ミニコース～専門技術セミナ～電気化学コース東京秋葉原UDX 2014 12.4 Modeling and Simulations of Electrochemical Systems in COMSOL COMSOLでの電気化学系のモデリングとシミュレーション December 2014 Ed Fontes COMSOL 和訳に誤りがある場合は英文を正とします。計測エンジニアリングシステム株式会社 Outline 概要 • Why and for whom? • Scope 範囲 • Theory 理論なぜ、そして誰にとって – How Physics interfaces are constructed フィジックスインターフェースをどのように構築するか – How to select Physics interfaces and Studies フィジックスインターフェースとスタディの選択方法 • The Modules – – – – モジュール Batteries & Fuel Cells バッテリー＆燃料電池 Corrosion 腐食 Electrochemistry 電気化学 Electrodeposition 電気めっき • Hands-on tutorial ハンズオンチュートリアル Why and for Whom? なぜ、そして誰にとって + Why and for Whom? Understand 理解 Predict 予測 Innovate 変革 Optimize 最適化 Control 制御 Why and for Whom? Researchers, scientists, developers 研究者、科学者、開発者 Engineers that build things ものづくりをするエンジニア Scope 範囲 Electrochemical Systems 電気化学系 • Electrochemical systems are devices or processes in which an ionic conductor mediates the inter-conversion of chemical and electrical energy 電気化学系とは、イオン伝導体が化学および電気のエネルギーの変換を担う装置あるいは過程を指す。 • The reactions by which this interconversion of energy occurs involve the transfer of charge (electrons) at the interface between an electronic conductor (the electrode) and an ionic conductor (the electrolyte) エネルギー変換によって生じる反応は電気伝導体（電極）とイオン伝導体（電解質）の界面で電荷（電子）の輸送を含む。界面電荷移行（ファラデー過程）電子電子伝導体（電極）イオン伝導体（電解質） Redox Reactions 酸化還元反応 • Individual electrode reactions are symbolized as reduction-oxidation (redox) processes with electrons as one of the reactants: 各電極反応は酸化還元反応で表現できる。その中に電子が反応種の一つとして含まれる。 − Ox + ne ⇔ Red Ox = oxidized species 酸化種 Red = reduced species 還元種 e- = electron 電子 n = electron stoichiometry coefficient. 電子の量論的係数 Redox Reactions 酸化還元反応電極表面電解質電極表面電解質 Thermochemical and Electrochemical Processes 熱化学および電気化学のプロセス熱化学プロセス電気化学プロセスイオンの直接輸送酸化される種還元される種電子の直接輸送負荷アノード酸化イオンの輸送還元カソード Energy Producing and Energy Consuming Electrochemical Processes エネルギー発生とエネルギー消費をする電気化学プロセスエネルギー発生プロセスエネルギー消費プロセス電気エネルギー燃料電池バッテリー燃料と酸化剤電解採取と電気めっき電解加工電解合成排出や副生成物反応物電気エネルギー生成物 Spontaneous Processes and Processes that Require Energy Input 自発的な反応と、エネルギーの投入が必要な反応自発的な反応エネルギーの投入を必要とする反応アノード反応アノード反応カソード反応カソード反応総括反応総括反応反応物生成物生成物反応物 Electrocatalysis 電気的触媒カソードでの還元の例エネルギー電極表面電極電位の変化反応物生成物反応座標反応物電解質生成物 Anodic and Cathodic Reactions アノード反応とカソード反応平衡自由エネルギー還元自由エネルギー反応座標酸化自由エネルギー反応座標反応座標 Transport and Electrochemical Reactions 輸送と電気化学反応 • Transport 輸送 – Diffusion, convection, and migration. The mobility and concentration of ions yields the mass transfer and Ohmic resistances in the electrolyte 拡散、対流、泳動。イオンの移動度と濃度は電解質内の質量輸送とオーム抵抗を生じる。 • Electrochemical reaction 電気化学反応 – Electrode kinetics for an electron charge transfer step yields potential-dependent reaction rate. The overpotential is a measure of the activation energy (Arrhenius equation -> Butler-Volmer equation) 電荷移行ステップを表す電極反応は電位依存の反応速度を生じる。過電圧は活性化エネルギーに相当する。（アーレ二ウス式---> バトラー・フォルマー式） The Overpotential 過電圧 Electronic current, Ionic current Electronic current, + Anodic reaction Cathodic reaction iloc - + E Discharge Negative Positive Multiple Processes 多重のプロセス • Charge balances in the electrodes and electrolyte 電極と電解質内の電荷の収支 • アノード e- I カソード Anode Cathode Material balances 材料収支 • Energy balance エネルギー収支多孔質電極 • Momentum balances 運動量収支 Porous electrodes The Anode Electrode Matrix アノード電極基質アノード e- I Anode カソード Cathode 電子伝導体 Electronic conduction The Anodic Reactions アノード反応アノード e- I Anode カソード Cathode 電極表面 Charge transfer reaction 電荷移行過程電解質 The Electrolyte 電解質 e- I アノードカソード Anode Cathode Transport of current: diff + migr Transport of species: diff + migr + adv 電流輸送：拡散＋泳動化学種輸送：拡散＋泳動＋移流 The Cathodic Reactions カソード反応アノード e- I Anode 電荷移行反応 Charge transfer reaction カソード Cathode 電極表面電解質 The Cathode Electrode Matrix カソード電極基質アノード e- I Anode カソード Cathode 電子伝導体 Electronic conduction Transport 輸送 • Transport 濃度 Concentration 拡散 Diffusivity 輸送 – Flux = diff. + conv. + migration 流束＝拡散＋対流＋泳動流速 Flow velocity 電荷 Charge Mobility N i = − Di ∇ci + ci u − zi mi Fci ∇φl ファラデー定数Faraday’s constant – Current density 電流密度 j = F  zi Ni i – Perfectly mixed primary and secondary 一次と二次の完全混合 Ionic potential イオン電位 sum of ch arg es    2 j = F   − zi Di ∇ci + u  zi ci − ∇φl  ( zi ) mi Fci   i  i i   – Electroneutrality 電気的中性条件 sum of charges = 0 電荷の総和＝０移動度   2 j = F   − zi Di ∇ci − ∇φl  ( zi ) mi Fci  i  i    2 j = −  F  ( zi ) mi Fci  ∇φl i    κ = conductivity 導電率 Conservation of Species and Charge 化学種と電荷の保存 • Conservation of species 化学種保存 n-1 species, n:th through charge conservation ∂ci = −∇ ⋅ ( − Di ∇ci + ci u − zi mi Fci ∇φl ) + Ri ∂t 未知数n-1個、n番目は電荷保存から決定 • Conservation of current 電流保存 •    2 ∇ ⋅ j = ∇ ⋅  F   − zi Di ∇ci − ∇φl  ( zi ) mi Fci   i    i Net current is not accumulated, produced   or consumed in the bulk electrolyte ∇⋅ F 正味電流はバルク電解質内で不増不滅 • Reaction rate For primary and secondary cases 一次および二次電流の場合  2 z D c φ z m Fc − ∇ − ∇   i i i l ( i ) i i  = 0 i    i ( ) ∇ ⋅ −κ ∇φl = 0 Selecting Physics Interfaces フィジックスインターフェースの選択 • Primary current density distribution 一次電流密度分布 – Accounts only for Ohmic effects in the simulation of current density distribution and performance of the cell 電流密度分布とセル性能のシミュレーションにおいて、オーム効果のみを考慮する。 • Secondary current density distribution 二次電流密度分布 – Accounts only for Ohmic effects and the effect of electrode kinetics in the simulation of current density distribution and performance of the cell 電流密度分布とセル性能のシミュレーションで、オーム効果と電極反応効果のみを考慮する。 • Tertiary current density distribution – Accounts for Ohmic effects, effects of electrode kinetics, and the effects of concentration variations on the performance of a cell セル性能への、オーム効果、電極反応効果、濃度変化をすべて考慮する。 Selecting Physics Interfaces フィジックスインターフェースの選択 • Non-porous electrodes 非多孔質電極 – Heterogeneous reactions 不均一反応 – Typically used for electrolysis, metal winning, and electrodeposition 代表的な利用分野は電気分解、金属の電解採取、電気めっきである。 • Porous electrodes 多孔質電極 – Reactions treated as homogeneous reaction in models although they are heterogeneous in reality 現実は不均一だけれどもモデル内で均質反応として扱う – Typically used for batteries, fuel cells, and in some cases also for electrolysis バッテリー、燃料電池が代表的、電気分解でも使用する場合あり。 • Electrolytes 電解質 Diluted and supporting electrolytes 希釈および支持電解質 Concentrated electrolytes 高濃度電気分解 ”Free” electrolytes with forced and free convection 強制・自由対流を使った自由な電解液 ”Immobilized” electrolytes through the use of porous matrixes, negligible free convection, rarely forced convection 多孔質基質中、無視できる自由対流、まれに強制対流中の、固定電解液 – Solid electrolytes, no convection 固体電解質、対流なし – – – – Selecting Studies スタディの選択 • Stationary 定常 • Transient 過渡 – With double-layer effects 二重層効果あり – Dynamic load curves 動的負荷曲線 – Constant Current – Constant Voltage mode switching by the use of Events イベントを利用した定電流－定電圧モードのスイッチング – Cyclic Voltammetry in Electroanalysis 電気分析でのサイクリックボルタンメトリ • Frequency domain 周波数領域 – Impedance spectroscopy (AC-impedance, electrochemical impedance) インピーダンススペクトロスコピー（ACインピーダンス、電気化学インピーダンス） “Always Check Your Results” (B. Finlayson) 常に自分の結果をチェックせよ。（B.フィンレイソン） • Verification 検証 – Does the numerical solution converge? • Tolerances, mesh resolution トレランス、メッシュ解像度 – “Are you solving the equations right?” • Validation 数値解は収束するか。方程式を正しく解いているか。確認 – Input data and sensitivity to this data 入力データ、そのデータへの感度 – Comparison with known studies in literature 周知の文献値との比較 – Qualitative and quantitative comparison with experimental observations 実験値との定性的かつ定量的比較 – “Are you solving the right equations?” 正しい方程式を解いているか。 References to the Theory Part 理論に関する参考書 • “Electrochemical Systems”, J. Newman, K.E. ThomasAlyea • “Modern Electrochemistry”, J.O’M. Bockris, A.K.N. Reddy Lead-acid battery electrode Spiral wound Li-ion battery The Batteries & Fuel Cells Module バッテリー＆燃料電池モジュール Serpentine fuel cell flow field Water-cooled Li-ion battery pack © Copyright 2014 COMSOL. Any of the images, text, and equations here may be copied and modified for your own internal use. All trademarks are the property of their respective owners. See www.comsol.com/trademarks. The Batteries and Fuel Cells Module • Specialized tool: 専用ツール – Models and simulates all major types of battery and fuel cell applications バッテリ、燃料電池の全ての主要タイプ計算用モデル • Ease-of-use 使いやすさ – Tailored functionality/interfaces for: • • • • Primary, secondary and tertiary current density distribution Porous and gas diffusion electrodes Dilute and concentrated electrolytes 一次、二次、三次の電流密度分布多孔質とガス拡散電極希釈種と高濃度種の電解液 Multiphysics マルチフィジックス解析 – Flow, electric fields, and heat transfer with electrochemical reactions 流れ、電場、電気化学反応を伴う伝熱 Temperature distribution in a PEMFC equipped with passive self-breathing electrodes Targeted Batteries and Fuel Cell Systems 対象とする電池・燃料電池システム • Batteries: – – – – – • Lithium-ion リチウムイオン All-solid-state lithium-ion 固体相リチウムイオン Nickel-metal hydride ニッケル金属水素化物 Lead-acid 鉛酸 Nickel-cadmium ニッケルカドミウ Flow Batteries: – – • 電池 Vanadium redox バラジウムレドックス Soluble lead-acid 可溶性鉛酸 Fuel Cells: – – – – 流れバッテリー燃料電池 Proton exchange membrane, プロトン交換膜 high and low temperature 高温、低温 Solid oxide 固体酸化物 Molten carbonate モルテンカーボナイト Direct methanol ダイレクトメタノール Discharge-recharge cycle for a lithium-ion battery simulated with the Lithium-ion battery interface. リチウムイオン電池インターフェースで計算されたリチウムイオン電池の充放電サイクル Battery Modeling and Simulations in COMSOL COMSOLでの電池モデリングとシミュレーション • Battery unit cells:電池ユニットセル Electronic current, Ionic current Electronic current, + Anodic reaction – Current collectors and feeders Cathodic reaction 集電と給電 – Porous electrodes 多孔質電極 – Pore electrolyte 多孔質間隙にある電解液 – Electrolyte 電解液 iloc - + E Discharge Negative Positive The scope of a typical model incorporates relatively detailed descriptions, such as intercalation and modeling of the SEI on the surface of the particles in porous electrodes. The Battery Modeling Interfaces 電池モデリングインターフェース • Lithium-ion battery リチウムイオン電池電極と電解質内の電荷均衡 Charge balances in the electrodes and electrolyte Material balances for the salt 塩分の物質収支 Energy balance including electrochemical reactions 電気化学反応を含むエネルギー収支 Material balance of intercalating species in electrode particles Solid electrolyte interface on electrode particles 電極粒子中のインターカレート種の物質収支電極粒子の固体電解質界面 Battery with binary electrolyte バイナリー電解質を用いた電池 – Generic interface for batteries with concentrated binary electrolytes – – – – – • • Lead-acid battery 鉛酸電池 – – • Generic physics interfaces 一般的なフィジックスインターフェース – – – • Porosity variation within electrodes coupled to electrode reactions and material balances 電極反応と物質収支とカップリングした電極内の多孔性の変化 Material balance for the salt in the electrolyte 電解質内の塩の物質収支 Primary Current Distribution 一次電流分布 Secondary Current Distribution 二次電流分布 Tertiary Current Distribution, Nernst-Planck 三次電流分布、N-P Predefined couplings with Heat Transfer interfaces, including heat sources from electrochemical reactions 電気化学反応から生じる発熱を含む伝熱インターフェースとの既定連成 Settings for electrode reactions in the Lithium-ion battery interface Fuel Cell Modeling and Simulations 燃料電池モデリングとシミュレーション • Fuel cell unit: 燃料電池ユニット Anode Electrolyte Cathode – Current collectors and feeders 集電および給電 – Gas channels ガス流路 – Gas diffusion electrodes (GDE) Electrolyte ガス拡散電極（GDE) – Pore electrolyte 多孔質間隙の電解質 – Electrolyte 電解質 Unit cell consisting of current collectors, gas channels, gas diffusion electrodes, electrolyte, and pore electrolyte. The Fuel Cell Modeling Interfaces 燃料電池モデリングインターフェース • Secondary Current Distribution – – • 二次電流分布 Include electrode kinetics: 電極反応を考慮 • Exchange current density • Equilibrium potential • Charge transfer coefficients • User-defined expressions Double layer currents 二重層電流 Predefined coupling with Chemical Species Transport interfaces 化学種輸送インターフェースとの既定連成 – Mass transport in gas channels – Mass transport in GDEs – Transport of charged species in supporting electrolyte • Predefined coupling with Heat Transfer interfaces 伝熱インターフェースとの既定連成 – Heat sources from electrochemical reactions and Joule heating 電気化学反応からの発熱とジュール発熱 Concentration distribution in a PEMFC. Model courtesy Center for Fuel Cell Technology (ZBT), Duisberg, Germany Generic Electrochemistry Interfaces 一般的な電気化学インターフェース • Porous and non-porous electrodes 多孔質/非多孔質の電極 – – • Electric conduction (electrons) 電気伝導（電子） – – – • Transport of neutral species and ions 中性種とイオンの輸送 Nernst-Planck, with or without electroneutrality N-P, 電気中性有無 Supporting electrolytes 支持電解質 Electroanalysis 電気分析 – • • Porous and non-porous domains 多孔質/非多孔質ドメイン Thin layers (shells) 薄層(シェル） Floating potential surfaces 浮遊電位表面 Mass and charge transport 質量輸送と電荷輸送 – – – • Arbitrary number of electrode reactions 任意数の電極反応 • Butler-Volmer reaction バトラーフォルマー • Tafel reactions ターフェル • User-defined current density option for full versatility ユーザー定義 Double layer capacitance 二重層キャパシタンス Cyclic Voltammetry サイクリックボルタンメトリ Momentum transport 運動量輸送 Heat transfer 伝熱 Discharge curves of an all-solid-state lithium-ion battery modeled by a combination of generic interfaces for mass transport and current distribution. The Physics Interfaces, Summary フィジックスインターフェース、まとめ • Electrochemistry • Chemical Species Transport 化学種輸送 – of Diluted Species 希釈種 – of Concentrated fluids 高濃度種流 – in Free and porous media 自由媒体と多孔質媒体 • 流体流れ Fluid flow 単相流 – Single-Phase Flow – Porous Media Flow 多孔質媒体内流れ – Free and Porous Media Flow 自由流れおよび多孔質媒体流れ • Heat Transfer – in Fluids 流体 – in Solids 固体 – in Porous Media 多孔質媒体 Physics list in the GUI in Batteries & Fuel Cells Module. The Batteries & Fuel Cells Material Library 電池・燃料電池材料ライブラリ • Inlcuded library based on literature data for the most common electrode and electrolyte materials for Lithium-ion, NiMH and lead acid batteries: – Electrolyte conductivities 電解質導電率 – Equilibrium potentials 平衡電位 – Diffusion coefficients 拡散係数 – Activitiy coefficients 活量係数 – Transport numbers 輸率 – Densities 密度 – Heat capacities* 熱容量 *All listed properties not available for all listed materials Study Types スタディのタイプ • Stationary 定常 • Transient 過渡 – With double-layer effects – Dynamic load curves – Constant Current – Constant Voltage mode switching by the use of Events – Cyclic Voltammetry in Electroanalysis • Frequency Domain 周波数領域 – AC-Impedance Spectroscopy Impedance spectroscopy study, Nyquist plot. Experimental data fitted to model. Battery drive cycle analysis Supporting Capabilities in COMSOL COMSOLによって提供されている諸機能 • Extended physics: 拡張されたフィジックス – – – – • Single-phase and multiphase flow: Extended laminar flow capabilities and turbulent flows in the CFD Module 単相流、多相流、乱流 Cooling: Extended thermal transport capabilities in the Heat Transfer Module 冷却 Thermal Expansion in the Structural Mechanics Module 構造の熱膨張 Equation-based modeling 方程式ベースモデリング Material properties and parametric estimation: 材料特性とパラメタの推定 – – • Thermodynamics and reaction kinetics in Chemical Reaction Engineering Module 化学反応工学モジュールの熱力学と反応論 Parametric estimation in Optimization Module 最適化モジュールによるパラメタ推定 CAD capabilities: CAD機能 – – – Include designs with the CAD Import Module Parametric sweeps on geometry LiveLink add-ons available for a number of common CAD software Air cooling of a cylindrical lithium-ion battery using the Heat Transfer Module together with the Batteries & Fuel Cells Module Corrosion Module 腐食モジュール General Introduction © Copyright 2014 COMSOL. Any of the images, text, and equations here may be copied and modified for your own internal use. All trademarks are the property of their respective owners. See www.comsol.com/trademarks. Contents 内容 • Overview 概要 – Purpose 目的 – Described processes 記述されたプロセス – Described phenomena 記述された現象 • Corrosion and corrosion protection, examples 腐食、防食、例 • The Corrosion Module interfaces and their theoretical background 腐食モジュールインターフェースと理論的背景 • Concluding remarks まとめ Purpose 目的 • Space-dependent modeling and simulation of corrosion of metallic structures 金属腐食の時空間モデル計算 – Understand corrosion processes in the context of a given geometry 腐食過程と形状の関係把握 – Optimize design to minimize corrosion 腐食最小化の最適設計 • Space-dependent models of corrosion protection of metallic structures 金属防食の時空間モデル – Design and optimize corrosion protection systems and operational conditions for a given geometry 防食システムと稼動条件の設計と最適化 Electrolyte potential surrounding a zinc galvanized nail with the iron core exposed at the point of the nail. Described Processes 記述されたプロセス • Space-dependent models of corrosion of metallic structures in water 水中に置かれた金属の腐食の時空間モデル – Galvanic corrosion ガルバニ腐食 – Crevice corrosion すきま腐食 – Pitting corrosion 孔腐食 – Corrosion due to stray currents 迷走電流による腐食 • Space-dependent models of corrosion protection of metallic structures 金属の防食に関する時空間モデル – Cathodic protection using external current (impressed current cathodic protection, ICCP) 外部電流を利用したカソード防食 – Cathodic protection with sacrificial anodes 犠牲アノードを利用したカソード防食 – Anodic protection (for example, small passivating currents that stabilize oxide films) アノード防食 Initial and deformed geometry before and after galvanic corrosion modeled using a moving mesh. Described Phenomena 記述された現象 • Material, current, and charge conservation in the electrolyte Electrolyte 電解質内の物質・電流・荷電収支 • Transport of cations, opposite for anions Electric current conservation in the metallic structures 金属構造物の電流収支 • Electrode kinetics with activation and concentration overpotential couple the electrolyte potential with the potential of the metallic structure at the metal surfaces Metal 1 e- Metal 2 System without external circuit 活性/濃度過電圧のある電極反応による電解質電位と金属面の金属電位の連成 Effect of geometry deformations and formation of resistive films on electrode surfaces 形状変形と電極面上での抵抗膜生成の影響 Transport of cations, opposite for anions System with external circuit Metal 2 金属面での多重反応、そこでは混合電位が、その表面が腐食あるいは防食されるかどうかを決める。 • e- Multiple reactions at the metal surface, where the mixed potential determines if a surface corrodes or is protected Metal 1 • Corrosion Module Interfaces 腐食モジュールインターフェース • Current and potential distribution based on: – – – – • 電流と電位分布 Current and charge balances 電荷と電流バランス Material transport 物質輸送流体流れ Fluid flow Heat transfer Corroding surfaces: 腐食する表面 – Electrode reactions coupled to surface species balances 表面種バランスとカップリングした電極反応 – Fixed and moving boundaries coupled to surface species balances 表面種バランスとカップリングした固定/移動境界 Physics list in the GUI of the Corrosion Module • Stationary and transient studies 定常及び過渡解析 Examples 例題 Galvanic Corrosion ガルバニ腐食 • Corrosion caused by two different metals being in electronic contact and also sharing the same electrolyte 二種類の金属が電気的に接触し、かつ同じ電解液に浸されている場合に生じる腐食 Protected metal Corroding metal Galvanic corrosion simulation with moving mesh. The figure shows the potential and current in the electrolyte. The two metal surfaces are aligned and flat at the beginning of the simulation. (The model is included in the Corrosion Module Model Library.) Crevice Corrosion すきま腐食 • Crevice corrosion of stainless steel in water 水に浸かったステンレス鋼のすきま腐食 Calculated concentration profiles in a crevice. The role of parameters such as pH inside the crevice, external potential, acid/base concentration of the solution and crevice geometry is studied. (From the Corrosion Module Model Library.) Crevice Corrosion with Deformation 電極変形を伴うすきま腐食 • Crevice corrosion of nickel in acid of high conductivity 高導電率の酸に浸かったニッケルのすきま腐食 Simulation of corrosion of Ni in a lab cell. Left: Polarization curve taken from experimental data. Right: Electrolyte potential and simulated geometry after 72 h. The model is included in the Corrosion Module Model Library. Corrosion due to Stray Currents 迷走電流による腐食 • Corrosion initiated by metallic structures being subjected to an external electric field 架空線 Traction Current トラクション電流 Overhead wire 外部電場による引き起こされる金属構造の腐食変電所線路 Sub Station Rail Track 迷走電流 Stray Current Traction Current トラクション電流迷走電流 Stray Current Buried Pipe in soil 埋設パイプ Corroding Area 腐食領域 Simulation of corrosion of steel reinforcement in concrete sheet piles induced by a corrosion protection system for pipe lines. Presented by Willy Peelen, TNO Building and Construction Research at the COMSOL User Conference, 2007. パイプラインの防食システムによって誘導されるコンクリート矢板の鉄筋の腐食シミュレーション。 COMSOLカンファレンス2007におけるTNO building and Construction Research社 Willy Peelen氏による研究成果発表。 Cathodic Protection カソード防食 • Protection of an propeller and shaft of a ship using impressed current cathodic protection (ICCP) 強制通電電流によるカソード防食を利用した船のプロペラとシャフトの防食プロペラ・シャフト表面の電流密度船体に沿う海水の電位 Right: Electrolyte (ocean) potential along the ship hull surface. Left: Current density on propeller and shaft Sacrificial Anode Protection 犠牲アノード防食 • Cathodic protection of a steel structure using sacrificial AlZnIn anodes AlZnIn犠牲陽極を用いた鋼構造のカソード式防食 Potential at the surface of the metal of a detail in an offshore platform. The leg of the platform is protected by 40 sacrificial anodes. More examples 他の例 • Anodic Protection アノード防食 – • CO2 corrosion – • CO2腐食 Electrode kinetics in combination with the mass transport rate and equilibrium reactions of electrolyte species govern the corrosion rate Atmospheric corrosion – • Imposes an anodic current that preserves the passivation of metal surfaces by stabilizing the protecting oxides 大気腐食 Formation of a thin moisture film, acting as electrolyte, on a metal surface in contact with air of varying humidity Formicary (ant’s nest) corrosion – 異常形態腐食 Complex interplay between organic compounds and passivation behavior of metal surfaces causing pitting corrosion on the micro scale The Corrosion Module Model Library 腐食モジュールのモデルライブラリ Cathodic Protection – – – Ship hull Off-shore structure Rebar in concrete Galvanic Corrosion – – – – ガルバニック腐食 With or without deformation Atmospheric corrosion Localized corrosion CO2 corrosion Crevice corrosion – – カソード防食すきま腐食 With or without deformation Similar to pitting corrosion General Electrochemistry 一般電気化学 – – Impedance Spectroscopy Cyclic Voltammetry Cyclic voltammetry tutorial done with the Electroanalysis interface Transport of Charged and Neutral Species • Flux in the electrolyte = diffusion + convection + migration フラックス = 拡散 + 対流 + 泳動濃度 Concentration 拡散係数 Diffusivity 流速 Flow velocity 電荷 Charge 移動度 Mobility N i = − Di ∇ci + ci u − zi mi Fci ∇φl Faraday’s constant Electrolyte potential ファラデー定数電解質電位 Transport of Charged and Neutral Species • Current density j = F  zi N i i 電流密度 sum of ch arg es    2 j = F   − zi Di ∇ci + u  zi ci − ∇φl  ( zi ) mi Fci   i  i i   • Electroneutrality, charge conservation sum of charges = 0 • Perfectly mixed primary and secondary 完全混合一次，二次 current distribution 電気的中立性, 電荷保存則電荷の和 = 0   2 j = F   − zi Di ∇ci − ∇φl  ( zi ) mi Fci  i  i    2 j = −  F  ( zi ) mi Fci  ∇φl i    κ = conductivity Conservation of Species, Current, and Charge • Conservation of species n-1 species, n:th through current and charge conservation (electroneutrality) ∂ci = −∇ ⋅ ( − Di ∇ci + ci u − zi mi Fci ∇φl ) + Ri ∂t Reaction rate 化学種保存 n-1 化学種, n:th 電流と電荷保存 (電気的中性) • Conservation of current, net current is not accumulated, produced nor consumed in the bulk electrolyte 電流保存正味電流はバルク電解質内で不増不滅 • For primary and secondary current distr. and current balance for metal structure. Shell interface for thin structures (avoid meshing across thickness of metal structures). 一次、二次のケースと金属構造の電流収支薄板構造のシェルインタフェース（厚さ方向へのメッシュ生成を避ける）反応速度    2 ∇ ⋅  F   − zi Di ∇ci − ∇φl  ( zi ) mi Fci   = 0 i    i 電解質 Electrolyte ( ) ∇ ⋅ −κ ∇φ l = 0 Metal structure ( ) 金属構造 ∇ ⋅ −κ ∇φsl = 0 Reactions at Metal Surfaces 金属表面での反応 • Described through kinetics expressions that include activation and concentration overpotential: j·n = i • 活性化過電圧と濃度過電圧を含む反応式で記述 Multiple reactions defined on a metal surface – – – – 金属表面で定義される複数反応 Anodic dissolution of metals 金属のアノード溶解アクティブ陽極における陽極反応：例）酸素・塩素発生 Anodic reactions at active anodes, for example oxygen and chlorine evolution 保護面における競争反応と Oxygen reduction and hydrogen evolution as competing reactions at protected surfaces しての酸素還元と水素放出 Heterogeneous reactions such as growth of oxide and hydroxide films on surfaces: film thickness included as model variable 表面における酸化・水酸化物膜の成長の様な不均質反応：モデル変数として膜厚を含む • Example: Kinetic expression for oxygen reduction and evolution 例: 酸素還元と発生の反応式 iO2 = i0,O2    0.5 F   pO2 φs − φl − Eeq ,O2  −  exp  −  RT   pO2 ,ref  ( )     0.25  c +  H  cH + ,ref     0.5 F   exp  φs − φl − Eeq ,O2     RT    ( ) Summary まとめ • Descriptions in the Corrosion Module 腐食モジュールの内容 Current and species conservation in electrolytes and solid structures Charge conservation in the electrolyte Shell interface for thin metal structures to account for ohmic losses in the metal Competing charge transfer reactions at metal-electrolyte surface Growth of oxide and hydroxide films and their influence on current an potential distribution – General surface reactions and homogeneous reactions in bulk solution – – – – – • The use in corrosion and corrosion protection: 腐食防食の応用 – Design metal structures to minimize corrosion – Control operating conditions to avoid corrosion – Optimize corrosion protection systems and estimate life Electrochemistry Module General Introduction 電気化学モジュール：概略紹介 COMSOL © Copyright 2014 COMSOL. Any of the images, text, and equations here may be copied and modified for your own internal use. All trademarks are the property of their respective owners. See www.comsol.com/trademarks. Contents 内容 • Applications 応用 • Key features 重要な機能 • Concluding remarks 結論 Impedance spectroscopy tutorial done with the Electroanalysis interface in Electrochemistry Module Applications 応用 Electroanalysis 電気分析 • Fundamental methods in electroanalysis: – – – – – • Coulometry クロノメトリ Potentiometry ポテンシオメトリ Voltammetry ボルタンメトリ Amperometry アンペロメトリ Electrochemical impedance spectroscopy 電気化学的インピーダンス法 Electrochemical sensors 電気化学センサー – Glucose sensors グルコースセンサー – Gas sensors ガスセンサー – Pressure sensors 圧力センサー • Electrophoresis 電気泳動 – Separation of biomolecules and ions 生体分子とイオンの分離 Concentration profile in the electrolyte in microdisk voltammetry Electrolysis 電気分解 • Chlor-alkali process 塩素アルカリ • Chlorate process 塩素酸塩 • Water electrolysis 水電解 – Hydrogen production – Oxygen production in submarines and space crafts Secondary current density distribution in a chlor-alkali electrodes-membrane unit cell. Chlorine evolution and oxygen evolution kinetics may be applied at the anode and hydrogen evolution kinetics are used at the cathode. Electrodialysis 電気透析 • Desalination 脱塩 – Seawater to potable water – Removal of salts in effluents (waste water treatment) • Electrodeionization 電気的脱イオン – Ultra-pure water production • Control of pH pHコントロール – Removal of acids from wine, juice and other "delicate“ solutions 2D model of membrane electrolysis representative unit cell. The cross section of the flux of chloride is shown. The position of the cation selective membrane is shown in red while the anion selective membrane is shown in blue. Bioelectrochemistry 生物電気化学 • Ablation 切除・融除 – Thermal 熱的 – Chemical 化学的 • Biosensors バイオセンサー Tutorial model of tumor ablation. The graph shows the selectivity of the anode for chlorine and oxygen evolution. pH as a function of distance from the anode at different times (s). Key Features 重要な機能 Current Distribution 電流分布 • Primary: Ohmic effects only • Secondary: Both ohmic and activation (reaction kinetic) effects 二次：オーム性および活性化（電極反応）の影響一次：オーム性影響のみ – Modeling of electrode kinetics for electrochemical reactions • Tertiary: Ohmic, activation, and concentration overpotential effects 三次：オーム性、活性化および濃度過電圧の影響 – Transport modeling for the concentrations of all solute species – Use when mass transfer and electric field are both significant in an electrochemical system Physics interfaces added or altered by Electrochemistry Module Electroanalysis Interface 電気分析インターフェース • Model electroanalytical experiments in the presence of excess supporting electrolyte 支持電解質における電気分析試験のモデリング • Transport of chemical species by diffusion and convection Full mass transfer description but no electric field Can also include electrochemically inert species and followup reaction chemistry 拡散と対流による化学種の輸送 – – • Automated multiphysics coupling of charge and mass transfer at electrode boundaries – – Built-in electrode kinetic expressions such as Butler-Volmer equation One interface: simplified model setup and computation 電極境界の上に電荷・質量の輸送の自動的マルチフィジックスのカップリング Dedicated interfaces for electroanalytical studies Cyclic Voltammetry サイクリックボルタンメトリー • Sets up the typical experimental condition and allows for a simple specification of sweeps in electric potential between two electrodes Cyclic voltammetry tutorial done with the Electroanalysis interface in Electrochemistry Module Chemical Species Transport 化学種輸送 • • • Diffusion-convection equation for electroanalysis 電気分析の拡散・対流方程式 Nernst-Planck for general applications ネルンスト・プランク式の一般的な応用 Homogenous, heterogeneous and equilibrium reactions in solutions 溶液中の均一系、不均一系および平衡反応 Boundary layer elements around a representative unit cell of a coated DSA with a micromesh substrate Other Capabilities in Transport Phenomena 輸送現象に関する他の機能 • Heat Transfer 伝熱 – Heat sources due to Joule heating, activation losses, and other electrochemical phenomena. • Fluid Flow (Laminar and Porous Media) 流体流れ（層流、多孔質内流れ） – Allows for the modeling of electroosmotic flow – Couple to Electroanalysis to model hydrodynamic methods (e.g. channel electrode) Flow field (arrows) and chloride concentration in the electrolyte surrounding a coated DSA on a micromesh substrate Studies スタディ • Stationary analysis (steady state) • Dynamic simulation 静解析動的シミュレーション – Time-dependent analysis, for example sweeps – Cyclic voltammetry – Current interrupt analysis 電気化学的インピーダンス分光法 • Electrochemical impedance spectroscopy (EIS) – Full phenomenological modeling in the frequency domain – Effects of Ohmic, activation, species transport, and adsorption (double layer discharge and recharge) using high-fidelity physical models – Lends physical meaning to equivalent circuits – Uses a steady-state nonlinear model and adds a small linear perturbation in potential – One physical model is applicable over a wide range of base polarizations Dedicated interfaces for EIS studies Concluding Remarks まとめ • Electrochemistry Module, the perfect tool for: – – – – • Electroanalytical chemistry 電気分析化学 Applied electrochemistry 応用電気化学 Electrochemical engineering 電気化学工学 Bioelectrochemistry 生物電気化学 Find more information about the use of COMSOL in electrochemistry: – http://www.comsol.com/papers/641/electrochemistry/ • Contact your local COMSOL representative for more information about the Electrochemistry Module • Browse the list of events for webinars, courses, and workshops near you: – http://www.comsol.com/events/ Moving geometry effects in 3D Surface catalytic effects The Electrodeposition Module 電気めっきモジュール Coupled diffusion-convection © Copyright 2014 COMSOL. Any of the images, text, and equations here may be copied and modified for your own internal use. All trademarks are the property of their respective owners. See www.comsol.com/trademarks. Current conduction in thin deposited layers Electrodeposited Layers, Typical Applications Targeted by the Module 電気めっき層、本モジュールでターゲットとする代表的な応用例 • Fabrication of electrical and thermal conductors 電気伝導体と熱伝導体の構成 – • Protection of metal parts – – • 金属部品の腐食保護 Corrosion protection of nuts, bolts, and other components Wear resistance coatings on bearings and shafts Decoration of metals and plastics 金属及びプラスチックの装飾 – – • Printed circuit boards, electrical contacts, and cooling devices Chromium coatings of automotive parts Nobel metals on jewelry and tableware Electroforming of parts with thin complex shapes 複雑な薄い部品の電鋳 – – Manufacturing of thin screens and shaver heads Manufacturing of MEMS devices The shaver cap in a Philips shaver is manufactured using electroforming, from COMSOL News 2008 Why Modeling and Simulations? • Cost effective way of understanding, optimizing, and controlling electrodeposition through… シミュレーションによって、電気めっき現象を理解しており、めっきプロセスを最適化やコントロールし、コスト効率のよい方法である。 • …investigating the influence of the めっき槽における膜厚分布及び膜の成 parameters below on the thickness 分への影響のパラメーターを検討する。 and composition of deposited layers: – – – – – Cell geometry めっき槽の構造 Electrolyte composition and mixing 溶液の組成及び混合成分 Electrode kinetics 電極特性 Operating potential and average current density 操作電圧及び平均電流密度 Temperature Thickness of the decorative deposited layer in a 温度 furniture fitting modeled using simulations based on secondary current distribution Electrochemical Reactions 電気化学反応 • The Electrodeposition Module is able to model arbitrary reaction 任意の数の反応メカニズムのモデリングが可能。 mechanisms: – Electrode kinetics using ButlerVolmer or by just typing in 電極特性にはバトラー・フォルマー式或いはユーザーの自定義の式 arbitrary expressions – Multiple competing reactions 多段の複数の反応 – Adsorption reactions including Settings windows for electrode reactions for diffusion of adsorbed species secondary current distribution at the electrode surface 電極表面に吸着種の拡散を含める吸着反応 The Deposited Layer and its Composition めっき皮膜及び膜の成分 • Material balances are defined for the deposited species 材料バランスはめっき皮膜の成分に対して定義される。 • Surface diffusion and active site density can be accounted for in the model 表面拡散と活性サイト密度はモデルに考慮可能 • The deposited layer’s thickness: めっき皮膜の厚み – Calculated on a fixed geometry or… 固定ジオメトリ上のモデリング – …modeled using moving boundaries based on the ALE method ALEによる移動境界面モデリング Settings windows for the deposited species. The concentration, density and molar mass determine the thickness of the layer 表面濃度、サイト密度及びモル質量によってめっき皮膜の厚さを決める。 Transport of Charged and Neutral Species • Flux = diffusion + convection + migration フラックス = 拡散 + 対流 + 泳動濃度 Concentration 拡散係数 Diffusivity 流速 Flow velocity 電荷 Charge 移動度 Mobility N i = − Di ∇ci + ci u − zi mi Fci ∇φl Faraday’s constant Electrolyte potential ファラデー定数電解質電位 Transport of Charged and Neutral Species • Current density j = F  zi N i i • 電流密度 sum of ch arg es    2 j = F   − zi Di ∇ci + u  zi ci − ∇φl  ( zi ) mi Fci   i  i i   Electroneutrality, charge conservation sum of charges = 0   2 j = F   − zi Di ∇ci − ∇φl  ( zi ) mi Fci  i  i  • Perfectly mixed primary and secondary current distribution   2 j = −  F  ( zi ) mi Fci  ∇φl i    κ = conductivity 電気的中立性, 電荷保存則電荷の和 = 0 完全混合一次，二次 Conservation of Species, Current, and Charge • Conservation of species n-1 species, n:th through current and charge conservation (electroneutrality) ∂ci = −∇ ⋅ ( − Di ∇ci + ci u − zi mi Fci ∇φl ) + Ri ∂t 化学種保存 n-1 化学種, n:th 電流と電荷保存 (電気的中性) • Conservation of current, net current is not accumulated, produced or consumed in the bulk electrolyte 電流保存正味電流はバルク電解質内で不増不滅 • For primary and secondary cases 一次、二次のケース Reaction rate 反応速度    2 ∇ ⋅  F   − zi Di ∇ci − ∇φl  ( zi ) mi Fci   = 0 i    i ( ) ∇ ⋅ −κ ∇φ l = 0 Tutorial from The Model Library • Copper deposition 銅めっき – Copper sulfate electrolyte 硫酸銅溶液 – Copper dissolution at the anode アノード上の銅の溶解 – Copper deposition at the cathode カソード上の銅の析出 Anode • Dependent variables 変数 – Copper concentration 銅イオンの濃度 – Sulfate ion concentration 硫酸イオン濃度 – Potential in the electrolyte 溶液中の電位 • Electrode kinetics – Butler-Volmer expression including concentration overpotential バトラー・フォルマー式には濃度の影響を含める。 Cathode Model geometry Tutorial from The Model Library, continued • Original boundary position 境界位置 – Gray colored line – Updated boundary position with automatic remeshing 自動再メッシュと共に電極の境界を移動する – Four automatic remeshing steps ４つの自動再メッシュ 1 2 Boundary displacement Boundary displacement 3 4 Copper ion concentration [mol/m3], current density (streamlines), and potential (contours) after 11 s of deposition Model Library Examples • Via Superfilling スーパーフィリング – Surface catalyst-enhanced deposition • Microconnector Bump マイクロコネクタバンプ – Mass transfer by coupled convectiondiffusion 対流と拡散の結合された質量輸送 Model Library Examples, continued • Inductor Coil インダクタコイル – Mass transfer and moving geometry effects in 3D 三次元モデルでの質量輸送と移動ジオメトリの影響 • Resistive Wafer レジスティブウエハ – Current distribution with changing lateral electric conductivity in a depositing layer めっき層の横方向導電率の変化による電流分布 Model Library Examples, continued • Electrochemical Machining 電解加工 – Removal of material with moving geometry effects • Electrophoretic Painting (Ecoating) – Dynamic current distribution due to a resistive paint layer 電着塗装 Model Library Examples, continued • Fountain Flow Effects on Rotating Wafer – – – – – Mass transfer due to convection and diffusion Current conduction in the electrolyte Potential drop in thin wafer Swirl Flow used to calculate 2D-axisymmetrical flow profile Note: CFD Module needed for Swirl Flow Electrode reaction current density on wafer 回転ウエハを伴うセル中の対流効果対流・拡散による質量輸送電解質中の電流伝導薄いウエハ層の中の電圧差渦巻流の計算用の二次元軸対称の流れプロフィル Concentration of ions in boundary layer Flow profile The Electrodeposition Module Interfaces • Current and potential distribution based on: – – – – 電流及び電位分布 Charge and current balances 電荷及び電流の保存則材料輸送 Material transport 流れ Fluid flow 熱伝達 Heat transfer めっき皮膜の厚さ及び膜の成分 • Deposited layer thickness and composition through: – Electrode reactions coupled to surface species balances 電極反応と表面種の収支 – Fixed and moving boundaries coupled to surface species balances 固定及び移動境界と表面種収支 Physics interfaces as listed in the GUI of the Electrodeposition Module 電気めっきモジュールにおける利用された物理インターフェース