ENZYME ELECTROCATALYSIS IN MEDIATED BIOELECTRODES By Deboleena Chakraborty A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Chemical Engineering 2010 ABSTRACT ENZYME ELECTROCATALYSIS IN MEDIATED BIOELECTRODES By Deboleena Chakraborty Enzymatic biofuel cells utilize the unique activity and selectivity of enzymes to convert chemical energy directly to electrical energy, and have the potential to be miniaturized for smallscale power devices. This research program seeks to study the characteristics, limitations, and potential for improvement of a mediated laccase-catalyzed electrode for the reduction of oxygen, focusing on the role of mediator redox potential in the catalytic mechanism. The bio-cathode system studied utilizes purified laccase from Trametes versicolor mediated by osmium (Os) centered redox polymers. The results of these studies can enable design of mediated electrodes for biofuel cell applications. Exposure of fuel cell cathodes to fuels like methanol can reduce fuel efficiency and cell voltage via competitive reactions, and can foul the cathode catalyst. Introduction of selective electrocatalysts such as enzymes can solve these problems, and introduces the possibility of a mixed-feed fuel cell system with reduced complexity. The effect of redox potential of a redox hydrogel mediator on the performance of the mediated bio-cathode under varying alcohol concentrations is described. This study demonstrates that the selectivity of mediated laccase oxygen cathodes can facilitate high methanol feed concentration as compared to conventional direct methanol fuel cells and under certain optimum operating conditions, the enzyme might serve as a better cathode catalyst in presence of contaminants like methanol than the conventional Pt/Ru catalysts. A non-competitive inhibition model is proposed to describe the influence of methanol on laccase-catalyzed oxygen reduction kinetics. Methanol replaces water in the enzyme and thereby affects the electron transfer environment near the enzyme active site. In collaboration with Northeastern University, we employ X-ray absorption techniques to characterize the oxygen reduction mechanism of an immobilized laccase while the electrode is operated in situ. The overall goal of this project is to map the oxygen reduction reaction mechanism by a mediated laccase electrode as a function of mediator redox potential, applied electrode potential and presence/absence of substrate (O2). We have successfully detected active Cu sites (in micro-molar concentration) and identified key relationships between oxidation state and mediator redox potential in the presence and absence of oxygen. Our collaborators at Northeastern University have applied the powerful Δµ technique to determine the exact configuration of oxygen attachment to the Cu active sites and to identify the intermediates of the oxygen reduction reaction for a mediated biocathode. Electron-conducting redox hydrogels electrically connect the redox centers of enzymes to electrodes, enabling multi-layer activation and higher current density output. The physicochemical state of these redox polymers and their electron transport mechanism depends on the swelling behavior of these hydrogels in an ionic media. We have fabricated and characterized homogeneous sub-micron sized thin redox hydrogel films with great precision and great repeatability. We have estimated the transport and kinetic parameters for mediated enzymatic systems with precision to have a better understanding of the reaction mechanisms in these complex systems. Copyright by DEBOLEENA CHAKRABORTY 2010 DEDICATED TO MY FAMILY v ACKNOWLEDGEMENTS My dream to pursue higher studies and earn a doctoral degree someday would not have been realized if I did not have the support, love and constant encouragement from my family. I am blessed with such wonderful parents and grand parents who have always taught me to smile through the odds and have encouraged me to move forward no matter how difficult the task or the situation is. I could not have done this without you Mom and Dad. My little sister had always been my greatest source of inspiration through out my career. And most importantly, I do not know where I would have been without my husband’s constant support, love and encouragement. Working towards my goal in life of being an achiever and not just a performer would not have been possible without you being so understanding Amit. Thank you for always being there for me. My life as a graduate student probably could not have been better and full of such fond memories if I were not a part of the Chemical Engineering and Materials Science Department at Michigan State University. I would like to thank Dr. K. Jayaraman for allowing me to get into this doctoral program at MSU. I would like to take this opportunity to formally thank my advisor, Dr. Scott Calabrese Barton for all his help, support, and guidance and for allowing me to pursue this research. You have always brought me back on track whenever I tend to digress, helped me plan and prioritize my work. I enjoyed the freedom at work. The collaborative projects have helped me gain knowledge on diversified fields of science and have also helped me with my people’s skills. I am thankful to you for providing me with the opportunities to attend conferences to give oral vi presentations. As I look back over the past four years, I realize that my experience under your leadership has helped me evolve as a better person, both intellectually and personally. I cannot think of a better model for a research advisor, I am truly blessed to have you guide me through this process. I have learnt so much from you except “how to be brief”, but I am working on it. I want to take this opportunity to thank Dr. S. Patrick Walton, Dr. R. Mark Worden, Dr. Gemma Reguera and Dr. Claire Vieille for serving in my committee and providing such valuable guidance. I am very fortunate to have such understanding and accommodating committee members. Thank you very much Dr. Walton for your encouraging and kind words especially when I needed them the most. I am very thankful to our collaborators at Northeastern University, Dr. Sanjeev Mukerjee and Dr. Thomas Arruda for the XANES work, Dr. Plamen Atanassov and Dr. Gautam Gupta at University of New Mexico for helping me develop the thin-film coating technique here at MSU, Dr. Vojtech Svoboda at CFDRC for providing valuable guidance for the ellipsometry measurements, Dr. Melinda Kay Frame at the Advanced Microscopy Center, MSU, for her help in confocal measurements, and Hazel-Ann Hosein at the Composite Materials And Structures Center, MSU for the AFM experiments. I would like to take this opportunity to express my sincere gratitude to my fellow colleagues, Dr. Joshua Gallaway, Dr. Nicholas Hudak, and Dr. R. Kothandaraman who helped me get started with my research during the early stages of my graduate studies. The team spirit of our group is truly amazing. I am so fortunate to have such encouraging colleagues and friends here at MSU. I want to thank Hao Wen, Vijayadurga Nallathambi, Hanzi Li, Harshal Bambhania, Nate Leonard and Dr. Piyush Kar for being such wonderful co-workers. Thank you vii all for all the unforgettable moments. Thank you Harshal and Bhushan for being so supportive and helpful. I would also like to sincerely acknowledge the undergraduates Erik McClellan and Robert Hasselbeck for helping me set up the film applicator instrument and for the initial trial experiments. I want to take this opportunity to thank the chemical engineering staffs, Jennifer Somerville, Jennifer Peterman, Donna Fernandez, Lauren Brown, and Nichole Shook for all the help. I cannot thank Ms. JoAnn Peterson enough for her help and support during my initial tough days here at MSU. You have all made my stay at Michigan State University a truly enjoyable experience. viii TABLE OF CONTENTS LIST OF TABLES........................................................................................................................ XI
 LIST OF FIGURES ..................................................................................................................... XII
 CHAPTER 1: INTRODUCTION ....................................................................................................1
 References ............................................................................................................. 24
 CHAPTER 2: INFLUENCE OF MEDIATOR REDOX POTENTIAL ON FUEL SENSITIVITY OF MEDIATED LACCASE OXYGEN REDUCTION ELECTRODES .............34
 Abstract ................................................................................................................. 34
 Introduction ........................................................................................................... 35
 Experimental ......................................................................................................... 38
 Results ................................................................................................................... 41
 Discussion ............................................................................................................. 47
 Conclusions ........................................................................................................... 49
 Acknowledgements ............................................................................................... 50
 References ............................................................................................................. 63
 CHAPTER 3: MODELING INHIBITION BY METHANOL IN MEDIATED LACCASE ELECTRODES FOR OXYGEN REDUCTION REACTION (ORR) ..................69
 Abstract ................................................................................................................. 69
 Introduction ........................................................................................................... 70
 Experimental ......................................................................................................... 74
 Results and discussion........................................................................................... 79
 Conclusions ........................................................................................................... 84
 Acknowledgements ............................................................................................... 85
 References ........................................................................................................... 103
 CHAPTER 4:
 IN-SITU XANES CHARACTERIZATION OF CU ACTIVE SITES OF LACCASE FROM TRAMETES VERSICOLOR IN A MEDIATED BIOCATHODE AS A FUNCTION OF MEDIATOR REDOX POTENTIAL...105
 Abstract ............................................................................................................... 105
 Introduction ......................................................................................................... 106
 Experimental ....................................................................................................... 110
 Results and discussion......................................................................................... 115
 Conclusions ......................................................................................................... 124
 Acknowledgements ............................................................................................. 125
 References ........................................................................................................... 145
 CHAPTER 5:
 CHARACTERIZATION OF ENZYME-REDOX HYDROGEL THIN-FILM ELECTRODES FOR PRECISE ESTIMATE OF HYDROGEL TRANSPORT PROPERTIES AND KINETIC PARAMETERS ................................................149
 ix Abstract ............................................................................................................... 149
 Introduction ......................................................................................................... 150
 Experimental ....................................................................................................... 152
 Results and discussion......................................................................................... 161
 Conclusions ......................................................................................................... 169
 Acknowledgements ............................................................................................. 170
 References ........................................................................................................... 197
 CHAPTER 6:
 SUMMARY .........................................................................................................203
 APPENDIX A. FUNCTION FOR EXTRACTING THE FILM THICKNESS FROM A COLORED CONFOCAL Z-SECTION IMAGE.................................................212
 APPENDIX B1: MATLAB CODE FOR FITTING CYCLIC VOLTAMMOGRAMS TO EXTRACT TAFEL SLOPE, ELECTRON DIFFUSION COEFFICIENT AND EXCHANGE CURRENT DENSITY ..................................................................214
 APPENDIX B2. INPUT FILE FOR THE CVFIT_P FUNCTION (FOR RP A MEDIATED SYSTEM): CCFILM4D_IN.................................................................................221
 APPENDIX C: MATLAB CODE FOR ONE-DIMENSIONAL FILM MODEL ......................224
 APPENDIX D1: MATLAB CODE FOR SOLVING ONE-DIMENSIONAL STEADY STATE CONCENTRATION PROFILES ........................................................................236
 APPENDIX D2. INPUT FILE FOR THE STEADY_STATE_BP FUNCTION (FOR RP A MEDIATED SYSTEM): INA_0M ......................................................................237
 x LIST OF TABLES Table 2.1:
 Redox polymer properties ..........................................................................................51
 Table 3.1:
 Redox polymer properties ..........................................................................................86
 Table 3.2:
 Physical parameters of the TvL – redox polymer hydrogel films ..............................87
 0 Table 3.3:
 Relationship between E1 2 and Em' ........................................................................88
 Table 3.4:
 Expected obtainable kinetic parameters through fitting.............................................89
 Table 4.1:
 Redox polymer properties ........................................................................................126
 Table 4.2:
 Mediator utilization for redox polymer B in terms of % active Os..........................127
 ® 12 * Table 4.3:
 Cm Dm estimates for the three mediated systems on composite Grafoil electrodes ⎛ F3 ⎞ 3 2 * 1 2 from Randles-Sevcik analysis, slope=0.4463 ⎜ ⎟ n Cm Dm .........................128
 ⎝ RT ⎠ Table 4.4:
 Specification of the potentials at which XAFS was collected in-situ ......................129
 Table 5.1:
 Redox polymer properties ........................................................................................171
 25 Table 5.2:
 Ellipsometric parameters for initial estimate of film thickness ............................172
 Table 5.3:
 Estimated refractive index of redox hydrogel films as determined by ellipsometry173
 -1 Table 5.4:
 Film thickness of enzyme-containing films (3 µL drop size, 20°, 20µm s )..........174
 Table 5.5:
 Electron diffusion coefficient estimation for thin-film redox hydrogel electrodes..175
 xi LIST OF FIGURES Figure 1.1:
 Illustration of mechanisms of electron transfer from an electrode surface to an enzyme. (a) Direct electron transfer (DET), and (b) Mediated electron transfer (MET) where the redox-active species shuttles the electron between the electrode and the enzyme. “For interpretation of the references to color in this and all other figures, the reader is referred to the electronic version of this dissertation.” ...........19
 Figure 1.2:
 Potential schematic of a glucose-oxygen biofuel cell. The potentials are referenced to the standard hydrogen electrode (SHE). ...................................................................20
 Figure 1.3:
 Generalized structures of the osmium based redox polymers illustrating the role of the chelated ligands in governing redox potential of the mediator...........................21
 Figure 1.4:
 Structure of laccase from Trametes versicolor (TvL). The four copper active sites are shown as blue spheres. Figure generated from its crystal structure using PyMol (pdb accession number 1GYC). ........................................................................................22
 Figure 2.1:
 Structure of redox mediators ......................................................................................52
 Figure 2.2:
 Oxygen reduction polarization mediated laccase electrodes. Polarization curves (iRcorrected) at three different methanol concentrations for (a) RP A; (b) RP B; (c) RP C mediated bio-cathode systems and; (d) plateau current densities (ipl) as a function -1 0 of methanol concentration and Em' Scan rate 1 mV s at 900 rpm in oxygen -2 saturated 100 mM, pH 4 citrate buffer at 40°C. Total loading 0.69 mg cm with Laccase: RP: cross-linker:: 32:61: 7 (wt %). ............................................................53
 Figure 2.3:
 Cyclic voltammograms (CVs) of representative planar enzyme electrodes containing (a) RP A; (b) RP B; (c) RP C at three different methanol concentrations (0, 2.5 and -1 10 M methanol) recorded at 50 mV s scan rate at 900 rpm in de-aerated 100 mM, pH 4 citrate buffer at 40°C; (d) relative reduction peak height obtained from 50 mV -1 s CVs in de-aerated buffers as a function of methanol concentration. Relative peak height at each methanol concentration is the reduction peak height relative to that of the 0 M case for the same electrode..........................................................................54
 Figure 2.4:
 (a) Plot of the difference current (idel) at the end of the forward and the reverse pulse of a square-wave cycle versus time for the three redox polymer containing films at -1 250 mV s scan rate; and (b) active Os content of the films as determined by square wave voltammetry in a de-aerated buffer. Experimental conditions: 900 rpm in de-aerated citrate buffer (100 mM, pH~4) at 40°C..............................................55
 xii Figure 2.5:
 (a) Randles-Sevcik analysis. Linearity of variation of peak current density (ipl) (for 0M) with square root of scan rate and the fitted curves passing through the origin is indicative of semi-infinite diffusion. (b) Apparent e- diffusion coefficient (Dm) of the mediators as a function of methanol concentration. Dm estimated by fitting the -1 CVs at 50 mV s scan rate in de-aerated buffers with or without methanol at 900 -1 rpm. (Inset) Experimental conditions: 900 rpm, 50 mV s scan rate, de-aerated citrate buffer (100 mM, pH~4, 40°C).......................................................................56
 Figure 2.6:
 (a) Film thickness was determined under ambient conditions by confocal microscopy using a Zeiss Pascal microscope, where the z-section of the film was mapped in terms of the intensity of the fluorophore, Fluorescein isothiocyanate (FITC) (0.03 µg) of a 3 mm diameter of cross-linked enzyme-containing redox hydrogel film on a cleaned glass slide. FITC containing films were excited with 488 nm Argon laser and the green emission was recorded with a 505 long pass filter. (b) Film thickness of the redox polymer and enzyme-containing hydrogels as a function of methanol -2 concentration. Total loading 0.69 mg cm with Laccase: RP: cross-linker:: 32:61: 7 (wt%).........................................................................................................................57
 Figure 2.7:
 Effect of methanol on (a) half-wave reduction potential (E1/2) of the steady state 0' catalytic reduction current and (b) formal potential ( Em ) of the mediated biocathode. The formal potentials were estimated from CVs as indicated in Fig. 2.3 and the half-wave potentials were estimated from steady state polarization curves as indicated in Fig. 2.2. E1/2 is the potential at which the steady state current density is half of that of the plateau current (ipl). .....................................................................58
 Figure 2.8:
 Oxygen reduction stability of the laccase containing mediated biocathodes in oxygen saturated 2 M methanol for the three different mediators under identical loading conditions. The electrode was poised at ~0.4 V | SHE for systems containing redox polymers B and C while at ~0.2 V | SHE for redox polymer A. Relative current density is defined as the ratio of the current density as a function of time and the max current density for the control in 0 M for the respective systems. Chronoamperommetric measurements were taken at 900 rpm, 40°C......................59
 Figure 2.9:
 Effect of variation of oxygen at various methanol concentrations for (a) RP A, (b) RP B, and (c) RP C. The data points represent plateau current density from chronoamperommetric measurements in oxygen saturated citrate buffer with or without methanol, 900 rpm, 40°C. The electrodes were poised at a potential in the plateau current region of the polarization curves (Fig. 2.2) for the respective systems......................................................................................................................60
 Figure 2.10:
 Residual effects of methanol exposure on (a) the catalytic performance of the planar biocathodes towards ORR (reduction plateau current density, ipl) in oxygen xiii saturated buffer, 900 rpm, 40°C and; (b) on apparent electron diffusion coefficients (Dm) for the three RPs. Residual changes were assessed in blank buffer following methanol exposure. ...................................................................................................61
 Figure 3.1:
 Structure of redox mediators. .....................................................................................90
 Figure 3.2:
 Schematic of electron flow in a biocathode. ..............................................................91
 Figure 3.3:
 Schematic of the non-competitive inhibition kinetics for both the substrates (S=Oxygen; Mred= reduced form of the mediator)...................................................92
 Figure 3.4:
 Effect of methanol on Tafel slope (b) for all the three mediated systems. The Tafel -1 slope was estimated by fitting the cyclic voltammograms at 50 mV s in de-aerated buffer (Figure 3.5).....................................................................................................93
 Figure 3.5:
 Fitting of the cathodic wave of a cyclic voltammogram of a representative system -1 obtained at 50 mV s scan rate in de-aerated 100 mM citrate buffer (pH 4, 40°C, 900 rpm)....................................................................................................................94
 Figure 3.6:
 Demonstration of the effect of methanol on (a) half-wave reduction potential (E1/2 ) 0 of the steady state catalytic reduction current and (b) formal potential ( Em' ) of the mediated biocathode. E1/2 was determined from the steady state polarization curves -1 0 (1 mV s ) in O2 saturated buffer (100 mM, pH~4, 40°C, 900 rpm), and Em' was -1 obtained from the cyclic voltammograms at 50 mV s in de-aerated citrate buffer (100 mM, pH~4, 40°C, 900 rpm).............................................................................95
 Figure 3.7:
 The relative magnitudes of half-wave reduction potential (E1/2) of the steady state 0' catalytic reduction current and formal potential ( Em ) of the mediated biocathode as a function of methanol concentration for (a) RP A, (b) RP B and (c) RP C mediated systems......................................................................................................................96
 Figure 3.8:
 Schematic of the electron transfer and the potential gradient elucidating the concept of electron transfer driving force between the Os redox center of the mediator and the T1-Cu2+ site of TvL.............................................................................................97
 Figure 3.9:
 Steady state concentration profiles for the mediator and substrate (O2) for (a) RP A, (b) RP B, and (c) RP C mediated biocathodes. The steady state concentration profiles were generated using bvp4c Matlab function, the governing equations and boundary conditions of which are defined in Equations 3.6 and 3.7 respectively (Appendix D). ...........................................................................................................98
 xiv Figure 3.10:
 Comparison of analyzed experimental data to the numerical prediction. (a) Plot of kinetic plateau current density (ipl,k) for varying oxygen mole fraction (diluted with nitrogen under 1 atm pressure). Each point is the result of a Koutecky-Levich analysis at the plateau current. (b) Ohmic and Koutecky-Levich corrected polarization curves in oxygen saturated 100 mM citrate buffer (pH 4, 40°C). Dashed lines in both (a) and (b) indicate numerical model results simultaneously fitted to the both the data sets. ..................................................................................99
 Figure 3.11:
 Variation of the enzyme turnover number with methanol concentration. The values of kcat were obtained by simultaneously fitting the oxygen variation data and the steady state polarization curves (Figure 3.10) with the numerical model. The error bars indicate standard deviation of at least three experiments................................100
 Figure 3.12:
 Variation of (a) the enzyme-oxygen binding constant (KS) and (b) the enzyme- mediator binding constant (KM) with methanol concentration. The values of kcat (s ⎛ k ⎞ 1 ) and kA (bimolecular rate constant ⎜ kA = cat ⎟ for the enzyme-mediator KM ⎠ ⎝ -1 -1 reaction, s M ) were obtained by simultaneously fitting the oxygen variation data and the steady state polarization curves (Figure 3.10) with the numerical model. The error bars indicate standard deviation of at least three experiments................101
 ® Figure 4.1:
 Structure of the composite Grafoil electrodes used for the in-situ and ex-situ measurements..........................................................................................................130
 Figure 4.2:
 Experimental set-up for in-situ XAS measurements at the X-3B beam line............131
 Figure 4.3:
 Structure of redox mediators. ...................................................................................132
 ® Figure 4.4:
 In-situ electrochemical response of the composite Grafoil electrode in a flowthrough cell set-up (Fig 4.1) in oxygen saturated citrate buffer (pH ~4, 100 mM, -1 25°C) circulated at 5 ml min rate through a peristaltic pump. Cyclic -1 voltammograms were collected at 10 mV s scan rate..........................................133
 ® Figure 4.5:
 Electrochemical response of the three mediated systems in composite Grafoil -1 electrodes (a) in de-aerated citrate buffer (at 50 mV s scan rate) and (b) in oxygen saturated citrate buffer (pH ~4, 100 mM, 25°C). The electrochemical measurements were taken in quiescent condition with constant sparging of N2 in (a) and O2 in (b). -1 -1 The cyclic voltammograms were obtained at 50 mV s for (a) and at 1 mV s scan rates for (b)..............................................................................................................134
 xv Figure 4.6:
 Square wave voltammetry of the three mediated systems drop deposited on ® composite Grafoil electrodes in de-aerated citrate buffer (pH ~4, 100 mM, 25°C). Area under the curve gives a direct measure of the electro-active species concentration...........................................................................................................135
 Figure 4.7:
 Randles-Sevcik analysis of the three mediated systems on composite Grafoil® 0 electrodes in de-aerated citrate buffer (pH ~4, 100 mM, 25°C). A ( Em' = 0.43 V | 0 0 SHE), B ( Em' = 0.77 V | SHE), and C ( Em' = 0.82 V | SHE), represents the three ® respective mediated TvL containing composite Grafoil electrodes.....................136
 Figure 4.8:
 In-situ Cu k-edge XANES spectra for unmediated laccase electrode in 100 mM pH~4 citrate buffer, 25°C, under (a) de-aerated condition and (b) oxygen saturated condition. ................................................................................................................137
 Figure 4.9:
 Sequential variation of potential and substrate for XAFS study. .............................138
 Figure 4.10:
 In-situ Cu k-edge XANES spectra for mediated laccase electrode in oxygen saturated 100 mM pH~4 citrate buffer, 25°C. The electrodes were poised at the respective open circuit potentials (Table 4.3), scenario 1 (Fig 4.9)........................139
 Figure 4.11:
 Electron energy and potential diagram elucidating the electron transfer efficacy 2+ between the Os redox centers of the mediators and the T1-Cu of TvL. .............140
 Figure 4.12:
 In-situ Cu k-edge XANES spectra for mediated laccase electrode in de-aerated citrate buffer (100 mM pH~4 citrate buffer, 25°C) for (a) redox polymer A, (b) redox polymer B and (c) redox polymer C mediated systems. The electrodes were poised at the respective potentials (Table 4.4)........................................................141
 Figure 4.13:
 In-situ Cu k-edge XANES spectra for mediated laccase electrode in de-aerated citrate buffer (100 mM pH~4 citrate buffer, 25°C) at (a) oxidizing potential, and (b) reducing potential for the three mediated systems. The electrodes were poised at the respective potentials (Table 4.4). ......................................................................142
 Figure 4.14:
 In-situ Cu k-edge XANES spectra for mediated laccase electrode in O2 satd. citrate buffer (100 mM pH~4 citrate buffer, 25°C) at (a) oxidizing potential, and (b) reducing potential for the three mediated systems. The electrodes were poised at the respective potentials (Table 4.4). ............................................................................143
 Figure 5.1:
 Structure of the redox mediators ..............................................................................176
 Figure 5.2:
 (a) The slide coater instrument set-up and (b) the slide coating platform, θ is the slide angle and v is the linear coating velocity. The slide angle θ was optimized to be -1 20°± 2° and the linear velocity v was optimized ~ 20 µm s for all the operations.177
 xvi Figure 5.3:
 (a) Effect of slide angle (θ), and (b) the linear velocity (v) on film morphology. The slide angle θ was optimized to be 20°± 2° and the linear velocity v was optimized ~ -1 20 µm s for all the operations...............................................................................178
 Figure 5.4:
 Optimization of instrument slide angle (θ) for RP A and B containing redox hydrogel films. The precursor solution contained RP:XL:: 90:10 wt% and 4.6 M ethanol as solvent. Effect of slide angle (θ) on (a) film electrode area, (b) film thickness and (c) overall film volume. The slide angle θ was optimized to be 20°± 2° and the -1 linear velocity v was optimized ~ 20 µm s for all the operations. .......................179
 Figure 5.5:
 Effect of ethanol content in precursor solution in controlling film morphology (film drying rate). Effect of film drying on (a) electrode area (geometric), and (b) film thickness of redox hydrogel films containing RP B (90 wt%) and XL (10 wt%). High ethanol content in the precursor solution resulted in thicker films with smaller area due to faster drying rate. The slide angle θ was optimized to be 20°± 2° and -1 the linear velocity v was optimized ~ 20 µm s for all the operations...................180
 Figure 5.6:
 Effect of ethanol content on enzyme activity toward ORR for RP A mediated system. The films were obtained from a 3µL drop of the precursor solutions with or without ethanol such that RP:Lac:XL:: 61:32:7 wt%. For Triton X-100 containing precursor solution RP:Lac:XL:Triton X-100 was present in 54:29:6:10 wt%. Experiments were conducted in O2 saturated citrate buffer (100 mM, pH~4, 40°C) under no rotation. ....................................................................................................181
 Figure 5.7:
 Optical microscope images of redox hydrogel films containing RP B (90 wt%) and XL (10 wt%). The drop deposited film (area =0.0707 cm2) was formed from 3µL drop of precursor solution on gold-coated glass slide. Thin film electrode was prepared by convective self-assembly technique from a 3 µL drop (θ ≈ 20° and v = -1 20 µm s ). The images were collected at 10X optical zoom. ................................182
 Figure 5.8:
 Demonstration of film homogeneity through AFM and confocal microscopy studies. (a) AFM of bare gold, (b) AFM of enzyme-containing redox hydrogel (RP C) film coated electrode. The scan size was 1 µm (x = 0.2 µm/div., z = 10 nm/div for (a) and 5 nm/div for (b) and scanning frequency was 0.5003 Hz.) Confocal microscopy image of thin film cast on glass slide (c) at the edge of the film, and (d) at the center. FITC containing films were excited with 488 nm Argon laser and the green emission was recorded with a 505 long pass filter. ................................................183
 Figure 5.9:
 Schematic of the theoretical principles of ellipsometric measurements. .................184
 Figure 5.10:
 Demonstration of improved fitting of the experimentally obtained data (ψ, Δ) with fitted refractive index for the respective systems. (a) Fitting of experimental data for the dry film before estimating the refractive index, (b) improved fitting of experimental data for the dry film with estimated values of refractive index, (c) xvii fitting of experimental data for the wet film before estimating the refractive index, and (d) improved fitting of experimental data for the wet film with estimated values of refractive index. ..................................................................................................185
 Figure 5.11:
 (a) Film thickness estimates (dry and in buffer soaked) of the redox hydrogel films (RP: XL:: 90:10 wt%) using ellipsometry. The films were obtained through convective self-assembly technique with varying drop size of the precursor solution containing 4.5 M ethanol, and (b) represents the relative swelling of the films obtained for the three different redox polymer systems. ........................................186
 Figure 5.12:
 Effect of incorporation of enzyme in the redox hydrogel to relative film swelling: (a) or RP A systems, (b) RP B systems, and (c) RP C systems. PVI represents the control for each system without enzyme or redox mediator, PVI + Lac demonstrates the effect of incorporation of enzyme alone, RP represents effect of incorporation of positively charged Os center while case 4 (RP+Lac) represents the effect of incorporation of both enzyme (negatively charged) and Os centers (positively charged) on relative film swelling. .........................................................................187
 Figure 5.13:
 DET versus MET. (a) MET generates higher catalytic activity towards ORR by 46 TvL. (b) DET prevails at more negative potential. The controls for the unmediated laccase response towards ORR are bare Au electrode in de-aerated and O2 saturated buffers and PVI coated Au electrode in O2 saturated buffer..............188
 Figure 5.14:
 Comparison of the square-wave voltammetry (SWV) demonstrating improved mediator utilization for thin film electrodes as compared to drop deposited film electrodes on RDE. The experiments were conducted at no rotation in de-aerated citrate buffer (100 mM, pH ~ 4, 40°C)...................................................................189
 Figure 5.15:
 Comparison of the % active Os content of a thin film electrode and a drop deposited film electrode on a glassy carbon RDE as obtained from SWV (Fig. 5.9) for (a) RP A, (b) RP B, (c) RP C. (d) demonstrates a comparison of the square-wave voltammetry demonstrating improved mediator utilization in thin film electrodes for the three mediated systems. Experimental conditions are same as that of Fig. 5.9.190
 Figure 5.16:
 Comparison of the enzyme utilizations of a thin film electrode and a drop deposited film electrode on a glassy carbon RDE for RP A mediated systems (3 µL precursor drop size was used for thin film and RDE experiments). (a) Polarization curves were obtained at no rotation in O2 saturated citrate buffer (100 mM, pH ~ 4, 40°C, -1 1mV s ), and (b) varying oxygen concentrations (diluted with N2 under atmospheric pressure). ............................................................................................191
 Figure 5.17:
 Randles-Sevcik analysis of the redox hydrogel thin films for the three redox mediators. The films were cast from a 3µL drop of the respective precursor solutions containing 4.5 M ethanol. The peak current densities were estimated from -1 cyclic voltammograms at 50 mV s in de-aerated buffer. .....................................192
 xviii Figure 5.18:
 Representative Impedance spectra for RP A containing system indicating the point of transition from semi-infinite to finite diffusion regime where the dimensionless 52 frequency Ki=1. Experimental conditions were similar to that of Fig. 5.14. ......193
 Figure 5.19:
 Representative plot of fitting of the peak current density and peak potential to 48 obtain electron diffusion coefficients (Aoki method). ........................................194
 Figure 5.20:
 Effect of methanol inhibition kinetics for laccase containing redox hydrogel formed from 3µL drop size of the precursor solution for (a) RP A, (b) RP B, and (c) RP C mediated systems. Experimental conditions were similar to Fig 5.16 b.................195
 xix Chapter 1: Introduction Fuel Cells: a general overview Worldwide demand for non-polluting and sustainable energy technology is growing steeply due to increased awareness of the irreversible damage that consumption of nonrenewable energy resources causes to the environment, and due to economic and political 1 concerns. Fuel cell technology, first introduced by independent studies by William R. Grove 2 and C.F. Schoenbein in 1839, continues to be extensively developed with the goal of environmentally friendly energy devices capable of converting chemical energy into electricity for applications spanning from automotive (kW-scale, high power density) to portable hand-held electronic devices (watt-scale, high energy density). Fuel cells, unlike batteries, require a constant supply of fuel (e.g. H2, methanol) at the anode and oxidant (air or O2) at the cathode for continuous operation without recharging. The most promising kind of fuel cells for realizable near-future applications are the low temperature polymer exchange membrane fuel cells (PEMFCs). Precious metals, such as platinum (Pt), ruthenium (Ru), and palladium (Pd), are the most commonly used catalysts for such conventional fuel cells. Though these catalysts are active under extreme conditions (such as high temperature, high/low pH), they are limited and expensive natural resources, and are highly unselective towards oxidants and fuels, which introduces design complications. Hence, extensive effort and resources are invested in finding alternative catalysts for sustained fuel cell applications and markets. 1 Biological fuel cells (BFCs): Microbial vs. Enzymatic Growing demand for low cost, non-precious metal electrocatalysts is coupled with the need for catalysts that can electroconvert biorenewable fuels to electrical energy. For this reason, the use of biocatalysts in fuel cells has rapidly gained scientific attention. As early as 1911, M.C. Potter demonstrated the electrical effects accompanying fermentation or putrefaction under the 3 influence of microorganisms such as Saccharomyces cerevisice and various species of bacteria. 4 In 1931, Cohen built a batch of BFCs that produced more than 35 V. Biofuel cells became popular in 1960s when the National Aeronautics and Space Administration (NASA) expressed interest in using organic wastes to generate electricity. The operational biofuel cell (BFC), as reported by Davis and Yarborough in 1962, was a glucose-glucose oxidase system using whole 5 microbes. BFCs are a subset of fuel cells that use biocatalysts at one or both the electrodes. Depending on the type of biocatalysts used, these fuel cells can be classified as microbial biofuel 6,7 cells (MFC) and enzymatic biofuel cells (EFCs). BFCs are capable of consuming a wide variety of readily available substrates and fuels, such as complex carbohydrates and macromolecules, and converting them into benign byproducts with concurrent electricity 8 generation. The advantages of MFCs over EFCs are longer lifetimes (up to 5 years as opposed to few days) and their ability to completely oxidize simple sugars to carbon dioxide and water. -2 The prime limitations of MFCs are low power densities (~ mW m ) due to slow substrate transport across the cell membrane. The main advantage of replacing an entire microbe with 6 isolated enzymes is a gain in volumetric catalytic activity. 2 Enzymatic biofuel cells: advantages, disadvantages, and applications The major advantages of using enzymes as catalysts are low cost of production and wide 9 availability from varied sources (plant, fungal, bacterial), high activity (per mole basis), high substrate specificity and selectivity in the presence of mixed reactants (which simplifies design 10-16 complexities of separating fuel and oxidant streams making miniaturization realizable), and capability of effectively oxidizing a wide range of alternative fuels such as glucose and ethanol under mild operating conditions (near neutral pH and 20-40°C). The challenges associated with EFCs involve incorporating extracellular enzymes in fuel cells to obtain a practical power source. Redox enzymes are large molecules (50-100 kDa) with catalytic sites that are often deeply embedded, resulting in low volumetric or area-specific activity. For example, laccase from Trametes versicolor can achieve a maximal monolayer -2 9,17 coverage of ~8 pmol cm . Hence, in order to obtain high current densities for practical applications, either the effective electrode surface area needs to be large, or enzyme multilayers 9,17,18 are required, both of which introduce mass transport limitations. Moreover, enzymes are often susceptible to harsh environments such as high temperature and extreme pH, and hence 9,19 long-term durability is difficult to achieve. With the advent of advanced design technologies, EFCs, instead of being used as generalized power generating devices, can be tuned to serve as portable, compact and sustainable micro-power sources. 19,20 Most recent studies on EFCs have focused on small-scale, low-power 21-23 electronic devices such as sensors for biological systems, 3 19 implantable devices, telemeters 21 immobilized in subcutaneous tissue, sources, 21 military or security applications based on ambient fuel battery-fuel cell hybrids for small scale portable electronic power sources and micro21,24 25 chip devices, radio controlled vehicles, 10,21 inexpensive enough to be disposable. 26 and music devices. These devices could be Vincent et al. have also demonstrated enzymatic fuel 27,28 cells that work on contaminated fuels. 29,30 For small-scale portable electronics applications, direct methanol fuel cell (DMFC) technology provides a path towards high energy density which drives growing research and 31-37 industrial interest. However, energy density and power density in DMFCs are limited by 36 low methanol feed concentration, which minimizes parasitic consumption of fuel but increases onboard water requirements. The resulting increased weight prevents mainstream DMFCs from -1 attaining the ~500 W L power density desirable for sustained operation in hand-held portable 38-40 devices. One promising solution is to use enzyme electrocatalysts at the cathode. Catalyst selectivity and specificity allow higher operating methanol concentrations and therefore higher 41 power density. Electron transport between enzyme and electrode: Direct vs. Mediated The issue of low power density of EFCs is tied directly to limitations in the rate of electron transfer between an enzyme electrocatalyst and a solid electrode surface. Electron transfer can be achieved by (a) direct electron transfer (DET) and (b) mediated electron transfer 4 42 (MET). DET, which involves direct transfer of electrons between the electrode and the enzyme active sites, requires specific orientations of enzymes with their active sites close to the electrode 19,21 to facilitate electron transfer through the electron tunneling distance. This makes DET operation, though a simple approach, slow and often irreproducible. On the other hand, in MET, in which small redox active centers facilitate electron transfer to the enzyme active site, orientation dependency is eliminated and multi-layer catalyst activation is enabled. The highest 15,43 kinetically-limited current density has been achieved by MET. Figure 1.1 illustrates these two general methods for electrical contact between the electrode and the enzyme. Mediated electron Transfer (MET): Co-immobilization techniques The basic need for improving electrical contact between the enzyme active sites and the electrode led to the advent of MET via small redox molecules that repeatedly cycle between oxidized and reduced state. As early as 1983, using tetramethyl-p-phenylenediamine as mediator with quinoprotein methanol dehydrogenase, a biofuel cell was shown to operate at a steady 44 current output decreasing by less than 10% over a 24-hour period of continuous operation. 45 Cass et al., in 1984 demonstrated the use of a substituted ferricinium ion as a mediator of electron transfer between immobilized glucose oxidase and a graphite electrode. An entirely new dimension was added to biofuel cell research with the advent of MET since 1990. The use of more stable osmium-based redox mediators, which could be crosslinked to be co-immobilized with the enzyme on the electrode surface to shuttle electrons between the electrode and the enzyme active sites opens the possibility of using a wide variety of redox 5 enzymes. For most of the redox enzymes, with the exception of redox transfer proteins like cytochrome c, the redox active sites are embedded deep inside an insulating protein sheath. Hence to obtain higher catalytic current density, it is necessary to use small redox molecules, which participate in the catalytic reaction by reacting directly with the enzyme active site or its cofactor, get oxidized or reduced, and diffuse to the electrode surface where rapid electron 46 transfer takes place. Various MET approaches have been reported wherein enzyme and mediator either coexist in free solution, or either one of them is immobilized on an electrode surface while the 19,44,47-51 other is free. Preferably, enzymes are co-immobilized on the electrode surface with mediators to facilitate repeated use of catalysts and prevent loss of the active species in the presence of flow. 17,52 Co-immobilization on the electrode surface has been achieved using ®53 micellar polymer materials such as Nafion of hydrogels, 43,56 57 by electrodeposition 7,54 and chitosan, 55 sol-gel entrapment, 58 or via layer-by-layer technique. formation The choice of immobilization technique depends on the enzyme, the electrode surface, and the specific 17 operational requirements. Immobilization of the electro-active species also dramatically simplifies fuel cell designs by eliminating seals, separators and casings. The enzyme is often stabilized, because it is protected from chemical and mechanical stresses, and optimal electron 59 transfer efficiency can be achieved due to high local concentrations of enzymes and mediators. However, there is often a trade off between enzyme activity and stability in immobilized 17 systems. 6 Choice of redox mediators: Os-based redox polymers Myriad of mediators, such as quinone, viologens, 2,2'-azino-bis(3-ethylbenzthiazoline-6sulphonic acid) (ABTS), complexes of iron (Fe), ruthenium (Ru), cobalt (Co), osmium (Os), 47,60,61 have been tested for MET particularly for biofuel cell applications. Of all these, the most successful designs are based on “wired” biocatalysts, using osmium redox polymers. Osmium redox species have been incorporated into polymer backbones such as poly-vinyl imidazole (PVI) and poly-vinyl pyridine (PVP) either after polymerization or in the monomer stage, forming electro-active polymer chains, termed as "redox polymers". Adam Heller, in 1990, first demonstrated the successful incorporation of enzymes (glucose oxidase) into films of cross62 linked Os redox polymers for biosensor applications. Osmium complexes are generally selected because of their fast redox kinetics, rich organometallic chemistry, broad range of 19,56 oxidation-reduction potentials and stability in both oxidized and reduced forms. Upon cross-linking, these water-soluble Os-based redox polymers create a water– swollen, ion-conducting redox active network known as a "redox hydrogel". Figure 1.2 demonstrates the schematic of a complete mediated biofuel cell indicating how the electronconducting redox hydrogel electrically connects the enzyme redox centers to electrodes. Electron transport through this electro-active mesh occurs by self-exchange as well as by electron hopping, allowing multiple layers of enzyme utilization, thereby increasing the overall current 63 density of the system. In this work, we have studied MET with Os-based redox polymers towards developing oxygen reducing biocathode systems for fuel cells. 7 Designing Os-based redox polymers for fuel cell applications The design of a suitable redox mediator for a particular application is based on the following criteria: (a) the mediator must be stable in both the oxidized and reduced states, (b) rapid kinetics between the enzyme and electrode should be achieved (c) minimum overpotential should be required and (d) the potential range should be appropriate to avoid any unwanted side reactions. 56 Figure 1.3 describes a library of Os-based mediators synthesized in our group. The 0' formal redox potential of the mediator, Em , is defined as the equilibrium potential of the species, which is characterized by relative concentrations of the oxidized and the reduced states under non-standard conditions and is governed by the Nernst Equation (Equation 1.1). The Nernst equation relates the thermodynamics of an electrochemical system by considering the 64 influences of concentration on electrochemical potential. * RT !CO # " $ E=E + nF !C * # " R$ 0' [1.1] * * where, E is the electrode potential, E 0' is the formal potential, CO and C R are the respective bulk concentrations of the oxidized and reduced species. This potential can be tailored to suit a particular application by altering the ligands 65-67 attached to the Os active site. The length of the polymer backbone (described by the number of repeat units, m, per Os complex) controls the active site loading (Os), and both of these 8 [ 56 parameters affect the electron transfer and the reaction kinetics. Os generally has a co- ordination number of six. As indicated in Fig. 1.3, attachment of two identical bidentate ligands and a chloride to the Os active center generates low potential mono-valent redox entities, while, mixed ligands with no chloride attached to the Os center generate high potential bi-valent 56,65,66,68,69 structures. Put simply, if the attached ligand is electron withdrawing (Lewis Acid), it reduces the overall electron cloud density on the central Os redox center, resulting in higher 2+/3+ oxidation state (Os ) of the central atom and increasing the overall redox potential of the complex. If an electron donating group (Lewis Base), such as a labile chloride atom, is attached to the central Os atom, it increases the overall electron cloud density on the redox center, thereby +/2+ decreasing its oxidation state (Os 0' ) and the mediator has a lower Em . The theoretical redox potential of these organometallic complexes can be predicted using 69 Lever analysis. The correlation predicting the mediator redox potential is given by, n E 0 / V = 0.711" ai E L Li ! 0.236 pred ( ) i=1 [1. 2] where, EL is the ligand parameter, Li is the ligand, ai is the degree of chelation of the ligand (for 0 example ai=2 and 3 for bipyridine and terpyridine respectively), and Epred is the predicted redox potential of the redox mediators. The detailed approach of this analysis and the synthetic 56 routes for the bipyridine based system used in this work are discussed elsewhere. 9 The generalized structure of the Os-based mediator is indicated in Figure 1.3. The central Os pendant, complexed with the polymer backbone, retains its capability of transferring electrons to the enzyme active site. The polymer and the cross-linker, poly (ethylene glycol) (400) diglycidyl ether (PEGDGE), bind to the electrode surface through Van der Waals interaction. The enzyme is entrapped within this redox hydrogel matrix either covalently or by electrostatic interactions. These immobilization forces are sufficient to prevent shear-induced detachment of the hydrogel from the electrode surface. Enzyme cathodes for oxygen (O2) reduction reaction (ORR) in biofuel cells ORR at low overpotentials, which is defined as the additional potential (beyond the 64 thermodynamic requirement) needed to drive a reaction at a certain rate, 70,71 in developing fuel cell technology due to sluggish kinetics. is a major challenge The performance of oxygen 72 reducing bio-cathodes often limits the overall performance of biocatalyzed fuel cell systems. Hence, in this work, we aim at characterizing ORR by incorporating laccase, an oxygen reducing catalyst, in an Os-based mediated system with varying mediator redox potential. Multi-copper oxidases: biocathode catalyst Multi-copper oxidases (MCOs) constitute a family of enzymes that couple one electron oxidation of a substrate (which could be an electrode) with the complete four-electron reduction 73-78 of oxygen to water without forming a hydrogen peroxide intermediate. This makes MCOs a popular class of enzymatic biocatalyst for the oxygen reduction reaction (ORR). The blue MCOs are characterized by the presence of at least four copper (Cu) active sites organized and classified depending on spectral properties and electron paramagnetic resonance (EPR) 10 74,78-81 parameters. Type 1 (T1) Cu has a distinct absorption band at 600 nm (which makes the -1 -1 enzyme blue) (extinction coefficient, ε ~ 4500-5000 M cm ), and is characterized by weak -4 -1 parallel hyperfine splitting in EPR spectra (g|| = 2.3, A|| = (40-95) × 10 cm ). Type 2 (T2) Cu is a mononuclear Cu center that is not detected spectrophotometrically, but exhibits hyperfine -4 -1 EPR splitting typical of Cu ions in tetragonal complexes (g|| = 2.24, A|| = (140-200) × 10 cm ). Antiferromagnetically coupled diamagnetic binuclear type 3 (T3) Cu centers, is not EPR active, but has an absorption shoulder at 330 nm. The T2 and T3 Cu constitute the trinuclear cluster. For these metalloproteins, even though the metal centers constitute approximately ~0.1 82 wt % of the molecule, these metal centers and the microenvironment around them are the key parameters governing the reactivity, substrate specificity, and oxygen binding capabilities of 74,79 these enzymes. Selective removal of the T2-Cu site results in substantial loss of enzyme 83 activities. Each MCO exhibits specificity to a wide variety of organic substrates such as aromatic 74 phenols and amines as reducing substrates, 84 mechanism consistent with Marcus theory 78 specific binding pocket. with substrate (oxygen) binding and ORR and outer- sphere oxidation of co-substrate with no Since co-substrate oxidation occurs at the outer T1 active site, co- substrate specificity is largely governed by the structure around T1 and not near the T2/T3 tri74 nuclear cluster. 11 Laccase: the blue oxidoreductase Laccase [EC 1.10.3.2] is the simplest of the MCOs that is capable of complete four85 electron reduction of oxygen to water without forming a peroxide intermediate. Laccase is an oxidoreductase enzyme, which accomplishes the oxidation of phenolic compounds to ortho- and para-quinones coupled with the ORR. Laccase was first discovered in the Japanese lacquer tree, 86 Rhus vernicifera. As shown in Figure 1.4, the enzyme contains one type 1 CuII (T1-Cu) site, located in close proximity to the surface, that couples four one-electron co-substrate oxidation steps to a four-electron reduction of oxygen to water at the tri-nuclear cluster, located 13 Å away 87 and connected with a His-Cys-His tripeptide linkage. II II One type 2 Cu (T2-Cu) and one type 3 II binuclear Cu -Cu moiety constitute the tri-nuclear cluster. Use of laccase as a biocatalyst The first use of laccase as an oxygen reducing electrocatalyst was reported by Tarasevich 88 et al. in 1979. He reported that unlike Pt and other noble metal catalysts, oxygen was catalytically reduced to water by adsorbed laccase on carbon black, pyrographite, glassy carbon and gold electrodes at potentials as high as 1.2V depending on the construction of the electrode. The electrode surface acted as the co-substrate (DET). Trudeau et al. were the first to incorporate laccase (Trametes versicolor) into cross-linked redox polymer film to act as the sodium azide sensor. 89 -2 This device operated at its maximum current density, 60 µA cm . Palmore and Kim 47 reported the first use of a laccase bio-cathode in a H2/O2 fuel cell. 12 Hudak et al. demonstrated a -2 cell generating a power density of 3.8 mW cm in oxygen saturated system against a H2 90 oxidizing platinum anode. Choice of fungal laccase (Trametes versicolor) as a biocathode catalyst In nature, laccase is found in many higher plants, fungi, and microorganisms. For the purpose of this study, laccase from a white rot fungus, Trametes versicolor, has been used as a bio-cathode catalyst to study ORR. The reason for this selection is primarily its higher redox 91 potential. The co-ordination geometry around the T1-Cu site determines the redox potential of 92 the enzyme. For example, the three coordinated T1-Cu site in fungal laccases (e.g., Trametes versicolor), exhibits higher redox potential (~0.79 V) than four co-ordinate T1 laccases (~ 0.43 V) (e.g., Rhus vernicifera). 74,92 As a power-producing device, it is expected that a biofuel cell should produce high current density (i) at a high cell potential (Ecell) such that the power density (P, Equation 1.3), 48 which is defined as power produced per geometric electrode area, is maximized. P = iEcell [1.3] Figure 1.2 shows the schematic of a complete biofuel cell with a glucose oxidizing anode and an oxygen-reducing cathode. The anodic and the cathodic reactions occur according to the following reactions (Equation 1.4): 13 Anodic reaction : C6 H12O6 ⎯⎯⎯⎯⎯⎯⎯ 2H + + 2e− + C6 H10O6 → (glucose) (gluconolactone) 1 laccase Cathodic reaction: O2 + 2H + + 2e− ⎯⎯⎯⎯ H 2O → 2 glucose oxidase [1.4] As illustrated in Fig. 1.2, for a functioning biofuel cell, the potential gradient in a complete cell exists as given by Equation 1.5. The approximate overall cell potential is the potential difference between the cathode and the anode mediators (Equation 1.6). 19 Magnitude 0' 0' of electron transfer driving force ( ΔET = Eenz − Em ) between the mediator and the enzyme 56 determines the electron transfer efficiency. Hence, the choice of mediator potential at each electrode is critical. Choosing a cathode enzyme with a high redox potential (as in the case of fungal laccase from Trametes versicolor, ~0.82V/SHE) enables high overall cell potential. Increasing ΔET between the enzyme and the mediator would increase the reaction rate just as increasing the overpotential between the mediators at the two electrodes would increase Ecell, and hence cell power density. Therefore, choice of fungal laccase from Trametes versicolor - (TvL) with its high redox potential and capability for full 4e reduction of O2 to water, provides a wide operating window for choosing cathode mediators suited for a particular application. 0 0 0 0 Eanode-enzyme < Eanode-mediator External!Circuit < Ecathode-mediator < Ecathode-enzyme 0 0 Ecell ! Ecathode-mediator " Eanode-mediator [1.5] [1.6] Mediator redox potential and its effect on electrode kinetics Reaction rate at the bio-cathode is often limited by mass transfer of dissolved oxygen through the micron-sized enzyme-containing films attached to the electrodes especially for 14 56 porous electrodes. The redox potential of the mediator and its diffusivity are the most critical and sensitive parameters in controlling the overall performance of the mediated bio-electrodes. The presence of denaturants such as short chain alcohols in the system further affects the enzyme functioning. Decoupling inhibition and denaturation effects of short chain alcohols, such as methanol, is often difficult. In Chapters 2 and 3, we detail the effect of methanol, as a contaminant, on the function of mediated laccase-catalyzed oxygen-reducing electrodes for direct methanol fuel cell (DMFC) applications. The inherent problem of cathode catalyst poisoning in conventional DMFCs restricts the feed concentration to maximum of 1-2 M 38,41,93,94 methanol. We demonstrate that, by virtue of enzyme selectivity and specificity, this optimum concentration can be increased. Oxygen reduction reaction by laccase 2+ 75,78 The native state of laccase Cu centers is fully oxidized (Cu ). In terms of ORR catalysis, the oxygen binding mechanism and possible intermediates have been studied. Their geometric and electronic structures and structural-functional relationships have been proposed by 87 spectroscopic and quantum mechanical approaches such as X-ray crystallography, X-Ray 74- Absorption Spectroscopy (XAS) and EPR, especially for laccases from Rhus vernicifera. 76,78,82,92 The main steps involved in the oxygen reduction mechanism by laccase in a mediated (n-1) system are (Fig 1.4): (i) reduction of the T1-Cu site by the reduced substrate (Os ), (ii) electron transfer (ET) from the T1-Cu site to the trinuclear cluster, and (iii) reduction of oxygen 74,78 at the trinuclear cluster. 15 It is expected that in a mediated system, where the potential difference between the Os 2+ center of the mediator and that of the T1-Cu center of the enzyme governs the electron transfer 56 efficiency, and in turn controls the kinetics and the overall performance of the system, the intermediates involved in ORR might not be exactly similar structurally as for the free enzyme at 77 K. In Chapter 4, in collaboration with Dr. Sanjeev Mukerjee's group at Northeastern University, we have studied the ORR mechanism by an immobilized laccase in a mediated system using XAS as a function of the redox potential of the mediators when operated in-situ under ambient conditions. Maximizing utilization of the electro-active species immobilized on electrode surface For making bio-fuel cells a realizable power source, it is necessary that the trade offs between the enzyme catalytic activity and stability be understood, manipulated and resolved. These redox enzymes catalyze reactions involving at least two co-substrates and the concentration of these species in the microenvironment around the enzyme largely dictates enzyme turnover. The ability to understand and control physical parameters (such as film thickness and morphology, film homogeneity and uniform distribution of the electro-active species) governing such transport would dramatically improve design approaches for such cells. Sub-micron sized, enzyme-containing redox hydrogel films have the potential to maximize the utilization of the electro-active species by improved and uniform distribution, lowered mass transfer barrier and film resistances there by improving the catalytic current density. A convective self-assembly technique, widely used for casting uniform patterned sol-gel 16 films, 95-97 is adopted as an approach in Chapter 5 to attain such sub-micron homogeneous redox hydrogel films, which are reproducible and allow fast transport of the electrons, substrates and products leading to significant improvements in catalytic current density (per mole basis). Overview of this work The overall goal of this work is to determine the role of the mediator redox potential on the catalytic performance of the mediated bioelectrodes: how it affects enzyme kinetics and stability and influences contaminant effects. This work considers the mechanism of ORR by immobilized enzymes in a MET system, and targets maximum utilization of the electro-active species, reproducibility of such systems and aims at fully characterizing the physical parameters governing the overall electrode performance. It is expected that the findings would enable design of mediated electrodes for biofuel cell applications. Chapter 2 describes the role of mediator redox potential in controlling the fuel sensitivity of laccase (TvL) towards oxygen reduction in presence of a contaminant such as methanol. It is demonstrated that the sensitivity of oxygen reduction current density to the presence of methanol at such electrodes depends strongly on mediator redox potential and that the selectivity of laccase cathodes towards oxygen reduction can facilitate methanol feed concentration up to 5 M in direct methanol fuel cells (DMFC). Chapter 3 describes the role of mediator redox potential in governing the inhibition mechanism by methanol. It is demonstrated that presence of methanol primarily decreases the turnover number of the enzyme rather than altering substrate binding, suggesting a noncompetitive inhibition mechanism. It is expected that this part of the study would help increase 17 understanding of the inhibition mechanism of methanol for laccase and help design a sustainable biocathode particularly for miniaturized DMFCs applications. Chapter 4 delineates structural and functional interactions between the enzyme active sites and redox centers of the mediators in an electrochemically operating oxygen reducing mediated biocathode. This work demonstrates that the Cu active sites of TvL could be probed by XAS at micro-molar concentration levels. The oxidation state of the Cu active site is correlated to structural changes as a function of applied electrode potential, presence or absence of substrate (O2), and mediator redox potential. This is the first of such study conducted for mediated biocathodes with immobilized enzymes operating under ambient conditions. This would help elucidate the ORR mechanism in a mediated biocathode under operation. In Chapter 5, it is demonstrated that the convective self-assembly technique could be applied for casting homogeneous sub-micron enzyme-containing redox hydrogel films with repeatability. It is shown that such thin film electrodes drastically improve the utilization of the electro-active species enabling significantly higher catalytic current density (per mole basis) than conventional drop deposition technique. This approach provides grounds for characterizing thinfilm redox hydrogel electrodes in terms of electron transport properties and film morphology and gives a precise estimate of kinetic parameters. Chapter 6 summarizes this work and describes future advancements and possible ways forward. 18 Figure 1.1: Illustration of mechanisms of electron transfer from an electrode surface to an enzyme. (a) Direct electron transfer (DET), and (b) Mediated electron transfer (MET) where the redox-active species shuttles the electron between the electrode and the enzyme. “For interpretation of the references to color in this and all other figures, the reader is referred to the electronic version of this dissertation.” 19 Figure 1.2: Potential schematic of a glucose-oxygen biofuel cell. The potentials are referenced to the standard hydrogen electrode (SHE). 20 Figure 1.3: Generalized structures of the osmium based redox polymers illustrating the role of the chelated ligands in governing redox potential of the mediator. 21 Figure 1.4: Structure of laccase from Trametes versicolor (TvL). The four copper active sites are shown as blue spheres. Figure generated from its crystal structure using PyMol (pdb accession number 1GYC). 22 REFERENCES 23 References 1. W. R. 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Fan, "Evaporation-induced self-assembly: Nanostructures made easy," Advanced Materials, 11(7), 579-+ (1999). 32 96. M. Etienne and A. Walcarius, "Evaporation induced self-assembly of templated silica and organosilica thin films on various electrode surfaces," Electrochemistry Communications, 7(12), 1449-1456 (2005). 97. Z. Yuan, D. N. Petsev, B. G. Prevo, O. D. Velev and P. Atanassov, "Two-dimensional nanoparticle arrays derived from ferritin monolayers," Langmuir, 23(10), 5498-5504 (2007). 33 Chapter 2: Influence of Mediator Redox Potential on Fuel Sensitivity of Mediated Laccase Oxygen Reduction Electrodes Abstract The impact of methanol on oxygen reduction activity is studied using a mediated biocathode catalyzed by laccase from Trametes versicolor. The sensitivity of oxygen reduction current density to the presence of methanol at such electrodes depends strongly on mediator redox potential. This study demonstrates that the selectivity of laccase cathodes towards oxygen reduction can facilitate methanol feed concentration up to 5 M in direct methanol fuel cells (DMFC). Within the 0-5 M concentration range, methanol primarily affects enzyme kinetics and not the electron transport via the mediator. For methanol concentrations of 0–2.5 M, laccase activity towards oxygen was largely maintained; approximately 30% loss of activity occurred in the 2.5–5 M range, and irreversible loss of enzyme activity was observed beyond 7.5 M. Presence of methanol primarily decreases the turnover number of the enzyme rather than altering substrate binding, suggesting a non-competitive inhibition mechanism. It is proposed that this reduction occurs due to changes in the electron transfer environment near the T1 binding pocket due to the presence of methanol. 34 Introduction Direct methanol fuel cell (DMFC) technology provides a path towards high energy 1,2 density in small-scale electronic applications, 3-9 interest. which drives growing research and industrial However, energy density and power density in DMFCs are limited by low methanol 8 feed concentration, which minimizes parasitic consumption of fuel but increases onboard water requirements. The resulting increased weight prevents mainstream DMFCs from attaining the -1 10-12 ~500 W L power density desirable for sustained operation in hand-held portable devices. One promising solution is to use enzyme electrocatalysts at the cathode. Due to low cost, high substrate specificity and selectivity of enzymes as catalysts, enzymatic bio-fuel cells have been employed in small-scale low-power electronic devices such as biosensors, portable music 13 players, 14 and radio-controlled cars. Catalyst selectivity and specificity allow higher operating methanol concentrations and therefore higher power density. Hudak et al. demonstrated a 6% increase in current density at 0.4 V cell potential when operated at 10 M methanol as compared 15 to 1 M by using a mediated laccase bio-cathode. Sun et al. demonstrated that with introduction of 1 M methanol, the performance of a conventional Pt-catalyzed oxygen cathode was reduced by 22% while with laccase from Trametes versicolor (TvL) as the cathode catalyst, the 16 performance decreased only by 4.5% under similar experimental conditions. Laccase is the simplest of the multicopper oxidases with four copper active sites capable of four-electron reduction of oxygen to water without forming a soluble peroxide 17,18 intermediate. As shown in Figure 1.3 (Chapter 1), the metal centers at the active sites are 35 19-22 classified into three types depending on their spectroscopic characteristics. II The type 1 Cu (T1-Cu) site, located in close proximity to the surface, is the primary electron acceptor site from the substrates that couples four one-electron oxidation of the substrate to a four-electron 20,21 reduction of oxygen to water at the tri-nuclear cluster located at a distance of 13 Å. II II One II type 2 Cu (T2-Cu) and one type 3 binuclear Cu -Cu moiety constitute the tri-nuclear cluster, the primary site for oxygen reduction reaction. The rate of oxygen reduction at the cathode often limits the overall performance of 23 biofuel cells. Denaturants such as short chain alcohols can significantly impact enzyme function. Several studies have considered the effect of various short-chain alkanols such as ethanol and methanol on the enzymatic activity of free laccase from various sources (Phlebia 24 radiata, 25 Panus tigrinus, Polyporos versicolor, 26 and Phlebia oryzae 26 oxidation of syringaldazine, 2,6-dimethoxyphenol, and catechol. 27 ) by monitoring the The effect of these substances on laccase redox activity, and the mechanism of inhibition, depends on enzyme source, substrate, 24,25,27 and solvent’s hydrophobicity. In the presence of ethanol, free laccase from C. versicolor follows competitive inhibition kinetics for oxidation of hydrophilic organic substrates like 2,624,27 dimethoxyphenol, while laccase from P. tigrinus follows mixed inhibition kinetics. Such inhibition is attributable to easy solvent accessibility to the substrate-binding site, which is in 28-30 close proximity to the enzyme surface and is easily accessible. However, the yellow laccase from P. tigrinus was found to be stabilized in the presence of ethanol, attributed to variations in 36 25 enzyme structure. 31 Mozhaev et al. have shown that there exists a critical alcohol concentration, beyond which the activity of laccase steeply declines due to protein denaturation. Slow electron transfer between the electrode and the enzyme active sites largely limits 32 the performance of bio-electrodes. Electron transfer can be achieved by (a) Direct electron transfer (DET) between the electrode and the enzyme active site and (b) Mediated electron transfer (MET) in which small redox-active centers facilitate electron transfer to the enzyme active site. DET requires specific orientation of enzymes with their active site close to the 33 electrode to facilitate electron tunneling. DET can be challenging to reproduce and limits enzyme immobilization to a monolayer on the electrode surface. MET eliminates orientation dependency and allows multi-layer catalyst immobilization. Very high kinetically-limited current 34,35 density has been achieved by MET. In this study we immobilize laccase within a chemically cross-linked redox polymer hydrogel that allows free transfer of electrons, ions, and 16,36,37 oxygen. The redox polymer hydrogels contain Os redox active centers attached to a 36 water-soluble polymer backbone (Figure 2.1). 38-40 the redox potential of the mediator, Ligands attached to the Os redox centers control the degree of polymer complexation controls the active 36 site loading, and all these parameters affect the electron transfer and the reaction kinetics. In this work, we study the effect of methanol concentration on the activity of immobilized TvL in a mediated oxygen-reducing bio-cathode as a function of redox potential of the mediator. The potential difference between the Os center of the mediator and that of the T1- 37 2+ Cu 36 center of the enzyme governs the electron transfer efficacy and in turn controls the kinetics and the overall performance of the system. Mediator redox potential is found to be a key parameter that affects electrode degradation in the presence of methanol. The goal of this work is to identify the concentration window in which TvL can provide sustained performance towards the oxygen reduction reaction (ORR) as a function of mediator redox potential. The effect of methanol exposure on mediator performance was estimated in de-aerated citrate buffer (100 mM, pH~4, 40°C, 900 rpm) and evaluated using transient techniques like cyclic voltammetry (CVs), square-wave voltammetry (SWV) and impedance spectroscopy. The catalytic activity of mediated TvL electrodes towards ORR as a function of various methanol concentrations was evaluated by varying oxygen concentrations in composition buffer with or without methanol (100 mM, pH~4, 40°C, 900 rpm). 0' To study the effect of mediator formal potential ( Em ) on fuel sensitivity of laccase, redox mediators for the present study were chosen such that they differed only in their redox potential values (Table 2.1) and share a N-poly-vinylimidazole backbone and similar charge 41,42 density, which governs the swelling behavior of the charged hydrogels. This provided a basis to discern mediator influences on methanol sensitivity of TvL electrodes. Experimental Reagents and Chemicals TvL was purchased from Sigma-Aldrich (St. Louis, MO) and purified as previously 15 reported. Sodium citrate and citric acid were obtained from Fisher Chemical (Suwanee, GA). 38 Poly(ethylene glycol) (400) diglycidyl ether (PEGDGE, Polysciences Inc., Warrington, PA) was used as received. All the solutions were made with ultra filtered DI water (18 MΩ·cm). The three redox polymers A, B and C (Figure 2.1) were synthesized in-house according to reported 36 procedures. Polyvinylimidazole (PVI, MW= 43 kDa, glass transition temperature, Tg = 177°C) was synthesized by free radical polymerization using 1-vinylimidazole (Sigma Aldrich, St. Louis, MO) and azobisisobutyronitrile (Fisher Chemical, Suwanee, GA) as reported 36 previously. Ammonium hexacholoroosmiate, potassium hexachloroosmiate, 2,2'-bipyridyl (bpy), 4,4'-dimethyl-2,2'-bipyridine (dm-bpy), 2,2':6',2"-terpyridine (tpy), sodium dithionite, acetone, ethanol, methanol, dimethylformamide, diethyl ether, ethylene glycol (EG), 2,2'azinobis(3-ethylbenzthiazoline-6-sulfonic acid) (ABTS) and fluorescein isothiocyante (FITC) were purchased from Sigma Aldrich (St. Louis, MO) and was used as such without any further purification. Ultra-pure oxygen, air and nitrogen were obtained from Air Gas Great Lakes Inc. (Lansing, MI). Laccase electrode fabrication Activity of purified TvL enzyme was determined spectrophotometrically with ABTS in 50 mM citrate buffer (pH~4, 25°C). The estimated enzyme activity at room temperature with respect to ABTS as substrate was 190 ± 30 U/mg and assuming 100% protein and molecular weight of TvL to be 65 kDa (determined using SDS plate), the equivalent turnover rate was 200 -1 ± 22 s . The redox potential of the enzyme was estimated to be ~0.82 V/SHE as was indicated by the open circuit potential measurements of TvL modified glassy carbon electrodes which was 36 in accordance with the previously reported value. 39 Glassy carbon rotating disc electrodes (RDEs) of 3 mm diameter were constructed in-house using type 1 glassy carbon rods (Alfa Aesar, Ward Hill, MA). The electrodes were sanded using sequentially 600, 800, 1200 and 2400 grit ultrafine sand paper (Buehler, IL) and polished with 0.3 μm alumina slurries followed by ultra sonication for about 5 min in DI water. No electrochemical features were observed when the cleaned bare glassy carbon RDEs were tested in citrate buffer (pH~4, 100 mM, 40°C) at 50 mV/s scan rate, 900 rpm rotation. The biocathodes were fabricated by drop depositing a 5µL aliquot containing TvL (32 wt%), redox polymer (10 mg/ml) (61 wt%) and PEGDGE (5mg/ml) 2 (7 wt%) at a total loading of 0.693 mg/cm on a 3 mm diameter glassy carbon RDE. The electrodes were cured in air at room temperature for at least 10 - 12 hours under controlled humidity (< 10% RH) before testing. Electrochemical Studies Electrochemical studies were conducted in 100 mM citrate buffer (pH 4, 40°C) at varying alcohol and oxygen concentrations. Working electrodes were rotated at 900 rpm using a Pine rotator (Pine Instrument Co., Grove City, PA). The counter electrode was platinum wire, with an Ag|AgCl reference electrode (BAS, West Lafayette, IN). Data were collected with a VST ® Potentiostat and EC-Lab software (Bio-Logic USA, LLC, Knoxville, TN). Electrodes were tested in the following sequence: (a) in methanol-free citrate buffer, (b) in buffer containing methanol of known concentration; (c) again in methanol-free citrate buffer. Experiment (a) was repeated to determine the reversibility of effects associated with methanol. 36 Working electrode potentials were corrected for uncompensated resistance 40 by measuring high frequency resistance (RΩ), the real component of the impedance spectra measured at 200 kHz modulating frequency. This correction was only significant for high scan rate voltammograms such as Figure 2.2 (a,b,c) where the correction was a maximum of 1.7 ± 0.2 mV. Film thickness Dry and wet film thicknesses were measured using confocal microscopy using a Zeiss Pascal microscope, where the z-section of the film was mapped in terms of the intensity of the fluorophore, FITC. FITC containing films were excited with 488 nm Argon laser and the green emission was recorded with a 505 long pass filter. The hydrogel films (~3 mm diameter) containing FITC (~0.03 µg) were cast on cleaned glass slides with the same composition as electrodes, under identical drying conditions. Dry film thicknesses of these enzyme-containing cross-linked redox hydrogels were estimated first (averaged over three different measurements concentrating only at the center) followed by hydrating the films with composition buffer with or without methanol for approximately 5 minutes, excess buffer removal, and repeated measurement. Film thickness was obtained using MATLAB image analysis routines where the film edge was defined as the point where intensity fell below 50% of peak intensity (AppendixA). This approach of estimating dry film thickness matched well with the reported value of dry 43 film thickness for redox polymer A estimated using Atomic Force Microscopy (AFM). Results Under the given experimental conditions, methanol was not found to be electrochemically active at the mediated laccase electrodes. Cyclic voltammograms (CVs) obtained both in presence and absence of methanol for bare glassy carbon electrodes, electrodes 41 containing only the redox polymers and for electrodes containing both enzyme and redox polymers showed no electrochemical features (data not shown), indicating that methanol remained electrochemically inactive under the given experimental conditions. Representative polarization curves of oxygen biocathodes with the three redox polymer mediators in solutions of three different methanol concentrations (0, 2.5 and 10 M) are shown in Figure 2.2 (a,b,c). The oxygen reduction current density is essentially zero at high potentials, and 0' increases at potentials just above the mediator redox potential, Em . Under similar experimental conditions, the onset potential, the kinetics and the magnitude of plateau current density (ipl) are 0' 0 largely governed by the electron transfer driving force, ΔET = Eenz − Em' . Therefore, the 0 mediator redox potential, Em' , is an important parameter controlling the overall electrode performance under a given set of experimental conditions. 0 At potentials far below Em' , a potential independent limiting plateau current is observed. For polymer A, plateau current densities, ipl, were obtained at ~0.2 V/SHE, while for polymers B and C, ipl was measured at ~0.4V/SHE. Variation of ipl with methanol concentration was considered as a measure of methanol sensitivity of the electrodes. Comparison of the methanol sensitivity of these three systems, as indicated in Fig. 2.2d, demonstrates that no significant difference was observed in overall electrode performance between the three mediated systems at low methanol concentration range (0.5 M - 2.5 M) while a 0 distinct dependence on Em' of the redox mediators emerges beyond 2.5 M. However, higher 42 concentrations of methanol (7.5 M onwards) had a deleterious effect on the enzyme resulting in significant loss of the oxygen reduction current. For the 10 M methanol case, hysteresis appeared -1 at low scan rate (1mV s ) cyclic voltammograms (CVs) indicating instability (Fig. 2.2 a,b,c), 24,26,27,31,44 which is in accordance to that reported in the literature. The dependency of enzyme 0 electrode performance on the Em' of the redox mediators is also indicated by the fact that the % reduction in the catalytic reduction current is much lower for polymer A (5% at 2.5 M methanol and 69% at 10 M) as compared to polymer B (7% and 93%) and polymer C (15% and 96%). Redox mediator performance Figure 2.3 (a,b,c) compares CVs of the three redox polymers at three different representative methanol concentrations. Figure 2.3 d shows the relative peak heights (relative to that of 0 M methanol) of these electrodes as a function of methanol concentration. Methanol appears to affect peak current similarly for all polymers (Fig. 2.3 d). Figure 2.4 indicates the effect of methanol on active Os content of the hydrogel films as determined by square wave voltammetry in de-aerated buffers with or without methanol. Squarewave voltammetry is a powerful electrochemical tool for estimating charge transferred due to faradaic reactions alone and hence gives a precise estimate of the electro-active species at the 45 electrode surface. A representative plot of the difference current (idel=iforward-ireverse) versus time is shown in Fig.2.4a for all the three mediated systems measured in de-aerated 100 mM citrate buffer (pH~4, 40°C, 900 rpm). The estimated accessible active Os content (Fig. 2.4b) also 43 substantiated the fact that methanol similarly affects the performances of all the three redox mediators over the entire concentration range studied. Electron transport Charge transport properties in these charged hydrogels are typically characterized by estimating the apparent electron diffusion coefficient, Dm, via cyclic voltammetry with scan -1 rates from 50 to 1000 mV s . The peak current densities (ip) from the cyclic voltammograms were found to vary linearly with square-root of scan rate indicating semi-infinite diffusion 46 (Figure 2.5a) as expressed by Randles-Sevcik equation ⎛ F3 ⎞ ip = 0.4463 ⎜ ⎟ ⎝ RT ⎠ 12 12 * n 3 2Cm Dm υ1 2 [2.1] where F is Faraday’s constant, R is the universal gas constant, T is the temperature, n is the * number of electrons transferred in the redox reaction, Cm is the bulk mediator concentration, and v is the scan rate. Figure 2.5b illustrates the effect of exposure of methanol on Dm of the mediators. Again, all three mediators were similarly sensitive to methanol in terms of their transport properties. Hydrogel thickness and swelling The thickness of the wet enzyme and mediator-containing hydrogel electrode impacts performance via transport and kinetic parameters. Inclusion of metal chelates within PVI hydrogels reduces swelling to a great extent as compared to PVI alone, and a swelling factor of 44 47,48 ~1.5 by mass of complexed hydrogels has been reported. Previous workers have used 49 various approaches such as environmental scanning electron microscopy 47 microscopy and atomic force to estimate water-swollen redox hydrogel film thicknesses. Here, we employ confocal microscopy combined with a fluorophore incorporated within the hydrogel film (Figure 2.6a). As indicated in Figure 2.6b, the swelling properties of these three different polymers were similarly affected in the concentration range studied. Addition of buffer to the film leads to swelling of ~1.5 to ~2.5 fold; this is equivalent to 0.56% to 1.7% on a weight basis at room temperature (assuming absorption of pure water). However, with increased methanol concentration, a relative deswelling of the hydrogel films was observed for all three systems. Polymer A de-swelled to a thickness somewhat below that of the dry state, possibly due to loss of material upon hydration. Polymers B and C oscillated in thickness with methanol concentration but ultimately reached thickness below the dry state as well. To summarize the above observations, increased methanol concentration leads to slight decrease in Dm, peak height, and accessible active Os content that may be related to de-swelling of the hydrogels as is indicated in Fig. 2.6b. Deswelling of the films is known to impact mobility 50 and accessibility of the bounded redox active species. Enzyme kinetics Though methanol had no significant effect on the electron transport via the redox polymers (Fig. 2.5b), a significant loss of electrode performance towards ORR was observed 45 with increasing methanol concentration (Fig. 2.2d). Beyond 2.5 M methanol, a distinct reduction 0 in the catalytic reduction current was observed for lower mediator Em' leading to lower sensitivity to methanol. We speculate that this reduction in the plateau current density (ipl) as a function of methanol concentration was primarily due to the impact of methanol on enzyme kinetics rather than transport effects. The half-wave potential (E1/2), defined as the potential at which the catalytic reduction current density is half of ipl, showed no dependence on methanol concentration for all three systems (Figure 2.7a). The formal potential of the mediators also remained unaffected by methanol for the entire concentration range studied (Figure 2.7b). Analysis of the data indicated that the apparent Michaelis-Menten binding constants remained almost unaffected for all the 51 three systems (Chapter 3). Therefore, we infer that the turnover number of the enzyme was affected primarily rather than the binding constants indicating non-competitive inhibition kinetics (Quantitative estimates are in Chapter 3). Electrode stability Figure 2.8 indicates representative relative stability of the three mediated systems under similar experimental conditions in 2 M methanol containing oxygen saturated citrate buffer 0 solution (100 mM, pH ~ 4, 40°C, 900 rpm). A distinct dependency on Em' of the mediators was observed in the stability studies at all methanol concentrations, with a steep initial decrease of the electrode performance as evident for polymer C with lowest electron transfer driving force as compared to a gradual loss of performance within the same time frame of the systems containing 46 polymer A with maximum driving force for electron transfer. Part of the decreased activity of the electrodes over a long period of time, however, is also attributable to loss of enzyme and mediators from the electrode surface due to high shear as well as denaturation of the enzyme. The stability studies were conducted at all the methanol concentrations and similar trend as in Fig. 2.8 was observed for all conditions. Sensitivity to substrate (Oxygen) Figure 2.9 shows the effect of varying oxygen concentrations in presence of methanol. The plateau current, ipl, was measured at 900 rpm by chronoamperometry, while the oxygen concentration was varied from 0 to 100% by diluting with nitrogen. Electrodes based on polymer C, with the lowest ΔET, become oxygen saturated at low oxygen concentrations (Fig. 2.9c). The response shows a distinct decrease in the plateau current density with methanol concentration for this system. Polymer A containing electrodes, in contrast, show no distinct sensitivity to increasing methanol concentration. For the intermediate redox potential (polymer B), the effect was found to be in between the two extreme cases of purely mediator kinetics controlled (polymer A) and purely enzyme kinetics controlled (polymer C) cases. Discussion Methanol induced a substantial loss of activity of the mediated TvL electrodes, particularly beyond 2.5 M concentrations where a distinct trend emerged indicating clear 21,28-30 0 dependency on Em' of the redox mediators. As indicated in literature, the microenvironment around the T1-Cu site in TvL and other multi-copper oxidases determines the redox potential as well as the substrate specificity of these enzymes. Methanol is a known 47 26 denaturant of proteins and acts as an inhibitor without affecting any specific active sites. As elucidated by Rodakiewicz-Nowak et al. and Bogdanovskaya et al., the denaturing effect of methanol as a solvent is associated with its capability of irreversibly replacing the hydrating 24-27 water molecules in enzymes beyond a certain effective concentration. Mozhaev et al. reported that for free laccase in aqueous solutions, there exists a certain critical concentration of water miscible organic solvents (usually 20-50% by volume, i.e. 4 M – 7.5 M) within which 31 spectral characteristics of free proteins change considerably indicating denaturation. However, immobilized enzymes may be less susceptible to these adversities due to restricted and more controlled microenvironments and hence the threshold for denaturation of an immobilized enzyme may be higher than that of a free enzyme. Replacement of the hydrating waters by solvent molecules would change the microenvironment around the more accessible T1-Cu site of 20,21,30 TvL due to its proximity to the surface and hence might alter the effective redox potential of the enzyme thereby modulating the electron transfer driving force as a function of methanol concentration. This exchange is however reversible at low methanol concentrations (< 25 vol % i.e. < 3 M) 26 24,31,52 and irreversible at higher concentrations (> 55 vol % i.e. > 7.5 M). Figure 2.10a indicates residual electrode activity after methanol exposure and subsequent removal, under similar experimental conditions as in Fig. 2.2. Three distinct methanol concentration windows could be segregated for the systems studied: (a) between 0.5 M – 2.5 M methanol concentration, limited or no significant difference in performance was observed due to the presence of methanol, (b) >2.5 M to ≤ 5 M where the modified electron transfer driving force plays a vital role in governing the performance of the mediated biocathode, and (c) beyond 5 M 48 and 7.5 M onwards, where the substantial irreversible reduction of catalytic performance is observed. Figure 2.10b depicts residual measurements of apparent electron diffusivity, Dm, of each electrode, again after methanol exposure and subsequent removal. No substantial reduction in Dm was indicated even at higher methanol concentrations. This data, combined with the activity data of Fig. 2.10a, further substantiates the theory that loss of performance of the mediated systems beyond 5 M methanol was primarily due to irreversible denaturation of the active enzymes. From the above discussion it can be concluded that the effect of methanol as a contaminant in the system for the mediated bio-cathodes under study largely depends on the methanol concentration regime. Within the 0-5 M concentration range methanol affects the enzyme kinetics more significantly than mediator transport properties and non-competitive inhibition kinetics has been proposed to explain the observed experimental trend. Conclusions The selectivity of mediated TvL oxygen cathodes could facilitate high methanol feed concentrations for DMFC applications. Short-chain alcohols like methanol are known denaturants of enzymes. In the present study, enzymatic performance versus methanol concentration indicated a threshold methanol concentration of ~5 M below which electrode sensitivity was reversible and above which the sensitivity was irreversible. Mediator transport performance, as measured by apparent electron diffusion, remained largely independent of 49 methanol concentration, and the small dependence that was observed is attributed to deswelling of the electrode films in the presence of methanol. These results suggest that a mediated laccase electrode may be applied in a direct methanol fuel cell operating on elevated methanol concentrations as long as those concentrations remain below 5M. A subsequent kinetics study will identify those kinetic parameters that are directly impacted by the presence of methanol. Acknowledgements The authors gratefully acknowledge support from the University of New Mexico under contract FA9550-06-1- 0264 from the Air Force Office of Scientific Research. 50 Table 2.1: Redox polymer properties − Length/ e % Os charge (Å) 0.43 Structural Formula Wt. SHE) RP 0 Em' (V | 11 30 0.39 0.77 6.6 25 0.05 0.82 9.2 18 ~0 +/2+ A poly (n-VI12[Os(bpy)2Cl] B poly (n-VI20[Os(tpy)(dm-bpy)] C poly (n-VI15[Os(tpy)(bpy)] ) 2+/3+ 2+/3+ ) ) 51 ΔET (V) Figure 2.1: Structure of redox mediators 52 Figure 2.2: Oxygen reduction polarization mediated laccase electrodes. Polarization curves (iR-corrected) at three different methanol concentrations for (a) RP A; (b) RP B; (c) RP C mediated bio-cathode systems and; (d) plateau current densities (ipl) as a -1 0 function of methanol concentration and Em' Scan rate 1 mV s at 900 rpm in oxygen -2 saturated 100 mM, pH 4 citrate buffer at 40°C. Total loading 0.69 mg cm with Laccase: RP: cross-linker :: 32:61: 7 (wt %). 53 Figure 2.3: Cyclic voltammograms (CVs) of representative planar enzyme electrodes containing (a) RP A; (b) RP B; (c) RP C at three different methanol concentrations (0, -1 2.5 and 10 M methanol) recorded at 50 mV s scan rate at 900 rpm in de-aerated 100 mM, pH 4 citrate buffer at 40°C; (d) relative reduction peak height obtained from 50 mV -1 s CVs in de-aerated buffers as a function of methanol concentration. Relative peak height at each methanol concentration is the reduction peak height relative to that of the 0 M case for the same electrode. 54 Figure 2.4: (a) Plot of the difference current (idel) at the end of the forward and the reverse pulse of a square-wave cycle versus time for the three redox polymer -1 containing films at 250 mV s scan rate; and (b) active Os content of the films as determined by square wave voltammetry in a de-aerated buffer. Experimental conditions: 900 rpm in de-aerated citrate buffer (100 mM, pH~4) at 40°C. 55 Figure 2.5: (a) Randles-Sevcik analysis. Linearity of variation of peak current density (ipl) (for 0M) with square root of scan rate and the fitted curves passing through the - origin is indicative of semi-infinite diffusion. (b) Apparent e diffusion coefficient (Dm) of the mediators as a function of methanol concentration. Dm estimated by fitting the CVs -1 at 50 mV s scan rate in de-aerated buffers with or without methanol at 900 rpm. -1 (Inset) Experimental conditions: 900 rpm, 50 mV s (100 mM, pH~4, 40°C). 56 scan rate, de-aerated citrate buffer Figure 2.6: (a) Film thickness was determined under ambient conditions by confocal microscopy using a Zeiss Pascal microscope, where the z-section of the film was mapped in terms of the intensity of the fluorophore, Fluorescein isothiocyanate (FITC) (0.03 µg) of a 3 mm diameter of cross-linked enzyme-containing redox hydrogel film on a cleaned glass slide. FITC containing films were excited with 488 nm Argon laser and the green emission was recorded with a 505 long pass filter. (b) Film thickness of the redox polymer and enzyme-containing hydrogels as a function of methanol -2 concentration. Total loading 0.69 mg cm with Laccase: RP: cross-linker:: 32:61: 7 (wt%). 57 Figure 2.7: Effect of methanol on (a) half-wave reduction potential (E1/2) of the steady 0' state catalytic reduction current and (b) formal potential ( Em ) of the mediated biocathode. The formal potentials were estimated from CVs as indicated in Fig. 2.3 and the half-wave potentials were estimated from steady state polarization curves as indicated in Fig. 2.2. E1/2 is the potential at which the steady state current density is half of that of the plateau current (ipl). 58 Figure 2.8: Oxygen reduction stability of the laccase containing mediated biocathodes in oxygen saturated 2 M methanol for the three different mediators under identical loading conditions. The electrode was poised at ~0.4 V | SHE for systems containing redox polymers B and C while at ~0.2 V | SHE for redox polymer A. Relative current density is defined as the ratio of the current density as a function of time and the max current density for the control in 0 M for the respective systems. Chronoamperommetric measurements were taken at 900 rpm, 40°C. 59 Figure 2.9: Effect of variation of oxygen at various methanol concentrations for (a) RP A, (b) RP B, and (c) RP C. The data points represent plateau current density from chronoamperommetric measurements in oxygen saturated citrate buffer with or without methanol, 900 rpm, 40°C. The electrodes were poised at a potential in the plateau current region of the polarization curves (Fig. 2.2) for the respective systems. 60 Figure 2.10: Residual effects of methanol exposure on (a) the catalytic performance of the planar biocathodes towards ORR (reduction plateau current density, ipl) in oxygen saturated buffer, 900 rpm, 40°C and; (b) on apparent electron diffusion coefficients (Dm) for the three RPs. 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Martinek, "Denaturation Capacity - a New Quantitative Criterion for Selection of Organic-Solvents as Reaction Media in Biocatalysis," European Journal of Biochemistry, 198(1), 31-41 (1991). 68 Chapter 3: Modeling Inhibition by Methanol in Mediated Laccase Electrodes for Oxygen Reduction Reaction (ORR) Abstract A quantitative study of the effect of methanol on the diffusion-reaction system within uniform mediated laccase redox hydrogel films immobilized on glassy carbon rotating disc electrodes is presented in this work. The impact of methanol on the oxygen reduction activity and sensitivity of a mediated biocathode catalyzed by laccase from Trametes versicolor depends strongly on mediator redox potential. Within 0-5 M concentration range, methanol primarily affects enzyme kinetics and not the electron transport via the mediator. It is demonstrated that methanol primarily decreases the turnover number (kcat) of the enzyme rather than altering substrate binding (KM, KS), suggesting a non-competitive inhibition mechanism. Mediator redox potential and diffusivity are shown to directly affect the magnitude of kcat. Above 2 M methanol, the loss of enzyme turnover number was steep. Depending on the relative magnitudes of halfwave potential and mediator redox potential for the three systems, overall electrode kinetics can be identified as mediator transport limited, mediator kinetics limited, or electrode kinetics limited. Mediator redox potential and the magnitude of electron diffusivity via the mediators are shown to directly affect the occurrences of various limiting cases. 69 Introduction It has been demonstrated in Chapter 2 that in a mediated system, the sustained performance of the TvL biocathode largely depends on the mediator redox potential. Within 05M concentration range, methanol affects the enzyme activity rather than electron transport via the mediators. This study would address to some extent the technological challenges associated with mixed reactant Direct Methanol Fuel Cell (DMFC) systems. Design and optimization of such systems require a detailed knowledge of the enzyme kinetics, accurate knowledge of substrate, co-substrate, and enzyme concentrations, and characteristic electrochemical response from the overall system. In this work, we focus on understanding and determining the kinetics of ORR by mediated TvL and the role of mediator redox potential in controlling the overall electrode kinetics. We identify the mechanism of inhibition due to presence of methanol. The structure and the properties of the redox polymers under consideration for this study are described in Figure 3.1 and Table 3.1. Figure 3.2 demonstrates a typical electron flow diagram in a mediated biocathode. In an ORR scheme, TvL catalyses the four electron reduction of oxygen to water coupled with four one-electron oxidations of substrate (mediator redox center) following bi-bi-ping-pong mechanism (Equation 3.1). 1,2 k k2 1" !!!! S + Ered #!!! ES ""# P + Eox ! k!1 k3 [3.1] k4 !!!! " M red + Eox #!!! EM ""# Ered + M ox ! k!3 The bi-bi-ping-pong mechanism is a two-substrate enzymatic reaction sequence where 3-5 the first product is released before the second substrate attaches to the enzyme. 70 S represents O2, P the product, Mred and Mox are the reduced and oxidized forms of the mediators respectively and Ered and Eox are the reduced and oxidized forms of the enzyme respectively. k1, k-1, k2, k3, k-3, and k4 are the rate constants of the respective steps. Assuming steady state kinetics, the enzymatic reaction rate is given by Equation 3.2, where is the total enzyme concentration, kcat is the enzyme turnover number and KM and KS are the Michaelis constants for Mred and S respectively. kcat , the enzyme turnover number, represents the maximum number of substrate molecules converted to products per active site, per 4 unit time. In a simple Michaelis-Menten mechanism, kcat is the first order rate constant for the chemical conversion of [ES] to product. In more complex systems such as in bi-bi-ping-pong kinetics, kcat is a function of all the first order rate constants. KM and KS are the apparent dissociation constants of the respective enzyme-bound species (Mred and S) and are defined as the substrate concentration at which the enzymatic reaction rate is half of that of the maximum rate of reaction. The expressions for kcat, KM, and KS are depicted in Equation 3.3. This enzymatic reaction is coupled with the electrochemical reduction of Mox at the electrode surface (Equation 3.4), which is characterized by fast electrode kinetics and follow Nernstian kinetics at the electrode surface. This system can be modeled as described elsewhere and the kinetic 1,6-8 parameters can be extracted by fitting the experimental data with the theoretical model. vE = kcat [ ET ][ S ][ M red ] K S [ M red ] + K M [ S ] + [ S ][ M red ] 71 [3.2] kcat = ( ( k−1 + k2 ) ; K = k2 ( k−3 + k4 ) ( k2 + k4 ) M k3 ( k2 + k4 ) k ; KS = 4 k2 + k4 k1 k2 k4 ) [3.3] " k !!!! " M ox + ne! #!! M red # k [3.4] In Chapter 2, it was demonstrated that methanol, within the concentration window of 0-5 M, acts as an inhibitor for TvL towards ORR by influencing enzyme activity rather than the electron transport properties via the mediators. From experimental observations it was hypothesized that methanol inhibits enzyme kinetics by affecting its turnover number rather than the binding constants. A non-competitive inhibition mechanism (Figure 3.3) was suggested for both the mediator and the substrate reaction, where the inhibitor (I) binds to both the free and complex forms of the enzyme. The enzymatic reaction rate expression for cases where methanol was present can be similarly derived and is of the same form as the bi-bi-ping-pong mechanism (Equation 3.5), where apparent kinetic constants incorporate the effect of inhibitor concentration. vE = kcat,app [ ET ][ S ][ M red ] K S,app [ M red ] + K M,app [ S ] + [ S ][ M red ] [3.5] For this kinetic study, 0-5 M methanol concentration range was chosen for the kinetic parameter estimations in order to capture the inhibitory effect of methanol on the mediated enzyme electrode performance rather than the denaturation kinetics. 72 Modeling electrochemical responses from systems containing immobilized enzymes trapped within redox hydrogel films on electrode surfaces is not straightforward because of the non-linear forms of the coupled diffusion-reaction equations. Approximate analytical solutions of these systems generally depend on identifying suitable limiting cases in which the non-linear coupled equations can be simplified, linearized, and solved. Figure 3.2 represents the operation of a laccase catalyzed oxygen reducing mediated biocathode where both the redox mediator and the enzyme are co-immobilized on the electrode surface. One substrate (O2) diffuses into the film from the solution while the charge transfer through the matrix occurs by diffusion of electrons via the mediators. So the overall performance of the electrodes largely depends on the relative rates of diffusion and reaction kinetics. When the mediator-enzyme reaction kinetics is rate determining, the overall current density out of the system does not depend on substrate mass transport or Michaelis-Menten kinetics, but depends on the applied electrode potential which directly controls mediator concentration within the film and hence the rate of reaction. When the enzyme-substrate kinetics is rate limiting, the system becomes complicated because of the presence of the non-linear Michaelis-Menten term. It is possible that the Michaelis-Menten kinetics is saturated at the filmsolution interface where [S] is large and unsaturated near the electrode surface where [S] is small. Bartlett and Pratt have identified such complicated limiting cases. They have discussed in details their simulation approaches and predicted electrochemical responses from these electrode 6 systems. Our approach in this work is to identify such limiting conditions as delineated by Bartlett and Pratt, to best fit the observed performance of the three mediated enzymatic systems under various operating conditions. This allows us to have a better understanding of the role that 73 a mediator plays in controlling the overall catalytic performance of a mediated biocathode system. Experimental Reagents and Chemicals All the reagents required for this work are listed in the experimental section of Chapter 2. Laccase Electrode Fabrication The activity of purified TvL enzyme was determined spectrophotometrically with ABTS in 50 mM citrate buffer (pH~4, 25°C). The estimated enzyme activity at room temperature with respect to ABTS as substrate was 190 ± 30 U/mg and assuming 100% protein and molecular weight of TvL to be 65 kDa (estimated using SDS PAGE), the equivalent turnover rate was 200 -1 ± 22 s . The redox potential of the enzyme was estimated to be ~0.82 V/SHE as was indicated by the open circuit potential measurements of TvL modified glassy carbon electrodes which was 1 in accordance with the previously reported value. Glassy carbon rotating disc electrodes (RDEs) of 3 mm diameter were constructed in-house using type 1 glassy carbon rods (Alfa Aesar, Ward Hill, MA). The electrodes were sanded using sequentially 600, 800, 1200 and 2400 grit ultrafine sand paper (Buehler, IL) and polished with 0.3 µm alumina slurries followed by sonication for about 5 min in DI water. No electrochemical features were observed when the cleaned bare glassy carbon RDEs were tested in citrate buffer (pH~4, 100 mM, 40°C) at 50 mV/s scan rate, 900 rpm rotation. The biocathodes were fabricated by drop depositing 5 µL aliquot containing TvL (32 wt%), redox polymer (10 mg/ml) (61 wt%) and chemical cross linker (PEGDGE) 2 (5mg/ml) (7 wt%) at a total loading of 0.6925 mg/cm on a 3 mm diameter glassy carbon 74 rotating disc electrode (RDE). The electrodes were cured in air at room temperature for at least 10 - 12 hours under controlled humidity (< 10% RH) before testing. Electrochemical Studies Electrochemical studies were conducted in 100 mM citrate buffer (pH 4, 40°C) at varying alcohol and oxygen concentrations. Working electrodes were rotated at 900 rpm using a Pine rotator (Pine Instrument Co., Grove City, PA). The counter electrode was platinum wire, with an Ag|AgCl reference electrode (BAS, West Lafayette, IN). Data were collected with a VST ® Potentiostat and EC-Lab software (Bio-Logic USA, LLC, Knoxville, TN). All the electrochemical experiments used for modeling these mediated biocathodes in presence or absence of methanol are described in details in Chapter 2. Mediated enzyme electrode model The reaction rate of the planar electrodes is limited by mediator electrode kinetics at the electrode surface, the mediator transport properties within the film, transport of the second 1,9 substrate (O2) from the bulk solution to the film, and enzyme kinetics. With the assumptions that the enzyme and the mediator are co-immobilized on the electrode surface and remain - contained within the homogeneous hydrogel film, and that transport of the reactive species (e and O2) within the film occurs only by diffusion, the following 1-D homogeneous reactiondiffusion balance equations for the mediator (Mred) and O2 (S) can be proposed to model the system (Equation 3.6). 1,6 The stoichiometric coefficients for the electrons transferred are assumed to be 1. 75 Dm d 2 M red dx 2 = kcat,app ⎡ ET ⎤ ⎡ S ⎤ ⎡ M red ⎤ ⎣ ⎦⎣ ⎦⎣ ⎦ KS,app ⎡ M red ⎤ + K M,app ⎡ S ⎤ + ⎡ S ⎤ ⎡ M red ⎤ ⎣ ⎦ ⎣ ⎦⎣ ⎣ ⎦ ⎦ 1 k ⎡ E ⎤ ⎡S ⎤ ⎡ M ⎤ 4 cat,app ⎣ T ⎦ ⎣ ⎦ ⎣ red ⎦ DS = dx 2 KS,app ⎡ M red ⎤ + K M,app ⎡ S ⎤ + ⎡ S ⎤ ⎡ M red ⎤ ⎣ ⎦ ⎣ ⎦⎣ ⎣ ⎦ ⎦ d 2S [3.6] The boundary conditions for solving the governing equations are given by Equation 3.7. At the electrode-film boundary (x=0), the current is given by Butler-Volmer expression, where the applied electrode potential (V) controls the reduced mediator concentration and there is no substrate (S) flux. At the film-solution interface (x=L, L = film thickness), the mediator flux is zero (the mediator is contained in the film) and the substrate concentration (S) is equal to that of 0 0' the bulk (S0). ⎡ M total ⎤ is the total bulk mediator concentration, Em is the mediator formal ⎣ ⎦ potential. The exchange current density (i0), as indicated in the Butler-Volmer expression, is an indicative measure of the mediator kinetics and was estimated to be very large indicating that the mediator kinetics is very fast at the electrode surface. Therefore, at any point of time, there exists Nernstian kind of equilibrium at the electrode surface, which determines the mediator concentration (Equation 3.8). Assuming Nernstian equilibrium at the electrode surface, the 0 relative [Mred] to ⎡ M total ⎤ is given by Equation 3.9, where η is the electrode overpotential ⎣ ⎦ defined as the potential difference between the applied electrode potential (V) and the mediator 0' formal potential ( Em ). 76 x = 0: dS = 0; dx i = −nFDm x=L : dM red dM red dx dx ⎧⎛ 0 ' ⎤⎫ ⎡ V − E0 ' ⎤ M ⎡ M red ⎞ ⎪ red exp ⎢ V − Em ⎥ ⎪ m ⎥− ⎢− ⎟ exp = i0 ⎨⎜ 1 − ⎬ 0 ⎢ ⎢ b ⎥⎪ b ⎥ M0 M total ⎟ ⎪⎜ ⎝ ⎠ x=0 ⎣ ⎦ ⎣ ⎦⎭ total ⎩ [3.7] = 0;S = S 0 RT ⎡ M ox ⎤ ⎦ E = E0 ' + ln ⎣ nF M red [ M red ] ⎡M 0 ⎤ ⎣ total ⎦ = [3.8] x=0 1 [3.9] ⎡ ⎛ 2η ⎞ ⎤ ⎢1 + exp ⎜ b ⎟ ⎥ ⎝ ⎠⎦ ⎣ The Tafel slope (b), which is a measure of quasi-reversibility of the redox species at the 1,10 electrode surface, was found to remain unaffected by methanol (Fig. 3.4). The fact that these hydrogels followed semi-infinite diffusion (as established in Chapter 2, Fig. 2.5a), allowed estimation of Dm,app and Tafel slope (b) for these three mediated systems from high scan rate (50 mV/s) CVs obtained in de-aerated buffer (Appendix B1). Figure 3.5 shows a representative fit of the CVs for the three mediated systems. Bounded diffusion (peak current varying linearly -1 with scan rate) was observed at scan rates below 50 mV s . The magnitudes of the diffusion coefficients estimated from fitting the cathodic waves were within limits of that estimated using Randles-Savcik analysis as described in Chapter 2 (Fig. 2.5b). For modeling these systems, DS -5 was assumed to be equal to 3×10 2 -1 9 cm s with no partitioning of Oxygen into the film. In the 77 context of an RDE experiment this is equivalent to infinite rotation, and can be accounted for by correcting the loss due to external mass transfer limitations using Koutecky-Levich (KL) analysis (Equation 3.10). 10 The measured film thickness (~ 2.5 µm or less) was much less than the 1 calculated diffusion layer thickness for these experiments (11 µm at 3600 rpm). 1 1 1 2 * = + ; ilim = 0.62nFDm 3υ −1 6ω 1 2CS ipl ilim ipl,k [3.10] where, ipl is the plateau current density, ilim is the limiting current density given by Levich ( -1 ) equation ilim! " , ipl,k is the kinetic plateau current density, ω is the rotation speed (rad s ), 2 -1 ν is the kinematic viscosity (cm s ), n is the number of electrons transferred, F is Faraday's * constant and CS is the bulk substrate (O2) concentration. All the biocathodes produced linear ( ) −1 KL plots ipl  vs ω −1 2 at all substrate concentrations such that the mass transport corrected kinetic plateau current density could be obtained from the extrapolation of the plot to the ordinate. Film thickness and Concentration estimations Dry and wet film thicknesses were measured using confocal microscopy using a Zeiss Pascal microscope, where the z-section of the film was mapped in terms of the intensity of the fluorophore, Fluorescein isothiocyanate (FITC). FITC containing films were excited with 488 nm Argon laser and the green emission was recorded with a 505 long pass filter. The hydrogel films (~3 mm diameter) containing FITC (~0.03 µg) were cast on cleaned glass slides from a 78 5µL drop of the precursor solution having the same composition as for the RDE experiments, under identical drying conditions. Dry film thicknesses of these enzyme-containing cross-linked redox hydrogels were estimated first (averaged over three different measurements concentrating only at the center) followed by hydrating the films with composition buffer with or without methanol for approximately 5 minutes, excess buffer removal, and repeated measurement. Film thickness was obtained using MATLAB image analysis routines where the film edge was defined as the point where intensity fell below 50% of peak intensity (Appendix-A). From the average film thickness measured, the film volume as well as the Osmium and enzyme concentrations could be determined using the known mass loadings (Table 3.2). Addition of buffer to the film leads to swelling of ~1.5 to ~2.5 fold; this is equivalent to 0.56% to 1.7% on a weight basis at room temperature (assuming absorption of pure water). However, with increased methanol concentration, a relative deswelling of the hydrogel films was observed for all three systems (Figure 2.6b). Polymer A de-swelled to a thickness somewhat below that of the dry state, possibly due to loss of material upon hydration. Polymers B and C oscillated in thickness with methanol concentration but ultimately reached thickness below the dry state as well. Results and discussion To obtain the parameters defining the enzyme-mediator and the enzyme-oxygen interactions, experiments were designed to vary one substrate at a time. Polarization curves as shown in Fig. 2.2 were obtained at constant O2 concentration while [Mred] was constantly varied with the applied electrode potential. For oxygen concentration variation data as in Fig. 2.9, 79 [Mred] was fixed by applying a constant electrode potential while O2 fraction (diluted with N2, under atmospheric pressure) in the buffer was varied. 0' Case studies: effect of Em in controlling overall electrode kinetics It has been demonstrated in Chapter 2 that even though there was a significant loss of catalytic reduction current density with increasing methanol concentration (Fig. 2.2, Chapter 2), the half-wave potential (E1/2), i.e. the potential at which the reduction current density was half 0' the magnitude of the plateau current density (ipl), and the formal potential of the mediators ( Em ) were found to be constant for the entire methanol concentration range (Figure 3.6). However, 0' when for each case, the relative magnitudes of E1/2 and Em were compared, three entirely different cases were observed as is indicated in Figure 3.7. Depending on the relationship between these two parameters, the systems could be identified as mediator transport limited (A: 0.43 V), mediator kinetics limited (B: 0.77 V), and electrode kinetics limited (C: 0.82 V). The 6 cases were identified as discussed by Bartlett and Pratt. The corresponding expressions for ipl and E1/2 as derived are tabulated in Table 3.3. It is evident that for each system, depending on the rate-limiting condition, certain set of kinetic parameters could be extracted by fitting the data (Table 3.4). When the applied electrode potential is much lower than the mediator redox potential 0' 0 (V<< Em ), all the mediator is expected to exist in its reduced form such that , M red ≈ M total , 0 where, M total is the total nominal bulk mediator concentration. The first step involved in ORR 80 2+ by TvL in a mediated system is the reduction of the T1-Cu center by Mred. The electron 1 transfer driving force largely governs the electron transfer efficiency between the mediator and + the enzyme active site as is depicted in Figure 3.8. The reduced T1-Cu center internally transfers the electron to the T2/T3 cluster rather rapidly where this electron is taken to reduce O2 11 to water. One mole of O2 reduced is associated with 4 moles of Mred oxidized. Hence, the 2+ faster the electron transfer between Mred and T1-Cu , the better would be the electrode kinetics. For a fixed substrate (O2) concentration, the factor determining the difference between E1/2 and ⎛M ⎞ is given by the factor − ln ⎜ 0 ⎟ , where M0 is the concentration of the reduced ⎝ KM ⎠ 0 mediator at the electrode-film interface. For systems, where M0 > KM, E1/2 < Em' and where M0 0 < KM, E1/2 > Em' . For systems following linear kinetics, where the current (i) varies linearly 0 with M0, it is expected that E1/2 ≈ Em' . Mediator kinetics limited scenario (Case VII) 6 For redox polymer (RP) A mediated systems, with the lowest (0.43 V | SHE), the electron transfer driving force is large enough to facilitate electron transfer between the Os center 2+ and the T1-Cu site, such that the ratio of diffusion to the reaction of the substrate is greater than that of the mediator i.e. DS K S Dm -1 -1 , where kA is the bimolecular rate constant (s M ) > kcat L kA L 81 for the enzyme-mediator interaction. Diffusion of S is predominant and the film remains saturated with O2 as is demonstrated by the steady state concentration profiles (Figure 3.9a) (Appendix D). The mediator concentration falls to zero within the film because the mediator diffusion coefficient is not fast enough to replenish the reduced mediator concentration throughout the film before reacting with the enzyme. So the reaction rate is limited by the enzyme-substrate interaction, as well as the electron diffusion coefficient via mediators, which controls the rate of regeneration of Mred. Hence, the current varies by the square root of mediator concentration and its diffusion coefficient. The kinetic parameters that could be theoretically obtained from the experimental data for RP A mediated systems are kcat and KS (Table 3.4). Mediator kinetics limited scenario (Case II) 6 0' For RP B mediated systems, with intermediate Em (0.77 V | SHE), the electrode performance becomes mediator kinetics limited, such that the mediator concentration profile is determined by the enzyme-mediator kinetics because of the reduced electron transfer driving force between them and since the substrate is replenished by diffusion into the film at a faster rate than consumed by the enzyme, as is evident from Fig. 3.9b. This arises for the cases where KS << [S] and for KM >> [Mred]. The mediator concentration falls to zero within the film (Fig. 3.9b) because the mediator diffusion coefficient is low, and can not replenish Mred at a faster rate than is consumed by the enzyme. This is characterized by linear dependency of current 0' density on mediator concentration at the electrode surface and E1 2 ≈ Em . The kinetic 82 parameters that could be theoretically obtained from the experimental data for RP B mediated systems are kcat and KM (Table 3.4). 6 Electrode kinetics limited scenario (Case I-V transition) For the highest potential mediator (RP C: 0.82 V | SHE) systems, the electron transfer driving force between the reduced Os center and the enzyme is too low to facilitate fast electron transfer and the reaction exhibits both substrate-limited and mediator-limited kinetics. The concentrations of both the mediator and the substrate remain practically constant throughout the 0' film (Fig 3.9c). This scenario is characterized by shifting of the half-wave potential, E1 2 < Em as the steady state polarization curve attains a plateau earlier than is expected for purely mediator kinetics limited case. For RP C mediated systems system, theoretically, it is possible to have an estimate of all the kinetic parameters (kcat, KM and KM) for this system (Table 3.4). Estimation of kinetic parameters For the experimental data obtained, the external O2 mass transport limitation was accounted by Koutecky-Levich analysis (inverse of the ordinate intercept of the extrapolated −1 ipl  vs ω −1 2 gives a measure of the kinetic current density, ik) and iR correction was applied to 1,10 all the electrode potentials to rule out the Ohmic loss. Figure 3.10 a shows the fitted data for the oxygen variation study for all the three systems. This data was used to obtain a preliminary estimate of kcat and KS. These estimated values were then used to extract kcat, KS, and kA (bi- 83 k -1 -1 molecular rate constant for the enzyme-mediator interaction, cat , s M ) by simultaneous fit KM of the oxygen variation data (Figure 3.10a) and the polarization curves (Figure 3.10b). Estimated magnitudes of the turnover number of the enzyme (kcat) indicate that magnitudes of kcat largely 0' depends on ET driving force (Figure 3.11); lower Em results in larger kcat,app. Beyond 2 M methanol concentration, the decline is steep. The enzyme-oxygen binding constant (KS) (Figure 3.12a) for polymers A and C mediated systems and enzyme-mediator binding constant (KM) for polymers B and C mediated systems were found to remain unaffected by methanol even when there was a marked decrease in the maximum current density with increasing methanol concentration (Fig. 3.12b). This is indicative of non-competitive inhibition kinetics by methanol. Conclusions Within 0-5 M concentration range, methanol affected the enzyme activity rather than the mediator transport properties. It is demonstrated that within this concentration range, methanol primary affects the enzyme turnover number rather than the binding constants indicating noncompetitive inhibition kinetics. The magnitude of kcat largely depends on the electron transfer 0' driving force between the enzyme and the mediator; lower Em results in larger kcat,app. Beyond 2 M methanol concentration, the decline in kcat was observed to be steep, indicating increased enzyme deactivation due to higher methanol concentration. It has been demonstrated that mediator redox potential and the electron diffusion coefficient via the mediators play a vital role in determining the overall electrode kinetics of mediated oxygen reducing TvL electrodes. 84 0' Depending on the relationship between the half-wave potential and Em , the systems could be identified as mediator transport limited (A: 0.43 V), mediator kinetics limited (B: 0.77 V), and electrode kinetics limited (C: 0.82 V). This limits the theoretical estimation of the kinetic parameters for the three mediated systems. It is expected that the detailed analysis of inhibition mechanism as delineated in this work would help design and optimize the performance of a TvL mediated bio-cathode especially for mixed-feed DMFC applications. Acknowledgements The authors gratefully acknowledge support from the University of New Mexico under contract FA9550-06-1- 0264 from the Air Force Office of Scientific Research. 85 Table 3.1: RP Redox polymer properties (V | Structural Formula Wt. Length/ e− ΔET SHE) poly (n-VI12[Os(bpy)2Cl] B poly (n-VI20[Os(tpy)(dm-bpy)] C poly (n-VI15[Os(tpy)(bpy)] 2+/3+ 2+/3+ ) ) 86 11 30 0.39 0.77 6.6 25 0.05 0.82 ) charge (Å) 0.43 +/2+ A % Os (V) 9.2 18 ~0 Table 3.2: MeOH Physical parameters of the TvL – redox polymer hydrogel films RP A: 11 wt% Os [S]** [ ET ] M mM 0 RP B: 6.6 wt% Os [ ET ] mM 0 ⎡ M total ⎤ ⎣ ⎦ mM 1.11 1.3 ± 0.3 1 1.15 1.1 ± 0.2 2 RP C: 9.2 wt% Os [ ET ] mM 0 ⎡ M total ⎤ ⎣ ⎦ mM mM 0 ⎡ M total ⎤ ⎣ ⎦ mM 96 ± 18 0.9 ± 0.2 37 ± 8 1.4 ± 0.2 82 ± 12 81 ± 15 1.4 ± 0.4 61 ± 18 2.1 ± 0.5 129 ± 27 1.19 3.0 ± 0.9 216 ± 63 2.4 ± 0.4 101 ± 17 2.2 ± 0.3 134 ± 17 2.5 1.21 2.5 ±0.9 182 ± 65 1.7 ± 0.5 74 ± 22 2.5 ± 0.5 150 ± 33 5 1.35 2.8 ± 0.6 199 ± 43 2.1 ± 0.5 89 ± 22 2.5 ± 0.4 149 ± 26 Conc. ** The oxygen solubility data in methanol-buffer system was obtained from Oxygen and 12 Ozone Handbook. 87 Table 3.3: 0 Relationship between E1 2 and Em' Observed RP 0' E1 2 vs. Em Case A 0 E1 2 > Em' 0 E1 2 ≈ Em' II C 0 E1 2 < Em' ipl (mA cm ) VII B -2 6 I-V −nF 2M 0 Dm kcat ETS ( KS + S ) −nFM total − 2Dm kcat ET KM E1 2 (V) 0 Em' + 0.549b 0 Em' nFkcat ETSM red ⎛ k M (K + S)⎞ 0 Em' − ln ⎜ A 0 S ⎟ ( KS M red + K M S + SM red ) kcat S ⎝ ⎠ 88 Table 3.4: Expected obtainable kinetic parameters through fitting 6 Redox Polymer 0 Em' (V) | SHE Case A 0.43 VII kcat, KS B 0.77 II kcat, kA C 0.82 I-V kcat, KS, kA 89 Fitted Parameters Figure 3.1: Structure of redox mediators. 90 Figure 3.2: Schematic of electron flow in a biocathode. 91 Figure 3.3: Schematic of the non-competitive inhibition kinetics for both the substrates (S=Oxygen; Mred= reduced form of the mediator). 92 Figure 3.4: Effect of methanol on Tafel slope (b) for all the three mediated systems. -1 The Tafel slope was estimated by fitting the cyclic voltammograms at 50 mV s in deaerated buffer (Figure 3.5). 93 Figure 3.5: Fitting of the cathodic wave of a cyclic voltammogram of a representative -1 system obtained at 50 mV s scan rate in de-aerated 100 mM citrate buffer (pH 4, 40°C, 900 rpm). 94 Figure 3.6: Demonstration of the effect of methanol on (a) half-wave reduction potential (E1/2 ) of the steady state catalytic reduction current and (b) formal potential 0 ( Em' ) of the mediated biocathode. E1/2 was determined from the steady state -1 polarization curves (1 mV s ) in O2 saturated buffer (100 mM, pH~4, 40°C, 900 rpm), 0 and Em' was obtained from the cyclic voltammograms at 50 mV s buffer (100 mM, pH~4, 40°C, 900 rpm). 95 -1 in de-aerated citrate Figure 3.7: The relative magnitudes of half-wave reduction potential (E1/2) of the 0' steady state catalytic reduction current and formal potential ( Em ) of the mediated biocathode as a function of methanol concentration for (a) RP A, (b) RP B and (c) RP C mediated systems. 96 Figure 3.8: Schematic of the electron transfer and the potential gradient elucidating the concept of electron transfer driving force between the Os redox center of the 2+ mediator and the T1-Cu site of TvL. 97 Figure 3.9: Steady state concentration profiles for the mediator and substrate (O2) for (a) RP A, (b) RP B, and (c) RP C mediated biocathodes. The steady state concentration profiles were generated using bvp4c Matlab function, the governing equations and boundary conditions of which are defined in Equations 3.6 and 3.7 respectively (Appendix D). 98 Figure 3.10: Comparison of analyzed experimental data to the numerical prediction. (a) Plot of kinetic plateau current density (ipl,k) for varying oxygen mole fraction (diluted with nitrogen under 1 atm. pressure). Each point is the result of a Koutecky-Levich analysis at the plateau current. (b) Ohmic and Koutecky-Levich corrected polarization curves in oxygen saturated 100 mM citrate buffer (pH 4, 40°C). Dashed lines in both (a) and (b) indicate numerical model results simultaneously fitted to the both the data sets. 99 Figure 3.11: Variation of the enzyme turnover number with methanol concentration. The values of kcat were obtained by simultaneously fitting the oxygen variation data and the steady state polarization curves (Figure 3.10) with the numerical model. 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Ikeda, "Theory of steady-state catalytic current of mediated bioelectrocatalysis," Journal of Electroanalytical Chemistry, 535(1-2), 37-40 (2002). 9. S. C. Barton, "Oxygen transport in composite mediated biocathodes," Electrochimica Acta, 50(10), 2145-2153 (2005). 10. A. J. Bard and L. R. Faulkner, Electrochemical methods : fundamentals and applications (Wiley, New York, 1980). 11. E. I. Solomon, U. M. Sundaram and T. E. Machonkin, "Multicopper oxidases and oxygenases," Chemical Reviews, 96(7), 2563-2605 (1996). 103 12. R. Battino, Oxygen and ozone (Pergamon, Oxford ; New York, 1981). 104 Chapter 4: In-situ XANES characterization of Cu active sites of laccase from Trametes versicolor in a mediated biocathode as a function of mediator redox potential† Abstract The Cu active sites of Laccase from Trametes versicolor (TvL) are studied using X-ray absorption spectroscopy (XAS) to characterize the transition state moieties and elucidate the mechanism of oxygen reduction catalyzed by immobilized TvL in a mediated biocathode as a function of mediator redox potential. The electrode is studied in-situ, with potential control under ambient conditions. This work demonstrates that the Cu active sites of TvL could be probed by XAS at micro-molar concentration levels. The oxidation states of the Cu active site is correlated to structural changes as a function of applied electrode potential, presence or absence of substrate (O2) and mediator redox potential. † Collaboration with Dr. Sanjeev Mukerjee and Dr. Thomas Arruda of Northeastern University. 105 Introduction Multi-copper oxidases (MCOs) constitute a family of enzymes that couple one electron oxidation of a substrate (which could even be an electrode) with the complete four-electron 1-6 reduction of oxygen to water without forming a soluble peroxide intermediate. This property makes MCOs a popular enzymatic bio-cathode catalyst for the oxygen reduction reaction (ORR). Blue MCOs are characterized by the presence of at least four copper (Cu) atoms organized and classified depending on spectral properties into type 1 (T1), type 2 (T2) and anti-ferro magnetically coupled diamagnetic binuclear type 3 (T3) Cu centers, of which the T2 and T3 Cu 2,6-9 active sites constitute the trinuclear cluster. For these metalloproteins, even though the metal 10 centers constitute approximately ~0.1 wt % of the molecule, the Cu active sites and the microenvironment around them are the key parameters governing the reactivity, substrate 2,7 specificity, and oxygen binding capabilities of these enzymes. Each MCO exhibits specificity to a wide variety of organic substrates like aromatic 2 phenols and amines as reducing substrates, with substrate (oxygen) binding and ORR 11 mechanism consistent with Marcus theory and outer sphere oxidation of co-substrate with no 6 specific binding pocket. Since co-substrate oxidation occurs at the outer T1 active site, cosubstrate specificity is largely governed by the structure around T1 and not near the T2-T3 tri2 nuclear cluster. 106 Laccase is the simplest of the multicopper oxidases that is capable of complete, four12 electron reduction of oxygen to water without forming a peroxide intermediate. As shown in II Figure 1.4 (Chapter 1), the enzyme contains one type 1 Cu (T1-Cu) site, located in close proximity to the surface, that couples four one-electron co-substrate oxidation steps to a fourelectron reduction of oxygen to water at the tri-nuclear cluster, located 13 Å away and connected 13 with a His-Cys-His tripeptide linkage. II II One type 2 Cu (T2-Cu) and one type 3 binuclear Cu - II Cu moiety constitute the tri-nuclear cluster. The co-ordination geometry around the T1-Cu site 14 determines the redox potential of the enzyme. For example, the three co-ordinate T1-Cu site in fungal laccases (e.g., Trametes versicolor) exhibit higher redox potential (~0.79 V) than four coordinate T1 laccases (~0.43 V) (e.g. Rhus vernicifera). 2,14 2+ 3,6 The native state of laccase Cu centers is fully oxidized (Cu ). In terms of ORR catalysis, the oxygen binding mechanism and possible intermediates have been studied and their geometric and electronic structures and structural-functional relationships studied by 2-4,6,10,14 spectroscopic and quantum mechanical approaches especially for laccases from Rhus vernicifera. For the present work, the fungal laccase from Trametes versicolor is used due to its - high redox potential and capability for full 4e reduction of O2 to water. The intermediates of laccase from Rhus vernicefera have been detected using X-ray absorption spectroscopy (XAS) and electron paramagnetic resonance spectroscopy (EPR) using a 12 chemical reducing agent and flash freezing in liquid N2. 107 Their study (Lee et al.) identified two fully oxidized states of the enzyme; (a) the native intermediate with an oxygen radical bound to the T2/T3 cluster, and (b) the fully oxidized resting state, which is the decayed form of the native intermediate differing only by structural changes associated with the binding of the bridging oxobyproducts. When operated in-situ in a mediated biocathode; the protein must share electrode volume with the mediator, which limits total protein loading. Detection of Cu active sites (micro-molar) is therefore quite challenging. Moreover, data acquired at liquid N2 temperatures may not be extrapolated to room temperature. This work aims at understanding the mechanism of ORR by laccase from Trametes versicolor (TvL) in an electrode operating under ambient conditions, by probing the active Cu sites of the enzyme using XAS and identifying the changes in the oxidation state of the active sites via XANES (X-ray absorption near edge spectra). Applied potential, O2 activity, and mediator characteristics are varied. The overall objective of this work is to identify and characterize the transition state moieties and elucidate the mechanism of oxygen reduction by immobilized laccase in a mediated system as a function of mediator redox potential. It is demonstrated that mediator redox potential has a strong effect in controlling enzyme oxidation. X-ray Absorption Spectroscopy (XAS): Basic operational principles XAS is an element specific core level spectroscopy, which is widely applied for studying systems and particles in solution, especially after the advent of the high intensity synchrotron radiation sources. When X-ray of specific energy hits a sample, it ejects a core shell electron from an atom, which escapes into the continuum without obstruction. The ejected electron 108 undergoes scattering as it approaches neighboring atoms producing an interference pattern. XAS spectrum is generally divided into four sections: (1) pre-edge where the energy of the incident beam ( ! ) is less than the edge-energy ( !0 ), (2) X-ray absorption near edge structure (XANES), where ! = !0 ±!10 ( eV ) , (3) near-edge X-ray absorption fine structure (NEXAFS), where !0 + 10 10 wt%), and where thin samples can be made, transmission mode of detection is used. For very dilute samples (element of interest < 10 wt%), particularly true for biological samples, fluorescence mode is preferably used. The sample preparation for this mode is less stringent and unlike transmission mode, thin samples are not a requirement. Cu-active sites in the mediated TvL electrodes accounted for ~0.36 wt% of Cu. Hence fluorescence mode of detection was used for this study. Experimental Chemicals and reagents TvL was purchased from Sigma-Aldrich (St. Louis, MO) and purified as previously 19 reported. Details of the reagents required for synthesizing the redox polymers are listed in the experimental section of Chapter 2. Ultra-pure oxygen, air, and nitrogen were obtained from Air ® Gas Great Lakes Inc. (Lansing, MI). Grafoil , planar flexible graphite sheets, obtained from GrafTech International Ltd. (Parma, OH), were used as such for making the electrodes. Carbon Toray paper (TGP-H-030 and TGP-H-060) obtained from E-TEK (Somerset, NJ) was used to prepare the composite bioelectrodes. 110 Laccase electrode fabrication on Rotating Disc Electrodes (RDEs) Activity of purified TvL enzyme was determined spectrophotometrically with ABTS in 50 mM citrate buffer (pH~4, 25°C). The estimated enzyme activity at room temperature with respect to ABTS as substrate was 190 ± 30 U/mg and assuming 100% protein and molecular weight of TvL to be 65 kDa (estimated using SDS page), the equivalent turnover rate was 200 ± -1 22 s . The redox potential of the enzyme was estimated to be ~0.82 V/SHE as was indicated by the open circuit potential measurements of TvL modified glassy carbon electrodes which was in 20 accordance with the previously reported value. The biocathodes were fabricated by drop depositing 8 µL aliquot containing TvL (37 wt%), redox polymer (10 mg/ml) (57 wt%) and PEGDGE (5 mg/ml) (6 wt%) at a total loading of 2 1.195 mg/cm on a 3 mm diameter glassy carbon rotating disc electrode (RDE). This proportion and loading were chosen to ensure high signal to noise ratio for both Os L3 - edge (redox mediators) and Cu k-edge (TvL). Composite RDEs were prepared by attaching 4 mm diameter discs of Toray paper (TP® 030) or Grafoil on glassy carbon RDEs using carbon black paint (spi-chem™, West Chester, PA) and then drop depositing 8 µL of the enzyme-containing redox hydrogel aliquots in the above mentioned proportions. The electrodes were cured in air at room temperature for at least 10 - 12 hours under controlled humidity (< 10% RH) before testing. 111 ® Composite laccase electrode fabrication on Grafoil -Toray paper (TP) ® Composite Grafoil electrodes (GCEs) were prepared by depositing mediator-enzyme ® hydrogel (HG) on Toray paper (TP) attached to Grafoil . Rectangular pieces (1 cm x 0.3 cm) of ® TP-030 were attached with carbon paint on Grafoil sheet exactly in the same position on either side of the sheet as is shown in Figure 4.1. This electrode configuration was chosen to maximize the loading of the active electrochemical species (enzyme and redox mediators) and also to ensure maximum exposure of the hydrogel to the X-ray beam when operated in-situ in a flow ® through cell. The TP attached to the Grafoil sheet was hydrophilized using oxygen plasma (Ithaca, NY). After adding 35.4 µL of the hydrogel aliquot to one side of CGEs, it was allowed to cure for about an hour under ambient temperature and < 10% RH. Then, a second 35.4 µL drop was added to the other side of the CGE and the electrode was allowed to cure for at least 18 hours under controlled humidity (<10% RH) before performing any experiments. The total -2 loading on CGEs was 2.49 mg cm . Electrochemical studies Electrochemical studies were conducted in 100 mM citrate buffer (pH 4, 25°C) in presence or absence of oxygen. The RDE experiments were performed at 1200 rpm for all estimations. The CGEs were evaluated in a quiescent solution with continuous sparging of either O2 or N2 gas. Experiments were performed using a VST potentiostat and rotators from Pine Instrument Company (Pine Instrument Co., Grove City, PA). The data were collected and 112 ® analyzed using EC-Lab software (Bio-Logic USA, LLC, Knoxville, TN). Characterization techniques included cyclic voltammetry, chronoamperometry, square wave voltammetry and impedance. Platinum gauze was used as a counter electrode. A standard Ag|AgCl reference electrode from BAS (West Lafayette, IN) was used for all the estimations. X-Ray Absorption Spectra (XAS) measurements All XAS measurements were carried out at room temperatures in a flow-through electrochemical cell (Figure 4.2). The cells were assembled and tested by Dr. Thomas Arruda of Dr. Sanjeev Mukerjee's Group (Northeastern University). The CGEs were used as working electrode (WE). A Grafoil counter electrode (CE) was used and situated parallel to the WE. ® Grafoil was chosen for its high X-ray transmittance properties and undetectable concentration -1 of Cu impurities. A flow rate of 5 ml min of the electrolyte (100 mM, pH 4 citrate buffer) deaerated or O2 saturated was pumped through the cell continuously using a peristaltic pump to ensure proper oxygenation/de-aeration levels. A sealed Ag/AgCl reference electrode (BAS) was used in the external electrolyte reservoir, which was connected to the interior of the cell via a salt bridge terminated with a vycor frit (BAS). The cell potential was controlled using an Autolab potentiostat (Metrohm USA, Inc.). Both Os and Cu standards were purchased from Alfa Aesar at > 98 % purity and stored in a glove box under Ar. The samples were prepared in the glove box by placing the necessary weight of material for an edge height of ~ 1 into Al sample holders sealed off with Kapton tape. The samples were stored in air-tight, sealed bags under Ar until use at the beam line. 113 Measurements were made at the X3-B beam line of the National Synchrotron Light Source (2.801 GeV at 300 – 150 mA) at Brookhaven National Laboratory, Upton NY. Cu kedge (8979 eV) XAS was collected (-200 eV to 14 k) using a double crystal Si (111) monochromator with a Bragg angle range of 8.5 – 35 degrees and located 16.5 m from the source (bending magnet). Beam line X3-B does not require detuning of the incident beam for harmonic rejection as it employs a Ni harmonic rejection mirror as well as a piezoelectric feedback system that adjusts the crystal to the maximum of the rocking curve at preset energy values. Once calibrated (ca. every three hours) the piezo voltage can be adjusted automatically throughout the energy scan to follow the calibration standard. Due to the low concentration of Cu, XAS data were collected in fluorescence mode using a Canberra 13-element solid state Ge detector. A minimum of six successive scans were collected for each scan condition i.e. potential or dissolved gas (experimental approach discussed in details under results and discussion section). The cell was placed between an incident beam detector (I0, 15 cm in length gas ionization detector filled with N2) and a transmittent beam detector (It, 15 cm also N2). A Cu reference foil was placed between It and a third ionization detector Iref (7 cm, N2 filled) for the purpose of energy calibration and to correct for any beam drift that may occur during the 12 hour life cycle 6 of the beam. The ionization detector amplifiers were typically adjusted to a gain value of 10 – 8 10 V/A for optimal signal to noise (S/N). (This paragraph is adopted from Dr. Thomas Arruda's 21 Thesis, Chapter 5) 114 Results and discussion The main steps involved in the oxygen reduction mechanism by laccase in a mediated system are: (i) reduction of the T1-Cu site by the reduced substrate, (ii) electron transfer (ET) from the T1-Cu site to the trinuclear cluster, and (iii) reduction of oxygen at the trinuclear 2 2+ cluster. The potential difference between the Os center of the mediator and that of the T1-Cu 20 center of the enzyme governs the electron transfer efficacy. The greater the driving force, under the given conditions, the more facile would be this electron transfer. The three mediated systems that are discussed in here have progressively decreasing electron transfer driving force from polymer A (0.43 V | SHE) to B (0.77 V | SHE) to C (0.82 V | SHE) due to increasing redox 0' potential of the mediators (Figure 4.3). To study the effect of mediator redox potential ( Em ) on ORR by immobilized laccase, redox mediators for the present study were chosen such that they 0' differed in their Em values (Table 4.1), and have the same N-poly-vinylimidazole backbone, and similar charge density (Chapter 2), which would ensure similar swelling behavior of the charged 0 hydrogels in an ionic media. It has been demonstrated in Chapter 2 that Em' is the only sensitive parameter controlling the overall electrode kinetics in a mediated TvL-containing oxygen reducing biocathode. The initial challenge of this study was to be able to identify and characterize the transition state moieties (Cu active sites of TvL and Os redox centers of the redox polymers). The copper active sites in laccase constitute only 0.36 wt%. For in-situ Os L3-edge measurements, a weak XANES sensitivity to electrode potential was detected. For the in-situ Cu k-edge spectra, XANES was found to be sensitive to the presence of O2, but potential 115 dependence was not observed under de-aerated conditions. Hence, the weight ratios of the electro-active species were optimized to increase the overall nominal loading and improve retention on the electrode surface for in-situ operations. There is a limitation to the amount of enzyme that could be incorporated in the redox hydrogel without having it salted out and rendering the system electrochemically inactive. Hence optimization of these weight ratios was an important aspect for the success of this study. Electrochemical measurements -1 Figure 4.4 shows a representative in-situ polarization curve at 10 mV s . Predominance 2 of capacitive current due to large exposed electrode area as compared to only 0.6 cm of active catalyst area makes in-situ electrochemical characterization meaningless. Hence, complete exsitu electrochemical characterization of these CGEs was conducted where the non-electro-active electrode area was masked with a hydrophobic coating. Figure 4.5 shows the ex-situ electrochemical characterization of the CGEs for the three ® systems in presence and absence of oxygen. Grafoil is a non-porous material with very low retention ability. Incorporation of a porous support (Toray Paper) doubled the mediator utilization (Table 4.2) for both the CGEs as well as the rotating disc electrode (RDE) studies, improved retention of the electro-active species on the electrode surface, increased the ORR current density by ~ 2.5 times (data not shown) and maintained the electrode structural integrity, but at the expense of limited O2 transport through the composite electrode (indicated by the hysteresis in steady state polarization curves in Fig. 4.5b), a condition that should not inhibit our ability to observe the copper active sites under steady-state conditions. 116 The active Os content of the mediated systems (Table 4.2) was estimated using squarewave voltammetry. Square-wave voltammetry is a powerful electrochemical tool for estimating charge transferred due to faradaic reactions alone and hence gives a precise estimate of the 22 electro-active species at the electrode surface. A representative plot of the difference current (idel=iforward-ireverse) versus time is shown in Figure 4.6 for the three mediated systems measured in de-aerated 100 mM citrate buffer (pH~4, 25°C). The area under the curve divided by a factor nF, where n is the number of electrons transferred in the electrochemical reaction, and F is Faraday’s constant, gives a direct measure of moles of electro-active Os content in the films. The electron transport properties of the CGEs via the mediators were estimated by measuring the apparent electron diffusion coefficient, Dm, via cyclic voltammetry with scans -1 rates varying from 50 -1000 mV s . The peak current densities (ip) from the cyclic voltammograms were found to vary linearly with square-root of scan rate indicating semi-infinite 23 diffusion (Figure 4.7) as expressed by the Randles-Sevcik equation ⎛ F3 ⎞ ip = 0.4463 ⎜ ⎟ ⎝ RT ⎠ 12 12 * n 3 2Cm Dm υ1 2 [4.1] where F is Faraday’s constant, R is the universal gas constant, T is the temperature, n is the * number of electrons transferred in the redox reaction, Cm is the mediator bulk concentration and v is the scan rate. With no knowledge of the film thickness of the redox hydrogel in the CGEs, 117 12 * the mediator bulk concentration was difficult to estimate. Hence, the parameter Cm Dm as estimated for the three systems is tabulated in Table 4.3. Cu k-edge XANES studies The edge energy (ΦO) is determined by taking the first maximum value of the first derivative of the XANES spectrum. The Cu k-edge spectrum of TvL is characterized by a dipole allowed 1s ! 4 p transition in the ΦO region. This transition has been shown to occur in laccase + 2+ when a reduced Cu species exists and has been to be absent in case of fully oxidized Cu 24 species. Energy to eject a core electron depends on the charge the ejecting electron experiences; hence the edge energy depends on the oxidation state of the metal. The Cu k-edge + 2+ energy is at 8.979 keV for Cu , however for Cu , it shifts up to 8.983 keV. White line intensities depend on the matrix elements and occupancy of any final states. Filling of orbitals 2+ suppresses the white line. Therefore it is expected that Cu + 9 (d ) configuration would result in 10 higher white line intensity as compared to Cu (d ). Figure 4.8 shows the in-situ Cu k-edge XANES spectra of "unmediated" laccase as a function of potential and presence/absence of oxygen. Though XANES sensitivity to O2 was demonstrated, potential dependence was not observed in the absence of O2. In O2 satd. buffer, at higher potential, an increase in white line intensity and a corresponding decrease in the pre-edge + feature were observed indicating a higher proportion of reduced Cu species at the reducing 118 potential. The spectra in Fig. 4.8 represent the presence of mixed valent Cu centers under all 2+ conditions, with the highest proportion of Cu at oxidizing potential in oxygen-saturated + buffers, while highest proportion of Cu was observed at reducing potential in de-aerated buffers. This is demonstrated by the fact that the pre-edge 1s ! 4 p transition always exists. One important breakthrough of this approach was that a fully reduced form of laccase was observed at low potential in de-aerated buffer under ambient conditions when it could be 24 observed only with freeze quenching under anaerobic state. Similar findings were reported by 25 Kau et al. for a Cu k-edge study of laccase from R. vernicefera. 2+ Cu standards (40 Cu They studied a wide variety of + and 19 Cu ) and in T2-Cu depleted enzymes, using hydrogen peroxide, 2+ they chemically reduced the T3-Cu center preferentially, producing a large transition at 8949 eV. Electron Paramagnetic Resonance (EPR) spectra revealed no change in T1-Cu oxidation state in this process. XAS is a bulk technique and the spectral measurements were taken over a long period of 3,6 time. The transition states are very short lived, as the reaction proceeds very fast. So the XANES spectra represent bulk-average oxidation states of all the Cu atoms during the period of measurements. The effect of potential can permeate only through a fraction of the total loading of the electro-active species (6 % accessible active Os; Table 4.2) while O2 present in the bulk solution can permeate throughout the film and can amplify the effect of potential on the oxidation states of the Cu active sites. Hence, to detect the electronic state of the Cu centers of 119 the enzyme, apart from increasing the total effective loading of the active species by introduction of CGEs, an experimental approach of systematic and sequential variation of potential and substrate (O2) was taken to encompass all the possible scenarios (Figure 4.9). The electrodes were poised at: (1) Open circuit potential (OCP) in oxygen saturated buffer, (2) oxidizing 0' potential, (Eapplied >> Em ), oxygen saturated, (3) oxidizing potential, de-aerated buffer, (4) 0' reducing potential, (Eapplied << Em ), de-aerated buffer, and (5) reducing potential in oxygen saturated buffer. This sequential and systematic variation of potential and substrate helped vary the oxidation states of the Cu centers in a controlled manner and the effect of mediator potential is evident in all scenarios. 0' Effect of potential on Cu oxidation state as a function of Em 6,12 It has been reported that laccase in presence of O2 exists in fully oxidized state. But an interesting trend emerges out in the mediated systems where the enzyme and the redox polymers co-exist in close proximity on the electrode surface. Figure 4.10 represents the in-situ Cu k-edge XANES spectra of mediated laccase electrodes (all three systems) at their respective OCPs in presence of O2 (Table. 4.4). Under these conditions, both the reduced and the oxidized forms of the mediator co-exist (Mred:Mox:: 50:50) and TvL, in presence of O2, exists in fully 2,3,6 oxidized state. 2+ But due to close proximity of the reduced Os redox center and the T1-Cu site, a spontaneous electron transfer takes place from the reduced mediator active site (at a lower 2+ potential) to the T1-Cu 20 site of the enzyme (0.82 V |SHE) 120 according to the following hypothesis: Os( n!1)+ + T1 ! Cu 2+ " Os n+ + T1 ! Cu + . In a mediated bio-electrode, the overall 0' electrode kinetics is largely controlled by Em and the electron transfer driving force between the 20 mediator and the enzyme active site. As the mediator redox potential increases from polymer A (0.43 V) to B (0.77 V) to C (0.83 V), the electron transfer driving force between the 2+ Os( n!1)+ centers to the oxidized T1-Cu site of the enzyme decreases (Figure 4.11), decreasing + the proportion of reduced T1-Cu sites. Thus, in Fig 4.10, a progressive decrease in the white line intensity and an increase of the pre-edge feature were observed from polymer C to B to A + mediated systems indicating an increased proportion of reduced T1-Cu site. Oxidizing vs. reducing potential, de-aerated systems (scenarios 3 vs. 4) To detect the effect of mediator redox potential on oxidation states of the T1-Cu active site of TvL, the in-situ Cu k-edge XANES collected at oxidizing and reducing potentials of each redox mediated systems in absence of O2 were compared as indicated in Figure 4.12. This represents the case study where the role of presence of fully oxidized mediator (Mox) at the oxidizing potential versus fully reduced mediator (Mred) at a reducing potential is evaluated in absence of substrate (O2). At the reducing potential, it can be assumed that all mediator redox sites are fully reduced. By varying the applied electrode potential, the concentration of the reduced form of the mediator was increased, but mediator formal potential as well as that of TvL remained unaffected. Hence, for a redox mediator (C) with potential close to or slightly greater than that of the enzyme, the effect of potential would not be evident. The effect of potential 121 would be prominent for the lowest potential redox mediator (A) and somewhat intermediate for polymer B. As evident in Fig 4.12, at a reducing potential, a decrease in the white line intensity and an increase in the 1s → 4 p pre-edge feature was noticed indicating presence of reduced + Cu species. This trend was prominent in polymer A and B mediated systems, while it was not so obvious for systems mediated by polymer C (0.82 V). Figure 4.13 represents the comparison of the XANES spectra observed for the three mediated systems at an oxidizing potential and a reducing potential in absence of O2. Though at the reducing potential (Fig 4.13b), a decrease in the white line intensity and an increase in the + 1s → 4 p pre-edge feature were noticed (both indicative of presence of Cu ) going from polymer C to B to A, no significant trend emerges out at the oxidizing potential. Oxidizing vs. reducing potential, O2 saturated systems (scenarios 2 vs. 5) Figure 4.14 compares the XANES spectra of the three mediated systems in O2 saturated citrate buffers at the respective oxidizing and reducing potentials. It is expected that in presence 2,3,5,6 of O2 all the Cu active sites of TvL should remain fully oxidized. However, the Cu k-edge XANES spectra with the existence of the 1s → 4 p pre-edge feature in all the three mediated 2+ systems indicate the existence of multi-variant Cu (Cu + and Cu ). Even though no significant difference in the white line intensity and the pre-edge feature exists for polymers B and C 0' (comparable Em ), there is a significant decrease in the white line intensity for polymer A (0.43 0' V, lowest Em ) at both potentials (scenarios 2 and 5, Fig 4.14). The 1s → 4 p pre-edge feature is 122 also enhanced for polymer A mediated systems at a reducing potential indicating a higher + proportion of Cu . Hypothesis of probable oxidation states of Cu active sites in TvL as a function of potential and presence/absence of substrate (O2) All these observations definitely aim at the fact that TvL behaves differently in a mediated system than when in a free solution. Close proximity to the Os redox centers in a mediated system results in the presence of multi-variant Cu active sites. The extent of reduced T1-Cu site depends on the mediator redox potential. Based on this the following hypothesis has been proposed to best describe the oxidation states of the Cu atoms in TvL in a mediated system: + 2+ 1. OCP, O2 saturated: partially reduced enzyme (T1-Cu and T2/T3- Cu ) + 2+ 2. Oxidizing potential, O2 saturated: partially reduced enzyme (T1-Cu and T2/T3- Cu ) + 2+ 3. Oxidizing potential, de-aerated buffer: partially reduced enzyme (T1-Cu and T2/T3- Cu ) + + 4. Reducing potential, de-aerated buffer: fully reduced enzyme (T1-Cu and T2/T3- Cu ) + 5. Reducing potential, O2 saturated buffer: partially reduced enzyme (T1-Cu and T2/T32+ Cu ) 6 So unlike free laccase, in O2 saturated cases, no "resting fully oxidized" state of the enzyme could be detected in a mediated system. Increased utilization of the electro-active species and sequential variation of the potential and the substrate allowed detection of mixed 123 valent states of Cu under all scenarios under ambient conditions when the cell was operated insitu. However, in any scenario, it has to be kept in mind that the short-lived intermediate species might be very difficult to measure under ambient conditions for steady state XAS measurements. At reducing potentials, in de-aerated buffers, the XANES spectra suggest the presence of the fully reduced form of the enzyme, which previously could not be identified unless freeze 25 quenched. A whole library of very important information about the Cu active sites of multi-copper 2-7,10,12,14,24-33 oxidases has been provided by the previous work done by Solomon et al. The XANES spectra analysis along with the complete FEFF8 XANES modeling using the !µ technique would help decipher the ORR mechanism by immobilized TvL in a mediated biocathode system. Conclusions This work demonstrates that the Cu active sites of TvL could be probed by XAS at micro-molar concentration levels. High sensitivity of the 13 element solid-state Ge detector coupled with improved electrodes and experimental conditions made this detection at micromolar concentration level feasible. We have demonstrated that oxidation states of the Cu active site can be correlated to structural changes as a function of applied electrode potential, presence or absence of substrate (O2) and mediator redox potential. It has also been shown that the 0' oxidation state of the T1-Cu center largely depends on the mediator redox potential ( Em ). These findings provide a very strong ground for elucidating the mechanism of oxygen reduction by immobilized laccase in a mediated system as a function of mediator redox potential. To the best 124 of our knowledge, this is the first effort at probing into the active site of immobilized TvL when operated in-situ. Acknowledgements This project was funded by Multi-University Research Initiative (MURI) and Air Force Office of Scientific Research under the contract number FA9550-06-1-0264. Sincere acknowledgement to Dr. Thomas Arruda in Dr. Sanjeev Mukerjee's group at Northeastern University for the help provided for collecting the data. XAS data were collected at the Case Western Reserve University beam line X3-B at the National Synchroton Light Source at Brookhaven National Laboratory (Upton, NY). 125 Table 4.1: RP A Redox polymer properties 0 E (V | SHE) +/2+ poly (n-VI12[Os(bpy)2Cl] ) B poly (n-VI20[Os(tpy)(dm-bpy)] C poly (n-VI15[Os(tpy)(bpy)] 2+/3+ 2+/3+ ) ) 126 Wt. % Os Length/ e− charge (Å) ΔET (V) 0.43 Structural Formula 11 30 0.39 0.77 6.6 25 0.05 0.82 9.2 18 ~0 Table 4.2: Mediator utilization for redox polymer B in terms of % active Os RDE (1200 rpm) Redox Polymer B: 0.77 V | SHE ® Grafoil substrate TvL+RP +XL ® on Grafoil disc TvL+RP +XL on Toray Paper disc TvL+RP +XL ® on Grafoil TvL+RP+XL on CGE 15 35 6 15 127 Table 4.3: 12 * Cm Dm estimates for the three mediated systems on composite Grafoil ⎛ F3 ⎞ 3 2 * 1 2 electrodes from Randles-Sevcik analysis, slope=0.4463 ⎜ ⎟ n Cm Dm ⎝ RT ⎠ 4 9 12 * Cm Dm × 10 Redox Polymers Slope × 10 A: 0.43 V | SHE 9.3 ± 1.9 3.47 ± 0.71 B: 0.77 V | SHE 14.6 ± 0.12 5.44 ± 0.04 C: 0.82 V | SHE 11.5 ± 0.12 4.28 ± 0.05 128 (mole cm -2 -1/2 s ) ® Table 4.4: Specification of the potentials at which XAFS was collected in-situ Redox polymer E (V) | SHE Open Circuit Potential (V) | SHE (O2 satd.) Oxidizing Potential (V) | SHE Reducing Potential (V) | SHE A 0.43 0.794 0.894 0.194 B 0.77 0.834 0.994 0.294 C 0.82 0.874 0.994 0.294 0 129 ® Figure 4.1: Structure of the composite Grafoil electrodes used for the in-situ and exsitu measurements. 130 Figure 4.2: Experimental set-up for in-situ XAS measurements at the X-3B beam line. 131 Figure 4.3: Structure of redox mediators. 132 ® Figure 4.4: In-situ electrochemical response of the composite Grafoil electrode in a flow-through cell set-up (Fig 4.1) in oxygen saturated citrate buffer (pH ~4, 100 mM, 25°C) circulated at 5 ml/min rate through a peristaltic pump. Cyclic voltammograms -1 were collected at 10 mV s scan rate. 133 Figure 4.5: Electrochemical response of the three mediated systems in composite ® -1 Grafoil electrodes (a) in de-aerated citrate buffer (at 50 mV s scan rate) and (b) in oxygen saturated citrate buffer (pH ~4, 100 mM, 25°C). The electrochemical measurements were taken in quiescent condition with constant sparging of N2 in (a) and O2 in (b). The cyclic voltammograms were obtained at 50 mV s mV s -1 scan rates for (b). 134 -1 for (a) and at 1 Figure 4.6: Square wave voltammetry of the three mediated systems drop deposited ® on composite Grafoil electrodes in de-aerated citrate buffer (pH ~4, 100 mM, 25°C). Area under the curve gives a direct measure of the electro-active species concentration. 135 Figure 4.7: Randles-Sevcik analysis of the three mediated systems on composite ® 0 Grafoil electrodes in de-aerated citrate buffer (pH ~4, 100 mM, 25°C). A ( Em' = 0.43 V 0 0 | SHE), B ( Em' = 0.77 V | SHE), and C ( Em' = 0.82 V | SHE), represents the three ® respective mediated TvL containing composite Grafoil electrodes. 136 Figure 4.8: In-situ Cu k-edge XANES spectra for unmediated laccase electrode in 100 mM pH~4 citrate buffer, 25°C, under (a) de-aerated condition and (b) oxygen saturated condition. 137 Figure 4.9: Sequential variation of potential and substrate for XAFS study. 138 Figure 4.10: In-situ Cu k-edge XANES spectra for mediated laccase electrode in oxygen saturated 100 mM pH~4 citrate buffer, 25°C. The electrodes were poised at the respective open circuit potentials (Table 4.3), scenario 1 (Fig 4.9). 139 Figure 4.11: Electron energy and potential diagram elucidating the electron transfer 2+ efficacy between the Os redox centers of the mediators and the T1-Cu of TvL. 140 Figure 4.12: In-situ Cu k-edge XANES spectra for mediated laccase electrode in deaerated citrate buffer (100 mM pH~4 citrate buffer, 25°C) for (a) redox polymer A, (b) redox polymer B and (c) redox polymer C mediated systems. The electrodes were poised at the respective potentials (Table 4.4). 141 Figure 4.13: In-situ Cu k-edge XANES spectra for mediated laccase electrode in deaerated citrate buffer (100 mM pH~4 citrate buffer, 25°C) at (a) oxidizing potential, and (b) reducing potential for the three mediated systems. 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 148 Chapter 5: Characterization of enzyme-redox hydrogel thin-film electrodes for precise estimate of hydrogel transport properties and kinetic parameters Abstract Homogeneous bioactive films of sub-micron (~ 10-50 nm) thickness on gold-coated glass slides were obtained via convective self-assembly. The sub-micron thickness allows higher mediator and enzyme utilization by lowering transport limitations. This study demonstrates control of redox hydrogel film morphology by manipulating hydrophilicity, spreading, and wetting properties of the hydrogel/electrode interface. Use of a non-ionic surfactant (Triton X100) enables improved spreading of the enzyme-containing precursor solutions with no negative impact on enzyme activity. Ellipsometry has been used to measure and quantify film-swelling properties of these systems under experimental conditions, and transport properties of these films, such as apparent electron diffusivity, can be estimated with greater precision. This study impacts the design of thin, highly active redox hydrogel films for biofuel cell applications. 149 Introduction Thin-film technologies enable increased sensitivity and selectivity in electrochemical sensors and biosensors, novel engineered nano-scale materials and micro-engineered catalytic 1-7 materials. Fabrication of thinner films allows faster response and rapid transport of substrates due to low mass transfer limitations. This provides means of characterizing redox species by enhancing the electrochemical current density by ruling out film resistances, often a significant factor for thin film measurements. Thin films therefore allow higher utilization of the electro active species due to rapid redox recycling and provide means for precise analytical estimations. In an effort to produce homogeneous films with high electro-active species utilization, various approaches like co-immobilization of the biocatalyst and the redox mediators on the ®8 9 electrode surface using Nafion , sol-gel entrapment, a cross-linking agent like polyethylene 10,11 glycol diglycidyl ether (PEGDGE), 13 technique 12 or by electrodeposition or via layer-by-layer have been reported. The choice of immobilization technique depends on the enzyme, 14 the electrode surface, and the specific operational requirements. The objective of this work is to prepare uniform sub-micron scale redox hydrogel films for biofuel cell applications. This is the first report where this convective self-assembly technique is used to cast sub-micron thick redox hydrogel films where co-immobilization is achieved using a chemical cross-linking agent (PEGDGE). Biomimetic approaches towards encapsulating proteins in well-defined meso-porous 15-17 structures have marked new avenues for synthesis and assembly of nanomaterials. 150 18,19 Convective self-assembly, first implemented by Denkov et al., 20 Velve, and improved by Prevo and is a well-established approach particularly to cast templated meso-porous films especially for applications such as membrane-based separators, selective catalysis, and sensors. 1,2,6,7 Two-dimensional protein arrays generated by this technique are of substantial 3,4,21 importance particularly for their potential applications in structural analysis, and as 5,22 architectures for micro-engineered catalytic devices for magnetic semiconductors. This technique relies on the principle of solvent evaporation leading to the formation of well-defined 6,7 micro-patterned films, which could be implemented in device fabrications. The mechanism of 6 controlled casting of these films using this technique is discussed in great details by Yuan et al. Sub-micron sized thin films are ideal as both practical and analytical electrodes. High utilization of the electro-active species (enzyme and mediator), ability to assess the electron transport properties and electrode kinetic parameters (kcat, KM, KS) with greater accuracy, and controllable film morphology make these electrodes promising candidates for practicable biofuel cell devices. In this study, we have demonstrated control on the redox hydrogel film morphology and thickness by manipulating substrate hydrophilicity, spreading and wetting ability of the precursor solutions, and its drying rate. Use of a non-ionic surfactant (Triton X-100) improved spreading of enzyme-containing precursor solutions with no negative impact on enzyme activity. Electron transport properties and enzyme kinetic parameters in these films could be measured with high precision and repeatability. This technique demonstrates rapid deposition of films containing 151 enzymes and redox polymers from minimal precursor volume (1-5 µL drop sizes). Reproducible films of dry film thickness ~10-50 nm were cast using this approach. Experimental Chemicals and Reagents TvL was purchased from Sigma-Aldrich (St. Louis, MO) and purified as previously reported.23 Sodium citrate and citric acid were obtained from Fisher Chemical (Suwanee, GA). Poly (ethylene glycol) diglycidyl ether (PEGDGE, Polysciences Inc., Warrington, PA) was used as received. All the solutions were made with ultra filtered DI water (18 MΩ·cm). The three redox polymers A, B and C (Figure 5.1) were synthesized in-house according to reported 10 procedures. Synthesis of the redox polymers is described in Chapter 2. Their structures and properties are tabulated in Table 5.1. Fluorescein isothiocyante (FITC) and Triton X-100 were purchased from Sigma Aldrich (St. Louis, MO) and were used as received. Ultra-pure oxygen, air, and nitrogen were obtained from Air Gas Great Lakes Inc. (Lansing, MI). Gold-coated glass slides and plain microscope glass slides were obtained from Fisher Chemical (Suwanee, GA) and were used as substrates for thin film electrodes. Fabrication of the slide coater The slide coater assembly is a modified single channel syringe pump (model #: 7490000) from Cole-Parmer Instrument company (Vernon Hills, IL) where the syringe housing, including the spring-loaded clamp above the driving motor box, was removed to mount the sample holding stage (Figure 5.2). This technology was obtained from Dr. Plamen Atanassov's 6,7 group in the University of New Mexico. 152 Physical parameters affecting film homogeneity The parameters that directly contribute in controlling film morphology and homogeneity are: (a) smoothness of the electrode surface, (b) hydrophilicity of the electrode surface (redox hydrogels are aqueous), (c) wetting and spreading ability of the precursor solution, (d) solution viscosity, and (e) drying rate. The root mean square (RMS) value of the surface roughness of a clean bare gold-coated glass slide as estimated by Atomic Force Microscopy (AFM) was ~ 0.8 ± 0.1 nm. AFM measurements in the dry state (scan size: 1 µm, scan rate: 0.5003 Hz) were performed in the tapping mode on a Digital Instrument Nanoscope – 4 (Santabarbara, CA) in air using NSC 15 tip (Umasch). Care was taken while cleaning the electrodes especially for reusing in order to avoid scratching. Proper cleaning of the electrode surfaces improved the surface hydrophilicity. For films containing only redox hydrogel, adding ethanol (1-5 M) to the precursor solution controlled wetting, spreading and drying of the films. For enzyme-containing films, addition of a non-ionic surfactant Triton X-100 (1 wt% solution) in place of alcohol, improved the homogeneity of the films. Instrument parameters controlling film homogeneity The slide angle (θ) and linear velocity (v) as indicated in Figure 5.2b, were the two important instrument parameters that impacted film homogeneity. Figure 5.3a demonstrates the effect of θ on film morphology. Low θ generated broader liquid meniscus at the glass slideelectrode juncture resulting in thin and long films, while high θ generated thick and short films. For the purpose of this study, the slide angle, θ, was optimized to be 20°± 2°. 153 Figure 5.3b demonstrates the role of coating velocity (v) in controlling film morphology. -1 A linear velocity v > 25µm s resulted in piling up of the precursor solution at the far end leading to the formation of a thicker crust. For low v, the precursor solution dried up faster leading to thick films (~ 10 times) with smaller electrode area. The optimal coating velocity for -1 this study was found to be ~ 20 µm s . Figure 5.4 shows the effect of variation of θ and v on film morphology. Electrode pre-treatment Pre-treatment technique of the gold-coated glass slides also affected the film 24 homogeneity and proper anchoring of the electro-active species to the electrode surface. The slides were washed with copious amounts of de-ionized (DI) water followed by a rinse with absolute alcohol and blow-drying in dry air stream. Before being reused, bare gold electrodes were soaked overnight in 50-50 mixture of ethanol-water (by volume) and then washed with DI water, dried and treated with O2 plasma for about 1-2 minutes followed by cleaning with DI water and ethanol and blow drying, as previously mentioned, immediately before casting new films. Additional treatment with ethanol always produced uniform films as compared to electrodes subjected to only plasma cleaning. Preparation of the coating solution  For films containing redox polymers Ethanol (2.5 M or 4.6 M) was added as a solvent to a precursor solution of redox polymer (RP) and cross-linker (XL) (90:10 wt%) to improve wetting and spreading ability of the solution on the electrode surface. Solvent content also directly affected the drying rate, hence allows 154 sufficient control on the film morphology. This observation substantiates the fact that by varying solvent content and drop size of the precursor solution, one can custom-make a film suited for a particular operation. For example, high ethanol content (4.6 M) resulted in thicker films with smaller geometric area due to faster drying rate (Figure 5.5).  For films containing enzymes and redox polymers An important factor affecting the nature and uniformity of the films cast by convective self-assembly technique is the drying rate. Precursor solution spreading well, but not drying fast enough (e.g. pure aqueous system) during the course of application, leads to non-homogeneous films with large geometric area. For obtaining uniform films, ethanol was used as a co-solvent (0.5 or 1 M) in the redox hydrogel precursor solution containing enzymes. Ethanol is a known denaturant of enzymes like laccase, and significant loss of catalytic activity was observed (Figure 5.6). Incorporation of Triton X-100 (1 wt% solution), a non-ionic surfactant often used for enzyme stabilization, improved spreading of the precursor solution and film homogeneity on gold (Fig. 5.3). Weight percentages of RP:XL:Triton X-100: Laccase were 54:6:10:29. These films were dried under ambient conditions in controlled relative humidity (RH< 10%, controlled by flow of dry air) for at least 12 hours before testing. Drop sizes from 1-5 µL were used for almost all the studies involving redox polymers only. Drop-sizes of more than 5 µL resulted in flooding of the meniscus at the applicatorsubstrate (glass slide-gold electrode) interface. For enzyme-containing systems, 3µL drop volume was used for all the studies. 155 Thin film versus drop deposited films: film homogeneity Convective self-assembly leads to uniform bulk averaged film thickness as opposed to drop deposition technique where a thick non-electroactive crust of the redox hydrogel is formed at the periphery, which detaches from the electrode surface during the course of experimentation. Figure 5.7 is a visual comparison of the relative electro-active species utilization in a film electrode generated by convective self-assembly technique as opposed to drop deposition (3 µL drop sizes). Optical microscope (Nikon, Eclipse LV150) images were collected using 10 X optical zoom. Figure 5.8a and b shows the AFM images of a bare gold substrate (RMS = 0.8 ± 0.1 nm) and a film-coated (3µL drop size) electrode (RMS = 0.5 ± 0.1 nm), indicating that the films are considerably homogeneous. Figure 5.8 c and d shows confocal microscopy images (Zeiss Pascal confocal microscope) of a film cast from 3µL drop size on a regular microscope slide. FITC (~0.03µg) was used as the fluorophore. These images also point at the fact that convective selfassembly generates uniform and homogeneous redox hydrogel films. Ellipsometry and film thickness measurements These sub-micron sized redox hydrogel films allow the use of ellipsometry, with Å to µm resolution, for determination of dry and wet film thicknesses. Ellipsometric determinations of film thicknesses are often straightforward and precise for transparent films. For non-transparent or absorbing films, such as films containing Os redox centers or Cu active sites, uncertainty of film thickness measurements arise due to improper knowledge about the film refractive index. A schematic of the working principle of ellipsometry is illustrated in Figure 5.9. The film refractive 156 index (n2, k2) depends on the wavelength of the plane polarized light, concentration of the absorbing sites, in-homogeneity of the films, film thickness, and ambient conditions. For the purpose of this study, a multi-wavelength fixed angle (75°) spectroscopic ellipsometer (J.A.Wollam Co. Inc.) with a 75 W Xenon light source (LPS 300) was used to measure the dry and buffer-soaked film thicknesses under ambient conditions. Ellipsometric calculations were done using WVASE32 software.  Theoretical and practical considerations Unlike transparent films with real refractive index, films that absorb light have a complex refractive index of the form given by Equation 5.1, [5.1] [5.2] where n2 and k2 are the real and imaginary components respectively all being a function of wave length (λ). The magnitude of the extinction coefficient, k2, (which is zero for transparent films), depends on the fraction of light absorbed by the film at the measuring wavelength. The ellipsometric parameter (ρ), given by Equation 5.2, depends on the experimental quantities Δ (measure of difference in phase shift due to the film) and ψ (measure of change in relative magnitude of the s and p polarized lights). These parameters depend on the measuring wavelength, refractive index of the surrounding media (n1=1 for air), film thickness (d) and 157 ~ refractive index ( n2 ), refractive index of the underlying substrate (Gold, n3, k3), and the angle of incidence (θi=75°) (Fig 5.9). The cauchy model has been used to fit the ellipsometric data for these redox polymer films (Equation 5.3), where An, Bn and Cn are constants of refraction, k is the extinction coefficient, λ is the wavelength, α is the extinction coefficient, β is the exponent factor, and γ is the band edge. B C n2 ( λ ) = An + n + n 2 λ4 λ ⎡ ⎛ ⎛ 1 1⎞⎞ ⎤ k2 ( λ ) = α exp ⎢ β ⎜ 12400 ⎜ − ⎟ ⎟ ⎥ ⎝ λ γ ⎠⎠ ⎦ ⎢ ⎥ ⎣ ⎝ [5.3] Because the complex refractive index is sensitive to the film structure, initial estimates of 25 An and kamp (α) were obtained from the reported values in the work by Larsson (Table 5.2) for the thick and the thin films with the assumption that the refractive index would not be much affected by replacing PVP with PVI backbone. Larsson demonstrated that for poly (4+/2+ vinylpyridine Os(bpy)2Cl) with varying PVP:Os ratio, n2 remains fairly constant while k2 is 25 sensitive to Os content, both for the thin and thick films (dry or in 0.1 M KCl). The polymer backbone (PVI or PVP) being fairly transparent, relative proportion of the absorbing Os redox centers in these films is directly a measure of film molar absorptivity. For a swollen film, Os content is diluted as compared to the dry films. During this initial estimate, only the film thickness (d) was fitted at 44 different wavelengths. A representative plot of the experimental 158 and model data for redox hydrogel film with polymer C, estimated with the assumed values of An and α from literature for the films in both dry and buffer soaked states is represented in Figure 5.10a and c. The values of Bn = 0.01, Cn=0, γ = 4000 and β=1.5 were used for all the measurements. Once the preliminary estimate of the film thickness (d) was obtained, n2 and k2 were fitted at multiple wavelengths (44) to have a better fit of the data and obtain the film refractive index for the various cases under consideration (Fig 5.10b and c). It is evident from Fig. 5.10, that the estimates of n2 and k2 as obtained by this approach gave a better fit to the experimental data. The estimated refractive indices at 631 nm for the redox polymer systems as evaluated in both dry state and in the presence of buffer are tabulated in Table 5.3. These estimates also demonstrate that the real part of the refractive index does not vary significantly with increasing concentration of the absorbing species (Os), but its complex part is sensitive to Os concentration and film thickness (dry/swollen state). The values of k2 as estimated for buffer swollen films are 25 an order of magnitude higher than that reported by Larsson. This could be directly related to ~10 times higher Os concentrations (~ 2500 mM) in these submicron-sized thin films as 25 compared to the films Larsson used in his study (~200 mM for the same Os:PVP ratio). The redox hydrogel films contained redox polymer (RP): cross-linker (XL) in 90:10 wt%. For wet film thickness and refractive index measurements, the films were soaked in buffer for ~ 5 min, blow-dried in dry air, and the measurements were taken under ambient conditions with no residual buffer on top of the films. For enzyme-containing films, presence of additional Cu 159 centers from the enzyme did not alter the k2 values of the films significantly probably because of their very low optical concentration. Electrochemical Studies Electrochemical studies were conducted in 100 mM citrate buffer (pH 4, 40°C). The thin film electrodes on gold-coated glass slides or drop-deposited films on glassy carbon RDEs were used as working electrodes. The counter electrode was platinum wire, with an Ag|AgCl reference ® electrode (BAS, West Lafayette, IN). Data were collected with a VST Potentiostat and EC-Lab software (Bio-Logic USA, LLC, Knoxville, TN). All measurements, including with the RDEs were taken at 0 rpm under constant sparging of N2 and/or O2. The mediator performances were estimated in de-aerated buffers using transient techniques like square-wave voltammetry (SWV), -1 cyclic voltammetry (at 50-1000 mV s ), and impedance spectroscopy. The catalytic activity of TvL towards ORR in mediated and unmediated systems were evaluated under varying O2 fractions under atmospheric pressure (diluted with N2) using steady state techniques like -1 chronoamperometry and steady state cyclic voltammetry (at 1 mV s ) in O2 saturated buffers. The inhibitory effect of methanol on the catalytic activity of TvL was studied in buffers containing methanol at varying concentrations (1-5 M) under similar experimental conditions. 160 Results and discussion Film thickness estimates Determination of the thickness of redox hydrogel films constitutes a very important aspect of their overall characterization, because of its impact on estimation of electron transport and kinetic parameters. There are various well-established techniques like quartz crystal 26-28 microbalance (QCM), AFM 29,30 10 profilometric techniques, scanning electron microscopy (SEM), 25,31,32 confocal microscopy (Chapter 2), and ellipsometry for determination of the dry film thickness with precision. Of these available techniques, confocal microscopy (0.5 µm resolution) could not be used for thickness measurements of these sub-micron sized films. QCM measurements can correlate the fractional mass change to the degree of film swelling/de28,33 swelling. In this work, ellipsometric techniques have been adapted to directly measure film swelling of these thin-film electrodes on gold-coated glass substrate. Estimation of dry film thickness is often of limited value, because charged redox hydrogels undergo swelling (or de-swelling) when exposed to ionic aqueous media, typical of experimental environments. The degree of film swelling depends on several properties of the film, including the extent of non-electroactive counter ion movements into or out of these films 34-37 to maintain the charge electro-neutrality. Since the differences between the wet and the dry film thicknesses could be large, it is essential to estimate the wet film thickness, for which only few techniques are appropriate. Profilometric techniques and AFM cannot be used for these estimations because swollen 161 hydrogels are too soft to be measured directly. QCM and environmental scanning electron 25,28,31 microscopy (ESEM)38 are some of the techniques other than ellipsometry that allow such thickness determinations of swollen hydrogels.  Factors affecting accuracy of film thickness measurements using ellipsometry Figure 5.11 gives an estimate of film swelling for the three different redox hydrogels as a function of drop volume. While ellipsometric measurements predict ~ 2.0 ± 0.1 times film swelling for the three systems (without enzyme), confocal microscopy approach for measuring the thickness of drop-deposited films demonstrates a ~ 2.7 ± 0.2 times film swelling for these systems. Details of confocal measurements are discussed in Chapter 2. Ellipsometry often underestimates the film thickness due to the following intrinsic assumptions, which might not be correct under all scenarios. Assumption that n3 and k3 of bare substrate are the same even for the film coated one is not always true; cleanliness and roughness of the substrate affect its refractive index. Because the measurements were taken under ambient conditions, dust and moisture could also affect the readings. These sub-micron sized films might not swell much due to large interfacial tensions 2 (electrode area ~ 3.5 ± 0.25 cm ) and better cross-linking. This is in accordance to the findings 25 of Larsson. Larsson in his work demonstrated that the extent of swelling differed significantly for thick and thin films of same Os:PVP ratio. For thin films he reported swelling factors of 1.9 to 2.7, while for the corresponding thick films, the swelling factor ranged from 2.3 to 3.4. He also reported that steric hindrances by larger dimension Os complexes (~13.5 Å from molecular 162 modeling as compared to Csp3-Csp3 bond length 1.54 Å), lead to lower degree of cross-linking of the polymer backbone in thicker films resulting in higher solvation of PVP fraction and increased swelling. Effect of incorporation of enzyme on film swelling For enzyme-containing films, a swelling factor of ~1.5 was estimated using ellipsometry, while confocal microscopy gave a factor of ~ 2. A comparison of the relative swelling factor of these films with or without enzyme and redox polymers is depicted in Figure 5.12. It is evident that films containing enzymes swell to relatively lesser extents, possibly due to electrostatic interactions between the negatively charged enzymes and positively charged redox polymers. The presence of enzyme may also increase the degree of chemical cross-linking. Table 5.4 lists the dry and wet film thicknesses of the enzyme-containing films for the redox polymers. Direct electron transfer (DET) vs. Mediated electron transfer (MET) 11,39-45 Laccase from Trametes versicolor (TvL) has been shown to exhibit DET on gold. Without any surface modification, it is demonstrated that DET is negligible in the potential range where MET generates significant oxygen reduction current density (Figure 5.13a). However at 46 significantly higher negative potential, which is in accordance to literature, TvL exhibits DET (Fig. 5.13b). The controls are background current from bare gold (Au) electrode in de-aerated and oxygen-saturated buffers, and PVI coated Au electrode in oxygen-saturated buffer. The onset potential for the ORR by unmediated laccase is shifted to a more negative potential than that of the mediated system indicating that under the given experimental conditions, MET gives higher catalytic current density at a much lower onset potential due to multi-layer of enzyme activation. 163 Electro-active species (mediator and enzyme) utilization Mediator utilization in these film electrodes was directly related to the active Os content of these films (thin-film and drop deposited films on glassy carbon RDEs) and was estimated using square-wave voltammetry (SWV). Square-wave voltammetry is a powerful electrochemical tool for estimating charge transferred due to faradaic reactions alone and hence 47 gives a precise estimate of the electro-active species at the electrode surface. A comparison of the difference current (idel=iforward-ireverse) versus time for RP A in a thin film and a drop deposited film is shown in Figure 5.14 measured in de-aerated 100 mM citrate buffer (pH~4, 40°C, 0 rpm). The area under the curve is a direct measure of the electro-active species content in the films. As indicated in Fig. 5.14 thin film electrodes exhibit relatively much higher Os redox center utilization as compared to drop-deposited films. Figure 5.15 represents the relative Os utilization in a thin film versus the drop-deposited films under similar experimental conditions. It is demonstrated that by avoiding limitations due to mass transport, thin film electrodes display significantly increased mediator utilization. Figure 5.16 shows the comparison of catalytic current density (per mg of laccase) for thin-films and drop-deposited films for RP A mediated systems. By virtue of eliminating film resistance to O2 transport and significantly improving mediator utilization, thin films display dramatically increased enzyme utilization. Similar results were obtained with the other two mediated systems (data not shown). 164 Estimation of electron transport properties Three different approaches have been taken to estimate electron transport properties in these sub-micron sized films. The charge transport process in redox polymer-coated electrodes is often one of the rate-determining steps, where the electro-active species may migrate by self exchange or electron hopping between adjacent redox active sites with migration of counter 37,48 ions. Whichever charged species may move through the films, rates of charge transport can 37,49,50 be quantified by estimating apparent diffusion coefficient.  Randles-Sevcik Analysis Charge transport properties in charged hydrogels are typically characterized by 37 estimating the apparent electron diffusion coefficient, Dm, via cyclic voltammetry with scan -1 rates from 50 to 1000 mV s . The peak current densities (ipeak) from the cyclic voltammograms were found to vary linearly with the square-root of the scan rate indicating semi-infinite diffusion 51 (Figure 5.17) as expressed by Randles-Sevcik equation (Equation 5.4) ⎛ F3 ⎞ ipeak = 0.4463 ⎜ ⎟ ⎝ RT ⎠ 12 12 * n 3 2Cm Dm υ1 2 [5.4] where, F is Faraday’s constant, R is the universal gas constant, T is the temperature, n is the * number of electrons transferred in the redox reaction, Cm is the bulk mediator concentration and v is the scan rate. Table 5.5 tabulates an estimate of Dm as a function of drop size. The estimates of Dm for thin film systems were found to be three orders of magnitude lower than those 165 reported for RDEs (Chapter 2). The most probable explanation for such low electron diffusion coefficients in these sub-micron sized films could be the fact that these films swell to a relatively lower extent than the drop-deposited films, leading to restricted mobility of the redox active sites and hence lower diffusion coefficients. No significant difference in the film thickness measurements (in buffer) was observed before and after the experiments indicating negligible mass loss from the electrode surface due to the presence of buffer during the course of the experiments.  Impedance Spectra The film electron transport properties (Dm) were also made from impedance spectra collected in de-aerated buffers. A representative impedance spectrum of RP A containing system in de-aerated buffer is shown in Figure 5.18. The dimensionless frequency (Ki) associated with convective diffusion of species i is equal to 1, at the point where transition from semi-infinite to finite diffusion occurs (Equation 5.5). 52 Ki ωδ 2 f Di [5.5] where, ω is the frequency in rad/s, δf is the film thickness, and Di is the diffusion coefficient of the diffusing species i. The estimates of Dm as obtained from impedance spectra was in good agreement with the estimates from Randles-Sevcik analysis (Table 5.5) 166  Aoki method: from empirical expressions of ipeak and Epeak During the course of a linear sweep voltammetry, the diffusion layer extends to the film- solution interface in the time frame of measurement, i.e. diffusion becomes semi-infinite to finite 53 as time lapses. However, this transition depends on the scan rate. For immobilized electro- active species with very fast reversible electrode kinetics (Nernstian equilibrium at the electrode surface), where diffusional mass transfer predominates, with identical diffusion coefficients of 48 the oxidized and reduced species, Akoi et al. developed approximate empirical expressions for peak current (ipeak) and peak potential (Epeak), which are valid in all modes of diffusion (semiinfinite or finite) (Equation 5.6). ⎛ C* D ⎞ 1 2 = 0.446 ⎜ m m ⎟ w tanh 0.56w1 2 + 0.05w nF ⎝ δf ⎠ ( ipeak ( ) ) ( ) ⎭⎦ 3 ⎫⎤ ⎧ ⎛ RT ⎞ ⎡ 0' Epeak = Em + 0.555 ⎜ 1 + tanh ⎨2.41 w 0.46 − 1.2 + w 0.46 − 1.2 ⎬ ⎥ ⎟⎢ ⎝ ⎠ ⎩ nF ⎣ [5.6] where, w is the dimensionless parameter, the square root of which denotes the ratio of diffusion 12 ⎡ RTDm ⎤ space (δf) and diffusion layer thickness ⎢ . To determine Dm by this approach, the ⎣ nFυ ⎥ ⎦ expressions for peak current and peak potential (Figure 5.19) were simultaneously fitted for the -1 entire scan rate range (5-1000 mV s ). 167 Table 5.5 gives a comparison of the estimates of the diffusion coefficients by these three approaches. The values reported, though low, agree within experimental error with estimates from the other two techniques. Enzyme kinetics and inhibition by methanol It is demonstrated in Chapters 2 and 3 that for the redox polymer A, B, and C mediated systems, the mode of inhibition by presence of a contaminant like methanol, largely depends on the mediator redox potential. The systems could be identified as mediator transport limited for RP A (0.43 V | SHE), mediator kinetics limited for RP B (0.77 V | SHE), and electrode kinetics limited for RP C (0.82 V | SHE). This allowed complete estimation of all the kinetic parameters (kcat, KM and KS) by fitting the electrochemical data, possible only for RP C. Figure 5.20 demonstrates that for thin-film systems, by eliminating mass transport limitations and maximizing the electro-active species utilization, inhibition kinetics by methanol are largely enzyme kinetics limited for the three mediated systems. The expression of the plateau current density (iplateau) for enzyme kinetics limited systems is given by Equation 5.7. This indicates that quantitative estimation of all the three kinetic parameters (kcat, KM, and KS) for the three mediated thin-film systems can be obtained by fitting. iplateau = ! nFkcat ETSM red ( KS M red + K M S + SM red ) 168 [5.7] Conclusions We have demonstrated that the convective self-assembly technique could be applied to cast uniform redox hydrogel films to create sub-micron bioactive electrodes. This approach of obtaining thin film electrodes is probably the first of its kind as per the best of our knowledge. These thin film electrodes get high mediator and enzyme utilized by eliminating transport limitations under certain conditions. We have demonstrated that film morphology in terms of film uniformity and homogeneity, and film thickness (dry and wet) could be estimated more precisely. Film refractive index for all the three systems has been estimated for ellipsometric measurements. Transport properties of these films could also be estimated with improved accuracy. However, the low diffusion coefficient estimates could be attributed to limited swelling of the thin films leading to restricted mobility of the redox centers. Enzymes could be incorporated within the redox hydrogel using a non-ionic surfactant, Triton X-100, with no negative impact on enzyme activity. It has been demonstrated that DET by TvL towards ORR is negligible within the potential range where MET predominates. However, significant oxygen reduction by DET in unmediated TvL electrodes (TvL entrapped in cross-linked PVI) is observed at higher negative potentials. It has been demonstrated that by eliminating transport limitations, inhibition kinetics by methanol towards ORR is purely enzyme kinetics controlled for the three mediated systems, unlike the RDE studies reported in Chapters 2 and 3. This allows estimation of all the enzyme kinetic parameters for these three mediated systems. This study presents an opportunity to design and optimize performances of bioelectrodes for a variety of applications. 169 Acknowledgements The authors gratefully acknowledge support from the University of New Mexico under contract FA9550-06-1- 0264 from the Air Force Office of Scientific Research. The authors would also like to sincerely acknowledge the undergraduates Erik McClellan and Robert Hasselbeck for setting up of the film applicator instrument and for the initial trial experiments. 170 Table 5.1: Redox polymer properties 0 − Wt. Length/ e (V | SHE) RP E % Os charge (Å) 0.43 11 30 0.39 0.77 6.6 25 0.05 0.82 9.2 18 ~0 Structural Formula +/2+ A poly (n-VI12[Os(bpy)2Cl] B poly (n-VI20[Os(tpy)(dm-bpy)] C poly (n-VI15[Os(tpy)(bpy)] ) 2+/3+ 2+/3+ ) ) 171 ΔET V Table 5.2: Ellipsometric parameters for initial estimate of film thickness Thick films RP PVI:Os An Thin films Wet (0.1 M Dry 10 2 An kamp× 10 Wet (0.1 M Dry KCl) kamp× 25 3 An KCl) kamp× 10 2 An kamp× 10 3 A 12:1 1.79 1.72 1.39 3.66 1.6 1.66 1.41 3.03 B 20:1 1.75 1.08 1.38 2.07 1.6 1.03 1.38 2.43 C 15:1 1.77 1.4 1.39 2.87 1.6 1.34 1.42 3.04 172 Table 5.3: Estimated refractive index of redox hydrogel films as determined by ellipsometry Dry RP PVI:Os Wet (0.1 M Citrate Buffer) Film thickness (nm) n2* k2*× 10 2 Film thickness (nm) n2* k2*× 10 2 A 12:1 9±2 1.5 ± 0.01 3.9 ± 1 16 ± 2 1.43±0.04 2.7 ± 0.3 B 20:1 6 ± 0.3 1.6 ± 0.01 0.9 ± 0.1 10 ± 1 1.40 ±0.2 0.97± 0.1 C 15:1 16 ± 3 1.6 ± 0.03 3.7 ± 0.5 28 ± 5 1.41±0.21 3.1 ± 0.7 * Reported n2 and k2 are estimated values at 631 nm wavelength 173 Table 5.4: -1 Film thickness of enzyme-containing films (3 µL drop size, 20°, 20µm s ) Film Thickness (nm) Redox Polymers Area (cm ) A 3.6 ± 0.48 32 ± 5 Wet (0.1 M Citrate buffer) 47 ± 5 B 3.2 ± 0.33 39 ± 2 52 ± 2 1.3 ± 0.03 C 2.3 ± 0.21 16 ± 3 28 ± 5 1.7 ± 0.1 2 Dry 174 Swelling Ratio 1.5 ± 0.1 Table 5.5: electrodes Electron diffusion coefficient estimation for thin-film redox hydrogel 2 -1 Redox polymer Drop size (µL) 13 Diffusion coefficient (cm s ) × 10 Impedance RS analysis Aoki method spectra 1 6.5 ± 0.5 6.3 ± 0.8 2.5 ± 0.1 3 5.7 ± 0.6 5.2 ± 1.1 3.1 ± 0.5 4.3 ± 0.9 3.7 ± 0.6 2.9 ± 0.2 5 3.8 ± 0.7 3.1 ± 0.9 2.7 ± 0.2 1 2.8 ± 0.2 3.0 ± 0.3 4.2 ± 0.3 2 1.3 ± 0.1 1.5 ± 0.1 2.5 ± 0.5 3 1.0 ± 0.4 1.1 ± 0.5 1.6 ± 0.3 4 1.0 ± 0.1 1.1 ± 0.8 1.4 ± 0.2 5 1.1 ± 0.1 1.0 ± 0.3 1.2 ± 0.3 1 6.3 ± 0.8 5.4 ± 0.4 3.4 ± 0.1 2 RP C: 0.82 V | SHE 2.7 ± 0.3 4 RP B: 0.77 V | SHE 4.4 ± 0.3 2 RP A: 0.43 V | SHE 5.9 ± 0.3 7.5 ± 0.4 7.0 ± 0.2 2.9 ± 0.1 3 6.1 ± 0.2 5.3 ± 0.5 2.3 ± 0.2 4 4.4 ± 0.4 3.4 ± 0.2 2.9 ± 0.2 5 6.1 ± 0.3 5.4 ± 0.5 2.1 ± 0.3 175 Figure 5.1: Structure of the redox mediators 176 Figure 5.2: (a) The slide coater instrument set-up and (b) the slide coating platform, θ is the slide angle and v is the linear coating velocity. The slide angle θ was optimized to -1 be 20°± 2° and the linear velocity v was optimized ~ 20 µm s for all the operations. 177 Figure 5.3: (a) Effect of slide angle (θ), and (b) the linear velocity (v) on film morphology. The slide angle θ was optimized to be 20°± 2° and the linear velocity v was optimized ~ 20 µm s -1 for all the operations. 178 Figure 5.4: Optimization of instrument slide angle (θ) for RP A and B containing redox hydrogel films. The precursor solution contained RP:XL:: 90:10 wt% and 4.6 M ethanol as solvent. Effect of slide angle (θ) on (a) film electrode area, (b) film thickness and (c) overall film volume. The slide angle θ was optimized to be 20°± 2° and the linear velocity v was optimized ~ 20 µm s -1 for all the operations. 179 Figure 5.5: Effect of ethanol content in precursor solution in controlling film morphology (film drying rate). Effect of film drying on (a) electrode area (geometric), and (b) film thickness of redox hydrogel films containing RP B (90 wt%) and XL (10 wt%). High ethanol content in the precursor solution resulted in thicker films with smaller area due to faster drying rate. The slide angle θ was optimized to be 20°± 2° and the linear velocity v was optimized ~ 20 µm s -1 for all the operations. 180 Figure 5.6: Effect of ethanol content on enzyme activity toward ORR for RP A mediated system. The films were obtained from a 3µL drop of the precursor solutions with or without ethanol such that RP:Lac:XL:: 61:32:7 wt%. For Triton X-100 containing precursor solution RP:Lac:XL:Triton X-100 was present in 54:29:6:10 wt%. Experiments were conducted in O2 saturated citrate buffer (100 mM, pH~4, 40°C) under no rotation. 181 Figure 5.7: Optical microscope images of redox hydrogel films containing RP B (90 2 wt%) and XL (10 wt%). The drop deposited film (area =0.0707 cm ) was formed from 3µL drop of precursor solution on gold-coated glass slide. Thin film electrode was prepared by convective self-assembly technique from a 3 µL drop (θ ≈ 20° and v = 20 -1 µm s ). The images were collected at 10X optical zoom. 182 Figure 5.8: Demonstration of film homogeneity through AFM and confocal microscopy studies. (a) AFM of bare gold, (b) AFM of enzyme-containing redox hydrogel (RP C) film coated electrode. The scan size was 1 µm (x = 0.2 µm/div., z = 10 nm/div for (a) and 5 nm/div for (b) and scanning frequency was 0.5003 Hz.) Confocal microscopy image of thin film cast on glass slide (c) at the edge of the film, and (d) at the center. FITC containing films were excited with 488 nm Argon laser and the green emission was recorded with a 505 long pass filter. 183 Figure 5.9: Schematic of the theoretical principles of ellipsometric measurements. 184 Figure 5.10: Demonstration of improved fitting of the experimentally obtained data (ψ, Δ) with fitted refractive index for the respective systems. (a) Fitting of experimental data for the dry film before estimating the refractive index, (b) improved fitting of experimental data for the dry film with estimated values of refractive index, (c) fitting of experimental data for the wet film before estimating the refractive index, and (d) improved fitting of experimental data for the wet film with estimated values of refractive index. 185 Figure 5.11: (a) Film thickness estimates (dry and in buffer soaked) of the redox hydrogel films (RP: XL:: 90:10 wt%) using ellipsometry. The films were obtained through convective self-assembly technique with varying drop size of the precursor solution containing 4.5 M ethanol, and (b) represents the relative swelling of the films obtained for the three different redox polymer systems. 186 Figure 5.12: Effect of incorporation of enzyme in the redox hydrogel to relative film swelling: (a) or RP A systems, (b) RP B systems, and (c) RP C systems. PVI represents the control for each system without enzyme or redox mediator, PVI + Lac demonstrates the effect of incorporation of enzyme alone, RP represents effect of incorporation of positively charged Os center while case 4 (RP+Lac) represents the effect of incorporation of both enzyme (negatively charged) and Os centers (positively charged) on relative film swelling. 187 Figure 5.13: DET versus MET. (a) MET generates higher catalytic activity towards 46 ORR by TvL. (b) DET prevails at more negative potential. The controls for the unmediated laccase response towards ORR are bare Au electrode in de-aerated and O2 saturated buffers and PVI coated Au electrode in O2 saturated buffer. 188 Figure 5.14: Comparison of the square-wave voltammetry (SWV) demonstrating improved mediator utilization for thin film electrodes as compared to drop deposited film electrodes on RDE. The experiments were conducted at no rotation in de-aerated citrate buffer (100 mM, pH ~ 4, 40°C). 189 Figure 5.15: Comparison of the % active Os content of a thin film electrode and a drop deposited film electrode on a glassy carbon RDE as obtained from SWV (Fig. 5.9) for (a) RP A, (b) RP B, (c) RP C. (d) demonstrates a comparison of the square-wave voltammetry demonstrating improved mediator utilization in thin film electrodes for the three mediated systems. Experimental conditions are same as that of Fig. 5.9. 190 Figure 5.16: Comparison of the enzyme utilizations of a thin film electrode and a drop deposited film electrode on a glassy carbon RDE for RP A mediated systems (3 µL precursor drop size was used for thin film and RDE experiments). (a) Polarization curves were obtained at no rotation in O2 saturated citrate buffer (100 mM, pH ~ 4, -1 40°C, 1mV s ), and (b) varying oxygen concentrations (diluted with N2 under atmospheric pressure). 191 Figure 5.17: Randles-Sevcik analysis of the redox hydrogel thin films for the three redox mediators. The films were cast from a 3µL drop of the respective precursor solutions containing 4.5 M ethanol. The peak current densities were estimated from -1 cyclic voltammograms at 50 mV s in de-aerated buffer. 192 Figure 5.18: Representative Impedance spectra for RP A containing system indicating the point of transition from semi-infinite to finite diffusion regime where the 52 dimensionless frequency Ki=1. Experimental conditions were similar to that of Fig. 5.14. 193 Figure 5.19: Representative plot of fitting of the peak current density and peak potential 48 to obtain electron diffusion coefficients (Aoki method). 194 Figure 5.20: Effect of methanol inhibition kinetics for laccase containing redox hydrogel formed from 3µL drop size of the precursor solution for (a) RP A, (b) RP B, and (c) RP C mediated systems. Experimental conditions were similar to Fig 5.16 b. 195 REFERENCES 196 References 1. C. J. Brinker, Y. F. Lu, A. Sellinger and H. Y. Fan, "Evaporation-induced self-assembly: Nanostructures made easy," Advanced Materials, 11(7), 579-+ (1999). 2. M. Etienne and A. 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Fungal laccase form TvL was used for this study because this enzyme has produced the highest current densities to date. Chemical crosslinking was used as an approach to retain the electro-active species on the electrode surface. The cross-linked redox polymers (positively charged) bind to the enzymes (negatively charged) through electrostatic interactions resulting in an electro-active redox hydrogel film. The results of these studies can enable the design of mediated electrodes for biofuel cell applications. The presence of denaturants such as short chain alcohols (methanol) in the system affects the enzyme functioning due to denaturation. Decoupling inhibition and denaturation effects of short chain alcohols, such as methanol, is often difficult. In Chapter 2, we discuss the effect of methanol as a contaminant towards functioning of mediated laccase catalyzed oxygen-reducing electrodes for direct methanol fuel cell (DMFC) applications. The inherent problem of cathode catalyst poisoning in conventional DMFCs restricts the feed concentration to a maximum of 1-2 M methanol. We demonstrate that by virtue of enzyme selectivity and specificity; the optimal operating conditions can be modulated to generate higher power output from the system. The sensitivity of oxygen reduction current density to the presence of methanol in mediated bio-cathodes depends strongly on mediator redox potential. This study demonstrates that the selectivity of laccase cathodes towards oxygen reduction can facilitate methanol feed concentrations up to 5 M in mixed-feed operations in a DMFC where both the electrodes are exposed to the fuel (methanol) as well as the oxidant (O2). We demonstrated that, within the 0-5 M concentration range, methanol primarily affects enzyme kinetics and not electron transport via 203 the mediator. For methanol concentrations of 0–2.5 M, laccase activity towards oxygen was largely maintained; approximately 30% loss of activity occurred in the 2.5–5 M range, and irreversible loss of enzyme activity was observed beyond 7.5 M predominantly due to enzyme denaturation (after effect study, Fig. 2.10a). The presence of methanol primarily decreases the turnover number (kcat) of the enzyme rather than altering substrate binding (KM, KS), suggesting a non-competitive inhibition mechanism. It is proposed that this reduction occurs due to changes in the electron transfer environment near the T1 binding pocket due to the presence of methanol. Enabling higher methanol feed concentration has the following advantages towards advancement of DMFC technology: (1) Less water handling would remove the weight constraint to a great extent. This would allow realizable hand-held device fabrication. (2) Higher feed concentration would lead to higher power density out of the system. (3) Using oxygen selective biocathodes would allow designing of mixed-feed systems, where both the electrodes are exposed to similar feed concentrations. Mixed-feed systems can allow considerable design simplification, such as removal of the membrane (expensive component) separating the cathode and the anode chambers. All of these factors would allow miniaturization of DMFC devices to a realizable extent. In Chapter 3, we have demonstrated that methanol exhibits non-competitive inhibition mechanism towards oxygen reduction by TvL in a mediated biocathode as a function of mediator redox potential. It has been demonstrated that the redox potential of the mediator and its diffusivity are the most critical and sensitive parameters in controlling the overall performance of the mediated bio-electrodes. The 0-5 M methanol concentration window was chosen for this study to capture the inhibitory effect of methanol on the enzyme performance rather than the 204 inactivation kinetics. TvL in oxygen reducing mediated biocathode systems is known to follow bi-bi-ping-pong kinetics, where the first product is released before the second substrate binds to the enzyme. The main steps involved in the oxygen reduction mechanism by laccase in a (n-1) mediated system are: (1) reduction of the T1-Cu site by the reduced substrate (Os ), (2) electron transfer from the T1-Cu site to the trinuclear cluster, and (3) reduction of oxygen at the trinuclear cluster. The electron transfer driving force (ΔET) between the Os redox center and the T1-Cu site of laccase largely governs step 1 of this mechanism. It has been demonstrated that enzyme turnover (kcat) also depends on ΔET, with a lower mediator redox potential resulting in a higher apparent kcat. Methanol binds to TvL in a nonspecific configuration, and does not compete with either substrate (mediator or O2) to the binding sites. It has been demonstrated that in the 0-5 M concentration range, methanol affects enzyme turnover, rather than its binding efficiencies, which further substantiates the hypothesis of non-competitive inhibition kinetics by methanol. It has been demonstrated that mediator redox potential and the electron diffusivities via the mediators within the film result in different limiting cases (substrate or mediator limited scenarios) . Depending on the relative magnitudes of the half-wave potential of the catalytic reduction current density and the mediator redox potential, the systems could be identified as mediator transport limited (A: 0.43 V | SHE), mediator kinetics limited (B: 0.77 V | SHE) and electrode kinetics limited (C: 0.82 V | SHE). The overall objective of this portion of the study was to quantify the performance of oxygen reducing mediated biocathode systems to enable design of mediated electrodes for biofuel cell applications, especially for DMFCs. 205 In Chapter 4, in collaboration with Dr. Sanjeev Mukerjee's group at Northeastern University, an effort has been made to elucidate the ORR mechanism by immobilized TvL in a mediated system using XAS as a function of the redox potential of the mediators when operated in-situ under ambient conditions. We delineated the structural and functional interactions between the enzyme active site and redox centers of the mediators with X-ray for an electrochemically operative oxygen-reducing mediated biocathode. This work demonstrates that the Cu active sites of TvL could be probed by XAS at micro-molar concentration levels. The oxidation states of the Cu active sites are correlated to structural changes as a function of applied electrode potential, presence or absence of substrate (O2) and mediator redox potential. It has also been shown that the oxidation state of the T1-Cu center largely depends on the mediator redox potential. These findings provide a very strong ground for elucidating the mechanism of oxygen reduction by immobilized laccase in a mediated system as a function of mediator redox potential. To the best of our knowledge, this is the first effort at probing into the active site of immobilized TvL when operated in-situ under ambient conditions. In Chapter 5, we have implemented a convective self-assembly technique to obtain homogeneous sub-micron (~ 10-50 nm) bioactive redox hydrogel films on gold-coated glass slides. The sub-micron sized electrodes allow higher mediator and enzyme utilization by lowering transport limitations. It has been demonstrated that the film morphology and electron transport properties of these films could be estimated with greater precision. Ellipsometry has been used to measure and quantify film-swelling properties of these systems under experimental conditions. The complex film refractive index had been estimated for these systems, which lead to improved precision in film thickness measurements by ellipsometric techniques. This study 206 demonstrates means to control redox hydrogel film morphology by manipulating substrate/electrode surface hydrophilicity, spreading and wetting properties of the precursor solution, and its drying rate. Use of a non-ionic surfactant (Triton X-100) enabled improved spreading of the enzyme-containing precursor solutions with no negative impact on enzyme activity. The evidence provided in this study can have a greater impact in designing homogeneous and reproducible enzyme-containing redox hydrogel films for biofuel cell applications. This dissertation presented a detailed study of a mediated bio-cathode system addressing ways to understand ORR by mediated laccase, determining the ORR kinetic parameters and elucidating the role of mediators in controlling the overall electrode performance, improving the understanding of ORR mechanism in a mediated system. Methods were enumerated for producing sub-micron sized enzyme-containing redox hydrogel films with better control and precision over controlling film morphology and repeatability. The findings of this study could be extended and implemented in improved designing of an oxygen reducing biocathode for biofuel cell applications. Future directions The development of BFCs to date has proven to have a huge potential for further improvements and application. Collaborative efforts between different fields of science are essential to make enzymatic biofuel cells a realizable potential applicant for improvements in human health and power generation. 207 Inherent low power density output, difficulty in incorporating enzymes on the electrode surface, establishing electrical connectivity between the immobilized enzymes and the electrode, and long-term stability of the bio-electrodes are the major obstacles that are keeping biofuel cell technology from being commercialized extensively. This technology, which relies on extracting energy from the readily available ambient energy sources, has the potential to address various civilian and military needs as well. By virtue of enzyme selectivity and activity under ambient conditions, enzyme-based biofuel cells can extract electrical energy form simple and complex carbohydrates readily available in nature. To enhance power density of an operable biofuel cell, it is required to increase the effective loading of the electro-active species. An ideal enzymatic electrode should be limited by enzyme loading and not by the electron transport between the enzyme active site and the electrode. In any biofuel cell configuration, the extent to which the electron transfer is achieved and the effect of surface interactions (for direct electron transfer) or mediator molecules (for mediated electron transfer) on the enzyme activity and stability are governed by the electrode/substrate properties, biocatalysts, and chemical reagents and mediator molecules in use. Understanding of these structure-function relationships between the enzyme-electrode and enzyme-mediator interactions must include extensive knowledge about the enzymes, mediators, substrates, immobilizing media, and electrode architecture. For a mediated system, promising advancement towards enhancing electron transport between the enzyme and the electrode could be achieved by improving the affinity of the mediator to enhance enzyme activity. Structural modifications towards developing stable mediators with enhanced electron transfer abilities could be a probable solution. It is expected 208 that the findings related to dependency of overall electrode performance on mediator redox potential and electron diffusivities via the mediators would help improve the fundamental understanding of this underlying scientific challenge as presented by the biofuel cell technology. Another approach to improve electron transport is to modify the immobilizing network such that significant control on catalyst, mediator and substrate distribution could be achieved. Redox enzymes catalyze reactions involving at least two co-substrates. The microenvironment around the immobilized enzymes within the matrix, substrate concentrations at the vicinity, local pH and ionic balances are certain factors that directly contribute to the enzyme turnover or efficiency, which dictates the system energy density. Mechanical integrity of the immobilizing scaffolds would improve retention of the electro-active species on the electrode surface, and their chemical stability, thereby directly dictating the system’s lifetime and degradation. Other immobilization techniques like electro-deposition could also enhance the electrode performance due to improved retention and interactions of the electro-active species with the electrodes. This technique could also allow fabricate films of desired thickness and catalyst loadings. As demonstrated in this work, convective self-assembly technique for casting submicron sized enzyme-containing redox hydrogel films could also be extended to cast such thin films on gas diffusion layers or membranes, which could be directly used as bioelectrodes. Meeting the challenges that biofuel cell technology presents requires complete mathematic quantification to relate structure-function interactions with performance. It is expected that the approach taken in this work to quantify the physical and kinetic parameters of these enzyme-containing redox hydrogel systems under various operating conditions would help 209 improve out scientific understanding on molecular scale and help optimize these systems for biofuel cell applications. Enzymes when taken out of a cell are generally not designed to function for extended periods of time in biofuel cell set-ups. Therefore, it is important to ascertain means to maximize the enzyme lifetime without sacrificing functionality. This could either be obtained by engineering the protein itself, or by controlling the microenvironment in which the protein operates. In silico technique is now widely been adopted to design proteins of comparable activity and functionality using computer modeling. For the purpose of successful designing of such macro molecules, it is essential to have knowledge about the amino acids which helps maintain the structural and functional integrities of the protein active sites. The XANES and the EXAFS study as presented in this thesis, could positively contribute towards such understanding for TvL. The structures of the intermediates as identified during ORR, give valuable information about the neighboring atoms and hence the amino acids directly involved in ORR. This could help engineer the enzyme to suit a particular application, improve the volumetric catalytic active site density, and increase the overall catalyst loading to obtain higher power density out of the system. With careful engineering, future biofuel cell devices could provide compact, portable, lightweight and robust power sources meeting the subtle needs of society. 210 APPENDICES 211 Appendix A. Function for extracting the film thickness from a colored confocal z* section image function [thm,data]=Filmthickness_Confocal_color(f) if nargin<1 [f,path]=uigetfile('*.*'); end %if fmt=f(max(strfind(f,'.'))+1:length(f)); % load the data file a=imread([path,f],fmt); % plot the data subplot(5,1,1);figure(gcf) imshow(a,[0 212]); title('Raw Data') % create a moving average filter over 50 points h = fspecial('average', [1,50]); % apply the filter to the data af=imfilter(a,h); % convert it to gray scale ag=rgb2gray(af); % extract the minimum value for baseline correction of the filtered data amin=min(ag); nrows=size(ag,1); Z=amin(ones(1,nrows),:); % generate matrix Z with min values of ag and of the same dimension agb=ag-Z; % base-line corrected filtered image in gray scale BW=edge(agb,'canny'); of the gray image % uses Canny method to determine the edge % plot the filtered data subplot(5,1,2);figure(gcf) imshow(af,[0 212]); * This code has been generously provided by my advisor Dr. Scott Calabrese Barton 212 title('Filtered Data') subplot(5,1,3);figure(gcf) imshow(agb,[0 212]); title('Filtered Data in Gray Scale') subplot(5,1,4);figure(gcf) imshow(BW,[0 212]); title('Edge determination') % create a matrix of max values for each column amax=max(agb); amax=amax(ones([size(agb,1),1]),:); % sum the values in each column that are greater than half the max % we ignore the ends because the filter is messed up there. % we assume here that the pixel thickness is 0.37 micron. adiff=(agb-amax*0.9)>0; th=0.2*sum(adiff(:,50:size(adiff,2)-50)); subplot(5,1,5);figure(gcf) plot(th); axis([-inf,inf,0,Inf]); xlabel('position');ylabel('thickness / micron') % The thickness is the pixel size * th % disp([mean(th),std(th)]); data.a=a; data.af=af; data.th=th; data.f=f; data.agb=agb; thm=[mean(th) std(th)]; 213 Appendix B1: MATLAB code for fitting cyclic voltammograms to extract Tafel slope, electron diffusion coefficient and exchange current density ∗ function out=cvfit_p(tviexp,in,params,wexp) tvisize=size(tviexp); tvicolumns=tvisize(2); if ((nargin==4) && (length(wexp)==tvisize(1))) DoWeight=true; else DoWeight=false; end if tvicolumns==2 % assume no time data vexp=tviexp(:,1); iexp=tviexp(:,2); dv=abs( vexp(2:length(vexp)) - vexp(1:length(vexp)-1) ); dt=dv/in.vscanrate; texp=[0; cumsum(dt)]; elseif tvicolumns==3 % assume time data in first column texp=tviexp(:,1); vexp=tviexp(:,2); iexp=tviexp(:,3); end %if %baseline correction %iexp=iexp-mean(iexp); % Match parameters to experiment as much as possible if tvicolumns==3 in.vscanrate=abs(vexp(2)-vexp(1))/(texp(2)-texp(1)); end %if in.Ebegin=vexp(1); in.Eend=in.Ebegin; ∗ This code has been generously provided by my advisor Dr. Scott Calabrese Barton 214 IsLowStart= abs(in.Ebegin-min(vexp(:))) < in.dEpot; in.Evertex=max(vexp)*IsLowStart + min(vexp)*~IsLowStart; % Check to be sure each wave has an integer number of points. Nhalfwave= ceil(abs(in.Ebegin - in.Evertex)/in.dEpot); Espan=Nhalfwave*in.dEpot; in.Evertex= in.Ebegin + Espan * (IsLowStart - ~IsLowStart); % Get the number of fitting parameters from the size of "params" x=size(params); nparams=x(2); % Extract initial guesses from guesses=zeros([1,nparams]); for ii=1:nparams guesses(ii)=params(ii).init; % Alternatively, this will extract from input structure "in" % guesses(ii)=eval(['in.',params(ii).param]); end %for beta0=ones(size(guesses)); %Set fitting options. options=statset; %options.Display='iter'; options.DerivStep=1e-2; %options.Robust='on'; % Do the fit and calculate precision metrics. % Method of Calculation with weights described here: % if DoWeight %FitFunW = @(b,x) sqrt(wexp) .* FitFun(b,x); % iexpW = sqrt(wexp).*iexp; [beta,resid,J,Sigma] = nlinfit(texp,iexpW,@FitFunW,beta0,options); beta_ci = nlparci(beta,resid,'covar',Sigma); [icfit, icfit_delta] = nlpredci(@FitFun,texp,beta,resid,'covar',Sigma); else 215 [beta,resid,J,Sigma] = nlinfit(texp,iexp,@FitFun,beta0,options); beta_ci = nlparci(beta,resid,'covar',Sigma); [icfit, icfit_delta] = nlpredci(@FitFun,texp,beta,resid,'covar',Sigma); end %if out.beta=beta.*guesses; out.beta_ci=beta_ci'.*guesses([1,1],:)-out.beta([1,1],:); out.icfit=icfit; out.icfit_delta=icfit_delta; out.icerror=out.icfit*[1 1]+out.icfit_delta*[-1 1]; disp(' ') for ii=1:nparams disp([params(ii).param,' = ',num2str(out.beta(ii)),' +',num2str(out.beta_ci(2,ii))]) end % for disp(' ') plot(vexp,out.icerror,'-m',vexp,iexp,'b',vexp,out.icfit,'r') legend('95% conf. intervals',' ','Experiment','Fit','Location','Northwest') ylabel('Current Density / mA cm^{-2}') xlabel('Potential / V re: SHE') function icfit=FitFunW(b,x) icfit=sqrt(wexp).*FitFun(b,x); end %FitFunW function icfit=FitFun(p,texp) %multiply the dummy parameters by the guesses p=p.*guesses; %plug the current parameter values into the input structure: for jj=1:length(p) eval(['in.',params(jj).param,'=',num2str(p(jj)),';']); end %for %Do only 5 sweeps in.Nsweeps=5; %CDhalf(jj)=p(4).*sqrt(p(2)); disp([p(:)']) 216 %obtain the predicted cv. we will average the last three waves. [out,c,v,t]=cv_pdepe(in); c=c*1000; % convert to mA/cm2 %interpolate fit to experimental time points icfit = interp1(t,c,texp,'spline'); %baseline correction %icfit=icfit-mean(icfit); % calculate error if DoWeight error = sum(wexp.*(icfit(:) - iexp(:)).^2); else error = sum((icfit(:) - iexp(:)).^2); end %if %Diff2*cinf2 = 4.28481E-09; % print some results: format short g disp([p(:)' error]) plot(vexp,[iexp, icfit]) legend('Exp','Fit','Location','Southeast'); figure(gcf), drawnow end %FitFun end %cvfit function [out,c,v,t]=cv_pdepe(in,DoPlot) in.n=in.z3-in.z2; F=96487; f=F/8.314/313; % Calculate sweep properties DoCV= (in.Ebegin==in.Eend); Espan = in.Evertex - in.Ebegin; in.Period= abs(Espan) * (1 + DoCV) / in.vscanrate; tmax= in.Period * (1 + DoCV*(in.Nsweeps - 1)); in.dtime= in.dEpot/in.vscanrate; % Constants in.ilim= in.n*F*in.Diff2*in.cinf2/in.xmax; in.irel= in.io/in.ilim; in.tau=in.xmax^2/in.Diff2; 217 tspan= 0:in.dtime:tmax; % dimensionAL time V= cvpot(tspan,in); % dimensionAL potential % --------------------------------m=0; x=[0 logspace(-4,0,81)]; t=tspan/in.tau; % dimensionless space % dimensionless time data= pdepe(m,@smppde,@smpic,@smpbc,x,t); % Calculate dimensional out.data=data; % still out.t=t; % still out.x=x; % still out.in=in; current dimensionless dimensionless dimensionless out.c= getwave(out,1,in.Nsweeps); [c,v,t]= getwave(out,3,3,true); c=c + in.CDoff /1000; % Add offset to improve comparison to experiment. % Convert to dimensional results out.t=tspan; % time in seconds out.v=V; % potential in V out.x=in.xmax*x; % position in cm. % Make plot if nargin==2 && DoPlot==true, plot(out.v,out.c,out.cvt_avg(:,2),out.cvt_avg(:,1)) xlabel ('Potential / V') ylabel ('Current Density / A cm^{-2}') figure(gcf) end %if % ------------------------------------------------------------------------function cinit=smpic(x) Epot= in.Ebegin; % eps_v= (in.n*f*(Epot - in.Eo)); eps_v= ((Epot - in.Eo)/2/in.beta); exp_v= exp(eps_v); cRnernst= 1/(1+exp_v); cinit=cRnernst; end % smpic 218 % ------------------------------------------------------------------------function [c,f,s] = smppde(x,t,u,DuDx) c=1; f=DuDx; s=0; end %smppde % ------------------------------------------------------------------------function [pl,ql,pr,qr] = smpbc(xl,cl,xr,cr,t) Epot= cvpot(t*in.tau,in); % eps_v= (in.n*f*(Epot - in.Eo)); eps_v= ((Epot - in.Eo)/2/in.beta); exp_v= exp(eps_v); cRnernst= 1/(1+exp_v); pl = in.irel*( -cl*(exp_v + 1.0/exp_v) + 1.0/exp_v ); ql = 1; % % pl= cl - cRnernst; ql= 0; pr = 0; qr = 1; end %smpbc end %cv_pdepe % ================================= function [E,Period]=cvpot(time,Eend,Ebegin,Evertex,vscanrate) % ================================= % Calculate potential for a given time for use in step and sweep transient calculations. if nargin == 2 in=Eend; Eend=in.Eend; Ebegin=in.Ebegin; Evertex=in.Evertex; vscanrate=in.vscanrate; end % if if Eend == Ebegin % Cyclic Voltammogram 219 Espan = Evertex - Ebegin; Period= 2*abs(Espan) / vscanrate; Tper=mod(time,Period)/Period; E= (Ebegin + Espan * 2* Tper ) .* (Tper <= 0.5) + (Evertex - Espan * 2*(Tper-0.5)) .* (Tper > 0.5); else % Linear Sweep Espan = Eend - Ebegin; Period= abs(Espan) / vscanrate; Tper=time/Period; E= Ebegin + Espan * Tper; end %if end % cvpot % ================================= function [c,v,t]= getwave(sol,firstwave,numwaves,DoAverage) % ================================= % [c,v,time]= getwave(sol,firstwave,numwaves,DoAverage); in=sol.in; gradc=zeros(size(sol.t)); for ii=1:length(sol.t) [cout,gradcout] = pdeval(0,sol.x,sol.data(ii,:),0); gradc(ii)=gradcout; end %for t=sol.t*in.tau; current= gradc*in.ilim; % units A/cm2, cathodic defined as negative [potential,Period]=cvpot(t,in); Nwave = round(Period/in.dtime); Nfirst= (firstwave-1)*Nwave + 1; Nlast= Nfirst + numwaves*Nwave; c=current(Nfirst:Nlast); if nargin==4 && DoAverage==true, 220 cmat=reshape(c(1:length(c)-1),Nwave,numwaves); lastline= [cmat(1,2:numwaves) c(length(c))]; cmat= [cmat ; lastline]; c=mean(cmat,2)'; v=potential(1:Nwave+1); t=t(1:Nwave+1); else v=potential(Nfirst:Nlast); t= t(Nfirst:Nlast); end % if end % getwave Appendix B2. Input file for the cvfit_p function (for RP A mediated system): ccfilm4d_in function in=ccfilm4d_in %info in.N=2; in.NJ=1001; in.itmax=100; iterations in.tol=1e-10; in.xmax= 3.30245e-4; in.Ro= 1e-4; films % Number of species % Number of points in domain % Maximum number of % Convergence tolerance % film thickness % Fiber radius for supported in.DoDimensionless=0; in.DoIter= 0; in.DoABDG=0; % Current offset (mA/cm2) in.CDoff=-0.030081; % transient in.DoStep=0; in.DoSweep=1; in.Ebegin=0.68; cyclic voltammogram AND step in.Eend=0.68; voltammogram AND step in.StepDeltaTime= 0; in.StepTotalTime= 1; % Beginning potential (V) for % Ending potential (V) for cyclic % Time increment for step (s). % Duration of step (s). 221 in.Evertex=.198; cyclic voltammogram in.vscanrate=.05; voltammogram in.dEpot=.002; voltammogram in.Nsweeps=5; voltammogram % Vertex potential (V) for % Scan rate (V/s) for cyclic % Potential step (V) for cyclic % Number of sweeps for cyclic %concentration in.cinf1= 1.1e-6; in.cinf2= 96.13e-6; in.cE=1.34e-6; in.Eo= 0.4072; in.T= 313; if (~in.DoStep & ~in.DoSweep) in.Epot= 0.2; end %if %transport in.z1 = 0.0; in.z2 = 2.0; in.z3 = 3.0; in.Diff1= in.Diff2= in.Diff3= in.Diff4= 3e-5; 9.3228e-10; in.Diff2; 2.05e-09; %kinetics in.kcat= 0; in.Ks= 78e-09; in.Km= 20e-09; in.io= 100000; in.beta= 0.067; in.sc1 = 0.250; in.sc2 = 1.0; in.sc3 = -1.0; in.sc4 = 0.d0; %impedance in.DoImpedance=1; in.etwid=.01; 222 in.cdl= 7.84e-6; in.fmax= 1e3; in.fmin= 0.1; in.nf=1; ImpLogScale= 1; %Dimensionless if in.DoDimensionless in.irel=10000000; in.eps_v= -24.1; in.chi=0.00000005; in.kappa= 0; in.eta= 1; in.sigma=.1; mu= .1; in.delta1 =1; in.delta2 =1; in.delta4 =1; in.tau=.1; % Baseline: kappa= 10000; eta= 0.1092E-01; sigma=1.344; mu= 262.0; end %if 223 ∗ Appendix C: MATLAB code for one-dimensional film model Function for solving the film model function [output]=bpband_fitter(instruct,datas,params) % kinetic_fitter5 % This version fits datas=[po2 v i] using arbitrary parameters. % Ideally, the input data should be corrected to eliminate external mass % transfer losses using a Koutecky-Levitch analysis. % Get the number of fitting parameters from the size of "params" nparams=size(params,2); paraminit=ones([1,nparams]); % The "X data" for this analysis is the row index of datas index=1:size(datas,1);index=index'; cox=datas(:,1)/1e6; potential=datas(:,2); iexp= datas(:,3); % convert from mM to mol/cm3 % V % mA/cm2 % Extract weighting data if available DoWeight=0; if size(datas,2)==4, wexp=datas(:,4); DoWeight=1; end %if % Extract initial guesses from the input structure "params" guesses=zeros(size(paraminit)); for jj=1:nparams guesses(jj)=params(jj).init; end %for %Set fitting options. options=statset; %options.Display='iter'; options.DerivStep=1e-2; options.Robust='on'; ∗ This code was assembled with the kind help of my advisor Dr. Scott Calabrese Barton 224 alpha=1-erf(1/sqrt(2)); % one standard deviation. default is two sigma. MATLAB % Method of Calculation with weights described here: % if DoWeight callfunctionW = @(b,x) sqrt(wexp).*callfunction(b,x); iexpW = sqrt(wexp).*iexp; [p,R,J,Sigma] = nlinfit(index,iexpW,callfunctionW,paraminit,options); ci=nlparci(p,R,'covar',Sigma,'alpha',alpha); [fitcurve, delta]=nlpredci(@callfunction,index,p,R,'covar',Sigma,'alpha',al pha); else [p,R,J,Sigma]=nlinfit(index,iexp,@callfunction,paraminit,options ); ci=nlparci(p,R,'covar',Sigma,'alpha',alpha); [fitcurve, delta]=nlpredci(@callfunction,index,p,R,'covar',Sigma,'alpha',al pha); end %if bounds=[fitcurve-delta,fitcurve+delta]; plot(index,iexp,'or',index,fitcurve,'-g',index,bounds,'--r'); figure(gcf); %plot(cox,iexp,'or',cox,fitcurve,'-g'); p=p.*guesses; ci=ci.*[guesses(:) guesses(:)]; % this multiplies the initial guesses by the fit proportions to give fit % kinetic parameters output.kinetics=p; output.ci=ci; output.fitcurve=fitcurve; for jj=1:nparams disp([params(jj).param,'= ',num2str(p(jj)),'+',num2str(ci(jj,2)-p(jj))]) end %for 225 % end of main program function result=callfunction(p,index) % p is the dummy fitting parameters; everything else is as named before %this multiplies the dummy parameters by the guesses out=[]; result=zeros(size(index)); p=p.*guesses; disp(p) for ii=1:length(p) if p(ii)<0 result=100*ones(size(index)); return end %if eval(['instruct.',params(ii).param,'=',num2str(p(ii)),';']); end %for result=zeros([length(index),1]); for ii=1:length(index) instruct.Epot=potential(ii); instruct.cinf(1)=cox(ii); instruct=GetNonDimParams(instruct); [out,jobs]=bartlett_band(instruct); out.in=instruct; out.dataline=GetDataline(out,jobs); result(ii)= out.dataline(1); end %for error_out=sum((result(:)-iexp).^2); format short g; disp([p error_out]) plot(index,iexp,'o',index,result,'-'); xlabel('index'),ylabel('Current Density / mA cm^{-2}') axis([0 Inf 0 Inf]);drawnow end %callfunction end %ss_fit function in=GetNonDimParams(in) 226 in.kappa= in.Diff(2) ); in.eta= in.kcat ; in.gamma= in.cinf(1); in.mu= in.eps_v= in.xmax * sqrt( in.sc(2) * in.kA * in.cE / in.Diff(1) * in.kA * in.Ks / in.Diff(2) / in.kA * in.cinf(2) * in.Ks / in.kcat / in.cinf(1)/in.Ks; ((in.Epot - in.Eo)*2/in.beta); end % GetNonDimParams function dataline=GetDataline(out,jobs) F= 96485; in=out.in; nk= in.z(3)-in.z(2); CurrentDensity= 1000 * nk/in.sc(2) * F * in.Diff(2) * in.cinf(2) / in.xmax * jobs; % mA/cm2 dataline= [CurrentDensity, in.Epot, in.kappa, in.eta, in.gamma, in.mu, in.eps_v]; end % GetDataline function [out,jobs]=bartlett_band(in) % [out,jobs]=bartlett_band(kappa,gamma,eta,mu,eps_v,DoPlot) % out=bartlett_band(10,.1,.2,0,10,true); kappa=in.kappa; gamma=in.gamma; eta=in.eta; mu=in.mu; eps_v=in.eps_v; disp([kappa,gamma,eta,mu,eps_v,bpcase(kappa,gamma,eta,mu)]); % displays which case of B&P the fit falls in according to Table-2 N=2; NJ=10001; tol=1e-8; itmax=100; [h,xpos,delx]=mesh(NJ); cold=zeros(N,NJ);delc=cold; cold=initial_guess(N,NJ,h); [iter,error]=bound_val; s=cold(1,:)'; a=cold(2,:)'; x=xpos; 227 R= kappa^2*a.*s./(gamma*a.*(1+mu*s)+s) .* (a >= 0) .* (s >= 0); dcdx=interpolate(cold,h); jobs=-dcdx(2,1); out.x = x; out.a = a; out.s = s; out.R = R; out.dcdx=dcdx; out.jobs=jobs; % % % % % % % % if nargin==6 && DoPlot cf=gcf; figure(2) plot(x,a,x,s,x,R/max(R(:)));figure(gcf); xlabel ('\chi') legend('a','s','R/R_{max}','location','east') figure(cf); end %if % The following are subfunctions of the main program. all have access to % any variable declared above, including in and cold. They % ================================= function [iter,error]=bound_val %================================= % Does the iterative, nonlinear boundary value problem. Works for transients % if DoTransient is true and cprev and delt are supplied. For steady % state, (DoTransient == false) cprev and delt are not required. for iter=1:itmax, [dcdx,d2cdx2]=interpolate(cold,h,2); [sma,smb,smd,smg]=fillmat; [ABD,G]=ABDGXY(N,NJ,sma,smb,smd,smg,h); % This calls a mex function band.mex* You'll get an error if band.mex* % is missing or doesn't work. If you can't fix that, use the function % BANDM as a relatively slow replacement. 228 delc= band(ABD,G); %delc= bandm(ABD,G); error=max(abs(delc(:))); %disp(sprintf('iter, error = %i,%g',iter,error)) delc=reshape(delc,N,NJ); cold=cold+delc; % This line prevents cold<0. It is generally needed when concentrations % are near zero. cold = cold .* (cold > 0) + (cold <= 0) * 1e-17; if error < tol, %sprintf('iter, error = %i,%g',iter,error) return end %if end %for return % ================================= function [sma,smb,smd,smg]=fillmat % ================================= % Defines the governing equations and boundary conditions. % There is no loop over j=1 to NJ here. Everything is done % in MATLAB vector format, so pay close attention to subscripts. %________first column refers to equation %________second column refers to position %________third column refers to species sma=zeros([N,NJ,N]); smb=sma;smd=sma; smg=zeros([N,NJ]); smp=zeros([N,N]);sme=smp;smf=zeros([N,1]); % ****** Ping-Pong Kinetics a=cold(2,:); s=cold(1,:); Denom= gamma*a .* (1+mu*s) + s ; R2= kappa^2 * a .* s ./ Denom; R1= gamma/eta * R2; 229 dR2dc1= R2 ./ s - (R2./Denom) .* ( gamma*mu*a + 1 dR2dc2= R2 ./ a - (R2./Denom) .* ( gamma*(1+mu*s) ) ); ; dR1dc1= gamma/eta * dR2dc1; dR1dc2= gamma/eta * dR2dc2; sma(1,:,1)= ones([1,NJ]); smd(1,:,1)= -dR1dc1; smd(1,:,2)= -dR1dc2; smd(1,:,1)= smd(1,:,1); smg(1,:)= -( d2cdx2(1,:) - R1 ) ; sma(2,:,2)= ones([1,NJ]); smd(2,:,1)= -dR2dc1; smd(2,:,2)= -dR2dc2; smd(2,:,2)= smd(2,:,2); smg(2,:)= -( d2cdx2(2,:) - R2 ) ; %__________________________________________________ Boundary-Condition 1 % sme => smd(:,1,:) % smp => smb(:,1,:) % smf => smg(:,1) smp=zeros([N,N]);sme=smp;smf=zeros([N,1]); % Zero flux BC on substrate smp(1,1)= 1.d0; smf(1)= -dcdx(1); % *** Concentration BC's on mediator % sme(2,2)= 1.d0 % smf(2)= 0.5-cold(2,j) % *** Nernst BC's on mediator % *** eps_v defined as -nF/RT (E-Eo) % *** exp(2*eps_v) used to match Butler-Vollmer for io or irel -> Inf % and only effects proper value of in.beta sme(2,2)= 1.d0; smf(2)= 1/(1+exp(eps_v)) - cold(2,1); % insert sme, smp, and smf into smd smb and smb. smd(:,1,:)= permute(sme,[1 3 2]); smb(:,1,:)= permute(smp,[1 3 2]); smg(:,1)= smf(:); 230 %_______________________________________________ Boundary-Condition 2 % sme => smd(:,NJ,:) % smp => smb(:,NJ,:) % smf => smg(:,NJ) smd(:,NJ,:)=zeros([N,1,N]); smb(:,NJ,:)=zeros([N,1,N]); smg(:,NJ) = zeros([N,1]); % Concentration BC on substrate (need to introduce RDE BL calculation!) smd(1,NJ,1)=1.0; smg(1,NJ)=1.0-cold(1,NJ); % Zero flux BC on mediator smb(2,NJ,2)=1.0; smg(2,NJ)=-dcdx(2,NJ); end % fillmat end % bound_val end % ccfilm %======================== function [h,xpos,delx]=mesh(NJ) %======================== % initializes the mesh. h is the most important output! h=1.d0/(NJ-1); delx = [0; h*ones([NJ-2,1]); 0]; % % % % delx(0)=1.0d0 delx(2:NJ-1)=h delx(NJ)= 0.0d0 delx(NJ+1)= 1.0d0 xpos=h*[0:NJ-1]'; end % mesh % ================================= function cold=initial_guess(N,NJ,h) % ================================= 231 % initial conditions for steady state calculations. be important. Should not cold(1,:)=ones([1,NJ]); cold(2,:)=0.5*ones([1,NJ]); end % initial_guess % ================================= function [ABD,G]=ABDGXY(N,NJ,sma,smb,smd,smg,h) % ================================= % Makes ABD (a 3-d array) and G (a 2-D matrix) to be sent to BAND. There is % no loop over j here- everything is done at all positions using vector variables. sma=permute(sma,[1 3 2]); smb=permute(smb,[1 3 2]); smd=permute(smd,[1 3 2]); % BigMat=spalloc(N*NJ,N*NJ,3*N^2*NJ); % BigG=zeros([N*NJ,1]); A=sma-h/2.0*smb ; B=-2.0*sma+h^2*smd; D=sma+h/2.0*smb; G=h^2*smg; B(:,:,1)=h*smd(:,:,1)-1.5*smb(:,:,1); D(:,:,1)=2.0*smb(:,:,1); X=-0.5*smb(:,:,1); G(:,1)=h*smg(:,1); B(:,:,NJ)=h*smd(:,:,NJ)+1.5*smb(:,:,NJ); A(:,:,NJ)=-2.0*smb(:,:,NJ); Y=0.5*smb(:,:,NJ); G(:,NJ)=h*smg(:,NJ); ABD=cat(3, [B(:,:,1 ) D(:,:,1) X ], ... [A(:,:,2:NJ-1) B(:,:,2:NJ-1) D(:,:,2:NJ-1)], ... [Y A(:,:,NJ) B(:,:,NJ) ] ); end %ABDGXY % ================================= function [dcdx,d2cdx2]=interpolate(c,h,order) 232 % ================================= % calculates first and second order derivatives in space for dependent variables. Ns=size(c); N=Ns(1); NJ=Ns(2); cE=[ c(:,2:NJ) cW=[zeros([N,1]) zeros([N,1])]; c(:,1:NJ-1)]; dcdx=(cE-cW)/2.d0/h; dcdx(:,1) = ( - 3.0*c(:,1 ) + 4.0*c(:,2 ) - c(:,3 ) ) /2.0 /h; dcdx(:,NJ) = ( 3.0*c(:,NJ) - 4.0*c(:,NJ-1) + c(:,NJ-2) ) /2.0 /h; if nargin>2 && order >= 2 d2cdx2= (cE + cW - 2*c)/h^2; d2cdx2(:,1) = zeros([1,N]); d2cdx2(:,NJ) = zeros([1,N]); end %if end %interpolate % ================================= function delc=bandm(ABD,G) % ================================= % MATLAB version of band.mex*. This is much slower than the mex file. ABDsize=size(ABD);N=ABDsize(1);NJ=ABDsize(3); BMrow=permute(reshape(1:N*NJ,N,NJ),[1 3 2]); BMrow=BMrow(:,ones([1,3*N]),:); a=1:3*N;a=a(ones([1,N]),:,ones([1,NJ])); b=0:N:N*(NJ-3);b=permute([b(1) b b(length(b))],[1 3 2]); b=b(ones([1,N]),ones([1,3*N]),:); BMcol=a+b; BigMat=sparse(BMrow(:),BMcol(:),ABD(:)); BigG= G(:); delc= BigMat\BigG; 233 end % bandm Function for determining the Bartlett and Pratt case: bpcase function Case=bpcase(kappa,gamma,eta,mu) % Case=bpcase(kappa,gamma,eta,mu) % Determine reaction-diffusion case based on Table 2 of % P. N. Bartlett and K. F. E. Pratt, J. of Electroanal.Chem., 397(1-2), 61-78 (1995). % bpcase(10,0.1,0.2,0)= 3 % bpcase(20,10,100,0)= 6 % bpcase(100,100,100)= 3 % bpcase(2,.1,0.01,0)= 7 if kappa > 1 Case=2; elseif kappa > sqrt(eta) / gamma / sqrt(1+mu/2) Case=4; elseif gamma*(1+mu)>1 Case=5; elseif kappa > sqrt(2*eta/gamma) && eta < 1 Case=6; else Case=1; end %if if Case==2 if kappa > 1 + eta/gamma Case=3; elseif kappa < gamma*(1+mu) Case=5; elseif gamma > 2*eta && eta < 1 Case=6; elseif gamma*(1+mu) > 2 && eta > 1 Case=7; end %if end %if if Case==3 if kappa*sqrt(eta) < (1+gamma)*sqrt(1+mu/2) Case=4; elseif kappa^2 < (1+mu)*(gamma + eta) Case=5; elseif 2*kappa^2 < 2 + gamma/eta + eta/gamma && eta < 1 234 Case=6; elseif gamma + eta > kappa*sqrt(2*gamma/(1+mu)) && eta > 1 Case=7; end %if end %if if Case==4 if kappa < (1+mu)*sqrt(eta/(1+mu*eta)) Case=5; elseif gamma*sqrt(1+mu/2) < 0.5 && eta < 1 Case=6; elseif eta*(1+mu) > 2*gamma*(1+mu/2) && eta > 1 Case=7; end %if end %if if Case==5 if kappa^2 > 2*gamma*(1+mu) && eta > 1 Case=7; end %if end %if 235 Appendix D1: MATLAB code for solving one-dimensional steady state concentration profiles Function for determining the steady state concentration profile: steady_state_BP function [out]=steady_state_BP(in) % Defining the constants k=in.l*sqrt((in.kcat*in.E)/(in.Da*in.Km)); %defines kappa gamma=in.B/in.S; % defines the balance between two forms of enzyme eta=in.Ds/in.Da; % describes the relative amounts of depletion substrate and oxidized mediator within the film meu=in.S/in.Km; % ratio of substrate conc within the film and Km eps=(in.e0-in.e)*in.n*in.F/in.R/in.T; % dimensionless potential ae=1/(1+exp(-eps)); % dimensionless mediator concentration at the electrode surface Xstar=1./(1+eta./(gamma*ae)); % Initialization solinit = bvpinit(linspace(0,1,10),[1 1 1 1]); % Solution sol= bvp4c(@goveq,@bc,solinit); % Solving & Plotting the data x=linspace(0,1); u=deval(sol,x); plot(x,u(1,:),'b',x,u(3,:),'r'),xlabel('\bfDistance from electrode','FontSize',11),ylabel('\bfConcentration Profile','FontSize',11) title('\bfSteady State Concentration profile of Mediator andSubstrate','FontSize',11) figure(gcf) out.xss=x'; out.ass=u(1,:)'; out.sss=u(3,:)'; % governing equation function dydx=goveq(x,u) 236 r1=k*k*u(1)*u(3)/(gamma*u(1)*(1+meu*u(3))+u(3))* (u(1)>=0) * (u(3)>=0); r2=r1/eta; dydx=[u(2) r1 u(4) r2]; end % end of governing equation % Defining the Boundary Conditions function res = bc(ua,ub) res=[ua(1)-ae ua(4) ub(3)-1 ub(2)]; end % end of Boundary value function end Appendix D2. Input file for the steady_state_BP function (for RP A mediated system): inA_0M function in=inA_0M % Biocathode, A=reduced mediator, B= Oxidized Mediator in.A=540e-6; in.n=4; in.T=313; in.R=8.314; in.F=96487; in.Cd=5.59e-5; in.l=1.0e-4; in.Da=2.58e-10; in.Ds=3.0e-5; 40oC in.kcat=400; in.Km=4.4e-6; in.Ks=1.5e-6; in.E=7.5e-6; in.Ka=1; species in the film % mol/cm3, concentration of reduced mediator [Ref: Josh's thesis] % number of electrons % K, Temperature of the system [40oC] % J/mol.K; Universal gas constant % C/mol; Faraday's Constant % Farad, double layer capacitance % cm, film thickness % cm2/s, electron diffusion coefficient % cm2/s, substrate diffusion coefficient at % % % % % s-1, turn over number mol/cc [Ref: Josh's thesis] mol/cc [Ref: Josh's thesis] mol/cc, total enzyme concentration partition coefficient of the reduced 237 in.e0=0.3866; in.e=0.1904; in.S=1.1e-6; in.B=540e-6; mediator in.ks=1; the film in.Area=0.0707; % % % % V,reversible potential of the system instantaneous potential of the system mol/cc, bulk substrate concentration mol/cc, concentration of the oxidized % partition coefficient of the substrate in % cm2, electrode surface area end 238