Mass Transport Enhancement in Copper Electrodeposition Due to Gas Co-Evolution

MASS TRANSPORT ENHANCEMENT IN COPPER ELECTRODEPOSITION DUE TO GAS CO-EVOLUTION

OMAR ISRAEL GONZÁLEZ PEÑA

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy

Dissertation Adviser: Professor Uziel Landau

Department of Chemical and Biomolecular Engineering

CASE WESTERN RESERVE UNIVERSITY

August, 2015

CASE WESTERN RESERVE UNIVERSITY

SCHOOL OF GRADUATE STUDIES

We hereby approve the thesis/dissertation of

Omar Israel González Peña ______

Candidate for the Doctor of Philosophy degree*.

(signed) Prof. Uziel Landau ______Committee Chair

Prof. Rohan Akolkar ______Committee Member

Prof. Donald F. Feke ______Committee Member

Prof. R. Mohan Sankaran ______Committee Member

Prof. Daniel A. Scherson ______Committee Member

(date) July 14, 2015 .

*We also certify that written approval has been obtained for any proprietary material contained therein.

Dedication:

Defeat your demons, even if they are as fearsome as James Clerk Maxwell’s demon. Remember that just as Josiah Willard Gibbs turned to his angel, you also in science will not be alone… I dedicate this thesis to my wife, Ismailia; without her arduous patience, love, and work in belief in me, I would never have defeated the internal fearful demons of our journey. I would also like to thank my parents-in-law, who are always on my team when Ismailia and I initiate a friendly debate.

Likewise, this work is dedicated to my mother, who has taught me how to keep the strength and optimism of a free spirit in the journey, even when one has to continue alone. To Rafael and Juan Jose, who taught me how to have strong brotherhood links despite the distance and time. To my father, who departed several years ago to other destinies, but not before persuading me not to become a professor and a chemical engineer as he was until the very last day; although in his wish, he encouraged me to never give up in following my internal voice as well as to have the hunger to discover wise masters, pillars, to emulate... I still keep looking for these pillars, and in the business of teaching and electrochemistry I have found two great ones:

“I believe that the best advice that I can give you to be successful in your life is that you have to work with earnestness. The arduous work, your personality and the way you interact with the world is more important than your net intelligence. I have seen a lot of people who are very intelligent but not reach success in their endeavors, and I have also seen a lot of people that they were not so intelligent that were very successful. I believe that if one has the conviction of work with earnestness, one is really motivated,

iii and one is interested in the things that one does, then one can be very successful.” –

Allen J. Bard. – [Neal R. Amundson Lecture Series, December 1st and 2nd, (2003),

University of Guadalajara, Mexico].

“Throughout my career the greatest inspiration for research came to me as a result of preparing for classes, and trying to present a rational story when there was none available. Without active engagement in research, a teacher cannot impart to his students the reasoning tools necessary for understanding and mastering nature”. – Charles W.

Tobias. – [The Electrochem. Soc. Interface, Fall (1994) 17-21].

Furthermore, I dedicate this dissertation to the professors who have taught me during the B.S., M.S., and PhD studies; also to my thesis committee, colleagues and friends. Their essential contributions continue to help me become a better person holistically.

“People need a goal in order to galvanize them”. – John C. Maxwell.– [“ Law 8th, the law of the intuition”, The 21 Irrefutable Laws of Leadership, Thomas Nelson; 2007].

Table of Contents

List of Tables………………………………………………………………..……….ix

List of Figures…………………………………………………………………...….xiii

Abstract………………………………………………………………………...…xxvii

Chapter 1: Introduction……………………………………………………….…….1

1.1. Problem Description………………………………………………….…………. 1

1.2. Significance…………………………………………………………….………...1

1.3. Hypothesis………….………………………………………………….…………2

1.4. Objective……………………………………………………………….…………2

1.5. Background Information:……………………………………………….………..2

1.5.1. Overview………………………………………………………….……….2

1.5.2. Reduction of Metal Ions (specifically, copper):………………….………11

1.5.2.1. Theory…………………………………………………….……...11

1.5.2.2. Experimental Observations……………………………….…...…13

1.6. Challenges:………………………………………………………………..….....15

1.6.1. Modeling Difficulties………………………………………………….….15

1.6.2. Experimental Difficulties……………………………………………...….15

1.7. Organization and Outline of the Thesis:………………………………….…….16

1.8. References……………………………………………………………….……..17

Chapter 2: Experimental Methodology…………………………………..………22

2.1. The Experimental Set-up………………………………………………..……...22

2.2. Chemistry………………………………………………………………..……...23

2.3. Experimental Procedures:……..……………………………………….….……23

2.3.1. Deposition of Copper in the Presence of Hydrogen Co-Evolution……..….24

2.3.2. Polarization Data for Hydrogen Evolution from Acid (w/o Copper)………25

2.3.3. Weight Measurements of Copper…………………………………………..26

2.3.4. Correction for Surface Roughness……………………………………….…26

2.3.5. Photography (still and video) of Bubbles…………………………………..29

2.3.6. Determination of Bubble Radii and Surface Coverage…………………….29

2.3.7. Pulse Experiments to Relate Bubble Generation to Enhancement………...30

2.4. References……………………………………………………………………...... 32

Chapter 3: Experimental Results………………..…………………………………33

3.1. Area Correction Accounting for Roughness……………………………………..33

3.2 Copper Current Density Determined from Weight Measurements of the Deposited

Copper ………………………………………………………………………...... 35

3.3. Polarization Data for Copper Deposition above the Limiting Current..…….…...38

3.4. Hydrogen Evolution under High Cathodic Polarization………………………... 44

3.5. Copper Deposition Rates Determined from Current Measurements.…..….…….45

3.6. Comparison of the Copper Current Densities as Determined from the Current

Measurements to those Determined from the Deposit Weight…….……………...….51

3.7. Pulse Generation of Bubbles – Linking Bubbles Presence to Transport

Enhancement…………………………………………………………………………55

3.8. Optical Observations of Bubbles Evolution and Displacement…………..……..58

3.9. References…………………………………………………………………….…63

Chapter 4: Discussion of the Results………………………………………………64

4.1. Comparing Mass Transport Enhancement Based on Deposit Weight to that Based on

Current Measurements (Polarization Data):………………………….……….…64

4.2. Analysis of the Pulsed Bubble Generation Experiments……………………...…69

4.3. Analysis of the Photographic Data……………….…………………….………..75

Chapter 5: Modeling the Bubble Induced Enhancement:……………….……….80

5.1. Model Description…………………………………………………………...…..80

5.2. Velocity Profile near a Rotating Disk ..……………..……………………..….…81

5.3. Forces Acting on the Bubble:……………..……………………………..….…...87

5.4. Bubble Generation and Growth ………………………………………….…..….92

5.5. Determination of the Characteristic Transition Time, t ……………………..….97

c 5.6. The Modelled Transport Enhancement…………………………………....…....101

5.7. Transport Enhancement – Discussion and Comparison with Experiments….....106

5.8. References……………………………………………………………………....113

Chapter 6: Conclusions and Suggestions for Future Work……………….….…116

6.1 Conclusions…………………………………………………………………...…116

6.2 Suggestions for Future Work…………………………………………………....117

Chapter 7: Nomenclature……………………………………………………….…119

Appendices:…………………………………………………………………….…..125

Appendix A……………………………………………………….…………….…..125

A.1. Polarization Data for Copper Deposition above the Limiting Current (Raw Data without Ohmic Correction)…………………………………………………..…..….125

A.2 Copper Deposition Rates Determined from Current Measurements (data for 20 mM cupric ion concentration – “dilute electrolyte”)………………………..…….…..…127

vii

Appendix B………………………………………………………………….……..131

Pulse Generation of Bubbles – Linking Bubbles Presence to Transport

Enhancement………………………………………………………………..….…..131

Appendix C…………………………………………………………………..……149

Length of the spiral path of a bubble…………………………………………..…..149

Bibliography……………………………………………………………….…..…151

viii

List of Tables:

Chapter 1:

Table 1.1: Selected Standard Electrode Potentials for Metals Reduction in Aqueous

Solution at 25oC…………………………………………………………………………(8)

Chapter 2:

Table 2. 1: Electrodeposition times (in seconds) selected for the experiments...... (25)

Table 2.2: Parameters of the double pulse experiments relating bubble generation to

mass transfer enhancement…………………………………………………………...(31)

Chapter 3:

Table 3.1: Experimental data providing the rough electrode area for the deposition

experiments in 20 mM CuSO4 at pH ≈ 0. The deposition times to generate the rough

areas are listed in table 2.1. Smooth disk area is 0.317cm2……………………..…..…(34)

Table 3.2: Experimental data providing the rough electrode area for the deposition

experiments in 200 mM CuSO4 at pH ≈ 0. The deposition times to generate the rough areas are listed in table 2.1. Smooth disk area is 0.317cm2……………………..…...... (34)

Table 3.3: Resistance values of the electrolyte solutions on a RDE………………...... (39)

Table 3.4: Calculated limiting current density for 20 and 200 mM CuSO4 at pH ≈0, and

different rotation rates according to the Levich equation. The disk area is 0.317 cm2...(43)

Table 3.5: Parameters obtained from the pulse experiment of figure 3.13; 20 mM CuSO4

at pH ≈ 0 at 50 rpm. Time of bubble generation was 8 seconds at the listed potentials.

Current predicted by the Levich equation = -1.092 mA………………………………(58)

Table 3.6: Photographs s of the bubble covered copper disk electrode at different potentials, and rotation rates. The electrolytic was sulfuric acid at pH ≈ 0…………...(60)

Table 3.7: Measurements of average bubble radii, fraction of surface coverage and standard deviation at different rotation speeds and potentials. Values were obtained from photographs of a RDE in aqueous H2SO4 pH~0………………………………………(61)

Table 3.8: Times of bubble sweep at different potentials. Values were obtained from

video recording of a RDE in dilute H2SO4 electrolyte at pH ≈ 0……………………..(63)

Chapter 5:

Table 5.1: Calculations of the average time for bubble to reach disk circumference,

, , the characteristic time of bubble generation, , and for different rotation

푎푎푎 푡푡�푡푡 푐 rates푡 …………………………………………………………………………………...(101)푡 훽

Appendix B.

Table B.1: Parameters obtained from the pulse experiments of figure B.1; 20 mM CuSO4

at pH ≈ 0 at 70 rpm. Time of bubble generation was 8 seconds at the listed potentials.

Current predicted by the Levich equation = -1.293 mA…………………………..…(133)

Table B.2: Parameters obtained from the pulse experiments of figure B.2; 20 mM CuSO4

at pH ≈ 0 at 100 rpm. Time of bubble generation was 8 seconds at the listed potentials.

Current predicted by the Levich equation = -1.545 mA………………………….….(135)

Table B.3: Parameters obtained from the pulse experiments of figure B.3; 20 mM CuSO4

at pH ≈ 0 at 100 rpm. Time of bubble generation was one second at the listed potentials.

Current predicted by the Levich equation = -1.545 mA………………………….….(137)

Table B.4: Parameters obtained from the pulse experiments of figure B.4; 20 mM CuSO4

at pH ≈ 0 at 100 rpm. Time of bubble generation was 2 seconds at the listed potentials.

Current predicted by the Levich equation = -1.545 mA……………………………..(139)

Table B.5: Parameters obtained from the pulse experiments of figure B.5; 20 mM CuSO4

at pH ≈ 0 at 400 rpm. Time of bubble generation was 8 seconds at the listed potentials.

Current predicted by the Levich equation = -3.09 mA………………………………(141)

Table B.6: Parameters obtained from the pulse experiments of figure B.6; 20 mM CuSO4

at pH ≈ 0 at 900 rpm. Time of bubble generation was 8 seconds at the listed potentials.

Current predicted by the Levich equation = - 4.635 mA………………………….....(143)

Table B.7: Parameters obtained from the pulse experiments of figure B.7; 200 mM

CuSO4 at pH ≈ 0 at 100 rpm. Time of bubble generation was 8 seconds at the listed potentials. Current predicted by the Levich equation = -15.451 mA……………..…(145)

Table B.8: Parameters obtained from the pulse experiments of figure B.8; 200 mM

CuSO4 at pH ≈ 0 at 400 rpm. Time of bubble generation was two seconds at the listed potentials. Current predicted by the Levich equation = -30.90 mA…………………(147)

Table B.9: Parameters obtained from the pulse experiments of figure B.9; 200 mM

CuSO4 at pH ≈ 0 at 900 rpm. Time of bubble generation was two seconds at the listed potentials. Current predicted by the Levich equation = - 46.352 mA……………….(148)

List of Figures:

Chapter 1:

Figure 1.1: Reduction branch for copper (schematic)……………………………….(12)

Figure 1.2: Schematic representation of the reduction current density of cupric ions……………………………………………………………………………………..(14)

Chapter 2:

Figure 2.1: Sketch of the electrochemical cell. The working electrode is copper RDE, the counter electrode is a platinum mesh and the reference electrode is a saturated calomel electrode (SCE)………………………………………………………………………...(22)

Figure 2.2: Schematic polarization curve on a RDE…………………………………..(27)

Figure 2.3: Schematic of the methodology used to obtain the electrode area

correction……………………………………………………………………………….(28)

Figure 2.4: Input voltage sketch (not to scale) of the double pulse experiment, relating bubble generation to mass transfer enhancement……………………………….……..(31)

Chapter 3:

Figure 3.1: Current densities in copper reduction from 20 mM CuSO4 at pH ≈ 0 obtained

from the weight of the electrodeposited copper, using Faraday’s law. Blue diamonds

represent the copper current density at 100 rpm. Red squares correspond to the copper

current density at 400 rpm. Green triangles indicate the copper current density at 900

rpm. The current density was determined by dividing the current calculated from

xii

Faraday’s law by the rough area of the electrode as reported in table 3.1. The applied voltages indicated were corrected for the IR drop……………………………………..(36)

Figure 3.2: Current densities in copper reduction from 200 mM CuSO4 at pH ≈ 0 obtained from the weight of the electrodeposited copper, using Faraday’s law. Blue diamonds represent the copper current density at 100 rpm. Red squares correspond to the copper current density at 400 rpm. Green triangles indicate the copper current density at

900 rpm. The current density was determined by dividing the current calculated from

Faraday’s law by the rough area of the electrode as reported in table 3.2. The applied voltages indicated were corrected for the IR drop…………………………………..…(38)

Figure 3.3: Polarization curve for 20 mM CuSO4 at pH ≈ 0. Blue diamonds indicate the total current density at 100 rpm. Red squares correspond to the total current density at

400rpm. Green triangles specify the total current density at 900 rpm. (A) The entire tested region. (B) Magnified view of the low current density region in (A). The surface area applied in determining the current density is the actual rough deposited surface as reported in table 3.1. The displayed voltage has been compensated for the IR drop…..(41)

Figure 3.4: Polarization curve in 200 mM CuSO4 at pH ≈ 0. Blue diamonds designate the total current density at 100 rpm. Red squares correspond to the total current density at

400rpm. Green triangles indicate the total current density at 900 rpm. The surface area applied in determining the current density is the actual rough deposited as reported in table 3.2. The displayed voltage has been compensated for the IR drop…………..…..(42)

xiii

Figure 3.5: Polarization curves in 1M H2SO4. Blue diamonds: hydrogen current at 100

rpm. Red squares: hydrogen current at 400 rpm. Green triangles: hydrogen current at 900

rpm. Data obtained by measuring the current during hydrogen evolution from sulfuric

acid on a copper RDE applying IR compensation……………………………………..(45)

Figure 3.6: Polarization curve of 200 mM CuSO4 at pH ≈ 0 at 100 rpm. Blue diamonds

correspond to the total current. Red triangles indicate the hydrogen current. The green

squares depict the copper current obtained by the subtraction of the hydrogen current

from the total current………………………………………………………………...…(47)

Figure 3.7: Polarization curve of 200 mM CuSO4 at pH ≈ 0 at 400 rpm. Blue diamonds

correspond to the total current. Red triangles indicate the hydrogen current. The green

squares depict the copper current obtained by the subtraction of the hydrogen current

from the total current…………………………………………………………………...(48)

Figure 3.8: Polarization curve of 200 mM CuSO4 at pH ≈ 0 at 900 rpm. Blue diamonds

correspond to the total current. Red triangles indicate the hydrogen current. The green

squares depict the copper current obtained by the subtraction of the hydrogen current

from the total current…………………………………………………………………...(49)

xiv

Figure 3.9: Current densities, determined from polarization data on RDE for copper deposition from 200 mM CuSO4 at pH ≈ 0 as a function of the overpotential at various rotation rates. Blue diamonds correspond to the copper current density at 100 rpm. Red squares indicate the copper current density at 400 rpm. Green triangles are the copper current density at 900 rpm. All copper current density were obtained by the subtraction of the hydrogen current density from the total current density. Hydrogen and total current densities were recorded by the potentiostat and divided by the rough area reported in table 3.2……………………………….………………………………….…………….(50)

Figure 3.10: Comparison of current densities in the electrodeposition of copper based on weight measurements (blue diamonds), and polarization data (red squares). The disk electrode was rotated at 100 rpm. Experiments were conducted in 200 mM CuSO4 at pH

0 ………………….……………………………………………………………….….(52)

≈Figure 3.11: Comparison of current densities in the electrodeposition of copper based on

weight measurements (blue diamonds), and polarization data (red squares). The disk

electrode was rotated at 400 rpm. Experiments were conducted in 200 mM CuSO4 at pH

≈ 0……………………………………………………………………………………....(53)

Figure 3.12: Compensation of current densities in the electrodeposition of copper based on weight measurements (blue diamonds), and polarization data (red squares). The disk electrode was rotated at 900 rpm. Experiments were conducted in 200 mM CuSO4 at pH

≈ 0…….………………………………………………………………………………...(54)

Figure 3.13: Current trace for pulse experiments in 20 mM CuSO4 at pH ≈ 0. The disk electrode was rotated at 50 rpm. The currents on the left (A) correspond to mainly hydrogen bubble generation (and some copper plating) at the listed highly negative potentials for 8 seconds. After 8 seconds, the potential was rapidly stepped to -0.2 V where hydrogen was no longer generated but plating of copper continues. (B) Magnified view of the region in (A) in the time-frame when the generation of bubbles was discontinued by switching the potentiostat to -0.2 V…………………………………..(56)

Figure 3.14: Schematic representation of the measurement procedure for determining the time of bubble displacement. Initially, the measured bubble is static and located approximately at 1/3 of the disk radius away from the center. Subsequently the bubble is swept towards the edge of the disk over the time t…………………………………..(62)

Chapter 4: ∆

Figure 4.1: Enhancement factor based on deposit weight measurements for 20 mM

CuSO4 at pH ≈ 0. Blue diamonds indicate the enhancement factor at 100 rpm. Red

squares correspond to the enhancement factor at 400 rpm. Green triangles refer to the

enhancement factor at 900 rpm. Currents were obtained from weight measured of the

deposited copper using Faraday’s law and accounting for the rough area of the electrode

as reported in table 3.1. The reported voltage has been corrected for the IR drop…….(67)

xvi

Figure 4.2: Enhancement factor based on weight measurement of 200 mM CuSO4 at pH

≈ 0. Blue diamonds correspond to the enhancement factor at 100 rpm. Red squares indicate the enhancement factor at 400 rpm. Green triangles refer to the enhancement factor at 900 rpm. Currents were obtained from weight measured of the deposited copper using Faraday’s law and accounting for the rough area of the electrode as reported in table 3.1. The reported voltage has been corrected for the IR drop……………………(68)

Figure 4.3: Enhancement factor based on weight measurements as indicated by equation

4.1 and 4.3 (blue diamonds), and based on the pulse experiments where Φ(pulse) is given by ICu-pulse/ILevich (green triangles). Experiments were carried at 100 rpm in 20 mM CuSO4

at pH ≈ 0. No ohmic correction was applied. In the pulse generation of bubbles, the

hydrogen evolution had been discontinued after 8 sec……………………….……….(70)

Figure 4.4: Enhancement factor based on weight measurements as indicated by equation

4.1 and 4.3 (blue diamonds), and based on the pulse experiments where Φ(pulse) is given

by ICu-pulse/ILevich (green triangles). Experiments were carried at 400 rpm in 20 mM CuSO4

at pH ≈ 0. No ohmic correction was applied. In the pulse generation of bubbles, the

hydrogen evolution had been discontinued after 8 sec………………………….….…(71)

Figure 4.5: Enhancement factor based on weight measurements as indicated by equation

4.1 and 4.3 (blue diamonds), and based on the pulse experiments where Φ(pulse) is given

by ICu-pulse/ILevich (green triangles). Experiments were carried at 900 rpm in 20 mM CuSO4

at pH ≈ 0. No ohmic correction was applied. In the pulse generation of bubbles, the

hydrogen evolution had been discontinued after 8 sec………………………….….,,,,(72)

xvii

Figure 4.6: Enhancement factor based on weight measurements as indicated by equation

4.1 and 4.3 (blue diamonds), and based on the pulse experiments where Φ(pulse) is given

by ICu-pulse/ILevich (green triangles). Experiments were carried at 100 rpm in 200 mM

CuSO4 at pH ≈ 0. No ohmic correction was applied. In the pulse generation of bubbles,

the hydrogen evolution had been discontinued after 8 sec………………………….…(73)

Figure 4.7: Enhancement factor based on weight measurements as indicated by equation

4.1 and 4.3 (blue diamonds), and based on the pulse experiments where Φ(pulse) is given

by ICu-pulse/ILevich (green triangles). Experiments were carried at 400 rpm in 200 mM

CuSO4 at pH ≈ 0. No ohmic correction was applied. In the pulse generation of bubbles,

the hydrogen evolution had been discontinued after 8 sec……………………….……(74)

Figure 4.8: Enhancement factor based on weight measurements as indicated by equation

4.1 and 4.3 (blue diamonds), and based on the pulse experiments where Φ(pulse) is given

by ICu-pulse/ILevich (green triangles). Experiments were carried at 900 rpm in 200 mM

CuSO4 at pH ≈ 0. No ohmic correction was applied. In the pulse generation of bubbles,

the hydrogen evolution had been discontinued after 8 sec…………………………….(75)

Figure 4.9: Surface coverage as a function of potential at different rotation rates. The

graph was constructed from numerous photographs similar to those shown in table

3.7………………………………………………………………………………………(77)

Figure 4.10: Mean bubble radii as a function of potential at different rotation rates. The

graph was constructed from the photographs similar to those shown in table 3.7.....…(78)

Figure 4.11: Mean bubble radii as a function of rotation rates at different potentials. The

graph was constructed from the photographs similar to those shown in table 3.7….....(79)

xviii

Chapter 5:

Figure 5.1: Sketch of the side view of a RDE indicating the electrolyte flow pattern due

to the disk rotation……………………………………………………………………...(81)

Figure 5.2: Sketch of the bottom view of a RDE, showing the spiral path of a

bubble…………………………………………………………………………………..(82)

Figure 5.3: Sketch of the bubble growth and translation. Step 1 is the initial state of bubble nucleation. Step 2 represents the process of bubble growth prior to translation. In

step 3 bubbles reach the critical radius where it starts to be swept the flow. The lowest figure describes the bubbles path, indicating regions where the conventional limiting current as given by Levich (ilim) prevails, and regions within the bubbles path, where a

higher, transient current density is expected……………………………….…....(84)

퐶퐶푡푡 Figure 5.4: Sketch of top view〈푖 of 〉bubble translation on the electrode. The time

푐 designates the delay time between two consecutive bubbles……………………..…....(85)푡

Figure 5.5: (A) Side view of a distorted bubble due to drag force by the fluid showing a

net component of the surface tension force parallel to the surface. This arises from the

distortion of the bubble geometry which gives rise to a difference in the contact angle

between the bubble and the surface in the advancing and receding directions. (B) Bottom

view of a distorted bubble due to drag force by the fluid. and are the surface

휑 � tension forces in angular and radial directions, respectively.휎 The 휎sketch follows a

presentation similar to Fig. 1(b) in Amirfazli’s publication [7]…………………….….(88)

Figure 5.6: Sketch of the force balance on a small hemispherical bubble attached to the

electrode within the boundary layer……………………………………………………(89)

xix

Figure 5.7: Mean bubble radius as a function of rotation rate. The logarithm of Rc and ω

were calculated in cm and rads/sec, respectively………………………………….…...(91)

Figure 5.8: Sketch of the volume renewal model…………………………………….(93)

Figure 5.9: Sketch of the depletion of cupric ion concentration within the boundary

layer…………………………………………………………………………………….(94)

Figure 5.10: Sketch of the transient response of the Cottrell equation…………….…(96)

Figure 5.11: Sketch of the system used for carrying a mass balance on bubbles that are

exiting from the disk electrode………………………………………………………....(99)

Figure 5.12: Sketch of the swept path of bubbles on the electrode surface. L is the

average bubble path length from the initial average bubble position to the circumference

of the disk……………………………………………………………………………..(103)

Figure 5.13: Comparison of modeled enhancement factor with experimental

enhancement factors at 100 rpm. Blue diamonds correspond to the weight measurements

data. Green triangles indicate the pulse experiments where Φ(pulse) is given by ICu-

pulse/ILevich. Red squares designated the enhancement factor based on polarization data.

The purple solid line corresponds to the model as described by equation 5.54. The

electrolyte is 200 mM CuSO4 at pH ≈ 0. No IR correction is applied to the data. In the

pulse experiment, the hydrogen evolution had been discontinued after 8 sec………..(108)

Figure 5.14: Comparison of modeled enhancement factor with experimental enhancement factors at 400 rpm. Blue diamonds correspond to the weight measurements

data. Green triangles indicate the pulse experiments where Φ(pulse) is given by ICu-

pulse/ILevich. Red squares designated the enhancement factor based on polarization data.

The purple solid line corresponds to the model as described by equation 5.54. The

electrolyte is 200 mM CuSO4 at pH ≈ 0. No IR correction is applied to the data. In the

pulse experiment, the hydrogen evolution had been discontinued after 8 sec……...... (109)

Figure 5.15: Comparison of modeled enhancement factor with experimental

enhancement factors at 900 rpm. Blue diamonds correspond to the weight measurements

data. Green triangles indicate the pulse experiments where Φ(pulse) is given by ICu-

pulse/ILevich. Red squares designated the enhancement factor based on polarization data.

The purple solid line corresponds to the model as described by equation 5.54. The

electrolyte is 200 mM CuSO4 at pH ≈ 0. No IR correction is applied to the data. In the

pulse experiment, the hydrogen evolution had been discontinued after 8 sec………..(110)

Figure 5.16: Comparison of modeled enhancement factor with experimental

enhancement factors at 100 rpm. Blue diamonds correspond to the weight measurements

data. Green triangles indicate the pulse experiments where Φ(pulse) is given by ICu-

pulse/ILevich. Red squares designated the enhancement factor based on polarization data.

The purple solid line corresponds to the model as described by equation 5.54. The

electrolyte is 20 mM CuSO4 at pH ≈ 0. No IR correction is applied to the data. In the

pulse experiment, the hydrogen evolution had been discontinued after 8 sec…….…(111)

xxi

Figure 5.17: Comparison of modeled enhancement factor with experimental enhancement factors at 400 rpm. Blue diamonds correspond to the weight measurements

data. Green triangles indicate the pulse experiments where Φ(pulse) is given by ICu-

pulse/ILevich. Red squares designated the enhancement factor based on polarization data.

The purple solid line corresponds to the model as described by equation 5.54. The

electrolyte is 20 mM CuSO4 at pH ≈ 0. No IR correction is applied to the data. In the

pulse experiment, the hydrogen evolution had been discontinued after 8 sec……....(112)

Figure 5.18: Comparison of modeled enhancement factor with experimental

enhancement factors at 900 rpm. Blue diamonds correspond to the weight measurements

data. Green triangles indicate the pulse experiments where Φ(pulse) is given by ICu-

pulse/ILevich. Red squares designated the enhancement factor based on polarization data.

The purple solid line corresponds to the model as described by equation 5.54. The

electrolyte is 20 mM CuSO4 at pH ≈ 0. No IR correction is applied to the data. In the

pulse experiment, the hydrogen evolution had been discontinued after 8 sec…….....(113)

Appendix A.

Figure A.1: Polarization curve for 20 mM CuSO4 at pH ≈ 0. Blue diamonds indicate the

total current density at 100 rpm. Red squares correspond to the total current density at

400rpm. Green triangles specify the total current density at 900 rpm. (A) The entire tested

region. (B) Magnified view of the low current density region in (A). The surface area

applied in determining the current density is the actual rough deposited surface as

reported in table 3.1…………………………………………………………………...(126)

xxii

Figure A.2: Polarization curve in 200 mM CuSO4 at pH ≈ 0. Blue diamonds designate

the total current density at 100 rpm. Red squares correspond to the total current density at

400rpm. Green triangles indicate the total current density at 900 rpm. The surface area

applied in determining the current density is the actual rough deposited and it is reported

in table 3.2…………………………………………………………………………….(127)

Figure A.3: Polarization curve of 20 mM CuSO4 at pH ≈0 at 100 rpm. Blue diamonds

correspond to the total current. Red triangles indicate the hydrogen current. The green

squares depict the copper current obtained by the subtraction of the hydrogen current

from the total current……………………………………………………………….…(128)

Figure A.4: Polarization curve of 20 mM CuSO4 at pH ≈ 0 at 400 rpm. Blue diamonds correspond to the total current. Red triangles indicate the hydrogen current. The green squares depict the copper current obtained by the subtraction of the hydrogen current from the total current……………………………………………………………….…(129)

Figure A.5: Polarization curve of 20 mM CuSO4 at pH ≈ 0 at 900 rpm. Blue diamonds correspond to the total current. Red triangles indicate the hydrogen current. The green squares depict the copper current obtained by the subtraction of the hydrogen current from the total current……………………………………………………………….…(130)

xxiii

Appendix B.

Figure B.1: Current trace for pulse experiments in 20 mM CuSO4 at pH ≈ 0; 70 rpm. The

currents on the left (A) correspond to mainly hydrogen bubble generation (and some

copper plating) at the listed highly negative potentials for 8 seconds. After 8 seconds, the

potential was rapidly stepped to -0.2 V where hydrogen was no longer generated but

plating of copper continues. (B) Magnified view of the region in (A) in the time region

when the generation of bubbles was discontinued by switching the potentiostat to -0.2

V………………………………………………………………………………………(132)

Figure B.2: Current trace for pulse experiments in 20 mM CuSO4 at pH ≈ 0 at 100 rpm.

The currents on the left (A) correspond to mainly hydrogen bubble generation (and some

copper plating) at the listed highly negative potentials for 8 seconds. After 8 seconds, the

potential was rapidly stepped to -0.2 V where hydrogen was no longer generated but

plating of copper continues. (B) Magnified view of the region in (A) in the time region

when the generation of bubbles was discontinued by switching the potentiostat to -0.2

V……………………………………………………………………………………....(134)

Figure B.3: Current trace for pulse experiments in 20 mM CuSO4 at pH ≈ 0 at 100 rpm.

The currents on the left (A) correspond to mainly hydrogen bubble generation (and some

copper plating) at the listed highly negative potentials for one second. After 1 second, the

potential was rapidly stepped to -0.2 V where hydrogen was no longer generated but

plating of copper continues. (B) Magnified view of the region in (A) in the time region

when the generation of bubbles was discontinued by switching the potentiostat to -0.2

V………………………………………………...…………………………………….(136)

xxiv

Figure B.4: Current trace for pulse experiments in 20 mM CuSO4 at pH ≈ 0 at 100 rpm.

The currents on the left (A) correspond to mainly hydrogen bubble generation (and some

copper plating) at the listed highly negative potentials for two seconds. After 2 second,

the potential was rapidly stepped to -0.2 V where hydrogen was no longer generated but

plating of copper continues. (B) Magnified view of the region in (A) in the time region

when the generation of bubbles was discontinued by switching the potentiostat to -0.2

V………………………………………………………………………………………(138)

Figure B.5: Current trace for pulse experiments in 20 mM CuSO4 at pH ≈ 0 at 400 rpm.

The currents on the left (A) correspond to mainly hydrogen bubble generation (and some

copper plating) at the listed highly negative potentials for eight seconds. After 8 second,

the potential was rapidly stepped to -0.2 V where hydrogen was no longer generated but

plating of copper continues. (B) Magnified view of the region in (A) in the time region

when the generation of bubbles was discontinued by switching the potentiostat to -

0.2V………………………………………………………………………………..…(140)

Figure B.6: Figure B.6: Current trace for pulse experiments in 20 mM CuSO4 at pH ≈ 0

at 900 rpm. The currents on the left (A) correspond to mainly hydrogen bubble

generation (and some copper plating) at the listed highly negative potentials for eight

seconds. After 8 second, the potential was rapidly stepped to -0.2 V where hydrogen was

no longer generated but plating of copper continues. (B) Magnified view of the region in

(A) in the time region when the generation of bubbles was discontinued by switching the

potentiostat to -0.2 V………………………………………………………………….(142)

xxv

Figure B.7: Current trace for pulse experiments in 200 mM CuSO4 at pH ≈ 0 at 100 rpm.

The currents on the left (A) correspond to mainly hydrogen bubble generation (and some

copper plating) at the listed highly negative potentials for eight seconds. After 8 second,

the potential was rapidly stepped to -0.2 V where hydrogen was no longer generated but

plating of copper continues. (B) Magnified view of the region in (A) in the time region

when the generation of bubbles was discontinued by switching the potentiostat to -0.2

V……………………………………………………………………………………....(144)

Figure B.8: Current trace for pulse experiments in 200 mM CuSO4 at pH ≈ 0 at 400 rpm.

The currents on the left (A) correspond to mainly hydrogen bubble generation (and some

copper plating) at the listed highly negative potentials for eight seconds. After 8 second,

the potential was rapidly stepped to -0.2 V where hydrogen was no longer generated but

plating of copper continues. (B) Magnified view of the region in (A) in the time region

when the generation of bubbles was discontinued by switching the potentiostat to -0.2

V……………………………………………………………………………………....(146)

Figure B.9: Current trace for pulse experiments in 200 mM CuSO4 at pH ≈ 0 at 900 rpm.

The currents on the left (A) correspond to mainly hydrogen bubble generation (and some

copper plating) at the listed highly negative potentials for eight seconds. After 8 second,

the potential was rapidly stepped to -0.2 V where hydrogen was no longer generated but

plating of copper continues. (B) Magnified view of the region in (A) in the time region

when the generation of bubbles was discontinued by switching the potentiostat to -0.2

V………………………………………………………………………………………(147)

xxvi

Acknowledgments:

To the National Council of Science and Technology, (CONACyT, Mexico), as well as to the Secretariat of Public Education, (SEP, Mexico) for the four years of fellowship to finance my PhD studies.

Likewise, to Prof. Uziel Landau, Prof. Rohan Akolkar, and the Landau’s research group for the helpful discussion and the facilities provided through Case Western Reserve

University for the realization of this research project. Finally, to the members of thesis committee for the review of this study.

xxvii

Mass Transport Enhancement in Copper Electrodeposition due to Gas Co- Evolution

Abstract

OMAR ISRAEL GONZÁLEZ PEÑA

Metal electrodeposition is often associated with simultaneous hydrogen co- evolution. The presence of bubbles complicates the design and control of electrodeposition processes. This is particularly relevant to the electrodeposition from aqueous electrolytes of numerous metals with standard potentials that are negative to hydrogen. As shown in this study, hydrogen co-evolution enhances the transport rates of the metal deposition reaction beyond those predicted by the classical, steady-state mass transport model.

Available models addressing transport in the presence of gas co-evolution are based on free convection that is enhanced by the rising bubble cloud. However, there are no models that address mass transfer enhancement by bubbles under forced convection, such as analyzed here for the commonly used, facing-down rotating disk electrode

(RDE). This study characterizes experimentally the phenomenon and introduces a model for quantifying it.

Experimental data was collected in plating copper at high cathodic overpotentials

(-0.4 to -1.0V vs SHE) from acidified copper sulfate on a RDE. The transport enhancement (~2-6 fold) was determined by measuring the copper deposition by

xxviii gravimetry. Pulse experiments, where the current decay was measured following a short bubble generation confirmed the linkage between the current enhancement and the presence of bubbles.

A model based on fresh electrolyte replenishing the volume vacated by the translating bubbles and thus subjecting regions of the electrode to enhanced transient currents has been derived. The model correlates the experimental data indicating higher transport enhancement with increasing cathodic polarization and dependence of the enhancement on the rotation rate and on the bulk copper concentration.

xxix

CHAPTER 1: Introduction.

1.1. Problem Description:

Unexplained enhanced mass transport, exceeding the predicted limiting current had been observed in the deposition metals in the presence of hydrogen gas co-evolution.

Models that address transport in the presence of gas co-evolution are all based on free convection that is enhanced by the rising bubble cloud [1, 2]. Other models address the effects of bubbles in convective systems without the presence of metal ions deposition.

However, there are no papers that address mass transfer enhancement in systems not driven by free convection, such as analyzed here. This study provides a qualitative and quantitative analysis of the phenomenon.

1.2. Significance:

Metal electrodeposition is often associated with simultaneous reactions at the cathode involving the reduction of metal ions and hydrogen co-evolution. The formation of hydrogen bubbles affects the region near the electrode, complicating the control and design of electrodeposition processes subject to gas co-evolution. As will be subsequently shown, the hydrogen co-evolution enhances the transport rates of the metal deposition reaction.

This work provides a better understanding of the transport rates in electrodeposition processes where hydrogen co-evolves. This occurs in deposition of metals with a standard potential that is more negative than that of hydrogen E < 0 V/SHE.

1.3. Hypothesis:

This study invokes the following hypothesis:

Mass transfer enhancement during copper deposition at very negative potentials is due to hydrogen gas bubble co-evolution, and the translation of the bubbles across the electrode.

1.4. Objective:

The objectives of this research project are two-fold. First, conduct systematic

experiments of electrodeposition of a metal, specifically, copper, on a down-facing

rotating disk electrode (RDE) in the presence of hydrogen co-evolution and quantitatively

characterize the phenomenon. Second, derive a theoretical model that explains and

simulates the effect of mass transfer enhancement in the copper electrodeposition.

1.5. Background Information:

1.5.1. Overview:

There are quite a number of industrial processes, where gases are generated or co-

generated by electrochemical reactions, e.g. the chlor-alkali process, electroless

deposition processes, electrolysis of water, and aluminum production. As a result, such systems involve three-phases. The formation of bubbles generates an increment in the

transport at the metal-solution interface. This enhanced transport has not been previously

fully characterized. This issue becomes more difficult when the systems consist of

complex geometries, or when the systems operate under forced convection. Theoretical

models are important because of the desire to achieve predictive design and improve the

efficiency in such electrochemical systems.

Cavendish was cited as being the first to call attention to the formation of bubbles at the electrode of an electrolysis experiment that was done for the first time in 1766 [3].

More recently, empirical correlations have been introduced relating the hydrogen production rate to input parameters, such as current or voltage for different geometries [4,

5]; nonetheless, these correlations do not provide a theoretical framework for fundamentally understanding the phenomena. Ibl and collaborators were the first to provide theoretical studies of hydrogen evolution [6,7]. In these early studies, the working electrode was a plate located at the bottom of the cell. As a result, bubbles were subject to buoyancy forces: initially formed bubbles grew to a critical size until the bubbles detached from the electrode; and rose to the surface of the solution, due to buoyancy. Ibl’s group constructed their model by considering the penetration model established by Higbie for mass transfer in mixtures under unsteady-state conditions. [6-

8].

The review of gas evolving electrodes by Vogt [2], discusses several subjects related to gas generation. Vogt analyzes bubble nucleation, bubble growth, and the applicability of the following equation proposed by Beck :

= (1.1) 푚푒 푉푔̇ 푘퐵 �푐푐푐� � 퐴 � , / and are the mass transfer coefficient ( ), volumetric flow rate divided

퐵 푔 � by푘 the�푉̇ geometric퐴� 푚 area of the electrode ( ), and 𝑐an empirical⁄� exponent, respectively.

Beck applied equation 1.1 in a system consisting𝑐⁄� of a separate electrolyzer and a reactor with a circulating loop of electrolyte.

Vogt’s review provides values of the exponent in equation 1.1 as listed in table

1 of his review [2]. The value of reported in various푚 experimental investigations of systems with different electrochemical푚 cell geometries, electrolyte solutions, and /or working electrodes is between 0.17 to 0.87. However, for our study the value of

reported in the Vogt’s review [2] is not very instructive because our working electrode푚

does not involve free convection, and the reported mass transport rates in equation 1.1

refer to the gas evolution reaction and not to enhancement effects on the accompanying

metal deposition.

Transport in the presence of hydrogen evolution has also been studied using

theoretical approaches. The phenomena underlying these theoretical models are: surface

renewal [6,7, 9, 10], microconvection [2], and hydrodynamics or macroconvection [10,

11]. As additional topics of his review, Vogt discussed also the effective conductivity in

the solution in the presence of bubbles, the rising velocity of gas bubbles, as well as the

current distribution and ohmic resistance in electrochemical systems incorporating

bubbles.

A review by Sides discusses the conductivity of the bulk solution in the presence

of bubbles [1]. The review discusses the conductivity in various regions of the system,

including the conductivity within the bubble layer. The review discusses also the

microscopic current distribution and the hyperpolarization of the electrode, when the

electrode reaction is not reversible and gas still does not supersaturate. A discussion of

the effect of gas bubbles on the concentration overpotential is also included in the Sides’

review.

A review by Mandin et. al. describes the parameters to consider in modeling the two-phase electrolysis process [12]. Additionally, qualitative discussion is presented for different geometries.

Wüthrich describes the coalescence of bubbles in the production of hydrogen on an electrode using the percolation theory [13]. Specifically, he considers bubble formation during micromachining using the electrochemical discharge technique (EDT).

Sequeira et. al. presented a review of the physics of electrolytic gas evolution

[14]. They pointed out some recent trends in the study of the evolution of bubbles at the electrode where interest is focus on generating nanobubbles, which behave differently than bubbles on the micron scale. Nanobubbles have a contact angle lower than expected from Young's law [14], therefore, they are more stable under conditions of rapid decompression. Wang et. al. presented a review of water electrolysis for hydrogen production where they state that it is possible to enhance the technology by applying an external field e. g. by using a magnetic field, an ultrasonic field, or by using a super gravity field to remove bubbles from the electrode [15].

A number of recent publications address the formation of nanobubbles on electrodes. Sample articles include publications by White et. al. [16, 17] and others, e.g.

[18, 19]. The focus of these publications has been on the study of nanoscale bubble nucleation on different substrates under different currents and potentials. These studies of nanobubbles do not address the translation of larger bubbles on the electrode due to flow and do not consider the bubbles effects on enhancing transport rates. Therefore, these publications bear little direct relevance to the current study.

Additional monographs, as well as review articles, describing gas formation

during electrolysis processes are available [20-23]; however, with the exception of Kadija

et. al. papers discussed below [24 – 26] none discusses bubbles formation on the common

configuration of a rotating disk electrode (RDE) facing downwards. Kadija et. al. had

studied the gas evolution on a rotating disk and ring electrode [24], and in a rotating two-

ring electrodes [25, 26]. at different pH values and in presence of ferricyanide ions. They

concluded that at higher limiting currents associated with higher hydrogen ion

concentrations and lower rotation rates the current measurements are compromised by the

bubble formation at the electrode. To minimize the impact of bubble formation, Kadija et.

al. suggested the use of ring-disk double ring electrodes. Kadija et. al. focused on investigating the rate of growth and detachment of bubbles that occurs at the ring.

However, Kadija et. al results [24-26] cannot be directly compared with the present study

because the substrate electrode, the electrolyte, and the electrode configuration were not

the same.

In conclusion, the nucleation, growth, coalescence, translation and detachment of

bubbles, and the mass transfer enhancement are steps in the evolution of gas at the

electrode that require further study.

The electrodeposition of single metals or alloys often requires a potential below

that of hydrogen evolution as shown in table 1.1. In such systems, parasitic reduction

reactions of hydrogen evolution also occur at the substrate. However, it is not possible to

observe the evolution of gas, until certain preconditions are met [21]; those are: 1) The

thermodynamics has to support a stable gas phase in the reduction of hydrogen subject to

the pressure and temperature in the system. 2) The electrode surface must provide

nucleation sites that can be activated to allow growth of bubbles. 3) The supersaturation

of the bulk solution with the dissolved gas must be sufficiently large to provide the stabilization of growth of very small bubbles present on the electrode. The bulk saturation depends on a number of factors, including the substrate material, since some materials are more catalytic than others to hydrogen reduction. This catalytic property can be associated with the exchange current density. Additionally, the current or potential must be of adequate magnitude, and applied for sufficient time to thermodynamically allow the reduction of hydrogen, as well as to grow and to accumulate bubbles. Furthermore, the wettability of a material can affect the bubble nucleation. As a result, the stabilization of tiny bubbles present on the electrode is affected by the polar forces in the medium. In addition, the dimensions of the electrochemical cell or geometry of the electrode is also important, because these affect the local overpotential and the local current density, as well as the convective conditions. Finally, the hydrogen gas evolution rate needs to be fast to provide the high gas concentration close to the interface. Indeed, the gas concentration close to the interface can reach values that are 80 times larger than the saturation concentration of the solution [21]. Additionally, it was found that the nucleation density decreases significantly with forced flow of the electrolyte [27, 28].

Table 1.1: Selected Standard Electrode Potentials for Metals Reduction in Aqueous

Solution at 25oC.

Reaction , V/SHE + 2 표 -0.277 2+ + 2 − 표 퐸 -0.9 퐶� 푒 ⇌ 퐶� 2+ + 2 − 표 -0.44 퐶퐶 푒 ⇌ 퐶퐶 2+ + 3 − 표 -0.549 퐹� 푒 ⇌ 퐹� 3+ + − 표 -0.2 퐺퐺 푒 ⇌ 퐺퐺 + + − 표 -0.14 퐺퐺 푒 ⇌ 퐺퐺 + + 3− 표 -0.3382 퐼� 푒 ⇌ 퐼� 3+ + 2 − 표 -1.18 퐼� 푒 ⇌ 퐼� 2+ + 2 − 표 -0.257 푀� 푒 ⇌ 푀� 2+ + 2 − 표 -0.1251 푁� 푒 ⇌ 푁� 2+ + 2 − 표 -0.1375 푃푃 푒 ⇌ 푃푃 2+ + 2 − 표 -0.7618 푆� 푒 ⇌ 푆� 2+ − 표 푍� 푒 ⇌ 푍�

Once the gas within the solution is supersaturated and the nucleation step

completed, the process of bubble growth takes place. The following step is the diffusion

of the dissolved gas to the surface of bubble growing on the electrode.

In the process of the bubble growth, the bubble size is controlled by a number of

factors, including the mass transfer coefficient, the electrolyte pH, and the applied current and/or potential. Thus the extent of supersaturation is strongly related to the operating conditions. In order to determinate the growth rate of the gas volume, it is necessary to know the mass transport flux from the electrolyte solution towards the bubble and the surface area.

The concept of surface area renewal is applicable when the bubbles on the electrode are sweep by the flow. This means that a hydrogen evolution occurs, and consequently new bubbles are generated until the electrolyte flow eventually displaces

8 the bubbles at the electrode surface. This surface area renewal is a cyclic process that is repeated at a given frequency.

Glas et al. found experimentally that the critical bubble radius remains in a pseudo equilibrium. [29]. They state that initially, surface tension force is significant in the process of bubble growth; therefore this initial process is slow. Once the bubble has a radius bigger than the critical radius, the bubble size grows asymptotically with time.

This transition process of bubble growth occurs very fast. Glas and collaborators explained that the reason for this fast process is associated with the metal substrate [29,

30], for instance, for nickel they measured with a high-speed camera a transition time of

0.6 milliseconds. However, in bubble evolution on platinum on copper, this transition time is not as fast as in the case of nickel. The difference in the transition times between metals might be associated with the different nucleation sizes of bubbles for these metals.

After polishing nickel, it exhibits a smoother surface than copper or platinum because it is a harder metal; therefore when the surface is smooth, bubbles have less resistance to pass the transition period of the initial process to reaches the critical size for the asymptotic growth. This implies that soft metals like copper or platinum which do not have a smooth surface as nickel after the polishing process have a longer transition period.

Epstein and Plesset obtained a solution of the asymptotic bubble growth rate by solving the diffusion equation assuming an initially uniformly supersaturated solution surrounding the growing bubble [31].

The analogy between the electrolysis of water and boiling heat transfer has been noted numerous times [2, 12, 21, 22, 32]. Relating both processes is helpful because the study of boiling has been ongoing for longer time and is better understood than gas evolution at electrodes. Some analogies between these physical processes are obvious, for instance, both involve first as a two-phase system of solid-liquid which is transformed into a three-phase system by the incorporation of bubbles in the gas phase. Similarly, in both processes the hydrodynamics of bubbles growth and departure from the solid substrate contributes to the mass or heat transfer. However, there are a number of considerations that are dissimilar in both systems. For example, the growth of gas bubbles on electrodes is controlled by mass transfer due to supersaturation that is serving as the driving force, while the growth of vapor bubbles in nucleate boiling is governed by both heat transfer and mass transfer, in which the gradient of temperature and gas concentration are providing the driving forces. Specifically, vapor bubbles are formed out of sufficiently superheated liquids at nucleation sites on heated surfaces to generate vapor. This means that initially a liquid microlayer at the base of the bubble is formed, until the departure size is reached. Heat transfer increases with superheating until a vapor film builds up, which cuts heat transfer down. At sufficiently high temperature, where radiation becomes dominant, the heat transport rate in boiling increases again.

The contact area of adhering bubbles is an insulated region, which does not contribute to current and to gas generation in the electrochemical system. In the boiling phenomena, heat conduction across the contact area of vapor bubbles varies; it is nonexistent at low and moderate temperatures because bubbles are acting like an insulator at the beginning of the heating process. However when the source of heat is at

10 high temperature radiation may become significant, increasing the transfer of heat through the bubbles. Nucleation, growth and detachment of bubbles from the substrate in the electrochemical system are not controlled by temperature; instead, mass transfer at the interface is governed in the electrolysis process.

Despite fact that the generation of hydrogen is a common electrochemical process, the mechanism of adsorption and reduction of hydrogen on the substrate is not fully understood. Additionally the problem becomes more complex when the nucleation and growth of bubbles takes place at rough electrodes or on complex geometries.

1.5.2. Reduction of Metal Ions (specifically, copper):

1.5.2.1. Theory:

The polarization curve (current density vs voltage) for copper deposition is shown schematically in figure 1.1. The reduction branch starts at 0.34V/SHE. The section close to 0.34V is controlled by ohmic and kinetics mechanisms.

At very negative potentials, the polarization line approaches a current plateau

(shown in red). This plateau corresponds to the mass transport limiting current density,

(mA/cm2), given by Levich’s equation [33]:

푖푙푙� [ ] = (1.4) 2+ 푏푏푏푏 −�푛푛 퐶퐶 푖푙푙� 훿푁

2 -

Mass transfer control

i, mA cm

- Kinetics and Ohmic control

ퟐ+ 풊푪푪 풍�풍 0.34V 풊 ퟐ 풊푯

0 V E, V/ SHE 퐻2 Figure 1.1: Reduction branch for copper (schematic).

Equation 1.4 applies in a well-supported solution. i.e., a solution that contains

excess supporting electrolyte. Here is the diffusivity (cm2/s); [ ] is the 2+ 푏𝑏푏 concentration of cupric ion in the bulk퐷 solution (mol/cm3), and 퐶퐶is the equivalent

푁 Nernst diffusion layer (cm). The latter depends on the convective훿 flow and on the

geometry of the system. Levich solved the convection-diffusion equation in cylindrical

coordinates ( , , ) for the RDE [29]. Equation 1.5 is the expression of limiting current

density on a RDE� 휙 푧under steady-state conditions.

= = 0.62 [ ] (1.5) 2⁄3 1⁄2 −1⁄6 2+ 푏𝑏푏 푙푙� 퐿𝐿𝐿ℎ 푖 푖 𝑛 퐷 휔 휐 퐶퐶

Here is the angular rotation rate (rad/s), and is the kinematic viscosity of

the electrolyte ( 휔 0.01 cm2/s). At steady-state, the equivalent휐 Nernst diffusion layer for a

RDE is found by≈ combining equation 1.4 and 1.5.

= 1.61 (1.6) 1⁄3 −1⁄2 1⁄6 푁 훿 퐷 휔 휐

The cupric ion flux, , at the electrode can be related to the current 2+ density by equation 1.7: 푁퐶퐶

[ ] = = (1.7) 휕퐶퐶�2+ 2+ � 2+ 퐶퐶 푧=0 퐶퐶 푁 �푛 − 퐷 � 휕� �푧=0

The reduction reaction of hydrogen is also shown schematically in Fig 1.1 as a green line, starting at the standard potential for hydrogen evolution, E = 0 V/SHE. At more negative potentials than 0 V/SHE, the formation of hydrogen gas as well as the copper reduction occurs simultaneously. When the applied potential is more negative than 0 V/SHE copper electrodeposition is typically under mass transfer control, while the hydrogen evolution is under kinetics control.

1.5.2.2. Experimental observations.

A schematic representation of the copper deposition for a rotating disk is shown in Fig. 1.2. It is observed that under very negative potentials (more negative than point ‘B’), the predicted trend of a limiting current plateau is not followed. Instead, the current density at potentials more negative than ‘B’ keeps increasing. Fig. 1.2. indicates two potentials designated as A, and B, corresponding to different regions of the polarization curve.

2 - Mass Transfer Control

mA cm i - Kinetic Control

풊푳푳푳�푳푳

E, V / SHE B 풊 A

Figure 1.2: Schematic representation of the reduction current density of cupric ions.

The kinetic control region is located at potential more positive than A. At potentials between A and B, figure 1.2 shows good agreement with the theoretical polarization curve plotted in figure 1.1 A well-defined plateau corresponding to the mass transfer control region is observed between the potentials A and B. However, at potentials more negative than B, a considerable increment in current is observed.

We hypothesize that the main cause of the discrepancy between the theoretical and experimental limiting current density at potentials in the region negative to B is due to the substantial evolution of bubbles at the cathode. We assume that the process of bubble formation on the cathode affects mass transport by decreasing the equivalent

Nernst diffusion layer. The equation 1.6 describes the equivalent Nernst diffusion layer on a rotating disk electrode.

1.6. Challenges:

1.6.1. Modeling Difficulties:

In general, gas bubbles develop first as nuclei, then grow in size, while

undergoing coalescence, displacement, and/or detachment from the electrode. As a result,

it is difficult to develop a comprehensive model that can consider all these phenomena,

particularly since all are not always present or noticeable under given experimental

conditions. Furthermore, sometimes the dynamic mechanism of the formation of a bubble

establishes unsteady-state conditions at the surface of the electrode. If we incorporate

metal ions, the system is even more complex because metal ions reduction is now

occurring simultaneously with hydrogen gas evolution at the cathode. Quantification of

the transport enhancement effects is challenging in the complex system.

1.6.2. Experimental Difficulties:

The transport rates in electrochemical systems are typically determined by

measuring the current. However measuring accurately the total current is difficult in

experiments with potentials more negative than -0.5 V/SHE. This problem is associated

with the fact that when hydrogen is co-evolving, there is partial surface coverage of the electrode by the gas bubbles which serve as insulators. Because of the periodic formation

and departure of the bubbles we observe noise in the current signal.

Furthermore, since only the total current can be measured, the separation of the total measured current to partial currents associated with hydrogen evolution and the reduction of copper becomes an issue.

Additionally, electrodeposition times are limited at large negative potentials, because electrodeposition at longer times generates rough deposits, causing difficulty in evaluation of the electroactive area, which is essential for determining the actual current density. By contrast, in electrodeposition for short times, the weight gain of the electrode is insufficient to provide an accurate measurement.

1.7. Organization and Outline of the Thesis:

The second chapter of the thesis discusses the experimental system and the experimental methodology.

The third chapter provides the results of enhanced transport measurements.

Measurements of the total current, the current associated with just the hydrogen evolution, and by subtraction, the net copper deposition currents are reported as a function of various system parameters including the applied voltage, the rotation rate and the cupric ion concentration. A procedure to account for the increased surface area of the electrode due to roughness associated with copper deposition under mass transport control is discussed and applied to the results. Direct measurements of weight gain of the copper deposit are also reported. Measurements of the deposition current following pulsed generation of hydrogen bubbles prove the linkage between gas evolution and the observed enhanced transport. Photographs (still and video) of the bubbles evolving and translating on the rotating disk electrode are also reported. Analysis of the photographs provides the mean bubble radius and the surface coverage of the electrode by the bubbles as a function of the operating conditions.

The fourth Chapter provides a discussion of the results. Analysis of the mass

transfer enhancement of copper electrodeposition was done by comparing the copper

deposition current density and the weight gain measurements. Additional analysis of the

mass transfer enhancement has been done by studying the transient response of the

current associated with pulse generation of bubbles. Finally, this chapter provides the analysis of bubble radius and the fraction of surface coverage, as a function of the potential and the rotation rate.

The fifth chapter provides a model for the enhanced transport due to the bubble

translation across the electrode. The model is based on the higher transport rates present

during the initial transient exposure of the polarized electrode to a fresh electrolyte. A

surface renewal model is applied to relate the short term transients of the current density

in streaks of translating bubble on the rotating disk electrode. Comparison of the

experimental data to the model predictions is provided.

The sixth chapter provides the conclusions of the study and suggestions for future work.

The seventh chapter provides a nomenclature.

Finally the appendices and bibliography are provided at the end of the thesis.

1.8. References:

[1] P. Sides, "Phenomena and Effects of Electrolytic Gas Evolution," Modern

Aspects of Electrochemistry, ed: R. White, J. O. M. Bockris, B. E. Conway, vol. 18, pp.

303-354, (1986).

[2] H. Vogt, "Gas-Evolving Electrodes," Comprehensive Treatise of

Electrochemistry, ed: E. Yeager, J. O. M. Bockris, B. Conway, S. Sarangapani, vol. 6, pp. 445-489, (1983).

[3] F. Seitz, "Henry Cavendish: the catalyst for the chemical revolution," Notes and

Records of the Royal Society, vol. 59, pp. 175-199, May 22, (2005).

[4] F. C. Walsh, "A first course in electrochemical engineering". Romsey:

Electrochemical Consultancy, pp. 257-338, (1993).

[5] F. Coeuret and J. Costa López, "Introducción a la ingeniería electroquímica".

Barcelona: Reverté, pp. 95-227, (1992).

[6] V. N. Ibl and J. Venczel, "Untersuchung des Stofftransports an gasentwickeln-den

Elektroden," Metalloberfläche, vol. 24, pp. 365-374, (1970).

[7] N. Ibl, "Probleme des Stofftransportes in der angewandten Elektrochemie,"

Chemie Ingenieur Technik, vol. 35, pp. 353-361, (1963).

[8] R. Higbie, "The rate of absorption of pure gas into a still liquid during short periods of exposure," Transactions of the American Institute of Chemical Engineers, vol.

31, p. 365, (1935).

[9] E. Adam, J. Venczel, and E. Schalch, "Stofftransport bei der Elektrolyse mit

Gasrührung," Chemie Ingenieur Technik, vol. 43, pp. 202-215, (1971).

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Chapter 2: Experimental Methodology.

This chapter describes the experimental set-up and the experimental procedures

applied in this research.

2.1. The Experimental Set-up:

An electrochemical cell, consisting of an open beaker, 7 cm in diameter, and 5 cm high with three electrodes, as shown in figure 2.1 was used in the copper deposition experiments. The working electrode was a copper RDE (0.317 cm2), the counter

electrode was a platinum mesh (6 cm by 2 cm) placed on one side of the RDE insulated

shaft and parallel to it, about 2.5 cm away. The reference electrode was a saturated

calomel electrode (SCE) [laced on the opposite side (from the counter electrode) of the

RDE shaft, about 2.3 cm away. Power was provided by a VSP Bio-logic potentiostat.

Figure 2.1: Sketch of the electrochemical cell. The working electrode is copper RDE, the

counter electrode is a platinum mesh and the reference electrode is a saturated calomel

electrode (SCE).

The camera used in photographing the bubbles was a Canon EOS Rebel T1i

(500D) Digital SLR with 18-55mm f/3.5-5.6 IS lens. The camera was positioned at the bottom of the glass electrochemical cell, and provided images of the bubble covered electrode. A balance (Startorius, model BP210D) provided the weight of the working electrode before and after electrodeposition. The resolution of the balance is 0.01 mg

with a maximum capability to weigh 210 g.

2.2. Chemistry:

Three solutions were used in this study:

1. 200 mM CuSO4 * 5H2O (Fisher Scientific, Certified ACS), at pH ≈ 0 as

adjusted by H2SO4 (Fisher Scientific, Certified ACS), (‘high cupric ions

concentration’ solution).

2. 20 mM CuSO4 * 5H2O (Fisher Scientific, Certified ACS), at pH ≈ 0 adjusted

by H2SO4 (Fisher, Certified ACS), (‘low cupric ions concentration’ solution).

3. 1M H2SO4 (Fisher Scientific, Certified ACS), without cupric ions.

2.3. Experimental Procedures:

The copper deposition rate was measured using three separate techniques:

a. Determining the copper deposition current by subtracting the hydrogen

evolution current from the total current recorded during copper deposition

experiments.

b. Determining the weight of the deposited copper during a measured time.

c. Measuring the current during the transient current decay (at a lower

potential) following a short pulse of bubble generation (and copper

deposition) at a very negative cathodic potential.

2.3.1. Deposition of Copper in the Presence of Hydrogen Co-Evolution:

Copper electrodeposition at different constant voltages, and disk rotations rates

for two cupric concentrations was studied.

The angular rotations applied were 100, 400 and 900 rpm. The constant potential applied was in the range: -1 < E< 0 V/SHE.

Table 2.1 list the different electrodeposition times for the experiments performed with high and low cupric ions concentrations. The times selected in the copper electrodeposition on table 2.1 are appropriate to quantify the weight gained by the electrode while not losing significant amount of the deposit due to powder formation.

The current recorded by the potentiostat has been used to generate the polarization

curves described in section 2.3.2. In the electrodeposition process under mass transport

control as studied here, the measured current is increasing in magnitude with time, as the

deposit becomes rougher. A methodology for determining the roughness area is described

in the section 2.3.3.

Table 2. 1: Electrodeposition times (in seconds) selected for the experiments.

200 mM CuSO4. 20 mM CuSO4. E, V/SHE ω, 100 ω, 400 ω, 900 ω, 100 ω, 400 ω, 900 rpm rpm rpm rpm rpm rpm 0.2412 6300 4080 4080 7200 6300 5400 0.1412 2700 960 960 3600 2400 2100 0 480 240 240 1500 1500 1200 -0.2 360 130 80 1020 900 270 -0.4 90 18 18 840 540 210 -0.5 120 30 17 840 600 270 -0.65 120 25 14 600 540 200 -0.8 60 25 14 540 480 160 -0.9 60 25 14 480 420 150 -1 60 25 14 420 360 140

2.3.2. Polarization Data for Hydrogen Evolution from Acid (w/o Copper):

Polarization curve for hydrogen evolution has been obtained from a solution absent of cupric ions, under the same potentials and rotation rates described in section 2.3.1.

By obtaining the total, hydrogen and copper currents, following the evaluation of the rough deposits area , as discussed in section 2.3.4., it is possible to determine

𝑟𝑟ℎ the net copper current.퐴 This is accomplished by subtracting the hydrogen current

(determined separately in the polarization study from pure acid on a similar copper substrate, and similar applied potential and rotation rates) from the total current measured in the copper deposition experiment.

2.3.3. Weight Measurements of Copper:

To obtain the copper current , and copper current density, , the electrode was

퐶퐶 퐶퐶 weighed (after drying it in air퐼 for 24 hours) before and after deposit푖 ion. The weight change can be related to the current density using Faraday’s law, accounting also for the deposit roughness:

= = (2.1) 퐼퐶� ∆푊∙�∙� 푖퐶퐶 퐴푟푟𝑟ℎ 푀푐�∙푡∙퐴푟푟𝑟ℎ is the weight difference of the electrode before and after electrodeposition. and are∆푊 the number of electrons that participate in the electrode reaction, and Faraday’s� constant퐹 96485 , respectively. is the molecular weight of copper 63.546 ; and 퐶 푔 푚𝑚 퐶퐶 푚𝑚 is the time of electrodeposition.푀 The rough area is evaluated according to the

𝑟𝑟ℎ methodology푡 described in section 2.3.4. 퐴

When the experiment is run at very negative potentials, noise in the current due to bubble evolution is occurring. Therefore, it is important to repeat the experiment numerous times in order to obtain a more reliable estimate of the accurate value.

2.3.4. Correction for Surface Roughness:

Rough deposit is typically generated when the deposition is carried under mass transport control such as encountered at very negative potentials.

Since the area of the electrode is increasing with time due to the rough deposit, a technique for determining the area of the rough electrode is needed.

Figure 2.4. describes schematically a polarization curve with highlighted region of the most negative potential applied in the electrodeposition of copper -1 < E < -0.4

V/SHE during the experiments. In this region the deposition of copper changes the area of the electrode.

350

300

250 Region of area correction

200 2 -

150 mA cm

100 , i - 50

0 -1.1 -0.9 -0.7 -0.5 -0.3 -0.1 0.1 0.3

E, V/ SHE

Figure 2.2: Schematic polarization curve on a RDE.

The methodology applied for determining the rough area is as follows:

I. A polished and flat disk electrode with a geometric area of 0.317 cm2 was

immersed in the solution for an electrodeposition process. This

electrodeposition was done for to the times listed in table 2.1.

II. Once the electrodeposition was completed, leaving the electrode in the

solution, the potential was shifted to a less cathodic value of +0.1 V/SHE.

Under these conditions, no hydrogen evolves.

III. When step II reaches steady-state, the current, , is read. Subsequently

푅𝑅�ℎ the electrode is air dried and weighed. It is assumed퐼 that during this relatively

short experiment, the additional amount of deposited copper is negligible.

IV. A second clean and flat electrode with a geometric area of 0.317 cm2 was

immersed in the bath for a polarization experiment. The applied constant

voltage was +0.1 V/SHE. (Identical to steps II and III)The current is

푆𝑆𝑆ℎ read once steady-state is reached. 퐼

The steps described above are illustrated in figure 2.5.

(E< -0.3) V / NHE +0.1 V / NHE

Electrode 1

Cu deposition

퐼푅𝑅�ℎ

Electrode 2

퐼푆𝑆𝑆ℎ Figure 2.3: Schematic of the methodology used to obtain the electrode area correction.

Recognizing that the current density at the tested applied potential (0.1 V) must be the same, irrespective of the electrode area, we have: = , and the rough 퐼푅𝑅�ℎ 퐼푆푆𝑆푆ℎ 퐴푅𝑅�ℎ 퐴푆푆𝑆푆ℎ area is given by:

= ( ) (2.2) 퐼푅𝑅�ℎ 퐴푅𝑅�ℎ 퐴푆𝑆𝑆ℎ 퐼푆푆𝑆푆ℎ

All currents can be normalized by dividing them by these rough areas to determinate the current densities.

2.3.5. Photography (still and video) of Bubbles:

The camera was located at the bottom of the glass electrochemical cell and provided videos and still pictures of the disk electrode as viewed from the bottom. The video was recorded at 60 frames per second with frame resolutions of 1280x720 pixels.

The still photographs were taken at 3456x3456 pixels, with an exposure time of 0.25 milliseconds.

2.3.6. Determination of Bubble Radii and Surface Coverage:

From the images of the disk covered by bubbles, measurements of the radii of all bubbles was obtained using the ImageJ software [1]. Likewise, the total blocked area of the electrode by the bubbles was determined. Consequently, the fraction of the surface area coverage by bubbles, , was obtained using the following ratio:

휃

= = � 2 �. 2 (2.3) ∑푗=1 휋푅푏푗 ∑푗=1 휋푅푏푗 2 휃 퐴푑푑푑� 0 317푐푚 Here, , is the radius of the bubble measured from the picture of the disk. In eqn. 2.3

푏푗 it has been푅 assumed that the bubbles are풋 round.

Since the size of bubbles varies on the electrode, averages and standard deviations were

determined for the bubble radii.

2.3.7. Pulse Experiments to Relate Bubble Generation to Enhancement:

To prove that the transport enhancement is associated with bubble generation,

pulse experiments were carried out, where the electrode potential was held for a brief

time at a cathodic potential where bubbles are generated and then the potential was

stepped rapidly to a less cathodic range where no hydrogen evolves but copper plating under transport control still goes on. The enhancement of the deposition rate due to the bubbles transport across the electrode was observed and measured, and the decay of the

enhancement once the bubbles evacuate the electrode was noted.

The pulse experiments follow a double pulse signal, as shown in figure 1.6.

Initially, the applied potential is sufficiently negative to generate bubbles in the

1 interval 1 0.65 / 퐸 . This potential was held for few seconds as listed in

table 2.2−. Next≤ ,퐸 the≤ potential− 푉 was푆𝑆 stepped to -0.2 V/SHE. At this potential bubbles are no

longer formed, but the potential is sufficiently negative to provide copper deposition

under mass transfer conditions. During this final step, the current transient decays rapidly

to a steady-state value which is consistent with the value indicated by the Levich

equation.

Negative direction

퐸

E, V / SHE V E,

2 = 0.2

퐸 − 푉

1 = 0 2 = 8 t, seconds 3 40 푡 � 푡 � 푡 ≈ � Figure 2.4: Input voltage sketch (not to scale) of the double pulse experiment, relating bubble generation to mass transfer enhancement.

Table 2.2: Parameters of the double pulse experiments relating bubble generation to mass transfer enhancement.

[CuSO4·5H2O], ω, H2(g) generation time, M rpm s 0.02 50 8 0.02 70 8 0.02 100 8 0.02 100 1 0.02 100 2 0.02 400 8 0.02 900 8 0.2 100 8 0.2 400 8 0.2 900 8

2.4. References:

[1] W. Rasband, "ImageJ," 1.49n, National Institute of Health, USA, (2014).

Chapter 3: Experimental Results.

3.1. Area Correction Accounting for Roughness.

Electrodeposition under mass transport control typically leads to rough deposit

texture. In order to determinate the current density we need to divide the total current by

the actual surface area. The corrected electrode areas, accounting for the surface

roughness resulting from the copper deposition at or above the limiting current has been

determined following the methodology described in chapter 2, specifically applying

equation 2.2.

Tables 3.1 and 3.2 list the experimental values obtained from the area correction for all rotation rates tested for 20 and 200 mM CuSO4 at pH ≈ 0. In the tests for

correcting the surface area, the current was always read at a potential of +0.1 V/SHE. At

this potential copper is expected to plate at its limiting current, but no significant amount

of hydrogen evolves.

It is not relevant to compare the values of the rough areas in both tables for a

given rotation rate and potential because the time of electrodeposition is not the same in

the different experiments. The deposition times have been adjusted to provide sufficient

amount of copper for weighing, while not generating excessive rough deposit which may

fall-off the electrode and which also will lead to a large distortion of the current due to

the much larger area. The listed rough areas were those at which the subsequently

analyzed data were collected.

Table 3.1: Experimental data providing the rough electrode area for the deposition experiments in 20 mM CuSO4 at pH ≈ 0. The deposition times to generate the rough areas are listed in table 2.1. Smooth disk area is 0.317 cm2.

100 rpm 400 rpm 900 rpm

I I I Roughness Rough I Rough I Rough I (measured Smooth (measured Smooth (measured Smooth generated (tested at (tested at (tested at at 0.1 V vs A at 0.1 V vs A at 0.1 V vs A at potential +0.1 V) rough +0.1 V) rough +0.1 V) rough SHE) SHE) SHE) (� 0.2 mA) (� 0.2 mA) (� 0.2 mA) (� 0.4 mA) (� 0.4 mA) (� 0.4 mA)

E, V/SHE mA mA cm2 mA mA cm2 mA mA cm2 -0.2 2.07 1.8 0.364 6.8 3.3 0.653 4.7 4.5 0.331 -0.4 1.9 1.675 0.36 6.05 3.1 0.616 10.75 4.5 0.757 -0.5 3.55 1.55 0.724 5.425 2.9 0.59 10.44 4.3 0.769 -0.65 1.958 1.6 0.387 4.675 2.9 0.51 7.018 4.3 0.517 -0.8 1.945 1.6 0.385 4.175 2.9 0.456 6.895 4.3 0.508 -0.9 2.075 1.6 0.411 3.963 2.9 0.433 5.503 4.3 0.405 -1 2.175 1.6 0.431 3.42 2.9 0.372 5.1 4.3 0.376

Table 3.2: Experimental data providing the rough electrode area for the deposition experiments in 200 mM CuSO4 at pH ≈ 0. The deposition times to generate the rough areas are listed in table 2.1. Smooth disk area is 0.317 cm2.

100 rpm 400 rpm 900 rpm

E, V/SHE mA mA cm2 mA mA cm2 mA mA cm2 -0.2 ------0.317 18.895 11.989 0.499 ------0.317 -0.4 17.148 9.009 0.603 20.642 12.577 0.52 24.85 15.013 0.524 -0.5 16.49 9.765 0.535 33.985 13.542 0.795 28.98 14.287 0.642 -0.65 18.883 10.148 0.589 29.291 13.75 0.675 28.922 12.676 0.723 -0.8 16.565 9.109 0.576 27.795 14.556 0.605 26.497 13.674 0.614 -0.9 18.677 11.01 0.537 22.558 13.883 0.515 24.13 12.201 0.626 -1 16.412 10.52 0.494 21.123 14.09 0.475 23.53 12.151 0.613

3.2. Copper Current Density Determined from Weight Measurements of the

Deposited Copper:

Following the methodology described in chapter 2, the copper transport rates (and copper densities) were determined from the weight of the electroplated copper. Using the copper weight measurement, and applying Faraday’s law, in conjunction with the corrected rough area reported in tables 3.1 and 3.2, the weight-based copper current

density was determined. This current density is displayed in figures 3.1 and 3.2 for 20

mM, and 200 mM CuSO4 at pH ≈ 0, respectively. The voltage reported in both figures is

IR corrected per the procedure described in section 3.3.

The trends observed in figures 3.1 and 3.2 support similar conclusions. At the most

positive potentials the polarization curves are controlled by kinetics; here, the current

increases as a function of potential and is insensitive to the rotation rate. At potentials in

the interval 0 > E > -0.4 V/SHE a plateau region is observed. In this region, mass transfer

controls the process. As a result, the current does not change as a function of potential,

but changes with the rotation rate. The current densities corresponding to the Levich

equation as reported in table 3.3 match the experimental values of the plateau region

located in the interval 0 > E > -0.4 V/SHE of figures 3.1 and 3.2; likewise, the copper

current density values obtained by weight are roughly the same as the total current

density indicated by the polarization curve in figure 3.3 and 3.4 in the plateau region on

section 3.2. This means that the amount of hydrogen gas is negligible with respect to the

amount of copper electrodeposited in the potential interval 0 > E > -0.4 V/SHE.

2 400-rpm - 40

900-rpm 30 100-rpm , mA cm Cu

i 20 -

0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Voltage (IR compensated), V / SHE

Figure 3.1: Current densities in copper reduction from 20 mM CuSO4 at pH ≈ 0 obtained

from the weight of the electrodeposited copper, using Faraday’s law. Blue diamonds

represent the copper current density at 100 rpm. Red squares correspond to the copper

current density at 400 rpm. Green triangles indicate the copper current density at 900

rpm. The current density was determined by dividing the current calculated from

Faraday’s law by the rough area of the electrode as reported in table 3.1. The applied

voltages indicated were corrected for the IR drop.

At potentials more negative than the plateau region, the measurements of the

copper weight incorporate fluctuations because the morphology of the deposit changes as

a function of potential. Specifically, at the most negative potentials the copper texture is

rough and powdery; the powder morphology is more pronounced when the rotation rate of the electrode increases. At potentials around -0.5 > E > -0.6 V/SHE, and for lower

rotation rates, the morphology of the electrodeposited copper shows large gaps or craters

36 between agglomerate grains. This roughness in the electrodeposit affects the weight measurements because the copper adhesion is compromised. However, after the correction for the rough area, the copper current density observed is increasing with the most negative potentials. This increase in the copper current density occurs simultaneously with the increase of hydrogen current density observed at potentials more negative than -0.5V in figure 3.5 in section 3.3. Therefore the increase in the mass transfer electrodeposition appears to be associated with the production of hydrogen gas.

This implies that there may be a decrease in the diffusion layer of copper associated with the hydrogen gas productions. However, to confirm that the hydrogen gas production leads to an enhancement in forced convection, additional experiments utilizing photography were conducted in order to associate the enhancement of mass transfer to the presence of translating bubbles on the surface.

450

400

350 400-rpm 100-rpm

300 2 - 900-rpm 250

200 , mA cm Cu

i 150 - 100

0 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Voltage (IR compensated), V / SHE

Figure 3.2: Current densities in copper reduction from 200 mM CuSO4 at pH ≈ 0

obtained from the weight of the electrodeposited copper, using Faraday’s law. Blue

diamonds represent the copper current density at 100 rpm. Red squares correspond to the

copper current density at 400 rpm. Green triangles indicate the copper current density at

900 rpm. The current density was determined by dividing the current calculated from

Faraday’s law by the rough area of the electrode as reported in table 3.2. The applied

voltages indicated were corrected for the IR drop.

3.3. Polarization Data for Copper Deposition above the Limiting Current.

Current interrupt technique has been applied in conjunction with an oscilloscope

(BK PRECISION, 20 MHz oscilloscope model 2120) to determine the IR contribution.

From those measurements, the resistance of the system has been measured as

approximately 1 ohm for the three electrolyte composition used. It should be noted that

separate conductivity measurements of the electrolyte were conducted and when

combined with Newman’s formula [1] for the rotating disk, indicated a resistance of 2

ohms. However, the non-standard system configuration used in the present study, where the counter electrode was small and placed on one side of the RDE shaft while the reference electrode was on the other side, outside the main current path may explain this discrepancy. Since a number of current interrupt tests were carried out and provided the same direct reading of the cell resistance as 1 Ω (+/- 0.04 Ω), this resistance value has been applied to the reported data. Table 3.3 lists the resistance values of the solution used in our system:

Table 3.3: Resistance values of the electrolyte solutions on a RDE.

Electrolyte solutions: R, Ω (+/- 0.04 Ω)

1M H2SO4 1.04

1M H2SO4 + 20mM CuSO4 0.96

1M H2SO4 + 200mM CuSO4 0.93

The ohmic correction provides the voltage difference between the cathode and the

electrostatic potential in the solution just outside the diffusion layer, Φ. As given by:

= + | | + | | (3.1) 표 푎 푐 And 푉 − Φ 퐸 휂 휂

= (3.2)

푅�푅 Ω Here, V is the working electrode푉 − 푉 potential− 퐼푅 , 푉 − ,Φ is the voltage of the reference

푅�푅 electrode, both measured with respect to the standard푉 hydrogen electrode. is the

electrostatic potential in solution at the outer edge of the boundary layer, Φwhich is

determined by the ohmic drop (IR) in solution between the working and reference

electrodes as denoted by equation 3.2. Eo is the standard electrode potential of the

electrode reaction. | | and | |, are the activation and concentration overpotentials,

a c respectively. η η

Figures 3.3 and 3.4 provide the total current density at different rotation rates for 20 and 200 mM CuSO4 (pH ≈ 0), respectively. The current densities were determined from

the total current reading of the potentiostat divided by the rough electrode area as

determined by the procedure described in chapter 2, applying the areas listed in Tables

3.1 and 3.2. It should be emphasized, however, that the total current densities reported

include both the current due to copper deposition and that associated with hydrogen co-

evolution. The current due to hydrogen evolution is absent at potential more positive than

zero, and as shown later, is negligibly small at potentials more positive than -0.4 V, but is

significant and dominant at potentials more negative than -0.4 V.

600

500 100-rpm

- 2

400 900-rpm 300 , mA cm , mA

(tot) 200 400-rpm - i (A) 100

0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Voltage (IR compensated), V / SHE

Figure 3.3: Polarization curve for 20 mM CuSO4 at pH ≈ 0. Blue diamonds indicate the total current density at 100 rpm. Red squares correspond to the total current density at

700

600

2 - 500 900-rpm 400 400-rpm 100-rpm 300 i (tot), mA cm - 200

100

0 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Voltage (IR compensated), V / SHE

Figure 3.4: Polarization curve in 200 mM CuSO4 at pH ≈ 0. Blue diamonds designate the

total current density at 100 rpm. Red squares correspond to the total current density at

400rpm. Green triangles indicate the total current density at 900 rpm. The surface area

applied in determining the current density is the actual rough deposited as reported in

table 3.2. The displayed voltage has been compensated for the IR drop.

The behavior of the total current density in figures 3.3 and 3.4 is similar.

At positive potentials a kinetics controlled region is observed. Here, the current increases as a function of potential and the rotation rates affect the current only in a secondary manner. At potentials in the interval 0 > E > -0.4 V/SHE a plateau region is observed. In this region mass transfer controls the process; as a result the current does not change as a function of potential, but changes with the rotation rate. The Levich equation [1] for the limiting current on a RDE (equation 1.5) applies to the RDE in this region of 0 > E > -0.4

V/SHE. The calculated limiting currents densities for different rotation rates and for the

two cupric ion concentrations utilized in this study are shown in table 3.4:

Table 3.4: Calculated limiting current density for 20 and 200 mM CuSO4 at pH ≈0, and

different rotation rates according to the Levich equation. The disk area is 0.317 cm2.

-2 i(Levich), mA*cm ω, rpm 20 mM Cu(II) 200 mM Cu(II) 100 4.879 48.79 400 9.757 97.57 900 14.636 146.36

The values of the plateau regions in the polarization curves of figures 3.3 and figure

3.4 match the calculated limiting currents indicated by the Levich equation. This

agreement suggests that in this potential range, the effects of the hydrogen co-evolution are negligible. This could be due to the hydrogen current densities being negligible within this potential region for all applied rotations rates. At potentials more negative than -.4V,

the observed current densities increases above the values indicated by the mass transport

limit as calculated by the Levich equation. In this range the total current density, for a

given cupric ion concentration, reaches almost the same magnitude regardless of rotation.

However, as stated above, the current shown in Figs. 3.3 and 3.4 are the total currents and

include contribution from hydrogen co-evolution which is substantial at the very negative

potentials.

3.4. Hydrogen Evolution under High Cathodic Polarization.

In order to measure the current density enhancement in the deposition of copper, we must distinguish in the total current measured, the contribution due to hydrogen and subtract it from the total current to obtain the net current associated with the copper deposition. To do this, the current due to hydrogen evolution alone was measured (on a smooth flat copper electrode) from an electrolyte that contained only sulfuric acid but not copper.

The polarization curve of hydrogen, shown in Fig. 3.5 provides the hydrogen current, as a function of the overpotential applying the IR correction due to the ohmic drop in the cell.

The current read from the experiment at potentials more negative than -0.5V/SHE increases significantly and exhibits noise, due to bubbles which act as transient insulating islands modifying the active electrode area. It can be presumed that the hydrogen current as reported in figure 3.5 is sensitive to the rotation rate because bubbles average size, surface coverage, and translation velocity on the electrode change with the rotation rate.

A more detailed discussion of the influence of these parameters is provided in chapter 5.

225 200 900-rpm 175

150 400-rpm 125 , mA ) 2 100 100-rpm (H

I 75 - 50 25 0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2

ηs, V / SHE

Figure 3.5: Polarization curves in 1M H2SO4. Blue diamonds: hydrogen current at 100

rpm. Red squares: hydrogen current at 400 rpm. Green triangles: hydrogen current at 900

rpm. Data obtained by measuring the current during hydrogen evolution from sulfuric

acid on a copper RDE applying IR compensation.

3.5. Copper Deposition Rates Determined from Current Measurements.

The net current density associated with the copper deposition can be determined

by subtracting from the total measured current the current due to hydrogen evolution. The

latter has been determined from the current observed when hydrogen evolves from aqueous sulfuric acid, as described in the previous section. In subtracting the current, attention must be given to the facts that (1) the experiments were run under different surface areas due to the roughness evolving during copper deposition at and above the limiting current and (2) the applied potential was different in the copper deposition and in

45 the hydrogen evolution experiments since the IR correction and the standard potentials varied between the two sets of experiments.

The following procedure has been applied:

The hydrogen current as measured on the smooth electrode has been multiplied by the roughness factor given by the ratio of Arough/Asmooth (to account for the increased area due to roughness) and plotted and tabulated vs. the applied potential corrected for the IR drop for the hydrogen evolution tests. This hydrogen current is plotted in Figs. 3.6, 3.7 and 3.8 for the 200 mM cupric electrolyte together with total current, both currents represented in terms of the common applied voltage V-IR. The plotted hydrogen current was then subtracted from the total current to yield the copper current on the rough electrode, as also shown in figures 3.6, 3.7 and 3.8 for 100, 400 and 900 rpm; respectively.

It should be pointed out that the procedure for determining the copper current from the current data involves the subtraction of two large numbers (total current and hydrogen current) with substantial noise, to obtain a small number (copper current). This procedure is inherently inaccurate. And indeed, the resulting copper current as displayed in Figs. 3.6 – 3.8 exhibits significant fluctuations.

300 100 RPM

250

200 I(H2)

150 I(Cu) I(tot)

I, mA 100 -

0 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3

Voltage (IR compensated), V / SHE

Figure 3.6: Polarization curve of 200 mM CuSO4 at pH ≈ 0 at 100 rpm. Blue diamonds correspond to the total current. Red triangles indicate the hydrogen current. The green squares depict the copper current obtained by the subtraction of the hydrogen current from the total current.

300 400 RPM 250 I(Cu)

200 I(H2)

150

I, mA 100 - I(tot) 50

0 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Voltage (IR compensated), V / SHE

Figure 3.7: Polarization curve of 200 mM CuSO4 at pH ≈ 0 at 400 rpm. Blue diamonds correspond to the total current. Red triangles indicate the hydrogen current. The green squares depict the copper current obtained by the subtraction of the hydrogen current from the total current.

400

350 900 RPM 300 I(Cu) 250

200

150

I, mA I(H2) - I(tot) 100

0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Voltage (IR compensated), V / SHE

Figure 3.8: Polarization curve of 200 mM CuSO4 at pH ≈ 0 at 900 rpm. Blue diamonds correspond to the total current. Red triangles indicate the hydrogen current. The green squares depict the copper current obtained by the subtraction of the hydrogen current from the total current.

The net copper currents in Figs. 3.6 - 3.8 for the 200 mM copper electrolyte has been converted to copper current densities by dividing the currents by the appropriate rough deposit areas reported in table 3.2. These current densities are plotted as function of the applied voltage (corrected for the IR drop) in figure 3.9.

450 400 350

400-rpm 900-rpm 2 - 300 100-rpm 250

, mA cm 200 Cu

i 150 - 100 50 0 -0.75 -0.70 -0.65 -0.60 -0.55 -0.50 -0.45 -0.40 -0.35 -0.30

Voltage (IR compensated),V / SHE

Figure 3.9: Current densities, determined from polarization data on RDE for copper

deposition from 200 mM CuSO4 at pH ≈ 0 as a function of the overpotential at various rotation rates. Blue diamonds correspond to the copper current density at 100 rpm. Red squares indicate the copper current density at 400 rpm. Green triangles are the copper current density at 900 rpm. All copper current density were obtained by the subtraction of the hydrogen current density from the total current density. Hydrogen and total current densities were recorded by the potentiostat and divided by the rough area reported in table 3.2.

The values of copper current density as shown on figures 3.9 are close to the current density calculated according to the Levich equation at -0.4V for all rotation rates.

The copper current densities for all rotations increase with negative potentials indicating enhancement of mass transfer rates. However, the current density data at the very

negative potentials is noisy due to the hydrogen evolution that increases substantially at those potentials.

The procedure applied above to the 200 mM copper electrolyte and displayed in the copper current and current density data in Figs. 3.6 -3.9 was also applied to the 20 mM copper electrolyte. However, for this dilute copper electrolyte, the copper currents were smaller by a factor of about 10 fold, and hence constituted only about 6% of the total current signal. Consequently, the subtraction of the two large and noisy signals (the total current and the hydrogen current) to yield a very small copper current was highly inaccurate and is not included in the main body of this Thesis. This data is provided, however, in Appendix A. As expected, the very small copper current obtained by subtracting the hydrogen current from the total current for the 20 mM electrolyte as shown in Appendix A, is erratic and does not correlate with the data obtained by weight or pulse measurements. It is not considered any further in the Thesis.

3.6. Comparison of the Copper Current Densities as Determined from the Current

Measurements to those Determined from the Deposit Weight.

Figures 3.10, 3.11 and 3.12 provide the copper current densities based on weight measurements and those obtained from polarization data (by subtraction of the hydrogen current density from the total current density) in 200 mM CuSO4 at pH ≈ 0 at 100, 400 and 900 rpm, respectively. The measured applied voltage has been corrected for the ohmic losses by subtracting the IR drop. Copper current densities were derived by dividing the measured currents by the rough electrode areas reported in table 3.2.

450

400 100 RPM

350

2 300

- i(Cu)-Polarization curve

250

200

, mA cm i(Cu)-Weight Cu

i 150 - 100

0 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Voltage (IR compensated), V / SHE

≈

400

350 400 RPM 300

2 - 250 i(Cu)-Polarization curve

200 i(Cu)-Weight , mA cm 150 Cu i - 100

0 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Voltage (IR compensated), V / SHE

Figure 3.11: Comparison of current densities in the electrodeposition of copper based on weight measurements (blue diamonds), and polarization data (red squares). The disk electrode was rotated at 400 rpm. Experiments were conducted in 200 mM CuSO4 at pH

≈ 0.

450 900 RPM i(Cu)-Polarization curve 350

2 - 250 i(Cu)-Weight

, mA cm 150 Cu i -

-50 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Voltage (IR compensated), V / SHE

Figure 3.12: Compensation of current densities in the electrodeposition of copper based

on weight measurements (blue diamonds), and polarization data (red squares). The disk

electrode was rotated at 900 rpm. Experiments were conducted in 200 mM CuSO4 at pH

≈ 0.

Figures 3.10, 3.11 and 3.12 show a good agreement between the copper current densities based on weight measurements and those based on polarization over the

potential interval tested. This indicates that the experimental procedure is not

compromised due to errors when the system is at the higher cupric ion concentration (0.2

M). As stated earlier, it is not feasible to perform this comparison for the lower, 20 mM solution due to the inability to accurately extract the low copper deposition current from the noisy data.

3.7. Pulse Generation of Bubbles – Linking Bubbles Presence to Transport

Enhancement.

In order to establish a direct link between bubble presence on the electrode and the transport enhancement, experiments were conducted at which bubbles were generated

on the electrode for only a short time and the transport rates were measured from the

transient current following the pulsed bubble generation. The pulse experiments were

conducted according to the methodology described in chapter 2. The setup conditions of

the pulse experiments have been listed in table 2.3. The following graph (Fig. 3.13)

depicts a typical pulse experiments data. Numerous additional similar experiments of

pulse generation of bubbles under different rotation speeds and electrolyte composition

are provided in Appendix B.

t, seconds 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

-45

-95 -0.65V

-145

I, mA -0.8V -0.9V -195

-245 -1.0V -295

Figure 3.13 shows current trace in pulse experiments conducted in 20 mM CuSO4 at pH ≈ 0, and a rotation rate of 50 rpm. The electrode was first held for 8 seconds at very negative potentials in the range of -0.65 V to -1 V, where the current was mainly due to hydrogen evolution (with some copper plating). After 8 seconds, the generation of bubbles was interrupted by switching the potential to -0.2 V where just copper plating

continued under mass transfer control. In the first 8 seconds the current reaches a steady-

state; however fluctuations in the current traces are noticed due the formation of bubbles.

Once the formation of bubbles was interrupted by stepping the potential to -0.2 V, the

remaining bubbles on the electrode surface were swept in a radial direction. It is

hypothesized that this motion of the bubbles leads to enhanced transport rates in copper

deposition, which then decays to the steady state value within a few seconds once the

bubble are removed from the surface. This final current matches the limiting current

calculated by the Levich equation.

Table 3.5 lists details of the pulse experiment shown in figure 3.13. IBubble Generation

is the current associated with the generation of bubbles measured when steady state is

reached; ICu-Max, is the maximum current associated with copper deposition as observed immediately after the generation of bubbles had been discontinued (at 8 sec.); ICu-SS, is

the copper deposition current at steady state. Table 3.5 indicates that the ratio of currents

or the enhancement increases with the negative potential. The current trace indicates that

steady-state, where presumably, all bubbles have left the electrode is reached within 0.9 -

1.8 sec.

Table 3.5: Parameters obtained from the pulse experiment of figure 3.13; 20 mM CuSO4

at pH ≈ 0 at 50 rpm. Time of bubble generation was 8 seconds at the listed potentials.

Current predicted by the Levich equation = -1.092 mA.

(A) Bubble generation region. (B) Transport response after bubble generation is discontinued.

Ibubble time to reach Φ(pulse), time to reach generation steady-state -ICu-pulse -ICu-ss Icu-pulse/ILevich steady-state E I (H2 )+I(Cu) V/SHE mA sec mA mA sec -0.2 no bubbles ------1.608 --- 0.9 -0.65 -43.68 2.05 3.606 1.977 3.30 0.9 -0.8 -126.02 3.44 7.212 1.945 6.60 1.8 -0.9 -152.2 2.82 7.739 1.696 7.09 1.7 -1 -209.83 3.57 8.826 1.907 8.08 1.7

It should be noted that in the pulse experiments, the time to reach steady-state on

the copper current, which is assumed to be equal to the translation time of the bubbles is

. × often close to the diffusion time constant, . = = = 6.26 . 2 × − 3 /2 훿 �5 6 10 푐�� −6 2 휏 �휏 � 5 10 푐푚 � �� In order to obtain further information about the bubbles size and surface coverage,

photographs of the disk surface during the gas evolution experiments were taken as described in the following section.

3.8. Optical Observations of Bubbles Evolution and Displacement.

Still photographs and videos of the disk electrode during deposition and bubble generation were taken. Sample photographs of the electrode covered by bubbles are displayed in table 3.6 showing top views of the disk electrode at different potentials and rotation rates. Due to the color of the copper solution and the dark color of the deposit, it was difficult to take clear pictures during actual copper deposition. Consequently, most

pictures and videos were taken during electrolytic hydrogen generation on a polished

copper electrode, from aqueous sulfuric acid at pH~0, in the absence of cupric ions, but

under conditions that otherwise mimic the copper deposition reaction.

The pictures in table 3.6 reveal a strong relationship between the average bubble

radius and the angular rotation. Indeed, at any constant potential bubble size decreases as

the rotation of the disk electrode increase. At constant angular rotation of the disk there is

not a major change in the average bubble size with the potential. The bubble size

distribution becomes smaller as the angular rotation increases. When the electrode is

rotated at the slower rate of 100 rpm it is possible to see a heterogeneous distribution of

different sizes of bubbles. In all experimental conditions, the distance between bubbles is

about constant, implying that the bubbles are evenly distributed on the disk electrode.

The rate of generation of gas at the electrode is considered to be under pseudo-steady state conditions, since no variation in size, number, or distribution of bubbles was

noticeable. Furthermore, no variation in bubble size as a function of the radial position was observed.

In the process of measuring the mean bubble radius, a small number of the biggest

bubbles were not included because these bubbles were touching the surface roughly in a

tangential manner. Few of these big bubbles is distinguishable in pictures designated as

A, D and E in table 3.6. While it is impossible from the plan views shown in the

photographs to determine the shape of the bubbles, it appears from the pictures, as well as

from the numerous videos taken, that the translating bubbles are about hemispherical.

Table 3.7 provides the measurements of the mean bubble radii, R , and the electrode

c fractional coverage by bubbles , , under different rotation rates and potentials.

θ 59

Table 3.6: Photographs s of the bubble covered copper disk electrode at different potentials, and rotation rates. The electrolytic was sulfuric acid at pH ≈ 0.

E, 100 rpm 400 rpm 900 rpm V/SHE -0.5

A B C -0.65

D E F -1.0

G H I

Table 3.7: Measurements of average bubble radii, fraction of surface coverage and

standard deviation at different rotation speeds and potentials. Values were obtained from

photographs of a RDE in aqueous H2SO4 pH~0.

100-rpm 400-rpm 900-rpm Rc, SD, SD, SD, E,V/SHE θ cm cm θ Rc, cm cm θ Rc, cm cm -0.5 0.15 0.012 0.005 0.09 0.007 0.001 0.04 0.004 0.001 -0.65 0.26 0.015 0.00∓ 3 0.11 0.007 0.002∓ 0.06 0.005 0.002∓ -0.8 0.35 0.015 0.003 0.12 0.008 0.002 0.10 0.005 0.001 -0.9 0.39 0.014 0.005 0.16 0.008 0.001 0.10 0.005 0.001 -1 0.40 0.013 0.003 0.20 0.008 0.002 0.11 0.004 0.001

A large number of photographs were analyzed and the standard deviation of the

measurements is reported. The standard deviation is larger for the lowest rotation rate

experiments. This implies that the bubble size is more homogeneous at higher rotations.

However, the standard deviation as a fraction of Rc is about the same for all rotation

rates. Table 3.7 also indicates that the surface coverage of the disk by bubbles decreases

with the rotation rate.

Videos movies provide a rough estimate of the bubble displacement on the

surface. The bubble displacement was determined following the procedure illustrated in

Fig 3.14: A stationary bubble located approximately at ~0.1 , away from the �푑푑푑� 3 center of the disk is initially identified. The time measurement is initiated𝑐 once the bubble

starts translating towards the rim of the disk. The displacement time t is the time measured until the bubble leaves the disk. ∆

Table 3.8 lists the approximate displacement times of the bubbles at different potentials and rotation rates. These values were obtained from video recording of a RDE in aqueous H2SO4 at pH ≈ 0.

At the highest rotation rate of 900 rpm, it was not possible to collect information of the time of displacement of the bubble because this process is very fast. At -0.5 V/SHE the measured times of bubble displacement fluctuates significantly. This fluctuation is associated with bubbles that are under pseudo-steady-state conditions. Table 3.8 illustrates that the time of bubble displacement becomes shorter as the rotation rate increases.

Disk electrode

Centrifugal forces

푑𝑑� �

Bubble, H2(g) 푑3𝑑� �

Figure 3.14: Schematic representation of the measurement procedure for determining the time of bubble displacement. Initially, the measured bubble is static and located approximately at 1/3 of the disk radius away from the center. Subsequently, the bubble is swept towards the edge of the disk over the time t.

∆

Table 3.8: Times of bubble sweep at different potentials. Values were obtained from video recording of a RDE in dilute H2SO4 electrolyte at pH ≈ 0.

100-rpm 400-rpm E, V/SHE ∆t, s ∆t, s -0.5 fluctuates 1 -0.65 3.1 0.6 -0.8 2.4 0.3 -0.9 1.4 0.2 -1 1.9 0.2

A more detailed discussion of the measured parameters including surface coverage, mean bubble radius, copper deposition current density, and mass transfer enhancement as a function of the applied potential and the RDE rotation rate, is provided in chapter 4.

3.9. References:

[1] J. Newman, "Resistance for flow of current to a disk", Journal of the

Electrochemical Society, vol. 113, pp. 501-502, (1966).

Chapter 4: Discussion of the Results:

4.1. Comparing Mass Transport Enhancement Based on Deposit Weight to that

Based on Current Measurements (Polarization Data).

In chapter 3 two methodologies for obtaining the partial current of copper were

presented, one based on the weight gain of the electrodeposits, and another based on the

subtraction of the hydrogen partial current from the total current read by the potentiostat.

Equations 4.1 and 4.2 describe these two methods.

Weight measurement:

= (4.1) 푤� �푛∆푚 퐼퐶퐶 푡푀퐶� Polarization data:

= , (4.2) 푝𝑝 퐴푅𝑅�ℎ 2 퐼퐶퐶 퐼푡�푡 − 퐼퐻 𝑓𝑓 ∙ �퐴푆푆𝑆푆ℎ� The expected mass transport limited current densities, as calculated by the Levich

equation were shown in table 3.4.

Figures 3.10, 3.11, and 3.12 indicate good agreement between the two methods of

obtaining the copper current density. This indicates that the agreement between both

methods is not compromised due to experimental errors when the system incorporates

high cupric ion concentration (0.2 M). Additionally, figures 3.10 to 3.12 describe an increment of copper current density over the limiting mass transport rates as predicted by

Levich at the most negative potentials; this potential region matches with the potentials when hydrogen evolution rate increase.

The polarizations data in Appendix A for the lower concentration electrolyte (20

mM) indicates highly variable and erratic data. The underlying reason for the discrepancy

of this data, has been discussed earlier and is attributed to the fact that the small (~6%)

copper current was obtained by subtracting two large and noisy currents. Also, the H2

current was not measured directly but calculated from a different experiment. Where the

hydrogen was evolved on a polished copper RDE. This required compensating the

measured hydrogen current for the actually larger rough deposit area and accounting for a

different applied potential due to different ohmic losses. This appears to have led to too

high H2 current.

The comparison of both methodologies, weight measurements and polarization data,

allows to reach conclusions about the reliability and limitations of both methods. First

both methods indicate an increase in the copper limiting current density beyond that

predicted by the Levich’s equations for all rotation rates at a potential of about -0.5 V.

This behavior may be linked to the initial stage of hydrogen evolution where photographs confirm that bubbles nucleate on the electrode surface at this potential. Likewise, both methods indicate for the 200 mM CuSO4 a smaller enhancement in the copper current density at the most negative potentials when the rotation rate increases. The dimensions of the bubbles as well as the bubble translation on the electrode are affected by the rotation rate. These parameters are likely to affect the electrolyte replenishment at the electrode and the mass transfer enhancement.

Conditions were identified where both methods lack precision in estimating the mass transfer enhancement. Specifically, the polarization curve data is inaccurate in the

potential region when the hydrogen evolution rate is substantial for the system with lower

cupric ion concentration.

The weight measurement method is sensitive to the quality and morphology of the

deposit. For instance, when the electrodeposition forms powder there is poor deposit adhesion. Since roughness increases with time, this imposes an upper limit on the deposition experiment. On the other hand, at short deposition times, the amount of deposit is not sufficient for weighing. In this study, the time selected for the electrodeposition experiments were optimized to provide acceptable quantification of the copper deposits with deposit weight of the order of mg; which can be accurately weighed.

The weight measurements are more accurate in providing the copper current densities than the polarization data.

It is convenient to analyze the current enhancement in terms of the enhancement factor, Φ, defined as the ratio of the measured copper current to the theoretical mass transport limit as indicated by the Levich equation, when both currents are based on the same electrode area (either rough or smooth). Care must be given to account correctly for the increased electrode roughness, such that the enhancement factor does not incorporate increased area effects.

Accordingly, the enhancement factor based on experimentally measured current

(either from weight or polarization data) is:

= = = = (4.3)

퐼푒푒푒 퐼푒푒푒 퐼푒푒푒 퐼푒푒푒 퐴 �푒� 퐿�퐿𝐿ℎ 퐿�퐿𝐿ℎ 푅𝑅�ℎ 푅𝑅�ℎ 퐿�퐿𝐿ℎ 𝑠𝑠�ℎ 퐴 Φ ≡ 퐼 � ∙퐴 퐿�퐿𝐿ℎ 𝑠𝑠�ℎ � ∙퐴 ∙� � ∙퐴 �퐴𝑠𝑠�ℎ � Here, I designates the total current measured on the rough electrode. The subscripts

‘exp’ and ‘Levich’ designate experimental values and those derived from theoretical

calculations following Levich’s model, respectively. The parameter ‘FA’ designates the

roughness factor given by the ratio of the rough electrode area to that of the smooth

electrode area.

Figure 4.1 and 4.2 provide the enhancement factor based on the weight measurement method at different rotation rates for 20 mM and 200 mM CuSO4 at pH 0, respectively.

The indicated voltage has been corrected for the IR drop. ≈

7 100-rpm 6

4 400-rpm

exp 3 900-rpm (wt)

Φ 2

0 -0.85 -0.80 -0.75 -0.70 -0.65 -0.60 -0.55 -0.50 -0.45

Voltage (IR compensated), V / SHE

Figure 4.1: Enhancement factor based on deposit weight measurements for 20 mM

CuSO4 at pH ≈ 0. Blue diamonds indicate the enhancement factor at 100 rpm. Red

squares correspond to the enhancement factor at 400 rpm. Green triangles refer to the

enhancement factor at 900 rpm. Currents were obtained from weight measured of the

deposited copper using Faraday’s law and accounting for the rough area of the electrode

as reported in table 3.1. The reported voltage has been corrected for the IR drop.

6 100-rpm

4 400-rpm

3 exp

(wt) 2 900-rpm Φ 1

0 -0.75 -0.70 -0.65 -0.60 -0.55 -0.50 -0.45 -0.40 -0.35 -0.30

Voltage (IR compensated), V / SHE

Figure 4.2: Enhancement factor based on weight measurement of 200 mM CuSO4 at pH

It is seen in figure 4.1, that the enhancement factor increases at all rotations tested with increasingly negative potential, in the potential range that is cathodic to -0.5 V. This corresponds to regions where the hydrogen evolution rate increases; furthermore, this enhancement factor is higher at lower rotation rates. This behavior may suggests that surface coverage by bubbles is larger at lower rotations or that the effect of the enhanced transport by the bubble motion is more pronounced at slower rotations when the fluid- flow induced transport is lower.

Figure 4.2 shows similar behavior to that of figure 4.1. This implies that the

enhancement factor is increasing roughly by the same magnitude regardless of the

electrolyte concentration. Likewise, the enhancement starts to increase at E < -0.5 V for

all rotations, most likely due to bubble presence on the surface.

4.2. Analysis of the Pulsed Bubble Generation Experiments:

Figures 4.3, 4.4 and 4.5 provide a comparison of different enhancement factors

based on weight measurements, and pulsed generation of bubbles. The data are shown with respect to the applied potential vs Standard Hydrogen Electrode (SHE); therefore, since the cell configuration is identical for comparative purposes the ohmic drop in figures 4.3 – 4.5 was not subtracted. The solution used was 20 mM CuSO4 at pH ≈ 0. The

rotation rates applied were 100 rpm, 400 rpm and 900 rpm in figures 4.3, 4.4 and 4.5,

respectively. In the pulse experiments, the generation of bubbles had been discontinued

after 8 seconds and the ensuing currents were measured immediately following this step.

The enhancement factor of these two methods provides roughly the same trend at

all potentials tested as shown in figures 4.3, 4.4 and 4.5. However in all figures the values

of the enhancement factor is higher for the weight measurements method. This may be

related to the method used to obtain the rough electrode area, which may have

underestimated the roughness of the copper deposits. The pulse generated data, was

collected during very short experiments and therefore is significantly less sensitive to

evolved roughness. The magnitude difference in the enhancement factor between these

two methods decreases with increased rotation rates. Figures 4.3, 4.4, and 4.5 show that

the enhancement factors trend to level at potentials more negative than -0.8V. This

suggests that the mass transfer enhancement does not increase at the most negative

potentials. It may be possible to associate the plateau region of the mass transfer enhancement with the fraction of surface coverage and mean bubble radius; mainly, because the model proposed in chapter 5 assumes that the mass transfer enhancement should not increase if the fraction of surface coverage and mean bubble radius are not changing in the observed potentials range where the plateau region is noted.

7 Φ(wt)exp

5 Φ(pulse) Factor Factor 4

Enhancement 100 RPM 1

0 -1.05 -1 -0.95 -0.9 -0.85 -0.8 -0.75 -0.7 -0.65 -0.6 -0.55 -0.5 -0.45 E, V/SHE

Figure 4.3: Enhancement factor based on weight measurements as indicated by equation

4.1 and 4.3 (blue diamonds), and based on the pulse experiments where Φ(pulse) is given

by ICu-pulse/ILevich (green triangles). Experiments were carried at 100 rpm in 20 mM CuSO4

at pH ≈ 0. No ohmic correction was applied. In the pulse generation of bubbles, the

hydrogen evolution had been discontinued after 8 sec.

Φ(pulse) 4 Φ(wt)exp

3 Factor Factor

Enhancement 400 RPM

0 -1.05 -1 -0.95 -0.9 -0.85 -0.8 -0.75 -0.7 -0.65 -0.6 -0.55 -0.5 -0.45 E, V/SHE

Figure 4.4: Enhancement factor based on weight measurements as indicated by equation

4.1 and 4.3 (blue diamonds), and based on the pulse experiments where Φ(pulse) is given by ICu-pulse/ILevich (green triangles). Experiments were carried at 400 rpm in 20 mM CuSO4 at pH ≈ 0. No ohmic correction was applied. In the pulse generation of bubbles, the hydrogen evolution had been discontinued after 8 sec.

4 Φ(pulse)

3 Φ(wt)exp Factor Factor

Enhancement 900 RPM 0 -1.05 -1 -0.95 -0.9 -0.85 -0.8 -0.75 -0.7 -0.65 -0.6 -0.55 -0.5 -0.45 E, V/SHE

Figure 4.5: Enhancement factor based on weight measurements as indicated by equation

4.1 and 4.3 (blue diamonds), and based on the pulse experiments where Φ(pulse) is given

by ICu-pulse/ILevich (green triangles). Experiments were carried at 900 rpm in 20 mM CuSO4

at pH ≈ 0. No ohmic correction was applied. In the pulse generation of bubbles, the

hydrogen evolution had been discontinued after 8 sec.

Figures 4.6, 4.7 and 4.8 provide a comparison of three different enhancement

factors in the more concentrated solution of 200 mM CuSO4 at pH ≈ 0.

Similar to the lower cupric concentration the enhancement factor based on weight

measurements is higher than that based on the pulse experiments at the lowest rotation rate, (100 rpm). When the experiments were conducted at mid and higher rotation rates

(400 and 900 rpm) all the three enhancement factors approximately agree. The magnitude difference between data taken using these three methods increases at the most negative potential. Furthermore at potentials more negative than -0.8 V figure 4.6 shows a decline

in the enhancement factor slope, suggesting that a plateau region might be present at

potentials more negative than -1.0 V.

9 Φ(pulse) Φ 8 (pol)exp

7 Φ(wt) 6 exp Factor 5

2 100 RPM

Enhancement 1

0 -1.05 -1 -0.95 -0.9 -0.85 -0.8 -0.75 -0.7 -0.65 -0.6 -0.55 -0.5 -0.45 E, V/SHE

Figure 4.6: Enhancement factor based on weight measurements as indicated by equation

4.1 and 4.3 (blue diamonds), and based on the pulse experiments where Φ(pulse) is given

by ICu-pulse/ILevich (green triangles). Experiments were carried at 100 rpm in 200 mM

CuSO4 at pH ≈ 0. No ohmic correction was applied. In the pulse generation of bubbles,

the hydrogen evolution had been discontinued after 8 sec.

Φ(pulse) Φ(pol)exp Φ(wt)exp 3

Factor 2

1 400 RPM Enhancement 0 -1.05 -1 -0.95 -0.9 -0.85 -0.8 -0.75 -0.7 -0.65 -0.6 -0.55 -0.5 -0.45 E, V/SHE

Figure 4.7: Enhancement factor based on weight measurements as indicated by equation

4.1 and 4.3 (blue diamonds), and based on the pulse experiments where Φ(pulse) is given

by ICu-pulse/ILevich (green triangles). Experiments were carried at 400 rpm in 200 mM

CuSO4 at pH ≈ 0. No ohmic correction was applied. In the pulse generation of bubbles,

the hydrogen evolution had been discontinued after 8 sec.

Φ(pulse)

Φ(pol)exp 2 Φ(wt)exp Factor

1 900 RPM Enhancement

0 -1.05 -1 -0.95 -0.9 -0.85 -0.8 -0.75 -0.7 -0.65 -0.6 -0.55 -0.5 -0.45 E, V/SHE

Figure 4.8: Enhancement factor based on weight measurements as indicated by equation

4.1 and 4.3 (blue diamonds), and based on the pulse experiments where Φ(pulse) is given

by ICu-pulse/ILevich (green triangles). Experiments were carried at 900 rpm in 200 mM

CuSO4 at pH ≈ 0. No ohmic correction was applied. In the pulse generation of bubbles,

the hydrogen evolution had been discontinued after 8 sec.

4.3 Analysis of the Photographic Data:

Figure 4.9 shows the fraction of surface coverage Θ, at different potentials, and

rotation rates. The graph was constructed based on numerous results similar to those

shown in table 3.7.

Measurements were conducted to estimate surface tension of the electrolyte

solutions. In all cases, the values obtained for the surface tension were about the same as

the surface tension of water, 71.8 dyne/cm; thus surface tension does not change

appreciably in presence of cupric solution in the system. It is therefore assumed that the

bubble size generated in our experiments are the same for all electrolyte tested for a given

potential and a rotation rate.

The surface coverage increases as the applied potential becomes more negative at

a constant rotation rate as shown in figure 4.9. Therefore, as the applied potential increases, so does the bubble growth per element of electrode area, since the voltage supplies the free energy or the electrochemical potential required to activate more nucleation sites on the electrode surface for hydrogen; subsequently, more bubbles can

grow per unit area. Furthermore, figure 4.9 represents an inverse relationship between the

angular rotation rate and the surface coverage. This means that the surface coverage is higher at lower rotation rates. Finally, the fraction of surface coverage is approaching a constant value at potentials more negative than -0.9 V. This coincides with the plateau

region observed in figures 4.3, 4.4 and 4.5.

0.45 100-rpm 0.40 0.35

θ 0.30 400-rpm 0.25

coverage, 0.20 900-rpm 0.15

surface 0.10 0.05 0.00 -1.1 -1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 E, V / SHE

Figure 4.9: Surface coverage as a function of potential at different rotation rates. The graph was constructed from numerous photographs similar to those shown in table 3.7.

Figure 4.10 shows the mean bubble radius R at different potentials, and rotation

c rates. The mean bubble radius decreases as the rotation rate increases. No significant correlation was observed between the mean bubble radius and potential.

Figure 4.11 shows the mean radius of bubbles at different rotation rates, and potentials. The mean bubble radius shows an asymptotic dependence on angular rotation.

The mean bubble radius does not change with the applied potentials at a given rotation rate. Additionally, an increase in the overpotential increases the number of bubbles. The bubble size distribution becomes narrower as the rotation rate increases. The distance between bubbles is roughly constant, thus bubbles are uniformly distributed on the disk electrode. The rate of generation of gas on the electrode is under pseudo-steady-state

conditions. The photographic images in table 3.6, does not exhibit a relation of the bubble

size to the position on the disk.

0.020 0.018 100-rpm 0.016 0.014

cm 0.012 400-rpm , c

R 0.010 0.008 0.006 0.004 0.002 900-rpm 0.000 -1.1 -1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 E, V / SHE

Figure 4.10: Mean bubble radii as a function of potential at different rotation

rates. The graph was constructed from the photographs similar to those shown in table

3.7.

0.0160 -0.5 V 0.0140 -0.65 V -0.8 V 0.0120 -0.9 V 0.0100 -1.0 V

0.0080 , cm c R 0.0060

0.0040

0.0020

0.0000 0 100 200 300 400 500 600 700 800 900 1000 ω, rpm

Figure 4.11: Mean bubble radii as a function of rotation rates at different potentials. The graph was constructed from the photographs similar to those shown in table 3.7.

Chapter 5: Modeling the Bubble Induced Enhancement:

5.1. Model Description:

We observed a current density in copper deposition that is increasing in magnitude with larger negative potentials. This current density exceeds substantially the limiting current density quantified by the Levich equation. Mass transfer enhancement, defined as the ratio of the experimental current divided by the limiting current obtained using the Levich model, has been noted at potentials more negative than -0.5 V. This is a region that coincides with substantial hydrogen evolution. The hypothesis of this study is that the mass transfer enhancement during the copper deposition is due to hydrogen gas bubble co-evolution, and the bubble translation on the electrode.

We present here a model that accounts for the mass transfer enhancement and associate it with the bubble translation on the electrode. The model suggests that the motion of bubbles along the surface of the electrode causes a mixing effect; this mixing effect has been quantify here in terms of the surface renewal model[1], or the penetration model [2]. The process initiates by provision of a large overpotential to nucleate bubbles on the electrode. The bubbles initially grow while being stationary on the electrode until they reach a critical radius. Once the bubble has a critical radius, the bubble starts to experience larger drag forces due to the flow that sweeps the bubble towards the circumference of the disk. As the bubble translates, the volume it occupies becomes displaced by fresh, non-depleted, electrolyte from the bulk. Therefore, the region which is exposed to the bubble streak becomes rejuvenated with fresh electrolyte and hence is no

longer under the lower mass transport limit predicted by the steady-state solution of the

Levich equation. Instead, we apply a transient transport model, described by the Cottrell equation, which predicts, higher transient transport rates to the bubble streak region. This model is quantified below.

5.2. Velocity Profile near a Rotating Disk:

Schematics of side and top views of a RDE indicating the flow pattern near the disk are shown in figures 5.1 and 5.2.

Teflon

Z direction Disk electrode

Bubble (gas)

Electrolyte solution

Figure 5.1: Sketch of the side view of a RDE indicating the electrolyte flow pattern due to the disk rotation.

Disk electrode

Bubble (H2) ω Figure 5.2: Sketch of the bottom view of a RDE, showing the spiral path of a bubble.

Figure 5.1 depicts a rotating disk electrode. This rotation generates motion of the electrolyte. The arrow indicates the direction of the angular rotation. This flow has been analyzed first by von Karman [3] who described it in terms of three velocity components in cylindrical coordinates. Cochran [4] related later these three velocity components to expansion series defined as F( ), G( ) and H( ): r direction: ξ ξ ξ

2 3 2 1 2 5 2 3 2 3 = ( ) = = 3 2 1 2 + 2 3 −2 ⁄ 3− ⁄ (5.1) 휉 �휉 휔 휐 푧 � �휔 휐 푧 � ⁄ − ⁄ � 푣 𝑟� 휉 𝑟 �𝑎 − − � �휔 휐 푧� − − ⋯ direction:

φ 3 5 2 3 2 3 = ( ) = 1 + + = + 3 2 1 2 + + 3 ⁄ 3− ⁄ (5.2) �휉 �휔 휐 푧 � ⁄ − ⁄ 휑 푣 𝑟� 휉 𝑟 � 𝑏 � 𝑟 �휔 휐 푧� ⋯ z direction:

3 4 2 1 3 5 2 3 2 4 = ( )1 2 ( ) = ( )1 2 2 + + = 3 2 1 2 2 + + + 3 6 3− ⁄ 6− ⁄ (5.3) 휉 �휉 휔 휐 푧 𝑏 휐 푧 ⁄ ⁄ ⁄ − ⁄ 푧 푣 휐휔 퐻 휉 𝑟 �−�휉 � −�휔 휐 푧 ⋯

is a dimensionless distance from the disk given by: = z . r and z are the radial ω ξ ξ �υ distance and the distance orthogonal to the disk surface, respectively. F( ), G( ) and H( ) are tabulated computed functions, a and b are numerical constants: a =ξ 0.51023;ξ b =ξ -

0.6159. Sparrow and Gregg [5] provided later the approximate expansion series on the

right-most side of equations 5.1-5.3, which we use later.

Reviewing the von Karman equations, we notice that the flow velocity is zero at the center of the disk and increases towards the circumference of the disk. When the bubbles reach a critical size as discussed below, they are swept by the electrolyte flow, following with some lag, the flow pattern. Figure 5.2 describes schematically the spiral path of a bubble on the electrode surface. If the rotation of the disk is in a

counterclockwise direction, the bubble will also rotate in a counterclockwise direction but

with an angular rotation speed smaller than that of the disk. Thus, relative to the disk

surface, the bubble moves in the clockwise direction, in a spiral path as it also moves

outward in the radial direction. Figure 5.3 provides a schematic description of how

bubbles are growing and moving on the electrode.

풕

Step 1: Nucleation Step 2: Growth Step 3: translation

� 풕 풂

푹� 풊푳𝑳

ω ퟐ+ 〈풊푪푪풕� 〉

Figure 5.3: Sketch of the bubble growth and translation. Step 1 is the initial state of bubble nucleation. Step 2 represents the process of bubble growth prior to translation. In

higher, transient current density is expected.

퐶퐶푡푡 〈푖 〉

Initially, as shown schematically in step 1, of figure 5.3, nucleating bubbles are

small and stationary because the surface tension force is larger than the drag force due to

the flow. Step 2, shows the growing bubbles which are increasing in size due to gas

diffusion and incorporation but still are not displaced. In step 3, the bubbles reach a critical size where the drag force due to flow on the larger surface of the bubbles

(proportional to R2), matches and starts to exceed the surface tension (proportional to R).

As a result, this step describes the moment when bubbles starts to be swept by the

solution in a spiral direction. In reality, the drag force is changing with the flow velocity.

The von Karman velocities in the r and direction increase with distance from the center, therefore the drag force reaches its maximumφ value at the edge of the disk, while at the center of the disk the drag force is zero. However, this model considers an average bubble size, as supported by the analysis of the photographs which do not exhibit large size variation, and therefore, an average drag force can be assumed.

Figure 5.4 shows schematically a bottom view of a growing and translating bubble on the electrode.

Time scale,

Figure 5.4: Sketch of bottom view of bubble 푡translation on the electrode. The time

푐 designates the delay time between two consecutive bubbles. 푡

The bubbles are assumed to be hemispheres (based on visual observations) and

the critical radius at which they start to translate is designated as R . Clearly, R depends

c c

on the local flow velocity and hence (per equations 5.1 and 5.2) on the radial position at

which the bubble nucleates, however, we assume a mean position with a mean critical

radius. The average nucleation time, for the bubble to reach the critical radius is also

푐 assumed to be uniform across the disk, and is designated as . This implies that푅 at any

푐 given nucleation site, a new bubble nucleates and starts translating푡 every seconds; in

푐 reality, however, the bubble growth is staggered. Hence, the average distance푡 between

the translating bubbles is: = . Here, is the average velocity of a bubble on

푎푎푎 푐 푎푎푎 the surface of the disk. Since� there푣 is∙ 푡 always friction,푣 the average velocity of a bubble is

less than the von Karman velocity. However the model assumes that the bubbles are

swept by the electrolyte flow, following a negligible lag. The fluid velocities relative to

the disk can be approximated, using the series expansions in Fig. 5.1 – 5.3, as:

= (5.4) 3⁄2 −1⁄2 푣� �휔 휐 푧� = 1 + + = + 3 3⁄2 3 3⁄2 (5.5) 𝑟� 𝑓𝑓 푑𝑑� 휔 푎푧 휔 휔 푎푧 휔 3⁄2 3⁄2 푣휑 푣휑 − 푣휑 ≈ 𝑟 � 𝑏�휐 3휐 � − 𝑟 𝑟� ��휐 3휐 � Dividing equation 5.5 by 5.4:

= 휔 푎푧3휔3⁄2 1.207 for small z (5.6) 푟𝑟 �푏�휐+ 3⁄2 � �휑 3휐 푏 �푟 휔 푧휔 푎 �푎�휐−2휐� ≈ ≈ The system describes bubbles that follow spiral paths; therefore the bubble

velocity relative to the disk is given by:

= + = ( + + ) (5.7) 1⁄2 𝑟𝑟𝑟𝑟 𝑟�2 2 휔 2 2 1⁄2 �푣푉푉 � �푣휑 푣� � 𝑟��휐 � � ⋯ = 0.8 (5.8) 𝑟𝑟𝑟𝑟 휔 �푣푉푉 � 𝑟��휐

5.3. Forces Acting on the Bubble:

The expected forces on the bubble are due to buoyancy, surface tension and drag force by the fluid. The buoyancy force is due to difference in density between the bubble and the surrounding fluid in the presence of a pressure gradient. Typically, bubbles subject to a radial pressure gradient such as encountered in centrifuges are expected to be propelled towards the axis of the rotation. This condition applies in the case of an unbounded (infinite) fluid, but in the case of a finite volume, the walls of the vessel would cause a pressure gradient to develop. In the case of a rotating disk there is not a radial pressure gradient as shown in a number of publications including [6]. Therefore, we may conclude that there is no buoyancy force acting on the bubble as it is the case when a RDE is much smaller than the radius of the vessel.

Surface tension force act in a direction parallel to the surface of the bubble at its contact with the disk. For a symmetrical bubble, i.e. when the bubble shape is not distorted, there is not net surface tension force, because the surface tension force components balance each other. However, when the bubble becomes distorted due to flow, the contact angle in the section of the bubble facing the fluid is different for that in the trailing, and hence a net force is expected. This is illustrated schematically in fig 5.5.

(A) (B)

Figure 5.5: (A) Side view of a distorted bubble due to drag force by the fluid showing a

net component of the surface tension force parallel to the surface. This arises from the

distortion of the bubble geometry which gives rise to a difference in the contact angle

between the bubble and the surface in the advancing and receding directions. (B) Bottom

view of a distorted bubble due to drag force by the fluid. and are the surface

휑 � tension forces in angular and radial directions, respectively.휎 The 휎sketch follows a

presentation similar to Fig. 1(b) in Amirfazli’s publication [7].

In a number of publications, including [7, 8], the net surface tension force, , is

푆푆 given by 퐹

= ( ) (5.9)

푆푆 푆푆 푆푆 푅 퐴 퐹 푅 푘 휎 �푐푐휗 − �푐푐휗

Where and are the receding contact angle and the advancing contact angle;

푅 퐴 respectively. 휗 is the휗 surface tension. is the characteristic length (radius of the

푆푆 bubble), and 휎 is a fitting parameter or푅 a constant of the shape for the contour of the

푆푆 bubble. In this푘 study is considered to be the mean bubble radius, . The balance of

푆푆 푐 forces can modify the푅 shape of the bubble and consequently they change푅 the value of

88 푘푆푆

When, the bubble is hemispherical the surface tension force in equation 5.9 can be

written as the right hand-side of equation 5.11.

Since we do not know accurately the surface tension force, , as well as how to

푆푆 measure accurately the receding and advancing contact angles of the퐹 distorted bubble, we

will assume that the force associate with the surface tension is constant across the disk.

This is compatible with our assumptions regarding the average bubble size and average

velocity.

The third force acting on the bubble is the drag force due to the flow. This force is

typically given by the Stokes’ law [9].

However, our bubble is assumed, based on observations, to be hemispherical and

is attached to the surface; hence, it is subject to a velocity gradient within the boundary layer.

Figure 5.6 describes schematically a balance of forces on a small hemispherical bubble attached to the electrode.

푩�푩푩𝑩 � 2R 푩𝑩푩 c ퟐ+ �푪푪 � 푣

direction =

(z) 푫 ퟐ+ 푭ca 푪푪

Bubble Bubble growth 푪 ퟎ 푺푺 흑 푭

Electrode

Figure 5.6: Sketch of the force balance on a small hemispherical bubble attached to the

electrode within the boundary layer.

The balance of forces on a bubble is given by:

= = = 0 (5.10)

푡�푡 � 푆푆 푏 is the drag force on the∑ 퐹 surface퐹 of− the퐹 bubble푚� due to the flow, and is the

� 푆푆 force due퐹 to surface tension attaching the bubble to the electrode. and 퐹 are the

푏 bubble mass, and its acceleration, respectively. 푚 �

We assume that the bubbles are moving at about a constant velocity, hence the acceleration, = 0; in reality the velocity of the bubbles changes with position, hence

푏 the acceleration� is not zero. However, we assume a constant average velocity and therefore, assumption of = 0 is consistent.

푏 Legendre et. al. [�10] solved the shear stress on the bubble due to a flow with a linear velocity gradient, , such as prevails within the boundary layer and derived the

푉푉 force presented in the left훼 hand-side of the equation 5.11:

= = = 2 (5.11) 7 4 퐹� 2 휋휋푅푐 �7 훼푉푉푅푐 − 푣퐵𝐵𝐵�� 퐹푆푆 휋 ∙ 푅푐 ∙ 휎

Here, 푟𝑟𝑟𝑟� (5.12) ��푉푉 � 푉푉 푧 And is the electrolyte viscosity.훼 Rearranging≡ equation 5.11:

µ = (5.13) 4 4∙휎 �7 훼푉푉푅푐 − 푣퐵𝐵𝐵�� 7휇 ≡ 퐾� Therefore:

= (5.14) 4 푣퐵𝐵𝐵� 7 훼푉푉푅푐 − 퐾� In equation 5.14, setting, = 0, provides the critical radius at which the

퐵𝐵𝐵� bubble starts translating: 푣

= (5.15) 7�퐷 푅푐 4훼푉푉

The substitution of equations 5.8 and 5.12 in equation 5.15 relates the critical

radius to the rotation rate:

= . = (5.16) . 7�퐷 −1 5 �푒 푐 휔 � � 푅 3 2𝑟� 휐 ≡ 퐾 휔 퐾 휔 is an empirical exponent, and is a constant given by:

� � � 퐾 = . (5.17) 7∙휐∙�퐷 � As stated above, since we퐾 could 3not2� detect experimentally variations of bubble

size with the radial position, we assumed an average bubble size and an average radial

position, to be discussed later. Hence, we include this average radial position as r in the constant.

Figure 5.7 shows the experimentally measured mean bubble radius as a function of rotation rate.

-1.6

-1.8

c -2 log R -2.2

-2.4

-2.6 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 log ω

Figure 5.7: Mean bubble radius as a function of rotation rate. Rc and ω are in cm and

rads/sec, respectively.

The empirical correlation of the data in figure 5.7 is logR = 0.4074log

. c 1.5137 or , = 0.0306 with a linear regression coefficient of− R = 0.9305ω −; −0 4074 2 푐 푎푎푎 accordingly푅 in equation 휔5.16 is -0.4074 (+/-0.36) instead of the theoretical value of -

� 1.5. This deviation� can be associated with the fact that equation 5.17 applies in bubbles with the same hemispherical shape on the surface of a disk. However, in our system, many bubbles have different distortion. More importantly, equation 5.17 was derived based on the assumption of zero acceleration and average bubble size, radial position, and velocity. As discussed above, while those assumptions are consistent with the inaccurate analysis of the photographs, the von Karman equations indicate that the flow and therefore the bubble translation must vary with position. Furthermore, we assume that the bubble size we observe is Rc, however, the bubbles should keep growing during

translation, leading to discrepancy.

5.4. Bubble Generation and Growth:

As described above, the model applies the penetration theory to quantify the concept of ‘volume renewal model’. Accordingly, the enhancement is due to fresh solution replacing depleted electrolyte in the bubble path. Figure 5.8 shows schematically how fresh electrolyte from the bulk replenishes depleted solution in the bubble path.

Fresh Electrolyte [ ] ퟐ+ 푩𝑩푩 푪푪

푣 tc

direction (z) (r) direction Electrode

Figure 5.8: Sketch of the volume renewal model.

As the bubble slides in the spiral path it evacuates a hemispherical volume

occupied by hydrogen gas. Immediately, this volume becomes replaced by fresh 2 3 3 푐 electrolyte� 휋푅 � from the bulk. This fresh electrolyte right next to the surface provides, for a short time, very high transport rates, far exceeding those associated with the steady-state

transport rates which are accounted for by Levich’s model. However, the electrolyte that

arrives from the bulk gradually becomes depleted, resulting in declining transport rates.

This implies that at the electrode the system starts to develop a diffusion boundary layer.

After some time, this concentration boundary layer extends all the way to the bulk region

and a steady-state concentration gradient is established. The steady-state transport rates

which are supported by this concentration gradient, as predicted by the Levich equation,

are much lower than the transient rates which are given by the Cottrell equation [11]. The

hydrogen bubbles which are released periodically (every t seconds on the average), re-

c introduce fresh electrolyte in their wake, bringing about the higher transient transport

rates along their path.

To quantify the process, the diffusion equation for the copper, as given by Fick’s second law must be solved.

= 2 (5.18) 휕퐶퐶� 휕 퐶퐶� 2 휕� 휕푧 Equation 5.18 is a simplified 퐷form� of �the convective-diffusion equation [9] with the convective term omitted since it is negligible within the diffusion layer. The depletion of cupric concentration within the boundary layer during the transient response is shown schematically in figure 5.9.

푵 𝒃𝒃 휹 푪푪푪 1

( )

퐶퐶퐶 푑𝑑� 푏𝑏푏 퐶퐶퐶

0 Distance from electrode

Figure 5.9: Sketch of the depletion of cupric ion concentration within the boundary layer.

Equation 5.18 is solved subject to the boundary conditions:

(0, ) = (5.19)

퐶퐶퐶( , 0푧) = 0퐶 퐶퐶 (5.20)

퐶퐶퐶( 푡, ) = (5.21)

The concentration gradient 퐶is퐶퐶 related푡 훿 to the퐶퐶퐶 current density by:

= (5.22) 퐶� 2+ 푑퐶 퐶퐶 푖 𝑛� 푑� �푧=표 The transient current density is given by the series solution:

= [ ] 1 + 2 (5.23) �푛푛 퐵𝐵� ∞ 2 푡 𝑡 푖퐶퐶 훿 퐶퐶 � ∑푚 푒푒푒 �−푚 훽�� = m Where 2 ; and is a non-zero positive integer. For short times, when 훿 2 훽 휋 � 1 (5.24) 푡 훽 ≪ Equation 5.23 can be simplified:

= (5.25) � 𝑡 푖퐶퐶 𝑛∆퐶퐶퐶�휋� Typically to assume good approximation of eq. 5.23 by eq. 5.25 is specified to 푡 훽 be smaller than 1, as indicated by eq. 5.24. However, Vetter [12] has shown that as long as < 3, the approximation given by eq. 5.25 is within 10 % of the eq. 5.23. 푡 훽 The trend of equation 5.23 is shown schematically in figure 5.10.

10 9 8 7 6 5 4 3 2 tc 1 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 time, s

Figure 5.10: Sketch of the transient response of the Cottrell equation.

Figure 5.10 shows that at short times the rates are time-dependent and much higher than the steady-state conditions. On the other hand, at longer times the system reaches steady-state; as a result, the Cottrell equation can be considered as that describing the current density at short times, replacing the steady-state Levich equation.

The time period over which the higher rates predicted by the transient Cottrell equation must be applied is equal to the depletion time of a fresh volume element which has reached the surface before it is replenished by a new bubble sweeping the same site.

We will designate this time, which will be determined later, as . Since the Cottrell

푐 equation indicates a varying current over the period , the average푡 high rates within the

푐 time interval must be determined by integrating a time푡 -average:

푡푐

0 = 푡� 퐷 = 2 (5.26) 퐶퐶� ∫ 𝑛∆퐶 휋�푑� 퐷 푡푡 〈푖퐶퐶 〉 푡� 𝑛∆퐶퐶퐶�휋푡� We are interested in the enhancement ratio of the current densities, , given by the

ratio of the high, time-averaged, transient current over the period to the휀 steady-state

푐 current density given by the Levich equation: 푡

= = 1.82 (5.27) 퐶�, 〈� 𝑡〉 2훿 −1⁄6 −1⁄2 1⁄6 −1⁄2 푐 휀 ≡ �퐶� 퐿𝐿 �휋�푡푐 퐷 휔 휐 푡 It should be noted that the current density ratio given by cannot be directly

measured and is not equal to the currents ratio which is measured onε the RDE, and has

been designated as Φ. The difference is due to the fact that not the entire RDE surface

experiences the enhanced current density as described by the transient Cottrell equation.

The electrode surface incorporates, as described in figure 5.3, a number of different regions, some swept by bubbles while others are not, with each providing a different current density. Prior to carrying out this current balance, we must, however, determine the transition time, .

푐 푡

5.5. Determination of the Characteristic Transition Time, :

푐 푡

In order to apply equation 5.26 or 5.27 we need to determinate if the following

relationship applies < 3 to assume that the equation 5.25 is within 10 % of 5.23. 푡푐 훽 However it is not easy to experimentally evaluate . Therefore, we carried calculations

푐 to estimate if is smaller than . Applying the von푡 Karman velocity in radial direction,

푐 it is possible to푡 obtain the average훽 time for bubble to reach disk circumference, , .

푎푎푎 푡푡�𝑛 Equation 5.4 can be written in a differential form as follow: 푡

= = (5.28) 3⁄2 −1⁄2 푑� 푣�푑� �휔 휐 푧𝑧� Integrating 5.27 we obtain:

= ( ) (5.29) �2 3⁄2 −1⁄2 푙� ��1� �휔 휐 푧 푡2 − 푡1 Equation 5.29 requires the swept average distance of a bubble on the disk in order

to set the values on r1 and r2. Equations 5.42 through 5.45, discussed latter, describe the

method for obtaining r1. r2 corresponds to the rim of the disk, rdisk. Accordingly, =

1 ; = ; and = . Equation 5.29 can then written as: � 2�푑푑푑� 푅푐 3 �2 �푑𝑑� 푧 2 . , = (5.30) 0 81093 3⁄2 −1⁄2 푡푎푎푎 푡푡�푡푡 푎∙푅푐∙휔 ∙휐 In equation 5.30 it is assumed that bubbles translate at about the same speed of the

flow. Numerical values of , , as indicated by equation 5.30, are shown in table

푎푎푎 푡푡�푡푡 5.1. 푡

Pulse experiments indicated that the copper current reaches steady-state in a time

of the order of a few seconds at 100 rpm to a fraction of a second at 400 and 900 rpm.

Since we already mentioned the difficulties in obtaining tc, we derive this critical time

indirectly by carrying a mass balance on the hydrogen bubbles that are swept past the

disk. We determine first the number or volume of hydrogen bubbles that exit from the

disk (at its circumference) and we match this, implying steady-state assumption, to the volume or number of hydrogen bubbles generated on the disk at any given time. Visual observations provide the number of bubbles on the electrode and their average size and volume under the experimental conditions, and thereby we can estimate the time that

takes a bubble to nucleate and grow, which is equal to . This procedure is outlined

푐 below. 푡

ω Axial Area 풅�풅� 풓

�푩�푩푩𝑩 Disk Bubble Figure 5.11: Sketch of the system used for carrying a mass balance on bubbles that are

exiting from the disk electrode.

The fluid egressing from the disk in a radial direction carries with it the bubbles.

We conduct a mass balance on the fluid + bubbles crossing a virtual boundary area

surrounding the circumference of the disk, with a height of the average hemispherical

bubble, . This area is:

푐 푅 = 2 (5.31)

푎𝑎푎� 푑𝑑� 푐 The fluid crossing this area퐴 carries with휋� it 푅bubbles at the rate of:

= (5.32) 퐵𝐵𝐵𝐵 � � 푏�푏푏𝑏� 푎𝑎푎� The radial velocity, , is given by the푣 ∙ 퐶radial component∙ 퐴 of the von Karman

� equation, 5.4, when substituting푣 in it the radial position r and the average height

disk 2.

푐 푅 ⁄ The bubble concentration is given by dividing the number of bubbles on the disk

at any given time, , by the control volume within the analyzed circumference:

푁 99

= (5.33) 푁 2 퐶푏�푏푏𝑏� 휋�푑푑푑�푅푐 After substitutions we get the rate at which bubbles exit the disk region:

= 2 = (5.34) 퐵𝐵𝐵𝐵 푅푐 휔 푁 휔 2 � �𝑎�푑𝑑� � 2 � �휐 � ∙ 휋�푑푑푑�푅푐 ∙ 휋�푑𝑑�푅푐 휔�푅푐 ��휐 � The rate given by eq. 5.34 must, under steady-state, be equal to the rate of bubble generation. The inverse of equation 5.34, after first dividing it by the number of bubbles,

, provides the average time for bubble generation, assuming that steady-state prevails.

This푁 time is also the characteristic time, , at which bubbles follow one another and

푐 hence equal to the depletion time of a volume푡 element before it is replenished by fresh

solution. Accordingly,

= 1⁄2 (5.35) 휐 3⁄2 푡푐 푎∙푅푐∙휔 The values of the average time for bubble to reach disk circumference, , ,

푎푎푎 푡푡�푡푡 the characteristic time of bubble generation, , and for the rotation rates studied푡 are

푐 shown in table 5.1. 푡 훽

As noted, the indicated times are of the order of 1 second, in agreement with the

transition times observed in the pulsing experiments. Table 5.1 also indicates that the

average time for bubble to reach disk circumference, , , and the characteristic

푎푎푎 푡푡�푡푡 time of bubble generation, decrease with the rotation 푡rate. Furthermore, the ,

푐 푡푡�푡푡 and ratios provide values푡 that are smaller than 3. This implies that the푡 current⁄훽

푐 density푡 ⁄ of훽 the transients as indicated by the approximate equation 5.23 is within 10 % of

the current density predicted by the Cottrell equation 5.26. Thus the truncation of the

series, as given by equation 5.23 is valid.

100

Table 5.1: Calculations of the average time for bubble to reach disk circumference,

, , the characteristic time of bubble generation, , and for different rotation

푎푎푎 푡푡�푡푡 푐 푡rates. 푡 훽

ω t , s t , s t t 50 0.950 1.171 0.634 1.497 1.847 trans c β trans⁄β c⁄β 70 0.610 0.753 0.453 1.347 1.661 100 0.369 0.455 0.317 1.164 1.435 150 0.241 0.297 0.211 1.138 1.403 400 0.074 0.092 0.079 0.937 1.155 900 0.042 0.052 0.035 1.200 1.479

Finally, using equations 5.26 and 5.27 with the substitution of as given by equation

푐 5.35, it is possible to rewrite the theoretical mass transfer enhancement푡 as:

= (1.82 ) (5.36) 1⁄2 −1⁄6 −1⁄12 1⁄2 1⁄4 푐 Equation 5.36 incorporates휀 R ;� which∙ 퐷 can 휐be substituted푅 휔 by the empirical equation

. c , = 0.0306 as indicated by correlating the data in figure 5.6. −0 4074 푐 푎푎푎 푅 휔

5.6. The Modelled Transport Enhancement:

The disk electrode incorporates three regions, as shown schematically in Fig 5.3:

1. A is the portion of the disk which is being swept by the translating bubbles and as

Swept a result experiences the higher current density of the transients.

2. A is the region on the disk that is covered by bubbles at any given time and

bubbles therefore acts as an insulating surface, passing no current.

3. A is the portion of the disk which is never swept by a bubble and hence

Not−Swept provides current that corresponds to the steady-state Levich equation.

101

Accordingly, the total current to the disk is given by:

= + (5.37)

퐼퐶퐶 �퐴푆𝑆𝑆 − 퐴퐵𝐵𝐵𝐵� ∙ 〈푖퐶퐶𝑡 〉 퐴푁𝑁−푆𝑆𝑆 ∙ 푖퐿𝐿 The first term on the right of Eq. 5.37 specifies that we need to subtract from the

swept area the area that is covered by bubbles and which carries no current at any given

time.

The second term on the right accounts for the area of the disk that is never

covered by bubbles:

= (5.38)

푁𝑁 푆𝑆𝑆 푑𝑑� 푆𝑆𝑆 The swept area is illustrated퐴 schematically퐴 − in퐴 Fig. 5.12 and can be estimated by:

= (5.39)

푆𝑆𝑆 Where N is the total number퐴 of bubbles푁 at∙ 퐿 any∙ 푊 given time on the electrode, L is the

path length, and W the width. In setting eqn. 5.37 it has been assumed that each bubble

has its own path and that once a bubble had started translating, a new bubble will

nucleate and start translating along the same path, , seconds later. Accordantly, any site

푐 along the swept path will be swept every , seconds.푡 We implicitly assume here, that the

푐 translation time is short compared to the stationary푡 nucleation time. If the nucleation time

is short with respect to the translation time, we may overestimate the swept area, since numerous bubbles may occupy the same swept path at any given time. This assumption will be checked later.

102

= 2 Swept 푊 푅푐

퐿

Bubble

Figure 5.12: Sketch of the swept path of bubbles on the electrode surface. L is the average bubble path length from the initial average bubble position to the circumference of the disk.

To estimate the average length of the swept path we need to describe this spiral path mathematically. The function can be obtained from the first term of the von Karman velocities indicated by equations 5.4 and 5.6 as shown in Appendix C.

The length of the spiral path (Appendix C) is given by:

= ( ) (5.40)

푑𝑑� 1 Here, is the initial bubble퐿 position퐵 � and− � is a constant given by:

�1 퐵

. . 1 + = 1 + = 1.5679 . . (5.41) 푏 푎 2 0 6159 0 51023 2 푎 � 푏 0 51023 � 0 6159 퐵 ≡ � � � �

As noted the spiral path is longer that the radial distance by about 1.5 times.

To estimate the initial position , we need to know the average radial position of the

1 bubbles on the disk. In order to� derive the average radial position of the bubble on the disk, we make use of the following general relationship.

103

( , ) = 푏 푑 (5.42) ∫푅 𝑓� ∫푎 ∫푐 � � 휑 푑� 퐴푑푑푑� 퐴푑푑�� Equation 5.42 is a ratio of the area integral divided by the area of the disk; here

the area element is the differential section of the disk: dA = rd dr. In order to satisfy eq. 5.42 we set ( , ) = φ

Accordingly:푓 � 휑 �

3 3 3 = = = [2 0] = (5.43) 3 �푑푑푑� �푑푑푑� 2휋 2 2휋 � 2휋 �푑𝑑� �푑𝑑� 2휋�푑𝑑� ∫0 ∫0 � 푑�푑휑 ∫0 � 3 �0 � 푑� ∫0 3 푑� 3 휋 − 3 Substituting this in 5.42.

( ) = = 2휋푟3 = 2휋푟3 = = 푑푑푑� 푑푑푑� 3 (5.44) ∫푅 𝑓� 3 3 2휋�푑푑푑� 2�푑푑푑� 2 2 �푎푎푎 푓𝑓� 푡ℎ푒 𝑐푐𝑐� 퐴푑푑푑� 퐴푑푑푑� 휋�푑푑푑� 3휋�푑푑푑� 3 Equation 5.44 indicates that the averages distance of the bubbles from the center

is . However, we are interested in the average distance from the circumference 2�푑푑푑� 3 which is given by 5.45

( ) = = (5.45) 2�푑푑푑� �푑푑푑� 푎푎푎 푑𝑑� The total� path푓𝑓� lengths푡ℎ푒 𝑐𝑐�covered푐𝑐𝑐 by N푐 𝑐bubbles� streaks− 3are giving3 by:

= = ( ) ( ) = (2 ) { } = �푑푑푑� �푑푑푑� 푁 2 퐿푁 ⟨푁 ∗ 퐿⟩ ∫0 푁 � ∗ 퐿 � 푑� ∫0 휋𝜋� �휋�푑푑푑�� 퐵 �푑𝑑� − �1 = (5.46) 2 3 �푑푑푑� 2푁� �푑푑푑�∙�1 �1 푁��푑푑푑� 2 �푑푑푑� � 2 − 3 ��1=0 3 Here, the integration covers the entire disk from = 0 to

1 푑𝑑� Therefore: � �

= = (5.47) 2푅푐푁��푑푑푑� 푆𝑆𝑆 3 Where was taken as 2 .(Fig.퐴 5.12).푁 ∙ 퐿 ∙ 푊

푊 푅푐

104

Once we have the value of the average swept path by the bubbles we need to determine the total area of the bubbles on the disk, :

퐵𝐵𝐵𝐵 = 퐴 (5.48)

퐵𝐵𝐵𝐵 푑𝑑� Here, is the fraction of the disk퐴 surface퐴 coverage휃 by bubbles. Since there are N bubbles, each θcovering an area of we can relate theta to N: 2 휋푅푐 = 2 (5.49) 푁�푅푐 휃 퐴푑푑푑� By substituting equations 5.38, 5.47 and 5.48 in equation 5.37 we obtain:

= + (5.50) 2푅푐푁��푑푑푑� 2푅푐푁��푑푑푑� 𝑡 퐼퐶퐶 � 3 − 퐴푑𝑑�휃� ∙ 〈푖퐶퐶 〉 �퐴푑𝑑� − 3 � ∙ 푖퐿𝐿 Equation 5.50 can be factorized by :

퐴푑𝑑� ∙ 푖퐿𝐿

= + 1 (5.51) 2푅푐푁� 〈�퐶�, 𝑡〉 2푅푐푁� 퐶퐶 푑𝑑� 퐿𝐿 퐼 퐴 ∙ 푖 ��3휋�푑푑푑� − 휃� ∙ �퐶� 퐿𝐿 � − 3휋�푑푑푑�� Substituting the values for the disk radius ( = 0.317 ), , L (from eq.

푑𝑑� 5.40), and (as given by eq. 5.49) into equation 5.51 �gives. 𝑐 퐵

휃 . . = 1 1 (5.52) 0 1 0 1 퐼퐶퐶 퐴푑𝑑� ∙ 푖퐿𝐿 ��푅푐 − � ∙ 휃 ∙ 휀 − �푅푐 휃 − �� Here, must be specified in cm.

푅푐 In terms of the enhancement ratio, , equation 5.52 gives:

, , Φ . . = = 1 1 (5.53) 퐼퐶� 𝑚𝑚𝑚�, 퐼퐶,� 𝑚𝑚𝑚� 0 1 0 1 Φ ≡ 퐼퐶� 퐿�퐿𝐿ℎ �퐶� 퐿�퐿𝐿ℎ∙퐴푑푑푑� ��푅푐 − � ∙ 휃 ∙ 휀 − �푅푐 휃 − �� Finally, equation 5.53 can be simplified to:

. = ( 1) + (1 ) (5.54) 0 1 Φ ��푅푐 휃� 휀 − � − 휃� 105

Equation 5.54 describes the enhancement factor that we can quantify and compare

to experimental results.

5.7. Transport Enhancement – Discussion and Comparison with Experiments:

Comparing the enhancement factor obtained using different experimental

methodologies as described in chapter 3, and 4 to the modeled enhancement factor as

described by equation 5.54, we note generally a reasonable good agreement. This

comparison is shown in figures 5.13 – 5.15. The enhancement factor predicted by the model agrees particularly well with the experimental enhancement data at the lowest rotation rate tested (100 rpm, fig. 5.13). Figures 5.13 – 5.15, indicate decreasing enhancement factor, (experimentally measured and modeled) with increasing rotation

rate. This might be due to a decrease in the surface coverage by the bubbles at high

rotation rates. As a result, less volume of the electrolyte solution is replaced on the

surface at higher rotation rates. At mid and higher rotation rates the model overestimate

the enhancement factor with respect to experimental data. It should be emphasized that

should not exceed . However, while the maximal values from are about 3.3 or less, weΦ

note maximal values,휀 both experimental and modeled, in range휀 of 6-8. The reason for

this discrepancyΦ may be due to a number of reasons or a combination of them.

1. The model as discussed above, does not account for a number of bubbles

following the same trajectory. All bubbles noted in the photographs are

counted and each designated its own trajectory. However, a number of

bubbles may have overlapping trajectories. This leads to an overestimate the

106

enhancement by a factor of about 1.5. This approximate figure is based on

comparing the estimated translation time of the bubbles to the nucleation time

and accounting for the bubbles distribution on the disk. Then, the fraction of

bubbles with regions that corresponds to multiple time constants of is 푡 푡푐 estimated.

2. The surface coverage by the bubbles, as determined from the photographs,

might have been overestimated, particularly at higher rotation rates.

3. The model assumes that the bubbles are distributed evenly across the disk in a

circular ring of bubbles. Therefore in this assumption all bubbles have the

same average translation velocity. In reality the bubbles that are near the

center move significantly slower than the bubbles that are closer to the disk

circumference.

107

9 Φ(pol)exp 8

7 Φ(pulse) Φ(wt)exp 6 Φ(model) 5 Factor 4

2 100 RPM 1

Enhancement 0 -1.05 -1 -0.95 -0.9 -0.85 -0.8 -0.75 -0.7 -0.65 -0.6 -0.55 -0.5 -0.45 E, V/SHE

Figure 5.13: Comparison of modeled enhancement factor with experimental enhancement

factors at 100 rpm. Blue diamonds correspond to the weight measurements data. Green

triangles indicate the pulse experiments where Φ(pulse) is given by ICu-pulse/ILevich. Red squares designated the enhancement factor based on polarization data. The purple solid line corresponds to the model as described by equation 5.54. The electrolyte is 200 mM

CuSO4 at pH ≈ 0. No IR correction is applied to the data. In the pulse experiment, the

hydrogen evolution had been discontinued after 8 sec.

108

Φ(pol)exp Φ(model) 5 Φ(wt)exp

Factor Φ(pulse) 4

2 400 RPM 1 Enhancement

0 -1.05 -1 -0.95 -0.9 -0.85 -0.8 -0.75 -0.7 -0.65 -0.6 -0.55 -0.5 -0.45 E, V/SHE

Figure 5.14: Comparison of modeled enhancement factor with experimental enhancement

factors at 400 rpm. Blue diamonds correspond to the weight measurements data. Green

CuSO4 at pH ≈ 0. No IR correction is applied to the data. In the pulse experiment, the

hydrogen evolution had been discontinued after 8 sec.

109

5 Φ (pulse) Φ(model) 4 Factor

Φ(pol)exp 3 Φ(wt)exp

1 900 RPM Enhancement

0 -1.05 -1 -0.95 -0.9 -0.85 -0.8 -0.75 -0.7 -0.65 -0.6 -0.55 -0.5 -0.45 E, V/SHE

Figure 5.15: Comparison of modeled enhancement factor with experimental enhancement factors at 900 rpm. Blue diamonds correspond to the weight measurements data. Green triangles indicate the pulse experiments where Φ(pulse) is given by ICu-pulse/ILevich. Red squares designated the enhancement factor based on polarization data. The purple solid line corresponds to the model as described by equation 5.54. The electrolyte is 200 mM

CuSO4 at pH ≈ 0. No IR correction is applied to the data. In the pulse experiment, the

hydrogen evolution had been discontinued after 8 sec.

Figures 5.16 - 5.18 show the enhancement factor for the lower cupric

concentration of (20 mM). Excellent agreement is noted for the 100 RPM data (Fig.

5.16). At the higher rotation rates, (400 and 900 RPM; Figs. 5.17 and 5.18) the model

over-predicts the enhancement, however, the trend of the lines are preserved.

110

In both cupric concentrations at a given rotation rate, the trend of the mass transfer enhancement as indicated by the model and experiments shoe a decrease in slope and approach a plateau at the most negative potentials.

7 Φ(wt)exp 6 Φ(model)

5 Φ(pulse)

Factor Factor 4

2 100 RPM 1 Enhancement

0 -1.05 -1 -0.95 -0.9 -0.85 -0.8 -0.75 -0.7 -0.65 -0.6 -0.55 -0.5 -0.45 E, V/SHE

Figure 5.16: Comparison of modeled enhancement factor with experimental enhancement

factors at 100 rpm. Blue diamonds correspond to the weight measurements data. Green

CuSO4 at pH ≈ 0. No IR correction is applied to the data. In the pulse experiment, the

hydrogen evolution had been discontinued after 8 sec.

111

Φ(wt) 5 exp Φ(model) Φ(pulse) h

Factor Factor 4

Enhancement 1 400 RPM

0 -1.05 -1 -0.95 -0.9 -0.85 -0.8 -0.75 -0.7 -0.65 -0.6 -0.55 -0.5 -0.45

E, V/SHE

Figure 5.17: Comparison of modeled enhancement factor with experimental enhancement

factors at 400 rpm. Blue diamonds correspond to the weight measurements data. Green

CuSO4 at pH ≈ 0. No IR correction is applied to the data. In the pulse experiment, the

hydrogen evolution had been discontinued after 8 sec.

112

Φ 4 (model) Φ(pulse) Φ(wt)exp Factor Factor

1 Enhancement 900 RPM 0 -1.05 -1 -0.95 -0.9 -0.85 -0.8 -0.75 -0.7 -0.65 -0.6 -0.55 -0.5 -0.45 E, V/SHE

Figure 5.18: Comparison of modeled enhancement factor with experimental enhancement

factors at 900 rpm. Blue diamonds correspond to the weight measurements data. Green

CuSO4 at pH ≈ 0. No IR correction is applied to the data. In the pulse experiment, the

hydrogen evolution had been discontinued after 8 sec.

5.8. References:

[1] P. V. Danckwerts, "Significance of Liquid-Film Coefficients in Gas Absorption,"

Industrial & Engineering Chemistry, vol. 43, pp. 1460-1467, (1951).

113

[2] R. Higbie, "The rate of absorption of pure gas into a still liquid during short

periods of exposure," Transactions of the American Institute of Chemical Engineers, vol.

31, pp. 365, (1935).

[3] T. V. Kármán, "Über laminare und turbulente Reibung," ZAMM - Journal of

Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und

Mechanik, vol. 1, pp. 233-252, (1921).

[4] W. G. Cochran, "The flow due to a rotating disc," Mathematical Proceedings of the Cambridge Philosophical Society, vol. 30, pp. 365-375, (1934).

[5] E. M. Sparrow and J. L. Gregg, "Mass Transfer, Flow, and Heat Transfer About a

Rotating Disk," Journal of Heat Transfer, vol. 82, pp. 294-302, (1960).

[6] W. B. Krantz, "Scaling Analysis in Modeling Transport and Reaction Processes",

John Wiley and Sons, pp. 79-84, (2007).

[7] E. Pierce, F. J. Carmona, A. Amirfazli, "Understanding of sliding and contact angle

results in tilted plate experiments", Colloids and Surfaces A: Physicochem. Eng. Aspects

323 (2008) 73-82.

[8] C. G. L. Furmidge, "Studies at Phase Interfaces I. The Sliding of Liquid Drops on

Solid Surfaces and a Theory for Spray Retention", Journal of Colloid Sciences, vol.17, pp. 309-324, (1962).

[9] R. B. Bird, W. E. Stewart, E. N. Lightfoot, "Transport phenomena", John Wiley and Sons, (1960).

114

[10] D. Legendre, C. Colin, and T. Coquard, "Lift, Drag and Added Mass of a

Hemispherical Bubble Sliding and Growing on a Wall in a Viscous Linear Shear Flow,"

Philosophical Transactions: Mathematical, Physical and Engineering Sciences, vol. 366, pp. 2233-2248, (2008).

[11] F. G. Cottrell, "Residual current in galvanic polarization, regarded as a diffusion

Problem", Z. Phys. Chem., vol. 42, pp. 385-431, (1903).

[12] K.J. Vetter, "Electrochemical kinetics: theoretical and experimental aspects,"

Academic Press, pp. 213-219 (1968).

115

Chapter 6: Conclusions and Suggestions for Future Work.

6.1 Conclusions:

The mass transport enhancement on RDE in region of gas co-evolution has been observed and quantified (~2-6 fold) for two cupric ions concentrations (20 and 200 mM) by direct polarization, from weight measurements, and pulse experiments. However, the methodology used to quantify the mass transfer enhancement based on polarization data provided uncertainties at the lower cupric concentration, (20 mM) because the small copper current at this concentration was derived by subtracting two large and noisy signals.

Pulse experiments, where the current decay was measured following a short bubble generation confirmed the linkage between the current enhancement and the presence of bubbles. Furthermore, the ratio, ICu-Max / ILevich, in the pulse experiments, provided good agreement with the enhancement factor determined in gravimetric experiments.

The enhancement observed in the experiments decreased with the rotation rate.

This might be due to the fact that the surface coverage by bubbles is larger at lower rotation rates and therefore, more bubbles are displacing more solution, or that these bubbles are larger in size and bring more bulk electrolyte to the surface. In addition, the enhancement factor levels off at the most negative potentials for all rotation rate and concentration tested. This suggests that the enhancement would reach a plateau at the potentials more negative than 1.0 V.

116

A model based on fresh electrolyte replenishing the volume vacated by the

translating bubbles and thus subjecting regions of the electrode to enhanced transient

currents, is presented. The semi-empirical model correlates the experimental data reasonably well, indicating higher enhancement with increasing cathodic polarization.

6.2. Suggestions for Future Work:

Additional experiments should be done with different disk areas than the area used in this study. This in order to verify the analysis used to determine the bubble swept path. Furthermore, more experiments should be done for a larger disk area in order to distinguish if the radius of the bubble changes with the position.

It is recommended to repeat the experiments on a camera with a fast exposure time, as well as for higher resolution in order to more accurately measure the mean bubble radius and the surface coverage at 400 and 900 rpm.

Precise ohmic drop measurement between the disk and the reference electrodes must be carried out with and without the presence of bubbles, to enable reliable IR correction. Such measurement can be done using fast current steps (‘IR interrupt’ method) or by frequency impedance technique. To eliminate the possibility of contamination of the solution with the dissolution of the counter electrode, it is recommended to use copper as the anode. This will prevent the reduction of traces of anode that can be produced in the working electrode. The counter electrode has to be

117 located at the bottom of the cell or surround symmetrically the disk electrode to provide a uniform current distribution on the disk.

The model predicts well the enhancement at 100 RPM, and exhibits the correct trends for the enhancement at the higher rotation rates (although it overestimates the enhancement at those rates). However, the model is semi-empirical, utilizing the measured surface coverage by the bubbles and the empirical correlation between the bubble radius and the rotation rate. More experiments should be done to verify if the model applies over broader composition ranges, or metals other than copper. Likewise, it is recommended to test if the model predicts an enhancement under different conditions such as in experiments with different chemistry where the pH is changed, as well as in presence of additives that can function as inhibitors for hydrogen evolution.

Finally the model can be improved by reducing the assumptions as discussed in chapter 5.

118

Chapter 7: Nomenclature.

= 0.51023 von Karman velocity constant.

� : Bubble acceleration.

푏 �: Geometric area of the electrode.

퐴 : Axial area used in determining the rate of bubble detachment (circumference of

푎𝑎푎� 퐴the disk times the average high of bubbles).

: Total area of all bubbles on the disk electrode.

퐵𝐵𝐵𝐵 퐴 : Disk electrode area (0.317 cm ). 2 푑𝑑� 퐴 : Disk area not swept by bubbles.

푁𝑁 푆𝑆𝑆 퐴 : Rough electrode area.

𝑟𝑟ℎ 퐴 : Smooth electrode area.

푆𝑆𝑆ℎ 퐴 : Average swept path of a bubble on the electrode.

푆𝑆𝑆 퐴 = -0.6159 von Karman velocity constant.

� 1 + = 1.5679, a constant. 푏 푎 2 퐵 ≡ 푎 � �푏� : Constant of integration.

퐶 : Bubble concentration on the disk.

푏�푏푏𝑏� 퐶 : Cupric concentration. 2+ 퐶퐶 [퐶 ] : Bulk cupric concentration. 2+ 푏𝑏푏 퐶퐶: Molecular diffusivity.

퐷 : Cupric ion diffusivity. 2+ 퐶퐶 퐷: Voltage applied.

퐸

119

: Standard Potential. 표 퐸: Faraday’s constant (96485C/equivalent).

퐹 : Drag force.

� 퐹 : Surface tension force.

푆푆 퐹 : Summation of all forces.

푡�푡 퐹( ): Series solution for the radial component in the von Karman solution of flow near a

퐹rotating휉 disk.

( ): Series solution for the angular component in the von Karman solution of flow near

a퐺 rotating휉 disk.

( ): Series solution for the axial component in the von Karman solution of flow near a

퐻rotating휉 disk.

: Copper current.

퐶퐶 퐼 : Copper current density.

퐶퐶 푖 : Copper transient current density. 2+ 퐶퐶𝑡 푖 : Average transient copper current density. 2+ 〈푖퐶퐶𝑡 〉 : Maximum copper current after bubble generation is discontinued in pulse

퐶퐶−푝𝑝𝑝 퐼experiments.

: Copper current at steady state after bubble generation is discontinued in pulse

퐶퐶−𝑠 experiments.퐼

: Copper current based on direct polarization method. 푝𝑝 퐶퐶 퐼 : Copper current based on weight measurement method. 푤� 퐶퐶 퐼 : Hydrogen current.

퐻2 퐼 : Hydrogen current density.

퐻2 푖 120

: Current density indicated by the Levich equation.

퐿𝐿𝐿ℎ 푖 : Limiting current density.

푙푙� 푖 : Total current on a rough electrode.

푅𝑅�ℎ 퐼 : Total current on a smooth electrode.

푆𝑆𝑆ℎ 퐼 : Total current.

푡�푡 퐼 : Total current density.

푡�푡 푖 : Mass transfer coefficient (cm s) in equation 1.1.

퐵 푘 : Fitting parameter, (dimensionless).⁄

푆푆 푘 : Constant in equation 5.13.

� 퐾 : Constant in equation 5.17.

� 퐾: Length of the swept bubble path.

퐿 : Bubble mass.

푚 : Copper molecular weight 63.546 . g 푐� mol 푀: Number of electrons participating� in the electrode� reaction.

� : Empirical exponent in equation 5.16.

� � : Numbers of bubbles on the disk electrode.

푁 : Cupric ion flux. 2+ 퐶퐶 푁: Radial coordinate.

� : Radius of the disk electrode (0.317cm ).

푑𝑑� � : Initial radial position of a bubble before it start to move.

1 � : (0.317cm ).

2 푑𝑑� � : �Radius of the bubbles.

푏 푅 : Mean bubble radius.

퐶 푅 121

: Electrolyte Resistance.

훺 푅 : Characteristic length (radius of the bubble) in equation 5.9.

푆푆 푅: Distance between two bubbles.

SD:� Standard variation.

: Time of electrodeposition.

∆푡 t: Translation time bubble from its initial position till it leaves the disk.

, : Average time for bubble to reach disk circumference.

푎푎푎 푡푡�푡푡 푡 : Characteristic time, (time of surface renewal).

푐 푡 : Average velocity of a bubble on the surface of the disk.

푎푎푎 푣 : Bubble velocity.

퐵𝐵𝐵� 푣 : Fluid velocity in r direction.

� 푣 : Fluid velocity in z direction.

푧 푣 : Fluid velocity in direction.

휑 푣 : Rotation velocityφ of the disk. 푑𝑑� 푣휑 : Flow velocity in direction. 𝑓𝑓 휑 푣 : Flow velocity to theφ disk in direction. 𝑟� 휑 푣 : Flow velocity in r and φ direction relative to disk. 𝑟𝑟𝑟𝑟 푉푉 푣 : Volumetric flow rate. φ 푔̇ 푉 : Width of the bubble swept path. Assumed equal to bubble diameter (= 2 )

푐 푊 : Weight difference of the electrode before and after electrodeposition. 푅

∆:푊 z-axis in cylindrical coordinates.

푧

122

Greek Letters:

: a parameter in equation 5.12.

훼푉푉: a parameter in equation 5.23.

훽: Surface tension ( 72 mN m).

휎 : Surface tension ≅forces in ⁄angular direction of the disk.

휑 휎 : Surface tension forces in radial direction of the disk.

휎 �: Enhancement factor defined in equation 5.27.

휀 : Dimensionless distance from the disk used in equations 5.1 – 5.3.

휉 : Activation overpotential.

휂푎: Concentration overpotential.

휂푐 : Ohmic drop in the electrolyte between the working and reference electrodes.

휂훺: Diffusion layer thickness.

훿 : Equivalent Nernst diffusion layer thickness.

훿푁 : -axis in cylindrical coordinates.

휑: φEnhancement factor defined as the ratio of the measured current to the theoretical currentΦ as predicted by Levich equation.

: Enhancement factor defined as the current obtained from polarization data divided 푝𝑝 �푒� Φby the theoretical current as predicted by Levich equation.

: Enhancement factor defined as the current obtained from weight measurement data 푤� �푒� dividedΦ by the theoretical current as predicted by Levich equation.

Φ(pulse): A ratio of the maximum copper current after bubble generation is discontinued

in pulse experiments divided the theoretical current as predicted by Levich equation.

123

: Electrical electrolyte conductivity.

휅 : Electrolyte viscosity ( 1 x 10-3 Pa s, N s/m2).

�: Pi number. ≅

휋: Fraction of the surface area coverage by bubbles.

휃 : Angular contact of the bubble to the surface( 90 ). o 휗푐�: Receding contact angle. ≈

휗푅: Advancing contact angle.

휗퐴: Kinematic viscosity of electrolyte (0.01 cm s). 2 휐 : Angular rotation rate (rad/s). ⁄

휔

124

Appendix A:

A.1. Polarization Data for Copper Deposition above the Limiting Current (Raw

Data without Ohmic Correction).

Figures A.1 and A.2 provide the total current density at different rotation rates for 20 and 200 mM CuSO4 at pH ≈ 0, respectively. The current densities were determined from

the total current reading of the potentiostat divided by the rough electrode area as

determined by the procedure described in chapter 2, applying the areas listed in Tables

3.1 and 3.2. It should be emphasized, however, that the total current densities reported

include both the current due to copper deposition and that associated with hydrogen co-

evolution. The current due to hydrogen evolution is absent at potential more positive than

zero, and as shown later, is negligibly small at potentials more positive than -0.4 V, but is

significant and dominant at potentials more negative than -0.4 V.

125

600

500 100-rpm

2 - 400 900-rpm 300 , mA cm

(tot) 400-rpm i

- 200

100 (A)

0 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

E, V / SHE

Figure A.1: Polarization curve for 20 mM CuSO4 at pH ≈ 0. Blue diamonds indicate the total current density at 100 rpm. Red squares correspond to the total current density at

126

700 400-rpm 600

2 - 500

400 100-rpm 900-rpm , mA cm 300 (tot) i - 200

100

0 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

E, V / SHE

Figure A.2: Polarization curve in 200 mM CuSO4 at pH ≈ 0. Blue diamonds designate the total current density at 100 rpm. Red squares correspond to the total current density at

400rpm. Green triangles indicate the total current density at 900 rpm. The surface area applied in determining the current density is the actual rough deposited and it is reported in table 3.2.

Discussion of this data, after correction of the IR drop, is provided in Ch3.

A.2 Copper Deposition Rates Determined from Current Measurements (data for 20 mM cupric ion concentration – “dilute electrolyte”).

This hydrogen current is plotted in Figs. A.3, A.4 and A.5 for the 20 mM cupric electrolyte together with total current, both currents represented in terms of the common applied voltage V-IR. The plotted hydrogen current was then subtracted from the total

127

current to yield the copper current on the rough electrode, as also shown in Figs. A.3,

A.4, and A.5 for 100, 400 and 900 rpm; respectively.

205

180 100 RPM I(H2) 155

130 I(tot)

105

55 I, mA

- I(Cu) 30

-20 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Voltage (IR compensated), V / SHE

Figure A.3: Polarization curve of 20 mM CuSO4 at pH ≈0 at 100 rpm. Blue diamonds

correspond to the total current. Red triangles indicate the hydrogen current. The green

squares depict the copper current obtained by the subtraction of the hydrogen current

from the total current.

128

205

180 400 RPM I(tot) 155

130 I(H ) 105 2

80 I(Cu) I, mA

- 55

-20 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Voltage (IR compensated), V / SHE

129

230 900 RPM I(tot)

180

I(H2)

130

I(Cu) 80 I, mA -

-20 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Voltage (IR compensated), V / SHE

Figure A.5: Polarization curve of 20 mM CuSO4 at pH ≈ 0 at 900 rpm. Blue diamonds

correspond to the total current. Red triangles indicate the hydrogen current. The green

squares depict the copper current obtained by the subtraction of the hydrogen current

from the total current.

As discussed in Chapters 3 and 4, the method by which these copper current densities incorporated high inaccuracies. The copper current density was obtained by subtracting from the total measured current the hydrogen current (which was obtained in a separate experiment). Both those currents displayed large fluctuations due to the presence of the bubbles. The measured copper current density, which was the difference between the two, amounted to only about 6% of the signal and was therefore highly inaccurate. These measurements are not discussed further in the thesis.

130

Appendix B:

Pulse Generation of Bubbles – Linking Bubbles Presence to Transport

Enhancement.

Figure B.1 describes similar experiments to that shown in figure 3.18 in chapter 3 but at higher rotation rate, of 70 rpm. Figure A.1 offers the same conclusion as figure

3.18. Table B.1 indicates that even though the Ipulse/ILevich ratio defined as enhancement factor, increases with the negative potential, the values of the enhancement factor are not higher than the values observed at 50 rpm and displayed in table 3.5.

131

t, seconds 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0

-50 -0.65V

-100 -0.8V I, mA -150 -0.9V

-200 -1.0V -250

Figure B.1: Current trace for pulse experiments in 20 mM CuSO4 at pH ≈ 0; 70 rpm. The currents on the left (A) correspond to mainly hydrogen bubble generation (and some copper plating) at the listed highly negative potentials for 8 seconds. After 8 seconds, the potential was rapidly stepped to -0.2 V where hydrogen was no longer generated but plating of copper continues. (B) Magnified view of the region in (A) in the time region when the generation of bubbles was discontinued by switching the potentiostat to -0.2 V.

132

Table B.1: Parameters obtained from the pulse experiments of figure B.1; 20 mM CuSO4

at pH ≈ 0 at 70 rpm. Time of bubble generation was 8 seconds at the listed potentials.

Current predicted by the Levich equation = -1.293 mA.

(A) Bubble generation region. (B) Transport response after bubble generation is discontinued. Φ(pulse), I bubble time to reach time to reach generation steady-state -ICu-pulse -I ss ICu-pulse /ILevich steady-state E I (H2)+I(Cu) V/SHE mA sec mA mA sec -0.2 no bubbles ------1.68 --- 1.5 -0.65 -37.29 3.44 3.669 1.658 2.84 1.5 -0.8 -76.74 3.55 5.871 2.126 4.54 1.9 -0.9 -130.67 3.46 7.034 2.039 5.44 1.9 -1 -180.76 4.63 8.044 2.309 6.22 1.9

Figure B.2 shows data corresponding to pulse experiments similar to that of figure

B.1, however, the rotation rate was changed to 100 rpm.

133

t, seconds 0 2 4 6 8 10 12 14

-0.2V -25

-0.8V -0.65V -75

I, mA -125

-0.9V -175

-225 -1.0V

Figure B.2: Current trace for pulse experiments in 20 mM CuSO4 at pH ≈ 0 at 100 rpm.

The currents on the left (A) correspond to mainly hydrogen bubble generation (and some copper plating) at the listed highly negative potentials for 8 seconds. After 8 seconds, the potential was rapidly stepped to -0.2 V where hydrogen was no longer generated but plating of copper continues. (B) Magnified view of the region in (A) in the time region when the generation of bubbles was discontinued by switching the potentiostat to -0.2 V.

134

Table B.2: Parameters obtained from the pulse experiments of figure B.2; 20 mM CuSO4 at pH ≈ 0 at 100 rpm. Time of bubble generation was 8 seconds at the listed potentials.

Current predicted by the Levich equation = -1.545 mA.

(A) Bubble generation region. (B) Transport response after bubble generation is discontinued. Φ(pulse), I bubble time to reach time to reach generation steady-state -ICu-pulse -I ss ICu-pulse /ILevich steady-state E I(H2)+I(Cu) V/SHE mA sec mA mA sec -0.2 no bubbles ------2.19 --- 1.5 -0.65 -32.25 2.01 2.709 2.496 1.75 0.2 -0.8 -94.09 2.05 7.352 2.516 4.76 1.7 -0.9 -128.36 2.03 7.498 2.12 4.85 1.5 -1 -167.66 2.01 8.178 2.771 5.29 1.5

The current read in the first eight seconds as listed in figure B.2 displays larger noise as the potential is more negative at 100 rpm. This noise can be associated to the possibility of increasing bubble density on the electrode causing larger fluctuations. By

comparing the column of the Ipulse/ILevich ratio of tables B.2 and table B.1 we can observe that both increase at negative potentials, but the enhancement factor values listed in table

B.2 are smaller than those in table B.1.

In figures 3.18, B.1 and B.2 the hydrogen generation portion of the pulse lasted 8 seconds. Figures B.3 and B.4, show data for hydrogen generation of 1 and 2 seconds, respectively at 20 mM CuSO4 at pH ≈ 0 and 100 rpm. These two experiments have been compared with figure B.2 in order to evaluate the effect of the bubble generation time.

135

t, seconds 0 1 2 3 4 5 0 -20 -0.2V -40 -60 -0.65V

-80 -100 -0.8V I, mA -120 -140 -0.9V -160

-180 -1.0V -200

Figure B.3: Current trace for pulse experiments in 20 mM CuSO4 at pH ≈ 0 at 100 rpm.

The currents on the left (A) correspond to mainly hydrogen bubble generation (and some copper plating) at the listed highly negative potentials for one second. After 1 second, the potential was rapidly stepped to -0.2 V where hydrogen was no longer generated but plating of copper continues. (B) Magnified view of the region in (A) in the time region when the generation of bubbles was discontinued by switching the potentiostat to -0.2 V.

136

Table B.3: Parameters obtained from the pulse experiments of figure B.3; 20 mM CuSO4

at pH ≈ 0 at 100 rpm. Time of bubble generation was one second at the listed potentials.

Current predicted by the Levich equation = -1.545 mA.

(A) Bubble generation region. (B) Transport response after bubble generation is discontinued.

Φ(pulse), I bubble time to reach time to reach generation steady-state -ICu-pulse -I ss ICu-pulse /ILevich steady-state E I(H2)+I(Cu) V/SHE mA sec mA mA sec -0.2 no bubbles ------2.19 --- 1.5 -0.65 -45.92 SS no reached 3.15 2.09 2.04 0.9 -0.8 -82.63 SS no reached 3.479 1.789 2.25 2.3 -0.9 -113.52 SS no reached 6.329 2.318 4.10 2.2 -1 -161.82 SS no reached 7.129 2.474 4.61 1.9

The table B.3 indicates that the time to reach the steady state in the bubble

generation had not been reached, this phenomena is noted in figure B.3. As a result the values of the ‘bubble generation current’ correspond to the magnitude of current reading at one second.

137

t, seconds 0 1 2 3 4 5 0 -20 -0.2V -40 -60 -0.65V -80

-100 -0.8V I, mA -120 -140 -0.9V -160 -180 -1.0V -200

Figure B.4: Current trace for pulse experiments in 20 mM CuSO4 at pH ≈ 0 at 100 rpm.

The currents on the left (A) correspond to mainly hydrogen bubble generation (and some copper plating) at the listed highly negative potentials for two seconds. After 2 second, the potential was rapidly stepped to -0.2 V where hydrogen was no longer generated but plating of copper continues. (B) Magnified view of the region in (A) in the time region when the generation of bubbles was discontinued by switching the potentiostat to -0.2 V.

138

Table B.4: Parameters obtained from the pulse experiments of figure B.4; 20 mM CuSO4

at pH ≈ 0 at 100 rpm. Time of bubble generation was 2 seconds at the listed potentials.

Current predicted by the Levich equation = -1.545 mA.

(A) Bubble generation region. (B) Transport response after bubble generation is discontinued.

time to reach Φ(pulse), time to reach I bubble generation steady-state -ICu-pulse -I ss ICu-pulse /ILevich steady-state E I(H2)+I(Cu) V/SHE mA sec mA mA sec -0.2 no bubbles ------2.19 --- 1.5 -0.65 -34.4 1.16 3.524 2.375 2.28 0.4 -0.8 -76.94 1.34 3.908 2.028 2.53 1 -0.9 -108.45 1.48 6.411 2.144 4.15 0.9 -1 -154.88 SS no reached 7.257 2.185 4.70 1.1

In table B.3, the values read of ‘bubble generation current' correspond to the magnitude of current reading at two seconds. Likewise at -1V/SHE, the time to reach the steady-state condition of bubble generation had not been reached. The values of table B.2 are somewhat greater than those in the table B.4, therefore, since both tables provide approximately the same values, it is possible to conclude that after two seconds steady-

state has almost been reached.

Additional experiments are shown in figure B.5 and B.6. Here the rotation rate

has been changed to 400 and 900 rpm, respectively with 8 seconds gas generation.

139

A B Figure B.5: Current trace for pulse experiments in 20 mM CuSO4 at pH ≈ 0 at 400 rpm.

The currents on the left (A) correspond to mainly hydrogen bubble generation (and some copper plating) at the listed highly negative potentials for eight seconds. After 8 second, the potential was rapidly stepped to -0.2 V where hydrogen was no longer generated but plating of copper continues. (B) Magnified view of the region in (A) in the time region when the generation of bubbles was discontinued by switching the potentiostat to -0.2V.

140

Table B.5: Parameters obtained from the pulse experiments of figure B.5; 20 mM CuSO4 at pH ≈ 0 at 400 rpm. Time of bubble generation was 8 seconds at the listed potentials.

Current predicted by the Levich equation = -3.09 mA.

(A) Bubble generation region. (B) Transport response after bubble generation is discontinued. Φ(pulse), I bubble time to reach time to reach generation steady state -ICu-pulse -I ss ICu-pulse /ILevich steady-state E I(H2)+I(Cu) V/SHE mA sec mA mA sec -0.2 no bubbles ------3.95 --- 2.86 -0.65 -43.94 1.19 6.678 4.828 2.16 0.2 -0.8 -82.19 1.27 7.39 4.282 2.39 0.29 -0.9 -122.79 1.82 9.125 4.879 2.95 0.33 -1 -194.71 1.77 9.29 4.727 3.01 0.33

141

A B Figure B.6: Current trace for pulse experiments in 20 mM CuSO4 at pH ≈ 0 at 900 rpm.

In figures B.5 and B.6 there is an increase of noise in the current since the potential is more negative and bubble generation is enhanced. Likewise, at a given potential, the noise enhance when the time of bubble generation increase in the experiment, this phenomenon can be associate with an increase in the bubble density on the surface; therefore since there are more insulating regions on the electrode, the current is affected and is fluctuating more.

142

Table B.6: Parameters obtained from the pulse experiments of figure B.6; 20 mM CuSO4

at pH ≈ 0 at 900 rpm. Time of bubble generation was 8 seconds at the listed potentials.

Current predicted by the Levich equation = - 4.635 mA.

(A) Bubble generation region. (B) Transport response after bubble generation is discontinued. Φ(pulse), I bubble time to reach time to reach generation steady state -ICu-pulse -I ss ICu-pulse /ILevich steady-state E I(H2)+I(Cu) V/SHE mA sec mA mA sec -0.2 no bubbles ------6.251 --- 0.667 -0.65 -30.985 0.632 7.552 6.121 1.63 0.246 -0.8 -81.716 0.618 8.374 6.233 1.81 0.17 -0.9 -133.64 0.582 9.481 6.105 2.05 0.13 -1 -170.78 0.464 10.091 6.108 2.18 0.13

The values in tables B.5 and B.6 describes that the copper current maximum as

well as the copper current at steady-state is greater in the system with 900 rpm than in the system at 400 rpm at a given potential. However, the ratio of ICu-pulse /ILevich decreases at

900 rpm. This decrease in the enhancement factor is associated with the fact that when the disk increases its rotation rate at a given potential, the regions covered by bubbles decrease. Finally, the time to evacuate the bubbles decreases at 900 rpm.

In figures B.7, B.8 and B.9 pulse experiments were compered at different rotations as was done in figures B.2, B.5 and B.6. However, in this case the cupric ion concentration was decreased to corroborate if the conclusions are the same at 200 mM

CuSO4 at pH ≈ 0.

143

A B Figure B.7: Current trace for pulse experiments in 200 mM CuSO4 at pH ≈ 0 at 100 rpm.

144

Table B.7: Parameters obtained from the pulse experiments of figure B.7; 200 mM

CuSO4 at pH ≈ 0 at 100 rpm. Time of bubble generation was 8 seconds at the listed

potentials. Current predicted by the Levich equation = -15.451 mA.

(A) Bubble generation region. (B) Transport response after bubble generation is discontinued. Φ(pulse), I bubble time to reach time to reach generation steady-state -ICu-pulse -I ss ICu-pulse /ILevich state-state E I(H2)+I(Cu) V/SHE mA sec mA mA sec no -0.2 bubbles ------19.667 --- 2.06 -0.65 -71.26 3.63 41.914 18.766 2.71 1.5 -0.8 -91.49 1.83 39.83 17.608 2.58 2 -0.9 -122.74 1.59 57.323 17.474 3.71 1.9 -1 -148.75 2.52 65.47 18.304 4.24 2.1

By comparing the values obtained in tables B.2 and B.7 it is possible to

distinguish that the I ‘bubble generation’, ICu-pulse and ISS are greater in the system with

higher cupric concentration; however the time to reach steady-state in the bubbles generation, the ICu-pulse /ILevich ratio and the time to reach steady-state in the deposition of

copper are roughly the same in both systems. This means that the enhancement ratio, and

both characteristic times measured in the pulse experiments are indistinguishable of the

cupric ion concentration in the system.

Similarly by comparing I ‘bubble generation’, Ipulse and ISS in both systems of

higher and lower cupric concentrations at the same rotations for 400 rpm and 900 rpm,

we observed that these currents are greater in the system with higher concentrations.

Likewise, the time to reach steady-state in the bubbles generation, the ICu-pulse /ILevich ratio

and the time to reach steady-state in the deposition of copper are roughly the same at any

cupric concentration tested for a given constant rotation rate.

145

A B Figure B.8: Current trace for pulse experiments in 200 mM CuSO4 at pH ≈ 0 at 400 rpm.

146

Table B.8: Parameters obtained from the pulse experiments of figure B.8; 200 mM

CuSO4 at pH ≈ 0 at 400 rpm. Time of bubble generation was two seconds at the listed potentials. Current predicted by the Levich equation = -30.90 mA.

(A) Bubble generation region. (B) Transport response after bubble generation is discontinued. time to reach Φ(pulse), time to reach I bubble generation steady-state -ICu-pulse -I ss ICu-pulse /ILevich steady-state E I(H2)+I(Cu) V/SHE mA sec mA mA sec -0.2 no bubbles ------36.685 --- 0.828 -0.65 -71.005 0.637 53.25 42.584 1.72 0.63 -0.8 -115.36 0.621 64.733 39.246 2.09 0.745 -0.9 -151.33 0.643 70.325 38.313 2.28 0.646 -1 -207 0.569 87.069 40.205 2.82 0.62

A B Figure B.9: Current trace for pulse experiments in 200 mM CuSO4 at pH ≈ 0 at 900 rpm.

The currents on the left (A) correspond to mainly hydrogen bubble generation (and some

copper plating) at the listed highly negative potentials for eight seconds. After 8 second,

the potential was rapidly stepped to -0.2 V where hydrogen was no longer generated but

plating of copper continues. (B) Magnified view of the region in (A) in the time region

when the generation of bubbles was discontinued by switching the potentiostat to -0.2 V.

147

Table B.9: Parameters obtained from the pulse experiments of figure B.9; 200 mM

CuSO4 at pH ≈ 0 at 900 rpm. Time of bubble generation was two seconds at the listed potentials. Current predicted by the Levich equation = - 46.352 mA.

(A) Bubble generation region. (B) Transport response after bubble generation is discontinued. Φ(pulse), I bubble time to reach time to reach generation steady-state -ICu-pulse -I ss ICu-pulse /ILevich steady-state E I(H2)+I(Cu) V/SHE mA sec mA mA sec -0.2 no bubbles ------53.082 --- 0.919 -0.65 -83.98 0.639 65.654 62.579 1.42 0.246 -0.8 -129.224 0.475 78.986 65.889 1.70 0.17 -0.9 -169.58 0.459 87.081 68.158 1.88 0.13 -1 -204.3 0.442 93.328 69.276 2.01 0.13

Finally we observed that the Ipulse/ILevich ratio decreases as the rotation rate

increases in the pulse experiments at 100, 400 and 900 rpm for any given cupric

concentration tested.

148

Appendix C

Length of the spiral path of a bubble:

The length of the spiral path can be derived, as follow:

= (C.1) 3⁄2 −1⁄2 푣� �휔 휐 푧� = 1 + (C.2) 𝑟� 𝑓𝑓 푑𝑑� 휔 푣휑 푣휑 − 푣휑 ≈ 𝑟 � 𝑏�휐 � − 𝑟 = (C.3) 𝑟� 𝑓표� 푑𝑑� 휔 푣휑 푣휑 − 푣휑 ≈ 𝑟� ��휐 � In a differential form we can write:

= (C.4) 푑� 𝑟휑 푟𝑟 �푟 �휑 = (C.5) 푑� 푎 � 푏 Integration yields: 푑휑

( ) = + (C.6) 푎 푙� � 푏 휑 퐶 or: = 푎 (C.7) �푏휑� � 퐶푒

= + (C.8) 푡2 푑� 2 푑푑 2 퐿 ∫푡1 ��푑�� 푑�� 푑� = + (C.9) 2 2 푡 2 푑� 퐿 ∫푡1 �� 푑휑� 푑휑

= 푎 (C.10) 2 �2푏휑� � 퐶푒 2 = 푎 2 (C.11) �2푏휑� 푎 𝑟� �퐶푒 � 푏 푑� = ; and = (C.12) 푑� 푎 푑� 2 푎 2 푑휑 푏 � �푑휑� �푏 �� 149

Thus: = 1 + ( ) ( ) (C.13) 푡2 푎 2 퐿 ∫푡1 � �푏� �2 − �1 ≡ 퐵 �2 − �1 The spiral path length from any position r to the disk circumference (radial

1 position r disk) is:

= ( ) (C.14)

푑𝑑� 1 퐿 퐵 � − �

Here B is a constant given by:

. . 1 + = 1 + = 1.5679 . . (C.15) 푏 푎 2 0 6159 0 51023 2 푎 � 푏 0 51023 � 0 6159 퐵 ≡ � � � �

We note that the spiral path length is 1.5 times longer than the radial distance.

150

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