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- Permanent Link:
- https://ufdc.ufl.edu/UF00100697/00001
## Material Information- Title:
- Electrochemical impedance spectroscopy for the characterization of corrosion and cathodic protection of buried pipelines
- Creator:
- Jeffers, Kenneth E. (
*Dissertant*) Orazem, Mark (*Thesis advisor*) Narayanan, Ranganathan (*Reviewer*) Ambrose, John (*Reviewer*) - Place of Publication:
- Florida
- Publisher:
- State University System of Florida
- Publication Date:
- 1999
- Copyright Date:
- 1999
- Language:
- English
## Subjects- Subjects / Keywords:
- Charge transfer ( jstor )
Corrosion ( jstor ) Current density ( jstor ) Cylinders ( jstor ) Electric current ( jstor ) Electrodes ( jstor ) Electrolytes ( jstor ) Oxygen ( jstor ) Regression analysis ( jstor ) Steels ( jstor ) Chemical Engineering thesis, M.S ( lcsh ) Dissertations, Academic -- Chemical Engineering -- UF ( lcsh ) Electrolytic corrosion ( lcsh ) Impedance spectroscopy ( lcsh ) Pipelines -- Cathodic protection ( lcsh ) - Genre:
- bibliography ( marcgt )
theses ( marcgt ) government publication (state, provincial, terriorial, dependent) ( marcgt ) non-fiction ( marcgt )
## Notes- Abstract:
- 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. ( , )
- Subject:
- KEYWORDS: electrochemical impedance spectroscopy, corrosion, pipeline steel, mathematical modeling, polarization, films, cathodic protection
- Thesis:
- Thesis (M.S.)--University of Florida, 1999.
- Bibliography:
- Includes bibliographical references (p. 202-205).
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- Mode of access: World Wide Web.
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- Title from first page of PDF file.
- General Note:
- Document formatted into pages; contains xx, 206 p.; also contains graphics.
- General Note:
- Vita.
- Statement of Responsibility:
- by Kenneth E. Jeffers.
## Record Information- Source Institution:
- University of Florida
- Holding Location:
- University of Florida
- Rights Management:
- All applicable rights reserved by the source institution and holding location.
- Resource Identifier:
- 45296340 ( OCLC )
002484335 ( AlephBibNum ) AMJ9949 ( NOTIS )
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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 Current-Potential 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 2-1. 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. . . . . . . ... 8 3-1. Chemical analysis of the supplied pipeline grade, 5LX52, steel coupons. ....... 46 3-2. 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 (3-7), for the cylinder electrode........... . .. 46 3-3. Calculated concentrations of ionic species included in simulated soil electrolyte. Molarity units are in moles/liter. The calculated conductivity is also included . ......... .......................... .. 47 3-4. Masses of salts in g/L added to water to prepare simulated soil electrolyte. The solution pH is included ............. ........................... .. 47 3-5. Experimental outline including electrode type and applied current density. ...... 48 5-1. Process model parameter values, at selected times, used to extrapolate the impedance response of the cylinder electrode maintained at the corrosion potential ............. ................................... 111 5-2. 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 5-3. Process model parameter values, at selected times, used to extrapolate the impedance response of the holiday electrode maintained at the corrosion potential. ................................................ 112 5-4. Extrapolated values for Re, Z(0), and Rp from regression of the process model and measurement models to the impedance data presented in Figure 5-43..... 112 LIST OF FIGURES Figure page 2-1. Calculated polarization curve of steel with the potential as a function of the applied current density. Current-potential curves are included for each reaction contributing to the total current density .................. ...... 9 2-2. Schematic diagram of a circuit containing a resistor in series with a Voigt circuit......... ................................... ........ 13 2-3. Nyquist plot for the circuit in Figure 2-2 with the parameter values Re = 10 Q, Cd= 10 F, andRt= 250 Q ................................ 13 2-4. Geometry for the diffusion model .............................. 26 3-1. Schematic of the simulated holiday electrode .............................. 49 3-2. Axisymmetric plane, including boundary conditions, of the 1/8" holiday electrode for BEM sim ulation.. . ......... .......................... 50 3-3. 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 3-4. Current density and potential distributions, generated from BEM simulation, as a function of axial position on the cylinder electrode. ......... 52 3-5. Schematic of corrosion cell body showing position of electrodes ......... . ... 53 3-6. Schematic of corrosion cell top cover piece .............................. 54 3-7. Corrosion cell flow diagram including instrumentation .. . . . . . . 55 3-8. 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 3-5 for the cylinder electrode experim ents . ......... ................................ 56 3-9. 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 Q-1cm-1, 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 4-1. The corrosion potential, measured with respect to a calomel reference electrode, as a function of time for the cylinder electrode ............. . 64 4-2. Nyquist plots at selected times for the impedance response of the cylinder electrode to variable amplitude galvanostatic modulation about zero applied current . . ....... ...................................... .. 64 4-3. 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 4-4. 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 4-5. 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 4-6. 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 4-7. 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 4-8. 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 4-9. 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 4-10. The corrosion potential, measured with respect to a calomel reference electrode, as a function of time for the holiday electrode ............ . 72 4-11. Nyquist plots at selected times for the impedance response of the holiday electrode to variable amplitude galvanostatic modulation about zero applied current .......... ........................................ 72 4-12. 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 4-13. 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 5-1. 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 5-2. Both the normalized real and imaginary component residual errors, as a function of frequency, resulting from process model regression to the data of Figure 5-1....... ................................... 80 5-3. The normalized real component residual errors, as a function of frequency, resulting from process model regression to the data of Figure 5-1. The estimated stochastic noise limits are included ........................... 81 5-4. The normalized imaginary component residual errors, as a function of frequency, resulting from process model regression to the data of Figure 5-1. The estimated stochastic noise limits are included............. 81 5-5. 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 5-6. 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 5-7. 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 5-8. 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 5-9. 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 5-10. 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 5-11. 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 5-12. The calculated film thickness in microns as a function of potential for the cylinder electrode with the applied current equal to zero ............ . 93 5-13. 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 5-14. The effective charge transfer resistance and WE potential as functions of time for the cylinder electrode with the applied current equal to zero......... 94 5-15. The effective charge transfer resistance as a function of potential for the cylinder electrode with the applied current equal to zero ............ . 94 5-16. 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 5-17. The charge transfer resistance for oxygen reduction as a function of potential for the cylinder electrode with the applied current equal to zero ..... 95 5-18. The diffusion impedance coefficient and WE potential as functions of time for the cylinder electrode with the applied current equal to zero......... 96 5-19. The diffusion impedance coefficient as a function of potential for the cylinder electrode with the applied current equal to zero ............. . 96 5-20. The cell capacitance and WE potential as functions of time for the cylinder electrode with the applied current equal to zero ............ . 97 5-21. The cell capacitance as a function of potential for the cylinder electrode with the applied current equal to zero......................... . ...... 97 5-22. The electrolyte resistance as a function of time for the cylinder electrode with the applied current equal to zero......................... . ...... 98 5-23. 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 5-24. 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 5-25. 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 5-26. 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 5-27. 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 5-28. The bulk layer diffusion time constant after 4 days of exposure plotted as a function of applied current density for the cylinder electrode......... ... 102 5-29. 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 5-30. The calculated film thickness in microns after 4 days of exposure plotted as a function of applied current density for the cylinder electrode........... 103 5-31. 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 5-32. The effective charge transfer resistance after 4 days of exposure plotted as a function of applied current density for the cylinder electrode........... 104 5-33. The diffusion impedance coefficient after 4 days of exposure plotted as a function of applied current density for the cylinder electrode .......... ... 105 5-34. The cell capacitance after 4 days of exposure plotted as a function of applied current density for the cylinder electrode ................ . 105 5-35. The electrolyte resistance after 4 days of exposure plotted as a function of applied current density for the cylinder electrode ............... . 106 5-36. 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 5-37. 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 5-38. 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 5-39. 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 5-40. 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 5-41. 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 5-42. 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 5-41 ................. . 116 5-43. 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 5-44. The slope of the polarization curve, calculated from the data presented in Figure 5-42, 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 5-43 ............. ....................... .. 118 5-45. 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 5-46. 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 5-47. 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 5-48. 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 A-1. The holiday electrode cell boundary including the x and y coordinates for each vertex. The edges are numbered for a total of 8.. . . . . . . 131 B-1. Flow chart for operation of main control, '1260/273_main_8/98.vi'........... 146 B-2. Flow chart for operation of 'I_V monitor.vi'. ........................... 147 B-3. Flow chart for operation of 'run impedance scan.vi'................ . 148 B-4. Flow chart for operation of 'poll 1260 for data.vi'. ................ 149 C-1. 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 C-2. 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 C-1. ........ ..................................... 155 C-3. The normalized residual errors with confidence intervals, as a function of frequency, between the imaginary data of Figure C-1 and the predicted imaginary component resulting from measurement model regression to the real com ponent of the data ............. ........................ .. 155 C-4. The data of Figure C-l, in Nyquist form, including the full set of replicate scans, after rejecting the high frequency artifacts ................. . 156 C-5. 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 C-6. 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 C-4 ............................. 157 C-7. 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 C-5 and Figure C-6, respectively. The model for the standard deviation includes the parameters, with values, P = 0.0017792 and 8 = 0.021916 ............. ..................... ... 158 C-8. The normalized residual errors, as a function of frequency, between the imaginary data of scan 1, shown in Figure C-4, 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 C-9. The normalized residual errors, as a function of frequency, between the real data of scan 1, shown in Figure C-4, 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 C-10. The normalized residual errors, as a function of frequency, for the imaginary component of scan 1, shown in Figure C-4, 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 C-11. 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 C-1. The confidence intervals and stochastic error structure limits are included .................... 162 C-12. 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 C-1. The confidence intervals and stochastic error structure limits are included ............... ..... 163 D-1. The electrolyte resistance as a function of time for the cylinder electrode with the applied current equal to zero ........................ . ...... 165 D-2. 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 D-3. The diffusion time constant for the film as a function of potential for the cylinder electrode with the applied current equal to zero ............ . .... 166 D-4. 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 D-5. The bulk layer diffusion time constant as a function of potential for the cylinder electrode with the applied current equal to zero ............ . .... 167 D-6. 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 D-7. 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 D-8. 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 D-9. The calculated film thickness in microns as a function of potential for the cylinder electrode with the applied current equal to zero ............ . .... 169 D-10. 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 D-1 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 D-12. The effective charge transfer resistance and cell potential as functions of time for the cylinder electrode with the applied current equal to zero. ....... 171 D-13. The effective charge transfer resistance as a function of potential for the cylinder electrode with the applied current equal to zero ............. . 171 D-14. 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 D-15. The charge transfer resistance for oxygen reduction as a function of potential for the cylinder electrode with the applied current equal to zero ..... 172 D-16. The diffusion impedance coefficient and cell potential as functions of time for the cylinder electrode with the applied current equal to zero. ....... 173 D-17. The diffusion impedance coefficient as a function of potential for the cylinder electrode with the applied current equal to zero ............. . 173 D-18. The cell capacitance and cell potential as functions of time for the cylinder electrode with the applied current equal to zero ............. . 174 D-19. The cell capacitance as a function of potential for the cylinder electrode with the applied current equal to zero ......................... 174 D-20. 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 D-21. 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 D-22. 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 D-23. 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 D-24. 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 D-25. 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 D-26. 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 D-27. 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 D-28. 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 D-29. 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 D-30. 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 D-31. 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 D-32. 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 D-33. 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 D-34. 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 D-35. 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 D-36. 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 D-37. 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 D-38. 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 D-39. 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 D-40. 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 D-41. 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 D-42. 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 D-43. 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 D-44. 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 D-45. 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 D-46. 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 D-47. 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 D-48. 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 D-49. 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 D-50. 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 D-51. 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 D-52. 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 D-53. 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 D-54. 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 D-55. 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 D-56. 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 D-57. 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 D-58. 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 D-59. 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 D-60. 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 D-61. 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 D-62. 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 D-63. 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 D-64. 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 D-65. 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 D-66. 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 D-67. 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 D-68. 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 D-69. 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 D-70. 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 right-of- 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 well-designed 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 potential-time 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 non-stationary 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 [9-11]. 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. Well-controlled 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 platinum-rhodium 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 non-stationary 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 oxidation-reduction, half-cell 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- (2-1) Reduction of oxygen is the cathodic reaction according to 02 + 2H20 + 4e- 40H- (2-2) 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- (2-3) The current density of the metal surface can be related to the rate of the electrochemical reactions according to Faraday's law r (2-4) 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 (2-1), (2-2), and (2-3) according to iot = iFe + i + iH (2-5) The sign convention for equation (2-5) is that anodic currents are positive and cathodic currents are negative. 2.2 Current-Potential Behavior of Steel The current-potential 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 [1-5], and is a tool for determining the corrosion potential, Tafel slopes, and corrosion rates [12, 13]. Typical current-potential behavior for steel is presented in Figure 2-1. 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 (2-6) lim, 02 The terms in equation (2-6) correspond to the current contributions from reactions (2-1), (2-2), and (2-3), 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) (2-7) 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+] (2-8) where EOFe is the standard potential for iron dissolution and [Fe2+] is the concentration of ferrous ions [12]. Figure 2-1 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 2-1. All potentials were referenced to the copper-copper 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 off-potential 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 2-1. 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 S-0.7 - -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 2-1. Calculated polarization curve of steel with the potential as a function of the applied current density. Current-potential 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 2-1), 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 pseudo-linear 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} (2-9) 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- )} (2-10) 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 (2-11) 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 2-2 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+ (2-12) 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 2-3. At high frequency, the denominator of the last term in equation (2-12) 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 2-3 where the left end of the semicircle intersects the real axis. At very low frequencies, jTco in equation (2-12) approaches zero, and the result for the impedance is Re + Rt, shown in Figure 2-3 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 o-MAr- Cd Rt -HE-- Figure 2-2. 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 2-3. Nyquist plot for the circuit in Figure 2-2 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 non-stationary behavior during the time required to generate an impedance spectrum. Impedance data collected under non-stationary conditions will fail to satisfy the Kramers- Kronig relations. Since most process models applied to impedance spectra assume the steady-state, 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 non-stationary behavior [16-21]. The measurement model takes the form of the line shape based on the Kramers-Kronig- consistent Voigt circuit (see Figure 2-2) with impedance given by Z(co) = Zo + -k (2-13) 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 (2-14) where Z is the model value for the complex impedance Z [19]. The approach is to collect consecutive pseudo-replicate 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 (2-15) 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) (2-16) 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 (2-17) 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- Kronig-consistent 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 (2-18) 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 de-emphasis of data with low- noise and high-noise 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}] (2-19) 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 2-4. The development follows principles reported by previous authors [9-11, 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 (2-20) i i+ ddt Substitution of Vfor Xin equation (2-19) yields the time derivative V = joVexp{jct} (2-21) dt Substituting equation (2-21) into equation (2-20), writing the total current in the form of equation (2-19), and cancelling the exponential term, yields an expression for the total current density in terms of oscillating variables according to if +jCoCdV (2-22) The faradaic current density is expressed as a function of the potential and concentration according to if = f(V, ci) (2-23) If the magnitude of the oscillating terms is sufficiently small, equation (2-23) can be linearized according to I cVf_ + (2-24) The charge transfer resistance is expressed as 1 R, (2-25) Combining equations (2-25) and (2-24) yields f= (R +c c (2-26) As previously stated by equation (2-5), 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 (2-1), is written in terms of the potential measured with respect to a reference electrode, V, according to Fe = nFeFkFeexp (V VFe) (2-27) 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 (2-24) where the amplitude of the potential perturbation is small, equation (2-27) can be linearized: FFeF 2 OXFeF _ Fe = nFe kFe RT exp RT--(V- VF) FV (2-28) 19 which can be expressed in terms of the charge transfer resistance as demonstrated by equation (2-25): Fe t- (2-29) t, Fe Similarly, the current contribution from hydrogen evolution, reaction (2-3), is H2 = Fkexp -( V VH) (2-30) [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 = (2-31) The contribution from the reduction of oxygen, reaction (2-2), can be expressed in terms of potential and concentration according to io= -no FkoZ,o0 exp ---(V- Vo) (2-32) RT(V V02) (2-32) which can be linearized with respect to potential and concentration given by 0oF2 [ aor0F ]1 io2 = no2ko co2, T exp--- (V-Vo)V (2-33) 02oF RT2 Also, the flux of oxygen away from the electrode surface is d 020 02= -n02Fk D02, = -n02Fk2 D02J 2' 0'(0) (2-34) y = 0 0,f where 6'(0) is the dimensionless flux at the surface. Equation (2-34) yields 10202f (2-35) 2,0 n02FD021f 6'(0) 2 The charge transfer resistance is expressed according to 1 to F2 [ arO2F ) 1 = no-ko -2- exp R- (F Vo2) (2-36) RRt, 02 02 ]2 02, RT After substituting equations (2-35) and (2-36) into equation (2-33) and solving for i02 the contribution due to oxygen reduction is simplified to 7o = k- (2-37) 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 (2-38) 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 (2-29), (2-30), and (2-37) into equation (2-20) for the faradaic current density, the total current density is 1 (.e+ 1 + I_ +jOCd) (2-39) 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 (2-40) By solving equation (2-40) for V substituting the result into equation (2-39), and rearranging, the complex impedance is given by UL 1 S Zr+JZ = Re+ 1 1 1 (2-41) + + +- ++ -- i+jcoCd Rt, Fe Rt, 02 D,2 Rt, H2 Equation (2-41) can be equally expressed by a series-parallel 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 2-4. 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 (2-42) 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 2-4, vr = 0. Also, the concentration is assumed to vary in the r-dimension only. Thus, equation (2-42) reduces to ac, 2ci + I3ci = Di r + (2-43) Wt ar2 rar which governs stagnant diffusion of i in the r-dimension 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 (2-43) reduces to S= D .- (2-44) at 'ay2 A coordinate system is imposed, as shown in Figure 2-4, where y represents the distance from the surface, the film-metal 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 (2-44) can be written for the two diffusion regions, and the appropriate boundary conditions are y = 0 if = ciO (2-45) y = 0 Di = ki, oexp(V/3) (2-46) y =0 y* = (y= ) if = i,b (2-47) f Ci, b i,f i,bb y* = 0(y = 8,,) D, f = D i, f ib(2-48) D = D i, b i, f i, b a Y* i, b(Y --o) i, b -- ci, o (2-49) 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 (2-19) as the sum of steady and oscillating contributions, ci = i+ Re[i.exp{jot}] (2-50) Substitution of equation (2-50) into equation (2-44) yields jcoc.ieJmt i e -- iemt-D = 0 (2-51) dy2 dy2 The steady term of equation (2-51) can be written for both regions as d2 if 2 dij = 0 i, b = 0 (2-52) dy2 dy*2 Solving equation (2-52) 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( (2-53)3) ib Ci, 0-- Ci, b, 0 + i, b, Ci, b = 8i, b where the concentration at the film-bulk diffusion layer interface is given by Ci. b.O Di, bCi, -/i, b Di,J 8if + [Di,f/kexp (V/3)] (2-54) Di, b + bi,b By imposing the dimensionless variables f if, o Ob 0 Ci, b, O Y i, f 6i, b (2-55) the oscillating part of equation (2-51) can be written for both regions according to d 2f f 4Y-JOif Of d Ob, 0 -djOTi, bOf = 0 d ln2 bf (2-56) 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, (2-57) 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 (2-56) for the film and bulk, respectively, are dO* Di b i. b b, 0 (2-58) (2-59) (2-60) (2-61) (2-62) Of = Mf exp{ jT 7(c } + Nf exp {- -j ( } (2-63) 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)} (2-64) Q,, --- 'b--- -(64 sinh( 0oC tb) and through the film as tanh( jcoT b)cosh{ I fjco (- 1)}- sinh { j (OCi 1) } Of =-'f (2-65) Di, b tanh( jcit b) cosh( (jcT; ) + -7sinh( (JT;1) Taking the first derivative of equation (2-65) with respect to , evaluating at = 0, and taking the reciprocal gives the dimensionless flux term of equation (2-38) as tanh( O ) + tanh( /C ) 1-_--tahi(f '1 (2-66) j0o) ,tanh( ) tanh( JoC ) + Di Replacement of i with 02 in equation (2-66) yields the reciprocal of the dimensionless flux of oxygen to the surface of the working electrode, necessary for equation (2-38). 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 2-4. 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. Pipeline-grade steel served as the working electrode, and platinum-rhodium 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: potential-time 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 well-controlled 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 (3-1) 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 current-controlled experiments guaranteed that one electrical quantity was held constant over the course of the experiment. From equation (3-1), 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 3-1. 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 3-1. 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 center-drilled 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 acrylic-metal crevices. Platinum-rhodium alloy mesh screens, supplied by Engelhard-Clal, 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 (3-2) Using the boundary element method (BEM), equation (3-2) 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 (3-2) 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 (3-3) The axisymmetric plane for the cell geometry containing the holiday electrode is presented, including the imposed boundary conditions, in Figure 3-2. 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 3-3. Whereas the current density was radially uniform, the results in Figure 3-3 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 3-4. 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 (3-4) 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 (3-5) 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 (3-6) 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 3-2, 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 3-2 includes values for Re calculated for the cylinder electrode from the anode resistance formula [12] Re In( 8L 1 (3-7) e 2n-KLn 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 3-3 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 3-4. 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 acrylic-metal 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 3-5. The top and bottom covers were sealed using O-rings 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 3-6. 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 3-5). 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 O-ring to seal around the top of the WE to prevent electrolyte leaks (see Figure 3-6). 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 3-7 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 three-electrode 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 switch-over 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 switch-over 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 3-7. 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 3-5. 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 2-1). 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 3-8. 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 3-9 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 3-9 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 3-9 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 (3-8) |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 2-point prediction is made from Z(mk) = 2Z(mk- )-Z(ck 2) (3-9) From the fourth point to the end of the sweep, the impedance is estimated using a 3-point prediction according to Z(ck) = 3Z(ck- 1)- 3Z(ck 2) + Z(ck 3) (3-10) 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 O-ring seal. The top cover was oriented to assure the following: * the flange O-ring 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. Current-potential 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 3-1. 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 3-2. 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 (3-7), for the cylinder electrode. E/Ke, Re determined from: Electrode A _cm- A/ cm-1 BEM eq. (3-7) EIS Cylinder 24.57611 81.6 74.6 65 Holiday 2.95274 679.5 --- 650 Table 3-3. 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 3-4. Masses of salts in g/L added to water to prepare simulated soil electrolyte. The solution pH is included. Salt Mass, g/L CaCl2-2H20 0.734 MgSO4 0.267 NaHCO3 0.023 pH 8.0 Table 3-5. 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 3-1. Schematic of the simulated holiday electrode. Holiday (WE)--* Counter -Electrode Surface Axis of Symmetry Figure 3-2. 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 3-3. 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 3-4. 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 F-1 + 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 3-5. Schematic of corrosion cell body showing position of electrodes. Cell Cover Piece diameter = 8 in. Fastener Screw (8) Figure 3-6. Schematic of corrosion cell top cover piece. Figure 3-7. 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 3-8. 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 3-5 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 3-9. 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 Q2-cm-1, 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 3-5. 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 (4-1) 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 4-6 and Figure 4-7 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 4-7, 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 4-6. 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 3-5 and in Figure 3-8. 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 potential-time data for the cylinder electrode maintained at the corrosion potential is presented in Figure 4-1. The plot provides evidence of non-stationary 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 4-1 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 4-2. Unlike the potential-time 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 4-3, 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- (4-2) 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 non-stationary 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 4-2. 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 potential-time trace of the WE in response to an applied current density bias of 1.6 pA/cm2 is presented in Figure 4-4. 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 4-5, 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 potential-time trace for this experiment is presented in Figure 4-6. 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 potential-time 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 4-7. 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 potential-time trace of the WE in response to an applied current density of 4.0 pA/cm2 is presented in Figure 4-8. 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 3-8. 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 4-9, 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 4-1. 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 4-2. 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 4-3. 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 4-4. 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 4-5. 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 4-6. 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 4-7. 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 4-8. 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 4-9. 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 o-4 ; 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 3-3, 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 potential-time trace for this experiment is presented in Figure 4-10. 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 4-11. 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 potential-time trace in response to a DC bias of 5.0 pA/cm2 is presented in Figure 4-12. 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 4-13, 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 4-10. 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 4-11. 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 4-12. 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 4-13. 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 least-squares (CNLS) algorithms [18, 31-35]. 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 non-stationary behavior and inconsistencies with the Kramers-Kronig 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 eight-parameter 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 (5-1) + + I +joCj Rt, Fe Rt, 02 + ZD, 02 Rt, H2 The diffusion impedance, ZD, 02 given by equation (2-38), 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) (5-2) 1 where depends on the angular frequency and is given by equation (2-66). By 0'(0) introducing the substitution Db/f (5-3) equation (2-66) can be simplified to 1 tanh( j OT b) + Dtbf tanh( jof) (5-4) '(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 (5-5) Reff t, Fe t, H2 equation (5-1) was simplified for regression analysis as follows: Zr +jZ = Re + 1 (5-6) + I +JCOCd eff Rt, o2 + ZD, o -I From equations (5-4) and (5-6), 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 (2-57), associated with diffusion through a porous film, * 0T2, b is the time constant in seconds associated with diffusion in the bulk, see equation (2-57), * 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 (5-5), * Rt, o is the charge transfer resistance associated with oxygen reduction in Q, given by equation (2-36), * ZD, o is the coefficient of the diffusion impedance in Q, see equation (5-2), * 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 (5-5), 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 (2-36) with substitution of So2 from equation (2-32) and solving for Rt, 0 yielded RT 1 Rt, o (5-7) t02 F 0 oA where A is the surface area of the WE. From equation (5-7), 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 mass-transfer-limited current, i.e., 02 = im, 02, as shown by the oxygen reduction plateau in Figure 2-1. 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 3-8. 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 (5-6) 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 5-1. 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 5-2, 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 5-3 and Figure 5-4, 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 5-5 and Figure 5-6. The 95.4% confidence interval, generated from Monte Carlo simulations at each frequency step, are included in Figure 5-5 and Figure 5-6 [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 sweep-time 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 5-1. 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 5-2. Both the normalized real and imaginary component residual errors, as a function of frequency, resulting from process model regression to the data of Figure 5-1. |