Schlesinger Modelling and Numerical Simulations II

1. Auflage 2009
ISBN: 978-0-387-49586-6
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 44, 518 Seiten

Reihe: Modern Aspects of Electrochemistry

The present volume is the second in a two-volume set dealing with modelling and numerical simulations in electrochemistry. Emphasis is placed on the aspect of nanoelectrochemical issues. It seems appropriate at this juncture to mention the n- growing body of opinion in some circles that George Box was right when he stated, three decades ago, that 'All models are wrong, but some are useful'. Actually, when the statement itself was made it would have been more appropriate to say that 'All models are inaccurate but most are useful nonetheless'. At present, however, the statement, as it was made, is far more appropriate and closer to the facts than ever before. Currently, we are in the midst of the age of massively abundant data. Today's philosophy seems to be that we do not need to know why one piece of information is better than another except through the statistics of incoming and outgoing links between information and this is good enough. It is why, both in principle and in practice, one can translate between two languages, without knowledge of either. While none of this can be ignored, and it may even be true that 'All models are wrong and increasingly you can succeed without them' the traditional approach of scienti?c modelling is still the order of the day. That approach may be stated as hypothesize - measure - model - test. It is in this light that the present volume should be viewed.

Autoren/Hrsg.

Schlesinger, Mordechay

Inhaltsverzeichnis

1;Preface;6
2;Contributors;19
3;Chapter 1 Numerical Modeling of Certain Electrochemical Processes;22
3.1;I. Elementary Aspects of Electrochemical Reaction;22
3.1.1;II. A Simple Mathematical Model;24
3.1.1.1;1. Boundary Conditions;27
3.1.2;III. Application in Cathodic Protection;29
3.1.2.1;1. Iteration Process;31
3.1.3;IV. Analytical Solution to Two Benchmark Problems;32
3.1.3.1;1. Corrosion Cell 1;33
3.1.3.2;2. Corrosion Cell 2;34
3.1.4;V. Application in Electrodeposition;35
3.1.5;VI. Analytical Solution to a One-Dimensional Electrodeposition Problem;37
3.1.6;VII. General Framework of Numerical Approximation;40
3.1.6.1;1. Finite-Difference Method;40
3.1.6.2;2. Finite-Element Method;41
3.1.6.3;3. Boundary-Element Method;43
3.1.7;VIII. Implementation of the Finite-Difference Method in Cathodic Protection;44
3.1.7.1;1. Choosing a Lattice;44
3.1.7.2;2. Discretization;45
3.1.7.3;3. Mesh Equations;46
3.1.7.4;4. Solving the Mesh Equations;47
3.1.8;IX. Implementation of the Boundary-Element Method in Cathodic Protection;52
3.1.9;X. Numerical Implementation of the Boundary-Element Method;54
3.1.9.1;1. Iteration Procedures;55
3.1.10;XI. Concluding Remarks;58
4;Chapter 2 Near-Field Optics for Heat-Assisted Magnetic Recording (Experiment, Theory, and Modeling);73
4.1;I. Near-Field Transducers for Heat-Assisted Magnetic Recording;73
4.1.1;II. Modeling Techniques;78
4.1.2;III. Near Field Compared With Far Field;79
4.1.3;IV. Figures of Merit;80
4.1.3.1;1. Far-Field Transmittance;81
4.1.3.2;2. Peak Field or Field Intensity;82
4.1.3.3;3. Percent Dissipated Power in the RecordingMedium;83
4.1.3.4;4. Temperature Rise in the Recording Medium;84
4.1.4;V. Mechanisms for Enhancement of the Figureof Merit;84
4.1.4.1;1. Localized Surface Plasmon Resonance;84
4.1.4.2;2. Lightning Rod Effect;90
4.1.4.3;3. Dual-Dipole Resonance;92
4.1.5;VI. Comparison Of Near-Field Transducers;93
4.1.5.1;1. Circular Aperture;95
4.1.5.2;2. Tapered Rectangular Aperture;96
4.1.5.3;3. Bow-Tie Aperture;99
4.1.5.4;4. C Aperture or Ridge Waveguide;102
4.1.5.5;5. Triangle Antenna;103
4.1.5.6;6. Bow-Tie Antenna;108
4.1.6;VII. Antenna and Aperture Relationship;111
4.1.7;VIII. Near-Field and Far-Field Relationship;112
4.1.7.1;1. Radiation from Antennas;116
4.1.7.2;2. Radiation from Apertures;117
4.1.7.3;3. Numerical Modeling;119
4.1.8;IX. Photonic Nanojets;124
4.1.9;X. Conclusion;129
5;Chapter 3 Symmetry Considerations in the Modelling of Light--Matter Interactions in Nanoelectrochemistry;132
5.1;I. Introduction;133
5.1.1;II. Optical Properties of Metal Nanoparticles;134
5.1.1.1;1. Macroscopic Theories;134
5.1.1.2;2. Discrete-Dipole Approximation;135
5.1.1.3;3. Optical Properties of Nanoparticles on a Surface;136
5.1.1.4;4. Towards an Optical Method of Surface Electrochemistry;137
5.1.2;III. Optical Manipulation of Semiconductor Quantum Dots;139
5.1.2.1;1. Atomic Model of Semiconductor Quantum Dots;139
5.1.2.2;2. Pseudospectral Method;143
5.1.2.3;3. Finite-Difference Method;144
5.1.3;IV. Summary;147
6;Chapter 4 Applications of Computer Simulations and Statistical Mechanics in Surface Electrochemistry;150
6.1;I. Introduction;151
6.1.1;II. Molecular Dynamics Simulations of Ion Intercalation in Lithium Batteries;152
6.1.1.1;1. Molecular Dynamics and Model System;152
6.1.1.2;2. Simulations and Results;153
6.1.2;III. Lattice-Gas Models of Chemisorbed Systems;155
6.1.3;IV. Calculation of Lattice-Gas Parameters by Density Functional Theory;156
6.1.4;V. Monte Carlo Simulations;161
6.1.4.1;1. Equilibrium Monte Carlo;161
6.1.4.2;2. Kinetic Monte Carlo;162
6.1.5;VI. Electrochemical First-Order Reversal CurveSimulations;163
6.1.6;VII. Conclusion;165
7;Chapter 5 AC-Electrogravimetry Investigation in Electroactive Thin Films;169
7.1;I. Introduction;169
7.1.1;II. General Considerations;171
7.1.1.1;1. Thermodynamics;171
7.1.1.2;2. Swelling;173
7.1.1.3;3. Conductivity;174
7.1.2;III. Electrochemical Approach of Electroactive Materials;175
7.1.2.1;1. Models of the Charge Transport Throughthe Electroactive Film;176
7.1.2.1.1;(i) Compact Model (Diffusion--MigrationModel);176
7.1.2.1.2;(ii) Porous Model (Transmission Line Model);179
7.1.2.2;2. Calculation of the Impedance;181
7.1.2.2.1;(i) Two-Species Problems;181
7.1.2.2.2;(ii) Three-Species Problems;185
7.1.2.2.3;(iii) Applications of Impedance Analysis;190
7.1.3;IV. Coupled Electrochemical and Gravimetric Approach for Electroactive Materials;192
7.1.3.1;1. Cyclic Voltammetry and Quartz CrystalMicrobalance;192
7.1.3.2;2. AC Electrogravimetry;201
7.1.3.2.1;(i) Steady State;208
7.1.3.2.2;(ii) Dynamic Regime;208
7.1.3.2.3;(iii) Electrochemical Impedance;209
7.1.3.2.4;(iv) Mass/Potential (Electrogravimetric) Transfer Function;213
7.1.3.2.5;(v) Diagnostic Criterion;214
7.1.3.2.6;(vi) Simulations;216
7.1.4;V. Experimental;223
7.1.4.1;1. Basic Microbalance Concepts;223
7.1.4.2;2. AC-Electrogravimetry Aspects;225
7.1.4.3;3. Dynamic Characterization of the Frequency/Voltage Converter;227
7.1.5;VI. Examples of Applications of AC Electrogravimetry;228
7.1.5.1;1. Prussian Blue;228
7.1.5.1.1;(i) Film Preparation;230
7.1.5.1.2;(ii) Voltammetric and Mass/Potential Curves;230
7.1.5.1.3;(iii) Electrogravimetric Transfer Function and Electrochemical Impedance;231
7.1.5.2;2. Polypyrrole;236
7.1.5.2.1;(i) Film Preparation;236
7.1.5.2.2;(ii) Voltammetric and Mass/Potential Curves;237
7.1.5.2.3;(iii) Electrogravimetric Transfer Function and Electrochemical Impedance;237
7.1.5.3;3. Complex Polymeric Structures;244
7.1.5.3.1;(i) Electrode Preparation;244
7.1.5.3.2;(ii) Electrogravimetric Transfer Function and Electrochemical Impedance;245
7.1.6;VII. Conclusion;249
8;Chapter 6 Monte Carlo Simulations of the Underpotential Deposition of Metal Layers on Metallic Substrates: Phase Transitions and Critical Phenomena;257
8.1;I. Introduction: Some Basic Aspects of the Underpotential Deposition Phenomenon;258
8.1.1;II. Some Thermodynamics on the UPD Phenomenon;264
8.1.2;III. Description of the Monte Carlo Simulation Method and the Model for Metal Deposition;269
8.1.2.1;1. The Lattice Model;269
8.1.2.2;2. The Grand Canonical Monte Carlo Method;270
8.1.2.2.1;(i) Change of Occupation;271
8.1.2.2.2;(ii) Diffusion;272
8.1.2.2.3;(iii) Calculation of the Coverage;273
8.1.2.3;3. Interatomic Potential: The Embedded-AtomMethod;273
8.1.2.4;4. Surface Defects;275
8.1.2.5;5. Energy Tables;276
8.1.3;IV. Adsorption Isotherms;277
8.1.3.1;1. Systems Studied and Adsorption Energies;277
8.1.3.2;2. Evaluation of Adsorption Isothermsfor Defect-Free Surfaces;280
8.1.3.2.1;(i) UPD Compared with OPD: First-Order Phase Transitions;280
8.1.3.2.2;(ii) The Influence of Temperatureon the Isotherms;283
8.1.3.3;3. Study of the Influence of Surface Defects;284
8.1.3.3.1;(i) Isotherms Corresponding to UPD Systems: The Effect of Kinks and Steps as Compared with the Complete Monolayer;284
8.1.3.3.2;(ii) Isotherms Corresponding to OPD Systems: The Formation of Surface Alloys;287
8.1.3.4;4. Comparison with Experiments;290
8.1.4;V. Dynamic Response of AG Monolayers Adsorbed on AU(100) Upon an Oscillatory Variation of the Chemical Potential;291
8.1.4.1;1. Dynamic Phase Transitions: Basic Concepts;291
8.1.4.2;2. Simulation Method;292
8.1.4.3;3. Dynamic Response of the Coverage Degree;293
8.1.4.4;4. Dynamic Phase Transitions;295
8.1.5;VI. Conclusions;301
9;Chapter 7 Topics in the Mathematical Modeling of Localized Corrosion;306
9.1;I. General Introduction;306
9.1.1;II. Pitting Corrosion;307
9.1.1.1;1. Introduction;307
9.1.1.2;2. General Structure of Pitting Models;309
9.1.1.3;3. Review of Recent Models;310
9.1.1.3.1;(i) Models of Pit Growth;310
9.1.1.3.2;(ii) Models of Pit Growth and Repassivation;315
9.1.1.4;4. Transport in Concentrated ElectrolyteSolutions;322
9.1.1.5;5. Concluding Remarks;328
9.1.2;III. Galvanic Coupling at the Interface BetweenTwo Metals;329
9.1.2.1;1. Theoretical Description of the Currents and Potentials at the Interface of Two Metals;329
9.1.2.2;2. Application to the Al--Cu Coupling;331
9.1.2.2.1;(i) Mathematical Model;331
9.1.2.2.2;(ii) Experimental;335
9.1.2.2.3;(iii) Experimental Results and Discussion;335
9.1.2.2.4;(iv) Comparison Between Theoretical Calculations and Experimental Observations;337
9.1.2.3;3. Conclusions;340
9.1.3;IV. Impedance in a Confined Medium;340
9.1.3.1;1. Introduction;340
9.1.3.2;2. Experimental;342
9.1.3.3;3. Theory;344
9.1.3.4;4. Results and Discussion;350
9.1.3.5;5. Conclusions;354
10;Chapter 8 Density-Functional Theory in External Electric and Magnetic Fields;358
10.1;I. Scope of this Chapter;358
10.1.1;II. Elements of the Quantum Mechanicsof Many-Electron Systems;360
10.1.1.1;1. Hamiltonians and Wave Functions;360
10.1.1.2;2. Density Matrices and Density Functionals;364
10.1.1.3;3. Functionals and Their Derivatives;369
10.1.2;III. The Hohenberg--Kohn Theorem;370
10.1.2.1;1. Enunciation and Discussionof the Hohenberg--Kohn Theorem;370
10.1.2.2;2. A Simple Example: Thomas--Fermi Theory;376
10.1.3;IV. The Exchange--Correlation Energy;378
10.1.3.1;1. Definition of the Exchange--Correlation Energy;378
10.1.3.2;2. Interpretation of the Exchange--Correlation Energy;381
10.1.3.3;3. Selected Exact Propertiesof the Exchange--Correlation Energy;382
10.1.4;V. The Kohn--Sham Equations;384
10.1.4.1;1. Self-Consistent Single-Particle Equations and Ground-State Energies;385
10.1.4.2;2. Single-Particle Eigenvalues and Excited-State Energies;388
10.1.5;VI. An Overview of Approximate Exchange--Correlation Functionals;392
10.1.5.1;1. Local Functionals: LDA;393
10.1.5.2;2. Semilocal Functionals: GEA, GGA and Beyond;396
10.1.5.3;3. Orbital Functionals and Other Nonlocal Approximations: Hybrids, Meta-GGA, SIC,OEP, etc.;398
10.1.5.4;4. Performance of Approximate Functionals:A Few Examples;403
10.1.6;VII. External Electric And Magnetic Fields;407
10.1.6.1;1. Magnetic Fields Coupling to the Spins: SDFT;407
10.1.6.2;2. Brief Remarks on Relativistic DFT;410
10.1.6.3;3. Magnetic Fields Coupling to Spins and Currents: CDFT;410
10.1.6.4;4. Electric Fields;415
10.1.6.5;5. Polarization and Magnetization;416
10.1.7;VIII. Outlook;418
11;Chapter 9 Acoustic Microscopy Applied to Nanostructured Thin Film Systems;426
11.1;I. Introduction;426
11.1.1;II. Principle of the Scanning Acoustic Microscope;429
11.1.1.1;1. Imaging Mechanism;429
11.1.1.2;2. Description of Acoustic Lens;432
11.1.1.2.1;(i) Piezoelectric Transducer;432
11.1.1.2.2;(ii) Buffer Rod;433
11.1.1.2.3;(iii) Lens;433
11.1.1.2.4;(iv) Acoustic Antireflection Coating;435
11.1.2;III. Resolution;436
11.1.3;IV. Principle Of Quantitative Data Acquisition;439
11.1.3.1;1. V(z) Curve;439
11.1.3.2;2. Phase Change;441
11.1.3.3;3. Theory of the Surface Acoustic Wave Velocity Measurement;444
11.1.3.4;4. Optimizing Measurement Precision;445
11.1.4;V. Contrast;446
11.1.4.1;1. Reflectance Function;446
11.1.4.2;2. Reflectance Function for Layered Media;447
11.1.4.3;3. Contrast Enhancement Caused by Discontinuities;453
11.1.4.4;4. Computer Simulation;457
11.1.4.5;5. Experimental Result;461
11.1.5;VI. Conclusion;465
12;Chapter 10 Current Distribution in Electrochemical Cells: Analytical and Numerical Modeling;468
12.1;I. Introduction and Overview;468
12.1.1;II. Significance of Modeling the Current Distribution;469
12.1.2;III. Experimental Determination of the CurrentDistribution;470
12.1.3;IV. Analytical Derivation of the Current Distribution;471
12.1.3.1;1. The Current Density;471
12.1.3.2;2. Material Balance;472
12.1.3.3;3. Boundary Conditions;474
12.1.3.4;4. General Solution Procedure;476
12.1.3.5;5. Thin Boundary Layer Approximation;477
12.1.4;V. Common Approximations for the Current Distribution;479
12.1.4.1;1. Primary Distribution: s+c;480
12.1.4.2;2. Secondary Distribution: +sc;483
12.1.4.3;3. Mass Transport Controlled Distribution: c+a;487
12.1.4.4;4. Tertiary Distribution: cs(``Mixed Control'');489
12.1.5;VI. Scaling Analysis of Electrochemical Cells;490
12.1.6;VII. Transport Effects On Kinetically Controlled Systems;494
12.1.7;VIII. Comparison of Analytical and Numerical Solutions;495
12.1.8;IX. A Simplified Solution Algorithm;496
12.1.9;X. Numerical Procedures for Solving the LaplaceEquation;497
12.1.9.1;1. The Finite-Difference Method;498
12.1.9.1.1;(i) Methods of Solving the Finite-Difference Equation;500
12.1.9.2;2. The Finite-Element Method;502
12.1.9.3;3. Boundary-Element Methods;502
12.1.9.4;4. Orthogonal Collocation;503
12.1.10;XI. Numerically Implemented Solutions for the Current Distribution;504
12.1.11;XII. Determination of the Current Distributionin Special Applications;506
12.1.11.1;1. Multiple Simultaneous Electrode Reactions, Including Alloy Codeposition and Gas Coevolution;506
12.1.11.2;2. Moving Boundaries in Deposition and Dissolution Applications;508
12.1.11.3;3. Electropolishing, Leveling, and Anodizing;509
12.1.11.4;4. Current Distribution on Resistive Electrodes;509
12.1.11.5;5. Current Distribution in the Metallization of Through-Holes, Blind Vias, and Trenches;510
13;Index;519