Theory and Experiment in Electrocatalysis (Modern Aspects of Electrochemistry)

MODERN ASPECTS OF ELECTROCHEMISTRY No. 50

Series Editors: Ralph E. White Department of Chemical Engineering University of South Carolina Columbia, SC 29208 Constantinos G. Vayenas Department of Chemical Engineering University of Patras Patras 265 00 Greece Managing Editor: Maria E. Gamboa-Aldeco 1107 Raymer Lane Superior, CO 80027

For further volumes: http://www.springer.com/series/6251

Perla B. Balbuena Venkat R. Subramanian Editors

Theory and Experiment in Electrocatalysis

1C

Editors Perla B. Balbuena Texas A & M University Department of Chemical Engineering 3122 TAMU College Station, TX 77843 USA [email protected]

Venkat R. Subramanian Washington University, Saint Louis Department of Energy, Environmental, & Chemical Engineering St. Louis, MO 63130 USA [email protected]

ISSN 0076-9924 ISBN 978-1-4419-5593-7 e-ISBN 978-1-4419-5594-4 DOI 10.1007/978-1-4419-5594-4 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010938296 © Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Preface Electrocatalysts are the heart of power devices where electricity is produced via conversion of chemical into electrical energy. Impressive advances in surface science techniques and in first principles computational design are providing new avenues for significant improvement of the overall efficiencies of such power devices, especially because of an increase in the understanding of electrocatalytic materials and processes. For example, the development of high resolution instrumentation including various electron and ion-scattering and in-situ synchrotron spectroscopies, electrochemical scanning tunneling microscopy, and a plethora of new developments in analytical chemistry and electrochemical techniques, permits the detailed characterization of atomic distribution, before, during, and after a reaction takes place, giving unprecedented information about the status of the catalyst during the reaction, and most importantly the time evolution of the exposed catalytic surfaces at the atomistic level. These techniques are complemented by the use of ab initio methods which do not require input from experimental information, and are based on numerical solutions of the time-independent Schrödinger equation including electron-electron and electron-atom interactions. These firstprinciples computational methods have reached a degree of maturity such that their use to provide guidelines for interpretation of experiments and for materials design has become a routine practice in academic and industrial communities. The outcome of the ab initio methods includes thermodynamic and kinetic characterization of mechanistic reaction pathways, analysis of catalytic behavior of specific alloy compositions, stability of catalytic surfaces under certain gas or liquid environments, and more recently these sophisticated techniques have been extended to comprise the complexity of electrochemical phenomena. Further, as shown in this book, outcomes from ab initio methods can be used as input to model Hamiltonians where other essential effects as solvation are included thus giving a more realistic description of electrocatalytic systems. Beyond ab initio methods that give us the details of the chemistry of the process, classical molecular simulation techniques v

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where the electron-electron, electron-atom, and atom-atom interactions are represented by effective force fields permit the investigation of millions of atoms, and provide additional extremely important insights for physical phenomena that arise from collective interactions, and from environmental aspects such as temperature, pressure, and solvent effects. In addition, coarse-grained methods such as Kinetic Monte Carlo techniques have been developed to address many important catalytic and electrochemical processes involving time scales of the order of minutes and length scales in the order of microns. The outcomes of coarse-grained methods are linked and serve as input to continuum-based models. This volume highlights advances in both theoretical and experimental techniques and points out both the progress made and the challenges remaining to be overcome in the near future to achieve further breakthroughs in electrocatalysis. The volume is organized by presenting the main thematic areas oriented towards specifics of electrodes, membranes and materials, experimental and computational design of proton-exchange membrane (PEM) and bio-fuel cells, along with recent developments in the synthesis and characterization of catalytic materials. In parallel, the occurrence of unwanted corrosion reactions and their subsequent effects on the lifetime of the electrocatalysts are analyzed both with the most advanced experimental techniques and with sophisticated computational methods. Several chapters address various aspects related to electrocatalysis in PEM fuel cells, especially the oxygen reduction reaction (ORR), but also the anode oxidation reactions. Chapter 1 by Goodman, Soriaga, and collaborators presents a thorough investigation of alloy cathode electrocatalysts. Specifically, they investigate Pt-Co surface phase diagrams and provide an assessment of metal dissolution in acid medium, by combining low-energy ion scattering spectroscopy, X-Ray photoelectron spectroscopy, Auger electron spectroscopy, high resolution electron energy loss spectroscopy, low-energy electron diffraction, temperature-programmed desorption, and electrochemical methods. Chapters 2 to 6 deal with theoretical aspects of electrocatalytic reactions. In Chapter 2, Santos and Schmickler introduce a new approach to model an electrochemical system using a model Hamiltonian that incorporates the solvent effect to gas-phase density functional theory (DFT) calculations. The model is illustrated for H2 oxida-

Preface



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tion, and preliminary studies of electrocatalysis in nanostructures are also investigated with the same theory. Chapter 3 by Keith and Jacob presents a DFT-based theoretical analysis of ORR mechanisms, including solvent effects and incorporating the electrode potential in an effective way. Selvan and Keffer in Chapter 4 address the structure of the PEM polymer electrolyte membrane, transport through hydrophilic regions, and connectivity of the water clusters, and the interactions of the electrolyte medium with the electrocatalysts. All of these effects are relevant to the catalysis taken place at the membrane/catalyst/reactants interface. The ORR is also investigated by Sotelo and Seminario in Chapter 5, through a DFT-Green function analysis of small clusters that provide implications of local reactivity in the catalytic process. A different system is studied by Idupulapati and Mainardi in Chapter 6 that presents DFT modeling of the catalytic action of enzymes for the direct oxidation of methanol, focusing on understanding mechanisms with the goal of biomimetic design. Chapter 7 by Soriaga and collaborators studies electrocatalytic oxidation and hydrogenation of chemisorbed aromatic compounds on palladium electrodes. Interfacial characterization using electron spectroscopy, low-energy electron diffraction, Auger electron spectroscopy, high resolution electron energy loss spectroscopy, scanning tunneling microscopy, and differential electrochemical mass spectrometry focus on benzene, hydroquinone, benzoquinone, and introduce an extensive analysis of the reaction mechanisms. Development of new models that connect the continuum descriptions with atomistic MonteCarlo simulations for the understanding of electrochemical systems is presented in Chapter 8 by Subramanian et al. In Chapter 9 by Balbuena and collaborators the ORR reaction in acid medium is revisited through DFT studies that address the complexity of Pt-based alloys in electrocatalytic processes, including surface segregation and metal dissolution processes. Chapter 10 by Coutanceau, Baranton, and Lamy gives a broad perspective of the use of surface science methods and electrochemical techniques to elucidate reaction mechanisms in electrocatalytic processes. Several modern techniques (spectroscopic and analytical) include infrared reflectance spectroscopy, electrochemical quartz crystal microbalance, differential electrochemical mass spectrometry, chemical radiotracers, and high performance liquid chromatography. Applications include analysis of reaction mechanisms of CO,

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methanol, and ethanol oxidation on Pt-based electrocatalysts, and ORR on Fe-Phtalocyanine. In Chapter 11 Mukerjee and Arruda describe the use of in-situ synchrotron spectroscopy to analyze electrocatalysts dispersed on nanomaterials. Applications to ORR Pt-based alloy cathode nanocatalysts, anode reformate catalysts, and ORR in enzymatic centers illustrate the value of this technique to obtain a detailed in situ characterization of materials and mechanisms in electrocatalysis. Perla B. Balbuena Texas A&M University College Station, TX, June 2010 Venkat R. Subramanian Washington University Saint Louis, Missouri



Contents Chapter 1

CHARACTERIZATION OF ALLOY ELECTROCATALYSTS BY COMBINED LOW-ENERGY ION SCATTERING SPECTROSCOPY AND ELECTROCHEMISTRY Stephanus Axnanda, Kyle D. Cummins, D. Wayne Goodman, and Manuel P. Soriaga I. Introduction .............................................................................. 1 II. Experimental Aspects 1. Low Energy Ion Scattering Spectroscopy ......................... 4 2. Preparation of Pt-Co Alloy Films ..................................... 7 3. Electrochemical Characterization ..................................... 7 4. Instrumentation ................................................................. 8 III. Case Study: Pt-Co Alloy Electrocatalysts for Oxygen Reduction ............................................................................... 10 1. Pt-Co Films and Alloys................................................... 10 2. Surface Elemental Composition and Surface Phase Diagrams ......................................................................... 12 3. Long-Range Surface Order ............................................. 14 4. Electrochemical Properties ............................................. 16 (i) OCP Values............................................................ 16 (ii) Cyclic Voltammogram of the Pt3Co Alloy ............ 17 (iii) Potential-Dependent Dissolution of Pt3Co ............ 18 5. Bulk Properties of the Pt3Co Alloy ................................. 20 (i) Relevance to Published Work ................................ 20 IV. Summary ................................................................................ 21 Acknowledgment ................................................................... 22 References ..................................................................................... 22

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Chapter 2

RECENT ADVANCES IN THEORETICAL ASPECTS OF ELECTROCATALYSIS Elizabeth Santos and Wolfgang Schmickler I. Introduction .......................................................................... 25 II. Classification of Electrochemical Reactions ....................... 27 III. Previous Approaches to Catalysis from the Surface Science ................................................................................. 31 IV. Previous Approaches to Bond Breaking Electrochemical Reactions .............................................................................. 34 V. Model Hamiltonian .............................................................. 36 VI. Interactions of the Atomic Orbitals of the Reactant with the Electronic States of the Electrode ........................................ 40 VII. Occupation Probability of the Electronic State of the Reactant ................................................................................ 45 VIII. 1-D And 3-D Potential Energy Representations................... 53 IX. Electrocatalysis by a Narrow d Band ................................... 59 X. Application to Real Systems – Hydrogen Evolution / Oxidation Reactions ............................................................. 67 XI. DFT Quantum Chemical Calculations as Input for the SKSHamiltonian .......................................................................... 70 XII. Electrocatalysis at Nanostructures........................................ 78 XIII. Conclusions .......................................................................... 84 Acknowledgements .............................................................. 86 References ............................................................................ 86

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Chapter 3

COMPUTATIONAL SIMULATIONS ON THE OXYGEN REDUCTION REACTION IN ELECTROCHEMICAL SYSTEMS John A. Keith and Timo Jacob I. Introduction ............................................................................ 89 II. Experimental Studies on the Oxygen Reduction Reaction..... 90 1. On Unmodified Pt Single Crystal Electrodes and Carbon Supports ............................................................. 90 2. On Bimetallic Surfaces and Alloys on Different Supports .......................................................................... 92 III. Theoretical Studies on the Oxygen Reduction Reaction ........ 94 1. Mechanistic Studies on the ORR .................................... 95 2. Treating Electrolyte Effects ............................................ 98 3. Simulations on Bimetallic Alloy Surfaces ...................... 99 4. Simulations on Low-Pt Electrocatalysts ....................... 102 IV. Methods ............................................................................... 103 1. DFT Calculations .......................................................... 103 (i) Finite Systems ...................................................... 103 (ii) Periodic Systems .................................................. 104 2. Thermodynamic Considerations ................................... 105 V. Results and Discussion......................................................... 106 1. Electrochemical Phase Diagram ................................... 107 2. Oxygen Reduction Reaction (ORR) ............................. 110 (i) O2 Dissociation .................................................... 111 (ii) OOH/H2O2 Formation .......................................... 117 (iii) Influence of Water Solvation ............................. 118 (iv) Eley–Rideal Mechanisms ..................................... 122 VI. Conclusions .......................................................................... 123 Acknowledgements .............................................................. 126 References ............................................................................ 127

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Chapter 4

MOLECULAR-LEVEL MODELING OF THE STRUCTURE AND PROTON TRANSPORT WITHIN THE MEMBRANE ELECTRODE ASSEMBLY OF HYDROGEN PROTON EXCHANGE MEMBRANE FUEL CELLS Myvizhi Esai Selvan and David J. Keffer I. Introduction .......................................................................... 133 II. Morphology.......................................................................... 137 1. Introduction................................................................... 137 2. Molecular Models and Simulation Details .................... 141 3. Results and Discussions ................................................ 147 (i) Visualization ........................................................ 147 (ii) Cluster Size Distribution and Connectivity.......... 150 (iii) Pair Correlation Function ..................................... 156 (iv) Hydronium Hydration Histogram ........................ 161 (v) Water Density Profile .......................................... 163 (vi) Hydronium Orientation at the Interface ............... 168 (vii) Critical Gap .......................................................... 169 III. Transport .............................................................................. 172 1. Introduction................................................................... 172 2. Coarse-Grained Reactive Molecular Dynamics Algorithm ...................................................................... 176 3. Proton Transport in Bulk Water .................................... 177 (i) Input from Macroscopic Model ........................... 177 (ii) Input from Quantum Mechanical Studies ............ 178 (iii) Instantaneous Reaction and Local Equilibration .. 182 (iv) Simulation Details ................................................ 183 (v) Results and Discussions ....................................... 184 4. Transport in Nafion ....................................................... 192 (i) Water and Vehicular Hydronium Diffusivities .... 192 (ii) Structural Diffusion of Protons ............................ 193 IV. Conclusions .......................................................................... 195 Acknowledgements .............................................................. 197 References ............................................................................ 198

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Chapter 5 SOME RECENT STUDIES ON THE LOCAL REACTIVITY OF O2 ON PT3 NANOISLANDS SUPPORTED ON MONO- AND BI-METALLIC BACKGROUNDS Juan C. Soteloand Jorge M. Seminario I. Introduction ........................................................................ 203 II. Methodology ...................................................................... 205 III. The Nanosystems ............................................................... 209 1. Clusters and Complexes ................................................ 210 2. Reactive Sites................................................................ 210 IV. DOS of BUBulkLK Co, Pt, Co3Pt, Ni, and Fe ................... 219 V. Electronic Characterization of the O2-Substrate System (LDOS) .................................................................. 222 VI. Local Reactivity of a Bimetallic Surface: Co3Pt ................ 225 1. Electronic Characterization ........................................... 225 VII. Local Reactivity of Supported Pt3 Islands .......................... 230 1. Electronic Characterization ........................................... 230 2. Structural Characterization ........................................... 232 3. Binding and Dissociation Adsorption Energies ............ 234 VII. Conclusions .......................................................................... 237 Acknowledgements .............................................................. 238 References ............................................................................ 239

Chapter 6 METHANOL ELECTRO-OXIDATION BY METHANOL DEHYDROGENASE ENZYMATIC CATALYST: A COMPUTATIONAL STUDY N. B. Idupulapati and D. S. Mainardi I. Introduction ........................................................................ 243 1. Enzymatic Catalysts for Fuel Cell Applications ........... 243 2. Methanol Dehydrogenase Enzyme ............................... 245

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Methanol Electro-oxidation by Methanol Dehydrogenase Enzymes .............................................. 246 II. Methodology ........................................................................ 252 III. Results and Discussion......................................................... 254 1. Methanol Dehydrogenase Active Site Models .............. 254 2. Methanol Electro-Oxidation Mechanisms .................... 256 (i) Addition-Elimination Mechanism ........................ 256 (ii) Hydride Transfer Mechanism .............................. 260 (iii) Methanol A-E versus H-T Electro-Oxidation Mechanisms by MDH .......................................... 267 IV. Conclusions .......................................................................... 269 References .......................................................................... 272

Chapter 7 ELECTROCATALYTIC REACTIONS OF CHEMISORBED AROMATIC COMPOUNDS: STUDIES BY ES, DEMS, STM AND EC

Jean Sanabria-Chinchilla, Youn-Geun Kim, Xiaole Chen, Ding Li, Helmut Baltruschat, and Manuel P. Soriaga I. Introduction .......................................................................... 275 II. Experimental Protocols ........................................................ 276 1. Preparation of Single-Crystal Electrode Surfaces ........... 277 2. Interfacial Characterization ............................................ 279 (i) Electron Spectroscopy (ES) ................................... 279 (ii) Scanning Tunneling Microscopy (STM) ............... 282 (iii) Differential Electrochemical Mass Spectrometry (DEMS) ................................................................ 285 III. The Chemisorption and Electrocatalytic Reactivity of Aromatic Compounds .......................................................... 286 1. Benzene .......................................................................... 286 (i) EC-STM................................................................. 286 (ii) HREELS ................................................................ 292 (iii) DEMS .................................................................... 294 2. Hydroquinone/Benzoquinone ....................................... 299 (i) HREELS ................................................................ 299

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(ii) EC-STM................................................................. 302 (iii) DEMS .................................................................... 304 IV. The Case for a Langmuir-Hinshelwood Mechanism ........... 308 Acknowledgements .............................................................. 312 References ............................................................................ 312

Chapter 8 A REVIEW OF CONTINUUM ELECTROCHEMICAL ENGINEERING MODELS AND A NOVEL MONTE CARLO APPROACH TO UNDERSTAND ELECTROCHEMICAL BEHAVIOR OF LITHIUM-ION BATTERIES Vinten D. Diwakar, S. Harinipriya and Venkat R. Subramanian I. Introduction .......................................................................... 315 II. Continuum Models for Predicting Battery Behavior ........... 316 1. Variables and Governing Equations in the Macro Scale .............................................................................. 318 (i) Cathode ................................................................ 318 (ii) Separator .............................................................. 320 (iii) Anode ................................................................... 321 2. Variables and Governing Equations on the Micro Scale .............................................................................. 322 3. Micro-Macro Scale Coupled Continuum Models ......... 324 4. Capabilities of Continuum Models ............................... 327 5. Limitations of Continuum Models ................................ 332 III. Modeling of Electrochemical Processes at the Micro and Nano Scale ........................................................................... 334 1. Performance Characteristics of Cathode Materials for Lithium Ion Batteries .................................................... 336 2. Methodology ................................................................. 338 3. Parameters Employed ................................................... 340 4. Results and Discussion ................................................. 340 (i) Discharge Behavior of LiCoO2 ............................ 341 (ii) Discharge Behavior of LiFePO4........................... 343

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5. Perspectives .................................................................. 345 6. Conclusions of the Present Work .................................. 345 IV. Scope for Future Work......................................................... 346 List of Symbols .................................................................... 346 References ............................................................................ 348

Chapter 9 CHALLENGES IN THE DESIGN OF ACTIVE AND DURABLE ALLOY NANOCATALYSTS FOR FUEL CELLS P. B. Balbuena, S. R. Calvo, R. Callejas-Tovar, Z. Gu, G. E. Ramirez-Caballero, P. Hirunsit, and Y. Ma I. II. III. IV. V.

Introduction .......................................................................... 351 Activity of Nanoalloy Catalysts Towards the ORR ............. 355 Surface Atomic Distribution of an Alloy Nanoparticle........ 372 Dissolution of Surface Atoms in Acid Medium ................... 385 Conclusions .......................................................................... 391 Acknowledgements .............................................................. 391 References ............................................................................ 391

Chapter 10 DETERMINATION OF REACTION MECHANISMS OCCURRING AT FUEL CELL ELECTROCATALYSTS USING ELECTROCHEMICAL METHODS, SPECTROELECTROCHEMICAL MEASUREMENTS AND ANALYTICAL TECHNIQUES C. Coutanceau, S. Baranton, and C. Lamy I. Introduction .......................................................................... 397 II. Coupled Experimental Methods ........................................... 399

Contents

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Infrared Reflectance Spectroscopy ............................... 399 Electrochemical Quartz Crystal Microbalance (EQCM) ........................................................................ 401 3. Differential Electrochemical Mass Spectrometry (DEMS)......................................................................... 402 4. Radiochemical Labeling ............................................... 403 5. High Performance Liquid Chromatography (HPLC) .... 405 III. CO Oxidation at Platinum Based Electrocatalysts ............... 406 1. Adsorption and Electro-Oxidation of CO at Pure Platinum Catalysts ................................................ 406 2. Adsorption and Electro-Oxidation of CO at Platinum Based Bimetallic Electrocatalysts ................................. 416 IV. Alcohol Oxidation at Platinum-Based Electrocatalysts ....... 422 1. The Electro-Oxidation of Methanol .............................. 423 (i) IR Studies of CH3OH Adsorption and Oxidation at Smooth Pt Electrodes ...................... 423 (ii) FTIR Studies of CH3OH Adsorption and Oxidation at Pt-Ru Bulk Alloys ............................................ 426 (iii) EQCM Studies of Methanol Adsorption and Oxidation ............................................................. 431 (iv) DEMS Study of Methanol Adsorption and Oxidation ............................................................. 434 (v) Radiochemical Labeling of Methanol Adsorption ........................................................... 439 (vi) Mechanism of the Electro-Oxidation of Methanol .............................................................. 449 2. The Electro-Oxidation of Ethanol ................................. 452 (i) IR Study of the Adsorption and Oxidation of Ethanol on Pt/C Catalysts .................................... 453 (ii) Comparison of Ethanol Electro-Oxidation on Pt and PtSn Catalysts ............................................... 456 (iii) DEMS Study of Ethanol Electro-Oxidation on PtBased Catalysts .................................................... 460 (iv) HPLC Investigation of Ethanol Electro-Oxidation on Pt Electrodes ................................................... 466 (v) HPLC Analysis of Ethanol Oxidation on Dispersed Pt-Based Anodes of a DEFC ................................ 469 (vi) Detailed Mechanisms of Ethanol Oxidation at PtBased Electrodes .................................................. 474

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V. Oxygen Reduction Reaction (ORR) ..................................... 477 1. Electrochemical Methods: Rotating Disk Electrode (RDE) and Rotating Ring Disk Electrodes (RRDE) ..... 477 2. Electrochemical Quartz Crystal Microbalance (EQCM) ........................................................................ 484 3. Electrochemistry Coupled with Fourier Transform Infrared Spectroscopy (FTIRS) ..................................... 490 VI. Conclusions .......................................................................... 493 References ............................................................................ 494

Chapter 11 IN-SITU SYNCHROTRON SPECTROSCOPIC STUDIES OF ELECTROCATALYSIS ON HIGHLY DISPERSED NANO-MATERIALS Sanjeev Mukerjee and Thomas Arruda I. Introduction .......................................................................... 503 II. Current State of the Art in Surface Science Tailored for Electrocatalysis Investigations ............................................. 504 III. Synchrotron Methods as a Probe of Metal Reaction Centers at an Electrochemical Interface ............................... 506 IV. In-Situ Synchrotron Spectroscopy: Methodology and Practice .......................................................................... 509 1. Overview of the Underlying Principle and Data Analysis ........................................................................ 510 (i) XANES ................................................................ 513 (ii) New In-Situ Site Specific Surface Probe Using Synchrotron Based XANES Spectroscopy: Some Recent Results............................................ 516 2. EXAFS .......................................................................... 519 V. Electrocatalysis for Low-Temperature Acid-Based Fuel Cells ..................................................................................... 523 1. Oxygen Reduction Reaction on Pt and Pt Alloy Electrocatalysts ............................................................. 523 2. Electrocatalysts for Anode Electrodes Using Pt Alloys ............................................................................ 526 (i) Reformate Tolerant Electrocatalysts .................... 526

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(ii) Direct Methanol Oxidation .................................. 528 Non Pt-Based Electrocatalysts ...................................... 530 (i) Current State of the Art in Non-Pt Chalcogenide Electrocatalyst Systems ................. 530 (ii) Oxygen Reduction on Unique Enzymatic Active Centers ................................................................. 531 VI. Understanding Electrocatalytic Pathways ............................ 533 1. Nanocluster Morphology and Unique Reaction Environment.................................................................. 533 (i) Highly Dispersed Pt based Electrocatalysts: Issue of Particle Size ............................................ 533 (ii) Nanophase Electrocatalysts: Surface Structure of Small Particles ..................................................... 534 (iii) Structural Effects on Electrocatalysis by Pt: Effect of Particle Size ..................................................... 536 2. Alloy Electrocatalysts: Electronic and Structural Effects on Electrocatalytic Properties of Platinum Alloys ............................................................................ 542 (i) Cathode ................................................................ 544 (ii) Water Activation Studies ..................................... 546 (iii) Anode ................................................................... 548 3. Chalcogenide Electrocatalysts ...................................... 553 4. Co-Porphyrin Systems .................................................. 557 5. XAS as a Probe in Enzymatic Fuel Cells ...................... 559 References ............................................................................ 565 3.

Index

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List of Contributors, MAE 50 Thomas Arruda Department of Chemistry and Chemical Biology, Laboratory for Electrochemical Advanced Power, Northeastern University Center for Renewable Energy Technology, Northeastern University, Boston, MA, USA, 02115 Stephanus Axnanda, Texas A&M University, College Station, TX, 77843, USA Perla B. Balbuena Department of Chemical Engineering, Texas A&M University, College Station, TX 77843 Helmut Baltruschat Institut fur Physikalische und Theoretische Chemie, Universität Bonn, 53117 Bonn, Germany S. Baranton Laboratory of Electrocatalysis, LACCO, UMR 6503, CNRSUniversité de Poitiers,40 venue du Recteur Pineau, 86022 Poitiers Cedex, France. R. Callejas-Tovar Department of Chemical Engineering, Texas A&M University, College Station, TX 77843 S. R. Calvo Department of Chemical Engineering, Texas A&M University, College Station, TX 77843 Xiaole Chen Department of Chemistry, Texas A&M University, College Station, TX 77843, USA

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Contributors

C. C. Coutanceau Laboratory of Electrocatalysis, LACCO, UMR 6503, CNRSUniversité de Poitiers,40 venue du Recteur Pineau, 86022 Poitiers Cedex, France Kyle D. Cummins Texas A&M University, College Station, TX, 77843, USA Vinten D. Diwakar Department of Chemical Engineering, Tennessee Technological University, Cookeville, Tennessee, 38501, USA D. Wayne Goodman Department of Chemistry, Texas A&M University, College Station, TX 77843, USA Z. Gu Department of Chemical Engineering, Texas A&M University, College Station, TX 77843 S. Harinipriya Department of Nanotechnology, SRM University, Chennai, 603203, Tamil Nadu, India P. Hirunsit Department of Chemical Engineering, Texas A&M University, College Station, TX 77843 N. B. Idupulapati Institute for Micromanufacturing, Chemical Engineering Program, Louisiana Tech University, Ruston, LA 71272 Timo Jacob Institute of Electrochemistry, University of Ulm, D-89069 Ulm, Germany David J. Keffer Department of Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, TN 37996-2200 [email protected], Tel: (865)-974-5322

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John A. Keith Institute of Electrochemistry, University of Ulm, D-89069 Ulm, Germany Youn-Geun Kim Department of Chemistry, Texas A&M University, College Station, TX 77843, USA C. Lamy Laboratory of Electrocatalysis, LACCO, UMR 6503, CNRSUniversité de Poitiers, 40 venue du Recteur Pineau, 86022 Poitiers Cedex, France. Ding Li Department of Chemistry, Texas A&M University, College Station, TX 77843, USA Y. Ma Department of Chemical Engineering, Texas A&M University, College Station, TX 77843 D. S. Mainardi Institute for Micromanufacturing, Chemical Engineering Program, Louisiana Tech University, Ruston, LA 71272 Sanjeev Mukerjee Department of Chemistry and Chemical Biology, Laboratory for Electrochemical Advanced Power, Northeastern University Center for Renewable Energy Technology, Northeastern University, Boston, MA, USA, 02115 G. E. Ramirez-Caballero Department of Chemical Engineering, Texas A&M University, College Station, TX 77843 Jean Sanabria-Chinchilla Department of Chemistry, Texas A&M University, College Station, TX 77843, USA

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Contributors

Elizabeth Santos Facultad de Matemática, Astronomía y Física, IFEG – CONICET, Universidad Nacional de Córdoba, Argentina. Wolfgang Schmickler Institute of Theoretical Chemistry, Ulm University, D-89069 Ulm, Germany. Myvizhi Esai Selvan Department of Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, TN 37996-2200 Jorge M. Seminario Department of Chemical Engineering and Department of Electrical and Computer Engineering, Texas A&M University, College Station, Texas, USA Manuel P. Soriaga Department of Chemistry, Texas A&M University, College Station, TX 77843, USA Juan C. Sotelo Department of Chemical Engineering, Texas A&M University, College Station, Texas, USA Venkat R. Subramanian Department of Energy Environmental & Chemical Engineering, Washington University, Saint Louis, One Brookings Drive, Box 1180, Saint Louis, Missouri – 63130, USA [email protected]

1

Characterization of Alloy Electrocatalysts by Combined Low-Energy Ion Scattering Spectroscopy and Electrochemistry Stephanus Axnanda, Kyle D. Cummins, D. Wayne Goodman, and Manuel P. Soriaga Texas A&M University, College Station, TX, 77843

I.

INTRODUCTION

A fuel cell can be thought of as a cold-combustion power source that generates electrical energy directly from (stored) chemical energy. Due to minimal heat transfers, it is unfettered by conversion-efficiency limitations characteristic of hot-combustion devices.1 Unlike batteries, but similar to internal combustion engines, a fuel cell is a continuous-flow system in which fuel and oxidant are externally supplied for operation. In a functional hydrogen-fuel cell, H2 gas is introduced through feed plates to the anode compartment.2 At the same time, but to the cathode in a separate chamber, O2 gas delivered. At the anode, H2 is oxidized to H+: 2 H2 o 4 H + + 4 e–

EAnode { –E°SHE = 0.000 V

P. Balbuena, V. Subramanian (eds.), Theory and Experiment in Electrocatalysis, Modern Aspects of Electrochemistry 50, DOI 10.1007/978-1-4419-5594-4_1, © Springer Science+Business Media, LLC 2010

(1)

1

2

S. Axnanda et al.

where E°SHE is the reduction potential for the standard hydrogen electrode. Both the protons and electrons are then transported to the cathode; the protons driven by diffusion through a solid membrane-electrolyte situated between the anode and cathode, and the electrons forced by migration through an external conductor. At the cathode, the protons and electrons serve to reduce O2: O2 + 4 H+ + 4 e– o 2 H2O

ECathode { E°SOE = 1.229 V

(2)

where E°SOE is the reduction potential for the standard oxygen electrode. The overall fuel-cell reaction is simply the sum of Eqs. (1) and (2): O2 + 2 H2 o 2 H2O

E°Cell = E°SOE – E°SHE = 1.229 V (3)

It must be noted that the standard potential given in reaction (2) is based upon thermochemical measurements rather than direct electrochemical determinations;3 the conversion is made possible by the well-known thermodynamic relationship: 'G° = –nFE°

(4)

where 'G° is the standard free-energy change, n the number of electrons transferred and F is the faraday. It is a fact that Reaction (3), while thermodynamically favorable, is kinetically hindered; hence, the activation of both dihydrogen and dioxygen at ambient conditions, requires the use of electrocatalysts. It has long been established that Pt is the most efficient singlemetal electrode for the catalysis of both reactions (1) and (2). In the case of dihydrogen activation, no metal electrocatalyst performs better than platinum. However, aside from the fact that platinum is a precious metal, a major drawback is that commercial (fossil-based) hydrogen contains residual amounts of impurities (e.g., carbon monoxide) that only serve to poison the catalyst surface.4 To address this particular problem, present research has focused on the employment of metal additives (e.g., Ru)5,6,7,8,9 or of molecular catalysts that mimic the impressive activity of biological materials (e.g., hydrogenase enzymes);10,11 the use of molecular catalysts appears to be the more attractive option since such com-

Characterization of Alloy Electrocatalysts

3

pounds would be less expensive and (via synthesis) more readily available than Pt. Based solely on technical, and sans economic, grounds, essentially little improvement can be gained with respect to the hydrogen oxidation reaction. On the other hand, much more can be attained by further research on the catalysis of the oxygen reduction reaction (ORR). For pure platinum, the highest possible cathode potential is ca. 0.65 V, which is 0.58 V lower than the thermodynamic value. Evolutionary improvements with regard only to the catalyst material have been achieved via the use of nanoparticles12,13 and Pt-based alloys.14,15 The primary complication with nanocluster-catalysis is the aggregation of the small (highly active) clusters into larger (less active) particles;16 this is a fundamental limitation for metals that display high surface activity due to Ostwald ripening,17 a phenomenon driven by the minimization of the surface free energy. Current research, therefore, is more active with respect to Pt-based mixed metals. Due to interfacial thermodynamics, however, alloys show a proclivity towards the enrichment of one constituent at the surface.18 As a consequence, the composition in the bulk is often quite different from that at the interface. Structure-composition-activity correlations of mixedmetal catalysts must therefore pay close attention to the nature of the alloy surface. It is this particular aspect that is the emphasis of this review article. II. EXPERIMENTAL ASPECTS The empirical approach adopted here integrates classical electrochemical methods with modern surface preparation and characterization techniques. As described in detail elsewhere,19,20 the actual experimental procedure involves surface analysis before and after a particular electrochemical process; the latter may vary from simple immersion of the electrode at a fixed potential to timed excursions between extreme oxidative and reductive potentials. Meticulous emphasis is placed on the synthesis of pre-selected surface alloys and the interrogation of such surfaces to monitor any electrochemistry-induced changes. The advantages in the use of electrons as surface probes such as in X-ray photoelectron spectroscopy (XPS), Auger electron spectroscopy (AES), high-resolution

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electron energy loss spectroscopy (HREELS), and low-energy electron diffraction (LEED) are now widely recognized; the same is true for temperature-programmed desorption (TPD). Hence, these methods will not be discussed further here. On the other hand, comparatively little is known to the non-practitioner about the unique sensitivity of low-energy ions to only atoms in the outermost layer. Low-energy ion scattering spectroscopy (LEISS)21 will thus be briefly introduced. In addition, a method for the preparation of the alloy film electrodes will be described. 1.

Low Energy Ion Scattering Spectroscopy

In a LEISS experiment,21 a target surface is irradiated with a beam of inert-gas ions (He+, Ne+ or Ar+) of energy between 20 eV to 500 eV, and the backscattered primary ions are energy-analyzed (Fig. 1). The backscattering can be modeled as a classical two-body inelastic collision between the incident ion and a topmost surface atom governed by the conservation laws of energy and momentum.

Figure 1. Schematic illustration of the low-energy ion scattering process. The inci-dent ion (mass Mi+) interacts only with an atom (mass MS) in the outermost layer and is backscattered at an angle T relative to the direction of the incident beam.

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If the incident ion has a mass of Mi+ and kinetic energy of E0, and the ion backscattered at an angle T (relative to the direction of the incident ion) has an energy of E1, the two-collision model allows the determination of the surface elemental composition based on the following equation: E1 E0

2 ª 1 º§ cos T r A2  sin 2 T ·¸ « 2 »¨© ¹ «¬ 1  A »¼

(5)

where Ms is the mass of the surface atom, A = MS/M1; the positive term represents solutions for A !1, whereas the negative term is for | sin T | d A d 1. Since the energy of the incident ion is relatively low, there is virtually no damage to the surface. In addition, because of the repulsive nature of the ion-atom interaction, a shadow cone is formed past the target surface atom and a blocking cone is generated at an adjacent surface atom; these cones prevent interactions between the incident ion and subsurface which renders LEISS its unique sensitivity only to the outermost atoms. In a LEISS spectrum (vide infra), the backscattered intensity is plotted against E1/E0; a high-intensity peak corresponds to a topmost atom of a given mass, and the relative intensities provide a measure of the relative surface concentrations. Since the atoms scatter with different intensities, sensitivity factors f for each element must be obtained by calibration. For example, for an alloy film consisting of Pt and Co, the surface concentrations CPt and CCo can be extracted from the following equations:22 C Pt

I Pt I Pt   f Pt Co I Co

(6)

CCo

I Co I Co   f Co  Pt I Co

(7)

where fPt-Co is the ratio of the scattering intensities for the pure Pt and pure Co films, and IPt and ICo are the scattering intensities from Pt and Co in the alloy. The power of LEISS lies in its unparalleled ability to assay the elemental composition of the outermost layer of an alloy surface.

Figure 2. The XPS break point metal-doser calibration method. The point at which the slope changes (the break point) signals the completion of one monolayer (ML) and the onset of the second monolayer. The data shown are for the Pt and Co dosers and a Mo(110) substrate.

Characterization of Alloy Electrocatalysts

2.

7

Preparation of Pt-Co Alloy Films

Thin films were prepared by physical vapor deposition in ultrahigh vacuum (UHV) as described previously.18 A doser was constructed by tightly winding wires of the Pt and Co metals in small segments around a Ta filament. The filament is heated resistively at a current sufficiently high to initiate sublimation of subject metals onto a cold (Ru or Mo) substrate; the latter is located close to the doser to enable a controllable deposition rate. Calibration of the dosing (film-formation) rate was conducted via an XPS breakpoint analysis23 In this procedure, a plot of the XPS intensity is obtained as a function of dosing time (Fig. 2); from submonolayer to full-monolayer coverages, the intensityversus-time plot has a fixed slope. The point at which the slope changes marks the time at which a second monolayer begins to form; it is also taken as the total time (tML) required to deposit one full monolayer. In the preparation of an n-ML film, the total dosing time was simply equated to (n u tML). At the end of each deposition, the alloy films were annealed at 900 K for 20 minutes to ensure that Pt and Co had become alloyed. Prior to and subsequent to the electrochemical experiments, interfacial composition was determined by LEISS, XPS or TPD, and surface structure by LEED. 3.

Electrochemical Characterization

In the study described in this review article, electrochemical experiments were limited to open-circuit potential (OCP) measurements, cyclic voltammetry (CV), and potential-dependent dissolution. The OCP values for test electrodes immersed in an electrolytic solution saturated with O2 gas are simple to determine; such values offer a reliable diagnostic on the viability of a given material to function as an oxygen cathode. With reference to Fig. 3, the theoretical OCP of an O2-saturated cathode relative to a standard hydrogen electrode (SHE), would be 1.229 V. Since the magnitude of a hydrogen fuel cell voltage (ECell) is given by ECathode – ESHE =

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Figure 3. Experimental configuration for the measurement of the open-circuit potential. In the present study, the solution is 0.1 M H2SO4 saturated with O2 gas.

ECathode, an alloy electrode that yields an OCP closest to the thermodynamic value would be the best choice. All electrochemical experiments were carried out with a commercial potentiostat (EG&G PARC 273) controlled by a personal computer. 4.

Instrumentation

Figure 4 shows a schematic diagram of an ultrahigh vacuum (5 u 10-10 Torr) apparatus that integrates LEED, XPS, TPD, LEISS, and electrochemistry (EC). The base pressure of the chamber is 5 x 1010 Torr. The sample is mounted on a probe, a tube fabricated out of stainless steel, at the top of the chamber. The probe allows experiments to be performed at very low temperatures; for example, the probe is filled with liquid nitrogen for experiments at 77 K. The sample can also be heated resistively (up to 1500 K) via copper wires attached to the sample; for still higher temperatures, an electron beam from a tungsten wire located behind the sample is employed. Temperature is monitored via a Re/W-Re thermocouple.

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Figure 4. Schematic diagram of an integrated LEED-TPD-XPS-LEISS-EC apparatus.

Details on the surface analytical methods can be found elsewhere18-20 and will not be repeated here. It will simply be noted that, for LEISS, the backscattered ions are energy-analyzed by a concentric hemispherical analyzer (PHI, SCA 10-360), the same unit employed for XPS. For electrochemical measurements, the sample is transferred from the UHV chamber to the ambient-pressure electrochemistry compartment through a series of differentially pumped sliding seals. The sliding seal consists of three Teflon seals between which are two pump-out ports; the lower port is linked to a mechanical pump, whereas the upper port is connected to a turbo pump. The

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inner diameter of the seals provides a perfect fit around the polished chrome-plated probe. After the probe is translated through the seals, the differential-pumping lines are connected prior to introduction of an inert gas (e.g., ultra-high purity N2) to the electrochemistry compartment to ensure that the surface analysis chamber is maintained under ultrahigh vacuum. III. CASE STUDY: Pt-Co ALLOY ELECTROCATALYSTS FOR OXYGEN REDUCTION 1.

Pt-Co Films and Alloys

The initial step in the preparation of the mixed-metal films consisted of vapor deposition, one metal at a time, onto a refractory substrate; sequential deposition was necessary in order to track the doser-calibration conditions. Alloy formation was then carried out by a high-temperature treatment. Figure 5 shows LEISS spectra of a Mo(110) substrate on which ten monolayers of a Pt-Co mixture, deposited in a 1:4 monolayer ratio, was heated to selected temperatures. In Fig. 5a, 2 ML of Pt were deposited first, followed by 8 ML of Co; in Fig. 5b, the reverse was done in which 8 ML of Co were generated first. The more notable features in the data shown in Fig. 5a are: (a) Below 600 K, no Pt LEISS peak is observable; this indicates that 8 ML of Co completely cover 2 ML of Pt. (b) At 700 K, a Pt peak emerges; this suggests that the Pt underlayer and the Co overlayer have started to intermix. The fact that a Mo peak is not observed, as when the sample was heated at 1000 K, means that the alterations in the Co and Pt signals are due to alloy formation and not to thermal desorption. (c) In the temperature range between 800 K and 1000 K, the ratio of the Pt and Co peak heights is invariant; this can be taken as evidence for the formation of a stable fixedcomposition alloy. (d) At T > 1000 K, the peak intensities for both Co and Pt decrease and a peak for Mo emerges; all are symptomatic of the high-temperature-induced desorption of Pt and Co.

0.95

 Pt

1.15

0.75

0.95

1.15

Figure 5. LEIS spectra of Pt-Co films on a Mo(110) substrate after a 30-minute treatment at the temperatures indicated. (a) 2 ML of Pt were deposited first followed by 8 ML of Co. (b) 8 ML of Co were deposited first followed by 2 ML of Pt. The peak at E/E0 ~ 0.83 is due to Co; that at E/E0 ~ 0.97 is for Pt. The LEISS spectra were collected at 300 K.

0.75

Co 

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In Fig. 5b: (a) Even at ambient temperatures, a LEISS peak for Co is observed; this signifies that 2 ML of Pt is not sufficient to completely mask 8 ML Co. (b) At temperatures between 800 K and 1000 K, the peakintensity ratios are identical to those in Fig. 5b; evidently, regardless of the order of metal deposition, the composition of the annealed (alloyed) film converges to the same value. (c) Above 1000 K, spectra identical to those in Fig. 5a are obtained in terms of the appearance the Mo peak and the disappearance of both Pt and Co peaks; since the same alloyed state is reached at 1000 K, the independence of thermal desorption on the deposition sequence is not unexpected. Additional Pt-Co films were prepared, each consisting of a total of ten monolayers but with variable Pt:Co ML ratios. The results, in terms of LEISS spectra, are summarized in Fig. 6. It is not shown in the Fig. 6 summary, but it was found that stable top most-layer alloys were always formed when the deposits were annealed at 1000 K. However, as can be seen in Fig. 6, the peakintensity ratios were not invariant and depended upon the initial Pt:Co vapor-deposition (ML) proportion. 2.

Surface Elemental Composition and Surface Phase Diagrams

Qualitatively, it can be readily gleaned from the data in Fig. 5 and Fig. 6 that, in the alloyed state generated at 1000 K, the elemental composition at the outermost layer, as measured by the LEISS Pt:Co peak-intensity ratio, is vastly different from that in the bulk. The peak intensities can be quantitatively converted to surface concentrations through the use of Eqs. (6) and (7) where the value of fPt-Co was determined from experiment to be equal to 0.5. The divergence between the elemental composition at the topmost layer and that in the bulk is appreciated best when the atom-percent composition of Pt (or Co) at the alloy surface is plotted as a function of the monolayer-percent composition of Pt (or Co) in the bulk. Such a plot, which represents the phase diagram of the outermost-layer Pt-Co alloy, is shown in Fig. 7; the open circles are data for when Pt was deposited initially, whereas the

Characterization of Alloy Electrocatalysts

0.75

13

0.95

Figure 6. LEIS spectra of Pt-Co alloys at various bulk compositions annealed at 1000 K for 30 minutes. Each spectrum was acquired at 300 K. The ML(Pt)-toML(Co) ratios for the films were as follows: (a) 1:9; (b) 2.5:7.5; (c) 5:5; (d) 7.5:2.5; (d) 8.8:1.2; and (f) 9.5:0.5.

closed circles are for when Co was deposited initially. Three features in the plot are noteworthy: (a) The surface phase diagram is independent of the order or sequence of metal deposition (b) The convergence between the surface and bulk compositions occurs only when the bulk composition is almost entirely Co or is predominantly Pt. (c) The discrepancy is most dramatic when the fraction of Co in the bulk is higher than 90%. For films in which the Co bulk composition is between 30% and 70%, the surface concentration of Pt is almost a constant at 70%. From these trends, it is plausible to infer that:

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Figure 7. Surface phase diagram (atomic% of Pt at the outermost layer versus atomic% of Pt in the bulk) of the Pt-Co films after annealing at 1000 K for 30 minutes.

(a) Pt preferentially segregates to the surface, not unexpected since it has a lower surface free energy than Co; and (b) for the interfacial alloy, the thermodynamically favored composition is essentially a 3:1 Pt-to-Co atom-percent ratio; that is, Pt3Co. 3.

Long-Range Surface Order

The two-dimensional order of the Pt-Co alloys was investigated by low-energy electron diffraction. The results, in terms of LEED patterns are shown in Fig. 8. First, the fact that distinct LEED spots are observed indicates that the alloy interface is wellordered. Figure 8a shows a typical LEED pattern for alloys that contained greater than 75 atom-percent of Pt; the hexagonal pattern is reminiscent of a pure Pt(111) surface. At such high Pt surface concentrations, the outermost layer is most likely heterogeneous, populated by comparatively wide Pt(111) domains. Fig. 8b shows that a different LEED pattern is obtained when the Pt:Co atom-percent ratio is 3:1. Under these conditions, it may be post-

Figure 8. LEED patterns of the annealed Pt-Co alloys at points in the surface phase diagram where: (a) the outermost layer is predominantly Pt3Co, and (b) the topmost layer is essentially pure Pt.

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ulated that the outermost layer is compositionally homogeneous (Pt3Co) and structurally non-amoprhous. 4.

Electrochemical Properties

(i) OCP Values Figure 9 shows a plot of the open-circuit potential as a function of the alloy-surface composition in an O2-saturated 0.1 M H2SO4 solution. The highest voltage, 0.86 V, was obtained for the alloy of composition that corresponded to Pt3Co. Such value was 0.68 V higher than for pure Co and 0.22 V better than for pure Pt. However, the value is still considerably lower than the ideal potential of 1.229 V. In a control experiment, in which the sulfuric acid solution was thoroughly deaerated with ultrapure N2, an OCP value (ca. 0.5 V) was obtained that was independent of the alloy surface composition.

Figure 9. Measured open-circuit potential values as a function of the surface concentration (atomic%) of Pt.

Characterization of Alloy Electrocatalysts

17

From the cyclic voltammogram of pure Pt in deaerated 0.1 M H2SO4, it can be seen that 0.68 V is a potential at which surface oxide (or hydroxide) has just started, and the amount formed is minuscule compared to that when the potential is at 1.229 V. In other words, even at saturation concentrations, O2 gas is unable to oxidize a pure Pt surface to the extent that the OCP is driven up to 1.229 V. The effect of Co has been surmised to facilitate O2 activation. It is further conjectured that the oxygen atoms formed on the Co sites irreversibly spill over to the Pt sites, to increase the amount of Pt-surface oxide and, consequently, the also the OCP.24 The present work suggests that the optimal Pt-Co surface concentration for such synergistic process is that of Pt3Co.25 (ii) Cyclic Voltammogram of the Pt3Co Alloy Cyclic voltammograms for alloys of different Pt-Co concentration ratios were collected in deaerated and O2-saturated 0.1 M H2SO4. A single-cycle set of CVs for the Pt3Co cathode is shown in Fig. 10; the voltammograms were started from the OCP and the

Figure 10. First-scan cyclic voltammograms for Pt3Co in 0.1 M H2SO4. Dotted curve: deaerated (N2-saturated) solution; solid curve: O2-saturated solution.

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potential was initially scanned in the negative direction to the hydrogen evolution region. The morphologies of the current-potential curves are not too different from those of pure Pt: (a) In deaerated solution, there is an appreciably wide doublelayer window between the hydrogen evolution and oxygen evolution regions. (b) In O2-saturated 0.1 M H2SO4, a massive cathodic wave, due to the reduction of dioxygen, appears at potentials immediately below the OCP; the high cathodic current persists even after the potential sweep is reversed in the positive drection. These results are not too different from those for pure Pt, as may be as expected since two-thirds of the surface is made up of Pt. (iii) Potential-Dependent Dissolution of Pt3Co Little can be gleaned about the nature of the alloy interface from only the cyclic current-potential curves. An important question that needs to be addressed is whether or not the cyclic voltammograms are accompanied by changes in the surface composition of the alloy; while a qualitative solution to this problem can easily be obtained from multiple voltammetric scans, a quantitative answer is fundamentally necessary. In fact, a more critical matter involves the stability the Pt3Co alloy under fuel-cell operating conditions; that is, after prolonged use at the OCP in an O2saturated solution. All of these issues can be simultaneously tackled if the surface composition of the Pt3Co alloy is monitored as a function of time at a given applied potential. For such measurements, the alloy electrode is withdrawn from the O2-saturated electrolyte at the test potential and, prior to transfer into the surface analysis chamber, rinsed in deaerated ultrapure (Millipore) water to remove emersed sulfuric acid. The results are shown in Fig.11. The following important trends are to be noted in Fig. 11: (a) Regardless of the applied potential, there is an immediate drop of ca. 10% of the original Co concentration. (b) Regardless of the external potential, the surface concentration of Co becomes independent of time after the initial rapid decrease.

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Figure 11. The dissolution profile of Pt3Co in terms of the amount of Co that remains at the outermost layer as a function of applied potential and time.

(c) At EApplied ” EOCP, the Co surface concentration quickly converges to a constant value of approximately 18%. (d) At potentials more positive than OCP, the initial decline in surface concentration is much more precipitous (from 20% to 11%) than at lower potentials (only form 20% to 18%); however, the amount of Co retained is unchanged even after extended periods. It can be seen in Fig. 10 that the anodic oxidation of the alloy surface takes place at potentials above the OCP. This may account for the observed 45% decrease in the Co surface concentration at EApplied > EOCP because the oxidized surface of Co is not impervious to acid-driven dissolution. The fact that 55% of the initial Co concentration is retained on the surface suggests that an appreciable quantity of Co is rendered comparatively inert towards anodic dissolution when alloyed to Pt.

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5.

Bulk Properties of the Pt3Co Alloy

The primary emphasis in this review article is to showcase the use of LEISS to examine the outermost layers of Pt-Co alloys in order to correlate interfacial composition with electrocatalytic reactivity towards oxygen reduction. In some instances, it is desirable to compare the properties of the outermost layer with those of the (near-surface) bulk; an example is when it becomes imperative to explain the unique stability the alloyed Co under anodic-oxidation potentials. In such cases, X-ray photoelectron spectroscopy and temperature-programmed desorption may be employed since both methods are also able to generate information on the electronic (binding-energy shift measurements by XPS)26 and thermochemical (adsorption enthalpy determinations by TPD)27 properties at the sub-surface. However, an in-depth discourse on these and related aspects was not intended to be part of this review article. (i) Relevance to Published Work The origin of Pt3Co activity towards the oxygen reduction reactions has been the subject of numerous studies.28,29,30 Among the scenarios advanced are: (a) an increase in the 5d orbital-vacancy in Pt;31 (b) changes in the interatomic distance and coordination number of Pt;8 and (c) dioxygen activation at (adjacent) Co sites.24 The latter is not inconsistent with the data given here. A combined LEISS-AES-EC study32 was earlier undertaken at crystalline Pt3Co and Pt3Ni alloy surfaces. It was reported that, when Pt3Co and Pt3Ni were annealed at 1000 K, only Pt atoms existed on the outermost layer; the latter was referred to as a Pt skin. This particular observation is not in agreement with the result here that Co actually co-exists with Pt at the outermost layer. Interestingly, when the Pt3Co surface in the earlier study was lightly sputtered, approximately 25% of the sputtered material was Co; this result suggests that Co is in fact present at the topmost layer. Why a discrepancy exists between the LEISS and depth-profile studies is unclear. But, for the difference between the present and previous LEISS work, the possibility exists that the interfacial be-

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havior of alloy crystals is slightly different than that of alloy films. A study to contrast the surface electrochemical properties of Pt3Co(111) single crystals with well-ordered Pt3Co films will have to be carried out. IV. SUMMARY The study of catalysis by mixed-metal electrodes is confronted with intricacies not encountered in work with single-metal surfaces. An important issue that is seldom addressed pertains to the character of the topmost layer of the electrocatalyst. Almost all of the structural and compositional analysis undertaken have employed methods that provide information not only of the outermost layer but also of the sub-surface environment; hence, ambiguities may reside in the results that lead to unreliable correlations between interfacial structure, composition and reactivity. In this article, the study of alloy electrodes by a combination of EC with LEISS is discussed. LEIS spectroscopy is unparalleled in its ability to interrogate only the outermost layer; this is because of the repulsive nature of ion-atom interactions that serves to mask interactions between sub-surface species with the probe ions. LEISS is an established surface physics technique; but its adoption in surface electrochemical investigations has not been pervasive. For the work reviewed here, an instrument that incorporates EC with LEISS, LEED, XPS and TPD was employed. To showcase the strengths of the combined LEISS-EC approach, recent results33 on the study of Pt-Co alloys as enhanced oxygen cathodes for fuel cells are presented. Through the use of LEISS, hitherto unknown phenomena have come to light. The more significant observations are: (a) Pt-Co films, regardless of initial bulk concentration, yield a stable and well-ordered alloy at the outermost layer when annealed at a sufficiently high temperature. (b) The surface phase diagram of the Pt-Co co-deposit documents a prominent divergence between the bulk and interfacial compositions; the difference is widest for Co-enriched films.

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(c) For films enriched in Co in the bulk, the structure and composition of the topmost layer is predominantly that of monocrystalline Pt3Co; for Pt-enriched deposits, the outermost layer consists primarily of Pt(111) domains. (d) In terms of the open-circuit cell potential in O2-saturated sulfuric acid electrolyte, the Pt3Co surface yields the highest value (0.86 V), a considerable improvement over pure Pt (0.64 V) or pure Co (0.20 V); unfortunately, it is still much lower than the thermodynamic value (1.23 V). (e) Based upon comparative stabilities towards potentialinduced dissolution, three types of Co exists on the Pt3Co interface: Approximately 10% of the Co are unstable at all potentials and are immediately dissolved upon immersion in the acid solution. About 35% are resistant to corrosion at potentials below the OCP but are anodically stripped at more positive potentials. The remainder (55%) is quite stable and resists dissolution even after prolonged periods above the OCP. ACKNOWLEDGMENT Acknowledgment is made to the Honda Research Institute USA and to the Welch Foundation (DWG: Welch Chair; MPS: A-1064) for financial support. REFERENCES 1

A. J. Appleby and F. R. Foulkes, Fuel Cell Handbook, Van Nostrand Reinhold, New York, 1989. B. Viswanathan and M. A. Scibioh, Fuel Cells: Principles and Applications, Universities Press, Hyderabad, India, 2007. 3 A. J. Bard, R. Parsons and J. Jordan, Standard Potentials in Aqueous Solution, M. Dekker, New York, 1985. 4 S. H. D. Lee, R. Kumar and M. Krumpelt, Removal of CO from Reformate for PEMFC Application. National Technical Information Service, Springfield, VA, 2001. 5 N. S. Marinkovic, M. B. Vukmirovic and R. R. Adzic, Mod. Aspects Electrochem., 42 (2008) 1. 6 T. Toda, H. Igarashi, H. Uchida and M. Watanabe, J. Electrochem. Soc., 146 (1999) 3750. 2

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Y. Wang and P. B. Balbuena, J. Phys. Chem. B, 109 (2005) 18902. V. Stamenkovic, T. J. Schmidt, N. M. Markovic and J. P. N. Ross, J. Phys. Chem. B, 106 (2002) 11970. 9 K. Kinoshita, Electrochemical Oxygen Technology, John Wiley, New York, 1992. 10 S. E. Lamle, K. A. Vincent, L. M. Halliwell, S. P. J. Albracht and F. A. Armstrong, Dalt. Trans., 2003 (2003) 4152. 11 D. Chong, I. P. Georgakaki, R. Mejia-Rodriguez, J. Sanabria-Chinchilla, M. P. Soriaga and M. Y. Darensbourg, Dalt. Trans., 2003 (2003) 4158. 12 K. J. J. Mayrhofer, M. Arenz, D. Strmcnik, B. B. Blizanac, V. Stamenkovic and N. M. Markovic, Electrochim. Acta, 53 (2008) 3181. 13 H. Ye, J. A. Crooks and R. M. Crooks, Langmuir, 23 (2007) 11901. 14 V. R. Stamenkovic, Science, 315 (2007) 493. 15 P. Strasser, S. Koh , and J. Greeley, Phys. Chem. Chem. Phys., 10 (2008) 3670. 16 A. K. Santra and D. W. Goodman, Electrochimica Acta, 47 (2002) 3595. 17 H. Ibach, Physics of Surfaces and Interfaces, Springer, New York, 2006. 18 C. W. Yi, K. Luo, T. Wei and D. W. Goodman, J. Phys. Chem. B, 109 (2005) 18535. 19 A. T. Hubbard, Acc. Chem. Res., 13 (1980) 177. 20 M. P. Soriaga, Prog. Surf. Sci., 39 (1992) 325. 21 H. Niehus, W. Heiland and E. Taglauer, Surf. Sci. Rep. 17 (1993) 213. 22 H. H. Brongersma, M. Draxler, M. de Ridder and P. Bauer, Surf. Sci. Rep. 62 (2007) 63. 23 D. Kumar, M. S. Chen and D. W. Goodman, Thin Solid Films, 515 (2007) 1475. 24 J. L. Fernandez, J. M. White, Y. Sun, W. Tang, G. Henkelman and A. J. Bard, Langmuir, 22 (2006) 10426. 25 J. L. Fernandez, D. A. Walsh and A. J. Bard, J. Am. Chem. Soc. 127 (2005) 357. 26 W. F. Egelhoff, Surf. Sci. Rep., 6 (1987) 253. 27 P. A. Redhead, Vacuum, 12 (1962). 28 C. A. Lucas, N. M. Markovic and P. N. Ross, Phys. Rev. B, 55 (1997) 7964. 29 B. C. Beard and P. N. Ross, J. Electrochem. Soc., 137 (1990) 3368. 30 J. T. Glass, G. L. Cahen and G. E. Stoner, J. Electrochem. Soc., 134 (1987) 58. 31 S. Mukerjee, S. Srinivasan, M. P. Soriaga and J. McBreen, J. Electrochem. Soc., 142 (1995) 1409. 32 V. Stamenkovic, T. J. Schmidt, P. N. Ross and N. M. Markovic, J. Electroanal. Chem., 554 (2003) 191. 33 S. Axnanda, K. D. Cummins, T. He, M. P. Soriaga and D. W. Goodman. To be submitted. 8

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Recent Advances in Theoretical Aspects of Electrocatalysis Elizabeth Santos and Wolfgang Schmickler Institute of Theoretical Chemistry, Ulm University, D-89069 Ulm, Germany. Facultad de Matemática, Astronomía y Física, IFEG – CONICET, Universidad Nacional de Córdoba, Argentina.

I.

INTRODUCTION

Although electrochemistry has much in common with surface science, the application of the principles of catalytic activity to the reactions taking place in an electrochemical environment is not straightforward. All electrochemical reactions of practical interest imply at least one step where an electron is transferred between species coming from the solution side or the electrode surface. Therefore electrochemical reactions occurring at the interfaces are governed by the interaction of the reactant both with the solvent and with the electrode. There is also an additional effect produced by the external applied potential, so that the Fermi level of the reactant can be easily tuned relative to the Fermi level of the electrode. Much research effort has been directed at understanding the mechanism of electrocatalysis. Various empirical attempts have been made to correlate the reaction rate with other quantities. Phe-

P. Balbuena, V. Subramanian (eds.), Theory and Experiment in Electrocatalysis, Modern Aspects of Electrochemistry 50, DOI 10.1007/978-1-4419-5594-4_2, © Springer Science+Business Media, LLC 2010

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Elizabeth Santos and Wolfgang Schmickler

nomenological correlations were established between the reaction rate and various properties such as the work function,1 the strength of the metal-hydrogen bond,2,3 and the presence of empty dorbitals.4 One of these approaches was the application of Sabatier’s principle,5 which states that for a reaction to proceed rapidly the intermediates should have an intermediate energy of adsorption; a weak adsorption proceeds too slowly, a strong adsorption blocks the surface. On this basis, a volcano plot of the reaction rate versus the energy of adsorption was proposed by several authors1-4,6-8 as indication of the electrocatalytic activity of different electrodes materials for the hydrogen oxidation. However, all the metals on the descending branch of such plots (Ti, Ta, Nb) are covered by an oxide film, which greatly reduces the rate, a fact that was not known when this relation was established. It is important to stress that this principle cannot be applied to the electrochemical hydrogen reaction in the same manner as for gas-phase surface reactions, since the free energy of adsorption of hydrogen from the solution varies with the electrode potential, and a metal that adsorbs hydrogen weakly at the equilibrium potential will adsorb strongly at more negative potentials. Taken to its logical conclusion, a simple application of Sabatier's principle would result in volcano-shaped current potential curves, which is absurd.9 Another aspect that has been widely discussed is the role of the d bands. All good catalysts, such as platinum and palladium, posess d bands. However, on other d metals such as nickel and cobalt the reaction proceeds quite slowly, and so the mere presence of a d band is not sufficient to assure good catalytic properties. A more quantitative treatment based on a model taking into account all contributions of the different components of an electrochemical system and the corresponding interactions must be considered. In a homogenous phase the determining factor for electron transfer between charged species is the reorganization of the solvent. This process is well understood within the Marcus and Hush theory.10,11 On the other hand, recent developments in theoretical approaches of surface science, especially those based on density functional theory (DFT),12-14 have contributed to a better understanding of surface processes and the effects of electronic interactions between reactants and catalysts. In this context, the relative energies of the electronic levels of the rectants and the catalyst and the corresponding coupling strengths play the key role. In order to

Recent Advances in Theoretical Aspects of Electrocatalysis

27

describe the reaction path (initial, transition and final states), different coordinates can be considered to represent the potential energy. In the case of reactions in the gas phase, the distance to the catalyst and the separation between the atoms taking part in reactions involving bonds breaking are usually employed. In electrochemical systems an additional coordinate, the normalized solvent coordinate, must also be considered. Realistic calculations must take into account all the diverse important contributions mentioned above. In our group we have developed a new approach for electrochemical system, using DFT calculations as input in the SKS Hamiltonian developed by Santos, Koper and Schmickler.15,16 In the framework of this model electronic interactions with the electrode and with the solvent can be included in a natural way. Before giving the details of this theory, we review the different phenomena involved in electrochemical reactions in order to understand the mechanism of electrocatalysis and the differences with catalysis in surface science. Next, a brief summary of previous models will be given, and finally the SKS Hamiltonian model will be discussed. We will show how the different particular approaches can be obtained on the basis of the generalized model. As a first step, idealized semielliptical bands shapes will be considered in order to understand the effect of different parameters on the electrocatalytic properties. Then, real systems will be characterized by means of DFT (Density Functional Theory). These calculations will be inserted as input in the SKS Hamiltonian. Applications to cases of practical interest will be examined including the effect not only of the nature of the material but also structural aspects, especially the electrocatalysis with different nanostructures. II. CLASSIFICATION OF ELECTROCHEMICAL REACTIONS When a reactive species approaches the electrode surface besides its interaction with the solvent also electronic interactions with the electrode come into play (see Figs. 1 and 2). Depending on their relative intensities the electrochemical reaction can proceed through two different mechanisms. If the interaction with the electrode is comparatively weak, the reactant preserves its whole sol-

(a)

- log (jo / A cm )

-14

-12

-10

-8

-6

-4

-2

0

2

Pt

Pd

H2/2H

+

Au

Cu

Ag

Hg

Tl/Pt Pb/Pt Tl/Au

Different Electrocatalysts

[Ru(NH3)6]

+2/+3

e

e

Z

e

Metal

e

B

A

(b)

inner sphere reactions

Metal

e

outer sphere reactions

Metal

Metal

Figure 1. (a) experimental values of the standard exchange current for an outer sphere reaction (filled symbols); data obtained from Refs. 17 and 18 and for an inner sphere reaction, such as the hydrogen oxidation reaction; data obtained from Ref. 3 and 4. (b) schematic representations of outer and inner sphere reactions.

-2

adiabatic processes

'Gact(O)

outer-sphere reactions on metal electrodes

reorganization of the solvent

no influence on the velocity:

electrocatalytic reactions (bond-breaking)

velocity increases: 'Gact (VRM) interaction with d bands

(fast electron exchange between reactant and electrode)

Figure 2. Classification of electrochemical reactions according to the strength of the interaction with the electrode.

electron transfer reactions at electrodes covered by thin films

velocity increases: A(VRM)

non-adiabatic processes

Classification of electrochemical reactions: j = A exp(-'Gact/kT) VRM: coupling constant with the electrode

VR

30

Elizabeth Santos and Wolfgang Schmickler

vation shell. This is an outer sphere electron transfer reaction; the reactant is not in direct contact with the electrode surface. At least one layer of solvent or some other ligand separates reactant and electrode. Although the reactant preserves its inner shell, the solvent in the vicinity of the reactant must reorient during the reaction because reactant and product carry different charges. The reaction rate is mainly determined by this reorganization of the solvation shell and the theoretical basis is given by the extension of Marcus – Hush model.10,11 In this case the nature of the metal does not play any important role; there is no catalysis, since the electrode behaves simply as an electron reservoir. These types of reactions are usually very fast since electrons can tunnel when the solvation sheath has acquired a suitable configuration. During the reaction no bonds are broken or formed, and no specific adsorption takes place. Typically such reactions occur adiabatically at bare metal electrodes and involve metal ions surrounded by inert ligands. The interactions between the reactant and the metal by adiabatic reactions are sufficiently strong such that the electron exchange takes place every time the system reaches the transition state. Thus the system is in electronic equilibrium for all solvent configurations. Because of the high velocities, there are experimental difficulties to determine the rate constants for these reactions, and fast transient methods or techniques forcing convection for the mass transport are required.17,18 Then, if appropriate measurements are performed, no appreciable dependence on the nature of the metal is observed, as it is shown in Fig. 1 for the redox reaction [Ru(NH3)6]2+/3+. In the case that the electronic interactions are weaker, the system can pass the saddle point of the reaction coordinate without an electron transfer, so that it subsequently returns to its initial state. These reactions are called non-adiabatic, and the interaction strength will enter into the pre-exponential factor of the expression for the velocity. They can be modelled by the perturbation theory through the Levich – Dogonadze approach.19 Examples of such reactions are electron transfers through thin films and we will not discuss them in this work. When reactions involve bonds rearrangement, or adsorption, the reacting species looses a part of its solvation shell and moves close to the electrode surface. They are called inner sphere electron transfer reactions and the electronic interactions with the electrode can be either weak or strong. Depending on the elec-

Recent Advances in Theoretical Aspects of Electrocatalysis

31

tronic structure of the electrode the reaction can be catalyzed or not. Two important electrochemical reactions which require catalysis are the hydrogen oxidation – evolution and the oxygen reduction – evolution reactions. The standard exchange current obtained for the first reaction with different electrode materials is also shown in Fig. 1. The reaction rate is much slower (about at least four order of magnitude lower) than the outer sphere reactions and a strong dependence on the nature of the metal is observed (about eight order of magnitude between the best and the worst electrocatalyst!!) In the literature there are several theoretical approaches that describe the different particular processes. The model we have proposed can explain all the different cases and takes into account all the possible interactions. III. PREVIOUS APPROACHES TO CATALYSIS FROM THE SURFACE SCIENCE There are in the literature several reviews about this topic (see for example Refs. 20-22). In this Section we discuss only the more relevant aspects related to the concepts that can be applied to electrochemical systems. The electronic of the catalyst determines its activity. In solid materials the electronic levels form bands of allowed energies separated by band gaps. At T = 0 the bands are filled up to a certain level, the Fermi level HF. It is a characteristic of metals that the Fermi level lies inside an energy band, which is therefore only partially filled. At finite temperatures, electrons can be excited thermally to higher levels. However, at room temperature the thermal energy is about 0.025 eV; often energies of this order of magnitude are negligible, and the Fermi-Dirac distribution can then be replaced by a step function. Usually the bands are labelled by the single orbitals of which they are composed. Thus, we can speak of a 1s or a 3d band. The bands are the wider, the greater the overlap between the orbitals. sp bands, which are composed of the s and p orbitals form rather large structureless bands. In contrast, d orbitals are more localized and form narrow d bands. Figure 3 shows schematically the band structure of a few typical electrode materials: A semiconductor or insulator, which could be also a

Elizabeth Santos and Wolfgang Schmickler

0

32

Eg band gap

Ethermal

EF

1

f (H) S Seem mii-cco on nd du uc ctto orr //IIn nssu ullaatto orr

Ag d-band s sp p--b ba an nd d

Au d-band

s sp p--b ba an nd d

Pt d-band

s sp p--b ba an nd d

m e t a l s Figure 3. Schematic representation of the electronic bands structure of different types of materials. The Fermi-Dirac distribution determines the occupation of the electronic states.

metal electrode covered by an oxide film, and three different metals. All three metals posess a wide sp band extending well above the Fermi level. However, the d bands are different. The position of the d band of silver is lower than that of gold, and both lie lower than that of platinum. In the latter case the d band even extends about 0.5 eV above the Fermi level. These differences are crucial for determining the electrocatalytical properties of these materials. Hammer and Nørskov23 have proposed a simple one-electron description of the quantum mechanics of atoms and molecules interacting with all valence states of the metal surfaces (see Fig. 4). This interaction is formally composed of a contribution (weak chemisorption) arising from the sp bands which leads to a broadening and a shift of the atomic level to lower energies (renormalization) and a second contribution (strong chemisorption) coming from the d bands. The latter involves a strong hybridization which produces a split in a bonding and an antibonding contribution just as in a simple two-state problem, where the whole d band is re-

Recent Advances in Theoretical Aspects of Electrocatalysis

33



AB

dband

HF

Hc

Ha

spband

B

Figure 4. Simple model regarding the whole d band as a single level located at its center and interacting with an adsorbate.

placed by an effective level located at its center. A similar concept has been previously developed for gas phase reactions,24 where the substrate frontier orbitals simultaneously play the role of the HOMO (highest occupied molecular orbital) and the LUMO (lowest unoccupied molecular orbital). This model provides a qualitative picture for the catalytic effect of the d bands. The higher the position of the center of the d band, the smaller is the occupation of the antibonding orbital and the more attractive results the interaction. They proposed a linear relationship between the d band center position shift įHc and the change in the chemisorption adsorption contribution įEads: GEads



V2 H cd

 Ha

GHcd

(1)

In the case of coin metals like Au and Ag (see Fig. 3), the center of the d band lies too low and thus both bonding and antibonding levels are situated below the Fermi level and in consequence are filled making the interaction repulsive. The opposite happens with Pt, which is a good catalyst. In this case, the center of the band is situated near the Fermi level, and thus the bonding

34

Elizabeth Santos and Wolfgang Schmickler

level appears below the Fermi level, while the antibonding lies above it. This intuitive approach is simple and provides a good tool to estimate the catalytic properties of different materials according to their electronic structures, particularly for comparing similar systems that only differ in the position of the d band center. However, in order to understand electrocatalysis in an electrochemical environment a more extensive framework is necessary. As we will see below, the position of the electronic level of the reactant can be shifted by fluctuations of the solvent configuration and by changing the applied potential. These effects make the analysis more complicated. IV. PREVIOUS APPROACHES TO BOND BREAKING ELECTROCHEMICAL REACTIONS The first approaches towards a theory for electrochemical reactions in which bonds are broken were given independently by German and Kuznetsov25 and Savéant26,27 for reactions such as: R—X + e- ĺ R. + XA simple model based on a Morse curve description of the potential energy surface for bond-breaking (see Fig. 5) has been proposed: V ( R)



De e 2DR  e DR

V ( R)

Dee 2DR



(2a) (2b)

The first equation represents the situation before, while the second one describes the behaviour after the bond breaking. De is the dissociation energy of the RX bond. This leads to a quadratic activation driving force free energy relationship: 'Gact

(O  De  eo K) 2 4(O  De )

(3)

Recent Advances in Theoretical Aspects of Electrocatalysis

35

R. + X-

RX

Figure 5. Simple model based on a Morse curve description of the non-adiabatic potential energy surface for bond-breaking.

If the system is under equilibrium conditions, the overpotential K is zero and the standard activation free energy becomes the sum of two contributions characterizing bond-breaking (De) and solvent reorganization (O), respectively: 'Go#

De  O 4

(4)

A further development of this theory has been carried out by Koper and Voth28,29 considering the electronic coupling with the electrode which was absent in Savéant’s model for calculating adiabatic potential energy surfaces: Hˆ tot

Hˆ electrode  Hˆ solvent  Hˆ aa

(5)

As in Savéant’s model they describe the R—X bond by a Morse potential and introduce an effective switching operator describing the bond breaking process:

36

Elizabeth Santos and Wolfgang Schmickler

Hˆ aa

De >1  n AB @^1  exp> J r  ro @`2

 De n AB exp> 2 J r  ro @

(6)

where De is the dissociation energy of R—X, nAB the occupation number operator of the antibonding orbital (AB), J is related to the bond vibration frequency, r is the bond distance and ro the equilibrium bond distance. The Koper–Voth model does not account for spin, and refers therefore to the exchange of one electron with a comparatively weak interaction. Kuznetsov et al. have introduced the spin interaction for bond breaking reactions30 in the usual Hartree–Fock approximation.31,32 In the limit of an infinitely wide, structureless metal conduction band, Kuznetsov and Medvedev33 have shown how to go beyond the Hartree–Fock approximation by using a solution of the Anderson Hamiltonian34 by Kawakami and Akiji,35 which is exact in this limit. They have also applied their model to bond-breaking electron transfer induced by a scanning tunneling microscope.36 An important limitation of all these contributions is that the potential energy curves for the intact molecule and for the two fragments were introduced in an ad hoc manner. This can either be done by the explicit introduction of an operator28,29 which switches between the states before and after bond breaking, or, equivalently, by introducing different potential energy curves in the presence and in the absence of the valence electrons.30 In order to understand the electrocatalysis process for strong interaction with the electrode important changes in these models are necessary. V. MODEL HAMILTONIAN A general model Hamiltonian for electron transfer in an electrochemical environment15,16 must contain terms for the different components of the system, i.e., the reactant, the electrode and the solvent, and their corresponding interactions: Hˆ tot

Hˆ electrode  Hˆ reac tan t  Hˆ solvent

(7)

Recent Advances in Theoretical Aspects of Electrocatalysis

37

It is more convenient to express the different contributions in second quantized form. Thus, we have for the electrode and its interaction with the reactant:

¦ Hk nk ,V  ¦ >Vak ck,Vca,V  Vak* ca,Vck ,V @

Hˆ electrode

k ,V

(8)

k , a ,V

k labels the electronic states in the electrode, nk are the corresponding number operators, and the last term effects electron exchange between the electrode and the different orbitals of the reactant labelled as a. c+ and c denote the creation and annihilation operators respectively. V is the spin index. The contributions of interactions between the solvent and the electrode itself are usually not important for the electrochemical rate,37 however they can be included if necessary. In order to describe the state of the solvent, we represent it as a bath of harmonic oscillators, which interact linearly with the reactant. The corresponding Hamiltonian is written in the form:

Hˆ solvent

1 2

¦ !ZQ ~pQ2  q~Q2  ¦ Z a  na,V ¦ !ZQ gQq~Q (9) Q

a,V

Q

Here Za is the charge number of the reactant a, Qlabels the phonon modes, which have frequencies ZQ, dimensionless coordinates q~Q and momenta ~ pQ , and gQ is the interaction constant of the reactant charge with the mode QFor a classical solvent the multidimensional representation given in Eq. (9) can be replaced by an equivalent one-dimensional model. Then the interaction between the solvent and the reactant can be characterized by a single energy of reorganization defined as: O

1

¦ 2 !ZQ g 2 Q

Q

(10)

Here the generalized coordinate q q~g has been normalized and has the following meaning: When the reactant having a charge –q is in equilibrium with a given configuration of the solvent, the sol-

38

Elizabeth Santos and Wolfgang Schmickler

vent state is characterized by the value of +q. Thus we can rewrite Eq. (9) in the following way: Hˆ solvent

ª º Z a  n a ,V q » O« p2  q 2  2 « » a ,V ¬ ¼

¦



(11)

The contribution of the reactant, consisting in the general case of a molecule composed of different atoms, can be expressed in the following generalized form15,16:

Hˆ reac

¦ a,V

ª «H a na,V  «¬

aa ' ¦ Eaa'caVca'V  E*aa'ca'VcaV  Vimag a'

(12)

 U a naV naV' @

Here a is the index for the different valence orbitals of the reactant participating in the reaction; n is a number operator which account for the occupation of the given state, the terms involving creation and annihilation operators effect electron exchange and are responsible for the bonding between two orbitals in the reactant and is related to the bonding energy. During the reaction of electron transfer the atoms of the molecule become charged due to the electron transfer process with the electrode. Charged species near a metal surface induce an image charge on the metal and interactions between the core of the reactant and the electrode surface take place (see Fig. 6). Then we have to add a term Vimag to the Hamiltonian, which is approximated as a dipole-dipole interaction term: aa ' Vimag

ª D dip « Z a  «¬

º

ºª

¦ na,V »».««Z a'  ¦ na',V »» V

¼¬

V

(13)

¼

where: D dip

4d Elec 2

r  2ro 3

(14)

Recent Advances in Theoretical Aspects of Electrocatalysis



39

r+2ro

G G

a

a’

G

a

a’

G

dMet

Figure 6. Dipole–dipole interaction produced as a consequence of the induced image charge on the metal by the partially charged species during the bond breaking, according to Ref. 16.

Za and Za’ are the charge numbers of the atoms a and a’ respectively when the atomic orbital a(a’) is empty; dElec is the distance of the atoms to the electrode surface, r is the distance between the atoms and ro is the equilibrium distance between the atoms. The last term containing U stands for the Coulomb repulsion between the electrons of opposite spin in the same orbital. The total Hamiltonian can be solved by Green’s function techniques38 using the Hartree-Fock approximation for the Coulomb repulsion terms:32,33 Uni n j | Uni n j  Un j ni  U ni n j

(15)

where denotes the expectation value. In particular the density of states of the different orbitals and their corresponding occupation numbers, and the energy can be calculated.

40

Elizabeth Santos and Wolfgang Schmickler

HF 

Ha /

'

Metal

Figure 7. Broadening and shift of the electronic level of an adsorbate approaching to the surface of a metal.

VI. INTERACTIONS OF THE ATOMIC ORBITALS OF THE REACTANT WITH THE ELECTRONIC STATES OF THE ELECTRODE

These phenomena are well described by Anderson-Newns Model34,39. Two main effects occur when an atomic orbital of the reactant interacts with the electronic levels of the electrode. When the reactant approaches the surface, the energy level of the orbital interacts with all electronic states on the electrode characterized by the electronic energy H. It shifts with respect to the position of the isolated species Ha, and simultaneously there is a broadening (see Fig. 7). It is no longer characterized by a sharp level, but by a density of states UaH . The binding of the reactant to the surface depends on the quantum-mechanical coupling of the reactant and on the electrode wave functions. These two effects are described through the chemisorption functions '(broadening) and /(shift) which are interrelated through a Hilbert transform:34,39 ' (H )

¦ Vak 2 G(H  H k ) ;

S

k

/ (H)

5 ' (H ) dH' S H  H'

³

(16)

Recent Advances in Theoretical Aspects of Electrocatalysis

41

where P denotes the Cauchy principal value. 'H is seen to be a weighted density of states functions corresponding to the electrode, with /H as its Hilbert transform. The parameter 'has a simple interpretation: an electron placed on the reactant decays with a lifetime of W ƫ' into empty states on the electrode; therefore ' can be thought of as a lifetime broadening, a manifestation of the Heisenberg uncertainty principle. Then, the projected density of states for the atomic orbital corresponding to the reactant is obtained from the imaginary part of the matrix elements of the Green functions and can be expressed through the following general form: U a (H )

1 ' (H ) S >H  ~Ha  /(H)@2  '(H) 2

(17)

~H is the position of the valence orbital at the surface and is afa fected not only by the interaction with the electrode but also with the electrochemical environment (see below, Section V). It contains also all exchange and correlations terms such as spin and image charges interactions missing in /H . The shape of UaH is determined by the strength of the interactions with the electrode 'H  which contains the coupling constants Vak and the electronic structure given by the density of states UelH . The simplest electrochemical reaction is an outer sphere electron transfer where the interactions with the electrode are weak. Hence, the details of the band structure are not important; we can ignore the k dependence of the coupling constants and replace them by a single effective value. The sum over k in Eq. (16) then reduces to the surface density of states corresponding to the electrode and the chemisorption function 'H can be taken as constant. It corresponds to the interaction with a wide, structureless band on the electrode. In this approximation40-42 the chemisorption /H functions vanishes (see Fig. 8a): ' (H )

Veff

2

U el (H)

const; /(H)

0

(18)

42

Elizabeth Santos and Wolfgang Schmickler

1 ,0

(a)structureless band

0 ,5

0 ,0

- 0 ,5

- 1 ,0 -1 0

-5

0

5

10 HH / e V c

1 ,0

(b)semielliptic wide band

chemisorption functions

0 ,5

0 ,0

- 0 ,5

- 1 ,0 -1 0

-5

0

5

10

H Hc / e V

0

5

10

H Hc / e V

1 ,0

0 ,5

(c)semielliptic thin band

0 ,0

- 0 ,5

- 1 ,0 -1 0

2 1

-5

(d)Pd(111) band (from DFT)

0 -1 -2 -4 0

-3 0

-2 0

-1 0

0

10

20 30 HHc / e V

Figure 8. Different approaches to describe the electronic structure of the metal through the chemisorption functions 'H (full lines) and /H (dotted lines).

Recent Advances in Theoretical Aspects of Electrocatalysis

43

In this case the density of states of the reactant takes the form of a Lorentzian as illustrated in Fig. 9a. In order to analyze the effects of the electronic structure on electrochemical reactions, it is useful to regard first idealized band shapes.43-45 For this purpose we consider semi-elliptical bands as proposed by Newns,39 where the density of states can be expressed by: 1/ 2

Uel (H )

ª § H  H ·2 º c «1  ¨ ¸ » «¬ © w ¹ »¼

>

T w2  H  H c 2

@

(19)

Here the Heaviside function T ensures that the contribution vanishes outside the bands. Hc and w indicate the center and the half width of the band, respectively. We still neglect any dependence of the coupling constants on k and consider an effective value, which is a good approximation for most cases. Then 'H is proportional to UelH but no more constant; /H can be easily obtained from equation (16). The effect on the density of states of the reactant UaH depends on the relative values of the parameters |Veff|2, H~a , Hc and w. In Fig. 8b and 8c we show the chemisorption functions for two semielliptic bands with different width, a wide band (Fig. 8b), which can represent a sp band, and a thinner one (Fig. 8c), which can describe a d band. Figure 9 shows the resulting densities of states of the reactant. Here, the position of H~a was selected such that it coincides with the center of the band Hc. The results for UaH  using a wide band (Fig. 9b) do not differ so much from the approximation with a constant '(compare with Fig. 9a). However, when a thin band is present the interaction produces a broadening of the orbital of the reactant and in the case that the coupling is strong enough the orbital splits into bonding and anti-bonding parts with respect to the electrode (see the sharp peaks at both sides of the band in Fig. 9c). A model employing several semielliptic shapes to represent d band of real systems is very good, as can be appreciated from Fig. 8d, where a real electronic structure calculated for Pd(111) surface with DFT is shown. The shape of the corresponding UaH is very similar to that of Fig. 9c as can be inferred from Fig. 9d.

44

Elizabeth Santos and Wolfgang Schmickler

3

2

Structureless band

1

0 3

2

-4

-2

0

2

4

0

2

4

0

2

4

H H c / eV

Semielliptic wide band

1

Ua / eV-1

0 3

2

-4

-2

H H c / eV

Semielliptic thin band

1

0 0,8

-4

-2

H H c / eV

Pd(111) band

0,6

0,4

0,2

0,0

-4

-2

0

2

4

H H c / eV

Figure 9. Density of states of the adsorbate a corresponding to the electronic structures of the metal given in Fig. 8

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45

VII. OCCUPATION PROBABILITY OF THE ELECTRONIC STATE OF THE REACTANT

The position of the electronic state of the reactant in the energy scale depends on a series of parameters, and in the following we will analyse them. Its occupation probability indicates if the electron transfer from (into) the electrode has occurred and to which extent. In the course of solvent fluctuations they may get energetically closer to the Fermi level or further away, and their density of states (DOS) changes accordingly. As a first example we consider outer sphere reactions with weak interactions with the electrode. In this case only one electron is transferred and thus we consider only one electronic state for the reactant.40 The first effect to be considered is the solvation. The reactant’s levels fluctuate with the solvent. Its position depends on the solvent configuration and the center is given through:

H~a

H a  2Oq

(20)

The other interactions terms considered in the Hamiltonian of Eq. (12), such as spin and bonding between atoms, do not play any role in this case. In the course of the electron transfer the reactant changes its charge and hence its solvation; this situation is illustrated in Fig. 10. In the adiabatic case the reactant shares its electron with the metal. We have referred the electronic energy to the Fermi level of the electrode, which is taken as zero for convenience. Thus, the occupation of the electronic state of the reactant is obtained by integrating the density of states up to this energy value (see Fig. 11). Since Delta is constant in this simple case, an analytical expression can be obtained:40 HF 0

na

³

f

U a H dH

1

S

arc cot

H~a '

(21)

The reactant can be neutral or a charged species. If an oxidation reaction takes places the electronic state lies well below the Fermi level and is completely occupied at the beginning of the reaction ( = 1); on the other hand, for a reduction reaction it

energy

Oxidation Reduction

Figure 10. Evolution of the density of states of an adsorbate in the absence of a d band for an oxidation reaction (left) and a reduction reaction (right).

Ua(H)

Recent Advances in Theoretical Aspects of Electrocatalysis



Ua(H)

Fermi Level

47

1,0

0,3

0,8 0,2

0,6

'

0,4 0,1 0,2 0,0 -15

-10

-5

0

HaO

5

10

15

20

0,0 25

energy / eV

Figure 11. Density of states of the adsorbate a and the corresponding occupation obtained by integration according to Eq. (21).

is completely empty and is above HF. The configuration of the solvation shell determines the value of the normalized solvent coordinate and is opposite to its charge as mentioned in Section III. During the reaction an electron is transferred from (reduction) or into (oxidation) the electrode. There is a rearrangement of the solvent configuration; as a consequence the position of the center of UaH shifts and the occupation of the reactant orbital changes. At the transition state the electronic level of the reactant is about half occupied and at the final state it is totally empty (oxidation) or fully occupied (reduction). The solvent is relaxed to its new equilibrium position for the product. Table 1 summarizes the different possibilities according to the type of reaction and the initial charge of the reactant. Also the values of the normalized coordinate q are given for the different cases. It is a great advantage of electrochemical system that the other parameter that produces a shift in the density of states of the reactant is the potential applied externally to the interface. The driving force of interfacial reactions can be varied with the elec-

Table 1 Different Types of Reactions and the Values of the Different Parameters (Normalized Solvent Coordinate and Occupation) for the Initial, the Transition and the Final States of the Reactant.

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49

trode potential producing changes of the order of electron volts in the position of the electronic state participating in the reaction. Thus we can express Ha for an oxidation (reduction) reaction as:40

Ha

H ared / ox  eoK red / ox

(22)

where H ared / ox is its position when the species a is in thermodynamic equilibrium with the corresponding oxidized (reduced) product; Kred/ox is the related overpotential. When the reactant is a molecule, we have to consider other terms coming from the interaction between the atoms forming the molecule. An interesting approach to understand the mechanisms of electron transfer in these cases is to describe the interaction of the molecule in terms of a tight-binding (or extended Hückel) model.15,16 We consider here a particular case of a homonuclear molecule (A – A) lying flat at the surface of the electrode; the molecule undergoes a simultaneous electron exchange with the electrode and the breaking of a single bond. Examples are the reduction of chlorine and the oxidation of hydrogen. However, an extension to more complicated cases, such as heteronuclear molecules (A – B) or the exchange of more electrons in molecules with multiple bonds (for example oxygen) is possible. The important electronic states on the molecule are the bonding (B) and antibonding (AB) molecular orbitals which result from the interaction of the valence atomic orbitals. Their positions for the isolated molecule result from solving the corresponding secular equation:46 A / AB H MO

H a  ES r E

(23)

where E is the off-diagonal element and S is the overlap between the atomic orbitals of the two atoms of the molecule. Both parameters depend exponentially with the separation distance between the atoms r. Assuming the Wolfsberg – Helmholz approximation47 we have:

E

a Vaa ' a '

 Eoe r / l ; S

a a'

JE

(24)

50

Elizabeth Santos and Wolfgang Schmickler

where l is a decay length and ER is positive. The parameter E is attractive while S is repulsive, resulting in a Morse curve for the potential between the two atoms. The corresponding binding energy per electron is: De



1 4J

Eo

(25)

2

Then we gather the terms containing the occupation numbers and redefine the position of the molecular orbitals as:

H~B,V

H a  2Oq  U na,V  D dip (1  na,V  na, V ) JE 2  E

H~AB,V

H~mol ,V  E

H a  2Oq  U na ,V  D dip (1  na ,V  na ,V )  JE 2  E

H~mol ,V  E

(26a)

(26b)

Note that now also appear the spin and image interactions. In this context the expression for the density of states of the molecule contains a term for the bonding and a term for the antibonding orbitals:

U mol

¦ U B,V  U AB,V V

½° (27) ­° ' '  ¾ ® S V ° H  H~B,V  / 2  '2 H  H~AB,V  / 2  '2 ° ¿ ¯ 1

¦ 







In the case of weak interactions with the electronic levels of the electrode (wide band approximation) Eq. (27) has the form of two Lorentz distributions centred at the energies of the bonding and antibonding states (see Fig. 12). The integral of Eq. (27) up to the Fermi level gives the occupation of both, bonding and antibonding orbitals and in the case of the wide band approximation it is an analytical expression:

Recent Advances in Theoretical Aspects of Electrocatalysis

Umol(H)

Fermi Level

51

1,00

E

0,15

0,75

0,10

0,50

0,05 0,00

0,25

-10

H~B

-5

H~

mol

0

H~AB

5

0,00

energy / eV

Figure 12. Density of states of the adsorbed molecule and the corresponding occupation obtained by integration according to Eqs. (27) and (28).

nmol

¦ V

1

S 1

S

2E nB,V  n AB,V

¦ ^arg>H~mol ,V  i' 2  E 2 @`

(28)

V

¦ ^arg H~B,V  i'  arg H~AB,V  i' ` V

where the argument has to be taken in the interval [0,2S]. This is really a set of self-consistent equations, since H~mol depends on the occupancy of the other spin orbital. In this case the development of the density of states of the molecule as the reaction is proceeding, is the following: Initially, it has a filled bonding orbital lying well below the Fermi level, and an empty antibonding orbital well above (see Fig. 13). In the final state, the bond has been broken, B and AB orbitals have collapsed into a single orbital which is either empty and lies above HF for a

Reduction

Figure 13. Evolution of the density of states of an adsorbed molecule in the absence of a d band for an oxidation reaction (left) and a reduction reaction (right).

Oxidation

Recent Advances in Theoretical Aspects of Electrocatalysis

53

oxidation reaction, or filled and lies below HF for a reduction reaction. For the reaction to proceed, a fluctuation of the solvent must shift the AB orbital below HF (for a reduction reaction) or the B orbital above HF (for an oxidation reaction). The critical phase (transition state) is when these orbitals actually pass the Fermi level. For the simple dissociation of the type: A2 ĺ 2A without electron transfer, the distance between the atoms increases till they separate; at the same time, the interaction between the atoms is diminished, the separation between B and AB orbitals becomes smaller till it finally disappears. The position of H~mol with respect to HF does not change during the reaction in this framework. VIII. 1-D AND 3-D POTENTIAL ENERGY REPRESENTATIONS The way in which the rate constant is obtained from the general SKS-Hamiltonian15,16 depends on the properties of the analysed system. In the simplest case where we consider that the interaction of the reactant with the electrode is weak, the expression for the energy of the system obtained from solving the Hamiltonian depends on the normalized solvent coordinate q according to Marcus – Hush model:10,11 E (q)

Oq 2  2Oq  H~a na

(29)

where H~a is given by Eq. (20). Here it is illustrative to analyse as an example the reaction given in the first row of Table 1 (see also Fig. 14): A ĺ A+ + e In the initial state we have a neutral species A, the occupation is = 1, the solvent coordinate qinitial = 0 and the expectation value for the energy <E>initial = HDAt the final state we have a cation A+, the occupation is zero ( = 0), the solvent coordinate equal to the opposite of the charge of the species (qfinal = –1)

54

Elizabeth Santos and Wolfgang Schmickler



1,0

0,5

0,0

energy / eV

-0,7

A+

A

-0,8 -0,9 -1,0 -1,5

-1,0 -0,5 0,0 solvent coordinate q

0,5

Figure 14. Occupation and adiabatic potential energy curves in thermodynamic equilibrium as a function of the solvent coordinate q for two limiting cases: strong interactions (full lines) and weak interactions (dotted lines). For the first case, it is also shown the electronic contribution (dotted dashed line, bottom plot).

and the expectation value of the energy <E>final = –O Then, the system is in thermodynamic equilibrium when Ha OIn this situation at the transition state the occupation is = 0.5, the solvent coordinate qtrans = –0.5 and the expectation value for the energy <E>trans = OHD which gives the same activation energy

Recent Advances in Theoretical Aspects of Electrocatalysis

55

like Marcus – Hush model.10,11 If an external potential is applied, the initial state is shifted according to Eq. (22). When we consider the interactions with the electrode an additional term appears in Eq. (29) which is obtained by multiplying the density of states with the energy H and then integrating up to the Fermi level: HF 0

Eelec

³ HUa (H )dH

(30)

f

In the case of weak interactions, according to the wide band approximation an analytical expression for the total expectation of the energy is obtained:41 E (q)

Oq 2  2Oq  H~a na 

' H~a2  '2 ln 2S H a2  '2

(31)

This equation gives the free energy curve of the reaction as a function of the solvent coordinate q. Figure 14 shows typical adiabatic potential energy curves in thermodynamic equilibrium for two limiting cases. For outer sphere reactions the level broadening 'is of the order of 10-3–10-2 eV, and thus much smaller than the energy of reorganization Owhich is typically in the range of 0.5–1.0 eV. Then the term that accounts for the electronic contribution is negligible, the occupation probability of Eq. (21) becomes a step function and we have a parabola with a minimum at q = 0 for A (initial state) and a parabola with a minimum at q = –1 for A+ (final state). The crossing of the parabolas gives the activated state with coordinate q = –0.5. The electronic term produce a decrease of the energy, mainly at the barrier as can be appreciated from the dashed-dotted line in the figure (plot of last term of Eq.31). In the case of simultaneous bond breaking and electron transfer, the contribution of the electronic interaction to the expectation value of the total energy can be also obtained from an equation similar to Eq. (30) but now involving the density of states of the molecular orbitals Umol. Now we have to consider an additional coordinate, namely the separation between the atoms of the molecule which changes during the reaction. An analytical expression

56

Elizabeth Santos and Wolfgang Schmickler

can be obtained for this term in the simplest case of wide band approximation:15,16

¦ ^H~B,V

Eelec (q, r )

n B,V  H~AB,V n AB,V

V

' ª' º½  « ln H~B,V  i'  ln H~AB,V  i' » ¾ S ¬S ¼¿

(32)

The total expectation value for the energy has contributions from the solvent, the spin and image interactions and the electronic term given by Eq. (32): Etot (q, r )





O q 2  2Zq  2U na,V na ,V



1  D dip 1  na ,V  na ,V 2

2 

Eelec (q, r )

(33)

The first term is the energy of the solvent when the spin orbitals are empty; the second and third terms avoid double counting for the Hartree Fock approximation. As an example, we chose the reaction of the fourth row of Table 1: A2 ĺ 2A+ + 2eWe consider a system where the molecule A2 is in equilibrium with two cations A+. The resulting 3D-potential energy surface (left) and the corresponding occupation (right) are shown in Fig. 15 using the solvent coordinate q and the bond distance r as reaction coordinates. A minimum centered at q = 0, r = ro corresponding to the molecule and a valley centered at q = –2 related to the two cations are clearly observed; both regions are separated by an energy barrier. The occupation probability shows the expected behaviour: = 2 and = 0 for the molecule and the two cations respectively. At the bottom of the figure are the projected 2-D contour plots. We will often employ this 2-D type of representation. Within our model the potential energy can be calculated for different reactions. Figure 16 shows contours plots of such poten-

Figure 15. Adiabatic potential energy and occupation surfaces in thermodynamic equilibrium as a function of the solvent coordinate q and the separation distance r-ro between the atoms of the molecule for an oxidation reaction with simultaneous bond breaking. At the bottom the contour projection of the 3D-surfaces are shown.

<Etot>



Figure 16. Contour projection of the 3D-adiabatic potential energy surfaces in thermodynamic equilibrium as a function of the solvent coordinate q and the separation distance r-ro between the atoms of the molecule for three different cases: a reduction, a dissociation and an oxidation reaction with simultaneous bond breaking. (Data obtained from Ref. 45.)

Recent Advances in Theoretical Aspects of Electrocatalysis

59

tial energy surfaces at a fixed distance of the reactant to the electrode for three different cases: the reduction of a molecule (a), the dissociation without electron transfer (b), and the oxidation (c). In all the cases we can follow the energy of the system and the occupation of the molecular orbitals along the whole reaction path. The initial state is a neutral molecule corresponding to a minimum at the solvent coordinate q = 0, and with the bond distance at its equilibrium value r = ro. The reaction goes through a saddle point (marked by a star) to the valley at a higher bond distance centered at a solvent coordinate qf, which is different in the three cases considered. In the first case, the reduction of the molecule produces two anions (a). Then the valley at higher separation between the atoms is centred at qf = +2. For the dissociation of the molecule to two atoms, the center of the final valley is located at qf = 0, and in (c) the molecule is oxidized to two cations with the valley at qf = – 2. In all cases the system has to overcome a saddle point situated at an intermediate value of the solvent coordinate q and the bond distance r. We note that the surfaces in this figure are meant to demonstrate the typical reactions paths, therefore they have been calculated for a constant chemisorption function ', which corresponds to the non-catalytic coupling to a sp wide band and to the absence of a d band. Model calculations performed for reactions on a metal surface in the gas phase, which can nowadays be routinely performed with the aid of quantum-chemical packages, can only describe the pure dissociation A2 Æ 2A, but not electron transfer with bond breaking. They may still illuminate certain aspects of these reactions, but are necessarily incomplete. IX. ELECTROCATALYSIS BY A NARROW d BAND The wide band approximation can be applied to describe very well the behaviour of metals with large, structureless sp bands. However, the more interesting materials showing electrocatalytic properties, such as platinum or ruthenium, posess narrow d bands. Then the next step in the development of the model is to abandon the wide band approximation and consider the electronic structure of the bands.43-45 Next, we discuss the superposition of a wide sp

Elizabeth Santos and Wolfgang Schmickler

chemisorption functions

60

0,4

'd 0,2

/ 0,0

Hc

-0,2 -15

-10

-5

0

5

10

15

20 25 HH c / eV

Figure 17. Chemisorption functions ' and / for the semiellipic model in the case of a superposition of a wide sp band and a thin d band.

band and a narrow d band. It is convenient to use semielliptical shapes for which several important properties can be calculated explicitly (Fig. 17):43-45 ' Total H ' sp H  ' d H and / Total H / sp H  / d H (34)

Equation (16) contains contributions from both the sp and the d band. Now it is no more possible to obtain an analytical expression for the occupation of the electronic states of the reactant, nor for the corresponding energy. However, the integrals in Eqs. (21) and (30) can be easily calculated numerically. Figure 18 shows the electronic contribution of the energy in the case of the superposition of a wide sp band with a narrow d band (wd = 1 eV) with a coupling constant |Veff| = 1.6 eV2 located at the Fermi level in comparison with the effect observed in the absence of the d band. In both cases the orbital is half occupied; however by the presence of the d band it is elongated to lower values of energy. This effect produces that the electronic contribution given by the integral up to the Fermi level of the product between the energy coordinate H and the density of states of the reactant Ua (Eq. 30) becomes more

Recent Advances in Theoretical Aspects of Electrocatalysis

61

0,25 1

0

0,00

-0,5

-0,1

-1,0

-0,2

-1,5

³ HUa dH

HUa

2

=³ Ua dH

Ua /eV-1

0,50

-0,3 -2,0 -2,5

-0,4 -4

-3

-2

-1

0

Figure 18. Upper plot: density of states of the adsorbate a and the corresponding occupation obtained by integration according to Eq. (21) for the semiellipic model in the case of a superposition of a wide sp band and a thin d band (full lines) in comparison with the case in the absence of the thin d band (dotted lines). Bottom plot: the corresponding illustration for the determination of the electronic contribution according to Eq. (32).

negative than in the absence of the narrow d band. Also, one notices a sharp peak at the border of the band that accounts for a binding with the electrode. Figure 19 is similar to Fig. 13 and shows the development of the states of the molecule for the oxidation and the reduction reactions but now when a strong interaction with a narrow d band cantered almost at the Fermi level takes place. The initial state corresponds to the molecule, where the density of states shows the familiar splitting into bonding below (filled) and antibonding states above the Fermi level (empty) according to Eq. (27). During the bond breaking the atoms of the

energy

Umol(H) Reduction

Figure 19. Evolution of the density of states of an adsorbate in the presence of a thin d band localized near the Fermi level for an oxidation reaction (left) and a reduction reaction (right).

Oxidation

Recent Advances in Theoretical Aspects of Electrocatalysis

63

molecule are separated and the energies of B and AB become closer. In the transition state the B (AB) orbital crosses the Fermi level for the oxidation (reduction) reaction, and due to the strong interaction with the narrow d band the orbital is elongated and split as described previously, thus decreasing the energy at the barrier. In the case of the oxidation the B orbital becomes partially empty while in the reduction reaction the AB orbital is partially filled. In the final state the bond has been broken, the atoms are separated, and B and AB orbitals have collapsed into single empty (filled) orbital lying above (below) of the Fermi level for the oxidation (reduction) reaction. Figure 20 shows the adiabatic potential energy surfaces obtained for the two cases described above. The decrease in the activation barrier by the presence of a narrow d band is evident. Then, in order to have an electrocatalytic effect, it is crucial to have a strong interaction of the molecular orbitals when they are passing the Fermi level. However, it is not only the position of the band but also other factors play a role in the mechanisms of decreasing the activation barrier. Next we analyse the effects of different parameters for the interaction of the d band with the AB orbital at the saddle point for the reduction reaction (Fig. 21). An important factor is the coupling constant |Veff|2, which is a measure of the overlapping between the reactant and the electrode. For a weak interaction, the AB states just gets broadened (upper left); with increasing strength it splits into two states: one that is bonding, and one that is antibonding with respect to the electrode. The bonding part lies substantially below the Fermi level and thus reduces the energy of the activated state. The center panel shows the effect of the width of the band: for a very large width, cantered at the Fermi-level, the AB peak gets smeared into a single, very broad peak. The panel at the right shows the effect of the position of the d band center. Obviously, a position near the Fermi-level is optimal. However, there is some asymmetric behaviour according to the type of reaction as can be observed from Fig. 22 (left). For the case of the oxidation the optimal position lies about 1 eV below the Fermi level for these conditions, while for the reduction it lies a little above. The dissociation reaction shows the major reactivity when the d band is positioned exactly at the Fermi level and the behaviour is symmetric around the Fermi level. For the case of the reduction, Fig. 22 (right) also shows, how the energy of activation varies as a func-

q

Eact

narrow d band

q

Figure 20. Adiabatic potential energy surfaces showing the decrease of the activation barrier produced by the presence of a narrow d band near the Fermi level.

Eact

wide sp band

0

2

4

6

8

0

2

4

6

8

0

2

4

6

8

0

2

4

6

8

-6

-4

-2

0

2

4

|Veff|2=2.0 eV2

|Veff|2=1.0 eV2

|Veff|2=0.5 eV2

_Veff|2=0.1 eV2

-6

-4

0

HHF / eV

-2

2

4

Wd=6.0 eV

Wd=4.0 eV

Wd=2.0 eV

Wd=1.0 eV

-6

-4

-2

0

2

4

Hc=-2.0 eV

Hc=-1.0 eV

Hc=0.00 eV

Hc=1.75 eV

Figure 21. Effect of different parameters of the d band on the density of states at the saddle point. Left: effect of the coupling constant. Center: effect of the width. Right: effect of the position of the center of the band. (Data obtained from Ref. 44.)

UmolH

0,0

0,1

0,2

0,3

0,4

0,5

0,6

-5

-4

-3

Oxidation

-2

-1

1

Hc /eV

0

Dissociation

2

3

Reduction

4

-13,7

-14,0

-13,9

-13,8

-4

-3

-2

-1

0

1

Hc /eV

wd=3eV wd=4eV

wd=1eV wd=2eV

2

3

4

Figure 22. Left: Effect of the position on the activation barrier of a narrow d band for an oxidation (squares), a dissociation (circles) and a reduction (triangles) reaction. Right: Effect of the width of the band on the activation barrier for a reduction reaction.

Ebarr-Emin / eV

-13,6

Ebarr / eV

Recent Advances in Theoretical Aspects of Electrocatalysis

67

tion of the position of the band center for various width. For a band centered near the Fermi level, a narrow width is favourable, while for a band far from HF a wider band is more favourable, which still reaches HF. It is important to take into account these effects in the design of electrocatalysts in the nanoscale range. It is well known that the introduction of some defects such as steps or the formation of clusters change the electronic properties of the electrode materials (see Sections below). Considering the examples of Fig. 22, a shift of the position of the d band to lower energies than the Fermi level (in this example from 0 to –1 eV) should improve the activity for the oxidation reaction but inhibit the reduction. X. APPLICATION TO REAL SYSTEMS – HYDROGEN EVOLUTION / OXIDATION REACTIONS Calculations with idealized band shapes are very useful for understanding the mechanism of electrocatalysis,43,44 but to predict the activity of real systems we need the real density of states of the metal and the corresponding coupling constant with the reactant. We have chosen as an illustrative example the hydrogen oxidation because it is one of the fundamental reactions of electrochemistry. It is the reaction which occurs at the anode of fuel cells and because of its relative simplicity, it is often considered to be the prototype of an electrocatalytic reaction, whose rate depends strongly on the nature of the electrode material as mentioned at the beginning of this chapter. Thus, we focus on the electrocatalytic activity of different materials and nanostructures for this reaction and its reverse, the hydrogen evolution. The latter occurs in two steps, mostly via the Volmer-Tafel mechanism:48 H+ + e– ĺ Had 2 Had ĺ H2

(Volmer reaction) (Tafel reaction)

The Tafel reaction has an alternative, the Heyrowsky reaction: H+ + Had +e- ĺ H2

(Heyrowsky reaction)

68

Elizabeth Santos and Wolfgang Schmickler

According to the energy balance the oxidation of hydrogen requires almost 32 eV; about 22 eV are provided by the hydration of the proton, 9–10 eV, twice the work function, by the metal, and the rest by the potential drop between the electrode and the bulk of the solution, which is the only part that we can control experimentally. Thus, solvation plays a dominant part in the energetics, and any model for the hydrogen reaction that neglects the solvent leaves out a most important part. Figure 23 shows the d band densities of states of nine different metals. The position and the shape of the d bands differ widely. Ir and Re have wide bands centered almost at the Fermi level. The bands of Ni, Co and Pt are somewhat thinner, but with a higher density of states at HF. Rh is an intermediate case between these two groups. On the other hand, the coin metals Ag, Cu and Au have very thin bands with a high density of states at its centre, but they are localized several eV below HF. The coupling constants, which are given in the same figure,23 are very different from one metal to the other and there is no correlation with the features of the bands. They depend on the extension of the orbitals, and thus increase when going down a column of the periodic table. The rate determining steps of the hydrogen evolution reaction may also be different for the various metals. In a first step we have calculated the activation energy for the hydrogen oxidation reaction applying our model according to the Hamiltonian of Eq. (5). The density of states for the metal and the corresponding coupling constant were obtained from DFT calculation. The interaction between the hydrogen atoms were regarded within the Hückel approximation (Eqs. 23-25). The obtained results are shown in Fig. 24. Here the experimental results compiled from3,4 for the exchange current density are plotted versus the activation energy calculated from our model.45,49 Except for Au and Ag, the experimental values in the literature vary by at most one order of magnitude. This is the kind of variation to be expected when different measuring techniques or different surfaces are used. Several of the data are 40–50 years old, but since that time there has been no significant advance in the measurement of kinetics, so the variation of the rate over six orders of magnitude is real. Where there has been a significant advance is in the pretreatment of noble metal electrodes by flame annealing.50 This may explain the large discrepancy in the data for gold and silver. The data point with the high exchange current for

-1

Uel /eV

-1

Uel /eV

-1

0,0 -8

0,2

0,4

0,6

0,0 -8

0,2

0,4

2

-4

-2

0

2

-4

2

-2

0

2

HHF /eV

4

4

-6

Ag

-4

-2

0

2

HHF /eV

|Veff| =5.52 eV

-6

Ni

2

HHF / eV

|Veff| =2.81 eV

-6

Ir

|Veff|2=10.63 eV2

-8

0,6

0,0

0,2

0,4

0,6

4

2

-1

-2

0

2

-4

-2

2

HHF / eV

0

2

HHF /eV

-6

Cu

-4

-2

0

2

4

2

4

HH F /eV

|Veff|2=2.42 eV

0,0 -8

0,2

0,4

0,6

-6

Co

2

-4

|Veff| =3.20 eV

0,0 -8

0,2

0,4

0,6

-6

Re

|Veff|2=14.42 eV2

0,0 -8

0,2

0,4

0,6

4

-8

-6

-2

0

2

HHF / eV

-4

-2

0

2

HHF /eV

-6

Au

-4

-2

0

2

HHF /eV

|Veff|2=8.10 eV

-6

Pt

|Veff|2=9.44 eV

-4

|Veff|2=7.93

Rh

0,0 -8

0,2

0,4

0,6

0,0 -8

0,2

0,4

0,6

0,0

0,2

0,4

0,6

4

2

4

2

4

Figure 23. Density of states for different metals obtained by DFT calculations and the corresponding coupling constants taken from Ref. 23. (Data obtained from Ref. 45.)

Uel / eV

-1 -1

Uel / eV -1

Uel / eV

-1

Uel /eV

-1

Uel / eV

Uel / eV

Uel /eV

70

Elizabeth Santos and Wolfgang Schmickler

sp

-log( jo

Exp

-2

/ A cm )

10

8

Ag

6

Co Ni Cu

Au 4

Ir

Rh

Pt Re

2 0,0

0,5

1,0

1,5

E act(Theory) /eV Figure 24. Correlation between experimental (compiled from Refs. 3 and 4) and theoretical results for the hydrogen oxidation reaction at different metal electrodes. The circle surrounds data without flame treatment. (Data obtained from Refs. 45 and 49).

silver was measured in our laboratory by pulse methods and with the flame treatment.51,52 XI. DFT QUANTUM CHEMICAL CALCULATIONS AS INPUT FOR THE SKS-HAMILTONIAN Now we go a step forward and combine the developed model for electrocatalysis with results of quantum chemical calculations to investigate the effect of the electrode’s electronic structure on the rate of the hydrogen oxidation reaction in a more realistic way.53-55 We consider just one reactant orbital interacting with the metal surface; in the model calculations reported below this will either be the 1s orbital of the hydrogen atom or the bonding orbital of the H2 molecule. Also, we include neither the Coulomb repulsion U between two electrons on the same orbital nor the dipole-dipole interaction term originated by the image charge, since those will be handled by DFT calculations. Also, we abandon the Hückel ap-

Recent Advances in Theoretical Aspects of Electrocatalysis

Au(111)d-band / H1s

Uel / 1s /eV

-1

1,2 1,0

71

del=0.8Å

0,8 0,6

del=1.2Å d band

0,4

del=3Å

del=1.6Å

0,2 0,0 -10

-8

-6

-4

HHF / eV

-2

0

Figure 25. Projected density of states on the d band of Au(111) (dotted line), and on the 1s orbital of hydrogen when the atom approaches to the surface (Data obtained from Ref. 55.)

proximation to treat the molecular bond and consider the interaction between the atoms in the DFT framework. We start considering the Volmer reaction, the first step of the hydrogen evolution reaction. First, calculations were performed for the bare metals, with relaxation of the upper two layers. Then, a hydrogen atom was added and the equilibrium position determined. There are several possible sites at the surface where the hydrogen atom can adsorbs. For the fcc metals Pt, Au, Ag, Cu, the optimum position for hydrogen adsorption was always the fcc three-fold hollow site; for Cd(0001) it was the threefold hollow site. Next we performed calculations of the projected density of states on the sp and d bands of the metal and on the 1s orbital of the hydrogen atom by means of the DFT formalism at different distances to the electrode. Figure 25 shows as an example the results obtained for the adsorption on Au(111). This situation corresponds to a solvent coordinate of q = 0. Since the hydrogen atom is completely discharged solvation effects are absent. Then we obtain the parameters ', /and H~a by fitting according to Eq. (17), and the electronic energy that we will call EDFT. Figure 26 shows the fitted parameters |Veff|2 and H~a for

72

Elizabeth Santos and Wolfgang Schmickler

2

|Veff| /eV

2

4

(a

3

Pt Au Cd

2 1 0

Pt Au Cd

-6

(b

Ha /eV

-8 -10 -12 1,0

1,5 2,0 del / Å

2,5

Figure 26. Interaction constants |Veff|2 as a function of the distances for the three selected metals, (a) and the hydrogen level H~a as a function of the distances del to the surface for the metals investigated (b), taking the vacuum as the reference level. (Data obtained from Ref. 55.) The normalization of the coupling constants differs by a factor of pi compared with those given in Fig. 23.

the three selected examples (Pt, Au and Cd). As expected, |Veff|2 decreases in the order Pt > Au > Cd, and fall off with the distance. For Cd the interaction is initially quite high, but falls off more rapidly with the distance than for the other metals. Since its d band lies so low, this comparatively large interaction has no catalytic

Recent Advances in Theoretical Aspects of Electrocatalysis

EDFT /eV

0

73

Pt Au Cd

(a

-1 -2 -3 0,0

0,5

1,0

1,5 del / Å

2,0

(b

2,5

EDFT / eV 2,5

Pt Au Cd

2,0 1,5 1,0 0,5 0,0 -0,5 1

1,0

s tom na e e tw be 4 ce r / Å n ta dis 2

1,5

2,0 2,5 diatan ce to th e meta l del / Å

3

3,0

Figure 27. Energy of an adsorbed H atom as a function of distance d to the surface (a) and of an adsorbed H2 molecule as a function of the bond length r and of the distance del to the surface (b). (Data obtained from Refs. 53 and 55.)

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Elizabeth Santos and Wolfgang Schmickler

effect. The hydrogen level H~a increases with distance, an effect that is well-known and mainly caused by the interaction with the sp band and the screening of the Coulomb repulsion between the two spin states. The increase is quite similar in all cases investigated, indicating that the behaviour of the sp bands differs little between these metals. Figure 27 shows the energy for the adsorption of a hydrogen atom (a) and for the dissociation of a hydrogen molecule (b) at different distances to the electrode for three different metals, Cd(0001) (a bad catalyst), Au(111) (a mediocre catalyst) and Pt(111) (an excellent catalyst). In the case of the dissociation of the hydrogen molecule, as the distance to the surface decreases, the separation between the two hydrogen atoms increases, until they are finally adsorbed in the threefold fcc hollow sites. On platinum, hydrogen dissociates practically without a barrier, on gold and cadmium dissociation is unfavourable and further requires the passing of an energy barrier; both the barrier and the energy of the adsorbed atom are much higher on cadmium than on gold. We calculate the electronic energy Emodel according to our model for the same configuration (for q = 0) from Eq. (30), the difference 'E between the results obtained by DFT and the integral of Eq. (30) is the exchange and correlation part that is now considered in a more realistic way than the Hartree Fock approximation for the spin and dipole-dipole interaction of the image charge: EF

'E (q

0)

Emod el (q

0)  EDFT

³ HU1S dH  EDFT

(35)

f

Because of its high ionization energy the adsorbed hydrogen is neutral on all metals, i.e., the occupation of the hydrogen orbital 1s is unity. As long as this occupation does not change, solvent fluctuations should have no effect on the electronic energy, and the DFT result applies. However, for large solvent fluctuations the occupancy changes and it finally becomes zero when the proton is formed. In the latter case the electronic energy also vanishes. We therefore use the following procedure: In order to obtain this cor-

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rection for arbitrary values of q, we assume that it is proportional to the occupation of the hydrogen orbital: 'E (q )

'E (q

0) n1s

(36)

Thus we use this linear interpolation to extrapolate the DFT results, which are valid for q = 0, to other values in the range 0 ” q ” 1. The interactions that are missing in DFT are those of charged species with the solvent. Then, we have to consider the energy of the proton with its environment. The energy of the proton would be just íO, but this is only the interaction with the slow solvent modes. The parts corresponding to the fast solvent modes, the image force, and its interaction with the electrostatic potential must be considered. Fortunately, we do not have to calculate them explicitly, since we know that at the equilibrium potential the free energy of the proton must be one half of the free energy EH2 of the hydrogen molecule. Therefore we write: E fast

E (1  n1s )( H 2  O ) 2

(37)

where the interaction has been assumed to be proportional to the charge. The energy of the H2 molecule is –31.73 eV, and the entropic contribution is –0.41 eV,3 which gives: 'GH2 = í32.11 eV. Again, we have used a simple and natural interpolation. Then, the total energy is the sum of the electronic energy calculated from Eq. (30) corrected by Eq. (36) and the solvent energy both, slow and fast contributions: EF

Etotal

³ HU1S dH  'E (q)  Oq

2

 2Oq  E fast

(38)

f

Us contains the fitted parameters ', /and H~a corrected by the solvent term 2Oq and the overpotential eo K

Now we can calculate the adiabatic potential free energy surfaces as a function of the solvent coordinate q and the distance to

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the electrode del for the Volmer reaction. Similar calculations can be also performed for the overall reaction H2 ĺ 2 H+ + 2 e–. However, here we have to take into account, that when the molecule approaches to the surface of the electrode, the distance between both hydrogen atoms simultaneously changes. As an example, both surfaces are shown in Figs. 28a and 28b for these reactions on Au(111). We show the energy as a function of the solvent coordinate q and the distance to the metal d for the Volmer reaction and as a function of the solvent coordinate q and the interatomic separation r for the overall reaction. In the latter case, we have to keep in mind that actually we have a third coordinate, i.e., the distance to the electrode. The distance between both atoms when the molecule approaches to the electrode, decreases as a consequence of the dissociation reaction (see Figure 27b). In Fig. 28a, at q = 0 and r = 0.76 Å, we observe a minimum corresponding to the stable molecule; the valley centered at q = –2 corresponds to 2H+. The direct oxidation of the molecule would require an activation energy of about 1.8 eV, the dissociation requires about 1.15 eV and is therefore favoured, even though it leads to an intermediate state with a higher energy. For the subsequent oxidation, we have to take into account that this diagram is for the simultaneous oxidation of two hydrogen atoms, which is less favourable than a consecutive oxidation of two atoms. Therefore we can infer from these results that the preferred mechanism is first the dissociation of the hydrogen molecule and then the oxidation of the adsorbed atom to proton but the reaction for the second step has to be calculated separately. We can represent these processes through the following diagram: H2

1

2 H+ + 2 e –

2

2 Hads

3

In Table 2 are summarized the energetics values for the different steps shown in this schema. We have considered for all the cases that the reaction (1) is in equilibrium, so its 'G = 0.

<Etot>

(b)

0

Figure 28. Adiabatic potential energy surfaces in thermodynamic equilibrium as a function of the solvent coordinate q and the separation distance r-ro between the atoms of the molecule for the overall reaction (a) and as a function of the solvent coordinate q and the distance del of the hydrogen atom to the surface for the Volmer reaction (b). At the bottom are shown the contour projection of the 3D-surfaces.

<Etot>

(a)

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Table 2 Energetics Values for the Different Steps of the Hydrogen Reaction According to the Schema Shown in the Text. Cd Au Pt

'Gbarrier 2.0 1.15 0

Cd Au Pt

6.0 1.8 1.75

Cd Au Pt

0.90 0.70 0.27

Electrode

'Greaction 0.91 0.41 –0.25 0 0 0 –0.91 –0.41 0.25

Reaction H2 ĺ 2 H

H2 ĺ 2 H+ + e–

H ĺ H+ + e–

XII. ELECTROCATALYSIS AT NANOSTRUCTURES It is well known that different nanostructures show different electrocatalytic properties. There is in the literature sufficient experimental evidence56-60 that clusters, steps, decorated steps, deposition of monolayers or submonolayers of foreign metals on different substrates can increase or inhibit the velocity of electrochemical reactions. Indeed, electrochemistry offers convenient means to generate various nanostructures such as metal overlayers, steps decorated by adatoms, or even monoatomic nanowires. The big scientific challenge is to understand, how the structure affects the chemical and physical properties of the materials, and how this in turn influences their reactivity. Although some empirical correlations have been successful and some DFT calculations for the gas phase have been extended to electrochemical systems, there is a lack of fundamental explanations. The theory that we have applied in the previous Sections to flat surfaces can be extended to nanostructures and preliminary results are promising. Figure 29 shows some of the different nanostructures for which we are performing calculations. There are several nano-scale and geometrical effects, such as electronic changes arising due to strain in the lattice of the supported metal generated from the bigger/smaller lattice constant

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of the substrate. For the reactive properties of metal electrodes the position and the width of the d bands are important. Thus, the dband position can be changed due to expansion or compression of the lattice constant. As expected, in the case of nanowires, the interatomic spacing is shorter than in the bulk metals.61 Because of the smaller number of neighbours, the d bands are much narrower than at surfaces, and show more pronounced peaks. Also the work functions are considerably larger in the wires, this effect being particularly large for gold. The large shift in the work function implies that the wires carry a negative excess charge in the hydrogen evolution region.62 As an example, Fig. 30 a-b shows the effect of the nanostructures on the electronic properties of the electrodes. The electronic structures of the d bands of Au and Pd are strongly influenced by the geometric structures of the material. These two examples are paradigmatic. Au as a flat surface is a mediocre electrocatalyst while as a wire the density of states shift up to the Fermi level. In the latter case the activation barrier for the hydrogen oxidation decreases from 0.7 eV for the flat surface down to 0.1 eV!61 as can be appreciated from Fig. 31. This effect can be also qualitatively explained in the following way: On a flat surface, the d band lies well below the Fermi level. In the wire, this is significantly shifted to higher values, and ends right at the Fermi level. Therefore, a part of the antibonding density of states of the hydrogen orbital now also extends above the Fermi level and is unfilled, so that the d band now contributes to the bonding. In the case of Pd deposited on different substrates, the largest effect occurs for the cluster. Here the density of states is strongly shifted towards the Fermi level, with a pronounced peak lying just below the Fermi level. On the monolayer, the density of states is also strongly shifted towards the Fermi level, but the effect is not quite as large as for the cluster. These shifts are qualitatively well explained by the d band model of Hammer and Nørskov:23 Since the lattice constant for the monolayer is smaller than for the bulk, the width of the d band is reduced. Since the total occupation of this band does not change, its center has to move towards the Fermi level. The hydrogen oxidation is about 2-3 order of magnitude

clusters

nanowires

submonolayers

decorated steps

monolayers

Figure 29. Different nanostructures of foreign metals deposited on different substrates.

embedded clusters

-1

0,0

0,2

0,4

0,6

-8

-7

-6

-5

-3

-2

HHF /eV

-4

Bulk 111 Surface wire

(a) Au d-band

-1

0

1

-1

0,0

0,2

0,4

0,6

0,8

-8

-7

-6

-5

-4

-2

HHF /eV

-3

Pd(111) Pd(ML)/Au(111) Pd(cluster)/Au(111) Pd(ML)/Cu(111)

(b) Pd d-band)

Figure 30. Density of states corresponding to the d-band of different nanostructures of Au (a) and Pd (b).

Uel / eV

0,8

Uel / eV )

-1

0

1

Figure 31. Contour projection of the 3D-adiabatic potential energy surfaces in thermodynamic equilibrium for the Volmer reaction as a function of the solvent coordinate q and the distance to the electrode del for a Au(111) surface and an infinite, monoatomic Au nanowire (Data obtained from Ref. 61.)

Figure 32. Contour projection of the 3D-adiabatic potential energy surfaces in thermodynamic equilibrium for the H2 overall reaction as a function of the solvent coordinate q and separation distance r-ro between the atoms of the H2 molecule for a monolayer of Pd on Au(111) and Cu(111).

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faster on a monolayer of Pd on Au(111) than on a monolayer on Cu(111) as can be observed from the contour plots of Fig. 32. A cluster of three atoms on Au(111) still shows a larger electrocatalytic activity. The last results correlate very well with experimental measurements.56 However, not only the change in the structures of the d bands plays a role in the electrocatalytic properties. There are a series of other factors, such as the interaction with the solvent and the type of reaction. For example, in the case of a reduction reaction, there is no important differences in the electrocatalytic activity of the monolayer on Au(111) and the Pd(111) surface. This differences in the electrocatalytic effect can be understood by taking into account that the optimal position of the d band is different for a reduction and an oxidation reaction (see Fig. 22). XIII. CONCLUSIONS For a long time the theory, and indeed the understanding, of electrochemical reactions had been limited to outer sphere electron transfer and the Marcus-Hush,10,11 Levich-Dogonadze19 kind of theory. The situation was so desperate that these theories were sometimes applied to reactions which were definitely not outer sphere, such as metal deposition or hydrogen evolution – with some regret; we refrain from giving a list of appropriate citations. But during the last one or two decades there has been a rapid, accelerating progress in understanding electrocatalysis. This progress can be traced to two factors: One is, of course, the availability of DFT codes12-14 combined with the ever increasing power of computers. The urgent need for better and cheaper electrocatalysts has entailed numerous DFT studies of fuel cell reactions, in particular oxygen reduction and hydrogen oxidation. Indeed, with the aid of DFT, if intelligently applied, the thermodynamics of many electrochemical reactions or reaction steps can be elucidated. However, as we pointed out in this article, DFT itself is not enough, since it cannot handle electron transfer, which involves collective solvent fluctuations. Therefore, a major development of reaction theory was required as a second factor. Its beginnings can be traced to the model for bond-breaking electron transfer initiated by Saveant,26,27 which was later generalized and formalized into the SKS Hamiltonian.15,16 These theories provide a

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framework, for the treatment of inner-sphere electron transfer. An important step in the development of these theories was the abandonment of the wide-band approximation, which is mathematically very tempting, since in many cases it allows analytical or semianalytical solutions. However, as its name implies, it is unsuited to describe the narrow d bands, which effect catalysis. For d bands, the simple model of semi-elliptic bands is very useful, since it reproduces and explains major features such as the formation of bonding and anti-bonding states between the valence orbital of the reactant and the metal d band.43-45 With hindsight, it seems a little strange that this model, which dates back to the original work of Newns39, was so late to arrive in electrochemistry. Combined with Hamiltonians like SKS, this model43-45 demonstrates very well what we think is the principle effect of catalysis, the dynamic broadening of the reactant’s density of states as it passes the Fermi level. For quantitative calculations, DFT and theories complement each other well. DFT can provide the electronic parameters for particular reactions, and can compensate the well-known shortcomings of Anderson-Newns34,39 like Hamiltonians. The first applications of the combination of DFT with theory to the hydrogen reaction, which we have presented above, are encouraging: They explain very well the different catalytic activities of the various metals, give the correct trend and order of magnitude for the rate constants. From a theoretical point of view, the major problem is the role of the solvent, which in the present version enters into two parameters: the energy of solvation of the reactant,49,53-55.61 which enters into the overall energy balance, and the energy of reorganization, which has been estimated based on experience with simple ions. With a major calculation effort, DFT should be able to provide a better basis for the reorganization energy. However, as long as one is only interested in catalysis, the role of solvent reorganization is of lesser importance. Since water interacts weakly with catalytically active metals, the role of the solvent will be about the same on all metals, and the reactivity will be determined by electronic effects alone. So far, our theory has been explicitly developed and applied only to the hydrogen reaction, and with good success. But even for this reaction there are many problems open, which can be tackled

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with the present methods. In particular, these are cases like Pt(111), on which more than one adsorbed species exist, the Heyrowski reaction, which requires an extension of the theory, and the roles of nanostructures such as steps and overlayers. In this respect, the first results reported in Section X are quite encouraging. The big problem is how to extend the theory and methods of electrocatalysis to other reactions. From a technological point of view, oxygen reduction is by far the most important reaction, since presently the performance of fuel cells is severely restricted by the inefficient and expensive catalysts for this reaction. At present, most of our understanding for this reaction is based on volcanotype correlations, first proposed by Trasatti,2 later version by Norskov et al.63 Obviously, a proper understanding of this reaction would require a detailed investigation of the most important steps, along the line that we have applied to the hydrogen reaction. That this is no simple task can be seen from a recent paper by Vassilev and Koper,64 who investigated the thermodynamics of a multitude of possible reaction steps. If one is not guided by economic necessities alone, there are other, simpler reactions, such as chloride evolution, which would be easier to investigate, and understand, within the present state of theory. ACKNOWLEDGEMENTS Financial support by the Deutsche Forschungsgemeinschaft (Schm 344/34-1,2 and Sa 1770/1-1,2) of the European Union under COST and FP7-People-2007-1-1 (ELCAT) is gratefully acknowledged. We thank CONICET for continued support. We thank our colleague Prof. A. Groß for useful discussions, and Dr. P. Quaino, Dr. A. Lundin, K. Pötting and G. Soldano. REFERENCES 1

S. Trasatti, J. Electroanal. Chem. 39 (1972) 163. S. Trasatti, Adv. Electrochem. Electrochem. Eng. and Electrochemical Engineering, Ed. by H. Gerischer and C.W. Tobias, Wiley, New York, Vol. 10, 1977 p. 213. 3 J. K. Nørskov, T. Bligaard, A. Logadottir, J. R. Kitchin, J. G. Chen, S. Pandelov, U. Stimming, J. Electrochem. Soc. 152 (2005) J23. 2

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B. E. Conway, E. M. Beatty, P. A. D. De Maine, Electrochim. Acta 7 (1962) 39. P. Sabatier. Ber. Dtsch. Chem. Ges. 44 (1984) 1911. J. Horiuti and M. Polanyi, Acta Physicochim. USSR 2 (1935) 505; H. Gerischer, Z. Phys. Chem. 8 (1956) 137. 7 R. Parsons, Trans .Farad. Soc. 94 (1958) 1059. 8 L. Krishtalik, Elektrokhimiya 2 (1966) 616. 9 W. Schmickler and S. Trasatti, J. Electrochem. Soc. 153 (2006) L31. 10 R. A. Marcus, J. Chem. Phys. 24 (1965) 966. 11 N. S. Hush, J. Chem. Phys. 28 (1958) 962. 12 W. Kohnand L. J. Sham, Phys. Rev. 140 (1965) A1133. 13 J. Perdew and A. Zunger, Phys. Rev. B 23 (1981) 5048. 14 R. G. Parr and W. Yang, in Density Functional Theory of Atoms and Molecules Oxford U. Press, NewYork, 1989. 15 E.Santos, M. T. M. Koper, W. Schmickler, Chem. Phys. Lett. 419 (2006) 421. 16 E.Santos, M. T. M. Koper, W. Schmickler, Chem. Phys. 344 (2008) 195. 17 T. Iwasita,W. Schmickler, J.W. Schultze, Ber. Bunsen-Ges. 89 (1985) 138. 18 E. Santos, T, Iwasita, W. Vielstich, Electrochim. Acta 31 (1986) 431. 19 V.G. Levich, in Kinetics of Reactions with Charge Transfer, in Physical Chemistry, an Advanced Treatise, Vol. Xb, ed. by H. Eyring, D. Henderson, and W. Jost, Academic Press, New York, 1970. 20 A. Groß, in Theoretical Surface Science – a microscopic perspective, Springer, Berlin, 2002. 21 A. Groß, in Adsorption at nanostructured surfaces, Chapter 89 of Handbook of Theoretical and Computational Nanotechnology, eds. Michael Rieth and Wolfram Schommers, American Scientific Publishers, 2006. 22 R.A. van Santen, M. Neurock, in Molecular heterogeneous catalysis, WileyVCH, Weinheim. 2006. 23 B. Hammer and J. K. Nørskov, Adv. Catal. 45 (2000) 71. 24 K. Fukui, Science 218 (1982) 747. 25 E.D. German, A.M. Kuznetsov, J. Phys. Chem. 98 (1994) 6120. 26 J.M. Savéant, J. Am. Chem. Soc. 109 (1987) 6788. 27 J.M. Savéant, Acc. Chem. Res. 26 (1993) 455. 28 M.T.M. Koper, G.A. Voth, Chem. Phys. Lett. 282 (1998) 100. 29 A. Calhoun, M.T.M. Koper, G.A. Voth, J. Phys. Chem. B 103 (1999) 3442. 30 A.M. Kuznetsov, I.G. Medvedev, J. Ulstrup, Electrochem. Commun. 2 (2000) 135. 31 D.R. Hartree, Proc. Cambridge Philos. Soc. 24 (1928) 328. 32 V. A. Fock, Z. Phys. 15 (1930) 126. 33 A.M. Kuznetsov, I.G. Medvedev, Russ. J. Electrochem. 39 (2003) 1107; I.G. Medvedev, Russ. J. Electrochem. 39 (2003) 39. 34 P.W. Anderson, Phys. Rev. 124 (1961) 41. 35 N. Kawakami, A. Akiji, J. Phys. Chem. Jpn. 51 (1982) 1143. 36 A.M. Kuznetsov, I.G. Medvedev, Electrochem. Commun. 9 (2007) 1624. 37 Y. Gohda, S. Schnur and A. Groß, Faraday Discuss. 140 (2009) 203. 38 S.G. Davison, K.W. Sulston, in Green Function Theory of Chemisorption, Springer-Verlag, London, in press. 39 D.M. Newns, Phys. Rev. 178 (1969) 1123. 40 W. Schmickler Electrochim Acta 21 (1976) 161. 41 W. Schmickler, J. Electroanal. Chem. 204 (1986) 31. 42 W. Schmickler, Chem. Phys. Lett. 237 (1995) 152. 5 6

88 43 44 45 46

47 48

49 50

51 52 53 54

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56

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Elizabeth Santos and Wolfgang Schmickler E. Santos and W. Schmickler, ChemPhysChem 7 (2006) 2282. E. Santos and W. Schmickler, Chem.Phys. 332 (2007) 39. E. Santos and W. Schmickler, Electrochim Acta 53 (2008) 6149. J. C. Slater, in Quantum Theory of Molecules and Solids, Addison-Wesley, Reading, Mass. 1972. M. Wolfsberg and L. Helmholz, J. Chem. Phys. 20 (1952) 837. Schmickler W. in Interfacial Electrochemistry, New York, Oxford University Press, 1996. E. Santos and W. Schmickler, Angew. Chem. Int. Ed. 46 (2007) 8262. J. Clavilier, R. Faure, G. Guinet, R. Durand, J. Electroanal. Chem. 107 (1980) 205. D. Eberhard, E. Santos, W. Schmickler, J. Electroanal. Chem. 461 (1999) 76. D. Eberhard, in Ph.D. thesis, University of Ulm, 1999. E.Santos, K. Pötting and W.Schmickler. Faraday Discussions 140 (2008) 209. E. Santos, A. Lundin, K. Pötting, P. Quaino and W. Schmickler. J. Solid State Electrochemistry 13 (2009) 1101, DOI: 10.1007/s10008-008-0702-4. (on line). E. Santos, A. Lundin, K. Pötting, P. Quaino and W. Schmickler Physical Review B 79 (2009) 235436. See e.g. S. Pandelov, and U. Stimming, Electrochim. Acta 52 (2007) 5548, and references therein. F. Hernandez and H. Baltruschat, J. Solid State Electrochem. 11 (2007) 877. H. Baltruschat, R. Bußar, S. Ernst and F. Hernandez, in: In-situ Spectroscopic Studies of Adsorption at the Electrode and Electrocatalysis Paul A. Christensen, Andrzej Wieckowski and Shi-Gang Sun (eds), Elsevier, 2007. R.R. Adzic, A.V. Tripkovic, and V.B. Vessovic, J. Electroanal. Chem. 204 (1986) 329. G. Garcia and M.T.M. Koper, Phys. Chem. Chem. Phys. 10 (2008) 3802. E. Santos, P. Quaino, G. Soldano, and W. Schmickler, Electrochem. Comm. 11 (2009) 1764. E. Leiva, P. Vélez, C. Sanchez, and W. Schmickler, Phys. Rev. B 74 (2006) 035422. J.K. Norskov et al., J. Phys. Chem. B 108 (2004) 17886. P. Vassilev and M.T.M. Koper, J. Phys. Chem. C 111 (2007) 2607.

3

Computational Simulations on the Oxygen Reduction Reaction in Electrochemical Systems John A. Keith and Timo Jacob Institute of Electrochemistry, University of Ulm, D-89069 Ulm, Germany

I.

INTRODUCTION

The oxygen reduction reaction (ORR) is a canonical chemical reaction due to its ubiquitous presence in combustion, corrosion, energy storage, as well as energy conversion processes. This chapter focuses on the ORR in the context of energy conversion, specifically in polymer-electrolyte membrane fuel cells or protonexchange membrane fuel cells (both conventionally abbreviated as PEMFCs). PEMFCs produce electricity through an electrocatalytic process whereby hydrogen and oxygen gases are fuels. Hydrogen intake is oxidized at the anode, and the resulting protons permeate through the polymer electrolyte membrane. Resulting electrons generate electrical current for the cell. Once protons have passed through the electrolyte, they combine with molecular oxygen and the electrons at the cathode. The ensuing ORR reaction is the key that enables PEMFCs to generate one of the ‘greenest’ of waste products possible: water.

P. Balbuena, V. Subramanian (eds.), Theory and Experiment in Electrocatalysis, Modern Aspects of Electrochemistry 50, DOI 10.1007/978-1-4419-5594-4_3, © Springer Science+Business Media, LLC 2010

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The net chemical reactions governing PEMFCs are elementary, Anode: 2 H2 o 4 H+ + 4 e– Eq = 0 V† + Eq = 1.229 V (1) Cathode: O2 + 4 H + 4 e– o 2 H2O ____________________________________________________ Net: 2 H2 + O2 o 2 H2O however, the fundamental mechanisms for these processes are not yet fully understood, and rational design of highly efficient fuel cells has been elusive. Traditional PEMFCs incorporate Pt and/or other noble metals at both anode and cathode components due to their unique catalytic properties. Unfortunately, the economics related to the scarcity of these metals is one of the key factors preventing fuel cells from being produced on a commercially large scale. Although it is the standard benchmark, the reaction rates for the ORR reaction in Pt fuel cells are slow,1 thus limiting chemical insights and experimental development. Developers of new fuel cells must address both cost and performance issues in order to create feasible fuel cells capable of assuaging the global dependence on fossil fuels. Many reviews have addressed different topics pertaining to the ORR. Here, we briefly review catalyst materials, preparation methods, and recent theoretical investigations that elucidate the fundamental ORR mechanisms. II. EXPERIMENTAL STUDIES ON THE OXYGEN REDUCTION REACTION 1.

On Unmodified Pt Single Crystal Electrodes and Carbon Supports

Well-defined single crystal surface studies have probed ORR activity.2 Rotating ring-disk electrode3,4 (RRDE) and hanging meniscus rotating-disc (HMRD)5 experiments investigated ORR kinetics on Pt, Au, and Ag single crystal surfaces in various electrolytes. The structural sensitivity and ORR reaction †

Defined as the Standard Hydrogen Electrode (SHE) potential.

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mechanisms strongly depend on the electrolyte used. Generally it is assumed that Pt electrodes under acidic media catalyze a fourelectron reduction of O2 to water, while in alkaline media different pathways coexist leading to either water or OH–.6 Furthermore, electrolytes can qualitatively change surface activities. In a highly acidic HClO4 electrolyte, the order of activity of low-index surfaces goes as Pt(110) > Pt(111) > Pt(100).7,8 In the presence of strongly adsorbing anions such as (bi)sulfate and halide ions, the order is changed to Pt(110) > Pt(100) > Pt(111).4,9 Finally, in alkaline KOH, the order is Pt(111) > Pt(110) > Pt(100).8 Besides single crystal surfaces low-content Pt alloy catalysts have been realized by generating Pt-based nanoparticles supported on larger carbon particles (Pt/C).10 Carbon support is resistant to corrosion and has acceptable conductivity and hydrophilicity.11 Among activated carbon, carbon black, graphite, and graphitized materials, carbon black is the most commonly used support because of its corrosion resistance, high conductivity, desired pore structure, and high surface area.11-13 However, recent RRDE experiments using single-wall carbon nanotubes (SWCNT) as support indicated a significantly enhanced catalytic activity for ORR compared to Pt/carbon black catalysts by showing lower onset potentials, higher electron-transfer rate constants, and improved stabilities.14,15 Carbon nanofibres (CNFs) grown on metal catalysts are also growing in popularity in catalyst development communities.16 Bezerra et al. extensively reviewed heat treatment and stability effects of various Pt/C, Pt-M/C, and C-supported Pt-free alloy catalysts, taking into account particle sizes and structural parameters.17 Appropriate heat treatment of Pt/C catalysts improves ORR activity by stabilizing the carbon support against corrosion, which in turn increases the cathode life time.18,19 Depositing mixed-metal Pt monolayers on carbon-supported metal nanoparticles20 or Pt monolayers on noble/non-noble core-shell nanoparticles21,22 leads to enhanced electrode performance. RRDE experiments on the catalytic activity of Pt-M (M = Au, Pd, Rh, Ir, Re or Os) monolayers on carbon-supported Pd nanoparticles showed that an 80:20 Pt:M ratio for the mixed monolayers performs better than commonly used Pt/C catalysts.23

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On Bimetallic Surfaces and Alloys on Different Supports

Bimetallic surfaces and alloys can be created via classical metallurgical and pseudomorphic metal film deposition techniques.24,25 Bimetallic surfaces of Co, Ni, Cr, Fe on Pt6,18,19,24,26-28 and Co on Pd, Ag, Ni, or Au29 single crystal surfaces all have increased electrocatalytic properties compared to unmodified surfaces. Spendelow and Wieckowski reviewed electrocatalytic activity of Pt and Ag alloys in acid and alkaline media.17 They found enhanced ORR catalytic activity after depositing pseudomorphic Pd films on Pt and Au surfaces in alkaline electrolytes.30,31 There is interest in depositing Pt monolayers on noble single crystal metals to eschew high fuel cell costs and provide enhanced catalytic activity. Dendrimer templating methods have built Pt nanoparticles with low size-dispersity, and RRDE measurements indicate that larger particles exhibit higher catalytic activity.32 Zhang et al. studied Pt nanoparticles and Pt monolayers galvanically deposited by displacing a Cu-UPD monolayer on Au(111), Ir(111), Pd(111), Rh(111), and Ru(0001).33-35 X-ray absorption spectroscopy (XAS) and STM studies on these catalysts concluded that a lower probability of Pt–OH formation leads to enhanced catalytic activity on Pt monolayers on Pd(111) and Pd nanoparticles. Different alloys display reactivities that, due to ion adsorption, vary with the nature of the electrolyte. In HClO4, the catalytic activity order for Pt-based alloys with cobalt and nickel was Pt3Co > Pt3Ni > Pt, whereas in H2SO4 the order changed to Pt3Ni > Pt3Co 28 > Pt. Ex situ and in situ surface sensitive studies on Pt3Ni(hkl) alloys in HClO4 solution also confirmed this, illustrating that Pt3Ni(111) is more active for ORR than Pt(111) or Pt/C catalysts. This may be because Pt3Ni(111) has more sites for O2 adsorption.36,37 One-step facile hydrothermal methods can synthesize novel nanoporous Pt/Ir38 and Pt on RuO2(110)39 catalysts for ORR. Ptfree catalysts such as Pd-Co, Pd-Ni, Pd-Cr, Pd-Ta, Co-Ni, and CoPd3 metal alloys40-43 as well as the chalcogenide Ru-S and RuSe catalysts44-46 are believed to be promising candidates. Modern studies on ORR electrocatalysts deal with nano-porous gold particles (10–20 nm) with large specific surface area that reduce

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oxygen to water via hydrogen peroxide,47 transition-metal catalysts of type M–C–N (with M = V, Cr, Mn, Fe, Co, or Ni) 48,49, or Pt1– 50 xCox (0 < x < 0.5) films deposited on glassy carbon (GC). Advances in scanning electrochemical microscopy (SECM) allow for detection of the hydrogen peroxide intermediate formed on Au, Pt, and Pd-Co/GC during the ORR.51 Noble metal deposition on single crystal surfaces, i.e., underpotential deposition (UPD), is one method to produce bimetallic surfaces and alloys, and UPD sometimes remarkably affects catalytic reduction of oxygen.17,24,30,52 Adzic has extensively studied the ORR on electrodes with UPD.35,53,54 CuUPD on Pt(111)55 displays inhibited activity in acidic solutions even when small quantities of Cu were deposited, suggesting that this surface lacks sufficient Pt active sites.24,55 Although not involving Pt, Ag-UPD on Au(111) coated with a self-assembled monolayer (SAM) of decanethiol displayed island size effects.56 HMRD measurements and STM images found two-electron reductions dominate on islands with 750 Ag atoms and fourelectron reductions dominate on islands consisting of 4000 Ag atoms. Yang et al. studied Pt-Ni bimetallic catalysts with different atomic compositions on Vulcan XC-72 carbon support prepared using carbonyl complexes.57 All Pt-Ni compositions had enhanced catalytic activity where the optimum was achieved with 30–40% Ni. Nanoparticles with different Pt:Ni ratios dispersed on carbon powder also formed a well-dispersed Pt-Ni/C catalyst and showed an increase in activity with increasing Ni content.58 Lima et al. studied Pt-M/C (M = V, Cr, and Co), Ag-Pt/C, different manganese oxides (MnO, Mn3O4, MnO2) on a carbon support, and Pt monolayers on PdCo/C59-63 using in situ XAS and X-ray absorption near-edge structure (XANES) techniques. While PtV/C had the highest activity among the Pt-M/C systems, MnO had a lower activity than MnO2 and Mn3O4.59 Strasser et al. studied the ORR activity on Pt–Cu and Pt–Cu-Co core–shell nanoparticles supported on carbon obtained by voltammetric dealloying of Cu from Cu-rich Pt-alloy precursors. They found two- and three-fold increases in activities compared to pure Pt.64 Although carbon-supported Pt and Pt-alloy catalysts show increased ORR electrocatalytic activities, the activities of most

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catalysts in terms of turn-over frequency (TOF), which represent the number of oxygen molecules reduced per time unit per active surface atom, are still lower than that of polycrystalline (pc) Pt.65 In this context, Paulus et al. evaluated the TOF of pure and Co/Nialloyed Pt catalysts (polycrystalline) with and without a carbon support.27 Without the support, they found the following TOF activity order: Pt3Co § Pt3Ni > Pt(pc). In the presence of a Vulcancarbon support, the order was PtCo/C > Pt3Co/C > Pt3Ni/C > Pt/C, where PtCo/C showed five times the activity as Pt/C. TOF data from Pt and Pt-alloys (without carbon-support) showed a 10× increase in activity compared to corresponding catalysts with carbon-support.65 Hence, it appears most meaningful to compare literature values related by mass as well as specific activities. Finally, Pt-free cathode catalysts are cheaper than Pt-based catalysts even though they have less TOF activities than Pt(pc).65,66 III. THEORETICAL STUDIES ON THE OXYGEN REDUCTION REACTION Understanding the ORR mechanism requires awareness of different electrocatalysts but also the nature and the coverage of reaction intermediates, features that are not usually observable through spectroscopy. Computational approaches addressing the ORR provide important insights regarding electronic structure and geometries of reaction intermediates and adsorption energies at metal/gas or metal/liquid interfaces. A major hindrance is simulating solvents (water in particular) and an electrode potential. So far, few reviews report over-arching progress understanding the ORR mechanism made from density functional theory (DFT), ab initio molecular dynamics (AIMD), or classical molecular dynamics (MD).67-69 These reviews summarize adsorption geometries of atomic and molecular oxygen on various single crystal surfaces of Pt, Ni, Pd, Cu, Ir, or Au and different alloys (e.g. Pt3Fe or Pt3Co), as well as their reduction mechanisms in acidic and basic media. Nevertheless, much more work can be discussed. Given the lack of accounts on this important subject, we review recent trends in quantum chemical simulations on the ORR. We focus primarily on studies on various metal surfaces such as

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single crystals, bimetals, transition metal complexes and the use of these methods in identifying improved electrocatalysts. Since the early 1950’s, theoretical studies have reported O and O2 adsorption energies on different metal surface sites with the intention of obtaining generalizable conclusions. Indeed, mechanistic studies on the ORR mainly focus on the stability of reaction intermediates since activation energies are often considered too demanding for ab initio calculations. Griffith,70 Pauling,71 and Yeager72 attempted to find a correlation between the binding energy of oxygen with the catalytic activity of particular metals. Hammer and Nørskov extended this motivation further to argue that metal d-band overlap with oxygen valence states determine catalytic behavior.73 Xu et al.’s calculations have revealed that the stronger a material binds atomic oxygen, the more effective it will be in breaking apart molecular oxygen, which is often used to screen oxygen reduction catalysts.74 1.

Mechanistic Studies on the ORR

Anderson and Albu investigated an outer-sphere oxygen reduction with ab initio calculations,75 whereby the electrode was assumed to not directly interact with the intermediate species. They proposed four one-electron transfer steps involving proton transfer from the electrolyte as: O 2 (g)  H  (aq)  e  HO2 (aq)  H  (aq)  e  H 2O 2 (aq)  H  (aq)  e  HO(g)  H  (aq)  e

o o o o

HO 2 (aq) H 2O 2 (aq) HO(g)  H 2O(aq) H 2O(aq)

(2)

Nørskov and coworkers have determined the stability of reaction intermediates (mostly oxygen) on many single crystals and alloys of noble metals.76 Energy corrections due to solvent, zero-point energy, and entropy effects afforded experimentally relevant free energies for each mechanistic step. Their calculations treated the electrode potential with the same approach as Anderson, whereby each proton transfer was coupled with an energy shift of –eU (U being the potential difference between

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electrode and counter electrode). This study simulated the electrolyte either by single water molecules (in case of low coverage) or water bilayers (in case of high coverage). They obtained free energies of intermediates in both the ''dissociative'' (Eq. 3) and ''associative'' (Eq. 4) reaction pathways from periodic DFT calculations. Dissociative mechanism: 1 2

O2 ad O  H   e

o O ad o HO ad

HO ad  H   e

o H 2O

(3)

Associative mechanism:

O2   O ad 2 H e   HO ad 2 H e   ad O H e HO ad  H   e 

o o o o o

O ad 2 HO ad 2 H 2 O  O ad HO ad H 2O

(4)

Very stable intermediates reside near the equilibrium potential for adsorbed oxygen and hydroxyl, and coupled proton/electron transfer to Oad and OHad dominates the overall reaction kinetics. In step 3 of Eq. (4), hydrogen peroxide may also form instead of water, and this ''associative'' hydrogen peroxide mechanism is believed to dominate for most noble metals. Recently, the Nørskov group applied a variable external electric field in their periodic DFT calculations to study the effects of a local electric field present in the electric double layer.77 Although the surface electric fields should be high (in the range of –0.5 to +0.5 V·Å–1), they observed minor changes in the adsorption energies of O, OH and OOH on different metal surfaces. This led to a small increase in the overpotential of the ORR without changing the order of the catalytic activity of the metals significantly.

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Greeley and coworkers estimated the ORR kinetics on (111), (100), and (211) surfaces of transition metal groups VIII–XI using periodic DFT and also studied their particle size effects in the ORR.78 For most metals (with the exception of Ir) the unreconstructed (100) faces showed similar or higher activities than (111) surface facets. In particular, Pt(100) displayed a comparable activity to Pt(111), which is contradictory to the results mentioned in Section II.1 that reported Pt(111) has higher ORR activities than Pt(100) in HClO4 and KOH8,30 but a lower activity than Pt(100) in H2SO4.4 This work also shows the observed increased activity of Au(100) with respect to Au(111) consistent with the experimental alkaline solution results.79 Furthermore, nanosteps (each modeled by a (211) surface) have lower ORR activity than the planar surfaces (except Au). This is usually attributed to the strong binding of O and OH reaction intermediates to the surfaces. Wulff-type models of Pt and Au clusters were used to investigate particle size effects, and Greeley concluded that the ORR activity of Au nanoparticles increases with decreasing particle size while Pt nanoparticles show the opposite effect. Combinations of RRDE experiments and DFT cluster studies of pure and N-doped graphite investigated the effects of various supports on the ORR.80 Experiments showed that the onsetpotential of N-doped carbon was 0.5 V (with respect to the SHE) but was 0.2 V for untreated carbon. Graphite simulation models used 4 and 14 hexagonal rings terminated by H atoms. The calculations illustrated that the carbon radical sites formed adjacent to substitutional N atoms (and far from sheet edges) permitting O2 electroreduction to hydrogen peroxide via an adsorbed OOH adduct. Weak adsorption of OOH on the Hterminated graphite edges likely cause untreated graphite’s lower activity. Recently, Shao et al. proposed superoxide (O2–) formation as the first step of the ORR on Pt films in alkaline solution (NaClO4 with pH=11) by analyzing spectral data of surface-enhanced infrared reflection absorption spectroscopy with attenuated total reflection (ATR–SEIRAS).81 This was further supported by Zhang and Anderson,82 who performed DFT cluster calculations for the ORR on Pt(111), Pt(100), and unreconstructed Pt(110). They

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found a higher binding energy for O2– than for neutral O2. Their simulations treated solvation of H2Oaq and (OH–)aq explicitly with two hydration shells. The concluding mechanism for the ORR in base electrolytes was proposed as:  O ad 2 e - ad (O 2 ) (O- )ad  H 2 O aq O ad  H 2 O aq  e OH ad  H 2 O aq  e

o o o o o

(O-2 )ad O ad  (O- )ad OH ad  (OH - )aq OH ad  (OH - )aq H 2 O ad  (OH - )aq

(5)

This mechanism received even more support from the calculated activation energy for superoxide formation, and corresponded well to the experimental observations for different Pt surfaces. 2.

Treating Electrolyte Effects

Computer simulations of metal/electrolyte interfaces are a great challenge. Explicit water molecules bring new degrees of freedom for atoms and electrons, and accurate and physically realistic simulations require solvent dynamics. Taylor and Neurock reviewed recent work on metal/water interfaces focusing on water structure and other interactions with electrode surfaces.83 Filhol and Neurock studied changes in the atomic structure of metal/water interfaces and reactivity as a function of an applied potential.84 In their ab initio molecular dynamic (AIMD) simulations, they calculated free energies for the adsorption of water, hydride, and hydroxide on Pd(111). They modeled the electrode potential by charging the metallic slab with a pre-defined number of excess electrons, which were compensated either by a homogeneously distributed background charge or by positioning single counter-ions at a defined distance from the surface. By this approach, the overall neutrality of the systems was maintained. In order to reduce computational time, a fixed cluster of hexagonally packed molecules represented interfacial water during MD simulation of the intermediates.

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Hartnig et al. investigated reactions and processes at electrochemical interfaces using classical MD approaches (forcefields) to treat solvent reorganization and AIMD simulations to obtain the water–vapor interface structure.67 They found solvent reorganization as a primary contribution to the activation barrier in simulations of the first electron transfer step of the ORR (i.e., superoxide formation) where direct interactions between O2 or O2– and the electrode surface were neglected.85 Additional DFT studies on OH–H2O overlayers on Rh(111) concluded fast proton hopping between adjacent water and surface-bound OH molecules plays a major role in the ORR.67 Wang and Balbuena performed Car–Parrinello molecular dynamics (CPMD) simulations for ORR on Pt(111).86 They used a three-layer slab of Pt (12 atoms per layer) in a 9.58 u 8.30 u 19.22 Å orthorhombic supercell with hydrated hydronium (H3O+(H2O)2) in the electrolyte region. Evidence suggests the first reduction step of oxygen requires a proton transfer from water leading to an OOH intermediate. OOH then undergoes reduction to H2O by following both the series (via formation of H2O2) and the direct (i.e., dissociation to O and OH) mechanisms simultaneously. Furthermore, adsorption and decomposition of OOH and H2O2 on several small to medium-sized Pt clusters (Pt3, Pt4, Pt6, and Pt10) were investigated with standard DFT calculations utilizing an explicitly solvated hydronium H3O+(H2O) 3.87 As the last contribution in this Section, DFT cluster studies and AIMD methods considered the role of water as proton carrier in the OOH formation step on Pt(111)88 and Au surfaces.89 These works considered H5O2+ in the presence and absence of surrounding water molecules. 3.

Simulations on Bimetallic Alloy Surfaces

Bimetallic alloys have modified electronic structures on the surface, and so adsorption energy changes of certain intermediates may enhance the overall catalytic activity. Zhang et al. have performed periodic DFT calculations on a Pt monolayer on Au(111), Rh(111), Pd(111), Ir(111), and Ru(0001) substrates.34,90 Zhang and coworkers have also undertaken simulations on mixed Pt-M (80:20) monolayers (M = Ir, Ru, Rh, Pd, Au, Re, or Os)

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deposited on Pd(111).23,91 Their studies focused on atomic oxygen’s binding energy, activation energies for O2 dissociation, and OH formation. The Pt monolayer on Au(111) [PtML/Au(111)] has the highest binding energy, thereby facilitating the bondbreaking step and inhibiting the OH formation. Low oxygen binding energies on PtML/Ru(0001), PtML/Ir(111), and PtML/Rh(111) enhance the bond formation step but not the bondbreaking step. A comparison of activation energies for these two reactions determined that the PtML/Pd(111) catalyst represents the optimum nature for both reaction steps, indicating an enhanced ORR activity.34 Destabilization of Pt–OH in the presence of oxygenated metal surfaces and changes in the adsorption and dissociation of O2 accounted for the activity of mixed Pt-M monolayers deposited on Pd(111).23,90 DFT calculations showed a strong oxygen binding for systems with M = Os or Re, thus suggesting a low probability of Pt–OH formation and enhanced ORR activity.23 The electrocatalytic activity of Pt-based bulk alloys and its dependence on its preparation method are important topics in ORR studies. Pt-M alloys prepared by conventional metallurgy are mostly a 3:1 ratio of Pt and another metal. On the other hand, Pt-M alloys prepared by either an appropriate pre-treatment under UHV conditions followed by mild sputtering with a 0.5 keV beam of Ar+ ions or by annealing to 1000 K have different compositions. Regarding the surfaces of these alloys, Stamenkoviü et al. found that low energy ion scattering (LEIS) spectra show almost exclusively Pt in the topmost layer and a Pt depletion in the second layer (as a result of the Pt surface segregation), leading to the socalled Pt-skin surfaces.28,36,37,92 Nørskov et al. also contributed to different ex situ and in situ experiments with DFT to investigate the catalytic activity of (111) surfaces of Pt3M alloys with M = Co, Ni, Fe, and Ti.28,36,92 Their simulations used four-layer slabs and assumed the first layer was always pure Pt and the second layer was always a 50:50 composition. They treated the electrolyte as adsorbed waterbilayers and the influence of an electrode potential by shifting the electrode Fermi-energy. Calculations suggested slightly weaker oxygen binding in a modified surface electronic structure leads to enhanced catalytic activity for these alloys compared to pure Pt. Similar calculations found a comparable behavior for the ORR

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activity of Pt-skin surfaces for Pt3Co(111) and Pt3Fe(111)74 as well as for Pt3Cr(111) alloys.93 Ma and Balbuena recently calculated segregation energies of Pt-skin on various Pt3M(111) surfaces (M = Ag, Au, Co, Cr, Cu, Fe, Ir, Mn, Mo, Ni, Pd, Re, Rh, Ru, Ti, and V).94 They found that the sub-surface atomic structure as well as atomic size and magnitude of the surface energy leads to surface segregation. Furthermore, these calculations show that electronic effects and not geometric effects are what cause enhanced ORR activity on Pt-skin surface: Pt3Ni(111) and Pt3Co(111). So far, various studies focused on developing catalyst materials with improved ORR activity, but only few reported the stability and durability of ORR catalysts. The study of accelerated durability tests (ADT) in conjunction with electron microprobe analysis (EMPA), LEED, and XRD techniques on Pt-based alloys65,95-101 observed 3d metal dissolution, diffusion of 3d metals into the membrane, formation of bulk oxides on the surface, and migration and agglomeration of Pt. Yu et al. compared the durability and activity of PtCo/C with Pt/C catalysts.101 Through determination of the electrochemically active surface area, mass, and specific activities with respect to the potential cycles, they found the overall cell performance of PtCo/C is higher than that of Pt/C. They also concluded that the observed dissolution of Co has no severe impact on the cell performance or membrane conductance. Additionally, Popov et al. studied the stability of PtxM/C for x = 1,3 and M = V, Fe, Ni, Co.97,98 ADT analyses revealed that Pt/C has the lowest activity when compared to Ptalloy catalysts, and that the metal dissolution is lower for a Pt:M ratio of 3:1 than compared to a 1:1 ratio. Also, Pt-Ni showed a lower dissolution rate than the other considered Pt-M alloys. Menning et al. performed periodic DFT calculations on the stability of Pt-based alloys through estimates of oxygen binding energies on surface and subsurface monolayers of Ti, V, Cr, Mn, Fe, Co, and Ni on Pt(111).102 This work did not include the influence of an acidic electrolyte. Simulations used three-layer slabs with 0.25 ML oxygen and the topmost layer and adsorbates were free to relax. They found that oxygen binding energy on metal alloy surfaces is less when 3d metals reside in the subsurface rather than when metals are on the top surface layer. However, most of the subsurface alloys are thermodynamically unstable after

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oxygen adsorption, leading to a segregation of the subsurface metal to the surface. The calculated diffusion barrier into the surface in an oxygen environment suggested better Pt-based bimetallic catalysts will require identification of both subsurface alloys with low oxygen binding energies and thermodynamically stable O/Pt-M-Pt(111) structures. This should be possible by identifying an alloying metal that has comparable rates for segregation to the surface and for diffusion into the subsurface. AES measurements confirmed that among the considered 3d transition metals, Co is most likely to fulfill this requirement and also shows a partially enhanced ORR catalytic activity. Further studies on Pt-M-Pt(100) surfaces concluded that Pt-M-Pt(100) systems with 0.5 ML of atomic oxygen have higher stabilities than Pt-M-Pt(111) structures.100 4.

Simulations on Low-Pt Electrocatalysts

Simulations on PtxPdy clusters and Pd monolayers on different metal surfaces have provided insight into low-Pt and Pt-free catalysts. Calvo et al. performed DFT calculations on finite PtxPdy clusters (with x + y = 10) focusing on the effects of geometry and local electronic structure on ORR.103 The Pt3Pd7 cluster is thermodynamically most favorable for the ORR in terms of reaction energies of OOH and water formation. The activity of Pd monolayers deposited on Ru(0001), Rh(111), Ir(111), Pt(111), and Au(111) surfaces were investigated with periodic DFT calculations.104 From calculated d-band center shifts, the following order in the ORR activity was proposed: Pd/Ru(0001) < Pd/Ir(111) < Pd/Rh(111) < Pd/Au(111) < Pd/Pt(111). A promising alternative to Pt catalysts in PEMFC’s is Pd mixed with other carbon supported transition metals. Bard et al. proposed a thermodynamic rule for designing such binary electrocatalytic materials where the bonding between two metals (each capable of dissociating O2 or reducing adsorbed atomic oxygen) should form a good bimetallic catalysts.29 Scanning electrochemical microscopy (SECM) and RRDE in conjunction with DFT calculations then examined the ORR activity of each Pd, Ag, and Au alloyed with Co and deposited on glassy carbon (GC).29,105 The SECM measurements showed that increased catalytic activity was found with 10–20% of Co to Pd, Ag, or Au.

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Periodic DFT calculations provided the O2 binding energy and dissociation barrier on Pd-Co/C.105 Improvements to this system have been attempted by probing lattice-strain and surface-ligand effects on Pd alloys.106 Lastly, Wang and Balbuena calculated free energies of intermediates for the four one-electron steps (as given in Eq. 2) on 17 metals from groups V to XII using DFT with finite clusters and modeling the solvated proton as H3O+(H2O)3.107 They also proposed a simple thermodynamic rule to design new bimetallic catalysts based on relative free energies of two key ORR mechanistic steps. In summary, in an MM’3 catalyst, if M promotes M-OOH formation and M’ promotes the cumulate free energy change of the remaining ORR steps, MM’3 has a high chance of being an efficient ORR catalyst. Based on this rule, Ma and Balbuena explained the selective and efficient catalytic activity of the Cytochrome-c-oxidase metalloenzyme, in which Fe and Cu were the active centers for ORR.108 We now continue with a summary of related work done within our group. IV. METHODS 1.

DFT Calculations

(i) Finite Systems

QM simulations on finite clusters of atoms used the Jaguar program suite.109 Simulations on the water-formation mechanisms used spin restricted density functional theory (DFT) with the B3LYP gradient-corrected exchange–correlation functional110,111 and included zero-point-energy (ZPE) corrections and implicit solvation when noted. Simulations on deprotonation utilized no ZPE corrections. The 60 core electrons in each Pt atom (1s – 4f) were treated with the Hay and Wadt core–valence relativistic effective-core potential (ECP),112 leaving 18 valence electrons to be treated with the LACVP** basis set. The other elements (H and O) were described with the all electron 6-31G** basis set. We found additional diffuse functions on the highly electronegative oxygen atom have only minor influence on the equilibrium

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adsorption energy (0.015 eV) and overall charge transfer (0.02 e–).113 Furthermore, usage of a density functional without exact exchange (BLYP) for metallic platinum has only a minor impact (0.057 eV) on the adsorption energy of O on Pt(111). We used a 35 atom Pt cluster to study water formation reaction mechanisms. We established this model gives cluster-size converged binding energies for the adsorption of atomic oxygen113 in agreement with experimental and theoretical (periodic slabcalculations) results for low oxygen coverages. Since the electronegative O is the most likely species to perturb the surface electronic structure, convergence for other intermediates along the oxygen reduction reaction was expected. The reliability of this model has already been demonstrated for the adsorption of various hydrocarbons.114 Geometry optimizations allowed adsorbates and the central four Pt atoms of the first layer to optimize completely while keeping all other Pt–Pt distances fixed to the bulk crystal value of 2.775 Å. By doing so, we minimized unphysical border effects to reproduce the (semi-)infinite Pt(111) surface. This model includes major surface relaxation effects, which were significant for some adsorbates. (ii) Periodic Systems

We calculated surface phase diagrams of Pt(111) using SeqQuest,115,116 a periodic DFT program with localized basis sets represented by a linear combination of Gaussian functions. We used the PBE117 generalized gradient approximation (GGA) exchange–correlation functional and a standard (non-local) normconserving pseudopotential118 that replaced 62 core electrons of each Pt, leaving the 5d- and 6s-electrons in the valence space and invoking a non-linear core correction.119 We optimized the remaining basis sets to a level analogous to a double-zeta split valence basis set plus polarization. Calculations with a plane-wave method tested for inaccuracies coming from localized basis sets on the most relevant adlayer structures on pure Pt(111).‡ We found ‡

Calculations used the CASTEP code120 with a plane-wave basis set (Ecutoff = 340 eV) and Vanderbilt-type ultrasoft pseudopotentials. The surface model as well as the k-point mesh was as described in Section IV.1.ii.

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almost identical binding energies. In these simulations, we modeled the pure Pt(111) surface with a six-layer slab. Geometry optimizations had the lowest three layers fixed at the calculated bulk-crystal structure. The (1u1)-unitcell used a 10u10 Monkhorst–Pack k-point mesh. 2.

Thermodynamic Considerations

Interfacial structures in thermal equilibrium with a bulk electrode and a bulk electrolyte have the lowest interfacial free energy defined as:

J T , ^ai `, I e , Is

º 1ª «G T , ^ai `, ^N i `  N i P~i T , ai , Ii » (6) A« »¼ i ¬

¦

The equation is dependent on the contact area, A, the Gibb’s free energy of the interface, G, the number of atoms (or molecules) of the ith-species, Ni, and the corresponding electrochemical potential of the reservoir at temperature T, activity ai and ~ (T , a , I ) . The sum over i involves electrostatic potential Ii, P i i i metal atoms (me), excess electrons (e) at the electrode, anions (a), cations (c), and neutral compounds (n). With this sumation expanded, the interfacial free energy now takes the form:

J T , ^ai `, I e , Is

1 >GT , ^ai `, ^N i `  N n P~n (7) A ~ ~ ~ ~  N me P me  N e P e  N a P a  N c P c @

As described in Refs. 1,121, and 122, an exact evaluation of the interfacial free energies is possible in principle, but it requires self-consistent modeling of the entire interfacial region, whose simulation cell length might range up to several 100 Å. Since this is beyond the capacity for modern ab initio approaches, we reduce our model to the electrode and the adlayer only and assume a constant influence of the electrolyte. This allows us to neglect its presence when studying relative stabilities of two similar systems

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of atoms and molecules. Consequently, the interfacial free energy then reduces to



J T , a H 2O , a me , 'I



>



1 bulk G T , a H 2O , a me  N me g me (T , a me ) A (8)  N O P H 2O T , a H 2O  2e ˜ 'I







@

where the last term comes from the assumption that every oxygen that adsorbs on the surface originates from a water splitting reaction, allowing us to reference the electrostatic potential of the electrode Ie to the reversible hydrogen electrode (RHE, IRHE as 'I = Ie – IRHE). G is thus the sum of free energies associated with the bulk is the Gibbs energy of the bulk electrode) electrode surface ( g me and the adlayer (one of the reservoirs the system should be in contact with). We assume the second reservoir to be mainly water and determine its properties from the chemical potential of the water present in the electrolyte:



P H 2O T , a H 2 O







§ a H 2O · ¸ 0 ¸ a ¹ ©

P H 2O T , a 0  k BT ln¨¨

(9)

Here, the first term on the right side denotes the standard chemical potential at temperature T and a water activity aH2O = 1. This expression allows us to evaluate the interfacial free energies from DFT calculations since all relevant quantities can be deduced from first principles. From these, we can obtain the electrochemical phase diagram. V. RESULTS AND DISCUSSION

Prior to investigating the oxygen reduction reaction itself, the morphology and composition of the catalyst surface must be better understood under realistic conditions. In electrochemical cells, the electrolyte surrounding the electrodes is mainly water. Under certain potential conditions, water might dissociate and lead to oxygen or OH adsorption. At higher electrode potentials, water may even cause a surface- or bulk-oxide to be formed. We first

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evaluate the corresponding electrochemical (a,T,'I)-phase diagram of Pt(111) in contact with an aqueous electrolyte. After specifying at which potential regions ''clean'' Pt-electrodes can be expected, we then describe DFT calculations on Langmuir– Hinshelwood and Eley–Rideal-type reaction pathways for the ORR. 1.

Electrochemical Phase Diagram

Experimental cyclic-voltammetry (CV) can identify processes occurring at electrode surfaces as function of the electrode potential and distinguish pronouced potential regions. For the electro-oxidation and oxide growth of Pt electrodes, distinct features can be assigned to initial interface charging, surface oxidation, and oxide formation at higher positive electrode potentials.141-143 Although experimental techniques such as CV, electrochemical quartz-crystal nanobalance (EQCN), or Auger electron spectroscopy (AES) help provide a better understanding of structural changes, even for the standard Pt electrode in aqueous H2SO4, there is still an ongoing debate regarding the adsorbate layer and the electrode structure. In electrooxidation, water molecules close to the electrode surface orient their dipoles according to the excess surface charge below an electrode potential of § 0.8 V. In this range the waters do not dissociate. Above this potential value, the onset of surface oxidation starts accompanied by a charge transfer. This leads to a finite current density in the corresponding CV-curve. Whether this is caused by adsorption of OH– or O2– is still under debate. While the presence of OH is commonly assumed,123,124 recent EQCN and CV measurements in H2SO4 by Jerkiewicz et al.125 show a molecular weight of the adsorbing species to be 15.8 g·mol–1 and concluded the presence of atomic oxygen only. Surface-oxide formation begins after an adsorbate layer of oxygen or an O-containing species on the electrode surface forms at more positive potentials (> 1.1 V). After time a bulk-oxide continues growing. While different electrochemical techniques126129 show evidence for oxide formation, the exact structure and thickness of this oxide is still unclear.124,125,130,131 The common view is that oxide-growth first begins with the formation of a thin

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layer of Pt-O, onto which a PtO2-composed oxide continues growing. In order to compare stabilities of different oxygen overlayers and evaluate the electrochemical surface phase diagram of Pt(111) in contact with an aqueous electrolyte, we performed periodic DFT calculations on the energetics and structures of oxygen adsorption at different coverages. Since the electrode is present in the solid phase, we assume the temperature and activity dependence of G to be small, and the contributions from configurational and bulk vibrational entropy to G will be mostly compensated by the g Pt term on the right side of Eq. (7). Therefore, the DFT-energies, which are obtained at T = 0 K, can be used instead. This finally leads to the (T, a, 'I)-phase diagram shown in Fig. 1. The left plot shows the interfacial free energy J of different adsorbate overlayers as function of the water chemical potential 'PH2O and the electrode potential (referenced to RHE). The most stable structures have the lowest interfacial free energy, and so the right figure shows the view to the bottom of the phase diagram. Each colored area corresponds to a different stable adsorbate structure. According to Eq. (8), 'PH2O can be related to temperature and activity. For a water activity of aH2O = 1 (ideal solution), the corresponding temperature scale has been added to the right plot of Fig. 1 and T = 298 K has been marked by a dashed horizontal line. This line crosses the 'I = 0 V line (dashed vertical line) in the area that corresponds to the clean Pt(111) surface with no oxygen adsorbed. Maintaining these aH2O- and T-conditions and increasing the electrode potential shows that from 0.95 to 1.20 V, a (2×2) oxygen overlayer structure with 0.25 ML coverage is dominant. When the electrode potential exceeds 1.20 V, our calculations predict the formation of Pt bulk-oxide. As discussed before, the experiments by Jerkiewicz et al.125 found the surface oxidation to occur from 0.85 to 1.1 V, followed by the oxide-formation above 1.1 V. The agreement between our phase diagram and the CVmeasurements is surprisingly good, but one must consider the ramifications of our simple interface model and that polycrystalline Pt had been used experimentally. The agreement might be due to the absence of specific ion adsorption on the

shows the view to the bottom. The temperature scale corresponding to aH2O = 1 (p = 1 atm) is given on the right side of the phase diagram.

and the electrode potential 'I (referenced against RHE). The figure on the right interfacial free energy J as function of 'P H 2O = P H 2O  EHDFT 2O

Figure 1. (a,T,'I)-phase diagram for the electrochemical oxidation of Pt(111) in an aqueous electrolyte. The figure on the left shows the

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electrode. Moreover, there might be a kinetic barrier to form the oxide, leading to higher oxygen-coverages prior to oxideformation and requiring higher electrode potentials to initiate this process. Jerkiewicz et al. performed their experiments with pure Pt electrodes and a H2SO4 electrolyte. However, carbon-supported Pt particles in HClO4 or realistic PEM-fuel cell systems show oxideformation at even lower electrode potentials, i.e., 0.7 V for Pt/C in HClO499 or ~0.8 V for Pt-black.65 The same was observed for Pt(111) in HClO4, where oxide formation occurs already at 0.6 V.8 The range of experimental values show the potential value at which oxidation or oxide formation occurs strongly depends on the structural nature of the electrode (i.e., supported or non-supported, single crystal or polycrystalline, etc.) as well as the nature of the electrolyte (i.e., composition, concentration, etc.). Consideration of all points makes direct comparison between theory and experiment difficult. Only oxygen adsorption has been studied here, and this phase diagram is only valid for electrode potentials where no H is adsorbed or hydride is formed on the surface. After having specified the electrode potential region at which the Pt(111) surface is not oxidized, we use this surface model to study the water formation reaction. 2.

Oxygen Reduction Reaction (ORR)

As mentioned in the introduction of this chapter, water formation from hydrogen and oxygen is one of the most important reactions occurring in fuel cells. At the cathode, four protons react with molecular oxygen to form two water molecules (see Eq. 1). Although possible intermediates only consist of hydrogen and oxygen, the exact reaction mechanism is still unknown. A realistic electrochemical system (such as a fuel cell) is an extremely complex system where catalytic reactions occur in a multicomponent environment and under conditions of finite temperature, pressure, and electrode potential. We now discuss the idealized case of platinum catalyzed hydrogen combustion in oxygen:

Computational Simulations on the Oxygen Reduction Reaction

H2 

1 O 2 o H 2O 2

111

(10)

which is interesting132 but still far from the realistic electrochemical system. So far no conclusive theoretical description of the electrode/electrolyte-interface structure or the electrode potential shape exists. Therefore, instead of applying simplified models and/or non-justified approximations, we temporarily restrict ourselves to studying the above reaction. To study pathways for reaction (10), we considered all possible intermediates separately: H, H2, O, O2, OH, OOH, H2O2, H2O. For each compound, we evaluated stable surface sites and binding energies on Pt(111), modeled by a finite 35 atom threelayer cluster surface model (see Fig. 2), and then obtained barriers for dissociation processes of the adsorbed molecules.133,134 We found transition states by optimizing structures around the single fixed coordinate corresponding to dissociation. With this data, as summarized in Table 1, we drew a picture of different pathways for the gas-phase reaction and showed their corresponding ratelimiting steps (see Fig. 3). Two major pathways can be distinguished. First, O ad can first 2 dissociate on the surface generating two Oad atoms and then react with Had atoms to form water. Second, the O ad molecule can react 2 . After the O–O with hydrogen to first form OOHad or then H 2 O ad 2 bond in these species breaks, the remaining species can form water. All pathways appear to be influenced by the presence of the electrolyte. In the following we first discuss the Langmuir– Hinshelwood-type mechanisms, where all reactions first adsorb on the surface, followed by Eley–Rideal-type mechanisms, where hydroniums in the electrolyte are the source of protons. (i) O2 Dissociation

Starting with molecular H2 in gas phase and the plain Pt surface (Pt35 cluster), we find adsorption of H2 on the surface is effectively barrierless.135 Adsorption lowers the energy of the whole system by 0.66 eV, or 0.33 eV per ½ H2. This value is twice

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Figure 2. Top- and side-views of the different geometry-optimized intermediates adsorbed on the Pt35 cluster. Dark spheres on the surface are oxygen atoms, and smaller light spheres are hydrogen atoms.

the binding energy of atomic hydrogen (calculated 2.60 eV, per H atom) minus the dissociation energy of gas-phase H2 (calculated = 4.54 eV, experiment = 4.48 eV). Since hydrogen has a low diffusion barrier of approximately 0.05 eV136 on Pt(111), we assume Had will always be present on the surface when hydrogen is available in the reaction.

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Table 1 Binding Energies and Dissociation Barriers for All Studied Molecules Before and After Adsorption on the Pt35 Cluster. Gas Phase Energies Without Zero Point Energy, and Those Energies with Zero Point Energy and Water Solvation are Reported. System

Ads. site

Ebind [eV]

Ediss [eV]

H2g,aq

–

no ZPE –

with ZPE –

solvated –

no ZPE 4.84

with solvated ZPE 4.81 4.54

O2g,aq

–

–

–

–

4.95

4.88

5.46

OHg,aq

–

–

–

–

4.57

4.31

4.83

OOHg,aq

– –

– –

– –

– –

OO–H: O–OH:

2.48 3.04

2.69 3.32

HOOHg,aq

– –

– –

– –

– –

H–OOH: HO–OH:

3.64 2.36

4.00 2.48

–

H2Og,aq

–

–

–

5.24

4.89

5.42

Pt35–H

top bridge

2.73 2.64

2.60 2.56

3.09 3.43

– –

– –

– –

Pt35–O

fcc hcp

3.24 3.03

3.14 2.96

4.40

– –

– –

– –

Pt35–O2

bridge fcc tilted

0.49 0.31 0.06

0.34 0.17 –0.07

1.31 1.64 0.85

1.34 1.03 0.22

1.30 1.00 0.22

0.81 1.11 –0.11

Pt35–OH

top

2.06

1.91

3.03

1.90

1.73

1.15

Pt35–OOH no-ring 1.03 ring 0.75

0.79 0.58

2.18 2.07

OO–H: O–OH: OO–H:

1.03 0.74 0.36

0.84 0.67 0.26

0.72 0.62 0.81

0.41

–0.07

1.36

H–OOH: 0.94 HO–OH: 0.46

0.76 0.35

0.96 0.43

0.60

0.41

0.83

1.29

1.13

0.86

Pt35–OOH bridge Pt35–H2O

top

When O2 adsorbs, three stable binding geometries are found: a bridge-site (BE = 0.34 eV), an fcc-site (BE = 0.17 eV), and an ontop tilted-site (BE = –0.07 eV) (see Fig. 2), where the latter configuration is only destabilized by ZPE effects. The most stable

Figure 3. Reaction mechanisms for gas phase O2ad dissociation, OOHad dissociation, and H2O2ad dissociation on a Pt(111) surface. Relative energies are in eV and include zero-point energy contributions. H atoms may freely diffuse, individual Oad atoms reside on fcc sites, and all other species reside on on-top sites.

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configuration has Oad bound at a bridge position, where both 2 oxygens use a doubly-occupied p-orbital to form weak surface then dissociates, but each adsorbed O2 structure yields bonds. Oad 2 a different dissociation barrier. The dissociation barrier at the bridge position is highest (1.30 eV), followed by the fcc position (1.00 eV), and the lowest dissociation barrier is found for the tilted (0.22 eV). This last structure is comparable to bridge-bound Oad 2 , except that its tilted structure allows the O=O double bond to Oad 2 form a donor–acceptor bond to an adjacent Pt atom. Although Oad 2 most likely binds at a bridge surface site, the tilted configuration is still 0.88 eV lower than the bridge site dissociation barrier. Thus, may undergo a structural change toward the tilted Oad 2 configuration while dissociating, in agreement with calculations by Eichler et al.137 This yields a drastically lower dissociation barrier. Instead of 1.30 eV, the new barrier is 0.63 eV, a value in better agreement with the 0.38 eV barrier measured by Ho et al.138 The final system contains two adsorbed oxygen atoms located in threefold sites: Ohcp/Ohcp, Ofcc/Ohcp, or Ofcc/Ofcc. These simulations show dissociation always leads to two oxygen atoms in nonOad 2 adjacent three-fold positions (separated by two lattice constants), also in excellent agreement with the STM experiments by dissociations occur at different Ho.139,140 When multiple O ad 2 surface positions, the final structure corresponds to a p(2u2) overlayer, exactly what was obtained from our phase diagram (see Fig. 1), as well as what is observed experimentally.141 Finally, this result allows us to treat both oxygen atoms as nearly independent adsorbates. Therefore, we will neglect the remaining O–O interaction of both dissociation fragments. Since the barrier to hop from hcp to a fcc site via a bridge position is only 0.24 eV, we expect most atomic oxygen will equilibrate into fcc sites after a finite time. The next reaction step is OHad formation, whose Langmuir– Hinschelwood barrier is 1.25 eV. In contrast to O ad dissociation, 2 no lower-energy trajectory is available. This process leads to

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adsorbed Had (mobile), O ad (partially hcp-bound), and OH ad . A fcc water molecule can then form on the surface and desorb as a gasphase water, the final product of the reaction. Both H 2 O ad and OHad adsorb on Pt(111) with the oxygen at an on top surface site. Forming water from Had and OHad is the sum of breaking the Pt– OH covalent bond (+1.91 eV), forming the Pt–OH2 bond from the oxygen lone pair orbital (–0.41 eV), breaking the surface Pt–H bond (+2.60 eV), the formation energy the OH–H bond (–4.89 eV). This leads to a lowering of the system energy by –0.80 eV. The barrier for water formation on the surface is only 0.33 eV. Finally, in order to desorb water from the surface, we have to break the Pt–H2O surface bond, which requires 0.41 eV, a value comparable to an experimental value of 0.52 eV.142 Assuming the reaction mechanism with the lowest barrier for each reaction step, we draw the picture of the whole Oad 2 dissociation pathway shown in Fig. 3. Energies include zero point energy corrections and are given in eV. In terms of intermediates, all reaction steps are exothermic except the last step, water desorption from the surface. Overall, the reaction enthalpy at 0 K is calculated as 2.22 eV per water molecule, a value comparable to the tabulated enthalpy value of 2.48 eV for this reaction. In this pathway, only three steps have barriers. The highest barrier is the + H ad o OH ad reaction, which is +1.25 eV. Dissociation of O ad fcc , which is mostly considered to be the limiting adsorbed Oad 2 process, is 0.63 eV. Dissociation of O2 in the absense of the heterogeneous catalyst is 4.95 eV. The last reaction barrier is the formation of water on the surface from OHad + Had, which again is 0.33 eV. From these calculations, the rate determining step would appear to be the OHad formation step. Literature values for ORR activation range from 0.1 to 1.0 eV, however, they also depend on the experimental system and measurement conditions.143 The difference to our calculated barrier indicates that this reaction process may not be relevant for the ORR, and so we continue presenting other possible pathways.

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117

(ii) OOH/H2O2 Formation

Another pair of possible reaction pathways includes OOHad or H 2 O ad as intermediates. Here, O ad first reacts with Had to form 2 2 OOHad and then may dissociate to form Oad and OHad. This pathway is also summarized in Fig. 3. In OOHad formation, the high mobility of Had means several different mechanisms should be considered. Had could approach O ad sideways (almost 2 perpendicular to the O–O direction) and then bind to one of the oxygens almost parallel to the surface. Electronic rearrangement from a O-O ʌ-bond to the stronger O–H ı-bond causes the other O atom to form a covalent surface bond with a barrier of 0.15 eV. When Had approaches Oad along the Pt–Pt bridge direction, 2 another stable OOHad structure forms, in which OOHad effectively forms a pseudo ''five-membered'' ring with two surface Pt atoms. A strong Pt–H interaction weakens the adjacent Pt–O donor–acceptor bond, resulting in barrierless Oad + H ad o OOH ad formation. 2 The resulting ring-structure is unstable and can easily change to the non-ring OOHad structure. Therefore, we consider only the non-ring OOHad structure as most relevant. OOHad dissociation has a barrier of 0.67 eV. The product of this dissociation process is an on-top bound OHad and an Oad bound at a three-fold surface site. The O–OH dissociation is along the O–O direction, and the single O atom migrates over an on-top site before moving to its three-fold site. There is no observed preference for Oad bound at either a fcc or hcp site. However, as in the O ad -dissociation pathway, an Oad at an hcp position can easily 2 equilibrate and hop over a bridge position (0.24 eV barrier) to an fcc site. Thus, we assume this Oad prefers an fcc position. Both final steps of this reaction pathway (OHad + Had o H2Oad o H2Og) are equal to those discussed for the Oad dissociation pathway. As 2 was the case before, every step of this pathway is exothermic except for the last reaction step. The OOHad formation pathway involves only two reaction steps with activation barriers: the dissociation of an oxygen from OOHad (0.67 eV) and the final water formation from OHad and Had (0.33 eV). Thus, the O–OH

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dissociation is found as rate-determining for the OOHad-formation pathway, and a comparitively more likely pathway than Oad 2 dissociation under gas phase conditions. OOHad may also undergo another hydrogenation step to form hydrogen peroxide ( H 2 O ad ) on the surface. This reaction step has 2 an energy barrier of 0.59 eV. Two OHad are then formed by dissociation of the HO–OH bond, which requires overcoming another energy barrier of 0.35 eV. The remaining intermediates have already been discussed. Overall, the highest barrier on the pathway is H 2 O ad formation in gas phase, but this barrier H 2 O ad 2 2 is 0.59 eV. This barrier is still 0.08 eV below the rate-determining step (RDS) for the OOH pathway and 0.66 eV lower than the RDS pathway. This pathway now shows a much better for the Oad 2 agreement with experimental observations and indicates the formation processes. So far relevance of the ORR OOHad/ H 2 O ad 2 we have neglected the presence of surrounding water, which might influence the overall reaction kinetics. We now repeat the previous studies including the presence of water. (iii) Influence of Water Solvation

Many experiments (especially electrochemical studies) are performed under wet conditions, and the presence of an electrolyte may change the overall energetics of gas phase reaction mechanisms. Of course, the ORR reaction creates water molecules as final reaction products. Eley–Rideal reaction mechanisms (which will be discussed in the next Section) also rely on the electrolyte as a source of hydrogen atoms. Although results from gas-phase calculations are sometimes used to interpret experiments performed in solution, we believe that at least some treatment of the water solvent is required to obtain relevant results. As mentioned earlier in this chapter, solvation presents a formidable problem for theory. Simulations treating all surrounding water molecules explicitly with quantum chemical approaches would not even provide the most accurate results. Rather, molecular dynamics simulations updated with quantum chemical forces (via ab initio molecular dynamics) should provide

Figure 4. Reaction mechanisms for solvated O2ad dissociation, OOHad dissociation, and H2O2ad dissociation on a Pt(111) surface. Relative energies are in eV and do not include zero-point energy contributions. H atoms are assumed to freely diffuse, individually adsorbed O atoms reside on fcc sites, and all other species reside on on-top sites.

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accuracy relevant to extended time scales, but the scaling of such methods quickly makes simulations too large and complex to simulate. An alternative approach is to treat solvation by describing the surface and the adsorbate by DFT while modeling the solvent as a surrounding continuum. Although this method lacks any dynamical information, it provides correct qualitative electrostatic behavior of molecular species. A self-consistent reaction field description (SCRF) of the water solvent augmented our studies on the water-formation reactions. The energetics (binding energies and barriers) of the previous mechanisms were compiled to create Fig. 4. Comparing gas phase results to solvated results shows a large stabilizations of adsorbed species. These effects are certainly due to the charge transfer between adsorbate and surface. In case of hydrogen, this results in a positive partial charge (G+), while each oxygen from an adsorbed Oad has a slight negative partial charge (G–). Those 2 charges interact with the water dipoles, polarizing the solvent, and thus stabilize the adsorbates. dissociation pathway, formation of two Oad speOn the Oad 2 cies is –1.71 eV downhill in solvent rather than –1.06 eV in gas phase. However, the barrier for this process hardly changes from 0.63 eV to only 0.68 eV. This is certainly due to the higher solvation of O ad compared to O ad . After dissociation of O ad , O ad re2 2 acts with a surface hydrogen to form OHad. Now, the overall energy for forming OHad from Oad + Had is effectively zero, instead of exothermic by 0.47 eV. The energy barrier to form OHad formation drops from 1.25 eV in gas phase to 1.15 eV in solution. A similar energy barrier of 1.10 eV is observed for the reaction step to form H2Oad, while in gas phase the barrier was only 0.33 eV. Thus, water solvation causes little change overall to the O ad disso2 ciation pathway. OHad formation is still calculated as a ratelimiting step, which does not yet conform with experimental expectations.144 Desorption of water from the solvated surface requires 0.83 eV, a value that is comparable to the binding energy of a water molecule within an entire water bilayer network.136,145147 There, the Pt–H2O bond energy is 0.38 eV, and each of the two hydrogen bonds to neighboring waters brings 0.28 eV. In total, 0.94 eV is required to remove H2Oad from a water bilayer network

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121

on top of the Pt(111) surface.136 Indeed, applications of a SCRF model in surface catalysis simulations is a relatively inexpensive means to reproduce the qualitative behavior from experiment. On the OOHad formation pathway, the initial steps are again equivalent to the Oad dissociation, but OOHad formation is now 2 0.22 eV uphill in solvent compared to –0.32 eV downhill in gas phase. The barrier to form OOHad is greatly increased from 0.15 eV in gas phase to 0.94 eV in solvent. Here, water substantially destabilizes both the transition state and OOHad. Water has little effect on the dissociation of OOHad to Oad and OHad though (0.67 eV in gas phase and 0.62 eV in solvent). Overall this reaction step is exothermic by –1.94 eV, compared to –1.22 eV more than in gas-phase. Here again, OHad formation should be the rate determining process for this pathway. For the H 2 O ad formation pathway and as with the OOHad 2 formation from Had and pathway, solvation greatly affects H 2 O ad 2 OOHad. The barrier that was 0.59 eV in gas phase is now 1.23 eV in solvent. HO–OH dissociation is also hardly affected by solvation just as O–OH was not (gas phase barrier = 0.35 eV, solvent phase barrier = 0.43 eV). Overall, the new rate determining step for this pathway is H 2 O ad formation. 2 Overally, solvation appears to have a drastic influence on forwhich mechanistic path is preferred. In gas phase, the H 2 O ad 2 mation was the overall RDS (0.59 eV). In solvent, the RDS step is formation is unOOHad dissociation (0.62 eV), and H 2 O ad 2 favorable. The energy barriers of the various reaction steps in both -dissociation and OOH ad -formation) appear influpathways ( Oad 2 enced by solvent within a range of 0.40 eV and 0.68 eV, comparable to available literature data on the ORR activation energy.143 In summary, in solvated systems, we found a preference against H 2 O ad formation, and both the O ad -dissociation and the 2 2 OOHad-formation reactions should occur with comparable probabilities. Furthermore, although these two reaction pathways produce adsorbed atomic oxygen, the Oad -dissociation pathway pro2

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duces Oad twice as frequently as the OOHad dissociation process, and thus will impact the reaction kinetics that form OHad. (iv) Eley–Rideal Mechanisms

Eley–Rideal mechanisms involve reactions between surface intermediates and the solvent. In this case, hydrogenations due to surface hydrogen are now assumed to come from a proton in the electrolyte. The initial thermodynamic resting state of hydrogens in solution is referenced to hydrogen gas. This convenient reference eschews the complexity of treating the electronic structure or protons in aqueous solution, a especially problematic simulation for theoretical methods. Indeed, a rigorous simulation for a fuel cell would consider a chemical equilibrium between Had and H+, but this is not necessary to represent relative thermodynamic energies. The key difference between reported Langmuir–Hinschelwood mechanisms and Eley–Rideal mechanisms is that hydrogen enters the simulation in the transition state for the hydrogenation process of Eley–Rideal processes, and is not first preadsorbed on the Pt surface as in Langmuir–Hinschelwood processes. Processes that do not involve hydrogenations are exactly the same at those for Langmuir–Hinschelwood mechanisms. Simulations on the O ad dissociation, the OOH ad dissociation, 2 dissociation provide substantially different reaction and the H 2 O ad 2 details than those previously reported. While along the Langmuir– Hinshelwood mechanisms the rate determining step for Oad 2 dissociation in solvent phase was OHad formation (1.14 eV), this process now has no barrier due to its reference to the highly acidic standard state (pH = 0) of the electrolyte whereby protons should rapidly and easily protonate Oad species. Thus, the resulting RDS for Oad dissociation is Oad dissociation itself (0.68 eV). For the 2 2 OOHad pathway, the RDS is also O–OH dissociation (0.62 eV), and for the H 2 O ad pathway HO–OH dissociation is the RDS (0.43 2 eV). Overall, treatment of Eley–Rideal mechanisms shows that all three pathways are potential candidates to be rate determing

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123

processes or ORR, and the H 2 O ad pathway is preferred at zero 2 potential. These results are summarized in Fig. 5. Of course, realistic fuel cell conditions include an electrode potential, and this effect can be approximated by shifting energy levels by +eU for every species where a hydrogen atom has moved from a gaseous species to one either on the surface as either Had or within the transition state for an Eley–Rideal process. When this approximation is employed to the most favorable Langmuir– Hinschelwood process as well as the most favorable Eley–Rideal process (Fig. 6), we see that both classes of reactions should be possible at electrode potentials near 1.23 eV, the reduction potential established by the Nernst equation. While individual Eley–Rideal reaction barriers appear to be lower than Langmuir– Hinschelwood barriers, the energies for the Oad, and OHad species, which are influential for both classes of reactions, are almost identical, and can therefore be expected to be competitive depending on ambient conditions within the fuel cell. In summary, it appears that ORR reaction processes can be reduced to elementary forms of Langmuir–Hinschelwood and Eley–Rideal mechanisms, and treated with high-quality QM approaches to obtain relavent thermodynamic stabilities of all species. Further studies considering the extent that these processes are coupled kinetically is the logical next step to providing insight to the complicated ORR mechanism. VI. CONCLUSIONS

The enormous variety of possible surface reactions still reveals many open questions regarding exact reaction pathways, kinetics, and/or structural information. The seemingly simple water formation reaction from H2 and O2 over a Pt-catalyst already shows many different reaction pathways. Regarding this reaction, we have performed periodic DFT calculations and thermodynamic considerations to evaluate the corresponding (a,T,'I)-surface phase diagram for Pt(111) on contact with an aqueous electrolyte. Our work determined that below 0.95 V no stable and ordered oxygen overlayer forms, and that between 0.95 and 1.20 V the

Figure 5. Eley–Rideal reaction pathways. Relative energies are in eV and do not include zero-point energy contributions. H atoms are assumed to come from electrolyte, individually adsorbed Oad atoms reside on fcc sites, and all other species reside on on-top sites.

Figure. 6. A composite of the most favored Langmuir–Hinshelwood mechanism under solvent conditions, O2addissociation, and the most favored Eley–Rideal mechanism, H2O2ad dissociation, is reported at an electrode potential of U = 1.23 eV.

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well known p(2×2)-O becomes thermodynamically stable. Further increasing the electrode potentials leads to a surface oxide or even PtO2 bulk oxide. After having specified the thermodynamic stable surface structures, the clean Pt(111) surface was used to study the oxygen reduction reaction. Among the two main reaction mechanisms (i.e., Oad dissociation and OOH ad / H 2 O ad formation) we 2 2 formation is preferred. When infound that in gas phase, H 2 O ad 2 cluding water solvation as an environmental effect, the overall kinetics are modified, leading to a nearly identical preference for dissociation and the OOH ad formation mechanisms, but the Oad 2 with a blocking of the hydrogen peroxide pathway. Since water is necessary for the proton transfer and is also produced by the ORR, we conclude the latter scenario to be more relevant Langmuir– Hinschelwood mechanism for fuel cells. Interestingly, inclusion of solvent permits different classes or reaction mechanisms centered around electron transfers and protonations at different electrode potentials. Eley–Rideal variants of the previously investigated mechanisms are all substantially lower in energy at an electrode potential of zero. However, inclusion an approximate influence of an electrode potential results in both a picture showing that both Langmuir–Hinschelwood and Eley–Rideal mechanisms could be at play under running fuel–cell conditions. Further evaluation of the kinetics of all paths should further elucidate the complicated nature of the ORR mechanism. ACKNOWLEDGMENTS

The authors gratefully acknowledge support from the Alexander von Humboldt Foundation (AvH), the "Fonds der Chemischen Industrie" (FCI), and the Deutsche Forschungsgemeinschaft (DFG) within the framework of the Emmy-Noether-Program.

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M. Gatrell and B. MacDougall In Handbook of Fuel Cells: Fundamentals, Technology, Applications; W. Vielstich, A. Lamm, H. A. Gasteiger, Eds.; WileyVCH: Weinheim, 2003; Vol. 2. 2 R. N. Ross Jr. In Handbook of Fuel Cells: Fundamentals, Technology, Applications; W. Vielstich, A. Lamm, H. A. Gasteiger, Eds.; Wiley-VCH: Weinheim, 2003; Vol. 2. 3 N. A. Anastasijevic, S. Strbac and R. R. Adzic, J. Electroanal. Chem. 240 (1988) 239. 4 N. M. Markoviü, H. A. Geistager and P. N. Ross, J. Phys. Chem. 99 (1995) 3411. 5 N. M. Markoviü, R. R. Adzic, B. D. Cahan and E. Yeager, J. Electroanal. Chem. 377 (1994) 249. 6 R. R. Adzic In Electrocatalysis; J. Lipkowski, P. N. Ross, Eds.; Wiley-VCH: New York, 1998, p. 197. 7 N. M. Markoviü, R. R. Adzic, B. D. Cahan and E. Yeager, ISE Proceedings (1991) 138. 8 N. M. Markoviü, H. A. Gasteiger and P. N. Ross, J. Electrochem. Soc. 144 (1997) 1591. 9 N. M. Markoviü, H. A. Gasteiger, B. N. Grgur and P. N. Ross, J. Electroanal. Chem. 467 (1999) 157. 10 T. Tada In Handbook of Fuel Cells: Fundamentals, Technology, Applications; W. Vielstich, A. Lamm, H. A. Gasteiger, Eds.; Wiley-VCH: Weinheim, 2003; Vol. 3. 11 S. Kim and S. J. Park, Electrochim. Acta 52 (2007) 3013. 12 E. Auer, A. Freund, J. Pietsch and T. Tacke, Appl. Catal. A: Gen. 173 (1998) 259. 13 G. Wang, G. Sun, Z. Zhou, J. Liu, Q. Wang, S. Wang, J. Guo, S. Yang, Q. Xin and B. Yi, Electrochem. Solid State Lett. 8 (2005) A12. 14 A. Kongkanand, S. Kuwabata, G. Girishkumar and P. Kamat, Langmuir 22 (2006) 2392. 15 C. Wang, M. Waje, X. Wang, J. M. Tang, R. C. Haddon and Y. S. Yan, Nano Lett. 4 (2004) 345. 16 J.-S. Zheng, X.-S. Zhang, P. Li, X.-G. Zhoua, D. Chenb, Y. Liuc and W.-K. Yuan, Electrochim. Acta 53 (2008) 3587. 17 J. S. Spendelow and A. Wieckowski, Phys. Chem. Chem. Phys. 9 (2007) 2654. 18 T. Toda, H. Igarashi, H. Uchida and M. Watanabe, J. Electrochem. Soc. 146 (1999) 3750. 19 L. Xiong, A. M. Kannan and A. Manthiram, Electrochem. Commun. 4 (2002) 898. 20 J. Zhang, Y. Mo, M. B. Vukmirovic, R. Klie, K. Sasaki and R. R. Adzic, J. Phys. Chem. B 108 (2004) 10955. 21 R. R. Adzic, J. Zhang, K. Sasaki, M. B. Vukmirovic, M. Shao, J. X. Wang, A. U. Nilekar, M. Mavrikakis, J. A. Valerio and F. Uribe, Top. Catal. 46 (2007) 249. 22 J. Zhang, F. H. B. Lima, M. H. Shao, K. Sasaki, J. X. Wang, J. Hanson and R. R. Adzic, J. Phys. Chem. B 109 (2005) 22701.

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J. Zhang, M. B. Vukmirovic, K. Sasaki, A. U. Nilekar, M. Mavrikakis and R. R. Adzic, J. Am. Chem. Soc. 127 (2005) 12480. N. M. Markoviü, T. J. Schmidt, V. Stamenkoviü and P. N. Ross, Fuel Cells 1 (2001) 105. 25 D. Thompsett In Handbook of Fuel Cells: Fundamentals, Technology, Applications; W. Vielstich, A. Lamm, H. A. Gasteiger, Eds.; Wiley-VCH: Weinheim, 2003; Vol. 3. 26 S. Mukerjee, S. Srinivasan and M. P. Soriaga, J. Electrochem. Soc. 142 (1995) 1409. 27 U. A. Paulus, A. Wokaun, G. G. Scherrer, T. J. Schmidt, V. Stamenkoviü, N. M. Markoviü and P. N. Ross, Electrochim. Acta 47 (2002) 3787. 28 V. Stamenkoviü, T. J. Schmidt, P. N. Ross and N. M. Markoviü, J. Phys. Chem. B 106 (2002) 11970. 29 J. L. Fernández, D. A. Walsh and A. J. Bard, J. Am. Chem. Soc. 127 (2005) 357. 30 N. M. Markoviü and P. N. Ross, Surf. Sci. Rep. 45 (2002) 117. 31 T. J. Schmidt, V. Stamenkoviü, M. Arenz, N. M. Markoviü and P. N. Ross, Electrochim. Acta 47 (2002) 3765. 32 H. Ye, J. A. Crooks and R. M. Crooks, Langmuir 23 (2007) 11901. 33 J. Zhang, M. B. Vukmirovic, K. Sasaki, F. Uribe and R. R. Adzic, J. Serb. Chem. Soc. 70 (2005) 513. 34 J. Zhang, M. B. Vukmirovic, Y. Xu, M. Mavrikakis and R. R. Adzic, Angew. Chem. Int. Ed. 44 (2005) 2132. 35 R. R. Adzic and F. H. B. Lima In Handbook of Fuel Cells: Advances in Electrocatalysis, Materials, Diagnostics and Durability; W. Vielstich, H. A. Gasteiger, H. Yokokawa, Eds.; Wiley-VCH: Weinheim, 2009; Vol. 5. 36 V. Stamenkoviü, B. Fowler, B. S. Mun, G. Wang, P. N. Ross, C. A. Lucas and N. M. Markoviü, Science 315 (2007) 493. 37 V. R. Stamenkoviü and N. M. Markoviü In Handbook of Fuel Cells: Advances in Electrocatalysis, Materials, Diagnostics and Durability; W. Vielstich, H. A. Gasteiger, H. Yokokawa, Eds.; Wiley-VCH: Weinheim, 2009; Vol. 5. 38 P. Holt-Hindle, Q. Yi, G. Wu, K. Koczkur and A. Chen, J. Electrochem. Soc. 155 (2008) K5. 39 M. B. Vukmirovic, P. Liu, J. T. Muckerman and R. R. Adzic, J. Phys. Chem. C 111 (2007) 15306. 40 M. A. García-Contreras, S. M. Fernández-Valverde and J. R. Vargas-García, J. Alloys and Compounds 434 (2007) 522. 41 W. E. Mustain and J. Prakash, J. Power Sources 170 (2007) 28. 42 O. Savadogo, K. Lee, K. Oishi, S. Mitsushima, N. Kamiya and K.-I. Ota, Electrochem. Commun. 6 (2004) 105. 43 M. Shao, P. Liu, J. Zhang and R. R. Adzic, J. Phys. Chem. B 111 (2007) 6772. 44 C. W. B. Bezerra, L. Zhang, H. Liu, K. Lee, A. L. B. Marques, E. B. Marques, H. Wang and J. Zhang, J. Power Sources 173 (2007) 891. 45 A. Lewera, J. Inukai, W. P. Zhoua, D. Caoa, H. T. Duonga, N. Alonso-Vante and A. Wieckowski, Electrochim. Acta 52 (2007) 5759. 46 N. Alonso-Vante In Handbook of Fuel Cells: Fundamentals, Technology, Applications; W. Vielstich, A. Lamm, H. A. Gasteiger, Eds.; Wiley-VCH: Weinheim, 2003; Vol. 2. 47 R. Zeis, T. Lei, K. Sieradzki, J. Snyder and J. Erlebacher, J. Catal. 253 (2008) 132. 24

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B. Ruscic, A. F. Wagner, L. B. Harding, R. L. Asher, D. Feller, D. A. Dixon, K. A. Peterson, Y. Song, X. M. Qian, C. Y. Ng, J. B. Liu, W. W. Chen and D. W. Schwenke, J. Phys. Chem. A 106 (2002) 2727.

4

Molecular-Level Modeling of the Structure and Proton Transport within the Membrane Electrode Assembly of Hydrogen Proton Exchange Membrane Fuel Cells Myvizhi Esai Selvan and David J. Keffer† Department of Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, TN 37996-2200

I.

INTRODUCTION

The creation of proton exchange membrane fuel cells (PEMFCs) in the early 1960’s attracted great interest with the prospect of serving as a highly efficient and eco-friendly power source. This nascent technology found a broad range of applications spanning from spacecrafts to automobiles and electronic devices. The PEMFC in its simplest form consists of an anode, where the hydrogen fuel is catalytically electro-oxidized (dissociated into protons and electrons), a cathode, where oxygen is catalytically electro-reduced (combined with protons to form water) and a polymer electrolyte membrane, which serves as the structural framework of the cell and transports protons from anode to cathode, while the electrons are forced through the external circuit generating elec†

Author to whom correspondence should be addressed

P. Balbuena, V. Subramanian (eds.), Theory and Experiment in Electrocatalysis, Modern Aspects of Electrochemistry 50, DOI 10.1007/978-1-4419-5594-4_4, © Springer Science+Business Media, LLC 2010

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tricity. Today, fuel cell remains one of the most promising means of generating energy from alternative fuels, with tremendous potential to reduce oil dependence and carbon emissions. However, current PEMFCs have a relatively narrow operational range and a high cost of production, thus requiring significant experimental and theoretical research to develop a thorough understanding of this technology (at both the molecular and macroscopic scale), which will ultimately render the fuel cell as an economically viable option. The presence of water is critical for operation but in current PEMFCs proper water management is a delicate issue and poor control can greatly reduce the efficiency of the device. An excess of water can flood the catalyst and porous transport layers impeding the transport of reactants and eventually drowning the fuel cell. At low water content, the polymer electrolyte membrane can become a poor conductor and the reactivity at the electrodes is affected. Local hot spots arising due to the inefficient operation result in early degradation of the cell.1 The temperature range of PEMFCs is also an issue. PEMFCs are commonly operated at temperatures less than 80 °C.2 Operating fuel cells at high temperatures would enhance the reaction kinetics and tolerance to CO poisoning, thereby, avoiding the usage of the expensive catalyst and purified hydrogen fuel.3 Furthermore, the need for the compressor can be eliminated4 and better water and heat management is provided. However, as the temperature increases, the amount of water adsorbed in the proton exchange membranes (PEMs) decreases, negatively impacting conductivity. Therefore, improved PEMs are desired to possess chemical and mechanical stability accompanied by high proton conductivity at high operational temperature and low humidity. Currently, none of the existing PEMs meets all these requirements. Nafion, a perfluorinated sulfonic acid (PFSA) polymer electrolyte developed and produced by the E. I. Dupont Company, has been extensively studied as a fuel cell membrane.5 Despite its age, it remains the industry standard membrane because of its relatively high proton conductivity, toughness and quick start capabilities. Attempts to build upon the strengths of Nafion have resulted in a class of PFSA polymer electrolytes,6 including the short-side-chain (SSC) PFSA polymer electrolyte, originally synthesized by Dow and now produced by Solvay Solexis. Structurally, PFSA polymer

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electrolytes have perfluorinated backbones and pendant side chains containing charged end groups (usually SO3H). Hydration of the material leads to spontaneous nanoscale segregation into hydrophobic regions (consisting of the perfluorinated backbone) and hydrophilic regions (consisting of water and the charged side groups of the polymer). It is important to understand the morphology of the hydrated material because it is through the hydrophilic domains that proton transport from the anode to the cathode takes place. Thus the size, shape and connectivity of the hydrophilic clusters within this aqueous phase dictate the conductivity of the membrane. The morphology of the aqueous phase is dependent on the polymer architecture7-10 and water content.11-14 The connectivity of the aqueous phase is important because a highly connected phase will, in the language of percolation theory, provide multiple sample-spanning clusters for proton transport. The size and shape of these clusters is important because they dictate the degree of confinement of the water and ions in the aqueous phase. In larger clusters, there may be a core of water molecules that act in a more bulk-like manner, while in smaller clusters or more elongated clusters, a majority of the water molecules may be adjacent to the hydrophobic phase and thus behave in a different way. Bulk water has different dynamics than water molecules confined in the nano-aqueous domains at low hydration level,15 which likely affect proton conductivity. In addition to the study of the morphology of the bulk membrane, it is also important to discern how this morphology changes at the interface of the electrolyte with the electrode. An understanding of the molecular-level structure and dynamics of protons at the interface between the electrode and electrolyte will offer new insights into the theory and mechanisms that control the important electrochemical and electrocatalytic processes and will help in the development of a predictive, continuum-level model of PEMFC operation. Clearly, a fundamental understanding of the key structure/property relationships, particularly membrane morphology and conductivity as a function of polymer electrolyte architecture and water content – both in the bulk hydrated membrane and at the various interfaces within the membrane electrode assembly (MEA), can provide guidance in the synthesis of novel materials or MEA manufacturing techniques that lead to the improvement in the efficiency and/or operating range of PEMFCs.

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The complexity and the heterogeneous nature of the system impede our understanding of the PFSA membranes based solely on experimental results. Molecular dynamics (MD) simulation is an effective approach for obtaining the atomistic level description with currently available computational resources. Taken together, data from experiment and simulation can provide a more complete picture of the system. In spite of the small length and time scale of the systems in MD simulations (relative to experiment) meaningful insights can be obtained from its molecular-level description. In this work, the report is organized into two tasks. The first task is a discussion of the molecular-level structure of PFSA membranes— in the bulk and at relevant interfaces within the MEA—as a function of polymer electrolyte architecture and degree of hydration, as obtained from classical MD simulation. The second task is a discussion of the mobility of protons in these nanoscale environments. Diffusion of protons in general occurs via a combination of two mechanisms—vehicular diffusion due to changes in the center of mass of the hydronium ions as well as structural diffusion, i.e., the Grotthuss mechanism due to proton hopping among the water molecules.16,17 The description of the overall transport process requires a multiscale modeling algorithm because of the disparate time and length scales associated with the various physical phenomena. The structural diffusion occurs on a timescale of picoseconds17 and the vehicular diffusion on nanoseconds. In order to capture both timescales, a coarse-grained reactive molecular dynamics (RMD) algorithm, which is based on a mapping of the transition state involved in the structural diffusion (determined by ab initio calculation) on to set of triggers to reproduce the macroscopic properties is employed. Thus, the first task provides a structure/property relationship between morphology and polymer electrolyte architecture and degree of hydration. The second task aims to determine proton transport as a function of the morphology. Connecting the two tasks together in sequence then leads to proton transport as a function of polymer electrolyte architecture and degree of hydration.

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catalyst nanoparticle (gold)

10 mm

carbon particles (gray)

ionomer film (blue)

10 mm

~800 Pm

~30 nm

cathode

anode

50 Pm 10 Pm

accessible wet catalyst accessible dry catalyst isolated catalyst buried catalyst

polymer backbone

vapor phase

aqueous phase

polymer electrolyte membrane catalyst layer (+ recast ionomer) carbon fiber + carbon layer

carbon particle

carbon particle

Figure 1. From the macroscale to the nanoscale: a membrane electrode assembly has a polymer electrolyte membrane sandwiched between two catalyst layers and gas diffusion layers. The catalyst layer is composed of carbon particles impregnated with catalyst nanoparticles. Effective utilization of the catalyst particles depends on their local environment.

II. MORPHOLOGY 1.

Introduction

An archetypal MEA consists of an electrolyte membrane sandwiched between two catalyst layers and two gas diffusion layers (GDLs) as shown in Fig. 1. The fuel and oxidant gases diffuse through the GDL to react in the catalyst layer between the electrode and electrolyte. The catalyst, typically Pt or Pt based alloy, are nanoparticles residing on carbon particles. In addition to its primary purpose as the center of reactivity, the catalyst must participate in the effective adsorption of the reactants, conduction of the electrons to/from the electrode and diffusion of protons to/from

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carbon support

membrane

1. Bulk hydrated membrane

catalyst H2 H+ H2

H+

H3O+

catalyst carbon support

4. membrane/vapor/Pt interface

3. membrane/vapor/C support interface

2. membrane/vapor interface

Figure 2. A schematic of the molecular-level interfaces present in a vapor filled idealized pore geometry at the anode of PEMFC

the hydrated polymer electrolyte membrane. A catalyst nanoparticle is not utilized if it cannot participate in any one of these three transport processes. Thus the structure of two- and three-phase interfaces present within the catalyst layer is one of the factors that controls the ultimate performance of a fuel cell.18 The three-phase boundary region can be increased either by altering the manufacturing procedure of the MEA or by introducing recast ionomer in the electrode, which improves catalyst utilization.19-21 The nanoscale structure of the electrode/electrolyte interface is a function of the manufacturing process and the composition of the catalyst. A schematic representation of an idealized pore at the interface within the MEA is shown in the Fig. 2 with an assumption the catalyst surface is not completely covered by ionomer. Though the specific geometry is highly idealized, four systems of interest in terms of proton transport can be identified (a) (b) (c) (d)

the bulk hydrated PEM (system I), membrane/vapor interface (system II), the membrane/vapor/support interface (system III), and membrane/vapor/catalyst interface (system IV).

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System I has been modeled with both Nafion and SSC PFSA membrane to study the effect of side chain length on the morphology.8,12 The interfacial systems have been studied using Nafion.2224 System II assumes that the pore is filled with water vapor as shown. Given the details of the operating conditions and the water management scheme used, it is possible that some pores would be filled with liquid water, a case which is under study but not included in this report. Graphite is used as the carbon support in system III. System IV uses platinum ([100] Pt) as the catalyst. Constant density and constant temperature (NVT) MD simulations were used to study the systems as a function of humidity level. In recent years many significant experimental and theoretical studies have been conducted in an attempt to understand the structural and dynamical properties of proton transport in a bulk hydrated PFSA membrane. Most of the studies have concentrated on Nafion. Diffraction and scattering techniques help in revealing the spatial organization of the distinct domains in the membrane. Microscopic studies help in understanding surface morphology. Small-angle X-ray scattering techniques13 (SAXS) along with small-angle neutron scattering (SANS) helps in characterizing the aqueous domain but the interpretation is based on numerical calculations. Wide-angle X-ray scattering experiments explored the crystallinity in Nafion.13,25 Scanning force spectroscopy concluded that the structure of Nafion is a fibril network consisting of twisted ribbons or helix chains.26 Raman spectra27 and infrared spectra indicate that hydrogen bonding of water in fully hydrated Nafion is considerably weaker than in liquid water at the same temperature.28 Morphological transformation in Nafion can be deduced as a function of temperature and hydration through the distinct spectral features 1H NMR spectroscopy of the confined water.29 Swelling and redistribution of the ionic clusters in Nafion during the uptake of water can be studied using atomic force microscopy30,31 and scanning force microscopy.26 Scanning probe microscopy along with electrical impedance spectroscopy can be used to characterize the surface morphology, electrical and interfacial properties.32 Modeling of the PFSA membrane has been investigated for the past two decades using phenomenological approaches33,34 based on experimental findings, atomistic modeling10,11,35-38 based on classical molecular mechanics, and mesoscale modeling39,40

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based on higher degrees of coarse graining. These models and the resulting morphologies of Nafion have been reviewed by many authors.5,41,42 The effect of water hydration, polymer architecture, temperature and placement of protogenic groups has been studied by the molecular-level models of PFSA membranes. But still the precise morphology of the hydrated PFSA membrane has not been definitively characterized. Vishnyakov and Neimark35 studied water clustering and suggested the water and ion transport takes place via short lived dynamic bridges than through channels between clusters. Jang et al.10 obtained a better phase segregation with a blocky monomeric sequence than the dispersed case. Urata et al.11 found the preferential orientation of the pendant chains perpendicular to the hydrophilic/hydrophobic interface with the water molecules bound only to the end groups. MD simulations also showed a dynamic formation and deformation of water cluster network at low hydration level and stable percolation at high water contents. Dupuis et al.14 studied the effect of water content on the coordination of the hydronium ions and water molecules to the sulfonate groups. Although much effort has been expended towards the molecular-level characterization of the bulk hydrated membrane, substantially less work has been concentrated on the other three regions in Fig. 2. Water and oxygen dynamics in polymer/catalyst/carbon interface have been previously investigated by molecular dynamics simulations43 at Ȝ = 5, 24 and 45 to find Pt cluster covered by Nafion especially by the hydrophilic sites, thereby, favoring water clustering. As the water content is varied the connectivity of the wet paths between the catalyst particles across the graphite increased. First-principles based reactive ReaxFF force field has been implemented by Goddard et al.44 to investigate all chemical processes involving the electrode reactions, proton transport and phase transformations at the electrode/electrolyte interface using finite Pt atom clusters (§ 20 Å in diameter). The triple phase boundary has been characterized experimentally45 by varying the platinum structure and studying the heterogeneous kinetics of the oxygen reduction reaction with impedance spectroscopy. Pt/Nafion interface has achieved special attention46,47 so far in terms of the oxygen reduction kinetics rather than molecular level structural analysis. Another region of interest is the water in contact with the Pt surface.48 Adsorption of water48 and time scale of proton trans-

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fer49 on the Pt surface has been studied by spectroscopic techniques. The molecular-level simulations discussed below have been performed to determine the structure of PFSA in the bulk and at relevant interfaces and provide information that is complementary to the above body of work. 2.

Molecular Models and Simulation Details

The validity of MD simulation is impacted by the choice of system, interaction potential and algorithm implemented. We first discuss the choice of system. In this work we chose to simulate Nafion with an equivalent weight (EW) of 1144 g/mol, which is a practically reasonable EW. In order to have a direct comparison of the effect of side chain length, SSC PFSA polymer electrolyte was simulated with an EW of 978 g/mol. (Commonly used SSC ionomer has an EW § 800 g/mol). The repeat units of these PFSA membranes are shown in Fig. 3. These two materials have the same backbone separating side chains; thus the only differentiating feature is side chain length. For most of the simulations performed, each polymer is modeled with three monomers, resulting in a total of 48 CFx (x = 2 or 3) groups along the backbone. The real structure of both the oligomers contains at least 90 monomer units.7 Our choice is motivated by the following considerations. The simulation time in an MD is limited to nanoseconds. Long polymer chains have a relaxation time that can be on the order of seconds.50 The choice the simulator must make is whether to simulate an artificially short

Figure 3. Chemical structures of the monomer used in the simulation (a) Nafion (EW 1144); and (b) Short side chain PFSA membrane (EW 978).

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chain at equilibrium or to simulate an unrelaxed long chain. We have chosen the first option because this allows the simulations to be reproducible, whereas simulation of an unequilibrated long chain is dependent on the initial condition. The future use of multiscale algorithms may allow simulation of fully equilibrated long chains. Regardless, before deciding that a chain length of three monomers was adequate, the results of our Nafion simulations were thoroughly compared with published simulation work, such as that of Urata et al.,11 who had used chains of 10 monomer units. Subsequently, we have performed MD simulations of both Nafion (EW 1144) and SSC (EW 978) with polymers composed of 15 repeat units in order to confirm that the trends observed as a function of side chain length were independent of molecular weight. In this first task, each excess proton is permanently attached to a hydronium ion. This assumption prohibits structural diffusion of the proton. However, for the purposes of the first task, namely the generation of molecular-level structure of the hydrated membrane and its interfaces, this approximation is adequate. For the second task, namely the generation of transport properties, this limitation is removed. Although, the classical MD simulations in task I cannot quantitatively characterize the structural diffusion mechanism, from the analysis of the hydration structure of the hydronium ions in these simulations the characteristics of Zundel and Eigen ion (which are necessary for structural diffusion)16,51 can be studied. The second important choice in an MD simulation is the interaction potential. Nafion and SSC have the same interaction potential described below with the exception of the partial charges used. The potential is fully flexible and atomistic, with the exception of the fluorine which are incorporated into CFx united atoms, interacting using Lennard-Jones (LJ) parameters developed by Cui et al.52,53 The united atoms are assigned a charge that is sum of the charges of the atomistic model. The backbone does not carry electric charge (except at the branch point). The bond lengths, bond angles, and partial charges for the side group are obtained from the work of Vishnyakov et al.35 The force constants for bond stretching and bond angle bending are taken from Gejji et al.54 and Cornell et al.55 The torsional potential is from Rivin et al.56 SSC is modeled very similar to Nafion but the partial charges on the side chain were normalized depending on the chain length.

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Both water and hydronium use the TIP3P57 model with certain modifications. Water is modeled with a flexible OH bond58 and hydronium is modeled with modified charges on the O and H atoms.11 The intermolecular interactions included the LJ and Coulombic interactions within a cut-off radii of 10 ǖ . Electrostatic interactions were calculated using the site-site reaction field method59 and long-range correction for LJ interactions was taken into account. The properties of all the systems were examined by performing NVT simulations at a temperature of 300 K at four water contents of 5%, 10%, 15%, and 20% by weight of the hydrated Nafion polymer electrolyte and these correspond to the Ȝ (defined as the number of water molecules per SO3H group) of 4.4, 6.4, 9.6, and 12.8, respectively. For the four levels of hydration, the experimentally60 determined overall densities of the hydrated Nafion are 1.95, 1.87, 1.80, and 1.74 g/cm3. SSC was also modeled using the same densities of Nafion because of their similar EW. For simulations that included a carbon support, a graphite surface was modeled four atomic layers deep with rigidly held carbon atoms. LJ potentials were used to describe their interaction with other atoms in the system through the parameters Vc = 3.4 Å and HC/k = 28.0 K.61 For simulations that included a catalyst surface, [100] Pt was modeled six atomic layers deep and was also held rigid and used the parameters VPt = 2.41 Å and HPt/k = 2336.0 K.62 The positions of carbon63 and Pt64 were taken from the literature. The number of graphite and Pt atoms used at various water contents is listed in Table 1. Third, one requires a systematic algorithm to perform MD simulations. Here we describe key features of the algorithm. The initial configuration of system I was obtained as follows. Isolated oligomers were relaxed in vacuum. The individually equilibrated structures of water, polymer electrolyte and hydronium ion were inserted by positioning the molecular center-of-mass of all the molecules randomly on cubic lattice points within the simulation volume. In order to avoid aphysical repulsion due to atomic overlap in this initial state, the LJ collision diameter all the atoms were initialized to zero (i.e., all the atoms were initially given zero size) and then were slowly increased to their full values during a molecular dynamics simulation (0.02 to 0.2 ns) to ensure that the initial configurations were created efficiently with non-overlapping atoms. In the study of both the bulk hydrated Nafion and SSC 64

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Table 1 Summary of the Simulated Systems System

Components

Number of molecules Ȝ = 6.4 Ȝ = 9.6 Ȝ = 12.8 64 64 64 1040 1656 2272 192 192 192

Bulk membrane system I

Polymer Water Hydronium

Ȝ = 4.4 64 660 192

Membrane/Vapor system II

Polymer Water Hydronium

256 2640 768

256 4160 768

256 6624 768

256 9088 768

Membrane/Vapor/Carbon Support system III

Polymer Water Hydronium Graphite

256 2640 768 3024

256 4160 768 3584

256 6624 768 3584

256 9088 768 3712

Membrane/Vapor/Catalyst system IV

Polymer Water Hydronium Platinum

256 2640 768 4872

256 4160 768 5400

256 6624 768 5580

256 9088 768 6144

polymer electrolyte molecules (192 monomers), 192 H3O+ ions (to neutralize the charges) and 660, 1040, 1656, and 2272 water molecules were used depending on water contents from Ȝ = 4.4 – 12.8. In the interfacial simulations, for better statistics, larger systems sizes were considered. Specifically, the simulation included 256 Nafion oligomers, 768 H3O+ ions and 2640, 4160, 6624, and 9088 water molecules for the four water contents. In the simulations with interfaces, an equilibrated bulk membrane was used as the initial configuration. The vapor volume was initially empty. The system was then equilibrated by drawing water molecules form the membrane into the vapor phase. The solid surface was artificially grown, i.e., the LJ collision diameter was gradually increased, over a period of 10 ps to avoid overlap with the molecules in the hydrated membrane. Once the solid surface is generated, the system is equilibrated by allowing the redistribution of water between the vapor, PEM, and solid surface. It is also to be kept in mind that Ȝ is calculated based on the initial configuration and may decrease slightly when the water leaves the hydrated membrane and enters the vapor phase. A small vapor phase was used to mitigate this effect.

Molecular-Level Modeling of Hydrogen PEM FC

(a)

(b) Figure 4. Final snapshots at Ȝ = 12.8 (a) bulk hydrated Nafion (b) membrane/vapor interface (c) membrane/vapor/catalyst support interface (d) membrane/vapor/catalyst interface. In the bulk hydrated membrane we can find the nano segregation of the hydrophilic and hydrophobic domains. Wetting of the catalyst surface is observed while there is none on the catalyst support. Gray, CFX groups; orange, sulfur; red, oxygen atom of H2O or SO3-; green, oxygen atom of H3O+; white, hydrogen.

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(c)

(d) Figure 4. Continuation.

Constant temperature is maintained by Nosé–Hoover thermostat65-67 and the equations of motion were integrated using the two time scale r-RESPA68 with a large time step of 2 fs and a small time step of 0.2 fs. Equilibration using these initial configurations was then carried out for at least 2 ns before beginning any produc-

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tion runs. Production runs were at least an additional 2 ns in duration. 3.

Results and Discussions

(i) Visualization Figure 4(a)–(d) shows the snapshots of the final configurations of the four systems studied at Ȝ = 12.8. By visual inspection of Fig. 4(a), the hydrophobic and hydrophilic segregation in a hydrated Nafion membrane can be seen. The hydrophobic regions are composed of the perfluorinated backbones. Water molecules, hydronium ions and some side chains are found in the hydrophilic domains. Figure 4(b) shows a snapshot of the interface between a Nafion membrane and the vapor phase. These systems are all periodic in three dimensions so the material that appears on the far right edge of Fig. 4(b)–(d) is simply the outermost layer of atoms of the interface on the far left side. Figure 4(c) shows the threephase interface between hydrated Nafion, water vapor and a carbon support (graphite) surface. There is no wetting of the graphite layer at Ȝ = 12.8, the highest water content studied in this set of simulations. In contrast, Fig. 4(d) reveals the wetting of the Pt catalyst surface by a mixture of Nafion, water and hydronium ions. Snapshots at lower water contents reveal lesser degrees of wetting of the catalyst surface.23 The morphology of the water clusters and their connectivity can be better understood with a visual aid as shown in Fig. 5 and 6 where the snapshots of hydrated Nafion (Fig. 5) and SSC (Fig. 6) PFSA membrane are presented with the ionomer rendered invisible at Ȝ = 4.4 and 9.6 respectively. The snapshots for both the membranes clearly indicate the presence of small clusters whose connectivity is poor at low water content and the clusters appears to have grown in size and more densely packed with better channel networks when the water content is increased. However, it is difficult, based solely on snapshots, to discern subtle differences in the size, shape and connectivity of the aqueous phase as a function of side chain length. In order to analyze these differences, we must invoke a more statistical characterization of the structure.

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(a)

(b) Figure 5. Snapshots of the final configurations of the bulk hydrated Nafion ionomer with the ionomers made invisible at hydration levels (a) Ȝ = 4.4, and (b) Ȝ = 9.6. A more connected water network is found at the higher water content.

Molecular-Level Modeling of Hydrogen PEM FC

(a)

(b) Figure 6. Snapshots of the final configurations of the bulk hydrated SSC PFSA membrane with the ionomers rendered invisible at hydration levels (a) Ȝ = 4.4, and (b) Ȝ = 9.6. A more connected water network is found at the higher water content.

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(ii) Cluster Size Distribution and Connectivity Proton transport through the membrane involves migration of distances several orders of magnitude larger than a typical cluster size indicating the importance of connectivity between the aqueous domains.69 A cluster size distribution analysis, which indicates the average number of clusters present in the system corresponding to a particular size, helps in the quantitative characterization of the connectivity. However, in any cluster size analysis, one must define a cut-off distance used to determine whether molecules reside within the same cluster or not. This choice of critical cut-off distance (Rc) is somewhat arbitrary and three values were chosen. The smallest value of Rc, 2.8 Å, corresponds to the position of the first peak in the pair correlation function (PCF) between the oxygen of the water molecules.12 We also used larger values of Rc = 3.5 and 4.5 Å for an understanding of how the connectivity changes with cut-off value. The cluster size distribution in Nafion and SSC at three Rc has been examined for water contents from Ȝ = 4.4 to 12.8. Figures 7 and 8 display the cluster size distribution for the Nafion and SSC bulk membranes respectively for the three Rc distances at the highest and lowest hydration levels (Ȝ = 4.4 and 12.8). Both Nafion and SSC show only the presence of small clusters within Rc = 2.8 Å whose size increases with water content. The presence of a single large sample-spanning cluster at higher water contents is observed for larger Rc for both Nafion and SSC. Again, it is difficult to obtain an intuitive grasp of the change in morphology from the quantitative information provided in the cluster size distributions. In an attempt to find a characterization metric that could clearly distinguish between the structures of Nafion and SSC, we tried examining the data in Figs. 5–8, from a variety of additional perspectives. We found cumulative probability distributions to be most useful. In Fig. 9, we plot the cumulative probability distribution for finding water molecules in a cluster of given size for both the membranes at Ȝ = 4.4 to 12.8 using all three cut-off distances. Two important asymptotes can be considered in this figure. An aqueous domain that is poorly connected will be composed of many small clusters. Therefore, the cumulative probability will quickly rise to 1.0, indicating that all water molecules are in small clusters. The

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151

100

0.030

O = 4.4

Rc = 2.8 Å

cluster distribution

0.025

Rc = 3.5 Å

80

Rc = 4.5 Å 0.020

60 0.015 40 0.010 20

0

0.005

0

5

10

15

20

400

600

800

0.000

cluster size

(a) 350

0.6

cluster distribution

O = 12.8

Rc = 2.8 Å

300

Rc = 3.5 Å

0.5

Rc = 4.5 Å

250

0.4 200 0.3 150 0.2 100 0.1

50 0

0

5

10

15

20

2360 2380 2400 2420 2440 2460

0.0

cluster size

Figure 7. Cluster size distribution for hydrated Nafion at water contents corresponding to (a) O = 4.4; (b) O = 12.8.

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0.030

100

O = 4.4

Rc = 2.8 Å

cluster distribution

0.025

Rc = 3.5 Å

80

Rc = 4.5 Å 0.020

60 0.015 40 0.010 20

0

0.005

0

5

10

15

20

400

600

800

0.000

cluster size

(a) 0.6

350

cluster distribution

O = 12.8

Rc = 2.8 Å

300

Rc = 3.5 Å

0.5

Rc = 4.5 Å

250

0.4 200 0.3 150 0.2 100 0.1

50 0

0

5

10

15

20

2360 2380 2400 2420 2440 2460

0.0

cluster size

(b) Figure 8. Cluster size distribution for SSC PFSA membrane at water contents corresponding to (a) O = 4.4; (b) O = 12.8.

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fraction of molecules in cluster

1.2 Nafion SSC PFSA membrane

O = 4.4

1.0

O = 6.4

O = 9.6 O = 12.8

0.8

0.6

0.4

(a)

0.2

0.0

0

20

40

60

80

100

120

140

cluster size

1.2

fraction of molecules in cluster

Nafion SSC PFSA membrane 1.0 O = 4.4

0.8

O = 6.4

O = 9.6

O = 12.8

0.6

0.4

0.2

0.0

(b) 0

500

1000

1500

2000

2500

3000

cluster size

Figure 9. Cumulative number of molecules in clusters in hydrated SSC PFSA ionomer and Nafion for Rc of (a) 2.8 Å; (b) 3.5 Å; and (c) 4.5 Å. Continuous line represents Nafion and dotted lines are for SSC PFSA membrane.

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1.2

fraction of molecules in cluster

Nafion SSC PFSA membrane 1.0 O = 4.4

O = 6.4

O = 9.6

O = 12.8

0.8

0.6

0.4

0.2

0.0

(c) 0

500

1000

1500

2000

2500

3000

cluster size

Figure 9. Continuation.

most pronounced example of this is the plot for Nafion at Ȝ = 4.4 with Rc = 2.8 Å in Fig. 9(a). The opposite asymptote occurs in a very well connected aqueous domain, in which all water molecules are part of a single large sample-spanning cluster and can be best seen by the plot for SSC at Ȝ = 12.8 with Rc = 4.5 Å in Fig. 9(c). All intermediate behavior can now be assessed based on its position between these two asymptotes. This provides a very useful and immediately visualizable understanding of the connectivity of the aqueous network. In Fig. 9(a), the cut-off, 2.8 Å, is small and based on this Rc, most of the water molecules are in small clusters. Certainly, the degree of connectivity increases with increasing water content as can be seen by the lowering of the initial rise in the curves. There is a small hint that SSC has better connectivity than Nafion in three of the four curves. For Rc = 3.5 Å in Fig. 9(b), we are able to distinguish between a poorly connected aqueous domain at Ȝ = 4.4 and highly connected aqueous domains at Ȝ = 9.6 and 12.8. At these high and low asymptotes, the differences between SSC and Nafion are small. However, at the intermediate water content of Ȝ = 6.4, we see a strong signature that the aqueous domain in SSC

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fraction of molecules in cluster

1.2

1.0

Nafion 3-mer (O = 6.4) SSC 3-mer (O = 6.4) Nafion 15-mer (O = 6) SSC 15-mer (O = 6)

0.8

0.6

0.4

0.2

0.0 0.0

0.2

0.4

0.6

0.8

1.0

cluster size

Figure 10. Cumulative number of molecules in clusters in hydrated SSC PFSA ionomer and Nafion for Rc = 3.5 Å as a function of molecular weight – 15mer (gray) and trimer (black).

PFSA membrane is better connected than that in Nafion. This signature of better connectivity of aqueous domains in SSC at intermediate hydration level shown for the small molecular weight chains (trimers), is also observed for the simulations of the chains composed of 15 repeat units as depicted in Fig. 10. In Fig. 9(c), the high value of Rc (4.5 Å) has shifted all the curves to larger cluster sizes. Still, where there is a difference between the two polymer electrolytes, SSC PFSA membrane shows a more connected aqueous domain. There are a number of useful points to be drawn from this analysis of the water cluster distribution. First, it appears that the cumulative water cluster distribution with a properly chosen cutoff distance is a metric that allows one to see clearly differences in connectivity of the aqueous domain as a function of both water content and polymer architecture. Clearly, Fig. 9(b) shows the connectivity of the aqueous domain moving from many small disconnected clusters to a single sample-spanning cluster as a func-

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tion of increasing water content and also that clusters in SSC is better connected than in Nafion. A word of caution is in order. A better connectivity in SSC cannot be instantly equated to higher conductivity. In the simulations of Nafion and SSC, the same amount of water is distributed in the same volume. A change in connectivity is almost certainly accompanied by a change in the characteristic dimension and geometry of the cluster channel. In other words, if one stretches out clusters in SSC in order to better connect them, under the constraint that the volume of the aqueous domain is the same as that in Nafion, then one must accept that the dimension of a channel in a clusters in SSC is smaller. (That the characteristic channel width in SSC is smaller than in Nafion has also been observed experimentally70 at least for the medium and high water contents.) This change in dimension can affect the environment of the water and hydronium ions. If the channel is smaller and more spread out in SSC PFSA membrane than in Nafion, then it has more surface area with the hydrophobic phase per unit volume. This additional interaction with the hydrophobic phase can be characterized as additional confinement. The effects of confinement on both the diffusion of water and the vehicular and structural components of diffusion of the proton are not fully understood. Thus it is important to corroborate the suggestions of this water cluster distribution analysis with other measures of structure and transport. (iii) Pair Correlation Function Just as water cluster distributions provide a more global measure of the structure of the aqueous domain, PCFs provide a more local measure of the structure. PCFs can be constructed between any two pairs of atoms or pairs of types of atoms and each PCF provides unique information. The S–S PCF provides information about the clustering of side groups while the oxygen of water– oxygen of water ( O H 2 O  O H 2 O ) PCF helps in describing the water network. The distribution of the hydronium ion in the aqueous domain can be characterized through the oxygen of hydronium– oxygen of hydronium ( O H O   O H O  ) PCF. These PCFs vary 3

3

depending on the polymer architecture, water content and interfacial regions.

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Figure 11 displays the total S–S PCF for Nafion and SSC membranes for a range of Ȝ from 4.4 to 12.8. The first feature to observe in these PCFs is that the association of sulfonate groups decreases (peak height decreases) with increasing water contents. The sulfonate group tries to remain in the aqueous domain. When there is very little water, the sulfonate groups are statistically grouped closer together sharing the little water that is available. Increasing the degree of hydration helps the sulfonate groups to spread out. The second feature to observe in the S–S PCF is that the first peaks are higher in Nafion than in SSC. The increased clustering of sulfonate groups in Nafion can be attributed to the longer side chain which enhances flexibility and increases the ability for sulfonate groups to rearrange their structure in order to optimize their interactions. The fact that the S–S clustering is more pronounced in Nafion than in SSC, especially at low and intermediate water contents is consistent with the water cluster distribution analysis that showed that the aqueous domain is less well connected in Nafion than in SSC. The logic can be stated as follows. If the sulfonate groups are more distributed in SSC and the sulfonate groups have a hydration shell around them, then the water distribution is also better distributed and therefore the connectivity of the aqueous domain increases. The O H O   O H O  PCF for Nafion and SSC has been dis3

3

played in Fig. 12. The H3O+ ions are counter ions of the sulfonate anions and are expected to be associated with them at low water contents.7,71 As the water content is increased they become more separated from the sulfonate groups. The general trends observed in both the membranes are the peaks at relatively long distance and the peak heights decreasing with hydration. Peak heights and their locations can indirectly characterize the size and nature of the aqueous regions. When the water content is low, the H3O+ ions are distributed in small clusters causing a strong correlation and enhanced peaks in Nafion compared to SSC is consistent with the cluster distribution and S–S PCF. Pair correlation functions can also be used to show differences in structure between the bulk PEM and interfacial regions. Figure 13 shows the difference in the water network in the aqueous domain of bulk membrane of Nafion to those adsorbed on to a catalyst surface through the O H 2 O  O H 2O PCF at all the water con-

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3.5

total -O3S

O = 4.4 O = 6.4 O = 9.6 O = 12.8

3.0 2.5

SO3-

(inter + intra)

g(r)

2.0 1.5 1.0 0.5 0.0

0

2

4

6

8

10

r(Å)

(a) 3.5 -

O = 4.4 O = 6.4 O = 9.6 O = 12.8

3.0 2.5

total O3S

SO3

-

(inter + intra)

g(r)

2.0 1.5 1.0 0.5 0.0

0

2

4

6

8

10

r(Å)

(b) Figure 11. Total sulfur-sulfur pair correlation functions at different hydration levels for hydrated (a) Nafion; and (b) SSC PFSA membrane

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2.5

H3O+

O = 4.4 O = 6.4 O = 9.6 O = 12.8

2.0

O+H3

g(r)

1.5

1.0

0.5

0.0

0

2

4

6

8

10

r(Å)

(a) 2.5 +

O = 4.4 O = 6.4 O = 9.6 O = 12.8

2.0

H 3O

+

O H3

g(r)

1.5

1.0

0.5

0.0

0

2

4

6

8

10

r(Å)

(b) Figure 12. O

H 3O 

O

H3O 

pair correlation functions at various water con-

tents for: (a) Nafion; and (b) SSC PFSA ionomer.

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30

H2O

25

O = 4.4 O = 6.4 O = 9.6 O = 12.8

OH2

g(r)

20

15

10

5

0

0

2

4

6

8

10

r(Å)

(a) 30

H2O

25

OH2

O = 4.4 O = 6.4 O = 9.6 O = 12.8

20

15

( ) 10

5

0

0

2

4

6

8

10

r (Å)

(b) Figure 13. O H 2O  O H 2O pair correlation functions for: (a) bulk Nafion; and (b) in the adsorbed phase on the catalyst at various water contents.

Molecular-Level Modeling of Hydrogen PEM FC

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tents. In a homogeneous system, PCF is unity at infinite separation since it is scaled by bulk density. But a membrane/vapor/catalyst (system IV) interface system can be divided into five regions (bulk membrane, vapor interface, membrane interface, bulk vapor and adsorbed surface) and the bulk density is the weighted average of all their individual phase densities. Therefore, the PCFs for each region have been scaled with their respective individual densities to obtain unity at infinite separation (here 10 Å). The adsorbed region in Fig. 13 (b) has been defined to include 10 Å above the catalyst surface. Both the regions show similar positions of their first peaks but the structure of the adsorbed phase is greater and more long-ranged than in the membrane. The enhanced structure can be attributed to the presence of the surface acting as a template for the adsorbed monolayer. The bulk and adsorbed phase show qualitatively similar behavior in terms of the increase in peak height with the decrease in Ȝ. (iv) Hydronium Hydration Histogram The hydration of the hydronium ions can be examined either by the O H O   O H 2O PCF or by creating a probability distribution 3

of finding hydronium ions with a certain degree of hydration. In this case, a probability distribution is built by counting the number of waters within 3.2 Å of the oxygen in each hydronium ion. This particular cut-off value was chosen to include the water molecules within the first hydration shell based on the O H O   O H 2O PCF.12 3

In Fig. 14 we study the effect of polymer architecture and water content on the hydration of hydronium ions. Better hydration of H3O+ ions (by • 3 water molecules) with increase in water contents can be seen by comparison of Fig. 14(a) with 14(b). The degree of hydration of hydronium has relevance to structural diffusion as it requires the presence of Eigen ion (H3O+ + 3 H2O), which is discussed in detail in Section III. Figure 14 supports the experimental observation of low proton conductivity at low water contents72 due in part to the reduction of structural diffusion because the probability of finding H3O+ surrounded by sufficient H2O molecules is lower. Figure 14 shows that at intermediate water contents, the probabilities for hydronium ions hydrated with three or more H2O molecules are higher in Nafion than in

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probability of H2O-H3O association

200 Nafion SSC PFSA membrane 150

O = 6.4

100

50

0

0

1

2

t3

number of water molecules associated

(a)

probability of H2O-H3O association

200 Nafion SSC PFSA membrane 150

O = 12.8

100

50

0

0

1

2

t 3

number of water molecules associated

(b) Figure 14. Distribution of hydrated hydronium complexes for the ionomers, Nafion and SSC PFSA membrane at the intermediate water contents (a) O = 6.4, (b)O = 9.6.

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SSC. The presence of more fully hydrated H3O+ ions in Nafion accords with the understanding of the less connected aqueous domain in Nafion. If the aqueous domains are less connected in Nafion, then there is less surface area with the hydrophobic domain and the hydronium ions have a higher probability of being surrounded by water molecules, as reflected in the hydration histogram in Fig. 14. The presence of a vapor interface changes the hydration of the hydronium ion.22 In Fig. 15, we have compared hydration of hydronium ions in Nafion for Ȝ = 4.4 and 12.8 as a function of different interfacial regions. These regions are the bulk membrane, the membrane-side of the interface and the vapor-side of the interface. In this case, the interface is an imaginary plane and the membraneside is material within 10 Å of the plane on the membrane side and the vapor-side contains materials within 10 Å of the plane on the other side. There is a slight decrease in the probability of finding a fully hydrated hydronium ion as we move towards the vapor phase at both the water contents. The decrease in hydration of the hydronium ion is likely to negatively impact structural diffusion in these regions. (v) Water Density Profile Water density profiles help to understand the interfacial width and the pathway for the protons. System II (membrane/vapor interface) has been used to measure the interfacial width. Systems III (membrane/vapor/graphite) and IV (membrane/vapor/catalyst) helps in identifying the pathway or lack thereof for transport of protons. In these systems water is being drawn out of the hydrated Nafion in order to establish equilibrium between the PEM and the vapor phase and/or the adsorbed phase. The average density profiles of systems II and IV are shown in Figs. 16 and 17 respectively with the zero coordinate on the x axis corresponding to the central location of the membrane/vapor interface. The density profile of system III has been not shown since even at the highest water content the wetting of the graphite surface has not been observed (Fig. 4c ) and hence it will have a trend similar to system II. (Admittedly, the graphite surface used in this simulation was completely free of defects and oxidation, which inhibits wetting.) Both plots show a dehydrated region near the interface. There is some

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probability of H2O-H3O association

1.0 bulk membrane membrane interface vapor interface

0.8

O = 4.4

0.6

0.4

0.2

0.0

0

1

2

t3

number of water molecules associated

(a)

probability of H2O-H3O association

1.0 bulk membrane membrane interface vapor interface

0.8

O = 12.8

0.6

0.4

0.2

0.0

0

1

2

t3

number of water molecules associated

(b) Figure 15. Hydration histogram for hydronium at various regions in the membrane/vapor interface for water content (a) O = 4.4, (b)O = 12.8.

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0.014

vapor

hydrated membrane

O = 4.4 O = 6.4 O = 9.6 O = 12.8 hyperbolic tangent

3

water density (molecule/Å )

0.012 0.010 0.008 0.006 0.004 0.002 0.000 -30

-20

-10

0

10

20

30

distance from interface (Å)

Figure 16. Water density profile along the z direction in the membrane/vapor interface (system II) at O = 4.4, 6.4, 9.6 and 12.8. Hyperbolic tangents have been fitted to determine the interface thickness.

noise in the water density on the membrane side of the systems since the system is spatially heterogeneous at the nanoscale and the simulations are not long enough to fully average the relaxation. It is typical to obtain the interfacial width in a two phase system by fitting the density distribution on to a hyperbolic tangent73 using the following equation

U ( z)

1 1 § 2z  ze · Ul  U g  Ul  U g tanh¨ ¸ d 2 2 © ¹







(1)

where d is the interfacial width, Ul and Ug correspond to the bulk membrane and bulk vapor density of water (can be calculated from simulation data) and ze location of the interface. The interfacial widths calculated from the hyperbolic tangents fitted to the simulated water density profile in system II are given in Table 2. There

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0.014

water density (molecule/Å3)

0.012

hydrated membrane

platinum surface O = 4.4 O = 6.4 O = 9.6 O = 12.8

0.010 0.008 0.006 0.004 0.002 0.000 -30

-20

-10

0

10

20

30

distance from interface (Å)

Figure 17. Density profile of water along the z direction in the membrane/vapor/Pt interface (system IV) at O = 4.4, 6.4, 9.6 and 12.8. Water density on the platinum surface increases with the hydration level.

is a decrease in the interfacial width with increase in the humidity which can be explained by the surface topology of the hydrated membrane at the interface. The surface roughness is mainly due to the relatively large and inflexible Nafion molecules and these valleys of roughness can be smoothed by filling them with small water molecules. Therefore, with the increase in water content the

Table 2 Membrane/Vapor Interfacial Width at Various Water Contents Water content (Ȝ) 4.4 6.4 9.6 12.8

Interfacial width į (Å) 9.0 8.6 8.0 7.7

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Figure 18. Snapshot of the final configuration taken normal to the catalyst surface in membrane/vapor/Pt interface at Ȝ = 12.8 to show distribution of the mixture (water, hydronium and Nafion) traversed across the catalyst surface via surface diffusion.

dehydrated region of the membrane near the interface decreases leading to thinner interfaces. The density profile of system IV in Fig. 17 shows that the water content on the platinum surface increases with water content. Moreover the snapshots taken at an angle normal to the catalyst surface (Ȝ = 12.8) given in Fig. 18 indicates a monolayer density of water on the catalyst surface with a two dimensional hydrogen bonding network. The water molecules can be adsorbed to the catalyst surface either by surface diffusion or by moving through the vapor phase. Since the wetting of the platinum is by a monolayer it suggests the predominance of the surface diffusion over the latter. Since only water molecules are found in the vapor phase, the presence of hydronium ion and Nafion molecules on the catalyst surface in the snapshot indicates that they must have traversed by surface diffusion. It is also recognized that the ordered structure of water molecules seen on Pt surface (Fig. 18) is different from other published structures48,74 owing to limitations in the description of the surface as rigid.

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(vi) Hydronium Orientation at the Interface The orientation of the hydronium ion can be measured in terms of angle between the hydronium axis (a line joining the midpoint of the three hydrogen atoms and the oxygen) and the z axis (perpendicular to the interface surface). Measurement of an angle of 0° corresponds to the oxygen atom protruding into the vapor phase and 180° corresponds to the oxygen atoms buried in the membrane. Figure 19, presents the probability distribution of the orientation of the hydronium ions in the different regions of membrane/vapor system at Ȝ = 12.8. The bulk membrane has a straight line distribution implying the isotropic orientation of the hydronium ions. However, at the interfaces, there is a strong preference for the hydronium ion to be oriented with the oxygen atom protruding into the vapor phase probably due to the fact that it is energetically favorable for the hydronium ion to maintain three hydro-

0.20 0.18 0.16

bulk membrane membrane interface vapor interface

probability

0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 -1.0

-0.5

0.0

0.5

1.0

cos theta

Figure 19. Probability distribution of the orientation of the hydronium ions with respect to z axis (perpendicular to interface) in the membrane/vapor system at Ȝ = 12.8. Bulk membrane shows an isotropic distribution and the interfaces have a preferential distribution with the oxygen atoms protruded into the vapor phase. Solid line, bulk membrane; dotted line, membrane interface; and dashed line, vapor interface.

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gen bonds between its hydrogen atoms and the oxygen atom of water molecules in the hydrated membrane. Previous experimental75,76 and simulation data77 also show similar preferential orientation along the liquid/vapor interface with enhanced concentration at the interface.78 (vii) Critical Gap Earlier discussions indicate that a mixture of Nafion, hydronium and water wet the catalyst surface by surface diffusion and no wetting takes place across the graphite interface. We also examined the effect of a small gap of carbon support (graphite) between the catalyst surface and the electrolyte on wetting as a function of water content.24 It can be considered as the second catalyst particle in Fig. 2, which is not in direct contact with the electrolyte. Wetting of the surface provides the path required for the diffusion of protons (dissociated from molecular hydrogen) as hydronium ions from the catalyst to the electrolyte. MD simulations were conducted with one unit cell of graphite (7.4 Å) and with two unit cells of graphite (14.8 Å) between the hydrated membrane and the catalyst surface for water contents Ȝ = 4.4 and 12.8.24 Figure 20, provides the snapshots of the final configurations of these four systems. Visual inspection of Fig. 20 (a) and (b), shows the wetting of the catalyst surface across the small hydrophobic graphite surface (7.4 Å) by the mixture of water, membrane and hydronium. The mixture traversing across the graphite gap (forming a bridge between the catalyst and membrane) increases with the water content, as can be seen. No wetting was found to have taken place by analyzing the snapshots with a larger gap size of 14.8 Å (Fig. 20 c and d) at both the lowest and highest water content. There is a probability for the water molecules that enter through vapor phase to accumulate on the catalyst surface in a very long time scale (when dynamic equilibrium is reached) which the nanosecond simulation can not observe, but still the vapor-phase diffusion of hydronium and Nafion is not possible since they do not enter the vapor phase and their path via surface diffusion is hindered by the large gap. Therefore, a graphite gap of about 14.8 Å is sufficient enough to block proton transport from the catalyst to membrane at all water contents. It is also to be noted that, in order to dispel the possibility of the gap

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(a)

(b)

(c)

(d)

Figure 20. Snapshots of the final configurations of the membrane/vapor/catalyst interface in the presence of a graphite gap, (a) Ȝ = 4.4 with graphite gap size of 7.4 Å, (b) Ȝ = 12.8 with graphite gap size of 7.4 Å, (c) Ȝ = 4.4 with graphite gap size of 14.8 Å, (d) Ȝ = 12.8 with graphite gap size of 14.8 Å. Wetting of the catalyst surface took place with a lower gap size while no wetting was observed with a larger graphite gap at both the water contents.

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no. of H2O molecules on solid surface

1000

800

O = 4.4 with no gap O = 12.8 with no gap O = 4.4 with gap of 7.4 Å O = 12.8 with gap of 7.4 Å

600

400

200

0 0.0

0.5

1.0

1.5

2.0

simulation time (ns)

Figure 21. Wetting dynamics of water at the solid surface with gap (graphite) of 7.4 Å (gray) and no gap (black) between the catalyst and membrane. Both the systems show a similar trend of increase in wetting with the water content.

size (14.8 Å) being a function of the cut-off radius chosen for the truncation of interaction potential (10 Å), independent simulations were run with a cut-off distance of 20 Å and similar results were found. A quantitative analysis of the wetting dynamics can be done by the recording the number of water molecules adsorbed on to the catalyst surface as a function of time. Figure 21 shows the wetting dynamics with no gap (system IV) and a gap of 7.4 Å and it can be obviously seen that wetting has dramatically lowered in the presence of even a small gap (7.4 Å).24

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III. TRANSPORT 1.

Introduction

In this work, we have approached the understanding of proton transport with two tasks. In the first task, described above, we have sought to identify the molecular-level structure of PFSA membranes and their relevant interfaces as a function of water content and polymer architecture. In the second task, described in this Section, we explain our efforts to model and quantify proton transport in these membranes and interfaces and their dependence on water content and polymer architecture. As in the task I, the tool employed is molecular dynamics (MD) simulation. A non-reactive algorithm is sufficient to generate the morphology of the membrane and its interfaces. It is also capable of providing some information about transport in the system such as diffusivities of water and the vehicular component of the proton diffusivity. Moreover, analysis of the hydration of hydronium ion provides indirect information about the structural component of proton diffusion, but a direct measure of the total proton diffusivity is beyond the capabilities of a non-reactive MD simulation. Therefore, in the task II, we develop and implement a reactive molecular dynamics algorithm that will lead to direct measurement of the total proton diffusivity. As the work is an active field, we report the work to date. Extensive experimental and modeling work has been performed to measure the dynamics of the various components in hydrated PFSA membranes. The dynamics of the Nafion can be investigated by NMR79 and dynamic viscoelastic and differential scanning calorimetric measurements.80 The backbone segments of Nafion far from branch points undergo fast uniaxial rotations around the chain axis and others near a branch point are restricted in dynamics.79,81 Similarly, the side branches in Nafion have higher mobility than the backbone, and are dependent on the level of hydration and length of the side chain.82 MD simulations of PFSA membranes have shown that the mobility of the side chains increases along its length and is maximum for the sulfonated end groups,82 whose motion can possibly enhance proton diffusion.36 Significant attention has also been given to the dynamics of water in PEMs.83,84 Various techniques have been applied, includ-

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ing far infrared spectroscopy,85 radiotracer study,86 NMR,87 quasielastic neutron scattering88,89 (QENS) and MD simulation.10,11,37,71,82,90 The general observation is the increase in the mobility of water molecules with the increase in the hydration level of the membrane.86,87 QENS experiment which can capture the dynamical behavior in restricted geometries has identified the local (within channel) and long range diffusion coefficients (within region) as a function of the water content. At Ȝ > 10, the local diffusivity resembles bulk water diffusivity suggesting the bulk-like motion within the channels with the increase in the uptake of water.88 MD simulations found water molecules experiencing greater diffusion in a more segregated structure.10 Water dynamics has also been probed as a function of polymer architecture70,82,91 and temperature.71 Macroscopically, ionic conductivity can be characterized through electrochemical and impedance analysis.92 Direct measurements of ionic conductivity in MD simulations are challenging based on system size and simulation duration constraints requiring unrealistically large fields. Protons play a vital role in energy transfer in PEMFCs and other areas like the acid-base reactions or enzymatic catalysis as it has high mobility compared to other cations of similar size and charge in aqueous media.93,94 In order to quantitatively understand how the structure of PFSA membranes impacts proton mobility, it may help to first step back and understand the mechanism for proton transport in bulk water. Various theories95-97 have been proposed to explain the high mobility of protons. The currently accepted explanation is that proton transport in aqueous media occurs through a combination of vehicular diffusion — movement of the center of mass of hydronium ions and structural diffusion or Grotthuss shuttling mechanism — proton shuttling through hydrogen bonded network.16,17 The structural diffusion of protons involves forming and breaking of hydrogen bonds in the second hydration shell with the continual shuttling of identities of the two predominant solvated complexes Zundel and Eigen cations.16,51 Molecular-level description of the above mechanism has been under investigation both experimentally and computationally for the past decade. The current interpretation and the details of the steps involved in structural diffusion of protons in bulk water has been discussed by Agmon et al.51 concluding that the structural diffu-

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(a)

(b)

Figure 22. Configurations of (a) Zundel98 (H5O2+) and (b) Eigen cation99 (H9O4+). Black, oxygen atom; white, hydrogen atom.

sion of proton occurred by the isomerization of the stable Eigen cation via transition Zundel structure performing a special-pair dance. Figure 22, shows a fully optimized structure of a Zundel98 (a) and Eigen ion99 (b). Though our understanding of proton transport in bulk water has significantly advanced it becomes unclear as we move on to the aqueous domains of the PFSA membranes. The dynamics of the protons in the membranes have been investigated by simulation tools10,37,38,71,82,90,100-102 and other theoretical methodologies like electronic structure calculations103 and nonequilibrium statistical models.104,105 Recently Elliot and Paddison41 have summarized the work on molecular level modeling of proton transport. Proton transport in Nafion has been investigated by numerous MD10,37,71,82,90 studies which cannot allow the diffusion of proton by Grotthuss mechanism because the theoretical characterization of proton shuttling mechanism would involve bond breaking and bond forming. At lower water content the simulation data are closer to experimental values but at higher water content they are lower than the experimental values.35 This could suggest that structural diffusion might become more important at high water content. The vehicular diffusion of proton was found to increase with the hydration level and temperature,71 but was found to be unaffected by the monomeric sequence of Nafion chain (blocky or dispersed) at high water con-

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tent.10 Instead of protons other cations such Na+ and K+ has also been studied.35,106 Some attempts to include structural diffusion exist. The mechanism of proton transport in bulk water has been studied by various molecular modeling techniques like the Car–Parinello ab initio molecular dynamics simulations17,107 (CPAIMD), mixed quantum and classical mechanics technique108,109 (QM/MM), EVB110 and its family,111-113 mixed MD/MC algorithm114 and Q–HOP MD.115 Different empirical valence bond (EVB) models, which enable the delocalization of the proton, have been employed to study structural diffusion in Nafion.38,100,101 Proton transport about the sulfonate region was found to proceed largely through the Grotthuss shuttling mechanism. The vehicular and structural component were found to be negatively correlated, in contrast to bulk water in which the two components are uncorrelated.38 Electronic structure calculations103 show the dissociation of the proton from sulfonate after three molecules of water have been added around the acid group, and also show the formation of a solvent-separated Eigen cation with a minimum of six molecules of water using triflic acid which closely resembles the acid activity in Nafion. Although substantial effort has been undertaken, the relationship between the molecular architecture of the PEM and proton conductivity continues to be of great interest.41 The connection between structure and transport still remains unclear9 due to the uncertainty in the mechanism of proton transport within the highly acidic and confined aqueous domains of the membrane, specifically the contribution and behavioral change in the two components of proton diffusion. Modeling proton transport in large systems requires some coarse graining due to current computational limits. The degree of coarse graining among the existing approaches used to model proton transport in bulk water varies dramatically. Based on the existing analysis of proton transport in bulk water and the challenges these approaches face when being applied to PFSA membranes, we chose to develop a new coarse-grained reactive RMD algorithm. The motivation for a more coarse-grained model comes from the fact that the environment around the excess proton in the PFSA membrane is much different than that in bulk water. A model that is very finely tied to the bulk water scenario may not respond to perturbations present in the PFSA membrane. The proposed RMD algorithm, being less detailed, may respond to envi-

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ronmental conditions to a first order. It is acknowledged that the approach will not model proton transport in bulk water as faithfully as more detailed models, such as ab initio molecular dynamics due to its generality. 2.

Coarse-Grained Reactive Molecular Dynamics Algorithm

At the quantum mechanical (QM) level, a chemical reaction is described by the structure of the product, reactant and transition state along with the free energy differences between the states. The description of the reaction at a macroscopic level involves the stoichiometry, heat of reaction, activation energy, rate constant and rate law. Thus, both the QM and macroscopic descriptions require energy changes and rate constants. The additional information in the QM description is the structure. The conceptual basis of the RMD algorithm is to impose the structure of the QM transition state into a classical simulation by the usage of a set of triggers whose values are adjusted to satisfy the known heat of reaction, activation energy, and rate constant. RMD is a generalized algorithm that can be used to describe any arbitrary chemical reaction in terms of three steps (a) satisfaction of the triggers, (b) instantaneous reaction, and (c) local equilibration. The RMD algorithm is implemented as an additional step at the end of each time step in a conventional MD simulation. Thus the interaction potentials used in the reactive simulation are nonreactive and are the same as those used to generate the membrane and interface morphologies described above. The first step of the RMD algorithm is to check whether the reactants are in a configuration near the transition state based on a set of geometric and energetic triggers. The molecules are never going to adopt the exact transition state because the configuration of the molecule is based on a non-reactive interaction potential. For example, covalent bonds modeled as Hookian springs will not break. However, one can identify those configurations that are permitted by the non-reactive potential which would lead to the transition state. This set of configurations is defined by the set of geometric and energetic triggers. The choice of the triggers are

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based on ground and transition state obtained from QM and are tuned to provide the correct macroscopic properties like the activation energy and rate constant. Once a reactant satisfies the complete set of triggers, the second step of the RMD algorithm is an instantaneous reaction where the reactants are replaced by products. In this way the information about the transition state from QM has been taken into account in step one but need not be explicitly included in step two. Instantaneous reactions are bound to disturb the system energetically and structurally. Thus, the third and final step is a local equilibration of the molecules participating in the reaction and those immediately adjacent. The purpose of the local equilibration is to re-establish a reasonable structure and satisfy the heat of reaction. Once the three steps of the RMD reaction are executed, the simulation proceeds to the next time step of the MD simulation. The first application of this RMD algorithm was to bulk water. This system is chosen since the QM and experimental understanding of this system is well-established. We believe that because the RMD algorithm is more coarse-grained and does not attempt to describe the movement of the reactants along the reaction path beyond the information contained in the triggers, that the RMD algorithm parameterized for a reaction in bulk water will, to a first order, function in the PFSA membrane. In other words, because the starting and ending points of the structural diffusion reaction are likely similar, whereas the details of the transition state may not be, a more coarse-grained approach based on end points is in order. 3.

Proton Transport in Bulk Water

(i) Input from Macroscopic Model The structural diffusion of proton can be represented by the following equation: 2 H 3O   H 2O m   o H 2 O  H 3O 

4H O

(2)

The minimum hydration number for the reaction to take place was chosen as four based on the Eigen cation structure and the details

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of the choice are discussed later. The reaction rate, r, describing the number of reactions per unit volume per time is given by116 r

k [H 3O  ][H 2 O]

(3)

where the square brackets represent the concentration and k is the rate constant. Therefore, for the structural diffusion of protons, the stoichiometry can be provided by Eq. (2). The rate law is provided by Eq. (3). The heat of reaction is zero (since the reactant and product are identical). The activation energy, Ea and rate constant prefactor, ko, can be obtained either from simulation117,118 or experiment,116,119-123 and are related to the rate constant in Eq. (3) by k

§ E · ko exp¨¨  a ¸¸ © k BT ¹

(4)

(ii) Input from Quantum Mechanical Studies The three configurations of the reactants, products and transition state have to be mapped onto the RMD algorithm. Existing non-reactive potentials of H2O57,124,125 and H3O+126-128 are used to describe the reactant and product configurations. Since Zundel and Eigen cations are the two limiting forms129 for the structural diffusion the set of geometric and energetic trigger should have their structural information embedded into them. Structural diffusion of protons in bulk water has been identified by a set of six geometric and one energetic trigger. Figure 23 shows the schematic representation of the six geometric triggers. The first trigger is an obvious condition which requires the oxygen of the reacting H3O+ (O*) to be less than or equal to a cut-off distance from the oxygen of the reacting H2O. The second trigger requires the O–H bond distance between the proton to be transferred (H*) and O* to be greater than some cut-off distance. The above two triggers will help to show that the molecules are moving toward the formation of Zundel ion. The third trigger requires the angle formed by O*–H*–O(H2O) to be linear, similar to a Zundel structure in Fig. 22 (a). The fourth trigger acknowledges that water has sp3 bond hybridization and requires the angles formed by the

Molecular-Level Modeling of Hydrogen PEM FC

(a)

(b)

rOO,Zundel ” rOO,Zundel,max

rOH,Zundel • rOH,eqlbm (d)

(c)

(e)

179

șOHO § 180°

rOO,Eigen ” rOO,Eigen,max

(f)

șHOH § 105°

rOO,hydration ” rOO,hydration,max

Figure 23. Description of six geometric triggers required for structural diffusion (a) O*–O separation must form a Zundel ion (b) O*–H* separation must exceed the equilibrium bond distance (c) ‘O*H*O is nearly linear in the Zundel ion (d) Lone pair of electrons in the water should point towards the proton (e) Initial H3O+ forms an Eigen ion (f) Eigen cation is formed around final H3O+. These six geometric triggers must be satisfied along with the energetic trigger for the reaction to take place. O of H3O+, gray; O of H2O, black; H, white.

H to be transferred, the O of the H2O, and each of the two H of the H2O be near the equilibrium H–O–H bond angles for H3O+. In, other words, one of the two lone electron pairs in the water must be directed at the incoming H. The fifth trigger requires the H3O+ to be properly hydrated. Examination of Eigen ion in Fig. 22 (b) reveals minimum level of hydration required. Each of the nonreactive H on H3O+ is required to be within certain distance of an O of adjacent non-reactive H2O by the trigger. The sixth and the

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final geometric trigger require the H2O involved in the reaction be properly hydrated. In other words, once the H2O receives the proton, it becomes the H3O+ at the center of an Eigen ion. This trigger is motivated by the fact that the proton rattles between the water molecules before it hops and stays on one of the water molecules to form hydronium.111,129-131 The only way to induce the occurrence of the reverse reaction with a non-negligible probability is to force the receiving H2O to be, by default in a configuration that can potentially satisfy the reverse reaction. Automatically, the reverse reaction will not occur if during the subsequent MD step any one or more of the geometric and energetic triggers is not satisfied. By the implementation of the last two triggers we have assumed the Eigen–Zundel–Eigen transition which is in agreement with the current interpretation of the proton transfer mechanism.51 A single energetic trigger checks whether the proton possesses sufficient energy to overcome the activation barrier associated with the reaction. This trigger will provide the temperature dependence to the reaction rate that and is measured in terms of total energy of H* composed of all components of the potential energy and kinetic energy projected along the linear axis shown in Fig. 23 (c). For a classical coarse-grained description of the QM process, this mapping should be sufficient to check whether the H3O+ is in a reactive state. Once the functional form of the set of six geometric triggers and one energetic trigger has been established, the numerical values of the triggers must be adjusted to generate the correct rate of reaction. The parameterization of the triggers is an iterative procedure. Each iteration involves three RMD simulations at temperatures, 280, 300 and 320 K with a fixed set of trigger values. The values of Ea,f and ko can be obtained from the regression of the Arrhenius plot generated with the rate constant calculated at these temperatures using the simulation. If the values are within the accepted tolerance of target values than the parameterization process is stopped and a good set of triggers is obtained. The numerical values of the triggers in the two systems are listed in Table 3. We find our parameters closer to the prior study values except for the energetic trigger which has a different definition. In some cases the triggers take the form of a range of values, which account for vibrations at finite temperature. Unlike the parameterization of the reactive potentials the parameterization of these seven triggers can

0.80 – 1.30b 0.957g • 0.965 • 0.965

2.3 – 2.75b 2.35 – 2.85f 2.35 – 2.80 2.35 – 2.78

Prior Studies Classical MD RSI parameters RSII parameters

173.73c – • 142 • 142

TOHO 115.8 – 118.2c § 104h 99 – 159 54 – 154

THOH 2.35 – 2.7b 2.35 – 2.85f 2.35 – 3.30 2.35 – 2.97

rOO,Eigen max Å

2.40 – 3.30d 2.50 – 3.40f 2.50 – 3.40 2.50 – 3.25

rOO,Hydration max Å

0.0167e • –0.181 • –0.149 • –0.148

Ea,f aJ

b

The graphical representation of the triggers is given in Fig. 23. The allowable range for the trigger is based on the following: The distribution of the first peak from the g(r) O(H3O+)–O(H2O), H(H3O+)–O(H3O+) in Zundel cation and O(H3O+)–O(H2O) in Eigen cation 140 c Bond angles of ‘O1H+O2 and ‘H3O2H+ from optimized isolated H5O2+ structure.98 d The distribution of the first peak from the g(r) O(H2O)–O(H2O) in quantum simulations of water.141 e Activation energy.123 f The distribution of the first peak from the g(r) of classical MD simulations where the system of hydronium ions and water molecules are treated classically. g Equilibrium bond distance of OH in H3O+ TIP3P model. h Equilibrium bond angle in TIP3P model.57

a

rOH,equilb Å

rOO,Zundel max Å

Triggers

Table 3 Numerical Values of the Geometric and Energetic Triggers after Parameterization a

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be expected to be easier due to the availability of the data from different sources as shown in the Table 3. (iii) Instantaneous Reaction and Local Equilibration The reaction for structural diffusion involves replacing the bond-stretching (harmonic) interaction of the O*–H* of the reactant H3O+ with a non-bonded interaction while the reverse switch is made for the reactant O(H2O) and the H*. Then the proton is moved along the O*O axis such that the ratio of O*–H and O–H distances are the same in the product molecules as they were in the reactant molecules. There is one important note that has to be taken into account during the calculation of the number of reactions, namely proton rattling. As mentioned above, it has been noted that the proton vibrates to and fro between water molecules with a time scale on the order of 100 fs.130 The macroscopic equation to which we are fitting has no such temporal resolution and hence a clear definition of rate constant is required. At the macroscopic scale, a reaction event occurs only if there is net movement of the proton and each forward and reverse motion of a vibrating proton would not constitute an independent reaction event. Therefore, if a proton started on molecule i and was vibrating between molecules i and j, a reaction is said to have occurred if and only if proton ended up on molecule j. Since the experiments to which we fit the simulation did not have femtosecond resolution while measuring the relaxation time, this interpretation is consistent with the experimental data, which are providing the target Ea and ko. The objective of local equilibration is to adjust the positions of the atoms in such a way that the system is not affected energetically and structurally due to the reaction. We have discussed two methods of local equilibration in this work. The first method involves the equilibration of the two reacting molecules until the correct heat of reaction is satisfied. In the results and discussion, the shortcomings of this approach will be presented. Our second method of local equilibration has an objective function that was a weighted combination of both the satisfaction of the heat of reaction and the restoration of a equilibrium hydrogen bonding network structure and is achieved through the equilibration of the proton transferred and the four hydrating molecules, as shown in trigger 5 and 6 of

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Fig. 23 (e and f). The objective function Fobj can be defined by the root mean square (RMS) error of the energy difference, 'URMS, and structural difference, 'g(r)RMS, with weighing factors w, to each term as follows Fobj

w1'U RMS  w2 'g (r ) RMS

(5)

The energetic component of the objective function, 'URMS, is calculated by the difference in the instantaneously calculated energy of the entire system before reaction, Ubefore, and after equilibration, Uafter,

'U

RMS

§ U after  U before ¨ ¨ U before ©

· ¸ ¸ ¹

2

(6)

The structural component of the objective function, 'g(r)RMS, is given by the following equation,

'g (r )

RMS

1 N pairs

j N pairs

¦ j 1

§ rij  rijtarget ¨ ¨ r target © ij

· ¸ ¸ ¹

2

(7)

where rij refers to the distance between the atoms i and j and Npairs refers to each such pair of atoms. From initial study, we chose Npairs = 12 and rijtarget was based on the location of peaks in the PCF between the atoms i and j in an analogous non-reactive simulation. Certainly, other more sophisticated local equilibration techniques are possible, but as of now we have explored only these two options. (iv) Simulation Details The simulation details such as force and energy calculation including the potential models of H2O and H3O+ are similar to the techniques and methods described in the earlier discussion. Unlike other simulations111,115,132 of an excess proton in bulk water we

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have considered 15 hydronium ions in a system of 1875 water molecules for better statistics. NVT simulations were performed at three temperatures 280 K, 300 K and 320 K with experimental measured water densities of 0.9999 g/cc, 0.9965 g/cc and 0.9891 g/cc respectively.133 Nosé–Hoover thermostat was operated with a slightly higher frequency of 0.01 fs-1 to remove the excess heat that might not have been removed during local equilibration after reaction. Three systems were studied at these temperatures: (a) a non-reactive system, in which there is no structural diffusion, (b) a reactive system with local equilibration scheme I (RSI), and (c) a reactive system with local equilibration scheme II (RSII). The Polak–Ribiere conjugate gradient method134 was used in RSII to perform the non-linear multivariate optimization of the objective function with the weighing factors, w1 1 and w2 10 . (v) Results and Discussions The six geometric and one energetic trigger that were discussed earlier were parameterized to fit the rates obtained from the proton magnetic relaxation measurements in 17O-enriched water using a line broadening technique. Luz and Meiboom123 represented the proton transfer reaction by Eq. (2) and provided numerical values of the constants in Eq. (4) as ko = 6.0x1011 l/mol/s and Ea = 2.4 kcal/mol. These values are in agreement with the other experimental values122,135,136 of 2.4 – 2.6 kcal/mol and gives rate constant, k , close to other experimental values.116,119,121 The rate constants in simulation were calculated using the expression k

N react 1 u time ˜ Vbox [H 2 O][H 3O  ]

(8)

where Vbox is the simulation box volume, Nreact is the number of molecules undergone reaction according to the definition discussed earlier, time is the length of the simulation and the squared brack-

Molecular-Level Modeling of Hydrogen PEM FC

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15 expt RSI RSII

rate constant (109 l/mol/s)

14 13 12 11 10 9 8 7 270

280

290

300

310

320

330

temperature (K)

Figure 24. The rate constant k, calculated in RSI (triangle) and RSII (square) using Eq. (8) is compared to the experimental (bold line) values (Ref. 123) as a function of temperature.

ets represent the concentration. The measured rate constants in RSI and RSII along with experimental values123 are represented in Fig. 24. These values were used to generate the Arrhenius plot from which the activation energy, Ea,f, and the rate constant prefactor,

Table 4 Activation Energy and Rate Constant Prefactor a System

ko 1011 l mol-1s-1

Ea,f kcal/mol

Experimental b 5.99 2.40 RSI 8.27 2.57 RSII 2.01 2.23 a Activation Energy, Ea,f and rate constant prefactor, ko are obtained from Arrhenius plot using the rate constants in Fig. 24. b Reference 123.

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ko, listed in Table 4, were obtained. The Ea,f and the rate constant k, calculated from both the systems agree within 7% of experimental value. The agreement of the prefactor is within 67% of the experimental value, which is sufficient for a rate constant, where order of magnitude agreement is acceptable. Other simulations117,118 obtained Ea,f of 2.5 – 2.7 kcal/mol. The total diffusivity of the charge can be determined without any ambiguity by just following the trajectory of the center-ofmass position of molecule to which the charge is covalently bonded. Using the mean square displacement, the total diffusivity can be calculated with the Einstein relation

Dtot

>r t  W  r t @2 lim

x of

2dW

(9)

where d is the dimensionality and IJ is the observation time. The decomposition of the total charge diffusivity into vehicular and structural components is obtained by enforcing the constraint, the total change in position of the charge at each step must be equal to the sum of the displacement attributed to vehicular and structural components: 'rtot

'rveh  'rstruct

(10)

When there is no reaction 'rstruct = 0 and entire displacement of the molecule is categorized as vehicular. During the charge transfer from one molecule to another, the displacement of the molecule by the classical MD step before reaction is considered as the vehicular contribution and the displacement of the reactant H3O+ from its location to the final position of the product H3O+ ion after the local equilibration is taken as the structural displacement. Therefore, the vehicular displacement is continuous while the structural trajectory of a proton can remain unchanged in the absence of a reaction. By fitting the rate constant, the structural diffusivity of the charge should be reproducible. An estimate of the structural diffusivity can be obtained using the Einstein relation

Molecular-Level Modeling of Hydrogen PEM FC

187

16 estimated RSI RSII

12

-5

2

structural diffusivity (10 cm /s)

14

10 8 6 4 2 0 270

280

290

300

310

320

330

temperature (K)

Figure 25. The estimated (bold line) structural diffusivity of the proton from Eq. (11) as a function of temperature is used as the reference for the structural diffusivities obtained from RSI (triangle) and RSII (square).

est D struct

>r t  W struct  r t @2

struct

6W struct

where Wstruct is the proton lifetime and

>r t  W  r t @ struct

(11) is the

hopping length. Wstruct can be calculated from the experimental rate constant k, as 2.2, 1.7 and 1.3 ps at the three temperatures 280, 300 and 320 K respectively using the following relationship:

W struct

1 k [ H 2 O]

(12)

A mean displacement as 2.65 Å was chosen, which is the average distance between O*–O of the two reacting molecules for the rOO,Zundel,max trigger of 2.8 Å. Figure 25 shows the estimated struc-

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Myvizhi Esai Selvan and David J. Keffer

vehicular diffusivity (10-5 cm2/s)

10 non-reactive system RSI RSII estimated

8

6

4

2

0 270

280

290

300

310

320

330

temperature (K) Figure 26. Vehicular diffusivity of the proton which measures the movement of the centre of mass of the hydronium ion is given as a function of temperature – bold line, non-reactive system; triangle, RSI; square, RSII; dot-dashed line, estimated using Eq. (13).

est along with the structural diffusivities from tural diffusivity, D struct the two systems RSI and RSII. The structural diffusivities of the est two systems agree with D struct within the standard deviations. The uncertainty in Fig. 25 is one standard deviation of the x, y, and z components of the diffusivity. It is relatively large due in part to the fact that we must have a dilute system of hydronium ions (15 hydronium ions in 1875 water molecules), for comparison with experiment. Work is underway to refine these current calculations and reduce the uncertainty. The vehicular diffusion components from the non-reactive system, RSI and RSII are plotted in Fig. 26. Diffusivities from the classical MD simulation, Dveh can be used as the reference value est for comparison. The expected vehicular component, Dveh can also be generated based on the experimental total diffusivity and the

Molecular-Level Modeling of Hydrogen PEM FC

189

est D struct from the previous Section to confirm our Dveh with the following relationship

expt Dtotal

est est Dveh  D struct

(13)

assuming the vehicular and structural diffusivities are uncorreest and Dveh values agree well. When lated. As can be seen, the Dveh the RMD algorithm is incorporated there is a marked increase in the vehicular component. The increase in RSI is much too high compared to RSII. The difference can be attributed to the type of local equilibration used. In RSI, the objective function is purely based on satisfying the heat of reaction and during equilibration it might create defects in the hydrogen bonding network. RSII can override this anomaly by the inclusion of the structural term in the objective function. The defects in the hydrogen bonding network can be explained by the O–O distance which is 1.6 Å for H3O+– H2O and 1.85 Å for H2O–H2O. During the absence of local equilibration the reaction in Eq. (2) takes place more specifically as 4 H 2O H 3O (1.6)  H 2 O (1.85) m o H 2 O (1.6)  H 3O (1.85)

(14a)

where the subscripts indicate the first peak positions in the PCF between the O of the molecule (H3O+ or H2O) and O(H2O). The products are in a non-equilibrium configuration. Out of the two modes of equilibration only RSII tries to attain the following reaction  2o H O H3O(1.6)  H 2O(1.85) m 2 (1.85)  H 3O(1.6) 4H O

(14b)

where the products and reactants are in equilibrium hydrogenbonding configuration. This can be further supported by comparing the O*(H3O+)–O(H2O) PCFs from the non-reactive system to those of RSI and RSII at the end of the local equilibration in Fig. 27. The reaction distorts the local structure, as expected, and the local equilibration tries to re-establish the structure. The distortion is still severe in RSI, since there is no attempt to maintain the hydrogen-bonding network during the equilibration. The placement

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Myvizhi Esai Selvan and David J. Keffer

8

H3O+*

non-reactive system RSI RSII

OH2

g(r)

6

4

2

0

2

3

4

5

6

distance (Å)

Figure 27. A comparison of the effect of equilibration schemes on O

H 3O 

 OH 2O

pair correlation functions. Local equilibration helps in restoring the disrupted hydrogen bond network due the reaction. The attainment of the structure of the nonreactive system (bold line) by the different local equilibration schemes in RSI (dotted) and RSII (dashed) is shown by the PCF of O*(H3O+)–O(H2O) at 300 K.

of the first peak is wrong and the second peak is lost. The implementation of the sophisticated equilibration scheme in RSII, has successfully relocated the first peak to the proper location and has restored the second peak. The structure is not perfect, but RSII definitely represents a significant improvement over RSI and a corresponding reduction in the vehicular diffusivity can be observed. Therefore, the source of the high vehicular diffusivity problem has been correctly identified. However, the vehicular diffusivity in RSII is still high compared to the non-reactive system. The modification of the local equilibration scheme to include more atoms would in all likelihood further reduce this difference. At this stage, the results of RSII are considered satisfactory. Figure 28 displays the experimental charge diffusivity and the total diffusivity in RSI and RSII. Both systems have higher diffu-

Molecular-Level Modeling of Hydrogen PEM FC

expt RSI RSII

20

total diffusivity (10-5 cm2/s)

191

15

10

5

0 270

280

290

300

310

320

330

temperature (K)

Figure 28. Total diffusion of charge in RSI (triangle) and RSII (square) are plotted with the experimental (bold line) values (Ref. 93 and 137) as a function of temperature.

sivities than the experimental values93,137 since the vehicular component contribution is high due to the reasons discussed above. The relationship among the structural, vehicular and total diffusivity can be further studied by analyzing the correlation between the structural and vehicular components. Combining Eqs. (9) and (10) we have

Dtot

lim

x of

2 2 'rveh  'rstruct  2 'rveh 'rstruct

2 dW

(15)

where Dveh, Dstruct and Dcorr can be used to represent the three terms respectively. The correlation term ¨rstructx¨rveh for the RSII was found fluctuate around zero signifying the absence of correlation between the two components of the charge diffusion which is in agreement with other work.38

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Myvizhi Esai Selvan and David J. Keffer

4.

Transport in Nafion

In this Section, we report on transport properties generated from the non-reactive simulations in the first task and discuss work in progress on extracting transport properties from the reactive simulations in task II applied to PFSA membranes. (i) Water and Vehicular Hydronium Diffusivities

The classical MD simulations performed in task I provide self-diffusion coefficients for water and also for hydronium ions, which is strictly the vehicular component of the proton diffusivity. These diffusion coefficients are calculated from the mean square displacement of H2O and H3O+ using the Einstein relation. The numerical values for Nafion and SSC membranes at the four hydration levels are listed in Table 5 along with the experimental values.70,72 First, both experiment and simulation agree that the diffusivity of water increases with increasing water content. This can be attributed to the facts that (a) the connectivity of the aqueous phase increases and (b) the degree of confinement in an individual channel decreases with increasing hydration level. Table 5 Diffusion Coefficientsa for Water and Hydronium Ions in Hydrated Nafion and SSC PFSA Membranes at Various Water Contents Diffusion coefficients u 10-6 cm2 s-1 SSC PFSA membrane Nafion H2O H3O+ H2O H3O+ b b c 4.4 0.91 (0.85) 0.11 (0.16) 1.02 (0.5) 0.20 (0.8)c 6.4 2.78 (1.4) 0.42 (0.9) 3.56 (2.0) 0.97 (1.8) 9.6 6.50 (4.5) 1.34 (6.0) 6.39 (4.4) 1.96 (5.0) 12.8 7.86 (5.0) 2.12 (10.0) 9.66 (5.2) 3.20 (9.0) a Calculated from mean square displacements. b Values in parentheses for both water and hydrated proton for the SSC PFSA membrane are experimental values70 of the Dow membrane with an EW of 1084 c Values in parentheses for both water and hydrated proton for the Nafion membrane are experimental values72 for Nafion 117. Water content O

Molecular-Level Modeling of Hydrogen PEM FC

193

It is known that the TIP3P potential model of water inherently has a larger diffusivity value138 in bulk water than the experimental value, and this limitation in the potential is also observed for the water diffusivities in both Nafion and SSC relative to experiment. In the simulation data as listed in the Table 5, the water diffusivities in Nafion are consistently higher than those in the SSC PFSA membrane (except at Ȝ = 9.6). Kreuer et al.70 measured high water diffusivities in Nafion (EW 1100) than in the SSC PFSA membrane (EW 1084) at low water contents and almost identical diffusion coefficients at high water contents (Ȝ > 15 – 20). The high water diffusivity in Nafion at low Ȝ was explained70 by the architecture of long flexible side chain in Nafion that can accommodate well connected water clusters at very low degree of hydration. Based on simulation results, we find the aqueous phase in Nafion to be less connected than that of SSC at the intermediate water content. We therefore suggest that, the higher diffusivity in Nafion is not due to increased connectivity but rather decreased degree of confinement in the individual channels, a point which is consistent with the larger channel widths of Nafion observed experimentally.70 The simulated and experimental hydronium diffusivities both increase with increasing water contents. The simulated values are lower than the experimental values,70,72 presumably, due to the fact that the simulations report only the vehicular contribution to the proton diffusivity, whereas the experiment measures the total proton diffusivity. Experimentally, Nafion has higher proton diffusivity than SSC at low water contents and lower proton diffusivity than SSC at high water contents. The vehicular diffusion coefficients of the hydronium ion measured from simulation are higher for Nafion than in SSC PFSA at all water contents. Clearly a detailed understanding of the total proton diffusivity as a function of polymer architecture requires a model capable of structural diffusion. (ii) Structural Diffusion of Protons

To date, our reactive molecular dynamics simulations of proton transport have been limited to bulk water. However, the extension of the RMD algorithm to proton transport in PFSA membranes is analogous to what has been done in bulk water and simi-

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Myvizhi Esai Selvan and David J. Keffer

larly requires an understanding of the reactions involved in the process. The structural diffusion of proton in a PFSA membrane can be described by three reactions depending upon the reactants and the surrounding environment. If the channels that compose the aqueous domain are sufficiently large, there may be a bulk-like region near the center of the channel, where the water structure is similar to bulk water and where, therefore, we can expect the reaction to take place as in Eq. (2), 2 H 3O   H 2O m   o H 2 O  H 3O 

4H O

(16a)

Along the walls of the aqueous domain, where the sulfonate groups are tethered, hydration of the reactants (either the hydronium ion or the water molecule) is possible by the oxygen atoms in SO3- because hydrated protons form Zundel-ion-like and Eigenion-like configurations with the end groups.139 This reaction can be represented by the following equation nH O /( 4  n ) SO



2 3 H 3O   H 2 O m    o H 2 O  H 3O 

(16b)

The third and final reaction is the dissociation of the protons from the sulfonic acid groups and is given by 2 SO 3 H  H 2 O m o SO 3  H 3O 

nH O

(16c)

The relative importance of each of these three reactions is likely a strong function of water content. In order for the bulk-like reaction (Eq. 16a) to take place, one must be at high degrees of hydration, where there is bulk-like water within the membrane. From electronic structure calculation103 we are aware that a minimum of three water molecules is required for the dissociation of protons from the sulfonic acid end group, it is likely that the reaction in Eq. (16c) is important only at very low water contents. The reaction in which oxygen atoms of the sulfonate groups act as part of the solvation shell, (Eq. 16b) is likely relevant across a range of intermediate hydration levels.

Molecular-Level Modeling of Hydrogen PEM FC

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The RMD algorithm can accommodate all the above reactions due to the nature of the triggers. The geometric triggers that are used to check for the presence of the four water molecules around the reactants in case of proton transport in Eq. (16a) can be altered to identify both water and sulfonic acid groups for the reaction in Eq. (16b). The energetic trigger can respond to the environment like the confinement in the aqueous nano-domains or low hydration. Having modeled the first reaction using the bulk water data the next step is to model the other two reactions, and finally to implement the RMD algorithm to measure diffusivities in hydrated PFSA membranes. This work is underway. IV. CONCLUSION

A molecular-level understanding of key structure/property relationships in PEMFCs will help guide the manufacture of improved devices. The focus of the work discussed here was to show how molecular dynamics simulations can provide unique input into key structure/property relationships, such as (a) the relationship between the morphology of hydrated PEMs and their interfaces as a function of polymer architecture and water content and (b) the relationship between transport in these membranes as a function of PEM morphology. Molecular dynamics simulations were performed to investigate the morphology and transport properties in the various regions of MEA as a function of water content from Ȝ = 4.4 to 12.8 and polymer architecture (by varying the side chain length). The aqueous phase in a hydrated membrane can be characterized in terms of its connectivity and degree of confinement. Aspects of the connectivity of the aqueous phase can be characterized in terms of cumulative probability water cluster distributions and pair correlation functions (PCFs), including the S–S PCF. The degree of confinement can be characterized through PCFs and hydronium ion hydration histograms. Using all of these metrics in concert, one can emerge with a consistent description of two key structure property relationships. First, as the amount of water in the membrane is increased, the aqueous phase becomes more connected

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Myvizhi Esai Selvan and David J. Keffer

and less confined. Second, as the length of the side chain increases from SSC to Nafion, the same suite of characterization metrics indicate that the aqueous phase is less connected and less confined. Because enhanced connectivity increases diffusivity, whereas increased confinement reduces diffusivity, the ultimate change on the diffusivity cannot be completely determined by strictly examining structure. The molecular-level structure of the electrode/electrolyte interface was studied using two- and three- phase systems, including membrane/vapor, membrane/vapor/catalyst and membrane/vapor/ graphite systems. The simulations of a membrane/vapor interface show a region of dehydration near the interface. The interfacial thickness measured from the water density profile was found to decrease in width with increasing humidity. Hydronium ions displayed a preferential orientation at the interface, with the oxygen exposed to the vapor phase. In the simulations of the membrane/vapor/catalyst interface wetting of the catalyst surface was found to take place. The degree of wetting was found to increase with water content and contained a mixture of Nafion, hydronium and water molecules which can create a pathway for proton transport from the catalyst surface to the electrolyte. However, in the simulations of the membrane/vapor/graphite interface, there no wetting of the graphite surface at any degree of hydration. The significance of the contact of the catalyst particle and the hydrated membrane has been illustrated by these simulations. We found a critical gap size of around 10 Å between the catalyst and electrolyte beyond which the wetting cannot take place and hence a bridge cannot be formed across the graphite surface for proton diffusion. Admittedly, the graphite surface used in this simulation was completely free of defects and oxidation. The diffusion coefficients of water calculated from the MD simulations exhibited good agreement with experiment both in terms of the trend with respect to increasing water content as well as the trend with respect to length of the side chain. The diffusivity of the hydronium ions calculated from classical MD simulation agreed with experiment in terms of the trend with respect to increasing water content, but were consistently too low and did not reflect the experimental dependence on length of the side chain,

Molecular-Level Modeling of Hydrogen PEM FC

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presumably due to the fact these simulations provide only the vehicular component of proton diffusion. In order to include the structural component of proton diffusion, a coarse-grained RMD algorithm has been developed to study structural diffusion. The algorithm is composed of three steps: (a) satisfaction of triggers, (b) instantaneous reaction, and (c) local equilibration. The functional form of the triggers are based on transition state, as determined by the quantum mechanical calculation and their numerical values are parameterized to satisfy the macroscopically determined rate constant and activation energy. Local equilibration at the end of the reaction helps in maintaining the correct heat of reaction and structure. For the validation of the algorithm, it has been implemented to study proton transport in bulk water. In bulk water the two components of the total diffusivity were found to be uncorrelated. Further, the coarse grained nature of the algorithm will allow the extension of modeling of proton transport in bulk water to PFSA membranes because hydrated protons form similar Zundelion-like structure and Eigen-ion-like structure with the oxygen of the sulfonate groups, which can be easily integrated into the RMD formalism. The development of a molecular-level understanding of key structure/property relationships in PEMFCs is an evolving field. Molecular simulations can play an important role in contributing information to our overall understanding. Ideally, the understanding of these structure/property relationships can provide guidance leading to the synthesis of PEMs with superior characteristics and manufacture of PEMFCs with improved performance. ACKNOWLEDGEMENTS

The work is supported by the United States Department of Energy (Office of Basic Energy Science) through a grant under the contract number DE-FG02-05ER15723. The simulations were performed using resources of the National Center for Computational

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Sciences (NCCS) at Oak Ridge National Laboratory, supported by the Office of Science, USDOE, as well as resources of the National Institute for Computational Sciences (NICS), supported by NSF under contract #OCI 07-11134. The authors also gratefully acknowledge the valuable insights and discussion offered by Dr. Shengting Cui, Dr. Brian J. Edwards, Junwu Liu and Dr. Stephen J. Paddison in the Department of Chemical and Biomolecular Engineering at the University of Tennessee, Knoxville. REFERENCES 1

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5

Some Recent Studies on the Local Reactivity of O2 on Pt3 Nanoislands Supported on Mono- and Bi-Metallic Backgrounds Juan C. Sotelo* and Jorge M. Seminario*,** * Department of Chemical Engineering and **Department of Electrical and Computer Engineering,Texas A&M University, College Station, Texas, USA

I.

INTRODUCTION

Small bimetallic clusters have shown in recent years their potential as catalysts and high-density magnetic data storage materials.1 These nanoscale alloys present a number of structures and phases different from those of their bulk counterparts. Taking advantage of this large spectrum of possibilities, it is in principle possible to design and build materials with specific novel properties dependent on the size and concentration of the nano-alloys. Some constituents are more amenable than others to be used as components of nanomaterials in this emerging paradigm. Transition-metal bimetallic clusters, for example, form an important class of the former, yet tailoring of desired properties of these clusters are sometimes difficult to achieve because of the complexity of their electronic structure.

P. Balbuena, V. Subramanian (eds.), Theory and Experiment in Electrocatalysis, Modern Aspects of Electrochemistry 50, DOI 10.1007/978-1-4419-5594-4_5, © Springer Science+Business Media, LLC 2010

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Small Pt clusters have been studied in detail by several groups using a variety of methods because of their importance in catalysis.2 Cobalt clusters, on the other hand, have been investigated because of their importance in magnetic storage devices.3,4 Understanding the electronic structure of small bimetallic Co-Pt clusters and their interaction with molecules and substrates, however, is still a challenging work. We review here our exploratory work on these issues from the basis of our ab initio procedure for materials participating in electron transfer reactions, the Generalized Electron-Nano-Interface Program (GENIP),5 to consider bi-atomic backgrounds (e.g., substrates, catalysts, electrodes). This procedure is an extension of our work on electron transport on nanojunctions of a molecule attached to contacts at both ends. Our aim is twofold: first, elucidate some of the basic mechanisms governing the interaction between a molecule and a catalyst. Second, analyze new class of catalysts, which may hold great promise for catalytic oxidation and reduction processes in modern fuel cells, as well as for hydrogenation reactions in liquid and gaseous phases Therefore, we also introduce and analyze a family of supported metal clusters based on the typical transition metal components. Supported metal clusters have been studied intensively in recent years because of their technological application in heterogeneous catalysis,6 magnetic storage devices,7 mesoscopic, 4,8 and nanoscopic9 electronics. The size-dependence of many physical and chemical properties at the nanoscale has been exploited to change, design, foment, and tailor these properties aimed at modifying or creating new systems with desired specifications, unsual or absent in their bulk counterparts. For example, the resistance or conductivity of a nanosystem may become fluctuating (AharonovBohn effect), 10 materials, molecules, or clusters that are commonly chemically inert in bulk can become catalytically active,11 nonmagnetic bulk materials can show magnetic behavior when scaledown to nanostructures,12 and no bandgap materials can become semiconductors.13 Platinum is the most widely used metal catalyst and many techniques have been proposed to modify other materials to emulate its properties. Pt-based bimetallic catalysis is a possibility as the reactivity of and adsorption on clusters and surfaces can be controlled by strategically changing the composition and structure

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of the bimetallic substrate. In addition, having just a layer of the catalyst with a core or substrate of less expensive bimetallic materials would not only reduce the costs but also would allow us to control the properties of the materials. Therefore, the use small supported islands of metallic particles are of strong industrial interest. Properties of supported catalysts by bimetallic substrates depend on the changes in geometry of the catalyst material by the strain of the substrate. Using a bimetallic substrate multiplies the possibilities to tune the catalyst to specific requirements. The chemistry of the nanosized overlayer is affected by the different orbital overlaps of atoms from the catalyst cluster and those from the substrate. Additionally, small supported metallic islands show low coordination and reduced near-neighbor distances thus their chemical properties are different with respect to those of flat surfaces.14 Reactivity of several bimetallics were also studied by Balbuena et al.,15 including bimetallics systems16. Norskov et al.17,18 found several relations for the d-band in slabs of such structures. Work on bimetallic systems considering local and nonlocal effects have also been reported.19 In this work, we focus on the properties of a Pt3 cluster absorbed on transition metal nanotips that have a variety of crystal structures: fcc(111) for Pt, Co3Pt, and Ni; hcp(0001) for Co; and bcc(110) for Fe in order to identify conditions where these structures have a dominant role in the modification of the behavior of multi-metallic supported clusters.20,21 II. METHODOLOGY Finite-cluster calculations are carried out using density functional theory (DFT), as implemented in the Gaussian 03 program,22 by means of the B3PW91 hybrid functional whereby the electron correlation energy is calculated using the non-local Perdew-Wang (PW91) functional23 and the exchange contribution is calculated with the hybrid Becke3 (B3).24 Besides the Becke-8825 nonlocal exchange, B3 includes a contribution obtained a la Hartree-Fock but using the Kohn-Sham molecular orbitals (MO) rather than the Hartree-Fock MOs. All these calculations are performed using the

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quasi-relativistic pseudopotential and basis set LANL2DZ26 for Co, Ni, Fe, and Pt, and the 6-31G(d,p) basis set for O.27 Geometry optimization of a finite cluster is performed using the Berny algorithm,28 which drives the structure towards a local minimum (a stationary point) on the potential energy surface. A second derivative of the energy with respect to the Cartesian energies (Hessian) at the optimized (equilibrium) geometry is done next to determine whether the stationary point is a minimum. If it is not, the geometry of the structure is changed accordingly to drive it to a minimum energy configuration. The convergence thresholds for each geometry optimization step are 10-8 for the density matrix and 10-6 for the energy. These settings provide five decimal figures of accuracy for the energies, three for the bond lengths and one for the bond angles within the level of theory used. Lattice constants and partial DOSs of the bulk phase of hcp Co(0001), fcc Pt(111), fcc Ni(111), bcc Fe(110) and fcc Co3Pt(111) have been computed using the Vienna ab initio simulation package (VASP29) with the projector augmented wave (PAW) all-electron frozen core potentials and the generalized gradient approximation to the exchange-correlation potential, PW91. Spin polarization has been included in all cases but for the fcc Pt(111). Lattice constants are obtained by fitting a cubic polynomial to the computed total energies at several different lattice parameters. For the hcp Co(0001), both lattice parameters a and c are optimized. In all cases, the partial DOSs have been computed using the linear tetrahedron method with Blöchl corrections.30 Cutoff energies are set to 400 eV for Co, Pt, Ni and Fe, and 600 eV for Co3Pt. Brillouin zone integrations are performed on a 21x21x17 grid of Monkhort-Pack points for Pt, Ni, Fe and Co3Pt, and on a 15x15x11 shifted mesh that includes the * point for Co. The coupling of a finite cluster with bulk metal material is treated through a Green function’s method.31,32 First, the density of states (DOS) of the bulk contact is calculated as indicated above. Next, the influence of the DOS of the bulk contact on the broadening and shifting of the discrete energy levels of the molecular orbitals (MO) of the cluster is accounted for via our DFT-Green function approach, as will be explained below.32,33 This yields the total DOS of the cluster as affected by the continuum. To compute the DOS at a reactive site considering the contributions of the discrete and continuum components we proceed as

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follows. The Green’s function of the adsorbed molecule, GM, is obtained from the Hamiltonian, H and overlap, S matrices of an extended molecule (adsorbed molecule plus a few surface atoms) as

GM ( E) [ ESMM  H MM  6 L ( E)]1 6 L (E)

(1)

ES ML  H ML g L ( ES LM  H LM )

(2)

where the subscripts M and L in the submatrices of H and S refer to the adsorbed molecule (M) and contact (L) indices. The selfenergy function 6L accounts for the coupling between the contact and the adsorbed molecule; it contributes to the shifting and broadening of the molecular levels and depends on the Green’s function of the contact, gL, defined as 0 º ª g L1  « gL (E) S i u «    »» «¬ 0  g LN »¼

ª( DOS ) LK s ( E ) 0 « 0 « 0 ¬«

g LK ( E )

where,

DOSLKs(E),

0 ( DOS ) LK p ( E ) 0

0 0

DOSLKp(E),

0

º » 0 » ( DOS ) LK d e ( E ) » g ¼ 0 0

( DOS ) LK dt

0

(3)

2g

(E)

DOSLK dt ( E ) , 2g

(4)

and

DOSLK de (E) are the local density of states of the bulk contacts g

projected onto the s, p, dt 2 g , and d e g subshells. The number of contact-atoms is such that the size of gL(E) equals the number of columns (rows) of the coupling matrix HML (HLM). The DOS (D) of the molecule adsorbed onto the bulk contact at the reactive site is then given by

D( E )

 Trace (i(GM ( E )  GM ( E ))S MM ).

(5)

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For a multi-metal substrate, the local DOS of each atom in the unit cell is taken as the average of the orbital-projected DOS onto atoms of the same species in the cell. We account in this way for the effect of each type of metallic atom in the unit cell. Alternatively, the average could be taken over all atoms in the unit cell, thus transforming each atom of the cell into an average atom with an effective orbital-projected DOS. Thus, the DOS of O2 adsorbed on the L12 phase of Co3Pt, for example, obtained considering average bimetallic substrate atoms differs by less than about 15% overall from that obtained considering the average Co and the average Pt substrate atoms.20 In what follows, unless otherwise stated, the Green’s function has been smeared using an infinitesimal energy of 0.04 eV along the imaginary axis. Two important quantities in the study of the interaction of oxygen with a substrate is the binding energy and dissociative adsorption energy. For bare and O2 chemisorbed Pt-islands on a sample XS of transition metal substrate atoms, several binding energies between the three components are evaluated according to



Eisland  X S  Eisland  E X S

Ex Eb



E X S O2  E X S  EO2



(4)



(5)

Eb,t

E X S island O2  E X S island  EO2





(6)

Eb, S

E X S island O2  Eisland O2  E X S





(7)

Here, Ex is the binding energy of the Pt-island with the substrate sample XS, Eb is the binding energy of O2 to XS, Eb,t is the binding energy of O2 to the island-XS complex (also referred to as nanotip), and Eb,S is binding energy of the O2 chemisorbed island to XS. The oxygen dissociative adsorption energy on the island (relative to free O2) with and without support XS, are computed as

Ediss, ads, S



E X S island  2O  E X S island  EO2

Ediss, ads



Eisland  2O  Eisland  EO2





(8) (9)

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209

where two oxygen atoms are considered in the equations. In all computed binding and dissociative adsorption energies, zero-point corrections are included. The nature of the oxygen absorption is analyzed locally considering, among other properties, the binding energy of the island to the substrate. Extra information on electronic changes occurring when O2 binds to a complex may be obtained through the difference electron density,34 U', defined as

U'

Ucomplex O2  Ucomplex  UO2

(10)

where Ucomplex+O2 is the total electron density of the complex and O2 system (an adduct), and Ucomplex and UO2 are the electron densities of the complex and O2 molecule, respectively. The atomic positions in the complex and molecule O2 are those of the relaxed adduct. U'shows those regions in the neighborhood of the adduct where the electron density has been depleted or increased as a result of the adsorption of O2 on the complex. III.

THE NANOSYSTEMS

The basic system we consider consists of a Pt ad-trimer adsorbed on top of a transition metal bulk substrate. We can think of the trimer as a defect or island on the substrate surface, or as the local site of a decorated nanocluster. As substrates we select fcc Pt(111), fcc Ni(111), hcp Co(0001), bcc Fe(011), and (bimetallic) fcc Co3Pt(111). Bulk samples (i.e., having a continuum electronic DOS) of these materials are collectively denoted by Xbulk (e.g., Ptbulk). Following the procedure outlined in Section II, we start our study of a Pt3 island adsorbed on an Xbulk substrate, Xbulk–Pt3, by selecting a local neighborhood of Pt3 composed of Pt3 itself extended with a finite sample of substrate atoms Xs. This yields an Xs-Pt3 extended molecule where Xs is the local interface with (or support of) Pt3. Most properties of the local interaction of Pt3 with Xbulk shall be extracted from their interaction in the Xs-Pt3 extended molecule. We emphasize this relationship by writing [Xbulk-Xs]-Pt3 for the Xbulk–Pt3 system. A similar notation is adopted in the analy-

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sis of the adsorption of an oxygen molecule or oxygen atoms on the supported Pt3 ad-trimer. That is, Xs-Pt3-O2 shall denote the extended molecule (local neighborhood) of Pt3-O2 (an O2 molecule adsorbed onto Pt3), and [Xbulk-Xs]-Pt3-O2 shall denote the O2 molecule adsorbed onto the supported Pt3. 1.

Clusters and Complexes

The ground states of Xs-Pt3, Xs-O2, Xs-Pt3-O2 and Xs-Pt3-2O clusters for Xs = Co2Pt, Co3Pt, Co3Pt3, Co7Pt2, Co3, Pt3, Pt6, Ni3, Fe3 are determined as expounded in Section I. Their geometries are displayed in Fig. 1, and a summary of their bond lengths, multiplicities, and energies is given in Table 1. For each cluster, the spin contamination of its noninteracting wavefunction, as reflected in the expectation value of the total spin <S2> for a ground state of multiplicity m = 2S + 1, is within 10% of S(S + 1), where S is the total spin of the cluster. Hereafter, clusters lacking oxygen atoms are also termed complexes and those including them adducts. Thus, in Table 1, 1-5, 11 and 13 are Xs-Pt3 complexes, 6-10, 12 and 14 are Xs-Pt3-O2 adducts, and 15-21 are Xs-Pt3-2O adducts: the Pt3 complex 22 and associated adducts 23-24 are shown as reference. Complexes 1-5, 11, and 13 can be thought of as local interfaces between the Pt3 island and the substrates. Upon adsorption of O2 on them, 3, 5, 11, and 13 keep the qualitative features of the original complexes (e.g., see adducts 8, 10, 12 and 14, respectively), but, to a large extent, 1, 2, and 4 suffer strong structural reorganization (e.g., see adducts 6, 7, and 9, respectively). Therefore, complexes having substrates of Pt, Fe or 50-50% concentration Co-Pt are able to maintain their structure after the attack by the O2 molecule, those having substrates of Co, Ni, or mixed Co-Pt with Co concentration higher than 0.5 are not able to do so. The analysis of this (limited) sample of clusters, has some bearing on the aging of catalysts, which favors strongly the use of Pt, it suggests Fe as a potential alternative, which needs to be further analyzed. 2.

Reactive Sites

When the Pt3 island adsorbs onto a metallic or bimetallic surface tensile strain develops in the island strain and a concomitant compressive strain develops on the substrate surface in a local neigh-

7

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8

3

9

4

10

5

12

11

14

13

Figure 1. Extended molecules Xs, Xs-Pt3 and corresponding adducts Xs-O2, Xs-Pt3-O2 and Xs-Pt3-2O. Xs = Co2Pt (1, 6 and 15), Co3 (2, 7 and 16), Pt3 (3, 8 and 17), Ni3 (4, 9 and 18), Fe3 (5, 10 and 19), Pt6 (11, 12 and 20), Co3Pt3 (13, 14 and 21). Trimer Pt3 (22) and its associated adducts (23-24) are shown as reference. Clusters without atomic or molecular oxygen are called complexes and those including them adducts. Atoms are color coded as follows: Co (blue), Pt (yellow), Ni (lime green), Fe (aqua marine) and O (red). Most lines connecting atoms are for visual aid.

2

1

16

23

30

15

22

29

31

24

17

Figure 1.Continuation

32

25

18

33

26

19

27

20

28

21

7

7

15

3 Pt3-Pt3

4 Ni3-Pt3

5 Fe3-Pt3

7

12

2 Co3-Pt3

6 Co2Pt-Pt3-O2

9

M

1 Co2Pt-Pt3

Cluster

1-2 = 2.666, 2-3 = 2.494, 1-3 = 2.493 1-5 = 2.456, 1-6 = 2.534, 2-5 = 2.458, 2-6 = 2.536 4-5 = 2.624, 4-6 = 2.645, 4-8 = 2.018, 7-8 = 1.288

1-2 = 2.491, 1-3 = 2.537, 2-3 = 2.534, 1-4 = 2.591 2-5 = 2.606, 3-6 = 2.545 4-5 = 4-6 = 2.642, 5-6 = 2.657

1-2 = 2.471, 1-3 = 2.400, 2-3 = 2.411, 1-4 = 2.472 1-5 = 2.521, 2-5 = 2.535, 3-6 = 2.454 4-5 = 2.655, 4-6 = 2.562, 5-6 = 2.665

1-2 = 2.563, 1-3 = 2.628, 2-3 = 2.613, 1-4 = 2.589 2-5 = 2.599, 3-6 = 2.568 4-5 = 2.561, 4-6 = 2.639, 5-6 = 2.604

1-2 = 2.358, 1-3 =2.542, 2-3 = 2.543, 1-4 = 2.568 2-5 = 2.563, 3-6 = 2.535, 4-5 = 5-6 = 2.640 4-6 = 2.656

1-2 = 2.442, 1-3 = 2.506, 2-3 = 2.501 1-4 = 2.541, 1-5 = 2.571, 2-5 = 2.528, 3-6 = 2.584 4-5 = 2.644, 4-6 = 2.586, 5-6 = 2.698

Bond lengths (Å)

–917.43124

–728.09385

–865.68405

–715.25733

–793.00963

–767.11671

Energy (Ha, eV)

12.08

56.00

12.00

12.00

35.75

20.00

<S2>

Table 1 Ground State Structures and Energies for Complexes and Adducts 1-24 Shown in Fig. 1. m = 2 S + 1, is the Multiplicity, with S the Total Electron Spin of the Molecule; i-j is The Bond Length Between Atoms i and j. <S2> is the Total Spin of the Auxiliary Wavefunction.

M 7

12

7

7

15

9

Cluster 6 Co2Pt-Pt3-O2

7 Co3-Pt3-O2

8 Pt3-Pt3-O2

9 Ni3-Pt3-O2

10 Fe3-Pt3-O2

11 Pt6-Pt3

1-2 = 2.590, 1-6 = 2.620, 2-3 = 2.611, 2-4 = 2.974 2-6 = 2.693, 3-4 = 2.605, 4-5 = 2.589, 5-6 = 2.610 1-7 = 2.640, 6-7 = 2.596, 2-7 = 2.780, 2-8 = 2.754 3-8 = 2.581, 4-8 = 2.951, 4-9 = 2.711, 5-9 = 2.606 6-9 = 3.332, 7-8 = 2.705, 7-9 = 2.683, 8-9 = 2.629

1-2 = 2.496, 1-3 = 3.133, 2-3 = 2.898, 1-4 = 2.694 1-6 = 2.472, 2-4 = 2.735, 2-5 = 2.444, 3-4 = 2.682 3-5 = 2.438, 3-6 = 2.456, 4-5 = 2.662, 4-6 = 2.629 4-7 = 2.066, 5-8 = 2.464, 7-8 = 1.301

1-2 = 2.419, 1-3 = 2.420, 2-3 = 2.724, 1-4 = 2.460 2-4 = 3-4 = 2.552, 2-6 = 2.457, 3-6 = 2.456 4-5 = 2.701, 5-6 = 2.602 4-7 = 2.098, 5-8 = 2.022, 7-8 = 1.334

1-2 = 2.589, 1-3 = 2.601, 1-4 = 2-5 = 2.566 3-6 = 2.538, 4-5 = 2.557, 4-6 = 5-6 = 2.658 4-7 = 5-8 = 2.060, 7-8 = 1.329

1-2 = 2.379, 1-3 = 2.668, 2-3 = 3.111, 1-4 = 2.445 1-5 = 2.790, 2-5 = 2.668, 2-6 = 2.461, 4-5 = 2.648 5-6 = 2.578, 4-7 = 2.175, 5-8 = 2.071, 7-8 = 1.316

Bond lengths (Å) 1-2 = 2.666, 2-3 = 2.494, 1-3 = 2.493 1-5 = 2.456, 1-6 = 2.534, 2-5 = 2.458, 2-6 = 2.536 4-5 = 2.624, 4-6 = 2.645, 4-8 = 2.018, 7-8 = 1.288

Table 1. Continuation.

–1072.99577

–878.39689

–1016.01450

–865.54610

–943.29618

Energy (Ha, eV) –917.43124

20.00

56.00

12.00

12.00

35.75

12.08

<S2>

5-7 = 1.795, 6-8 = 1.792, 7-8 = 5.406 5-7 = 6-8 = 1.780, 7-8 = 5.473

10

9

12

9

7

15

14 Co3Pt3-Pt3-O2

15 Co2Pt-Pt3-2O

16 Co3-Pt3-2O

17 Pt3-Pt3-2O

18 Ni3-Pt3-2O

19 Fe3-Pt3-2O

5-7 = 1.806, 4-8 = 1.809, 7-8 = 5.543

6-7 = 1.785, 4-8 = 1.780, 7-8 = 5.507

4-7 = 1.781, 6-8 = 1.795, 7-8 = 5.148

1-2 = 2.467, 1-6 = 2.452, 2-3 = 2.466, 2-4 = 2.633 2-6 = 2.626, 3-4 = 2.448, 4-5 = 2.494, 5-6 = 2.484 1-7 = 2.588, 6-7 = 3.216, 2-7 = 2.749, 2-8 = 2.727 3-8 = 2.584, 4-8 = 3.250, 4-9 = 2.514, 5-9 = 2.602 6-9 = 2.515, 7-8 = 2.776, 7-9 = 2.682, 8-9 = 2.683 7-10 = 1.995, 8-11 = 2.002, 10-11 = 1.332

1-2 = 2.461, 1-6 = 2.463, 2-3 = 2.488, 2-4 = 2.617 2-6 = 2.640, 3-4 = 2.473, 4-5 = 2.478, 5-6 = 2.467 1-7 = 2.626, 6-7 = 2.720, 2-7 = 3.227, 2-8 = 2.519 3-8 = 2.640, 4-8 = 2.557, 4-9 = 2.945, 5-9 = 2.615 6-9 = 2.701, 7-8 = 2.648, 7-9 = 2.620, 8-9 = 2.626

12

13 Co3-Pt3-Pt3

Bond lengths (Å) 1-2 = 2.585, 1-6 = 2.595, 2-3 = 2.596, 2-4 = 2.582 2-6 = 3.032, 3-4 = 2.582, 4-5 = 2.605, 5-6 = 2.617 1-7 = 2.554, 2-7 = 2.795, 2-8 = 2.816, 3-8 = 2.565 4-9 = 2.602, 5-9 = 2.624, 6-9 = 2.589 7-8 = 2.852, 7-9 = 2.695, 8-9 = 2.752 7-11 = 1.995, 8-10 = 1.982, 10-11 = 1.330

M 7

Cluster 12 Pt6-Pt3-O2

Table 1. Continuation.

–878.40506

–1016.02547

–865.56890

–943.31896

–917.42110

–1301.10114

–1150.79471

Energy (Ha, eV) –1223.30268

56.00

12.01

20.00

35.75

20.04

24.79

35.75

12.01

<S2>

M 9

12

1

3

5

7

7

7

8

8

8

Cluster 20 Pt6-Pt3-2O

21 Co3Pt3-Pt3-2O

22 Pt3

23 Pt3-O2

24 Pt3-2O

25 Co2Pt-O2

26 Co2Pt-O2

27 Co2Pt-O2

28 Co3Pt-O2

29 Co3Pt-O2

30 Co3Pt-O2

1-2 = 2.633, 1-3 = 2.363, 1-4 = 1.959, 1-6 = 2.470 2-3 = 2.558, 2-5 = 2.007, 2-6 = 2.622, 3-4 = 1.953 3-6 = 2.473, 4-5 = 1.465

1-2 = 2.525, 1-3 = 2.438, 1-5=3-4 = 1.797, 1-6=3-6 = 2.540 2-3 = 2.524, 2-6 = 2.435, 4-5 = 1.443

1-2 = 2.533, 1-3 = 2.377, 1-6 = 2.623, 2-3 = 2.482 2-6 = 2.516, 3-5 = 1.933, 3-6 = 2.472, 4-6 = 1.886 4-5 = 1.488

4-5 = 1.455, 4-1 = 1.973, 4-3 = 1.979, 5-2 = 2.040 1-2 = 2.528, 1-3 = 2.359, 3-2 = 2.517

4-5 = 1.423, 5-1=4-3 = 1.797, 1-2=2-3 = 2.397 1-3= 2.596

4-5 = 1.467, 1-4=3-5=1-5 = 1.993, 3-4 = 1.997 1-3 = 2.528, 1-2 = 2.410, 2-3 = 2.411

1-4 = 1.770, 3-5 = 1.785, 4-5 = 5.310

1-2 = 2.611, 1-3 = 2.608, 2-3 = 2.412 4-5 = 1.323, 2-5 = 2.054, 3-4 = 2.055

1-2 = 1-3 = 2-3 = 2.498

Bond lengths (Å) 3-11 = 1.897, 8-11 = 1.958, 1-10 = 1.891 7-10 = 1.997, 10-11 = 5.668 3-11 = 1.912, 8-11 = 1.960, 9-10 = 1.910

Table 1. Continuation.

–704.80917

–704.85305

–704.86608

–559.67656

–559.73488

–559.73522

–507.87004

–507.84858

–357.56051

–1301.08623

Energy (Ha, eV) –1223.29726

15.75

15.75

15.75

12.00

12.00

12.00

6.00

2.00

0

35.76

<S2> 20.00

M 12

12

3

Cluster 31 Co7Pt2

32 Co7Pt2-O2

33 Pt4-O2

1-2 = 2.525, 1-3=1-4 = 2.726, 2-3=2-4 = 2.718 3-4 = 2.431, 3-6 = 2.024, 4-5 = 2.023, 5-6 = 1.350

1-3 = 2.643, 2-3 = 2.659, 6-3 = 2.527, 7-3 = 2.564 9-3 = 2.530, 10-3 = 2.662, 1-8 = 2.498, 1-11 = 2.622, 2-11 = 2.533, 8-11 = 2.607, 9-11 = 2.627, 10-11 = 2.591 2-1 = 2.639, 2-4 = 1.918, 3-5 = 2.274, 4-5 = 1.480 2-8 = 2.571, 2-7 = 2.731, 2-10 = 2.871, 7-10 = 2.457 9-10 = 2.597, 1-9 = 2.509, 1-6 = 2.503, 6-9 = 2.633

Bond lengths (Å) 1-3 = 2.619, 2-3 = 2.567, 4-3 = 2.519, 5-3 = 2.510 7-3 = 2.636, 8-3 = 2.615, 1-9 = 2.654, 2-9 = 2.541 6-9 = 2.617, 7-9 = 2.589, 8-9 = 2.529, 1-2 = 2.505 1-6 = 2.485, 1-4 = 2.516, 2-8 = 2.473, 5-8 = 2.579 7-8 = 2.648, 7-1 = 2.560, 2-5 = 2.575, 2-6 = 2.508 7-4 = 2.642

Table 1. Continuation.

–627.08123

–1404.61472

Energy (Ha, eV) –1254.31651

2.00

38.56

36.41

<S2>

218

Juan C. Sotelo and Jorge M. Seminario

borhood of the adsorption sites. The strains on the local neighborhood Xs-Pt3 can be estimated relative to the nearest neighbor distance in the standalone Pt3 island, 2.498 Å (Table 1), the in-plane nearest neighbor distances in bulk Pt(111), 2.77 Å, Co3Pt(111), 2.59 Å, Ni(111), 2.49 Å, and Co(0001), 2.51 Å, and the average side of the smallest in-plane triangle in Fe(110), 2.61 Å. First, we note that whereas the Pt3-Pt3 complex has an eclipsed geometry, all other Xs-Pt3 complexes show stable staggered geometries (Table 1 and Fig. 1). Compared with its value in the isolated Pt3 island the average Pt—Pt bond length in Xs-Pt3 increases to adapt to the bond lengths in Xs. The resulting tensile strain is then ~6% when the support is Co2Pt, Co3 or Fe3, and about 4%, 5% and 7% when the supports are Pt3, Ni3 and Pt6, respectively. Thus, on average the Pt—Pt bond expands by ~5.7% relative to its value in a freestanding Pt3 cluster, but contracts by ~4.7% relative to its value on a fcc Pt(111). The ensuing average compressive strain on the bonds of the Xs support is about 1% in Co3, 3% in Ni3 and Fe3, 4% in Co2Pt and Pt6, and 6% in Pt3. The development of strain on Xs-Pt3 occurs concurrently with the relaxation to equilibrium of the distance between Xs and Pt3. In fact, relative to the interlayer distance in the Xbulk crystal, the island–support distance (Table 2) decreases by 6% in Co2Pt-Pt3 and 2% in Pt6-Pt3, but increases by 2% in Co3-Pt3, 3% in Ni3-Pt3, 4% in Fe3-Pt3 and 11% in Pt3-Pt3. These on average island-substrate equilibrium distances as well as tensile and compressive strains may be considered as upper bounds for those observed at the interface of Pt3 with the Xbulk substrates. Table 2 Electronic and Geometric Structure Parameters for Pt3 in a [Xbulk-Xs]-Pt3 Substrate-Island System. Support metal, Xbulk Co3Pt Co Pt Ni Fe Pt Co3Pt

Support sample, Xs

d-band center (eV)

Co2Pt Co3 Pt3 Ni3 Fe3 Pt6 Co3Pt3

-2.07 -1.48 -1.63 -1.56 -2.12 -1.92 -2.39

Xs-Pt3 binding energy (eV/atom) -1.52 -1.84 -1.24 -1.48 -1.95 -1.73 -1.74

Distance to support surface (Å) 2.00 2.08 2.52 2.09 2.10 2.21 2.26

O2 Reactivity on Pt3 Nanoislands on Mono- and Bi-Metallic Backgrounds

219

In short, in the Xs-Pt3 complex, the Pt3 island stretches (relative to the standalone Pt3) to match the bond length of the support Xs, or increases its distance to Xs, or both. Accordingly, the concomitant strain on Xs contracts its bonds (at the interface) relative to their bulk values. This contraction is enhanced for a small flat support Xs to compensate for the low coordination of the Xs-Pt3 complex. The average compressive strain of a bond in a Pt3 support, for instance, is 6%, which is greater than that observed in a Pt6, 4%. Moreover, the relative distance support-island increases by 11% for Pt3, whereas it decreases by 2 % for Pt6. As a result of these geometric adjustments, the binding energy of the Pt3 island to the Pt6 support, –1.74 eV/atom, is stronger than that to the Pt3 support, –1.24 eV/atom (see Table 2). IV. DOS OF BULK Co, Pt, Co3Pt, Ni, AND Fe The DOS of bulk Co, Pt, Ni, Fe, and Co3Pt (L12 cubic phase) are calculated as indicated in Section II. The s, p, and d contributions to the DOSs are used to calculate the electron transport characteristics of the XS-island-adsorbate systems (and subsystems). As an example, the DOS for the Co3Pt(111) is shown in Fig. 2 where the corresponding components for Pt and Co are shown as well as their spin contribution with the d-character yielding the largest contribution to the DOS at the Fermi level. In particular, the L12 bulk cubic phase of Co3Pt is known to be a strong ferromagnet with a filled majority band,35 thus any addition of electrons to the configuration of the phase will affect the minority band. Indeed, the spin-projected DOS per unit cell of this phase of Co3Pt (Ref. 1, Fig. 3a) yields a net magnetization of 5.59 PB per unit cell: Co has an average magnetic moment of 1.78PB, Pt 0.38PB. The total DOS at the Fermi level (zero-energy in Fig 3a, Ref. 1) is 5.95 states/eV/unit cell, with the 3d states of the Co atoms contributing the most, 4.99 states/eV/unit cell. These values compare well with those found in the literature 36,37 (values in parentheses are from the second reference): 5.28 (5.54)PB/unit cell for the net magnetization; 1.64(1.39)PB for the magnetic moment of Co atoms; 0.36(0.38)PB for the magnetic moment of Pt atoms;

220

Juan C. Sotelo and Jorge M. Seminario

Figure 2. Spin- and site-projected DOS of s, p, dt2g and deg characters for Co (right) and Pt (left) in bulk Co3Pt. In all panels, the vertical dashed line at zero-energy marks the Fermi level.

and 6.10 (5.91) states/eV/unit cell for the total DOS at the Fermi level. The spin-resolved partial DOS per unit cell for Co and Pt atoms projected onto the s, p, dt2g and deg subshells displays a strong hybridization of the Co and Pt states in the energy range 10–12 eV. Below –6.5 eV, the bands are predominantly of s cha

O2 Reactivity on Pt3 Nanoislands on Mono- and Bi-Metallic Backgrounds

Figure 3. Partial density of states projected on the d-band of Pt3 for bare [Xbulk-Xs]-Pt3 (red) and oxygen-chemisorbed [Xbulk-Xs]-Pt3-O2 (blue) clusters. The samples of surface atoms Xs considered are: (a) Co2Pt, (b) Co3, (c) Pt3, (d) Ni3 and (e) Fe3. The d-band of bulk Pt (shaded green) is shown as reference. In all panels, the vertical dashed line at zero-energy marks the Fermi level.

221

222

Juan C. Sotelo and Jorge M. Seminario

racter and Co/Pt mixed type; above –6.5 eV, they are on the whole of d character, showing large hybridization between the Pd 5d and Co 3d states. Moreover, the 3d states of Co present much larger exchange splitting than that of the 5d states of Pt. The sharp peak structures at ~–4.5 eV for the majority spin and ~–4 eV for the minority spin of the 5d states of Pt, indicate the presence of rather localized states at these energies resulting from flat energy bands in the direction from X to M in the first Brillouin zone of Co3Pt.36 The projected DOS also reveals some spin polarization of the Pt atoms which is known to be induced by the spins of their neighboring Co atoms.37 V. ELECTRONIC CHARACTERIZATION OF THE O2-SUBSTRATE SYSTEM (LDOS) On a first approximation, for transition metals substrates (including bimetallics) one can correlate the location of the center of mass of the surface d-band with the reactivity of the surface (d-band model).18 The influence of second nearest neighbors, however, becomes important for overlayer systems (alloyed surfaces with one type of atoms forming the surface), as there the effect of the support can be felt over a few overlayers (depending on the interlayer distance).38 Furthermore, the accuracy of the d-band model depends as well on the adsorbate-substrate interaction strength, the stronger the coupling between an adsorbate and the substrate the less accurate the model becomes.38 The strength of the adsorption of an oxygen molecule onto the Pt3-island-substrate system is basically governed by the local interaction between the Pt3 island and the substrate. The same holds for the extent of changes in reactivity of the substrate surface triggered by the adsorption. Insight into this local interaction may be gained through analysis of the electronic structure of the islandsubstrate complexes. Projecting the total density of states on the Pt3 island, for example, can give information on the effects of metallic bonds formation on the Pt3-substrate interaction. The projected density of states on the d-band of Pt3 for bare [Xbulk-Xs]-Pt3 (red) and oxygen-chemisorbed [Xbulk-Xs]-Pt3-O2 (blue) surfaces (Fig. 3) reveals in each case a d-DOS spectrum of the adsorbed Pt3 island narrower and shifted to higher energies

O2 Reactivity on Pt3 Nanoislands on Mono- and Bi-Metallic Backgrounds

223

relative to the d-DOS of bulk Pt(111). For a supported Pt3 island two opposing effects on the location of its d-band are reported.39 First, the reduction of the Pt–Pt bond length (~4.7%) relative to its bulk Pt(111) value should yield an energy downshift of the island d-band. Second, the lower coordination of the island atoms (not greater than 5) should yield an energy upshift of the d-band. In all the Pt3 island-substrate structures analyzed in this work, the second effect dominates. Table 2 gives the location of the island’s d-band center for such structures. In particular, on a Pt substrate, the center shifts up to –1.63 eV for the about on-top island in 3, whose atoms have coordination number 3, and up to –1.93 eV for the staggered island in 11, whose atoms have average coordination number of four. On a bimetallic substrate Co3Pt, on the other hand, just as on a Pt substrate, the d-band shifts upward farther for the lower coordinated island in 1, till –2.07 eV, than for the higher coordinated island in 13, till –2.39 eV. In this case, however, the type of atoms present in the immediate neighborhood of the island may also contribute to the shift difference—the island is staggered on top of a Co2Pt cluster in 1 but on top of a Co3 cluster in 13. Let us explore the electronic structure of the bare supported island [Ptbulk-XS]-Pt3 in some more detail. The orbital resolved dDOS of the Pt3 island supported on Co3Pt (1), Co (2), Pt (3), Ni (4) and Fe (5) reveals that the d-band orbitals without z-component, d xy and d x 2  y 2 , couple weakly to the substrate in all cases, as inferred from their narrow–peaked spectra (e.g., see 3 in Fig. 4). For [Ptbulk-Pt3]-Pt3, this may be due to each atom in the island bonding with the Pt atom directly underneath (3, Fig. 1). Increasing the island coordination with the Pt substrate, as in local neighborhood 11 in [Ptbulk-Pt6]-Pt3, leads to a broadening of the d xy and

d x 2  y 2 orbitals (Fig. 4, left, 11), evidencing their stronger coupling to the substrate. A similar increment of the island coordination with the bimetallic substrate Co3Pt, as in local neighborhood 13 in [Co3PtbulkCo3Pt3]-Pt3, still yields discrete-like spectra for d xy and d x 2  y 2 (Fig. 4, left, 13), suggesting that when interacting with a Co3Pt substrate these orbitals remain localized in the island for various

224

Juan C. Sotelo and Jorge M. Seminario

Figure 4. Orbital resolved d-band of Pt3 for bare [Xbulk-Xs]-Pt3 (left) and oxygenchemisorbed [Xbulk-Xs]-Pt3-O2 (right) surfaces. The spectra are numbered after the extended molecule Xs-Pt3 (see Fig. 1) used in the surface description. The corresponding bulk surfaces Xbulk are: 3, 8, Pt (red); 11, 12, Pt (blue); and 13, 14, Co3Pt (chocolate). The orbital resolved d-band of the standalone Pt3 trimer (green, left) is shown as reference. In all panels, the Fermi level is the energy zero. All molecules are oriented such that the Pt3 cluster is in the X-Y plane.

adsorption geometries. The d-subbands possessing z-component, dyz, d3z 2  r 2 and dxz, on the other hand, are broad in all cases studied (e.g., see Fig. 4, left), indicating significant coupling to each of the surfaces regardless of the island position on the surfaces. In summary then, the d xy and d x 2  y 2 orbitals are confined within the island for all surfaces except [Ptbulk-Pt6]-Pt3, whereas dyz,

O2 Reactivity on Pt3 Nanoislands on Mono- and Bi-Metallic Backgrounds

225

d3z 2  r 2 and dxz are significantly coupled with the substrates in all cases. In particular, all d-orbitals are strongly coupled with the substrate in [Ptbulk-Pt6]-Pt3. VI. LOCAL REACTIVITY OF A BIMETALLIC SURFACE: Co3Pt 1.

Electronic Characterization

An oxygen molecule reacts with a surface through its antibonding

S* orbitals. We trace the molecule-surface interaction with the

orbital resolved decomposition of the DOS of the molecule-surface system, [Xbulk-Xs]-O2 (Fig. 5). The p-orbital resolved projected DOS (PDOS) of O2 in 25–30, for example, reveals that the bonding S states are located at the tail of the d-band of bulk Co3Pt (the substrate) whereas the antibonding S* states extend around the vicinity of the Fermi level. As a result, the S* states are partially filled, as can be deduced as well from analysis of the difference electron density and spin density maps (not shown, see Fig. 6.)20 Also the oxygen molecule S states in the spectra of [Co3PtbulkCo3Pt]-O2 (derived from 28–30) are pushed up in energy by less than 1 eV relative to same states in the spectra of [Co3PtbulkCo2Pt]-O2 (derived from 25–27). At the same time, the Vg-bonding almost overlaps with the bonding Su states in all but the spectra derived from 26 and 29 where the Su states are shifted to higher energies, yielding the smallest separations of S-bonding and S*-antibonding states in the spectra of [Co3Ptbulk-Co2Pt]-O2 and [Co3Ptbulk-Co3Pt]-O2, respectively. Consequently, the major effect of the background on the DOS of the adsorbed oxygen molecule is the shifting of its filled bonding Vg and Su and antibonding Sg* states towards higher energies. This effect is a manifestation of the local neighborhood of the oxygen molecule considered in the evaluation of the spectra (see Section II). In adducts 27 and 30, for example, the O2 molecule sees the same nearest neighbors (Fig. 1); the net effect of the extra Co atom in 30 being to slightly shift the bonding Vg and Su states to higher energies (Figs. 5e, f). In contrast, the presence of the ex-

Figure 5. P-orbital resolved partial DOS for molecule O2 chemisorbed on a bulk Co3Pt surface with local neighborhoods 25 (a), 26 (c), 27 (e), 28 (b), 29 (e), 30 (f), and 32 (g). The Fermi energy of bulk Co3Pt is taken as the zero-energy point in all panels. Each DOS has been computed in two ways: in the first, c (red curves), each Co and Pt atom has been assigned the orbital-projected DOS of bulk Co3Pt averaged over a unit cell; in the second, a (blue curves), each Co and Pt atom has been assigned the average over a unit cell of the orbital-projected DOS of bulk Co3Pt onto Co and Pt atoms, respectively. The d-band of bulk Co3Pt (green curve) is shown as a reference. (h) Isosurface of the difference electron density U' (top) and spin density (difference between D and E densities, bottom) for local neighborhood 32. Charge flows from green to red regions. Pt atoms are colored yellow, Co atoms blue, and O atoms red. Spin density of the free O2 molecule (bottom, right) is shown as reference. Isovalue for isosurfaces is 0.004 in all cases.

Figure 5. Continuation.

Figure 5. Continuation.

O2 Reactivity on Pt3 Nanoislands on Mono- and Bi-Metallic Backgrounds

229

Figure 6. Partial DOS projected onto the O atoms (red) and d-band of Pt atoms (blue) for oxygen-chemisorbed [Xbulk-Xs]-Pt3-O2 surfaces. The right panels show an expanded view of the O2 spectra (red) using as reference the spectrum of free O2 (green, labels are given in the top panel). A V antibonding is indexed according to whether it originates from s- or p-orbitals. The bulk surfaces are 6, Co3Pt, 7, Co, 8, Pt, 9, Ni, and 10, Fe. The d-band of bulk Pt—left panel, shaded area—is shown as a reference. The Fermi level is the energy zero in all cases.

tra Co atom in 28 changes substantially the local neighborhood of O2 with respect to that in 25 (Fig. 1). This gives the molecule better coupling to the surface (broader peaks) and greater stability (shifting of the Sg*-antibonding to higher energies). Some further insight may be gained by analyzing the p-orbital resolved PDOS of chemisorbed O2 onto bulk Co3Pt with local neighborhood 32, [Co3Ptbulk-Co7Pt2]-O2. In 32, the support has nine

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atoms, about twice as many as those in 28–30, and O2 has the same bonding geometry as in 28 (albeit with one of its atoms now bonded to a Pt atom). In this case, Su appears in the spectrum of O2 as a small shoulder to the right of the Vg peak, just as it happened with 28. Also, since the empty Sg*-antibonding seats at the Fermi level, it will become partially filled, and hence will weaken the O2 bond. The difference electron density and spin density maps of 32 [Fig. 4h; see also Fig. 6(21)]20 clearly display the partial filling of the Sg*-antibonding states. Notice the reduction in spin density of chemisorbed O2 relative to that in gas phase. We now briefly compare the characteristics of O2 when chemisorbed to a Co3Pt bimetallic surface with those when chemisorbed to a Pt surface. Using the local neighborhood 29 in the chemisorbed surface [Co3Ptbulk-Co3Pt]-O2 and 33 in [Ptbulk-Pt4]-O2, we find that in either case O2 adsorbs parallel to a surface atomic bridge at a height of ~1.24 Å. Nevertheless, the O-O bond length in 29, 1.443 Å, is larger than that in 33, 1.350 Å. Accordingly, the bond stretching frequency in the former, 842 cm-1, is smaller than that in the latter, 940 cm-1. Moreover, the binding energy for O2 in 29, -1.19 eV/atom, is stronger than in 33, –0.30 eV/atom or, in fact, any of the other adducts in 25-33. This suggests that for oxygen reduction the Pt(111) surface is more reactive than the bimetallic Co3Pt(111) surface. Another way to look at this is by noting that because the S states of O2 in [Ptbulk-Pt4]-O2 are shifted to lower energies with respect to their positions in [Co3Ptbulk-Co3Pt]-O2, the molecule’s S*-antibonding states are more populated in the former system than in the latter, thereby leading to a lower binding energy. VII. LOCAL REACTIVITY OF SUPPORTED Pt3 ISLANDS 1.

Electronic Characterization

To study the reactivity of metal nanosurfaces of Co3Pt, Co, Pt, Ni, and Fe decorated with a Pt3 island, we shall analyze the absorption of an oxygen molecule on the edges of the supported island. Although in general it is inadequate to associate binding energies strength with surface reactivity, still the interaction strength of

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231

molecules with surfaces is reported to be correlated with the reactivity in catalytic reactions.40 Upon adsorption of O2 on the island, the island and its support (1-5, 11, and 13) suffer different degrees of reconstruction (6-10, 12, and 14, respectively), with neighborhoods 3, 11 and 13 being the least affected. Changes in the other neighborhoods yield configurations that may be interpreted as adsorption of O2 on a singleatom, 6, or a dimer-bridge (7, 9, and 10) Pt defect on a bimetallic alloyed surface. These geometrical changes already hint at the island d-band being significantly altered by oxygen adsorption. Indeed, overall, the peaks of the band are broadened and the band itself is slightly pushed down in energy for all substrates (Fig. 3): a large shift occurrs only for the island on a Pt substrate (Fig. 3c). In particular, the density of states around –4 eV increases for each of the island d-subbands in [Ptbulk-Pt6]-Pt3-O2 relative to that on the bare surface [Ptbulk-Pt6]-Pt3, signaling a strong coupling of these subbands with the 1Sg bonding orbitals of O2. The island d xy and

d x 2  y 2 subbands in [Ptbulk-Pt3]-Pt3-O2, on the other hand, remain narrowly peaked, just as they were in [Ptbulk-Pt3]-Pt3 (Fig. 4), indicating their essential confinement to the island. These results demonstrate the strong coupling between the substrate, Pt3 island and adsorbed O2. The adsorption of the oxygen molecule on the island also leads to a group of small split-off states appearing at the tail of the island d-band (Fig. 6). These states are centered in the region (–8.0)-(–7.4) eV for all substrates21 and correspond to the bonding overlap of the d-band with the 1Sg and 3Vg bonding orbitals of O2 (denoted S and Vp, respectively, in Fig. 6). The d-band overlaps too with the 2Su (S* in Fig. 6) antibonding orbital of O2 above the Fermi level between 1.5 and 2.5 eV. The strength of this interaction is seen, for example, in the splitting of the island d-band antibonding on the [Ptbulk-Pt3]-Pt3 surface [Fig. 6 (8)]. Let us see in some detail the partial DOS of O2 as this gives extra information on the binding of the molecule to the surfaces. The DOSs of O2 chemisorbed surfaces with local neighborhoods 6-10 are shown in an expanded range in Fig. 6 (right panels); the molecular orbitals of O2 in gas phase are shown too as reference— These orbitals are the lower lying bonding 1Vg and antibonding

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2Vu*, the bonding 3Vg and 1Sg and antibonding 2Su (3Vg lies between the spin-split 1Sg). The Fermi level is located between the spin-split 2Su. Now, the partial filling of the 2Su antibonding states of the chemisorbed O2 suggests that this molecule, just as when adsorbed on a bridge site on a Pt(111) surface, is in a paramagnetic superoxolike O2– phase 41 when adsorbed on the edges (bridges) of the Pt3 island. The reduced exchange splitting of 1Vg and 2Vu* tells the adsorbed O2 has weaker magnetic moment than in gas phase, whereas the reduced 1Vg-2Vu* splitting indicates that the molecule is, in addition, stretched. 2.

Structural Characterization

The O-O bond length in the O2 chemisorbed supported island ranges in fact from 1.29 Å for a Co3Pt substrate to 1.33 Å for Ni (see Table 3); its gas-phase value is 1.21 Å. By way of comparison, for an O2 molecule adsorbed on a bridge-site on a Pt(111) surface the experimental value of its bond length is in the range 1.37–1.39 Å.41 Because of stretching, the O–O bond weakens and its vibration frequency diminishes from its gas-phase value of 1696 cm-1 to values in the range 1055-1265 cm-1. For instance, a change in local neighborhoods of O2 in [Ptbulk-Xs]-Pt3-O2 from 8 to 12 produces ~1% reduction in both bond length and frequency, whereas a similar change in [Co3Ptbulk-Xs]-Pt3-O2 from 6 to 14 produces ~2% increase in bond length and ~17% reduction in frequency. This dissimilarity in the effect of increasing the size of Xs in the second case may be attributed to Xs sampling different surface neighborhoods of Co3Pt: in 6 it is a Co2Pt cluster, in 14 a Co3 cluster. As such, the bond length and vibration frequency of the adsorbed O2 in 14 compare better with those found for the local neighborhood 7 (Table 3). For comparison, the O–O bond stretching frequency for an O2 molecule adsorbed on a bridge–site on a Pt(111) surface is in the range 860–875 cm-1.41

Table 3 O-O Bond Lengths, O-O Vibrational Frequencies, and Binding Energies (Eb) of O2 in Adducts (Complex-O2) 6-10, 12, 14, 23, and 31-33. The Binding Energy (Eb,S) of Pt3-O2 in the same Adducts (Except 23) and the Oxygen Dissociation Energy (Ediss,ads) on Complexes 1-5, 11, 13 and 22 are Also Included. For Reference, the Binding Energies of O2 on Pt4 and Co7Pt2 are Included in the Last Two Rows. O2 2O Complex Adduct O-O Eb Eb,S Adduct Ediss,ads Q22 -1 (eV) (Å) (eV) (eV) (cm ) 1, Co2Pt-Pt3 1.288 1265 –1.25 –5.12 –0.99 6 15 2, Co3-Pt3 1.316 1126 –0.48 –5.33 –1.12 7 16 1.329 1057 –0.55 –3.47 –1.21 3, Pt3-Pt3 8 17 1.334 1055 –1.66 –5.44 –2.00 4, Ni3-Pt3 9 18 1.301 1186 –0.90 –6.09 –1.18 5, Fe3-Pt3 10 19 1.330 1045 –0.97 –5.37 –0.85 11, Pt6-Pt3 12 20 1.332 1049 –0.93 –5.55 –0.56 13, Co3Pt3-Pt3 14 21 1.323 1058 –0.60 –1.22 22, Pt3 23 24 1.350 940 –0.60 Pt4 33 1.480 795 –0.74 31, Co7Pt2 32

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3.

Binding and Dissociation Adsorption Energies

O2 bindnig energy (eV)

Molecular oxygen-surface reactions play an important role at the surfaces of fuel cell electrocatalysts whereby oxygen molecules dissociate on the cathode and oxygen atoms get reduced.42 A key aspect of these processes is the adsorption of the molecule to the surfaces. As pointed out earlier, we shall study the trends of binding energies of O2 on a Pt3 island on Co3Pt, Co, Pt, Ni and Fe substrate surfaces as a means to elucidate the reactivity of the island. These interaction energies are computed on local neighborhoods of the reaction sites on Pt3, namely, 6 and 14 (Co3Pt), 7 (Co), 8 and 12 (Pt), 9 (Ni), and 10 (Fe). We plot in Fig. 7(a) the O2 binding energy as a function of the support-Pt3 binding energy (Table 3). No apparent correlation between these two quantities seems to emerge. Nevertheless, for 9, 6, 14, 12, and 7 a stronger binding of

-0.5

Co(7) Co Pt(14)

Pt(8)

3

-1 Fe(10)

Co Pt(6)

Pt(12)

3

-1.5 -2

Ni(9) -1.8

-1.6

-1.4

-1.2

Pt3 binding energy to XS (eV/atom) (a) Figure 7. (a) Molecular O2 binding energy in XS-Pt3-O2 vs. Pt3 binding energy in XS-Pt3. (b) Pt3-O2 binding energy to XS in XS-Pt3-O2 vs. Pt3 binding energy in XS-Pt3. (c) Oxygen dissociative adsorption energy in XS-Pt3-2O vs. Pt3 binding energy in XS-Pt3. The horizontal red line at 0.60 eV in (a) marks the O2 binding energy to 12 (the freestanding Pt3) and that at -1.22 eV in (c) marks the oxygen dissociative adsorption energy on 22. Points are labeled by the supporting surfaces of the Pttrimer and by the adducts (a-b) or complexes (c) (given as superscripts).

Pt3-O2 binding energy to XS (eV)

O2 Reactivity on Pt3 Nanoislands on Mono- and Bi-Metallic Backgrounds

b

-3

235

Pt(8) -4 Co

-5

(7)

Co Pt(6) 3

(12)

Pt

Co Pt(14)

-6 Fe(10) -7 -2

Ni(9)

3

-1.8

-1.6

-1.4

-1.2

Pt3 binding energy to XS (eV/atom)

Dissociation adsorption energy (eV)

(b)

c

-0.5

Co Pt(13) 3

-1

-1.5

Co(2) Pt(11) Fe

Co Pt(1)

Pt(3)

3

(5)

Ni(4) -2 -2

-1.8

-1.6

-1.4

-1.2

Pt3 binding energy to XS (eV/atom) (c) Figure 7. Continuation.

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Pt3 to the support Xs leads to a weaker binding of O2 to the supported Pt3. In particular, because of the strong interaction between Pt3 and Co3 in 2, O2 binds to Pt3 in 7 weaker than in 23 by 0.12 eV (Fig. 7a, red line). O2 also adsorbs to Pt3 in 8 weaker than in 23, however, here the coupling between Pt3 and its support is weaker than in 7 by ~0.6 eV; the end result being an oxygen chemisorbed Pt3 island loosely coupled to its Pt3 support (Fig. 7b). Indeed, as seen in Table 2, the distance between the Pt3 island and the Pt3 substrate expands from 2.27 Å to 2.54 Å upon molecular oxygen chemisorption on the island. This increased separation reduces significantly the binding of the oxygen chemisorbed island to the substrate support resulting on a weak binding of O2 to the island-support complex (3), –0.55 eV (Table 3), weaker than its binding to the free Pt3 island, –0.60 eV (Table 3, see also Fig. 7b) and to a bridge site on a Pt(111) surface, –0.72 eV.41 Figure 7(c) shows the oxygen dissociation adsorption energy on complexes 1-5, 11 and 13 as computed from their corresponding associated adducts 15-21. On complexes other than 4 (Ni substrate sample) these energies are weaker than on the free Pt3 island (–1.22 eV), the weakest dissociation energy being achieved on complex 13. For comparison the oxygen dissociation adsorption energy on the (preferred) fcc sites of a Pt(111) surface is -1.65 eV.41 It thus follows that on complexes 2 and 3 both the O2 binding energy and oxygen dissociation adsorption energy are weaker than those on a Pt(111) surface. The trends of bond lengths and stretching frequencies of the O2 molecule as a function of the binding energy of Pt to the substrate support XS are shown in Fig. 8. Although these two quantities are correlated with one another—the shorter the bond, the higher the frequency—there is, however, no apparent correlation between either of them and the binding energy of O2, as can be seen by comparing Figs. 7(a) and 8. We emphasize that the O–O bond length in Fe(10) (adduct 10 whose support is Fe3) is one of the shortest simply because in 10 O2 bonds to the complex on just one oxygen whereas in all other adducts it bonds on both oxygen atoms.

O-O bond length (Å)

O2 Reactivity on Pt3 Nanoislands on Mono- and Bi-Metallic Backgrounds

a

1.35

(14)

Co3Pt 1.3 Fe

(10)

Co

(12)

(7)

-1

Q O-O (cm )

(9)

(8)

Pt

(6)

-1.8 -1.6 -1.4 Pt3 binding energy to XS (eV)

-1.2

b

1300

(6)

1200

1000 -2

Ni

Pt

Co3Pt

1.25 -2

1100

237

Fe

(10)

Co

Co3Pt

(7)

(8)

(14)

Co3Pt

(12)

Pt

Ni

(9)

-1.8 -1.6 -1.4 Pt3 binding energy to XS (eV)

Pt

-1.2

Figure 8. O—O bond length (a) and stretching frequency (b) for molecular O2 in adducts 6-10, 12, and 14. Points are labeled by the supporting surfaces of the Ptisland and by the adducts.

VII. CONCLUSIONS Electron transfer processes are at the heart of all oxidationreduction reactions including those associated with electrochemistry and, in particular, electrocatalysis. An extended version of our procedure GENIP has been presented to deal with single-metal and bimetallic backgrounds or supports, amalgamating the physics and chemistry of electron transfer reactions at interfaces using ab initio molecular orbital theories. A thorough application of this procedure to analyze the effect of O2 adsorption on a bimetallic surface of Pt/Co yields results compatible with existing experimental evidence. The absorption of O2 onto the metallic surface is determined by a chemical contribution, resulting from the interaction of the molecule with the d-band states of the metal surface, and a geometrical contribution, depending on the near neighbor distances in the metallic lattice (the local microstructure), determining

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to what extent the O—O bond strength can be weakened by stretching so that the metal-oxygen bond is sufficiently strong to break it. Details of the electrons characteristics such as their structural symmetry and their character for reactions between the metal substrate and the attacking molecule are established bearing in mind the bimetallic nature of the substrate as well. The local reactivity of defects on surfaces modeled as a Pt3 island supported on pure Co, Pt, Ni, and Fe and bimetallic Co3Pt bulk substrates have also been addressed. These bimetallic neighborhoods exhibit properties beyond those of their single components. Pt, Fe and a 50%-50% CoPt substrates are structurally more stable to the Pt island oxidation. Both the average compression of the island by ~4.7% relative to a minimal triangular fragment in Pt(111) as well as the strong interaction between the island and the substrates lead to oxygen adsorption energies on the Pt3 island that are, relative to that on the bulk Pt surface, stronger on Fe, Ni and Co3Pt, weaker on Co, and both weaker and stronger on Pt, depending on the particular neighborhood of the island. The trend of reactivity of these islands on substrate surfaces, as probed by the binding energy of an oxygen molecule on them, seems uncorrelated to the (local) binding energy of the Pt3 island to the substrates. Further study of the changes in island reactivity as a function of shape, size and thickness of the nanoislands should provide a better guide to our understanding of the effects of the substrate on the interaction adsorbate-island. Although a great deal is known about the effect of electric fields on the reactivity of surfaces, little is known about the effects on their counterpart magnetic fields. A unified treatment of these effects would certainly increase the feasibility of locally tuning the electronic and magnetic properties of bi- or multi-metallic defects leading to a new generation of catalysts with engineered nanoscale features. ACKNOWLEDGEMNTS We acknowledge financial support from the US Department of Energy (DOE) and the US Defense Threat Reduction Agency (DTRA) through the US Army Research Office (ARO).

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Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. AlLaham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, C. Gonzalez, and J. A. Pople, Gaussian-2003, Revision B.4 (Gaussian, Inc., Pittsburgh PA, 2003). J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh, and C. Fiolhais, Phys. Rev. B 46 (11), (1992) 6671; J. P. Perdew and Y. Wang, Phys. Rev. B 45 (23), (1992) 13244. A. D. Becke, J. Chem. Phys. 98, (1993) 1372. A. D. Becke, Phys. Rev. A 38 (6), (1988) 3098. W. R. Wadt and P. J. Hay, J. Chem. Phys. 82 (1), (1985) 284; P. J. Hay and W. R. Wadt, J. Chem. Phys. 82 (1), (1985) 270; P. J. Hay, J. Chem. Phys. 66 (10), (1977) 4377. P. C. Hariharan and J. A. Pople, Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta) 28 (3), (1973) 213; W. J. Hehre, R. Ditchfield, and J. A. Pople, J. Chem. Phys. 56 (5), (1972) 2257. H. B. Schlegel, J. Comput. Chem. 3, (1982) 214. G. Y. Sun, J. Kurti, P. Rajczy, M. Kertesz, J. Hafner, and G. Kresse, Journal of Molecular Structure-Theochem 624, (2003) 37; J. Paier, R. Hirschl, M. Marsman, and G. Kresse, Journal of Chemical Physics 122 (23) (2005) 234102(1-13); D. Hobbs, G. Kresse, and J. Hafner, Physical Review B 62 (17), (2000) 11556; G. Kresse and J. Furthmuller, Physical Review B 54 (16), (1996) 11169. P. E. Blöchl, O. Jepsen, and O. K. Andersen, Physical Review B 49 (23) (1994) 16223. J. M. Seminario, A. G. Zacarias, and J. M. Tour, J. Phys. Chem. A 103 (39) (1999) 7883; J. M. Seminario, C. E. De La Cruz, and P. A. Derosa, J. Am. Chem. Soc. 123 (2001) 5616; J. M. Seminario, Proc. IEEE Nanotech. Conf. 4 (2004) 518; J. M. Seminario, C. De La Cruz, P. A. Derosa, and L. Yan, J. Phys. Chem. B 108 (46), 17879 (2004); J. M. Seminario, Nature Materials 4 (2) (2005) 111; J. M. Seminario, L. Yan, and Y. Ma, Proc. IEEE 93 (10) (2005) 1753. P. A. Derosa and J. M. Seminario, J. Phys. Chem. B 105 (2) (2001) 471; J. M. Seminario, A. G. Zacarias, and P. A. Derosa, J. Chem. Phys. 116 (2002) 1671; J. M. Seminario, L. E. Cordova, and P. A. Derosa, Proc. IEEE 91 (11) (2003) 1958; J. M. Seminario and L. Yan, Int. J. Quantum Chem. 102 (2005) 711. L. Yan and J. M. Seminario, J. Phys. Chem. A 109 (30) (2005) 6628; J. C. Sotelo, L. Yan, M. Wang, and J. M. Seminario, Physical Review A (Atomic, Molecular, and Optical Physics) 75 (2) (2007) 022511. A. Eichler and J. Hafner, Physical Review Letters 79 (22) (1997) 4481. S. Inagaki, Journal of the Physical Society of Japan 75 (4) (2006) 044706(1-4); S. Tang and J. E. Hirsch, Physical Review B 42 (1), (1990) 771; Y. Nagaoka, Physical Review 147 (1) (1966) 392.

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A. Kootte, C. Haas, and R. A. d. Groot, Journal of Physics: Condensed Matter 3 (9) (1991) 1133. A. Kashyap, K. B. Garg, A. K. Solanki, T. Nautiyal, and S. Auluck, Physical Review B 60 (4) (1999) 2262. A. Roudgar and A. Groß, Journal of Electroanalytical Chemistry 548, (2003) 121. A. Roudgar and A. Gross, Surface Science 559 (2-3) (2004) L180. J. K. Norskov, T. Bligaard, A. Logadottir, S. Bahn, L. B. Hansen, M. Bollinger, H. Bengaard, B. Hammer, Z. Sljivancanin, M. Mavrikakis, Y. Xu, S. Dahl, and C. J. H. Jacobsen, Journal of Catalysis 209 (2) (2002) 275. A. Eichler, F. Mittendorfer, and J. Hafner, Physical Review B 62 (7), (2000) 4744. R. Adzic, in Electrocatalysis, edited by J. Lipkowski and P. N. Ross (WileyVCH, New York, 1998), p. 197.

6

Methanol Electro-Oxidation by Meth anol Dehydrogenase Enzymatic Catalysts: A Computational Study N. B. Idupulapati and D. S. Mainardi Institute for Micromanufacturing, Chemical Engineering Program, Louisiana Tech University, Ruston, LA 71272

I. 1.

INTRODUCTION

Enzymatic Catalysts for Fuel Cell Applications

The high-cost of materials and efficiency limitations that chemical fuel cells currently have is a topic of primary concern. For a fuel cell to be effective, strong acidic or alkaline solutions, high temperatures and pressures are needed.1 Most fuel cells use platinum as catalyst, which is expensive, limited in availability, and easily poisoned by carbon monoxide (CO), a by-product of many hydrogen production reactions in the fuel cell anode chamber.1,2 In proton exchange membrane (PEM) fuel cells, the type of fuel used dictates the appropriate type of catalyst needed. Within this context, tolerance to CO is an important issue. It has been shown that the PEM fuel cell performance drops significantly with a CO con-

P. Balbuena, V. Subramanian (eds.), Theory and Experiment in Electrocatalysis, Modern Aspects of Electrochemistry 50, DOI 10.1007/978-1-4419-5594-4_6, © Springer Science+Business Media, LLC 2010

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centration of only several parts per million, due to the strong chemisorption force of CO onto the catalyst.3,4 Numerous studies have been aimed toward reducing the amount of platinum required in current fuel cells.1,5-11 For catalyst materials, tertiary platinum/ruthenium-based alloys seem to offer the best performance when CO poisoning is of concern.1,9,11 In an attempt to keep reducing the amount of platinum used, small atomic clusters of platinum deposited on carbon supports 5,12 and platinum-based bimetallic catalysts8-11 were proposed, but metal-metal and metal-adsorbate interactions13-15 were observed to affect their reactivity.7,16-19 In spite of environmental, social, and political concerns surrounding the use of platinum and other more rare and valuable metals in fuel cells, the use of platinum-based alloys has been the focus of study in the last decades.20 Bioelectrochemical generation of power by enzymes has also been considered.21-24 The usage of enzymes as catalysts in fuel cells has been vastly experimented,25-28 and currently some enzymatic fuel cells are being used to produce electricity to power many number of electrical devices, like: pumps, valves and pacemakers, or electronic devices, like: radios, sensors, controllers, and processors.22 At present however, enzymatic fuel cells have been reported22-24,29,30 to have power output and stability limitations (0.15 micro-Watts/cm2 for 30 days of continuous work,29 50 micro-Watts /cm2 for two days of continuous operation),30 which are restricting the use of this kind of fuel cell to small electronic devices. Enzymes as electrocatalysts are able to improve the performance characteristics of chemical fuel cells since their use avoids the problem of poisoning the fuel cell anode with carbon monoxide present in reforming gas, allowing the use of cheap hydrogencontaining fuels such as methanol and glucose. The stability of the biological catalysts can be drastically improved by their immobilization on electrode supports, which may provide the development of commercially competitive bio fuel cells.22 Recently, miniature enzymatic fuel cells producing 4.3 micro-Watts were built by wiring the enzyme using electron-conducting hydrogels, avoiding the need of an electrolyte membrane.23 This minimizes costs and simplifies the design of bio fuel cells allowing their miniaturization. Moreover, an approach to imitate the photosynthetic process that involves a dye-sensitized nanoparticulate semiconductor photo

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anode working in combination with an enzyme-catalyzed bio fuel cell has been proposed in principle to provide more power than either process working independently.24 Recent advances in nano/bio technology are eliminating the past well-known power output limitations that bio-fuel cells (~micro-Watts/cm2) faced with respect to chemical fuel cells (Watts/cm2 to mega-Watts/cm2). For instance, a methanol-fed biocatalytic fuel cell that uses bacterial Methanol Dehydrogenase (MDH) enzyme immobilized on N,N,N’,N’-tetramethyl-p-phenylenediamine (TPMD)-functionalized carbon paste electrode as the anode catalyst, produces a continuous power output of 0.25 milliWatts/cm2 for 30 days of continuous operation.31 It is believed that the TPMD mediator, responsible for electron transfer resulting from the fuel oxidation by the enzyme to the electrode, is the major factor limiting the power output that deteriorates the fuel cell performance (expectedtheoreticaloutput is 100 milli-Watts/ cm2.)32 Particularly, the oligomerization (the forming of polymers by the combination of relatively few monomers) of the mediator molecules seems to be increased when stimulating the fuel cell operating conditions by subjecting the mediator to repeated charge-discharge cycles. This oligomerization causes the fuel cell performance to be deteriorated due to reduced electron transfer from the enzyme to the electrode. Moreover, another cause for this bio-fuel cell limited performance is associated to the formation of the by-product formaldehyde (formic acid) as result of methanol (fuel) oxidation by MDH.28 The continuous accumulation of such a strong acid in the bio-fuel cell may slowly reduce the activity of the enzyme, thus limiting the overall power output.28 Providing power output limitations are overcome, enzymatic fuel cells might offer potentially attractive power sources for some consumer electronic devices. Hence in this chapter, a clear understanding of the reactivity of MDH enzymes at molecular level is proposed to unravel the secret of its catalytic activity towards methanol electro-oxidation. 2.

Methanol Dehydrogenase Enzyme

Methanol dehydrogenase (MDH) enzyme is found in the periplasm of methylotrophic bacteria, and plays a crucial role in the metabolism of these organisms.33 It catalyzes the oxidation of methanol

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(and other primary alcohols) to the corresponding aldehydes, with the release of two protons and two electrons.33,34 The catalytic center of MDH involves quinone containing prosthetic group pyrroloquinoline quinone (PQQ), which acts as its cofactor.33 Apart from the PQQ cofactor, MDH active center contains a divalent calcium cation for its catalytic activity.33,34 The X-ray structure of methanol dehydrogenase from the Methylophilus methylotrophus W3A1 (M.W3A1) organism was obtained at various resolutions,35,36 and unequivocally determined that the MDH enzyme structure consists of a Į2ȕ2 heterotetramer in which molecular masses of the two subunits Į and ȕ are 62 and 8 kDa, respectively.37-39 Each heavy subunit contains a Ca2+ cation and a PQQ cofactor not covalently bound to the protein. The oxygen atoms of the PQQ are involved in several hydrogen bonds with the residues GLU55, ARG109, THR159, SER174, ARG331 and ASN394 (Fig. 1b). The calcium ion is coordinated to the O5, N6 and O10 atoms of PQQ, O11 of ASN261, the O12 and O13 of Glu171.35-39 Additionally from Xray crystallographic studies, it was observed that there are several water molecules present in the active site of MDH (Fig. 1b). Water molecules W362, W615 and W213 form hydrogen bonds with Ca2+, PQQ and GLU171 in the active site, while water molecules W130, W131, W134 and W198 form a cluster on the left upper portion of PQQ (Fig. 1b). 3.

Methanol Electro-oxidation by Methanol Dehydrogenase Enzymes

Two possible mechanisms for methanol oxidation by MDH enzymes have been proposed in the literature, the AdditionElimination (A-E) and the Hydride Transfer (H-T) mechanisms.33,34 The A-E is a three-step mechanism (Fig. 2a) that involves a proton transfer from methanol to an active site base, which is proposed to be ASP303. It is believed that the presence of this catalytic base at the MDH active site initiates the oxidation reactions by subtracting a proton (H16) from methanol (Fig. 2a). This proton addition to ASP303 leads to the formation of a covalent hemiketal intermediate, since the resulting oxyanion (O16–) in the methanol molecule is then attracted to the C5 of PQQ. The second step consists of the proton (H16) elimination from ASP303 and transfer to O5 of PQQ, and the final step is characterized by a

Enzymatic Methanol Electro-Oxidation: A Computational Study

(a) 

(b)

247





Figure 1. (a) View of the inside of the Methanol Dehydrogenase (MDH) enzyme with the active site in stick model. The solid surface represents the solventaccessible MDH external surface showing the binding pocket. (b) View from the binding pocket of the entire MDH active site. Amino acids labels denote their location in the sequence obtained from the entry 1W6S (Methylobacterium Extorquens W3A136) of the Protein Data Bank.

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second proton (H17) transfer from the methanol molecule to the O4 of PQQ (Fig. 2a), resulting in the formation of the by-product formaldehyde (CH2O).33,34 The Hydride transfer (H-T) is proposed to be a four-step mechanism (Fig. 2b). The first step involves two proton transfers: H16 and H17 from the methanol molecule to ASP303 and C5 of PQQ respectively, resulting in the formation of the by-product formaldehyde. In the second step, there is a proton (H16) transfer from ASP303 to the C5 of PQQ. The third step involves the proton (H17) transfer from the C5 of PQQ to ASP303, and the final step consists of the transfer of H17 from ASP303 to the O4 of PQQ (Fig. 2b).33,34 Irrespective of the mechanism under consideration, the rate-determining step for methanol oxidation by MDH is believed to be the breaking of the Cmet-H17 bond leading to the second proton transfer, which occurs in steps 3 and 1 (Fig. 2a and b) of the A-E and H-T mechanisms respectively.33,34 Several experimental studies were devoted to the elucidation of the preferred methanol electro-oxidation mechanism by Methanol Dehydrogenase enzymes. Experimental studies by Frank et al.40 suggested that the C5 carbonyl of the isolated PQQ (Fig. 1b) molecule is very reactive towards nucleophilic reagents, suggesting that a covalent PQQ-substrate complex (hemiketal intermediate) formation would be possible in agreement with the A-E mechanism.40 This hemiketal complex formation was also anticipated since the absorption and fluorescence spectra of covalent adduct of PQQ and methanol are almost identical to spectra of the MDHmethanol complexes in favor of the A-E over the H-T mechanism.41,42 Itoh et al.43,44 from their theoretical and spectroscopic measurements showed that PQQ systems in organic solution can oxidize methanol, ethanol and 2-proponal to their corresponding aldehydes via A-E mechanism. These authors reported that the crystal structure of one of the isolated hemiketal adducts showed methanol bound to C5 of PQQ.43,44 Crystallographic studies by Xia et al.36 on MDH from Methylophilus W3A1 in the presence of methanol indicated that in the MDH-PQQ-methanol complex, the methanol hydroxyl group is closer to the PQQ C5 atom (3.1 Å) than the methyl group (3.9 Å). According to these authors36, the hydride ion transfer (H17 to C5 of PQQ) from the more distant methyl group of methanol would not be possible, also supporting

(INT1) (a)

(INT2)

(Product)

Figure 2. (a) Addition-Elimination (A-E) and (b) Hydride-Transfer (H-T) methanol electro-oxidation mechanisms by Methanol Dehydrogenase Enzyme proposed in the literature.

(Reactant)

(Reactant)

(INT1)

Figure 2. Continuation.

(b)

(INT2)

(INT3)

(Product)

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the formation of a hemiketal intermediate as suggested by the A-E mechanism. Other authors, however found the H-T mechanism the preferred one for methanol oxidation by MDH, as reported by Zheng et al.45,46 on MDH enzymes obtained from several sources, and confirmed by Reddy et al.47,48 from molecular simulations studies. Recently, Kay and co-workers49, through electron paramagnetic resonance (EPR) studies on substrate binding to PQQ-Ca2+ in ethanol dehydrogenase, indicated a strong coordination of the substrate to the calcium cation which should be broken during the addition–elimination process. For this reason, the A-E mechanism is unlikely to happen in alcohol dehydrogenases as suggested by these authors.49 Goodwin et al.50 performed experimental kinetics and thermodynamic calculations on the whole Ca2+-MDH enzyme in the presence of ammonium chloride solution and methanol. The reported activation energy for the oxidation of methanol at pH 9 was 35.4 kJ/mol (~8.5 kcal/mol), however these authors did not particularly relate this activation energy to a step of the methanol oxidation mechanisms already proposed in the literature.50 In 2007, Leopoldini et al.51 theoretically investigated the two proposed A-E and HT mechanisms at the B3LYP density functional theory level and 6-31+G* basis set for all atoms except calcium (LANL2DZ was used). Their model for the MDH active site included the PQQ cofactor, the Ca2+ ion, the amino acids having coordination with the calcium ion (GLU171, ASN261, ASP303) and also five nearby amino acids which form a sphere around the PQQ molecule (ARG331, GLU55, ARG109, THR153, SER174). In their calculations however, only the reactive groups (CH3COO- and NH3COCH3) of the amino acids having coordination with the calcium ion and the PQQ molecule were considered in the calculation, and one hydrogen atom of each reactive group were frozen to prevent unreliable expansion of model during optimization procedure.51 Their calculated energy barriers for the rate-determining step, i.e., for the cleavage of Cmet-H17 bond of methanol for the two proposed mechanisms (34.6 kcal/mol for A-E, 32.3 kcal/mol for H-T) were well above the general kinetic requirements of an enzymatic catalytic process (15-20 kcal/mol).51 So, Leopoldini et al.51 postulated an alternative mechanism, the Additionelimination-protonation, in which the first step is the same as in

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the A-E mechanism (step 1), but the second step consists of the proton (H17) elimination from the hemiketal methyl group and transfer to O4. The final step in their mechanism is characterized by the proton transfer (H16, protonation) from the ASP303 to the O5 of PQQ. This new proposed mechanism reduced the energy barrier of the rate-determining step to 16 kcal/mol.51 To the best of our knowledge, no consensus has been reached in the literature on methanol electro-oxidation by MDH enzymes. Hence, a detailed theoretical investigation is carried on the already proposed methanol oxidation mechanisms (A-E and H-T) by using more extended MDH active site models considering protein environment.

II. METHODOLOGY The Generalized Gradient Approximation (GGA)52 within the Density Functional Theory formalism53 is implemented in this study as provided by the module DMOL3 in Materials Studio® software developed by Accelrys Inc.54 All geometry optimization calculations are performed using the Becke-Lee-Yang-Parr BLYP exchange correlation functional55 and the double numerical with polarization (DNP) basis set since it is the best set available in DMOL3. This basis set considers a polarization d function on heavy atoms and a polarization p function on hydrogen atoms. It compares to the split-valence double zeta 6-31G** in size; however it is more accurate than the Gaussian basis sets of the same size.56 When this theory level is used in combination with several split-valence basis sets with polarization and diffuse functions, errors are expected to be in the second decimal for calculated bond lengths (Å) and in the order of 4–10 (kcal/mol) in absolute energies.57 Harmonic vibrational frequency calculations are performed to ensure that stationary points on the Potential Energy Surface of the systems are in fact local minima (all real frequencies) or transition states (only one imaginary frequency). Spin multiplicity states are also checked in all calculations and ground state geometries are presented. Appropriate reactants and products involved in each step of the A-E mechanism are considered for defining atom pairing, so

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that a 3D trajectory file representing the reaction path preview is generated for each step with the Reaction Preview tool of the Materials Studio® software. Then, these 3D trajectory files are used as inputs to obtain the corresponding transition states, using the linear synchronous transit and quadratic synchronous transit (LST/QST) calculation with conjugate gradient (CG) minimization58 within the Transition State search tool in DMOL3. This methodology starts with a LST/optimization (bracketing the maximum between the reactant and product and performing energy minimization of the obtained maximum in the reaction pathway).58 The Transition State hence obtained is used as starting point for performing a finer search with the QST/optimization followed by a conjugate gradient (CG) minimization.58 This cycle is repeated until a stationary point with only one imaginary frequency (transition state) is found, since in many cases several imaginary frequencies are found. In the later situation, the corresponding (imaginary) modes of vibrations are animated in order to visualize the mode that would eventually follow the intended step from a particular reactant to product. That particular mode is then selected to perform the transition state optimization to verify whether the obtained geometry is indeed a transition state. The transition state finally obtained by the LST/QST/CG method may not be the transition state connecting the intended reactant and product for a particular reaction step. Therefore, in order to thoroughly investigate the reaction paths, the intrinsic reaction coordinate (IRC) analysis is performed. In DMOL,3 the IRC calculations are included in the Transition State Confirmation tool. This tool starts at the transition state and locates successive minima in the direction of the reactant and product paths. This path is known as the minimum energy path, which should connect the supposed transition state to the presumed reactants and products.59 It uses the nudged elastic band method to validate a transition state by introducing a fictitious spring force which connects the neighboring points to ensure continuity of the path and then it projects the force, so that the system converges to the minimum energy path.59 It has become a quite common procedure to use relatively small models of enzyme active sites and apply quantum chemical methods to study their reaction mechanisms.60-66 According to this approach, the rest of the enzyme is usually treated using a homogeneous polarizable medium with some assumed dielectric con-

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stant, and then Density Functional Theory calculations are performed to obtain reaction barriers. Various studies60,61,63-65 showed that the calculated energies are often sufficient to verify or rule out a suggested reaction mechanism. In general, the experience has been that a well-chosen quantum model is able to reproduce the chemistry taking place at an enzyme active site to such a high degree, that it can provide detailed insight into reaction mechanisms. The presence of protein environment on the selected active site models is implemented with a continuum solvation model known as COSMO67-69 (conductor-like screening model) in the DMOL3 module.56 This model works in such a way that the solute molecule forms a cavity within the dielectric continuum of permittivity, İ, that represents the solvent.67-69 The charge distribution of the solute polarizes the dielectric medium. The response of the dielectric medium is described by the generation of screening (or polarization) charges on the cavity surface. The dielectric constant (İ) was chosen to be four, which is the standard value used in modeling protein surroundings.60-65 Geometry optimizations were performed in the presence of this solvation model so that the final total energy includes the DMOL3/COSMO electrostatic energy.56

III. RESULTS AND DISCUSSION 1.

Methanol Dehydrogenase Active Site Models

Relevant portions (models) of the complete MDH active site are considered to reduce the number of atoms to conduct accurate electronic structure calculations. The two MDH active site models selected in this work (Models A and B) consisted of the Ca2+ ion, since it is part of the active site and its role is still unknown, the PQQ molecule, since it is MDH’s co-factor, and relevant amino acids carefully selected based on the current state of knowledge on methanol oxidation by MDH.34,47,48,50 Model A (Fig. 3a) consists of the PQQ molecule, the Ca2+ ion and aspartic acid (ASP303), and Model B (Figure 3b) contains glutamic acid (GLU177), asparagine (ASN261) in addition to the contents of Model A (as shown in Figure 3). When these active site Models A (in gas-phase) and B (in gas-phase & protein environment) are used to test the A-E and

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H-T, it was observed that the reaction barriers for the ratedetermining steps were well above the general kinetic requirements of an enzymatic catalytic process (15–20 kcal/mol).66 Then, the three water molecules (W362, W615, W213) in the catalysis area were also taken into account by adding them to the contents of Model B so that the Ca2+ first-shell coordination sphere is complete and tested upon methanol oxidation in protein environment to provide extended analysis on the oxidation mechanisms.66,70 MDH active site models were geometry minimized at the BLYP/DNP level with no constrains, and further tested upon methanol oxidation as explained in the following Section. The reaction mechanisms are tested in gas-phase only for Model A, since the inclusion of solvation effects (for protein environment) generally creates a pronounced effect on the calculated energetics for this model as observed from the literature60,61 because of the incomplete representation of the first-coordination shell of Ca2+. Model B, which considers the complete coordination sphere of the ion, was used for testing the mechanism with and without the pres-

(a)

(b)

Figure 3. Geometry optimized models representing the Methylobacterium Extorquens MDH (1W6S) active site. (a) Model A: PQQ molecule, the Ca2+ ion and aspartic acid (ASP303). (b) Model B: PQQ molecule, the Ca2+ ion, aspartic acid

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(ASP303), glutamic acid (GLU177), asparagine (ASN261) and three water molecules (W362, W615, W213).

ence of dielectric solvation and with water molecules considered. As discussed earlier in the Methodology Section, to estimate the energetic effects of protein environment not included in the quantum chemical model chosen, solvation effects were employed on the model with a dielectric constant of 4. The choice of dielectric constant value is somewhat arbitrary, but a value of 4 was used frequently in similar enzymatic studies.51,60-63 2.

Methanol Electro-Oxidation Mechanisms

The initial reactants in both, the A-E and H-T methanol oxidation mechanisms by MDH (Fig. 2) are the same complex. Hence, a methanol molecule is added to Models A and B, and the complete complex is geometry optimized at the BLYP/DNP theory level. Minimum energy reactant complex of the Model B including protein environment and three water molecules showed that the basic features of the X-ray crystal structure of the active site are well preserved. In such a case, the Ca2+ coordinates with the nitrogen and oxygen atoms of PQQ (at 2.57, 2.41 and 2.56 Å respectively), the carbonyl oxygen atoms of ASN261 (at 2.23 Å), GLU177 (at 2.50 Å), and both oxygen atoms of water molecules W362 and W615 (at 2.37 and 2.42 Å) respectively. Also W615 and W213 maintain hydrogen bonding with respect to PQQ, PQQ and GLU177 respectively in accordance with the literature. Hence, the corresponding bond distances for all the steps for A-E (and later on for H-T) are discussed from here on with respect to Model B in the presence of three water and protein environment. (i) Addition-Elimination Mechanism (a) Step 1: Proton addition to ASP303 by methanol In step 1 of A-E (Fig. 2a) a proton (H16) transfer from methanol to ASP303 and the nucleophilic addition of the CH3O– complex to the C5 of PQQ is proposed to take place. When Model B is considered, the O14-H16 distance reduces (Table 1) from 1.74 (Reactant) to 1.01 (transition state TS1) and to 0.98 Å (INT1), and the C5-O16 bond distance changes from 4.10 (Reactant) to 2.78

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Table 1 Selected Bond Lengths Corresponding to the Optimized Structures of Reactant (Reactant of Step 1), Transition States TS1, TS2 and TS3 for Steps 1, 2 and 3 Respectively, Intermediates INT1 (Product of Step 1) and INT2 (Product of Step 2), and the Product (Final Product) During the Methanol A-E Oxidation Mechanism by MDH Model B with Water and Protein Environment. Bond length (Å)

Reactant

TS1

INT1

TS2

INT2

TS3

Product

O14-H16

1.74

1.01

0.98

1.58

2.60

2.89

2.60

C5-O16 O5-H16 O4-H17 Cmet-H17

4.10 3.55 5.21 1.10

2.78 3.53 4.91 1.11

1.54 3.43 2.83 1.10

1.48 1.40 2.51 1.10

1.89 1.03 2.51 1.10

3.47 1.00 1.01 1.47

4.33 1.00 0.99 2.82

(TS1) and to 1.54 Å (INT1) indicating that the formation of OmetC5 and the shift of proton from alcoholic OH group of methanol to ASP occurs in a concerted way (Fig. 4). The methoxide (CH3O-) addition to the PQQ results in the formation of first intermediate (INT1) where the Omet-C5 bond is completely formed (1.54 Å). The hydrogen bonding of water molecule (W362) with respect to ASP303 decreases as the reaction proceeds to INT1 and gradually increases with respect to O5 of PQQ. It is easy to rationalize these results considering that the reaction step under study is a proton transfer that results in a positive charge on the aspartic acid and an additional negative charge on the substrate methanol molecule. The PQQ C5-O5 bond lengthens from 1.21 Å in the reactant species to 1.26 Å for TS1 (Table 1). In gas-phase for Models A and B, the free energy barriers for this step is 29 and 33 kcal/mol respectively (Table 2) which is well above the general kinetic requirements of an enzymatic catalytic process (15–20 kcal/mol).66 But in the presence of water and protein environment effects (Model B), the free energy barrier for this step is 19 kcal/mol (Table 2), which is kinetically plausible (Fig. 4). As discussed earlier, the Ca2+ coordinating with only three atoms of PQQ as opposed to seven-coordination from the x-ray

Figure 4. Geometry optimized structures involved in step 1 for the A-E methanol oxidation mechanism by MDH active site Model B.

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Table 2 Energy Barriers (kcal/mol) Corresponding to Steps 1 to 3 of the Methanol A-E Oxidation Mechanism Calculated at the BLPY/DNP Theory Level for Models A and B.

Step 1 Step 2 Step 3

Model A (gas phase)

Model B (gas phase)

29 7 18

33 10 22

Model B (Dielec. sol. E = 4) 28 7 21

Model B (Dielec. sol. E = 4 + 3W) 19 4 21

crystallography might be one of the reason for the first step high energy barrier for Model A. (b) Step 2: Proton elimination from ASP-303 and transfer to PQQ In step 2, a proton (H16) transfer is proposed to occur from ASP to the O5 of PQQ via a transition state (TS2) (Figure 2a). When Model B is considered, the proton is shared between the oxygen atoms of PQQ (at 1.40 Å) and the ASP303 (at 1.58 Å) respectively. The CH3O- tilts its orientation with respect to INT1 in such a way that the distance between O4 of PQQ and H17 of methanol is 2.51 Å compared to 2.83 Å in INT1 (Table 1). The proton transfer leads to the formation of a second intermediate (INT2) along the overall reaction profile. For this INT2, the CH3 group of attached methanol orients towards O4 of PQQ, so that the latter is in a good position in breaking the H-CH2 bond (the H17-O4 of PQQ is 2.51 Å.) Gas phase energy barriers are 7 and 10 kcal /mol for Models A and B respectively (Table 2). Dielectric solvation reduces the free energy barrier by 3 kcal/mol for B, and with both solvation and water effects, the barrier is further reduced to 4 kcal/mol (Table 2). The geometrical features of this transition state (TS2) are very similar to the INT1. The hydrogen bonding of the W362 to the O5 of PQQ is completely lost as the reaction proceeds to INT2, but the bonding with respect to ASP303 remains intact.

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(c) Step 3: Formaldehyde formation The final transition state TS3 which leads to the formation of PQQH2 reduced species is located with Cmet-H17 and O4-H17 distances at 1.47 and 1.01 Å respectively (Table 1). The bond between O16 and C5 of PQQ lengthens up to 3.47 Å indicating the breakage to form by-product formaldehyde (Fig. 5). Even though the O4 of PQQ and H17 of methanol appear close to each other during the previous steps, in reality they are not (Table 1) until this step takes place. The free energy required to overcome the transition barrier for this step is 18 and 22 kcal/mol with respect to INT2 for Models A and B in gas-phase respectively (Table 2).66 There is not much change in this barrier (~1 kcal/mol) even in the presence of protein environment and water for Model B. Water molecules W362 and W615 maintain their coordination with calcium, and ASP303 and calcium respectively throughout this proposed reaction path until the formation of the final product (Fig. 5). Of the three steps, step 2 was observed to be the fastest irrespective of the model or environment (Table 2). In the presence of dielectric solvation and water effects, step 3 is the slowest, which corresponds to the cleavage of the Cmet and H17 bond. It can also be observed that the energy barriers for steps 1 and 3 are almost the same (~20 kcal/mol), making both of them rate-determining as opposed to the literature, where only step 3 for the A-E mechanism is proposed to be the rate-limiting one (Table 2).34 Hence water and protein environment effects are necessary for the A-E reaction mechanism to be plausible with respect to the active site Model B selected (Fig. 6). (ii) Hydride Transfer Mechanism (a) Step 1: Formaldehyde formation According to step 1 of the H-T methanol oxidation mechanism (Fig. 2b), there should be a direct hydride transfer (H17) from methanol to C5 of PQQ in concert with proton abstraction (H16) by O14 of ASP, thus resulting in the formation of by-

Figure 5. Geometry Optimized structures involved in step 3 for A-E methanol oxidation mechanism by MDH active site Model B.

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Figure 6. Gas-Phase Potential Energy Surface (PES) for methanol A-E oxidation mechanism by MDH active site Models A and B. Reactant-relative energies calculated at the BLPY/DNP theory level are in kcal/mol. GP = Gas Phase, dielectric solvation (E = 4) and EW represents water effects with addition of the three W362, W615 and W213 water molecules.

product formaldehyde. Hence, the first transition state evolves into the first intermediate (INT1), where the by-product formaldehyde formed leaves the active site. From our calculations at the BLYP/DNP level, it is found that O14-H16 bond length evolves from 2.00 (reactant) to 1.12 (TS1) to 1.00 (INT1) Å (Table 3), showing the binding of the H16 proton to ASP303 (Fig. 7). The C5-H17 distance from the initial reactant is reduced from 3.69 to 1.22 and finally to 1.12 Å, evidencing the second hydride transfer to the C5 of PQQ. The gas-phase free energy barrier for transition state TS1 to be formed is 29 and 33 kcal/mol with respect to the initial reactant complex for Models A and B respectively in gas-phase (Table 4). In presence of protein environment, the barrier is reduced by 6 kcal/mol for Model B, but still above the general kinetic requirements (15–20 kcal/mol). When water effects are added in addition to protein environment, the barrier gradually reduces to 20 kcal/mol (Table 4, Fig. 8). Water molecule W362 maintains hydrogen bonding with respect to both ASP303 and O5 of PQQ for this particular step.

2.00

3.39

4.23

1.10

O5-H16

O14-H17

Cmet-H17

Reactant

O14-H16

Bond length (Å)

2.81

3.28

2.58

1.12

TS1

4.50

3.53

1.36

1.00

INT1

6.05

3.54

1.30

1.26

TS2

5.67

2.98

1.04

1.53

INT2

5.03

2.65

1.05

2.37

TS3

TS4 2.94 1.04 1.40 3.47

INT3 3.01 1.04 1.02 5.12

3.52

1.72

1.04

2.98

Product

Table 3 Selected Bond Lengths Corresponding to the Optimized Structures of Reactant (reactant of step 1), Transition States TS1, TS2 and TS3 for steps 1, 2 and 3 Respectively, Intermediates INT1 (Product of Step 1) and INT2 (Product of Step 2), and the Product (Final Product) During the Methanol H-T Oxidation Mechanism by MDH Model B with Water and Protein Environment.

Figure 7. Geometry optimized structures involved in step 1 of the methanol Hydride-Transfer oxidation mechanism by MDH active site Model B.

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Table 4 Energy Barriers (kcal/mol) Corresponding to Steps One to Four of the H-T Methanol Oxidation Mechanism Calculated at the BLPY/DNP Theory Level for Models A and B.

Step 1 Step 2 Step 3 Step 4

Model A (gas phase)

Model B (gas phase)

29 14 15 7

33 8 15 12

Model B (Dielec. sol. E = 4) 27 7 11 16

Model B (Dielec. sol. E = 4 + 3W) 20 3 9 7

Figure 8. Gas-Phase Potential Energy Surface (PES) for active site models A and B for H-T. Reactant-relative energies calculated at the BLPY/DNP theory level are in kcal/mol. GP = Gas Phase, dielectric solvation (E = 4) and EW represents explicit water effects with addition of the three W362, W615 and W213 water molecules.

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(b) Step 2: Proton transfer from ASP to PQQ According to the proposed step 2 in the H-T mechanism (Fig. 2b), there should be a proton transfer from ASP303 to the O5 of PQQ, thus resulting in the formation of a second intermediate (INT2). From our calculations is found that the transition state for this step (TS2) shows an intermediate location of H16 on its way from O14 of ASP to the PQQ carbonyl oxygen O5, with H16-O5 = 1.30 Å and H16-O14 = 1.26 Å (Table 3). The hydrogen bonding of W362 with respect to O5 of PQQ increases as this step proceeds. Since the geometrical characteristics of TS2 are similar to those of INT1, a low energy barrier is anticipated for this step. When both protein environment and water effects are considered, the free energy barrier for this state with respect to INT1 is 3 kcal/mol, reduced by 11 kcal/mol with respect to Model A and 4 kcal/mol with respect to Model B with just dielectric solvation (Table 4, Fig. 8). (c) Steps 3 and 4: Proton transfer from PQQ to ASP (step 3) and back to PQQ (step 4) Proposed steps 3 and 4 of the methanol H-T mechanism involve the transfer of a proton (H17) from C5 to O4 of PQQ mediated by ASP303, emphasizing the role of this amino acid as a the base catalyst (Fig. 2b). Step 3 shows the breaking of C5-H17 bond and the formation of O14-H17 bond. For this step, the transition state shows an intermediate location of H17 on its way from PQQ carbon C5 to the O14 of ASP, with H17-C5 = 2.83 Å and H17O14 = 2.65 Å (Table 3). The hydrogen bonding of W362 with O5 of PQQ is completely lost by the end of this step. The free energy required for step 3 is 15 kcal/mol with respect to INT2 for both Models A and B in gas-phase. There is a reduction of 6 kcal/mol in the barrier value in the presence of protein environment and water (Table 4, Fig. 8). During the final step, the distance O14-H17 has been increased from 1.02 (INT3) to 1.40 (TS4) to 1.72 (Product) Å, and O4-H17 decreased from 1.67 (INT3) to 1.50 (TS4) to 1.01 (Product) Å respectively, indicating that PQQ is finally reduced. The transition state for this step is 7 kcal/mol less stable than INT3 for Model A in gas phase (Table 4). For Model B, the lowest value of

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7 kcal/mol is observed in the presence of dielectric solvation and water. Throughout this reaction step, W362 and W615 maintain coordination with Ca2+ and W615, and W213 maintain hydrogen bonding with PQQ and GLU-177 respectively. Among the four steps, step 2 seems to be the fastest with very low energy barrier in any phase (Table 4). Even when dielectric solvation or water are present or not especially for Model B, step 1 is observed to be the rate-determining one for the tested H-T mechanism in accordance with the literature.33,34 (iii) Methanol A-E versus H-T Electro-Oxidation Mechanisms by MDH From our energetic profile calculations on the two proposed mechanism using Model B, the initial proton transfer to ASP303 and formation of hemiketal intermediate with C5 of PQQ (step 1), conversion of INT2 to final products through TS3 (step 3) are two rate-limiting steps for the methanol A-E oxidation mechanism by MDH, where as the two hydride transfers in step 1 of the H-T mechanism is the rate-determining step according to the calculated energy barriers. At the BLYP/DNP theory level it is found, however the possibility of oxidizing methanol through an alternative mechanism, which we call the two-step hydride transfer (2 step H-T) mechanism as shown in Fig. 9. According to step 1 of this mechanism, two hydrides (H16 and H17) are transferred to ASP303 and the O4 of PQQ respectively, resulting in the formation of formaldehyde. During the second and final step another proton transfer (H16) from the catalytic base to O5 of PQQ takes place, thus reducing PQQ. From the obtained geometry optimized structures at the BLYP/DNP theory level, it is found that the O14-H16 bond is formed in TS1 representing the first transfer to ASP303, and the O4-H17 and Cmet-H17 distances are 1.66 and 1.96 Å respectively (Fig. 8). The free energy barrier for obtaining this transition state is 15 kcal/mol compared to 20 kcal/mol with respect to the first transition state for step 1 of H-T. This reduction in the barrier may be due to the more stable intermediate of this step as compared to INT1 (~ 10 kcal/mol from Fig. 8) of the original H-T in presence

Figure 9. The alternative methanol two-step hydride transfer mechanism by MDH enzymes proposed in this work.

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of protein environment and water. Also the H17 of methanol is in more appropriate position for transferring to O4 than to the C5 of PQQ in the reactant species (O4-H17 = 2.42 Å and C5-H17 = 3.69 Å, Fig. 10). According to step 2, the proton transfer from ASP303 to the PQQ is characterized by the second transition state (TS2) where the O5-H16 and O14-H16 bond lengths are 1.80 and 2.10 Å respectively. IV. CONCLUSIONS Enzymes have been considered in bio fuel cells as anode electrocatalysts since their use avoids the problem of poisoning the anode with carbon monoxide present in reforming gas, allowing the use of cheap hydrogen-containing fuels such as methanol. Even though enzymatic fuel cells have been reported to have power output and stability limitations, some of them are currently being used to produce electricity to power small electrical devices with power demands in the order of micro- and milli- Watts as power output limitations are overcome. Bacterial Methanol Dehydrogenase (MDH) is an enzyme that electro-oxidizes methanol to formaldehyde. When MDH is used as the anode catalyst in methanol-fed fuel cells, a continuous power output of 100 milli-Watts/cm2 has been theoretically predicted for 30 days of continuous operation.32 However, due to current losses during the electron transfer resulting from the fuel oxidation by the enzyme to the electrode, this enzymatic fuel cells performs only 0.25% of the expected power output. Understanding of the reactivity of MDH enzymes at molecular level is the main goal of this work in order to unravel the secret of its catalytic activity towards methanol electro-oxidation. Two Methanol Addition-Elimination (A-E) and Hydride Transfer (H-T) oxidation mechanisms by PQQcontaining Methanol Dehydrogenase (MDH) are proposed in the literature, however no consensus has been reached on the methanol electro-oxidation that operates in nature by MDH enzymes. Hence, in this work a detailed theoretical investigation is carried out on the already proposed methanol oxidation mechanisms (A-E and HT) by using extended MDH active site models considering protein environment.

Figure 10. Geometry Optimized structures involved in step 1 of the alternative methanol two-step hydride transfer mechanism by MDH active site Model B.

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Relevant portions (models) of the complete MDH active site are considered in this work to reduce the number of atoms to conduct accurate electronic structure calculations. The two MDH active site models selected in this work (Models A and B) consisted of the Ca2+ ion, since it is part of the active site and its role is still unknown, the PQQ molecule, since it is MDH’s co-factor, and relevant amino acids carefully selected based on the current state of knowledge on methanol oxidation by MDH. Model A consists of the PQQ molecule, the Ca2+ ion and aspartic acid (ASP303), and Model B contains glutamic acid (GLU177), asparagine (ASN261) in addition to the contents of Model A. Then, the three water molecules (W362, W615, W213) in the catalysis area were also taken into account by adding them to the contents of Model B so that the Ca2+ first-shell coordination sphere is complete and tested upon methanol oxidation in protein environment to provide extended analysis on the oxidation mechanisms. The Generalized Gradient Approximation within the Density Functional Theory formalism53 is implemented in this study as provided by the module DMOL3 in Materials Studio® software at the BLYP/DNP theory level. The presence of protein environment on the selected active site models is implemented with the COSMO continuum solvation model. Our results indicate that both methanol A-E and H-T electro-oxidation mechanisms seem to be plausible when the active site model contains water and considers the effects of protein environment (Model B). From theoretical calculations by Leopoldini et al.51 there is a rate-determining step each for the two mechanisms (34.6 kcal/mol for step 3 of A-E, 32.3 kcal/mol for step 1 of H-T), and both of them are not kinetically favorable according to the general kinetic requirements of an enzymatic catalytic process (15–20 kcal/mol). However, from our calculations, for A-E, there are two rate-determining steps (step 1, 19 kcal/mol & step 3, 21 kcal/mol) as opposed to the findings by Leopoldini et al.51 and Anthony et al.33,34 Even for the new Addition-elimination-protonation proposed by Leopoldini et al.,51 the barrier for the rate-limiting step has been reduced to 16 kcal/mol, however step 1 remains the same as that of A-E, which was found to be kinetically slower from our calculations. For the H-T mechanism we found only one rate-limiting step (step 1, 20 kcal/mol) at the BLYP/DNP theory level in accordance with the literature,33,34,51 but still the energy barriers of the rate-determining steps

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were in the upper domain of usual limits for an enzymatic catalytic process (15-20 kcal/mol). Hence, a third mechanism (two-step hydride transfer) is proposed in this work, where its rate-limiting step involves two simultaneous hydride transfers from methanol to ASP303 and O4 of PQQ respectively. The free energy barrier calculated for this step is 15 kcal/mol, which is consistent with the requirements of an enzymatic catalytic process. REFERENCES 1 2

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Electrocatalytic Reactions of Chemisorbed Aromatic Compounds: Studies by ES, DEMS, STM and EC Jean Sanabria-Chinchilla, Youn-Geun Kim, Xiaole Chen, Ding Li, Helmut Baltruschat,† and Manuel P. Soriaga Department of Chemistry, Texas A&M University, College Station, TX 77843, USA † Institut fur Physikalische und Theoretische Chemie, Universität Bonn, 53117 Bonn, Germany

I.

INTRODUCTION

The interaction of organic molecules with, and their subsequent reactivities at, electrode surfaces are among the more critical aspects of modern electrochemical surface science. However, the study of these processes is an exceedingly difficult proposition. In the past, experimental probes were limited to conventional electrochemical techniques.1-3 But the information content of these methods is limited to the macroscopic properties of the electrodeelectrolyte interface. Consequently, results from surface studies based merely on ensemble thermodynamic and kinetic measurements can be rationalized only phenomenologically with little basis for interpretations at the molecular level.4-6 Over the past few

P. Balbuena, V. Subramanian (eds.), Theory and Experiment in Electrocatalysis, Modern Aspects of Electrochemistry 50, DOI 10.1007/978-1-4419-5594-4_7, © Springer Science+Business Media, LLC 2010

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decades, a slew of surface-physics techniques7-10 were developed for the study of interfacial processes, and present-day research in surface electrochemistry has taken advantage of such methods. Since it is clear that no single empirical technique can ever hope to unravel all the nuances of heterogeneous reactions, the use of multiple complementary techniques in surface science has become the standard approach. Unfortunately, the surface-characterization methods, while quite powerful, are also rather intricate and quite expensive to implement. As a consequence, less than a handful of (judiciously selected) surface-physics methods have actually been employed in electrochemical research laboratories. Ultrahigh vacuum-electrochemistry (UHV-EC) is a term ascribed to the approach that rests upon the integration of classical electrochemical methods with surface-sensitive analytical techniques.11-16 Despite the fact that the UHV-EC approach includes experiments that emerse the electrode from the solution, its unequaled value lies in its ability to help resolve fundamental issues that intertwine atomic-level interfacial structure and composition with electrochemical reactivity. It is in this context that the present review is written. Here, we describe results from recent studies on the electrocatalytic oxidation and hydrogenation of prototypical aromatic compounds on palladium electrodes to showcase the unique capabilities of an experimental strategy that combines EC with electron spectroscopy (ES), differential electrochemical mass spectrometry (DEMS) and scanning tunneling microscopy (STM). Specific ES methods are low-energy electron diffraction (LEED), Auger electron spectroscopy (AES) and high-resolution electron energy loss spectroscopy (HREELS). II. EXPERIMENTAL PROTOCOLS If chemisorption and related electrocatalytic processes are to be described in terms of the making and breaking of metal-organic surface chemical bonds, experiments need to be conducted in such a manner that ambiguities in data interpretation are minimized. Towards this objective, studies of model interfacial ensembles must include the following experimental protocols:

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a)

the use of compositionally pure and structurally wellcharacterized starting materials, b) the detailed structural and compositional analysis of important surface intermediates, and c) the identification and subsequent quantitative analysis not only of reaction product distributions but also of species retained on the surface. It is in view of these mandates that our investigations, as illustrated schematically in Fig. 1, are based upon the use of single-crystal electrodes and surface-sensitive analytical methods. 1.

Preparation of Single-Crystal Electrode Surfaces

We have adopted two procedures to prepare oriented monocrystalline surfaces. In one, most common in gas-solid interfacial studies, single-crystal rods grown by zone refining are oriented by Laué back-reflection and then cut, preferably by spark-erosion, along the desired crystal face. The near-surface layers, rendered amorphous by the cutting process, are removed by chemical dissolution. Metallographic polishing is subsequently done with successively finer grades of alumina or diamond paste in order to obtain a uniformly smooth surface. Oriented and polished single-crystal electrodes are available commercially (Goodfellow, London, England); such crystals, cm2-disks whose mm-thin edges (rims) were also polished but not oriented, were employed in our UHV-EC work. The other procedure, lately referred to as the Clavilier method,16 is based on the fact that a spherical single-crystal bead is obtained when a polycrystalline Pt wire is melted in a hydrogenoxygen flame; single-crystal facets, of which the (111) and (100) planes (Fig. 2A) are visually observable, are formed on the surface of the beads (Fig. 2B). Our STM experiments were performed on the (111) face without further treatment. For voltammetric measurements, however, the selected facet had to be enlarged by metallographic polishing; the bead-surface electrode was then reannealed to repair the damaged selvedge. Figure 2(C) shows such electrode in a meniscus configuration for EC experiments. Clavilier-type single-crystal beads of various metals can be purchased commercially (Icryst, Julich, Germany).

Figure 1. T he characterization of an electrocatalytic reaction must include not only the analysis of the products in solution but also of species remnant on the surface.

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Figure 2. (A): The arrangement of single-crystal basal planes in a flame-annealed Clavilier bead. (B): Single-crystal facets on a Clavilier bead of Pt. (C). Hangingmeniscus configuration for voltammetric experiments with a single-crystal facet of a Clavilier bead.

2.

Interfacial Characterization

The cleanliness and single crystallinity of electrode surfaces are not assumed even if the preparative steps outlined above are followed. The verification or identification of initial, intermediate, and final interfacial structures and compositions is an essential ingredient in our studies. The interfacial characterization methods employed to date have been conveniently classified in terms of whether they are conducted under reaction conditions (in situ) or outside the electrochemical cell (ex situ). In situ methods here consisted of cyclic voltammetry (CV), EC-STM and DEMS. Ex situ methods included LEED, AES, and HREELS. (i) Electron Spectroscopy (ES) This group of techniques is based upon the analysis of electrons backscattered or emitted from metal surfaces. The shallow escape depths of these particles make their use most suitable for interfacial studies since the information they bear are characteristic only of the near-surface layers; on the other hand, the short meanfree paths necessitate a high-vacuum environment. The major limitation has always been the possibility of structural and compositional changes upon emersion (removal from solution under potential control) and transfer of the electrode into the UHV environment. However, numerous studies have established that the compact layer remains largely unperturbed upon emersion,16-19 unless the emersed layer contains feebly bound non-condensed species.

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EC-ES methods are now well known and will only be summarily described here. (a) Low-energy electron diffraction (LEED)7-16 In this method, the electrode surface is subjected to a beam of low-energy (50 to 500 eV) electrons, and the elastically backscattered electrons are collected onto a phosphor screen. The appearance of distinct diffraction spots (LEED patterns) on the screen indicates an ordered near-surface region. For known monatomic and small-molecule adsorbates, the adlayer structural symmetry may be deduced readily from the LEED pattern, especially when information on the surface coverage is available from other experiments. For complex molecules, extraction of the substrateadsorbate interfacial structure from digitized LEED data is a nontrivial computational task.20 (b) Auger electron spectroscopy (AES)7-16 In AES, core-hole excitations are created when a beam of electrons, typically with energies between 1 to 10 KeV, is impinged onto the surface. In the decay process, one upper-level electron falls into the vacant core level and a second electron, the Auger electron, is ejected. Since the kinetic energy of the emitted Auger electron is characteristic of the (doubly-ionized) atom, AES is a sensitive technique that provides information on the elemental composition (except H and He) of the interfacial region. Analytical procedures that enable the use of AES as a quantitative technique have been suggested.7-16 (c) High-resolution electron energy loss spectroscopy (HREELS).7-16,21,22 This is a surface vibrational spectroscopic technique that involves the irradiation of the adsorbate-metal interface with a beam of low-energy (2 to 10 eV) electrons and the measurement of the energies of the backscattered electrons; energy losses below 0.5 eV are due mainly to inelastic interactions with metal-surface phonons and adsorbate vibrational excitations. The extremely high sensitivity of HREELS makes possible measurements of adsor-

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bate-metal vibrational energies which lie in the far-infrared region; however, its resolution rather low (at best, ca. 16 cm-1).Detection of backscattered electrons in the specular direction (dipole scattering) leads to vibrational loss spectra governed by the metal-surface dipole selection rule. Electrons scattered at non-specular angles (impact scattering) provide loss spectra that are not subject to simple selection rules and allow the observation of vibrational motions parallel to the metal surface. Vibrational modes that are strong dipole scatterers are weak impact scatterers; conversely, modes that produce poor dipole scattering lead to intense impact scattering. A fairly comprehensive surface vibrational analysis can thus be achieved if both specular and non-specular HREELS spectra are acquired. An instrument that integrates ES with EC is shown in Fig. 3; a residual gas analyzer is also available in this apparatus for temperature-programmed desorption (TPD) but the use of such technique is beyond the scope of the research described here.

Figure 3. Integrated UHV-EC instrument, where UHV signifies AES, HREELS, LEED and TPD surface characterization techniques.

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(ii) Scanning Tunneling Microscopy (STM) The invention of the scanning tunneling microscope23 and the developmental work24-26 that ensued to adapt the technique in the study of the electrode-electrolyte interface under reaction conditions, have led to significant advances in electrochemical surface science. The singular power of STM lies in x x

its adaptability for measurements under reaction conditions, and its ability to resolve localized nanometer-scale structural features.

Consequently, STM quickly became a pillar among the many powerful techniques employed in surface science. While such advances may tempt a few to regard EC-STM as the elixir of the myriad problems in interfacial electrochemical science, the enthusiasm has to be tempered by the realization that tunneling microscopy is unable to probe other fundamental issues such as surface energetics, composition, and electronic structure; EC-STM will always require additional surface characterization techniques if a more complete understanding of complex heterogeneous processes is desired. The early applications of STM in electrochemistry were based upon a two-electrode configuration in which electrons tunneled through the gap between the electrode surface and the probe tip upon imposition of a potential difference across the gap. In such an arrangement, however, potentionstatic conditions between the tip and sample are difficult to maintain since both are polarizable electrodes. In conventional electrochemistry, this problem is circumvented by a three-electrode arrangement in which a potentiostat controls the voltage applied to the working (sample) electrode (WE) relative to a reference electrode (RE) even as current flows between the WE and an auxiliary (counter) electrode (AE). When coupled to an STM, the potential of the tip, relative to that of the WE must also be independently adjustable. Both EC and STM requirements are simultaneously addressed by the use of a bipotentiostat27 (Fig. 4A) in a four-electrode cell (Fig. 4B). In this configuration, one potentiostat controls the tunneling bias between the tip and the WE while a second potentiostat adjusts the voltage imposed on the WE. Additional circuitry allows for the separate mea-

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Figure 4. EC-STM configuration. (A): Electronic (bipotentiostat) circuitry. (B): Four-electrode experimental set-up.

surement of the tunneling and faradaic currents. Electrochemical currents are typically in the μA range whereas tunneling currents may be as low as pA level. Hence, faradaic currents must be kept to a minimum; this is accomplished by the use of a tip coated with a non-conductor such that only the outermost part is in contact with the electrolyte (Fig. 4B). EC-STM was carried out with a Nanoscope E microscope (Veeco Metrology, Santa Barbara, CA) equipped with a custombuilt Kel-F electrochemical cell. The tunneling tips were prepared by electrochemically etching a tungsten wire, 0.25-mm in diameter, in 1 M KOH at 15 VAC. The attainment of atomically sharp STM tips may be confirmed with a microscope of at least 1000fold magnification. The choice tips were then coated with transpa-

Figure 5. Schematic illustration of a DEMS instrument.

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rent nail polish to minimize the faradaic currents. Routine atomically resolved EC-STM images of the clean Pd(111) surface have demonstrated the lack of contamination from the nail polish. (iii) Differential Electrochemical Mass Spectrometry (DEMS) The primary use of DEMS28,29 is for the determination of volatile hydrophobic compounds generated from an electrode reaction. It is based on an uncannily simple principle: When a porous hydrophobic membrane is placed between an electrochemical cell and a differentially pumped mass spectrometer, all species that are simultaneously hydrophobic and volatile will be drawn out from the cell and directed into the mass analyzer where they can be identified based on mass-to-charge ratios and/or fragmentation patterns. A schematic diagram of the DEMS apparatus is shown in Fig. 5. The electrochemistry compartment consists of a circular block of passivated titanium (a) that rests above a stainless-steel support (l) connected to the mass spectrometer. The space between the cell body and the support is a Teflon® membrane (j) embedded on a steel mesh (k); the membrane is 75 Pm thick, has 50% porosity and pore width of 0.02 Pm. The single-crystal disk (h) is the working electrode; its face is in contact with the electrolyte solution and separated from the cell body by another Teflon® membrane (i) that functions as a spacer to form a ca. 100-Pm thick electrolyte layer (j). Stop-flow or continuous-flow electrolysis can be performed with this arrangement. For the latter, flow rates have to be minimal, ca. 1 PL/s, to allow ample time (ca. 2 s) for the electrogenerated products to diffuse to the upper Teflon® membrane. Two capillaries positioned at opposite sides of the cell body (b, e) serve as electrolyte inlet and outlet as well as connection ports to the reference (f) and two auxiliary Pt-wire electrodes (d, f). The DEMS system requires two turbomolecular pumps. A 200-L/s pump located in the ionization chamber to maintain a vacuum at the 10-4 torr level, and a 50-L/s pump in the analyzer section for evacuation to a pressure below 10-5 torr. A shutter between the ionization and analyzer compartments preserves the differential pressure. Reaction products that are able to pass through the hydrophobic membrane are ionized by electron impact and separated

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according to mass-to-charge (m/z) ratio by a quadrupole mass analyzer (QMA). The mass-peak intensities can be displayed either as current transients, with current i plotted as a function of time t, and/or as mass spectrometric cyclic voltammograms (MSCV), with i plotted as a function of applied potential. In a typical DEMS experiment, the clean electrode is first characterized for cleanliness and structural integrity by cyclic voltammetry30 in 0.1 M H2SO4. It is then emersed at potentials within the double-layer region and immediately transferred the thin-layer EC cell where it is exposed to adsorbate solution for 180 s at opencircuit potentials. To ensure that unadsorbed material is removed prior to the DEMS experiments, the EC cell is rinsed with organicfree 0.1 M H2SO4. Multiple voltammetric cycles are ordinarily run until changes are no longer observed in both the current-potential and mass-spectral plots. Other aspects of the DEMS methodology, such as productformation rates and mass-spectrometry calibration have been discussed in detail elsewhere.28-30 III. THE CHEMISORPTION AND ELECTROCATALYTIC REACTIVITY OF AROMATIC COMPOUNDS Figure 6 shows the LEED pattern and AES spectrum of a typical UHV-prepared clean and well-ordered Pd(111) electrode surface. For a representative Pd(111) facet on a flame-annealed Clavilier bead, STM images obtained under an Ar atmosphere and in sulfuric acid under (double-layer) potential control are shown in Fig. 7. It will be mentioned that no experiments are carried out unless the surfaces are verified to be as untainted and as highly organized as those exemplified in Figs. 6 and 7. 1.

Benzene

(i) EC-STM The chemisorption of benzene on a Pd(111) Clavilier-bead facet yielded two stable structures, as depicted by the EC-STM images in Fig. 8, that depended upon the applied potential within the

Electrocatalytic Reactions of Chemisorbed Aromatic Compounds

(A)

(B)

Figure 6. Surface characterization of a UHV-prepared Pd(111) electrode. (A): LEED pattern. Beam energy: 60 eV; screen voltage: 3 kV. (B): AES spectrum. Beam energy: 2 keV; beam current: 1.5 PA.

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(A)

(B) Figure 7. High-resolution EC-STM images of a Pd(111) facet on a Clavilier bead. Bias voltage: 60 mV; tunneling current: 20 nA. (A) In an environment of highpurity argon. (B) In 0.01 M H2SO4 at potentials in the double-layer region.

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double-layer region.31 A Fourier-filtered EC-STM image of benzene chemisorbed at 0.55 V (RHE) is displayed in Figure 8(A). The image is not completely atom-resolved but certain structural aspects of the chemisorbed organic are nevertheless discernible. For example, the benzene molecules are pseudo-triangular in shape and are slightly tilted (corrugation of 0.05 r 0.01 nm) instead of completely parallel to the metal surface. The adlayer is characterized by a rectangular unit cell whose lattice vectors are 0.95 nm and 0.82 nm; respectively, these are 2—3 and 3 times longer than the vectors of the substrate unit mesh. This adlattice is thus designated as c(2—3u3)-rect in which the surface coverage 4C6H6 is equal to 0.17 benzene molecules per Pd atom. At potentials between 0.5 V and 0.7 V, only the Pd(111)-c(2—3u3)-rect-C6H6 phase was found. At potentials lower than 0.5 V, a reconstruction in the adlayer structure was noted. Figure 8(B) shows a highly ordered adlattice of hexagonal symmetry when the potential was decreased to 0.3 V. (It will be mentioned that patches of hexagonal symmetry start to emerge at 0.4 although domains of c(2—3u3)-rect are still predominant.) It is evident in Fig. 8(B) that alterations not only in the two-dimensional structure but also in the molecular shape are brought about by the change in applied potential. Analysis of the adlayer structure with respect to the substrate symmetry allows the designation of the hexagonal phase as Pd(111)-(3u3)-C6H6 with surface coverage 4C6H6 equal to 0.11. The triangular shape of the adsorbed benzene molecules is quite well defined. In addition, the decrease in intermolecular corrugation (from 0.05 nm to 0.02 nm) indicates that, at the lower coverage, the benzene molecules are oriented more closely parallel to the surface. A recent study32 on the coverage-dependence of benzene adsorbed from the gas phase onto Pd(111) showed that, at 4C6H6 t 0.16, a significant fraction of the benzene molecules are oriented perpendicularly to the surface. Structural models of the Pd(111)-c(2—3u3)-rect-C6H6 adlattice are proposed in Figs. 9(A) and 9(B). In Fig. 9(A), each benzene molecule is spread out over four metal-surface atoms but centered on two-fold bridging sites; this helps rationalize the dumb-bell shape of the aromatic molecules. To account for the pseudotriangular shape of the molecular image, the model in Fig. 9(B) is

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suggested. Here, each molecule is situated at a spot intermediate between two-fold and three-fold sites, and each molecule straddles only three metal-surface atoms. It should be noted that, in this

Figure 8. (A) Height-shaded plot of the Pd(111)c(2¥3x3)-rect-C6H6 adlayer. Bias voltage: 120 mV; tunneling current: 30 nA. (B) Height-shaded plot of the Pd(111)-(3x3)-C6H6 adlayer. Bias voltage: 100 mV; tunneling current: 30 nA.

Electrocatalytic Reactions of Chemisorbed Aromatic Compounds

Figure 9. (A) and (B): Schematic illustrations of two possible real-space structures of the Pd(111)c(2¥3x3)-rect-C6H6 adlayer. In (A), the benzene molecules occupy two-fold bridge sites; in (B), the slightly tilted admolecules occupy three-fold hollow sites. (C): Real-space structural model of the Pd(111)-( 3x3)-C6H6 adlayer; all molecules are situated on three-fold hollow sites.

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model, the molecules are in van der Waals contact with one another; hence, the easing of the surface-packing congestion may be a driving force for the molecules to adopt a slightly titled orientation. The structural model of the Pd(111)-(3u3)-C6H6 adlattice is shown in Fig. 9(C), where each benzene molecule is situated at a three-fold hollow site. The image for such a model would be three spots arranged as an equilateral triangle, an expectation borne out by the results shown by the EC-STM image in Fig. 8(B). It is important to note that there are two unoccupied three-fold hollow sites inside the molecular unit cell; these are of sufficient size to hold at least one water molecule. The existence of coadsorbed water would account for the extra (smaller and less bright) spots observed in Fig. 8(B). (ii) HREELS Unfortunately, no distinct LEED patterns could be generated from the adlayer of benzene chemisorbed on a Pd(111) singlecrystal electrode; hence, meaningful results were obtained only from the HREELS experiments. Figure 10(A) shows the HREEL spectrum of benzene on Pd(111) formed and emersed at 0.5 V; based upon the above EC-STM results, a Pd(111)-c(2—3u3)-rectC6H6 adlayer (4C6H6 = 0.17) was assumed to be present on the surface. Except for the peak at 1717 cm-1, which is due to adventitious CO, all the peaks, when compared to published vibrational spectra of unadsorbed33 and adsorbed34 benzene, are attributable to chemisorbed starting material. Unique to the surface-immobilized aromatic are the peaks labeled (a), 265 cm-1, and (b), 515 cm-1, which arise from direct metal-adsorbate (Pd-C) chemical bonds. Peaks (c) and (d) are out-of-plane C-H bends, J(C-H); peaks (e) and (i) are in-plane stretches, Q(C-H), whereas peaks (f) and (g) are both inplane bends, G(C-H). In order to deduce the orientation of the chemisorbed molecules, the metal-surface dipole selection rule21,22 needs to be invoked; this states that only vibrations with components perpendicular to the metal surface are HREELS-active. That is, if benzene

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Figure 10. HREEL spectrum of a Pd(111) surface after emersion at (A) 0.5 V and (B) 0.3 V from a solution that contained 1 mM benzene in 100 mM tetrafluoroacetic acid. The intensities of the peaks were normalized with respect to that of the elastic peak.

were oriented completely parallel to the Pd surface, only the outof-plane vibrations would manifest HREELS activity. In addition, attention has to be focused on the intensity ratios of the in-plane and out-of-plane vibrations for the adsorbed and unadsorbed species. The appropriate analysis of the vibrational-spectral data sug-

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gests that the adsorbed benzene molecule is not completely parallel to the surface but is slightly tilted. This conclusion is in agreement with the EC-STM measurements described above. The HREEL spectrum for the adlayer formed and emersed at 0.3 V is shown in Figure 10(B); based upon the EC-STM results, a Pd(111)-(3u3)-C6H6 adlayer (4C6H6 = 0.11) is presumed. It can be seen that the ratios of the intensities of the in-plane vibrations (notably peaks f and g) to that of the most prominent out-of-plane vibration (peak c) have all decreased substantially. This result indicates: x x

a decrease in the surface coverage of benzene, and a decrease in the fraction of tilted-adsorbed molecules.

Such indications are in consonance with the EC-STM results in that: x x

the coverage of benzene is decreased as the potential is made less positive, and at lower coverages, benzene is oriented more closely parallel to the surface.

Further indication of negative-potential-induced decrease in coverage is the noticeable increase in the CO peak intensity; that is, electrodesorption of benzene leads to vacant sites that become occupied by adventitious CO. The possibility exists that an increase in the coverage of coadsorbed CO may enforce the slightly tilted orientation of benzene; such occurrence would help account for the persistence of the (supposedly inactive) in-plane vibrations in the HREEL spectrum in Figure 10(B). (iii)

DEMS

The cathodic hydrogenation and anodic oxidation of benzene have been investigated by DEMS at Au(111) and Au(332) electrode surfaces electrodeposited with ultrathin Pd films. The use of submonolayer Pd films was to eliminate possible interferences by (sub-surface) hydrogen absorbed in crystalline or thick-film Pd. The Au(332) surface was selected because, at fairly low submonolayer coverages (e.g., 0.14 monolayer), Pd preferentially deposits on the step sites; as the coverage is increased (e.g., 0.82 ML), the

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Au(332)

Figure 11. Model representation of a Au(332) surface. Ideally this surface consists of monoatomic steps with (111) step facets and (111) terraces that span 5.5 atomic rows (l = 12 Å).

Pd then plates onto the terrace sites (Fig. 11). On Au(111), only terrace sites are exposed. In this manner, the surface electrochemical properties of the subject compounds at the steps and on the terraces surfaces can be compared. It should be recalled that aromatic molecules chemisorb only on Pd but not on Au;4-6 the expectation is then that the lower the Pd coverage, the lower the amount (and subsequent electrocatalysis) of chemisorbed benzene. The CV and MSCV plots, started from the double-layer region and swept in the cathodic direction, for benzene at Au(332) modified with 0.82 ML of Pd [hereafter designated as Au(332)0.82ML-Pd] are shown in Figure 12. The reversible peaks at ca. 0.25 V in subsequent cycles (at which most of the benzene have already been desorbed) are due to the hydrogen adsorptiondesorption reactions that transpire only on ultrathin Pd films. The prominent peak at 1.15 V on the first (reverse) anodic scan corres-

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ponds to the electrochemical oxidation of chemisorbed benzene; it is considerably diminished in the second cycle. The smaller peaks that emerge in subsequent scans are attributable to Pd surfaceoxide formation. The cathodic peak at 1.20 V is due to the reduction of Au surface-oxide formed above 1.5 V; the peak at 0.75 V arises from the reduction of the Pd surface-oxide. After a few more current-potential scans, a portion of the Pd-oxide film dissolves in the acid electrolyte, and patches of the Au underlayer are exposed; this is evidenced by the fact the Pd-oxide reduction peak has decreased while the Au-oxide reduction peak has increased. The other notable features in Fig. 12 are: a) Only benzene is observed in the MSCV in the hydrogen region. This behavior, in which benzene is simply electrodesorbed but not hydrogenated, is identical to that observed for benzene on Pt(111).35 b) A prominent anodic oxidation peak appears at ca. 1.15 V. The charge under this peak, however, is not the maximum amount because of benzene desorption in the initial negative-potential scan. The shoulder that is seen at 1.0 V may be attributed to oxide formation on the Pd at the terrace sites left vacant by benzene electrodesorption. c) It takes at least two oxidation cycles before the Pd surface is rendered essentially free of organic adsorbates. d) The anodic oxidation peak in the CV is accompanied not only by the detection of considerable amounts of CO2 in the MSCV but also by the emergence of a small quantity of benzene. It is not difficult to determine that the ratio of the areas of the benzene peaks at 1.13 V and at 0.05 V (A1.13V/A0.05V) = 0.65. e) If the stoichiometric factor (6 mol CO2/1 mol C6H6) were applied to the MSCV data in the anodic oxidation region, the results will be that a greater fraction of benzene is actually electrodesorbed instead of anodically oxidized. The CV and MSCV data for benzene chemisorbed at Au(332)-0.14ML-Pd, where the Pd are only on the step sites, are shown in Fig. 13. The same trends as for the Au(332)-0.82ML-Pd electrode were observed except that the relative intensities of the peak areas in the hydrogenation and oxidation regions are now reversed: (A1.13V/A0.05V) = 5.0. This result strongly signifies that:

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E vs. RHE/V

Figure 12. (a) Cyclic voltammetric (CV) curve and mass spectrometric cyclic voltammetric (MSCV) curves of (b) at m/z = 78 (benzene) and of (c) m/z = 44 (CO2) for benzene chemisorbed on Au(332)-0.82ML-Pd surfaces in benzene-free 0.1 M H2SO4. The potential scans were initiated in the negative direction. Scan rate: 10 mV/s. The potentials are referenced against the reversible hydrogen electrode (RHE).

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Figure 13. CV and MSCV plots for benzene chemisorbed on Au(332)-0.14ML-Pd electrodes in 0.1 M H2SO4. Experimental conditions were as in Fig. 12.

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benzene electrodesorption induced by hydrogen (or negative potentials) is more facile at the terrace sites than at the step sites; but the electrodesorption of benzene at the anodic oxidation region potential occurs more easily at step sites instead of at terrace sites.

Although the data are not shown here, it will be mentioned that the CV and MSCV plots for benzene at Au(111)-0.6ML-Pd are not too different from those for Au(332)-0.82ML-Pd. In other words, reactions that occur at terrace sites are similar even if the structures of the underlying substrates are different [i.e., (111) vs. (332)]. Any noticeable divergence most likely arises from topographic differences as the smoother Au(111)-Pd contains more contiguous uniform sites than the more corrugated Au(332)-Pd electrode surface. 2.

Hydroquinone/Benzoquinone

(i) HREELS The HREEL spectrum that results when the palladium surface is emersed from an aqueous 0.1 mM hydroquinone (H2Q) solution is shown in Fig. 14. Three features in this spectrum warrant attention: the absence of a peak at 3600 cm-1 which, by comparison with the gas-phase H2Q spectrum,36 would have indicated an in-plane Q(OH) stretch; b) the presence of peaks 2, 3 and 4 which, if the adsorbed molecule retained its aromatic functionality, would correspond to in-plane bending [G(CH)] and stretch [Q(CC) and Q(CH)] modes, respectively;36,37 and c) the appearance of peak 1 that could be attributed to an outof-plane bending mode, J(CH),36,37 the intensity of which is the highest of all observed peaks. a)

The absence of a Q(O-H) peak indicates either the absence of a phenolic O-H functional group and/or the imposition of a rigidly flat (K6) adsorbed-aromatic orientation; in the latter configuration,

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Figure 14. HREEL spectrum of a Pd(100) surface after emersion from a 0.1 mM aqueous solution of hydroquinone in 1 mM tetrafluoroacetic acid.

the metal-surface dipole selection rule would render the O-H stretch HREELS-inactive.21,22 However, if the dipole selection rule were to be strictly observed, peaks 2, 3 and 4 (if those were actually in-plane aromatic-ring modes) would likewise have been HREELS-inactive. Hence, the appearance of peaks 2 to 4 could be taken as an indication that the adsorbed molecule is not completely oriented parallel to the surface but is tilted, albeit only slightly. That the off-parallel tilt is minimal is evidenced by the out-ofplane peak being at least three times more intense than the in-plane modes. In the infrared spectrum of unbound hydroquinone36, the reverse is true: the in-plane modes are actually three times more intense than the out-of-plane vibration. It should also be noted that, for gas-phase hydroquinone, the O-H peak is considerably more

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intense than the C-H stretch; yet the HREEL spectrum of chemisorbed H2Q shows only the C-H, without the O-H, peak. It may thus be postulated that H2Q is oxidatively chemisorbed as benzoquinone (Q) in a slightly tilted K6 orientation: Pd + H2Q(aq) o Pd-K6-Q(ads) + H2(g)

(1)

An observed rest-potential shift in the negative direction upon chemisorption of H2Q provides evidence for an oxidativechemisorption reaction. The H2Q(aq)-to-Pd-K6-Q(ads) chemisorption process has also been reported for Pt.38,39 To investigate further the nature of the adsorbed species, identical HREELS experiments were carried out using benzoquinone and Pd(111). It must first be mentioned that, unlike the case for H2Q, no rest-potential shift was observed upon chemisorption of Q; that is, only simple chemisorption, neither oxidative nor reductive, occurs when Q interacts with Pd: Pd + Q(aq) o Pd-K6-Q(ads)

(2)

The HREEL spectrum obtained after emersion of the Pd(111) surface from an aqueous 0.1 mM Q solution is shown in Fig. 15. It is clear that this spectrum is identical to that shown in Fig. 14. The virtual identity of the two spectra indicates that the adsorbed species derived from aqueous H2Q is the same as that generated from aqueous Q. Such species is almost certainly benzoquinone; its surface coordination bond should be the same as in the organometallic complex, L2Pt-K6-Q, where the ligand L is triphenyl phosphine (PPh3)40 and the quinone is chelated via its two double bonds to the Pt atom. Studies on the infrared spectra40 of L2Pt-K6-Q and the related organometallic complex, Zeise’s salt, PtL2(C2H2),41 reveals that: x x

the frequency of the carbonyl C=O stretch can be lowered from 30 to 260 cm-1 upon coordination of the quinone; and S-backbonding from the metal to the S* antibonding orbital of the olefin weakens the C=C bond by up to 140 cm-1.

Based on these coordination-induced frequency shifts, it may be conjectured that the HREEL spectra in Figs. 14 and 15 are due to a

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Figure 15. HREEL spectrum of a Pd(100) surface after emersion from a 0.1 mM aqueous solution of benzoquinone in 1 mM tetrafluoroacetic acid.

slightly tilted Pd-K6-Q(ads) surface complex. In such a case, the frequency assignments would probably be as follows: peak 1 ~ J(CH); peak 2 ~ Q(CC) and/or G(CH); peak 3 ~ Q(CO); and peak 4 ~ Q(CH). All but the (CH)-based peaks in the surface complex are red-shifted relative to those of the unbound Q. The small offparallel tilt allows for the HREELS-activation of the in-plane modes. (ii) EC-STM Figure 16 shows unfiltered high-resolution EC-STM images of the ordered Q adlattice acquired at 0.5 V. In Fig. 16(A), a molecular array of hexagonal symmetry in registry with the Pd(111)

Electrocatalytic Reactions of Chemisorbed Aromatic Compounds

Figure 16. Unfiltered high-resolution EC-STM image of a (3x3) benzoquinone adlayer at 0.5 V (RHE). (A): Normal view. (B): Enlarged view. Bias voltage: 100 mV; tunneling current: 20 nA.

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substrate can be observed in which the Q molecular entities are equidistantly separated by 0.82 nm. The latter intermolecular separation is 3 times longer than the substrate nearest-neighbor distance; hence, it establishes the organic adlattice to be (3u3)-Q, with a surface coverage, 4Q of 0.11. An enlargement of the ECSTM image (Fig. 16B) provides important details of the individual Q molecules within the (3u3)-Q adlattice. While the carbon atoms in the aromatic ring cannot be distinguished individually, the asymmetric Q molecule can be suitably outlined (traced) to locate the para-oxygen atoms. The Q molecule thus appears as a set of two conjoined spots of uneven brightness separated by elongated features also of uneven brightness. The latter elongated features are separated by 0.55 nm, the same distance that separates the two p-oxygen atoms in benzoquinone. Based on this detail, a representation of the Q molecule is superimposed on one of the EC-STM spots to illustrate the structure of an individual benzoquinone molecule within the adlayer. Not evident in the idealized rendition is the fact that, as indicated by the uneven brightness of the individual images, the K6-attached Q molecule is slightly tilted with the 1,2-positions closer to the surface than the 4,5-positions. It may also be noted from Fig. 16 that the molecular C2 axis that connects the p-oxygen atoms is rotated 30q with respect to the hexagonal close-packed [1C10] direction of the substrate. Two structural models for the (3u3)-Q adlattice, each consistent with the present results, are depicted in Fig. 17. In the first, the O atoms occupy atop sites; in the second, the O atoms are located at two-fold bridge sites. Unfortunately, the EC-STM images obtained in this study are unable to differentiate between the two possible models. In both structures, the center of the quinonoid ring is located on a two-fold site. (iii)

DEMS

Figure 18 shows the CV and MSCV for the oxidation of Q at Au(332)-0.72ML-Pd in which Pd atoms are situated at both terrace and step sites. When the potential scan was initiated in the anodic direction, a single prominent peak at 1.15 V was observed, Fig. 18a. This peak corresponds to the anodic oxidation of chemisorbed Q; as in the case of benzene (Fig. 12), the anodic peak is consid-

Electrocatalytic Reactions of Chemisorbed Aromatic Compounds

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Figure 17. Schematic illustration of two different real-space structures of the Pd(111)-(3x3)-Q adlayer. In both cases, the benzoquinone molecules occupy twofold bridge sites.

erably, but not completely, diminished in the second anodic cycle. In contrast, however, the clean Pd-oxide-formation features are regenerated only after additional multiple cycles; that is, the oxidative desorption of Q (to CO2) is not complete after only a single scan. Further anodic oxidation occurs on subsequent scans as evidenced from both CV and MSCV plots. The latter shows that appreciable CO2 is generated in the second cycle and that oxidation is exhaustive only on a third cycle. Peak-area measurements indicate that 72% of the total CO2 is evolved in the first anodic scan, 27% in the second, and 1% in the third cycle.42 Figure 19 shows the DEMS results when the potentiodynamic scans were started in the negative direction. The three most significant observations are: x x

x

No MSCV peaks are generated near the HER; that is, if any hydrogenation had taken place, the products were neither volatile nor hydrophobic. Anodic oxidation peaks are found in both the CV and MSCV curves when the potential scan was reversed in the positive direction; in addition, electrochemical oxidation was completed only in a third cycle. Peak-area measurements reveal that the total yield of CO2 was about 25% higher when the scan was started in the anodic direction than when it was commenced in the reduc-

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tion direction. This indicates that hydrogenation did take place but only to a minor extent. But the possibility exists that simple electrodesorption may have also occurred (vide infra).

Figure 18. CV and MSCV (m/z = 44 for CO2) plot for hydroquinone (H2Q) chemisorbed on Au(332)0.72 ML-Pd electrodes in H2Q-free 0.1 M H2SO4. Experimental conditions as in Fig. 12. Potential can started in positive direction.

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Figure 19. CV and MSCV (m/z = 44 for CO2) plot for hydroquinone (H2Q) chemisorbed on Au(332)0.72ML-Pd electrodes in H2Q-free 0.1 M H2SO4. Experimental conditions as in Fig. 12. Scan started in negative direction.

A possible hydrogenation product is 1,4-cyclohexanediol. It is hydrophilic and would not be detected by DEMS; it is also surface-inert and cannot be anodically oxidized. The above experiments were repeated for a Au(111)-0.6MLPd electrode surface. The results are not that dramatically different from those for the Au(332)-0.72ML-Pd surface except for the lowered amount (by approximately 30%) of CO2 evolved after a cathodic scan.

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IV. THE CASE FOR A LANGMUIR-HINSHELWOOD MECHANISM In the electrocatalytic hydrogenation and oxidation of chemisorbed Q described above, repetitive mention was made of the fact that it took at least three anodic cycles before oxidative desorption of Q to CO2 was exhausted. This result elicits questions that relate to what actually transpires. For instance: Are a fraction of the anodically generated products only incompletely oxidized? If so, the partially oxidized species would have to retain a surface-active functional group if they were to be re-adsorbed when the oxided electrode is reduced back to the metal. Or is a fraction of the chemisorbed Q able to remain intact on the surface while other adsorbed molecules are oxidized completely to CO2? If true, this would imply that desorption does not occur unless organic oxidation proceeds all the way to CO2. With respect to the hydrogenation of Q: Does the absence of a DEMS-detectable product indicate plain electrodesorption? Or are the hydrogenation products (e.g., 1,4-dihydroxycyclohexane) merely surface-inactive as well as non-volatile and/or hydrophilic? In the hydrogenation, the results already presented supports the notion that electrodesorption of Q does not occur. This is because desorption of Q at these potentials would have resulted in an immediate Q(aq)-to-H2Q(aq) reduction reaction; but no cathodic peak for such a process appears in the voltammetric curves (Figures 18 and 19). This view enjoys further support from HREELS and ECSTM data. Figure 20 shows HREELS spectra of Q as the emersion potential is made progressively more negative. The most significant result is that the spectral features observed prior to hydrogenation are retained, albeit with lower intensities, as the extent of hydrogenation is increased. This indicates that a copious amount of Q is able to forestall hydrogenation even in the chemisorbed state; in addition, the surface species are not reaction residues but, in fact, are the original adsorbed molecules. Figure 21 displays an EC-STM image at quiescent potentials after a first-cycle hydrogenation. It is quite remarkable, but consistent with the HREELS data, that intact well-ordered (3u3)-Q domains persist after hydrogenation. The presence of the pure (3u3)-Q patches can only mean that Q molecules were neither hydrogenated nor electrodesorbed; an electrodesorption-rechemisorption mechanism would have pro-

Electrocatalytic Reactions of Chemisorbed Aromatic Compounds

309

duced randomly distributed (non-agglomerated) chemisorbed Q molecules. Equally important is the implication that the reactions do not occur at random locations but proceeds along the edges of the ordered domains. The anodic oxidation of chemisorbed Q also appears to follow the above reaction pathway. Evidence is provided by HREELS spectra (Fig. 22) obtained when the potentials are made progressively more positive. It can be seen that the spectral features for unimpaired Q persist, but with diminished intensities, at anodicoxidation potentials. The new peaks above 3000 cm-1 are due to the formation of hydrated surface oxides. Evidently, a small fraction of chemisorbed Q is also able to resist anodic oxidation. Unfortunately, no acceptable EC-STM images could be obtained due



Figure 20. HREEL spectrum of a benzoquinone-precoated Pd(100) surface after emersion at pre-selected hydrogenation potentials (RHE) in 0.1 M H2SO4.

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Figure 21. High-resolution EC-STM image at potentials in the double-layer region after only one cycle of hydrogenation. Bias voltage: 100 mV; tunneling current: 20 nA.

to the presence of surface oxides that severely disordered the surface; upon return to double-layer potentials, however, feeble hints of (3u3)-Q patches appear. These results strongly suggest that the hydrogenation and oxidation of chemisorbed Q proceeds via a Langmuir-Hinshelwood mechanism. For the hydrogenation reaction, the following (possible) reactions may be written: e– + H+(aq) o H(ads)

(3a)

C6H4O2(ads) + 8 H(ads) o C6H10(OH)2(aq)

(3b)

The generation of 1,4-dihydroxycyclohexane [C6H10(OH)2] in has neither been confirmed nor invalidated. For the anodic oxidation:

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311

H2O o OH(ads) + e– + H+(aq)

(4a)

C6H4O2(ads) + 24 OH(ads) l 6 CO2(g)(aq) + 14 H2O

(4b)

It bears repetition that, based upon the EC-STM image in Fig. 21, the hydrogenative (or oxidative) attack of the adsorbed Q by the surface hydrides (or hydroxyls) occurs at the periphery of the ordered organic adlattices.

Figure 22. HREEL spectrum of a benzoquinone-precoated Pd(100) surface after emersion at pre-selected oxidation potentials (RHE) in 0.1 M H2SO4.

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ACKNOWLEDGMENTS Acknowledgment is made to The Welch Foundation (A-1064), the Deutsche Forschungsgemeinschaft, and the German Academic Exchange Service for support of the research described in this review article. REFERENCES 1

E. Yeager and J. Kuta, in Physical Chemistry: An Advanced Treatise, Vol. IXA, Ed. by H. Eyring, D. Henderson, and W. Jost, Academic Press, New York, 1970. A. J. Bard and L. R. Faulkner, Electrochemical Methods, John Wiley, New York, 1980. 3 R. E. White, J. O’M. Bockris, B. E. Conway, and E. Yeager, Eds, Comprehensive Treatise of Electrochemistry, Vol. VIII, Plenum Press, New York, 1984. 4 B. B. Damaskin, O. A. Petrii, and V. V. Batrakov. Adsorption of Organic Compounds on Electrodes, Plenum Press, New York, 1971. 5 J. L. Stickney, M. P. Soriaga, A. T. Hubbard, and S. E. Anderson, J. Electroanal. Chem. 125 (1981) 73. 6 S. L. Michelhaugh, C. Bhardwaj, G. J. Cali, B. G. Bravo, M.E. Bothwell, G. M. Berry, and M. P. Soriaga, Corrosion. 47 (1991) 322. 7 G. A. Somorjai, Chemistry in Two Dimensions: Surfaces, Cornell University Press, New York, 1981. 8 G. Ertl and J. Kuppers, Low Energy Electrons and Surface Chemistry, VCH Publishers, New York, 1985. 9 D. P. Woodruff and T. A. Delchar, Modern Techniques of Surface Science, Cambridge University Press, New York, 1986. 10 J. T. Yates, Experimental Innovations in Surface Science: A Guide to Practical Laboratory Methods and Instruments, AIP Press, New York, 1997. 11 A. T. Hubbard, Accts. Chem. Res. 13 (1980) 177. 12 P. N. Ross, in Chemistry and Physics of Solid Surfaces, Ed. by R. Vaneslow and R. Howe, Springer-Verlag, New York, 1982. 13 E. Yeager, A. Homa, B. D. Cahan, and D. J. Scherson, Vac. Sci. Technol. 20 (1982) 628. 14 D. M. Z. Kolb, Phys. Chem. N. F.. 154 (1987) 179. 15 M. P. Soriaga, in Structure of Electrified Surfaces, Ed. by J. Lipkowski and P. N. Ross, VCH, New York, 1993. 16 M. P. Soriaga, Prog. Surf. Sci. 39 (1992) 325. 17 W. N. Hansen, D. M. Kolb, and D. W. Lynch, Eds, Electronic and Molecular Structure of Electrode-Electrolyte Interfaces, Elsevier, Amsterdam, 1983. 18 T. E. Furtak, K. L. Kliewer, and D. W. Lynch, Eds, Non-Traditional Approaches to the Study of the Solid-Electrolyte Interface, North-Holland, Amsterdam, 1980. 19 O. Hofman, K. Doblhofer, and H. Gerischer, J. Electroanal. Chem. 161 (1984) 337. 20 M. A. Van Hove, in The Nature of the Surface Chemical Bond, Ed. by T. H. Rhodin and G. Ertl, North-Holland Publishing, New York, 1979. 2

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H. Ibach and D. A. Mills, Electron Energy Loss Spectroscopy. Academic Press, New York, 1982. M. P. Soriaga, X. Chen, D. L. Li, and J. L. Stickney, in Applications of Physical Methods to Inorganic and Bioinorganic Chemistry, Ed. by R. A. Scott, Wiley, New York, 2007. 23 G. Binnig and H. Rohrer, Surf. Sci. 157 (1985) L373. 24 M. M. Dvek, M. J. Heben, N. S. Lewis, R. M. Penner, and C. F. Quate, in Electrochemical Surface Science, Ed. by M. P. Soriaga. ACS Books, Washington, 1988. 25 A. A. Gewirth and H. Siegenthaler, Eds, Nanoscale Probes of the Solid-Liquid Interface, Kluwer Academic, London, 1995. 26 K. Itaya, Prog. Surf. Sci. 58 (1998) 121. 27 K. Itaya and E. Tomita, Surf. Sci. 201 (1988) L507. 28 O. Wolter and J. Heitbaum, Ber. Bunsenges. Phys. Chem. 88 (1984) 2. 29 H. Baltruschat, in Interfacial Electrochemistry: Theory, Experiment, and Applications, Ed. by A. Wieckowski, Marcel Dekker, New York, 1999. 30 H. J. Baltruschat, Am. Soc. Mass Spectrom. 15 (2004) 1693. 31 Y.-G. Kim, J. E. Soto, X. Chen, Y.-S. Park, and M. P. Soriaga. J. Electroanal. Chem. 554 (2003) 167. 32 A. F. Lee, K. Wilson, R. M. Lambert, A. Goldoni, A. Baraldi, and G. J. Paolucci, Phys. Chem. B. 104 (2000) 11729. 33 G. D. Waddill and L. L. Kesmodel, Phys. Rev. B. 8 (1985) 4940. 34 L. M. Sverdlow, M. A. Kovner, and E. P. Krainov, Vibrational Spectra of Polyatomic Molecules, Wiley, New York, 1974. 35 T. Hartung, U. Schmiemann, U. Kamphausen, and H. Baltruschat, Anal. Chem. 63 (1991) 44. 36 T. Shimanouchi, Standard Reference Database, NIST, Washington, 1998. 37 L. K. Kesmodel, in Surface Imaging and Visualization, Ed. by A. T. Hubbard, CRC Press, Boca Raton, 1995. 38 M. P. Soriaga, E. Binamira-Soriaga, A. T. Hubbard, J. B. Benziger, and K. W. P. Pang, Inorg. Chem. 24 (1985) 65. 39 K. W. P. Pang, J. B. Benziger, M. P. Soriaga, and A. T. Hubbard, J. Phys. Chem. 88 (1984) 4583. 40 F. R. Hartley, The Chemistry of Platinum and Palladium, Wiley, New York, 1973. 41 U. Belluco, Organometallic and Corodination Chemistry of Platinum, Academic Press, New York, 1974. 42 S.-C. Sanabria, Electrochemical Hydrogenation of Aromatic Compounds at Polycrystalline and Single-Crystal Pd Surfaces, Texas A&M University, College Station, 2006. 22

8

A review of Continuum Electrochemical Engineering Models and a Novel Monte Carlo Approach to Understand Electrochemical Behavior of Lithium-Ion Batteries Vinten D. Diwakar,* S. Harinipriya** and Venkat R. Subramanian*** *

Department of Chemical Engineering, Tennessee Technological University, Cookeville, Tennessee – 38501, USA ** Department of Nanotechnology, SRM University, Chennai – 603203, Tamil Nadu, India *** Department of Energy Environmental & Chemical Engineering, Washington University, Saint Louis, One Brookings Drive, Box 1180, Saint Louis, Missouri – 63130, USA

I.

INTRODUCTION

Electrochemical phenomenon associated with systems from electrochemical energy (Batteries, Fuel cells and capacitors) to electro deposition are multistep and multi-phenomena processes and hence can be very tedious to simulate. The multi-phenomena characteristics of the processes involved in electro deposition and other electrochemical systems including electrochemical power

P. Balbuena, V. Subramanian (eds.), Theory and Experiment in Electrocatalysis, Modern Aspects of Electrochemistry 50, DOI 10.1007/978-1-4419-5594-4_8, © Springer Science+Business Media, LLC 2010

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sources pose inherent difficulties in writing efficient algorithms. These processes also encompass varied length and time scales again posing barriers to efficient simulation. Traditionally, continuum models have been used to simulate electrochemical systems and have been the chief tool for researchers in this field. The behavior of battery systems for example have been sufficiently described by continuum models for the last two decades.1,2 Continuum modeling is an attractive tool for battery systems design and optimization studies apart from its ability to predict transport and thermal behavior. In this chapter, a brief review of continuum electrochemical engineering models for lithium-ion batteries is provided. The capabilities and limitations of these models are discussed. Next, a continuum Monte Carlo approach is proposed to characterize the cathode material of lithium-ion batteries. II. CONTINUUM MODELS FOR PREDICTING BATTERY BEHAVIOR Engineering (continuum) models are being used to optimize and predict lithium ion battery performance since the last two decades.1,2 The electrochemical behavior can be predicted by modeling the transport and kinetic processes that occur within the battery system. These models usually describe the dependent variables of interest (for example, solid phase concentration, solution phase concentration, etc.) by a system of partial differential equations with corresponding initial and boundary conditions. A typical schematic of the battery system is shown in Fig. 1. The anode and the cathode electrodes are composite materials, and they are typically represented as spherical particles. During a discharge process the lithium ions de-intercalate from the anode (negative electrode), diffuse through the separator/electrolyte and intercalate into the cathode (positive electrode).3 The opposite is true during charging of the battery. Newman and co-workers developed a successful model for lithium-ion sandwich that consists of a porous electrode, separator and a current collector.4 This model is based on concentrated solution theory1 and this important work paved the way for further model developments due to the fact that the model has a general framework robust enough to include further developments in a battery system and also gener-

Continuum and Monte Carlo Models for Lithium-Ion Batteries Separator

Anode

Current collector

Current collector

Cathode

317

LP

LS

LN

Figure 1. Lithium ion cell.

ic enough for many secondary batteries with two porous electrodes.5-11 There are many reviews on mathematical models for lithium ion batteries. Botte et al. presented an extensive review on mathematical modeling of rechargeable lithium batteries.3 A review of mathematical models of lithium and nickel battery systems is discussed in literature.12-13 Experimental developments in the field can be found in a recent review article that describes new solutions, new measurement procedures and new materials for Li-ion batteries.14 Apart from the enormous body of work on modeling of Li-ion batteries, efforts have also been made in making these continuum models more computationally efficient to simulate.41 Computationally efficient models can not only be used to predict battery behavior but can also be used in situations where real-time parameter estimation is needed, for example, situations where super accurate determination of State of Health (SOH) of a battery is critical, adding a new dimension to the capabilities of continuum models. Continuum battery models consist of two scales, namely, the micro and the macro scale. The model equations are briefly described below.

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Variables and Governing Equations in the Macro Scale

A Li-ion battery usually consists of a composite cathode, a separator and an anode. The outer ends of the batteries are connected to a current collector that channels the electrons produced out to the load circuit. (i) Cathode The composite cathode usually consists of an inert conducting material, the polymer/salt electrolyte, and the solid active insertion particles. The key requirements for a material to be successfully used as a cathode in a rechargeable lithium battery are as follows:15 (a) The material contains a readily reducible/ oxidizable ion, for example a transition metal. (b) The material reacts with lithium in a reversible manner. This dictates an intercalation-type reaction in which the host structure essentially does not change as lithium is added. (c) The material needs to reacts with lithium with a high free energy of reaction for two reasons. First, high capacity, preferably at least one lithium per transition metal. Second, high voltage, preferably around 4 V (as limited by the stability of the electrolyte). The direct result of this leads to a high-energy storage. (d) The material reacts with lithium very rapidly both on insertion and removal. This leads to high power density, which is needed to replace the Ni/Cd battery or for batteries that can be recharged using HEV regenerative braking. (e) The material needs to be a good electronic conductor, preferably a metal. This allows for the easy addition or removal of electrons during the electrochemical reaction. This allows for reaction at all contact points between the cathode active material and the electrolyte rather than at ternary contact points between the cathode active material, the electrolyte, and the electronic conductor (such as carbon black).This minimizes the need for inactive conductive diluents, which take away from the overall energy density.

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319

(f) The material needs to be stable, i.e., not change structure or otherwise degrade, to overdischarge and overcharge. (g) The material needs to be available at low cost. (h) The material has to be environmentally benign. LiCoO2 is a standard candidate which has been successfully used in the portable electronics industry. Porous electrode theory assumes that medium is a superposition of continuous solid and electrolyte phases with a known volume fraction.16 The solid phase potential of the positive electrode is because of electronic conduction: Veff,p

w 2)1 wx 2

(1)

ap Fjp

The solid phase current is related to the potential gradient as i1

Veff,p

w)1 wx

(2)

To account for current in the solution phase, the modified Ohm’s law is used: i2

 N eff, p

w) 2 2N eff, p RT 1  t  w ln c  wx wx F

(3)

The second term on the right hand side arises from concentrated solution theory. The sum of the currents of the two phases is equal to the applied current at any point in the electrode, i1 + i2 = I

(4)

where I is the applied current density (the current divided by the projected electrode area). The convention of I being positive when charging the cell is commonly used. The lithium concentration in the electrolyte phase is governed by material balance at any point inside the porous electrode and is given by: Hp

wc wt

Deff,p

w 2c wx

2

 1  t ap jp 

ip dt F dc

(5)

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Typically transfer number is assumed to be a constant or fit to experimental data corresponding to the ion concentration. For constant transfer numbers, the electrolyte phase concentration equation is reduced to Hp

wc wt

Deff,p

w 2c wx 2

 1  t ap jp

(6)

The effective diffusivity is introduced to handle the tortuosity of the electrode. Typically they are related by the equation Deff, i

brugg i

i = p, s, n

DH i

(7)

where Bruggman coefficient assumes a value of 1.5 and is used as a correction factor accounting for the porosity of the electrodes. The reaction occurs at the electrode/electrolyte interface (solid/liquid interface at the surface of the particle). This reaction occurs as a source term in the equations for the macro scale. In the model equations, jp accounts for the electrochemical kinetics, (intercalation reaction from the electrolyte phase into the solid matrix and vice-versa). It is a modified form of the Butler-Volmer kinetics, and is given by the following expression: jp

§ · 2k p ¨ cs, p, max  cs, p ¸ r R p © ¹

0.5

0.5

§ · ¨ cs, p ¸ r R p © ¹ ª 0.5F º 0.5 ˜ c sinh « )1  ) 2  U p » ¬ RT ¼



(8)



The equation for calculating the pore wall flux jp also accounts for the interaction between the electronic and ionic phases in the battery. (ii) Separator The principal function of a separator in a Li-ion battery is to keep the positive and negative electrodes apart. This is needed to prevent electrical short circuits and at the same time allow for rapid transport of ionic charge carriers that are critical to complete the

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circuit during the passage of current in the battery. The considerations that are important and influence the selection of the separator include the following:17 (a) It should be a good electronic insulator (b) The electrolyte (ionic) resistance should be minimal (c) The separator should offer mechanical and dimensional stability (d) Sufficient physical strength to allow easy handling (e) Chemical resistance to degradation by electrolyte, impurities, and electrode reactants and products (f) It should be an effective barrier to prevent migration of particles or colloidal or soluble species between the two electrodes (g) The separator has to be easily wet by electrolyte (h) Uniform in thickness and other properties There are two dependent variables in the separator: the solution phase concentration (c) and the solution phase potential (ĭ2). The solution phase concentration is governed by the material balance for lithium in the solution phase of the separator: Hs

wc wt

Deff,s

w 2c wx 2

(9)

The potential distribution in the separator is given by: I

 N eff,s

w) 2 2N eff,s RT 1  t w ln c  wx wx F

(10)

(iii) Anode As before for cathode, the governing equations are: The solid phase potential of the negative electrode is because of electronic conduction: Veff,n

w 2)1 wx 2

an Fjn

(11)

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The solid phase current is related to the potential gradient as i1

Veff,n

w)1 wx

(12)

To account for current in the solution phase, the modified Ohm’s law is used: i2

 Neff,n

w) 2 2N eff,n RT 1  t w ln c  wx wx F

(13)

The second term on the right hand side arises from concentrated solution theory. The sum of the currents of the two phases is equal to the applied current at any point in the electrode, (14) i1 + i2 = I The electrolyte phase concentration equation for the negative electrode is given by: Hn

2.

wc wt

Deff,n

w 2c wx 2

 1  t an jn

(15)

Variables and Governing Equations on the Micro Scale

Continuum models encompass both micro and macro scales and in li-ion models the microscale is governed by the solid phase diffusion equation. The coupling of the microscale and the macroscale variables pose computational limitations. The concentration of lithium at the solid/solution interface, , is obtained by solving the Fick’s law in spherical coorc s, p r R p

dinates, for the concentration of lithium inside the solid phase: wcs, p wt

§ w 2cs, p 2 wcs, p · ¸  Ds, p ¨ ¨ wr 2 r wr ¸ ¹ ©

The initial and boundary conditions for Eq. (16) are given by:

(16)

Continuum and Monte Carlo Models for Lithium-Ion Batteries

cs, p

t 0

cs, p,0

(17)

0

(18)

wcs, p wr r 0  Ds, p

323

wcs, p

jp

wr r R p

(19)

The porewall flux jp occurs as a boundary condition for the micro-scale as opposed to being a source term for the macroscale. For certain battery chemistries rectangular or cylindrical diffusion might be more relevant. Also, the diffusion coefficient, which is assumed to be a constant for most modeling purposes, sometimes needs to be functionalized. In cases where the diffusion coefficient depends nonlinearly on concentration the coupling becomes much harder. When the diffusivity changes as a function of concentration (SOC), the governing equation is wcs, p wt

wc · 1 w § 2 ¨ r D cs, p s, p ¸ 2 wr ¨ wr ¸¹ r ©



(20)

In many cases, for example, NiMH batteries, a moving boundary situation arises because of phase transition during the discharge process. An example of solving this moving boundary is shown by Subramanian et al.18 For example, from ȕ to Į phase transfer during discharge of metal hydride electrode, the governing equations are similar to the solid state diffusion equation. The phase boundary from beta to alpha phase is a moving interface. The boundary condition for the expanding/contracting phase is given by:

c0  cD wrc wt

DD

wc wr r rc

(21)

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Along similar lines, new cathode materials that show a phase transition during charging and discharge in lithium ion batteries, for example LiFePO4, have also been addressed in similar ways with appropriate modifications for the chemistry and materials.19 Addition of fundamental physics and their effects on the microscale and macroscale scale have been reported by researchers, for example, the effects of pressure variation during the lithiation process during charging/discharging on the diffusion in the solid phase.20 Table 1 summarizes the governing equations and the corresponding boundary conditions for the lithium ion battery. Table 2 presents values of typical constants (LiCoO2-LiC6 system) used in simulation. Table 3 presents additional equations to solve the system of equations given in Table 1. 3.

Micro-Macro Scale Coupled Continuum Models

There is an inherent coupling of the behavior of the micro-scale variables to the behavior of macro-scale variables. This in itself presents complications when simulating these models. A few researchers have tried to address this problem of coupling of scales in these models.21,22 The solid state concentration term defined by the micro scale diffusion equation need to be coupled with the governing equations for the macro-scale to predict electrochemical behavior. Wang and co-workers used volume averaged equations and a parabolic profile approximation for solid-phase concentration.21 Subramanian et al. developed approximations assuming that the solid-state concentration inside the spherical electrode particle can be expressed as a polynomial in the spatial direction.22 Simulation of continuum lithium ion battery models involve the first principles based derivation of governing equations along with setting up appropriate initial and boundary conditions as shown in Table 1. This is followed by solving the governing equations using different solution methodologies. The usual and most common methodology is to use numeric methods to solve these equations, this is done because the equations are highly non-linear and coupled and these equations do not facilitate simpler analytical solutions. The most common method to solve continuum models is using the finite difference method (FDM). It is possible to have a combination of analytical and numerical techniques to solve a cer-

Region

Cathode

Separator

wc wt

Deff,p

2

Governing equations

 ț eff,s

I

6

wx



F

2ț eff,s RT

w 2c wx 2

w) 2

Deff,s

wc wt

İs

1  t wx

w ln c

wc  ap 1  t jp initial condition c t 0 c0 wx 2 w)1 w) 2 2ț eff,p RT w ln c V eff,p  ț eff,p  I 1  t wx wx F wx 2 w )1 ap Fjp V eff,p wx 2 wcs Ds,p w § 2 wcs · ¨r ¸ initial condition cs t 0 0.5cs ,max, p wt r 2 wr © wr ¹

İp

5

4

3

2

1

Eq. No.

 ț eff,p



wx

w) 2

wx

x lp , 

x lp , 

 Deff,p

 ț eff,s

wx

wc

wx

w) 2

 Deff,s

x lp , 

r Rp

w) 1 wx

&ț

eff,s

wx

w) 2

wx

wc

0

x lp  ls , 

 ț eff,n

wx

x lp  ls , 

wx

wc

w) 2

 Deff,n

x lp , 

x lp  l s , 

x lp , 

w) 2 wx

wc wx  ț eff,s

 Deff,s

x lp  l s , 

x lp

x lp , 

x l p ,

w) 2 wx

wc wx

&  Deff,s

w cs wr

x lp , 

 Ds,p

&  ı eff,p

0 &  ț eff,p I ı eff,p

x 0

0 &

= 0 & jp

wc

r 0

 Deff,p

w cs wr

x 0

 ț eff,p w) 1 wx

w) 2 wx

x 0

wc wx

 D eff,p

Boundary conditions

Table 1 Governing Equations for the Lithium-Ion Battery

Region

Anode

10

9

8

7

Eq. No.

wc wt

Deff,n

w 2c  an 1  t jn initial condition c t wx 2 0

V eff,n

w)1 w) 2 2ț eff,n RT w ln c I  ț eff,n  1  t F wx wx wx 2 w )1 an Fjn V eff,n wx 2 wcs Ds,n w § 2 wcs · ¨r ¸ initial condition cs t 0 0.85cs ,max,n wt r 2 wr © wr ¹

Hn

Governing equations

c0

= 0 & jn r 0

w cs wr

x lp  ls

w) 1 wx

V eff,n

x lp  l s , 

x lp  l s , 

w) 2 wx

wc wx

 ț eff,s

 D eff,s

Table 1. Continuation.

 Ds,n

0& w cs wr

x l p  ls  l n

r Rn

w) 1 wx



x l p  ls  l n

x l p  ls  l n

wc wx

V eff,n

I

& )2

&  D eff,n

x lp  l s , 

x lp  l s , 

w) 2 wx

wc wx

 ț eff,n

 D eff,n

Boundary conditions

0

0

Continuum and Monte Carlo Models for Lithium-Ion Batteries

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Table 2 Typical Set of Simulation Parameters for a LiCoO2-LiC6 Chemistry Based Battery Symbol

Unit

ıi İf,i İi brugg Ds,i D

S/m

m2/s m2/s

1.0×10-14

ki cs,i,max cs,i0

mol/(sǜm2)/(mol/m3)1+Įa,i mol/m3 mol/m3

2.334×10-11 51554 0.4955×51554

mol/m3 m m ȍǜm2

2.0×10-6 80×10-6

c0 Rp li RSEI t+ F R T

C/mol J/(molǜK) K

Positive electrode 100 0.025 0.385

Separator

0.724 4 7.5×10

-10

Negative electrode 100 0.0326 0.485 3.9×10-14 5.0307×10-11 30555 0.8551×30555

1000 25×10-6

2.0×10-6 88×10-6 0.0123

0.363 96487 8.314 298.15

tain set of equations. Even when considering robust numeric simulation it is often needed to condition the initial conditions to avoid numerical instabilities in initial value problem DAE solvers like DASSL because of singularity issues. A more elaborate reading on simulation methods for continuum Li-ion models can be found elsewhere.46 4.

Capabilities of Continuum Models

There are numerous advantages of using continuum models. They are widely used for system design and optimization. Continuum models tell us important information about the system, e.g., discharge curves, state-of-health of the battery, cycle life behavior and subsequently capacity fade rate, etc. Battery models are also useful in predicting non-measurable internal variables such as solution phase concentration, solid phase concentration etc. This can be used to observe or measure buildup or loss of a certain chemical species within the domain of the battery and can be used efficient-

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Table 3 List of Additional Expressions Defining Effective Ionic Conductivity, Effective Electronic Conductivity, Effective Diffusivity Term Corrected for Porosity and Open Circuit Potentials for a LiCoO2-LiC6 Li-Ion Battery bruggi

N eff,i

Hi

4.1253x10

2

 5.007 x10 -4 c  4.7212x10 7 c 2  1.5094x10



V eff, i

Vi 1  H i  H f, i

Deff, i

DH i

ai

Up

10 3

c  1.6018x10

i p, s, n 14 4



i p, n

bruggi



3 1  H i  H f,i Ri

i p, s, n



i p, n

 4 .656  88 .669 T 2p  401 .119 T 4p  342 .909 T 6p  462 .471 T 8p  433 .434 T10 p  1 .0  18 .933 T 2p  79 .532 T 4p  37 .311 T 6p  73 .083 T 8p  95 .96 T10 p

where T p

Un



c ,

0 .7222  0 .1387 T n  0 .029 T 0.5 n 





0 .0172 Tn





cs,p

r Rp

cs,p,max

0.0019 T1n.5

 0.2808exp 0.90  15 T n  0 .7984 exp 0 .4465 T n  0 .4108

where T n

cs,n

r Rn

cs,n,max

Continuum and Monte Carlo Models for Lithium-Ion Batteries

329

(d) (c) (b) (a) (a) (b) (c) (d)

Figure 2. Distribution of electrolyte concentration as a function of discharge time at various interfaces (discharged at 1C rate).

(a) (b) (c) (d)

(b)

(a)

(d)

(c)

Figure 3. Distribution of solid phase concentration as a function of discharge time at various interfaces (discharged at 1C rate).

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Vinten D. Diwakar et al.

(c) (b) (a)

(d)

(a) (b) (c) (d)

Figure 4. Distribution of electrolyte phase potential as a function of discharge time at various interfaces (discharged at 1C rate).

(a) (b) (a) (b) (c) (d)

(c)

(d)

Figure 5. Distribution of solid phase potential as a function of discharge time at various interfaces (discharged at 1C rate).

Continuum and Monte Carlo Models for Lithium-Ion Batteries

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4.2

Discharge voltage, V

3.8

3.4

3.0

2.6

1C

C/2

C/4

2.2 0

3000

6000

9000

12000

15000

Discharge time, s Figure 6. Typical discharge curves for varying C rates for a LiCoO2 cathode based li-ion battery.

ly as an investigative tool. Figures 2-6 illustrate some of the internal variables that can be simulated by the continuum models. Another important aspect of modeling of lithium ion batteries is determining capacity fade. It has been addressed by various researchers over the years and with varying degrees of sophistication. Most commonly, the coupling of a rate expression for the build-up of the SEI (Solid Electrolyte Interface) layer is used in determining the discharge curves as the cycles increase.23 The nature and behavior of SEI determine the cycling rate, power capability, performance and to a certain extent even the safety of the battery. Few researchers have also been looking at the formation of the SEI layer from the molecular level using molecular dynamic and ab-initio studies.24 Theoretical molecular investigations have given decisive insights into the formation of the SEI layer and their detrimental effects on the performance of the Li-ion battery at different cycles. Including capacity fade mechanisms portrays a complete picture of the working of the Li-ion battery. Continuum models are also an important design tool. They are used to optimize system design data (e.g., length and thickness of

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the electrodes, length and thickness of the separator layer, etc.) for efficient use of materials based on application needs. Effect of material parameters, for example, particle size, porosity, overpotential data etc., on the battery behavior, can be studied by applying the parameters as inputs to the models. Ragone plots define the performance of a battery by plotting the energy density against the power density. It paints a very informative picture of how much deliverable power is available for a given battery chemistry. Also, formulation of battery usage strategies, for example, operating the battery at a certain discharge rate can be initiated by understanding Ragone charts. Continuum models can be easily modified to calculate the energy density and the power density. Even though certain optimization studies have been reported, the design calculations and optimization involve simulating the battery models for many number of runs to get one Ragone plot. Impedance measurements provide valuable insight into factors limiting the battery. Impedance measurements can also be used to quantify the resistances and measure important properties such as diffusion coefficients etc. Impedance curves for a battery system can be simulated using electrochemical engineering continuum models.25,26,27 The continuum models facilitate the inversion of governing equations from the time domain to the frequency domain easily. An important aspect of impedance models being explored is using control engineering to better utilize battery systems. 5.

Limitations of Continuum Models

The electronic conductivity Veff, and the effective diffusivity Deff, are averaged functions for simulation purposes and are assumed to have a constant value. It is known that these values are strong functions of concentration. Accommodating the concentration dependencies create non-linearities in the model. The transfer number, t+ is assumed to be a constant for ease of simulation. It has been shown that the transfer number is a function of concentration distribution, but the available data in the literature is not sufficient. The solid phase diffusion coefficients at both electrodes, Dsp, Dsn are affected by changes in ambient and operational temperatures. They are also affected by concentration distribution. In most simu-

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333

lation cases the effect of temperature and concentration on the diffusion coefficients are not accounted for and an average value is taken into consideration. For transportation purposes an important criterion is the ability of the battery to withstand a wide range in temperature. The United States council for automotive research (USCAR) mandates that the battery should be able to withstand temperatures ranging from -40oC to 50oC.47 Parameter data for this entire range or unexpected temperatures are not known. This results in the failure of continuum model to predict performance at elevated temperatures. The effect of size distribution in the solid matrix phase in the electrode material also adds another degree of complexity to the models. Although an empirical size distribution can be used to approximate the effects of particle size distribution the stochastic nature of the problem cannot be overlooked. Enough experimental data is not available at this point to demonstrate the effects of particle size distribution on the electrochemical behavior of electrode materials. Another interesting problem along similar lines is the effect of surface roughness of the particles on the electrochemical behavior. It is common to approximate and represent the solid particles as full spheres. Adding roughness will add another degree of complexity to the continuum models. Surface roughness has been found to play an important role in instigating particles breaking. Population balance models have been widely used in the engineering field to address issues associated with accounting particle breakage. These problems in general can be solved with the use of continuum models but valuable information can be lost in making simplifying assumptions on the continuum scale. This necessitates a multiscale simulation approach. Continuum models find application in many areas where process variables need to be optimized to attain the best possible working scenario for the system. In the case of lithium ion batteries, this would mean predicting the effect of varying load conditions, the SOH and the state-of-charge (SOC) of the battery, etc. This can be achieved for a given chemistry when all data and material parameters are known. Where a continuum model would ideally not be suited is when designing new materials and understanding fundamental processes affecting both microscopic and macroscopic behavior. Although it can be argued that both design and fundamental understanding are very similar we shall treat

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them as separate entities. For designing new materials, one needs to look at material properties and/or be able to predict material properties given the operating constraints of the material in a battery. Operating constraints, for example, could mean development of a battery chemistry to electrochemically behave in a predictable manner at a certain galvanostatic discharge rate at elevated temperatures. Development of models that predict properties at the molecular level are not in the domain of continuum models. A need therefore would be to use stochastic models, i.e., ab-initio, Molecular Dynamics, etc. From Table 1, we can also see that the computational framework can become tedious and intensive very quickly for large number of node points, this would reflect on the fact that multi-scale simulation would be much more laborious and intensive. To address the short comings of continuum models and yet be able to predict the discharge behavior or capacity fade is an important task. The solution suggested is by developing a novel Monte Carlo method that takes into account design properties, for example, thickness of the cathode, and use it in conjunction with microscopic properties, for example, diffusion in solid phase to predict system level properties of interest. The Monte Carlo algorithm can be considered to follow the framework of continuum models. The next section illustrates the usefulness of the Monte Carlo strategy. III. MODELING OF ELECTROCHEMICAL PROCESSES AT THE MICRO AND NANO SCALE Modeling at the molecular level gives a lot of insight into the working of any chemical system. Modeling methods at this length scale vary from atomistic for e.g., ab-initio methods, quantum methods etc to more coarse grained methods such as the classical molecular dynamics approach. At this length scale most methods are computationally intensive and expensive. Although tedious, there are many excellent advantages of modeling at small length scales. One of the most important advantages is the ability to predict properties of materials. Modeling of materials with specific properties is of prime importance in meeting the emerging needs of electrochemical energy sources, particular, battery materials.

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In general, Kinetic Monte Carlo codes and Molecular Dynamics simulations are very slow and time consuming, especially when several particle jumps and particle diffusion on surfaces and interfaces are considered. Most Monte Carlo and Molecular Dynamics simulations are considered when addressing very specific and isolated problems associated with electrochemical systems, for example, SEI layer growth in Li-ion batteries.24 There have been both engineering (continuum) models and theoretical models at the molecular level to address this specific problem. Much insight has been gained from molecular level theoretical studies to study the mechanisms of SEI layer growth. The drawback however has been the lack of efficient ways to couple valuable information at the molecular level with the operation of the battery as a whole, i.e., predicting discharge curves. The multi-scale nature of this problem poses two important questions, (a) How do we efficiently bridge the gap between different time and length scales, and (b) Can we make the algorithms more computationally efficient? An answer therefore could be a less time consuming and novel multistep Continuum Monte Carlo technique to solve problems created by multiphenomena characteristics of electrochemical processes and power sources. In the case shown for a lithium ion battery cathode material three different types of Continuum Monte Carlo codes are written to solve three different electrochemical phenomena. All the codes are based on fundamental electrochemical principles, therefore invaluable physics is not lost while deriving useable data. In the present work, a simulation strategy is formulated to study the performance of cathode materials in lithium ion batteries. Here micro scale properties, for example, diffusion of spherical electrode particle within the periodic boundary condition, 0<x