1 to F2 [ arO2F )
1 = noko 2 exp R (F Vo2) (236)
RRt, 02 02 ]2 02, RT
After substituting equations (235) and (236) into equation (233) and solving for i02 the
contribution due to oxygen reduction is simplified to
7o = k (237)
2 ko 02, 1 F Rt, 02 + ZD, 02
R 2 oD (0) exp )(V_ Vo)
where the diffusion impedance is given by
ZD,02 = 02J RT ( 1 (238)
2 n02F2Do2,f 02,0 (02 0'(0)
1
The dimensionless flux term,  will be developed in the next section. After
6'(0)
substituting the sum of equations (229), (230), and (237) into equation (220) for the
faradaic current density, the total current density is
1 (.e+ 1 + I_ +jOCd) (239)
Rt, Fe +R, 02 + ZD, 02 Rt, H2
The cell potential is the sum of the ohmic drop, due to current flow through the cell
electrolyte, and the surface overpotential given by
U = i Re+ V (240)
By solving equation (240) for V substituting the result into equation (239), and
rearranging, the complex impedance is given by
UL 1
S Zr+JZ = Re+ 1 1 1 (241)
+ + + ++  i+jcoCd
Rt, Fe Rt, 02 D,2 Rt, H2
Equation (241) can be equally expressed by a seriesparallel combination of electrical
circuit elements. However, the advantage of the development is that the model parameters
are explicit impedance response measures in terms of specific proposed kinetic and
transport processes.
2.6.2 Transport
This section develops the impedance associated with diffusion of oxygen due to
concentration gradients within the bulk soil electrolyte surrounding the steel electrode.
The development follows the work of DesLouis and Tribollet for transport of a reacting
species through a porous film to the surface of a rotating disc electrode [11]. As will be
explained in CHAPTER 3, a cylindrical steel coupon served as the working electrode.
After imposing several approximations, as will be demonstrated, the system geometry was
modeled in rectangular coordinates as presented in Figure 24. Two regions of stagnant
diffusion were proposed to exist: a bulk diffusion layer and a porous film adsorbed onto
the metal surface. The film was allowed to be rust layers, calcareous deposits, or resistive
polymer coatings.
Model development begins by considering, for dilute solutions, the concentration
within a diffusion region to be governed by
aci aci acI 7 2Ci + I i a 2C c
W + r = Dir2 r (242)
for cylindrical coordinates where ci and Di are the concentration and diffusivity of
species i, respectively. Since the direction of electrolyte flow is parallel to the metal
surface, as shown in Figure 24, vr = 0. Also, the concentration is assumed to vary in the
rdimension only. Thus, equation (242) reduces to
ac, 2ci + I3ci
= Di r + (243)
Wt ar2 rar
which governs stagnant diffusion of i in the rdimension to and from the metal surface. If
the radius of the cylindrical electrode is large compared to the thickness of the film or
1 ci
diffusion layer, i.e., r >> 8, the term can be assumed to be negligible. By replacing r
rar
by y, equation (243) reduces to
S= D . (244)
at 'ay2
A coordinate system is imposed, as shown in Figure 24, where y represents the distance
from the surface, the filmmetal interface is at y = 0 with film thickness 8i, and the
bulk diffusion layer begins at y* = 0 (y = 8i,f) with thickness 8i, b. Equation (244) can
be written for the two diffusion regions, and the appropriate boundary conditions are
y = 0 if = ciO (245)
y = 0 Di = ki, oexp(V/3) (246)
y =0
y* = (y= ) if = i,b (247)
f Ci, b
i,f i,bb
y* = 0(y = 8,,) D, f = D i,
f ib(248)
D = D i, b
i, f i, b a
Y* i, b(Y o) i, b  ci, o (249)
i, b  0
For the electrochemical system with oscillating voltage and current signals, ci also
oscillates and can be expressed in the form of equation (219) as the sum of steady and
oscillating contributions,
ci = i+ Re[i.exp{jot}] (250)
Substitution of equation (250) into equation (244) yields
jcoc.ieJmt i e  iemtD = 0 (251)
dy2 dy2
The steady term of equation (251) can be written for both regions as
d2 if 2
dij = 0 i, b = 0 (252)
dy2 dy*2
Solving equation (252) and applying the steady boundary conditions yields equations for
the concentration of i in the film and the bulk, respectively:
_Di, b C i, CiJ D i 1
CiJ D(ci, 8i, b i, + kexp( (253)3)
ib Ci, 0 Ci, b, 0 + i, b,
Ci, b = 8i, b
where the concentration at the filmbulk diffusion layer interface is given by
Ci. b.O
Di, bCi, /i, b
Di,J
8if + [Di,f/kexp (V/3)]
(254)
Di, b
+
bi,b
By imposing the dimensionless variables
f if, o
Ob 0
Ci, b, O
Y
i, f
6i, b
(255)
the oscillating part of equation (251) can be written for both regions according to
d 2f f
4YJOif Of
d Ob,
0 djOTi, bOf = 0
d ln2 bf
(256)
where the time constants associated with diffusion of i through the film and the bulk,
respectively, are given by
if
'Jf Iij
b 2
,b 8 bi,
(257)
The dimensionless forms of the boundary conditions for the oscillating concentrations are
= =0
S= I1
* = 0 (= 1) Ci, fo f=i, b, O b
D. dO1
* = 0 = 1 i,f ~
 0 1) ai, f ,O d~
* = 0 6b
* = 1 Ob
The general forms of the solutions to (256) for the film and bulk, respectively, are
dO*
Di b
i. b b, 0
(258)
(259)
(260)
(261)
(262)
Of = Mf exp{ jT 7(c } + Nf exp { j ( }
(263)
0b Mbexp{ Job* } + Nb exp { Jc b* }
The constants Mf, Nf, Mb, and Nb are determined by applying the boundary conditions
yielding the solutions for the oscillating concentration profile of i in the bulk as
6b = sinh{ j (c * 1)} (264)
Q,,  'b (64
sinh( 0oC tb)
and through the film as
tanh( jcoT b)cosh{ I fjco ( 1)} sinh { j (OCi 1) }
Of ='f (265)
Di, b
tanh( jcit b) cosh( (jcT; ) + 7sinh( (JT;1)
Taking the first derivative of equation (265) with respect to , evaluating at = 0, and
taking the reciprocal gives the dimensionless flux term of equation (238) as
tanh( O ) + tanh( /C )
1_tahi(f '1 (266)
j0o) ,tanh( ) tanh( JoC ) + Di
Replacement of i with 02 in equation (266) yields the reciprocal of the dimensionless
flux of oxygen to the surface of the working electrode, necessary for equation (238).
Surface
EBulk Electrolyte
Buk Flow
c(0) Bulk Electrolyte
Film .
Diffusion
z ___ Layer I
y=0 y=6i,f Y* i,b
y y*=0 y,y* oo
Figure 24. Geometry for the diffusion model.
2.7 Application
Here, the theories governing methods for characterizing the electrochemical
behavior of pipeline steel have been presented. In the proceeding chapters, the application
of process models to the understanding of impedance data will be demonstrated. By
regression of process models to impedance data, parameters can be extracted which lead
not only to an understanding of the polarization behavior of steel, but also to an
understanding of the physics of surface charge transfer reactions and transport of reacting
species through resistive media. Since information can be obtained from individual scans,
the temporal evolution of the system can also be explored. EIS will be shown to be a
useful alternative to DC current and potential measurement techniques.
CHAPTER 3
EXPERIMENTAL METHODS
3.1 Summary
The purpose of this work was to measure the electrochemical impedance response
of pipeline grade steel exposed to a typical soil environment. Two field conditions were
simulated: (1) bare steel and (2) coated steel containing a discrete holiday. To ensure
symmetrical current distributions on the conductive surfaces, a cylindrical electrochemical
cell was designed to contain stationary cylindrical electrodes. Uniform or symmetrical
current distributions allowed for simpler model development and measurement of
averaged electrical quantities. Pipelinegrade steel served as the working electrode, and
platinumrhodium alloy screens served as the counter electrodes. Potentials were
measured in reference to a saturated calomel electrode. Electrolyte was prepared
containing species known to contribute to the formation of calcareous films. Tests were
performed under galvanostatic control at the open circuit or corrosion potential and at
applied DC cathodic current densities. Two forms of data were collected: potentialtime
traces and impedance data sets at snap shot intervals over the course of an experiment.
The time duration for a typical experiment was 4 to 7 days. Models were regressed to the
impedance data to determine the measurement errors and to extract parameters describing
the effect of film formation on transport processes and reaction kinetics.
3.2 Experimental Apparatus
Steps were taken to design wellcontrolled experiments. Since electrochemical
reaction rates are strong functions of temperature, the testing apparatus was isolated
within a controlled environment. To avoid localized activity at specific points on the
electrode surface, the corrosion cell was designed to assure symmetrical current
distributions. To maintain constant chemistry, fresh electrolyte was continuously
delivered to the cell. Galvanostatic control, i.e., current control, proved to be
advantageous over potentiostatic, i.e., potential, control. The cell potential, measured with
respect to a reference electrode, is the sum of the surface potential and the IR drop due to
current flow through the resistive electrolyte between the working and counter electrodes
according to
V = ] + iRe (31)
When holding V constant, film formation will cause the current to change as the
resistance of the surface increases. In addition to changing current, which changes the IR
drop, the surface potential adjusts accordingly. Thus, no surface electrical quantities are
held constant. Use of currentcontrolled experiments guaranteed that one electrical
quantity was held constant over the course of the experiment. From equation (31), at the
corrosion potential, where i is equal to zero, the measured cell potential, V, is equal to
the surface potential, l .
3.2.1 Electrodes
Test sample coupons were supplied by Metal Samples. The coupons were
machined from pipeline grade API5LX52 steel to cylindrical rods eight inches in length
and half an inch in diameter. The chemical analysis and component weight percent for
the steel are given in Table 31. The coupons were used as received without any
metallurgical pretreatment such as annealing.
As previously stated, two working electrode types were used simulating buried
uncoated or bare steel and buried coated steel with a discrete holiday with surface area
small in comparison to the overall area of the electrode. The cylindrical rod coupons
served as the bare steel case. A schematic for the holiday electrode is presented in Figure
31. It consisted of two end pieces, fabricated from acrylic rods, sandwiching a thin metal
band. Several bands were cut from the supplied 5LX52 steel rods to 1/8" in thickness.
The diameter of the acrylic pieces and the metal bands were machined to 0.485 inch. To
assemble the holiday electrode, the acrylic pieces and the band were centerdrilled and
tapped. A threaded metal rod was inserted through the top acrylic piece with the threads
protruding out the bottom end. The band was then screwed on followed by the bottom
acrylic piece. Before assembly, the top and bottom surfaces of the disc were covered with
a thin layer of silicon grease to seal the acrylicmetal crevices.
Platinumrhodium alloy mesh screens, supplied by EngelhardClal, served as the
counter electrodes. Two screens were fabricated to 235 mm by 150 mm with the
following specifications:
* 95% platinum, 5% rhodium alloy
* 80 mesh gauze with wire diameter 0.003"
* 0.5 mm diameter Pt border wire with 50 mm extension.
The screens were pliable and designed to be formed along the inside wall of the cell body.
The fact that the counter electrode fully circled a cylindrical working electrode assured
uniform radial current on the working electrode surface.
3.2.2 Current Distribution
Since the cylinder electrode extended the length of the cell with the counter
electrodes, the current distribution on the surface was uniform, and the electrolyte
resistance could be estimated by a simple analytic formula. The current distribution on the
holiday electrode, however, is nonuniform, and an analytic formula is not available for the
electrolyte resistance. Thus, numerical simulations were performed to determine the
current and potential distributions for the cell arrangement with the holiday electrode.
Under the assumption of electroneutrality, uniform concentration gradients and
constant conductivity, the potential field of the corrosion cell is governed by Laplace's
equation [23]
V2c = 0 (32)
Using the boundary element method (BEM), equation (32) was transformed to an integral
equation for axisymmetric geometries describing the boundaries of the corrosion cell [24].
The FORTRAN code, developed for numerical solution of equation (32) using BEM, is
given in APPENDIX A. By discretizing the cell boundaries into constant elements a
numerical solution was obtained by specifying either an essential boundary condition, for
(D, or a natural boundary condition, for Vc, which was constant over the length of each
element. The solution results yielded both a value for ( and Vc for each individual
element. The current density, scaled by the electrolyte conductivity, is equivalent to Vc
by rearrangement of Ohm's law according to
Vc (33)
The axisymmetric plane for the cell geometry containing the holiday electrode is
presented, including the imposed boundary conditions, in Figure 32. The holiday surface
is shown as being slightly recessed due to machining errors or surface polishing, which
can impact current distributions significantly [25]. For the electrode surface, the boundary
condition was specified as ( = 1. The boundary condition for the counter electrode, the
opposite extent of the geometry, was specified as ( = 0. For the remaining nonconducting
surfaces, the current density, Vc, was specified to be 0. By imposing constant boundary
conditions, the scaled primary current distribution, which accounts only for geometric
influences, was obtained [23].
The results for the current density and potential along the holiday electrode are
shown in Figure 33. Whereas the current density was radially uniform, the results in
Figure 33 show a high degree of axial nonuniformities with the location of highest
current density being the ends of the holiday. The results for the potential are uniform
along the surface and shown to decrease rapidly when moving away from the ends of the
conducting metal band.
The current density and potential distributions were also calculated for the cylinder
electrode. The boundary conditions were similarly specified for the working and counter
electrode surfaces and the insulating surfaces of the top and bottom cell covers. The
results for the current density and potential as a function of axial position along the steel
rod are plotted in Figure 34. The results show that the potential was uniform the full
length of the electrode and the current was uniform except for slight variation at the
extreme edges.
From the solution conductivity and the results from the BEM calculations for the
current distribution on the electrode, the ohmic or electrolyte resistance, Re, was
I
calculated. First, the total scaled current, , was calculated by integrating the distribution
over the electrode surface. Since constant elements were used for the BEM calculations,
the current density value was constant over the length of each element. This allowed for
the integration to be simplified to a summation of rectangle areas with height and width
Ax, the element length. Over the length of the electrode the total current was thus:
N
S= Axj (34)
j 1
Since the corrosion cell was filled with a solid matrix, the solution conductivity was
corrected for the porosity of the matrix. The effective conductivity was approximated
according to
K = Ko01 (35)
where Ki is the conductivity of the solution outside any porous structure and e is the
porosity or void fraction of the solid matrix [23]. Finally, Re was calculated by Ohm's
law according to
Re (36)
where Acb = 1, the potential difference between the working and counter electrodes as
specified by the boundary conditions. The results for the calculated value of Re for the
two electrode types are listed in Table 32, including values determined from the high
frequency limit of the impedance measurements (the impedance results will be discussed
in CHAPTER 4 and CHAPTER 5). For comparison with the BEM results, Table 32
includes values for Re calculated for the cylinder electrode from the anode resistance
formula [12]
Re In( 8L 1 (37)
e 2nKLn d
where L is the length of the electrode and d is the diameter.
3.2.3 Cell Electrolyte
Typical soil conditions were simulated by filling the cell with inert silica sand and
feeding electrolyte containing species known to participate in precipitation reactions that
form calcareous deposits. Electrolyte containing Ca2+, Mg2+, and HCO3 was prepared by
dissolving reagent grade CaC12, MgSO4, and NaHCO3 in water. Table 33 is a list of the
desired concentrations for the charged species included in the electrolyte prepared for this
work. The actual masses of the salts added to produce 50 L of solution are given in Table
34. The concentrations of Ca2+, Mg2+, and HCO3 were in agreement with values
typically reported in the field [26, 27].
3.2.4 Corrosion Cell Design
Since measuring or controlling the current at a specific point on the working
electrode was not possible, the overall cell current was controlled. Thus, it was desired to
design a cell to exhibit symmetric current and potential distributions. Thus, the cell was
designed with cylindrical geometry to guarantee uniform distributions axially and radially
with the cylinder electrode and uniform radial distribution for the holiday electrode. Both
electrode types were oriented in the cell vertically with the ends at right angles to the top
and bottom cell boundaries. For the cylinder electrode, the active surface extended the
entire length of the cell. For the holiday electrode, nonuniform current density was
present along the length of the metal band due to edge effects at the acrylicmetal
boundaries and the differing lengths between the working and counter electrodes.
The cell was fabricated from plexiglass and consisted of a tubular cell body with
flanged ends and two circular cover pieces. A schematic for the cell body is shown in
Figure 35. The top and bottom covers were sealed using Orings and fastened to the
flanged ends of the cell body with 8 screws each. A schematic for the top cover piece is
shown in Figure 36. The active portion of the cell measured six inches in internal
diameter and six inches in length.
The working electrode (WE) was inserted in the cell perpendicular to the bottom
cover. The bottom cover had a recessed seat with a small piece of rubber tubing (see
Figure 35). To prevent exposure of its bottom circular surface, the WE was pressed into
the rubber seal in the seat. The top one and a quarter inches of the WE protruded out the
top of the cell to facilitate connection of lead wires from the instrumentation. For the
cylinder electrode, the length exposed to the soil environment was 6 inches making the
total active surface area 60.8 cm2. For the holiday electrode, the metal band was centered
in the cell body and fully exposed to the soil environment. The total active metal surface
area for the holiday electrode was 1.23 cm2. The top cover had a drilled hole fitted with
an Oring to seal around the top of the WE to prevent electrolyte leaks (see Figure 36).
To assure 02 saturation and maintain constant chemistry over the course of the
experiment, fresh electrolyte was fed to the bottom of the cell. From the top of the cell,
the electrolyte overflowed into the side of a flask containing a calomel reference electrode
inserted through a rubber stopper sealing the top of the flask. The arrangement for the
reference electrode essentially placed it at infinity since most of the change in potential
occurred at a small distance from the WE surface. Electrolyte then overflowed the flask
through tubing inserted in the stopper. The flow then dripped into a funnel to prevent
siphoning and was subsequently discarded through the drain. Tygon tubing was used for
the electrolyte feed and overflow lines. All the lines between the cell and the reference
electrode flask were primed with electrolyte and purged of air to guarantee continuous
electrical contact. In order to neglect the effects of forced convection associated with
flowing fluid, the electrolyte feed was pumped at a slow rate, approximately 7 liters per
day, using a peristaltic pump.
For electrical connection to measuring instrumentation, a wire was soldered into a
hole drilled in the top of the cylinder electrode. For the holiday electrode, the center rod
protruded out the top and was machined thin enough to allow fastening the lead wire using
an alligator clip. For connection to the counter electrodes, two holes were drilled and
tapped into the cell top cover piece. Small diameter tubing adapters were screwed into the
holes. The counter electrode extension wires were then inserted through the fittings to
allow them to protrude out the top of the cell after fastening the cover piece. The small
spaces between the fittings and the extension wires were sealed by packing putty in the
gaps and wrapping with teflon tape.
A schematic of the corrosion cell is presented in Figure 37 including electrolyte
lines, electrical connections, and instrumentation. For temperature control, the cell was
placed inside a plexiglass booth with a 2 ft. X 2 ft. square base and measuring 3 ft. in
height. The booth enclosure was fitted with a drain fitting and had holes cut into the sides
and bulkhead fittings installed for insertion of lead wires, power cords, heat exchange
tubing, and electrolyte feed tubing. The temperature inside the booth was controlled to
24 1 C by blowing the air over heat exchange coils containing water at 15 C supplied
by a water chiller. The air inside the booth was circulated using a PC panel mount fan.
Several feet of tubing connected to the electrolyte feed pump were coiled around the cell
to allow the electrolyte to equilibrate to the ambient temperature inside the booth.
During initial testing, it was observed that the fluorescent ceiling lights inside the
laboratory added a significant amount of noise to the current and potential signals. To
prevent the influence of outside electric fields on measurements, the inside of the booth
was wrapped with aluminum foil. The plexiglass booth had dual roles of maintaining a
controlled temperature environment and serving as a Faraday cage.
3.2.5 Instrumentation and Data Collection
As previously stated, the experiments were performed under galvanostatic control.
A threeelectrode cell arrangement was used for potential measurement between the
working and reference electrode with the current between the working electrode and the
counter electrode controlled using an EG&G Instruments, PAR 273 Potentiostat/
galvanostat. Connections to the electrodes were made via lead wires from the
electrometer [14].
The PAR 273 had an array of current measuring resistors ranging from 1 Q to 1000
kQ for controlling or measuring the current in the range of 2 A down to 15 nA. Each
measuring resistor had a range of 15% to 190% of the full scale value. For example, the
100 pA current range (10 kQ resistor) was suitable for currents ranging from 15 PA to 190
pA. An optimization technique was used for selecting the appropriate current range for a
desired applied current condition. A switchover factor ranging from 1.55 to 1.85 could
be imposed by the user to initiate selection of an adjacent current range. For example, let
the desired applied current be 175 pA. Normally, the 100 pA current range would be
selected. However, by having a switchover factor of 1.7, a restriction is imposed on the
maximum allowable current for a given current range of 170%. Thus the next higher
current range of 1 mA (or smaller measuring resistor of 1 kQ) would be selected.
For oscillating signal generation and impedance measurements, a Solartron
Instruments 1260 Gain Phase Analyzer was used. For impedance determination, the
Solartron 1260 employs frequency response analysis of two voltage signals [9, 28]. The
connections of the 1260 to the PAR 273 are presented in Figure 37. The 1260 generator
output is connected to the external input on the front panel of the PAR 273. The I monitor
and E monitor connections of the PAR 273 were connected to the VI and V2 inputs on the
1260, respectively. The 1260 generator superimposed a sinusoid, additively, on the
applied DC signal controlled by the PAR 273 via the connection at the external input. Two
sinusoidal voltage signals were then output to the 1260 from the I monitor and the E
monitor. The signal from the I monitor was the voltage across the current measuring
resistor according to Ohm's Law. The 1260 performed the analysis of the two signals
while integrating on the measured signal. In the case of galvanostatic control, VI, the
current, was the controlled signal coming from the I monitor while V2, the potential, was
the measured signal coming from the E monitor. Thus, the 1260 was set to integrate on
V2. The result for the impedance was the ratio of the two signals, i.e., V2/V1.
Both the 1260 and the PAR 273 were connected in parallel to a GPIB card installed
in a personal computer. Virtual Instruments (VIs) were developed using LabVIEWTM 5.0
graphical programming software for controlling experiments and data acquisition.
LabVIEWTM VIs have a front panel display which includes all the control settings, dials,
and buttons. The front panel serves as the interface between the user and the actual
instruments. The VIs also have a rear panel wiring diagram which maps out all
information flow, decision making, and calculations necessary to execute control of the
physical instruments and data acquisition. All initial settings and control parameters were
made from the VI front panels using the PC, avoiding any instrumental front panel
executions other than powering on and off. Experimental data was output to the screen
and displayed using virtual strip charts and graphs. Data was also saved to memory files
for later analysis. The VIs initiated the PAR 273 to record the WE potential at a rate
determined by the user, typically one measurement per minute. The user could also
initiate and stop individual or sets of impedance scans at any time during the experiment.
The virtual instruments used to control the 1260 in tandem with the PAR 273 are outlined
and described in more detail in APPENDIX B.
3.3 Experimental Procedures
Experiments were set up to allow the working electrode to reach a steady level of
polarization in response to an applied current condition and to measure the impedance at
snap shot intervals over the course of the experiment. It was desired to see the effect of
film growth and polarization on the impedance over time. Impedance scans were run in
sets of 3 to 4 consecutive scans. The replicate scans were necessary for statistical analysis
to determine the error structure of the measurements (see section 2.5). All experiments
were begun using a WE with a clean and polished surface. Typical experiments lasted 100
to 150 hours. A summary of the experiments conducted for this work is outlined in Table
35.
3.3.1 Applied DC Bias and Frequency Range
Experiments were conducted at the corrosion potential (zero net current) and at
applied cathodic currents. For the cathodic experiments, it was desired to control the
current to a point lying on the oxygen reduction plateau (see Figure 21). Preliminary
galvanodynamic scans were performed to determine the appropriate range of values. An
experimentally generated cathodic polarization curve for pipeline grade steel is presented
in Figure 38. Oxygen reduction appeared to be the dominant reaction between 680 and
900 mV (SCE), corresponding to a range of current densities from 1 to 6 pA/cm2.
As previously stated, the sinusoid generator superimposes a signal on the DC bias
controlled by the PAR 273. Small amplitude signals were used to assure restriction within
an approximately linear range of the polarization curve. Even though the experiments
were performed galvanostatically, the generator applies an AC potential signal resulting
from the product of the applied current perturbation and the optimized measuring resistor.
The resulting signal was superimposed on the cell potential measured with respect to a
reference electrode, and the current signal oscillated between the limits of the desired
amplitude.
Since corrosion reactions are typically slow and generating impedance spectra
requires low frequency measurements [9, 12], preliminary scans were performed to
determine the appropriate testing frequency range. The results of the impedance response
for the cylinder electrode in liquid electrolyte only, without the sand matrix, are presented
in Figure 39 including the calculated spectrum (application of models for predicting
impedance spectra will be discussed in CHAPTER 5). The tested frequency range was
1000 Hz to 0.01 Hz in increments of 7 frequency steps per decade. The data in Figure 39
show the imaginary component of the impedance to be large at 1000 Hz and then decrease
to a minimum at 24 Hz with a corresponding real component of approximately 29 to 30 Q.
Using parameters obtained from regression of models to the data led to the extrapolation
of Re to be approximately 0. Using the current distribution calculated from the BEM
simulations and the solution conductivity, Re was calculated to be 33.4 Q. The calculation
for Re agreed with the value determined from the impedance data in the high frequency
range where the imaginary component was at a minimum value.
The initial high frequency data with capacitive behavior in Figure 39 were
considered to be the results of an instrumental artifact. Similar high frequency artifacts
were also observed when performing preliminary experiments using steel rotating disc
electrodes. The fluid mechanics for the rotating disc electrode (RDE) have been shown to
be well defined, and the electrolyte resistance is easily calculated knowing the solution
conductivity [23]. The results from calculating the electrolyte resistance of the RDE cell
also led to rejection of high frequency data and narrowing of the tested frequency range.
To avoid collecting artifact data, the high frequency limit for testing was set to 100 Hz.
Typically, measurements were collected from low frequency values of 0.01 Hz to 0.001
Hz.
The 1260 analyzer needed many cycles to obtain a converged result for the
impedance at a given frequency. Typically, the analyzer required three to six cycles at the
low frequencies, 1 to 10 mHz. Since a sinusoid with frequency close to 1 mHz has a
period on the order of 1000 seconds, the number of points per scan was optimized to
reduce the time duration to complete each scan. All impedance scans were conducted by
sweeping down from high to low frequency. Frequency transitions were made in log
steps. Usually, 7 or 8 log steps per decade were used. A typical scan sweeping from 100
Hz to 0.001 Hz included 35 to 40 points and required approximately 3 to 4 hours to
complete.
3.3.2 Variable Amplitude Galvanostatic Modulation
Over the range of frequency values swept for a given scan, the impedance can
change by several orders of magnitude. If operating under constant amplitude
galvanostatic control, the resulting amplitude of the potential signal will also change by
several orders of magnitude, and the signal will likely be oscillating outside a linear
segment of the polarization curve. Small amplitude oscillating signals allowed for
simplification of modeling equations by linearization as demonstrated in CHAPTER 2.
Also, since current density is a function of potential, the reaction kinetics will be greatly
influenced by large potential fluctuations. Large potential fluctuations and changes in
reaction kinetics can disrupt surface films and upset the natural time dependent behavior
of the system.
A predictive method for adjusting the amplitude of the applied current signal while
maintaining the amplitude of the potential signal at some target value was developed and
dubbed variable amplitude galvanostatic (VAG) modulation [29, 30]. The method
prevents large perturbations in the potential signal at low frequencies. The algorithm
calculates the applied current amplitude according to
I = Vtarget (38)
Z(l) estimated
At the first frequency in the sweep, an initial guess is used as the estimated impedance.
For impedance scans swept from high to low frequency, a good guess was the electrolyte
resistance. If Re was unknown or could not be easily calculated, a value was obtained by
conducting a high frequency scan using constant amplitude galvanostatic control and
extrapolating the real component where the nyquist plot intersects the real axis. At the
second frequency, the initial guess is again used as the estimate. At the third frequency, a
2point prediction is made from
Z(mk) = 2Z(mk )Z(ck 2) (39)
From the fourth point to the end of the sweep, the impedance is estimated using a 3point
prediction according to
Z(ck) = 3Z(ck 1) 3Z(ck 2) + Z(ck 3) (310)
The algorithm was incorporated into LabVIEWTM virtual instrument controls to
automatically set the current signal and optimize selection of the appropriate measuring
resistor. For the experiments of this work, the potential target amplitude was usually set to
10 mV.
3.3.3 Initial Preparation
Electrolyte was prepared in quantities of 50 L which would last approximately 7
days. Oxygen saturation was achieved by bubbling air through the solution, using an
aquarium air pump, for about 24 hours prior to use. The air was first dried and scrubbed
of CO2 by feeding it to the bottom of a column up through a layer of drierite crystals and
through a layer of ascarite II crystals before entering the solution jug. The drierite served
to dry the air while the ascarite scrubbed out any CO2 present.
The working electrode was prepared by polishing the surface to a near mirror
finish and cleaning with ethanol. Polishing was accomplished by using a lathe to spin the
electrode and buffing using silicon carbide grit papers of roughness varying from course to
extremely fine. The electrode was buffed to a shine using a cloth soaked with alumina
slurries. The holiday electrodes were spun for polishing by threading a screw through the
metal band and inserting the screw into the chuck on the lathe.
Before preparing the cell, the chiller was started to circulate temperature controlled
water through the heat exchange coils in the isolation booth. The fan was also started to
circulate the air. The cell was then prepared by first inserting the electrode into the rubber
seal in the recessed seat in the bottom cover of the cell housing. If the holiday electrode
was used, it was first assembled as described in section 3.2.1. After inserting the WE, the
counter electrodes were installed by forming the screens around the inside contour of the
cell, arranged to completely circle the WE. The cell was then filled with all purpose silica
sand. The active surface area for the bare steel electrode was 60.8 cm2 and 1.23 cm2 for
the 1/8" band holiday electrode.
After filling the cell with sand, the top cover was placed by pressing it over the top
portion of the WE allowing it to slide through the Oring seal. The top cover was oriented
to assure the following:
* the flange Oring seal was seated properly in its groove
* the extension wires of the counter electrode protruded through the threaded holes for
connection to instrumentation lead wires
* the holes for the fastening screws in the cover lined up with those in the flange.
After fastening the top cover, fittings were installed over the counter electrode extension
wires and sealed as described in section 3.2.4 by packing putty in the gaps and wrapping
with teflon tape. Finally, the reference electrode was placed in the flask and sealed with
the rubber stopper, and all necessary tubing lines were connected.
After the cell was completely assembled and sealed, it was filled using a peristaltic
pump with a variable speed control. The fill pump was connected in parallel with the
continuous flow feed pump. This arrangement allowed rapid filling of the cell. Air
bubbles were purged from the cell by throttling the fill pump and tipping the cell to drive
the bubbles out the top of the cell. The line connected the top of the cell to the reference
electrode flask had a teed line running to the top of the isolation booth and open to the
atmosphere. This provided a pressure head and allowed any air bubbles to easily escape.
Once the cell was full, the fill pump was stopped and the feed pump started.
Provided there were no electrolyte leaks, the electrodes were connected to the
electrometer. The controlling PC was also prepared ahead of time for data acquisition and
initialization of the instruments. The experiment was begun by engaging the cell enable
switch on the PAR 273, starting the main LabVIEWTM VI, and setting the desired applied
current bias. The Lab VIEWTM VIs automatically measured and stored potential
measurements at the specified data collection rate. Impedance scans were conducted at
any time with the push of a virtual button from the front panel of the VI. Currentpotential
data files included the potential in mV, the applied current bias in pA, and the time in
seconds from the beginning of the experiment at which the measurement was taken.
Impedance data files included the initial parameters including the date and time of the
scan, the target potential amplitude, the applied current bias, and the initial impedance
guess value. The experimental point by point quantities of the impedance spectrum
included the frequency, the real component, the imaginary component, instrumental error
codes, the selected measuring resistor, the amplitude of the applied current signal, the
modulus of the impedance, and the phase angle.
Table 31. Chemical analysis of the supplied pipeline grade, 5LX52, steel coupons.
Chemical Component Weight Percent
Al 0.040%
C 0.090%
Fe 98.487%
Mn 1.070%
P 0.007%
S 0.009%
Si 0.250%
V 0.047%
Table 32. Results for the total current integrated on the electrode surface determined
from the current distribution resulting from the BEM simulations. Also included is the
calculated electrolyte resistance for both electrode types while accounting for the porosity
of the solid matrix. The porosity or void fraction assumed for the calculation was 0.40.
Also included are the results from impedance measurements and from using the anode
resistance formula, equation (37), for the cylinder electrode.
E/Ke, Re determined from:
Electrode A _cm
A/ cm1 BEM eq. (37) EIS
Cylinder 24.57611 81.6 74.6 65
Holiday 2.95274 679.5  650
Table 33. Calculated concentrations of ionic species included in simulated soil
electrolyte. Molarity units are in moles/liter. The calculated conductivity is also included.
Species moles/L ppm
Ca2+ 0.004994 90
Mg2+ 0.002220 40
Na+ 0.000277 5
HCO3 0.000277 5
SO42 0.002220 40
Cl 0.009989 180
K, cm 1 0.00197
Table 34. Masses of salts in g/L added to water to prepare simulated soil electrolyte. The
solution pH is included.
Salt Mass, g/L
CaCl22H20 0.734
MgSO4 0.267
NaHCO3 0.023
pH 8.0
Table 35. Experimental outline including electrode type and applied current density.
Applied Current, Electrode Area, iapp,
Electrode type A cm2 A/cm2
tA cm2 pA/cm2
cylinder 0.0 60.33 0.0
cylinder 100.0 60.80 1.6
cylinder 150.8 60.33 2.5
cylinder 241.3 60.30 4.0
holiday 0.0 1.22 0.0
holiday 6.1 1.23 5.0
Acrylic End Pieces
II
II
II
II
II
II
I Threaded Connection Rod
II
II
 Steel Band Electrode
7l
Figure 31. Schematic of the simulated holiday electrode.
Holiday (WE)*
Counter
Electrode
Surface
Axis of Symmetry
Figure 32. Axisymmetric plane, including boundary conditions, of the 1/8" holiday
electrode for BEM simulation.
0.020    1.2
Current Density ....... Potential
0.015 1.0
c 0.8 >
0.010
0.64
0.005
/0.4
0.000 0.2
0.005 0.0
0.005 ,,,,,,, 0.0
2 3 4
Position, in
Figure 33. Current density and potential distributions, generated from BEM simulation,
as a function of axial position on the 1/8" holiday electrode. The center of the holiday or
conductive metal band was located 3" from the end of the bottom acrylic insulating piece.
0.0010
0.0008
0 1 2 3
Position, in
4 5 6
Figure 34. Current density and potential distributions, generated from BEM simulation,
as a function of axial position on the cylinder electrode.
'7
Current ....... Potential
i i i i i i i I i i i i I i i i
0.0006
0.0004
0.0002
0.0000
2.0
1.5
1.0 0
0
0.5
0.0
53
Counter Electrode Lead Wires
Electrolyte
Out
F1 +
II
II
II I
II I
I I
I I
A
I I
I I
Electrolyte
Out
4
Fm
II I* Cover
I II
I II
I Flange
I I
I I
I I
I Working
Electrode
I I
I I
I I
I I Cell Body
I I ID =6 in.
I I L =6 in.
I I
I I
I I
I I
I I I I I I
] \ 11 Flange
II I I I II Flangover
II I I
Electrolyte In
Electrolyte In
Working Electrode Seat
Figure 35. Schematic of corrosion cell body showing position of electrodes.
Cell Cover Piece
diameter = 8 in.
Fastener Screw (8)
Figure 36. Schematic of corrosion cell top cover piece.
Figure 37. Corrosion cell flow diagram including instrumentation.
56
4 0 0 . . .... .. .. . .
500
 600
Ll
S 700
E
800
( 900
1000 Polarization Curve
1100 0o Experimental Points
1100
1 2 0 0 . . . . . . . . .. . . .
0.01 0.1 1 10 100
iapp, PA/cm2
Figure 38. Preliminary experimental polarization curve for pipeline grade steel,
generated from a galvanodynamic sweep from anodic to cathodic current densities at a
rate of 0.3 pA/cm2 per minute. The closed circles correspond to the applied conditions
listed in Table 35 for the cylinder electrode experiments.
o / 1000 Hz
20 o
24 Hz 0.01 Hz o
0 20 40 60 80 100 120
Zr,
o Data  Calculated Spectrum
Figure 39. Preliminary impedance spectrum in Nyquist form to identify high frequency
instrumental artifacts. The response is from the cylinder electrode in liquid electrolyte
only, with K = 0.00122 Q2cm1, to variable amplitude galvanostatic modulation about the
corrosion potential. The tested frequency range was 1000 Hz to 0.01 Hz. The calculated
spectrum was generated from measurement model regression parameters.
CHAPTER 4
EXPERIMENTAL RESULTS
4.1 Corrected Cell Potential
This chapter presents the results for the experiments outlined in Table 35.
Experiments were conducted over a period of several days with the current flow between
the working and counter electrodes controlled to simulate various levels of cathodic
protection. For each experiment, the DC potential of the WE was measured with respect
to a reference electrode, and impedance scans were conducted, in sets of 3 or 4 replicates,
at various times during system evolution. Impedance data were generated from variable
amplitude galvanostatic modulation about the applied DC bias to prevent large
fluctuations in the output potential signal (see section 3.3.2).
The total cell potential had to be corrected for the ohmic resistance resulting from
the influence of the cell geometry and the current flow through the resistive electrolyte
between the working and counter electrodes. The total cell potential can be expressed by
Corrected = Vmeas + IRe (41)
where Vmeas is the potential of WE measured with respect to a reference electrode. For
the instrumentation used, cathodic currents were positive in sign. As an example for
determining IR drop, Figure 46 and Figure 47 present the measured potential and the
impedance response, respectively, for an experiment conducted on the cylinder electrode
with the applied current density equal to 2.5 ptA/cm2. From the impedance plots in
Figure 47, Re was approximately 50 Q and the corresponding IR drop for the cell was
calculated to 7.5 mV. The resulting corrected potential was slightly more positive and
hardly noticeable when compared to the data for the measured potential in Figure 46. For
experiments conducted at the corrosion potential by setting the total current to zero, IR
compensation was not necessary.
EIS proved to be more reliable for determining the ohmic resistance than using
current interrupt techniques. In previous work employing similar cell arrangements and
electrolytes, current interrupt techniques led to determination of the IR drop to be on the
order of 100 mV [6, 26, 27].
4.2 Cylinder Electrode Experiments
Experiments were conducted with the cylinder electrode at several applied current
densities as indicated in Table 35 and in Figure 38. Operation at the corrosion potential
was accomplished under galvanostatic control by setting the applied DC current to 0 A.
4.2.1 Experiment 1 Modulation About the Corrosion Potential
The potentialtime data for the cylinder electrode maintained at the corrosion
potential is presented in Figure 41. The plot provides evidence of nonstationary
behavior during film formation with the initial potential transient occurring within the first
20 hours of the experiment. During the transient, the WE potential shifted by as much as
several hundred millivolts in the negative direction before reaching a steady value. The
large potential shift was consistent with the increased resistance and blocking effects due
to the formation of surface films [6, 7, 27].
The gaps in the trace of Figure 41 correspond to times when impedance scans
were performed and the DC potential was not recorded. Between gaps, no peaks in the
potential measurement were observed, verifying that the VAG modulation technique was
noninvasive and did not disrupt surface characteristics. Such was the case for all other
experiments. The impedance data generated during this experiment are presented as
Nyquist plots in Figure 42. Unlike the potentialtime trace, where the system appeared to
reach steady state within about 20 hours, the impedance results demonstrated that the
system was still evolving after several days. Increases in the magnitude of the impedance,
after the potential steadied, are consistent with films making the surface more resistive to
charge transfer reactions and to diffusion of oxygen, leading to decreases in the rates of
iron dissolution and oxygen reduction.
The semicircle observed in the Nyquist plot represents the capacitive behavior of
the cell. Upon inspection of the Bode plot for the negative of the imaginary component as
a function of frequency, presented in Figure 43, it was observed that the characteristic
frequency, where the magnitude of the imaginary component was a maximum, decreased
with time. The reciprocal of the characteristic frequency has units of time according to
S (42)
f
The time constant, t, was proportional to a characteristic diffusion length or layer
thickness. Increases in the characteristic time constant, over the course of the experiment,
give evidence supporting the evolution of film growth.
Each individual impedance scan was considered to be a snap shot of the state of
the system at the time the scan was conducted. At early times in the experiment, during
the initial potential transient, generation of complete spectra could not be achieved since
sweeping down to the 1 mHz range required several hours. To observe changes in the
impedance during this time of highly nonstationary behavior, shorter scans were
conducted by sweeping to the 10 mHz range, which required about 20 minutes to
complete. As the potential stabilized, sweeps to lower frequencies were accomplished.
The beginnings of a second semicircle or capacitive loop were observed to develop
in the low frequency range of the spectra presented in the Nyquist plots of Figure 42. A
complete semicircle would correspond to a second local maximum in the Bode plot. This
result suggested the presence of two diffusion regions from the bulk of the electrolyte to
the surface of the WE.
4.2.2 Experiment 2 Modulation About 1.6 pIA/cm2
The purpose of this experiment was to measure the impedance response when the
working electrode was polarized to a slightly cathodic level. The potentialtime trace of
the WE in response to an applied current density bias of 1.6 pA/cm2 is presented in
Figure 44. The initial transient lasted approximately 10 hours before reaching a steady
potential, similar to the experiment conducted at the corrosion potential. The IR drop was
determined to be approximately 6 mV using the high frequency impedance results. Upon
resetting the applied current to 0 at the end of the experiment, the potential would relax in
the positive direction to the corrosion potential.
The impedance response, presented in Figure 45, was observed to increase more
significantly over time than for the experiment conducted at the corrosion potential. The
increases in the measured impedance were consistent with film growth causing reductions
in corrosion current and oxygen reduction current. Both the real and negative imaginary
impedance components were increasing after several days, and the beginnings of a second
capacitive loop, or semicircle, were observed in the low frequency range.
4.2.3 Experiment 3 Modulation about 2.5 pA/cm2
The purpose of this experiment was to measure the impedance response of
cathodically protected steel. With the applied current density at 2.5 PA/cm2, oxygen
reduction became the dominant electrochemical reaction, with the WE polarized to a
position on the oxygen reduction plateau [12, 13, 23]. The potentialtime trace for this
experiment is presented in Figure 46. As indicated by the plot, the initial potential
transient occurred within the first 20 hours of exposure. However, after the 4th set of
impedance scans, started after approximately 24 hours of exposure, the potential
continued to decrease with further cathodic polarization. After approximately 60 hours
the potential began to increase. The erratic behavior of the potentialtime trace could have
been caused by film formation changing the mass transfer limited current density. At such
a level of applied cathodic current, the majority of the total current density was due to
oxygen reduction, and small changes in the mass transfer limited current density resulted
in large changes in the cell potential.
The impedance response is presented in Figure 47. Significant increases in the
impedance were observed over the course of the experiment. Although impedance data
were generated for low frequencies, as low as 1 mHz, complete capacitive semicircles
were not observed.
4.2.4 Experiment 4 Modulation about 4.0 pIA/cm2
The purpose of this experiment was to measure the impedance response of steel at
a higher level of cathodic protection. The potentialtime trace of the WE in response to an
applied current density of 4.0 pA/cm2 is presented in Figure 48. The initial transient
lasted approximately 12 hours before reaching a steady potential, which was much more
negative than the value measured for the same applied current density in the polarization
curve shown in Figure 38. The IR drop was determined to be approximately 6 mV using
the high frequency impedance results. Upon resetting the applied current to 0, the
potential would relax in the positive direction to the corrosion potential.
The impedance response, presented in Figure 49, was observed to decrease over
the course of the experiment with most of the change occurring within the first day of
exposure. The decrease in the measured impedance, after reaching a steady WE potential,
is consistent with increasing rates of hydrogen evolution, the dominating reaction at
higher applied cathodic currents. Hydrogen bubbles forming at and diffusing away from
the WE surface can disrupt film formation. As the impedance was observed to be steady
after one day of exposure, it follows that a lack in the presence of films caused the surface
to be less resistive to charge transfer reactions and oxygen transport.
500
600
700
800
900
20 40 60 80 100
120
t, hr
Figure 41. The corrosion potential, measured with respect to a calomel reference
electrode, as a function of time for the cylinder electrode.
100
. 50
N
0
50 100 150 200 250
Zr, Q
300
o 1hr 6 hr
A 21hr 46 hr o72 hr
Figure 42. Nyquist plots at selected times for the impedance response of the cylinder
electrode to variable amplitude galvanostatic modulation about zero applied current.
60 .
S AO 0
A8 A
40 O o "o o
0 o Ioo
20 o
0%
20
0.001 0.01 0.1 1 10 100
Frequency, Hz
o 1 hr m 6 hr A 21 hr *46 hr o 72 hr
Figure 43. Bode plots of the negative imaginary component as a function of frequency, at
selected times, for the cylinder electrode in response to variable amplitude galvanostatic
modulation about zero applied current.
500
600
700
800
900
0 20 40 60
80 100 120 140
t, hr
Figure 44. The cell potential, measured with respect to a calomel reference electrode, as
a function of time for the cylinder electrode maintained at an applied cathodic current
density of 1.6 pA/cm2.
200
100
100
200
300
400
Zr,
Figure 45. Nyquist plots at selected times for the impedance response of the cylinder
electrode to variable amplitude galvanostatic modulation about an applied cathodic DC
current density bias of 1.6 pA/cm2.
or 90 E3 6MMM 6 6
o 1 hr m24hr A45hr *70hr o129hr
0. .
O A A A A A I I
0 A
%0 AAAA
0 Oo 0AA
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
500
600
700
800
900
1000
0 20 40
60 80
100 120 140
Figure 46. The cell potential, measured with respect to a calomel reference electrode, as
a function of time for the cylinder electrode maintained at an applied cathodic current
density of 2.5 [lA/cm2.
0 Nw )00
000
 oc
800
600
; 400
200
0
200
o 2 hr m 6 hr A 24 hr
* 72 hr o 119 hr
i i I I i I i i I i i i i
400
600
800
Zr,
Figure 47. Nyquist plots at selected times for the impedance response of the cylinder
electrode to variable amplitude galvanostatic modulation about an applied cathodic DC
current density bias of 2.5 pA/cm2.
0
*A
0 *A
0 .A
o
o U
So'"
/oc e eee
1000
600
700
800
900
1000
1100
0 20 40 60 80 100
t, hr
Figure 48. The cell potential, measured with respect to a calomel reference electrode, as
a function of time for the cylinder electrode maintained at an applied cathodic current
density of 4.0 pA/cm2.
200
S100
0
200
300
400
Zr,
o 1 hr 5 hr A12hr *24hr o49hr 73hr A 94hr
Figure 49. Nyquist plots at selected times for the impedance response of the cylinder
electrode to variable amplitude galvanostatic modulation about an applied cathodic DC
current density bias of 4.0 [lA/cm2.
o0am = Caumo o m a 0 (3mimmo 4P
0 0
0
o4 ; a 4 & &
4O
O
. . . . . . . . . . . .
4.3 Discrete Holiday Experiments
To characterize the impedance response of a localized conductive area
surrounded by highly resistive material as is the case for a coating holiday, experiments
were conducted using the simulated holiday electrode. The results from the holiday
experiments were also used to identify experimental high frequency artifacts by
comparing the electrolyte resistance measured by EIS to the results calculated from the
BEM simulations (see section 3.2.2). Similar to the cylinder electrode experiments, the
current flow between the working and counter electrodes was controlled, and the WE
potential was measured with respect to a reference electrode. Impedance scans were
conducted at snap shot intervals over the course of the experiment. Consistent with the
localized activity indicated as occurring on the surface by the plot for the current
distribution in Figure 33, corrosion products were observed to be concentrated on the
edges of the metal band upon removing the electrode from the cell.
4.3.1 Holiday Experiment 1 Modulation About the Corrosion Potential
The purpose of this experiment was to measure the impedance response for a
simulated coating holiday with the electrode maintained at the corrosion potential. The
potentialtime trace for this experiment is presented in Figure 410. The potential shifted
approximately 150 mV to a steady value within the first 5 hours of the experiment. The
impedance response data are presented in Figure 411. Much of the spectrum was
generated with the beginnings of a low frequency loop appearing at later times in the
experiment. The results were consistent with the presence of two diffusion regions.
Similar to the behavior observed using the cylinder electrode, the impedance
response for the holiday electrode appeared to be steady after the first day of exposure.
As the experiment progressed, more details were observed in the low frequency features
of the spectra. Because of the geometric effects and the smaller conductive surface area,
the ohmic resistance of the holiday electrode was an order of magnitude larger than that
for the cylinder electrode. The larger impedance values were consistent with the fact that
for a given current density distribution, the total current integrated over the conductive
surface was much smaller for the holiday electrode than the cylinder electrode.
4.3.2 Holiday Experiment 2 Modulation About 5.0 pIA/cm2
The purpose of this experiment was to measure the impedance response for a
simulated cathodically protected coating holiday. The potentialtime trace in response to a
DC bias of 5.0 pA/cm2 is presented in Figure 412. The initial transient lasted about 20
hours before the potential reached a steady value. Using the ohmic resistance determined
from the impedance plots, the IR drop was determined to be approximately 4 mV.
Consistent with other experiments, the impedance response, presented in Figure 413,
continued to increase with time, long after the WE potential had stabilized. The
magnitude of the impedance was larger than for the corrosion potential experiment,
suggesting a reduction in the corrosion current due to film formation. Low frequency
loops were observed as the experiment progressed.
500
L 600
03
E 700
0 800
13
900
20 40
60 80
t, hr
Figure 410. The corrosion potential, measured with respect to a calomel reference
electrode, as a function of time for the holiday electrode.
2000
o1000
0
1000
o 6 hr
2000
3000
4000
5000
Zr,
m 22 hr
A 46 hr
* 99 hr
Figure 411. Nyquist plots at selected times for the impedance response of the holiday
electrode to variable amplitude galvanostatic modulation about zero applied current.
 0 0 I
100
120
,0o 0
0 a
ai o
IIIo" o o o111 *111 1
~mm~
500
600
700
800
900
. l i I II. I i . d 1 1 1 1 1 1 II
20 40
60 80
t, hr
Figure 412. The cell potential, measured with respect to a calomel reference electrode, as
a function of time for the holiday electrode maintained at an applied cathodic current
density of 5 pA/cm2. The increase in the potential at the end of the trace occurred after
resetting the applied current to 0.
4000
. 2000
0
o2hr m23hr A 73 hr *114hr
/ ii I i i I
2000
4000
Zr,
I I I I
U"44
6000
8000
Figure 413. Nyquist plots at selected times for the impedance response of the holiday
electrode to variable amplitude galvanostatic modulation about an applied cathodic DC
current density bias of 5.0 [tA/cm2.
S 9 9
120
CHAPTER 5
DATA ANALYSIS
5.1 Overview
This chapter discusses the analyses performed on the impedance data generated for
this work. Mathematical models for the impedance response were regressed to the data to
assess measurement errors and to describe physical phenomena. Since the models
contained nonlinear terms and complex quantities, regression procedures were performed
using complex nonlinear leastsquares (CNLS) algorithms [18, 3135]. The CNLS
technique allowed for a set of common parameters to be determined from simultaneous
model regression to both the real and imaginary components of the collected data.
Statistical data analysis was performed using the measurement model approach, to
identify nonstationary behavior and inconsistencies with the KramersKronig relations
and to determine an estimate for the stochastic measurement errors. An example for
applying the measurement model approach is presented in APPENDIX C. For detailed
analysis of the physical phenomena, an eightparameter process model was regressed to
data sets, individually, to obtain values describing the transport and kinetic processes
associated with the electrochemistry of the cell. The regressed parameters were plotted as
a function of exposure time to identify time dependent changes of the WE when subjected
to a particular level of polarization. Finally, the regressed values were related to
polarization parameters and used to extrapolate impedance spectra at frequencies outside
the tested range.
5.2 Process Model Regression Analysis
A mathematical model for the impedance response of a stationary cylindrical steel
electrode was developed (see section 2.6) and regressed to data generated for this work.
The model accounted for the kinetics of the electrochemical reactions including iron
dissolution, oxygen reduction, and hydrogen evolution, and it accounted for the diffusion
of oxygen from the surrounding bulk electrolyte to the steel electrode surface. The model
was used to obtain values for parameters changing with time.
5.2.1 Model Parameters
The model expresses the transfer function relating an input oscillating current
signal to an output oscillating potential signal as the complex electrochemical impedance
according to
Zr +1jZ = Re+ 11 (51)
+ + I +joCj
Rt, Fe Rt, 02 + ZD, 02 Rt, H2
The diffusion impedance, ZD, 02 given by equation (238), depends on the oscillating flux
1
of oxygen at the surface. By combining the variables preceding  into the lumped
0'(0)
coefficient ZD, 0, the diffusion impedance can be expressed as
ZD, 02 = ZDO( 1 I) (52)
1
where depends on the angular frequency and is given by equation (266). By
0'(0)
introducing the substitution
Db/f (53)
equation (266) can be simplified to
1 tanh( j OT b) + Dtbf tanh( jof)
(54)
'(0) JJ o2,fJ [tanh( jo, fT ) tanh( jco 2 b) + jDb]
By combining the charge transfer resistances due to iron dissolution and hydrogen
evolution into one effective charge transfer resistance parameter given by
1 + 1 (55)
Reff t, Fe t, H2
equation (51) was simplified for regression analysis as follows:
Zr +jZ = Re + 1 (56)
+ I +JCOCd
eff Rt, o2 + ZD, o I
From equations (54) and (56), the complex electrochemical impedance response
of the steel WE was described as a function of angular frequency, co, with eight parameter
constants summarized as follows:
* T 02 is the time constant in seconds, given by equation (257), associated with
diffusion through a porous film,
* 0T2, b is the time constant in seconds associated with diffusion in the bulk, see
equation (257),
* Db/f is the ratio of the diffusivity of oxygen in the bulk to that in the film,
* Reff is an effective charge transfer resistance in Q given by equation (55),
* Rt, o is the charge transfer resistance associated with oxygen reduction in Q, given by
equation (236),
* ZD, o is the coefficient of the diffusion impedance in Q, see equation (52),
* Cd is the cell capacitance associated with double layer charging in Farads, and
* Re is the electrolyte or ohmic resistance in Q.
Depending on the applied current density, Reff could be simplified with
assumptions regarding the comparative rates of iron dissolution and hydrogen evolution.
For experiments conducted with the cylinder WE maintained at the corrosion potential,
the corrosion current and the oxygen reduction current are assumed to be balanced, and
the hydrogen evolution current is assumed small enough to be neglected. The charge
transfer resistance for hydrogen evolution, Rt, H2 is then large and, by equation (55), Reff
is approximately equal to Rt, Fe As the applied current density becomes much more
cathodic, the rate of iron dissolution becomes small compared to hydrogen evolution and
Rt, Fe becomes large allowing for Reff to be equated to Rt, H.
In some cases, including the parameter Rt, 02 in the regression procedure proved
difficult without constraining its value. Simplifying equation (236) with substitution of
So2 from equation (232) and solving for Rt, 0 yielded
RT 1
Rt, o (57)
t02 F 0 oA
where A is the surface area of the WE. From equation (57), a reasonable estimate for
Rt, 0 required an appropriate value for io2 and A. At cathodic current densities,
polarizing the WE to more negative potentials, as applied during the experiments for this
work, the contribution to the current flow due to oxygen reduction was equivalent to the
masstransferlimited current, i.e., 02 = im, 02, as shown by the oxygen reduction
plateau in Figure 21. From dynamic sweep data, ilim, o was estimated to be in the range
of 4 to 6 pA/cm2, as, for example, in the plot in Figure 38. Substituting the apparent
surface area for A, approximately 60 cm2 for the cylinder electrode, Rt, 02 was calculated
to a value on the order of 100 Q.
In most cases, an initial guess of 100 Q for Rt, 02, proved to be large, and
regression of equation (56) to impedance data usually failed to converge. In cases where
the regression did converge, the parameter estimation for Rt, 02 was much less than 1, and
the calculated confidence interval for the parameter estimation included zero. In such
cases, the regressions were performed by fixing the value of Rt, o to zero. Values for
Rt, o2 were successfully obtained only for the experiment conducted using the cylinder
electrode maintained at the corrosion potential.
5.2.2 Quality of Regression
Results from the regression analyses showed reasonable agreement between the
process model and the measured data. For example, the impedance response of the
cylinder electrode to variable amplitude galvanostatic modulation about the corrosion
potential, after 24 hours of exposure, is presented in Nyquist form in Figure 51. The
figure includes the expected response yielded from the process model. Upon inspection of
the Nyquist plot, the model appeared to fit the data well with the curve passing through the
data points. The residual errors, presented as a function of frequency for both the real and
imaginary parts in Figure 52, are on the order of 1 to 2 percent of the model prediction.
In the high frequency region, the fitting errors were larger, approximately 6 to 8 percent of
the model prediction. Though the residual errors appeared to be small, they exhibited
oscillating behavior about the zero line. This result suggests that the fit could be improved
upon with further development of the process model.
The residual errors were also compared to the estimated stochastic noise level,
estimated from the measurement model regression analyses. In some cases, as shown in
Figure 53 and Figure 54, the residual errors were larger than the estimated noise limits.
In other cases, the errors were on the order of the noise level, as shown in Figure 55 and
Figure 56. The 95.4% confidence interval, generated from Monte Carlo simulations at
each frequency step, are included in Figure 55 and Figure 56 [20]. The confidence
interval gave insight to parts of the spectrum where regression uncertainties appeared.
Typically, the confidence intervals were broader in the low frequency range than the high
frequency range. Because of sweeptime limitations, only the first few points of the low
frequency features could be obtained, thus reducing the certainty of the process model
prediction. Severe lack of fit errors were evident where data points lay outside the
confidence intervals.
80
100 .
o Data Model
0 100 200 300
Zr,Q
Figure 51. The impedance response in Nyquist form of the cylinder electrode to variable
amplitude galvanostatic modulation about the corrosion potential, including the results for
the process model regression using modulus weighting. The error bars represent the
95.4% confidence intervals for the model estimation for both the real and imaginary
components. The data were generated 24 hours after the WE was exposed to the
electrolytic environment.
0 .1 0 0. . ... . . ... . . ... . . ...
= 0.050 
0
N 0.050 
SReal Errors Imaginary Errors
0.100 1 1 1 111111 1 1 1 1 1 11111 1 1 1 11 ]
0.001 0.01 0.1 1 10
Frequency, Hz
0.100 . .....'.....' .....'. ...
Figure 52. Both the normalized real and imaginary component residual errors, as a
function of frequency, resulting from process model regression to the data of Figure 51.
