Outline MAE 493R/593V- Renewable Energy Devices • Basics of electrochemistry • Polymer electrolyte membrane (PEM) fuel cells Fuel Cells and Hydrogen • Solid oxide fuel cells (SOFCs) • Hydrogen production and storage • Coal-fired plants and integrated gasifier fuel cell (IGFC) systems Basics of Electrochemistry Why Study Electrochemistry? • Batteries, fuel cells, and solar cells • Corrosion • Industrial production of chemicals such as Cl2, NaOH, F2 and Al All course notes only for class students. The slides are modified from the original slide provided by Dr. C. S. Wang at University of Maryland • Biological redox reactions The heme group Why Study Electrochemistry? Why Study Electrochemistry? Conventional fossil energy devices: Renewable energy devices: For example, fuel cells are to directly convert chemical energy to electric work http://www.fueleconomy.gov/feg/tech/fuelcell.gif Anode side: 2H2 →4H+ + 4eCathode side: O2 + 4H+ + 4e- →2H2O Fossil fuels combustion (hydrocarbons+ oxygen)→ energy stored in the working fluid (internal energy or enthalpy) converted to mechanical energy by passing the working fluid to devices (such as turbines) Net reaction: 2H2 + O2 →2H2O Operating temp: around 80 oC Image from: http://en.wikipedia.org/wiki/File:Fc_diagram_pem.gif 6 Basic knowledge of electrochemistry Terminology for Redox Reactions Table of Contents: redox reaction -oxidation reaction and reduction reaction - reducing agent and oxidation agent electrochemical cells - electrolyte, anode, cathode - voltaic cells, electrolytic cells cell potential and Nernst equation Gibbs free energy Kinetic of electrochemical reaction - polarization (ohmic, activation and concentration polarization) Oxidation Reaction Example: 2 Cu + O2 → 2 CuO Reduction Reaction Example: CuO + H2 → Cu + H2O • loss of electrons • increase in oxidation state • addition of oxygen • loss of hydrogen • gain of electrons • decrease in oxidation state • loss of oxygen • addition of hydrogen copper is losing electrons Cu 2+ in CuO is gaining electrons voltammetry (CV) - linear-sweep voltammetry - cyclic voltammetry electrochemical impedance spectroscopy (EIS) You can’t have one… without the other! Terminology for Redox Reactions • Reduction (gaining electrons) can’t happen without an oxidation to provide the electrons. • You can’t have 2 oxidations or 2 reductions in the same equation. Reduction has to occur at the cost of oxidation • OXIDATION— OXIDATION—loss of electron(s) by a species; increase in oxidation number; increase in oxygen. • REDUCTION REDUCTION— —gain of electron(s); decrease in oxidation number; decrease in oxygen; increase in hydrogen. LEO the lion says GER GER!! o l x s e i e c d t a r t o i n o s n • OXIDIZING AGENT— OXIDIZING AGENT—electron acceptor; species is reduced. a l e i e d n c u t c r t o i n o s n • REDUCING AGENT REDUCING AGENT— —electron donor; species is oxidized. GER! Review of Oxidation Numbers Oxidation‐Reduction Reactions: A Quick Review The charge the atom would have in a molecule (or an ionic compound) if electrons were completely transferred. Cu(s) in AgNO3(aq) 1. Free elements (uncombined state) have an oxidation number of zero. Na Be, Na, Be K K, Pb Pb, H2, O2, P4 = 0 2. In monatomic ions, the oxidation number is equal to the charge on the ion. Li+ (+1); Fe3+ (+3); O2- (-2) 3. The oxidation number of oxygen is usually –2. In H2O2 and O22- it is –1. 4.4 Cu → Cu2+ QuickTime Cu → Cu2+ + 2e– Movie Ag+ → Ag Ag+ + ee– → Ag 2Ag+ + 2e– → 2Ag Cu → Cu2+ + 2e– Overall cell reaction: Cu +2Ag+→2Ag + Cu2+ Cu loses e‐: oxidized Ag+ gains e‐: reduced Redox Reactions • Zinc is added to a blue solution of copper(II) sulfate Harnessing the Electricity • Electrons flow from the zinc atoms to the copper ions During the spontaneous redox reaction. Zn (s) + CuSO4 (aq) ' ZnSO4 (aq) + Cu (s) • The blue colour disappears…the zinc metal “dissolves”, metal dissolves , and and solid copper metal precipitates on the zinc strip • Electricity can be thought of as the “flow of electric charge”. • The zinc is oxidized (loses electrons) Zn (s) + Cu2+ (aq) ' Zn2+ (aq) + Cu (s) • The copper ions are reduced (gain electrons) • Electrochemical Cell – a device that uses a spontaneous redox reaction to produce electricity • Anode – the electrode where oxidation occurs • Cathode – the electrode where reduction occurs • Salt Bridge – connects two “half-cells” to complete the electric circuit. – for example, a U-tube filled with salt solution • How to utilize the electricity: the flow of electrons from the zinc atoms to the copper ions? Answer: Separate the Cu ions from the Zn atoms. This will force the electrons from the zinc atoms to travel through an external path to reach the copper ions. Electrochemical Cells Terms Used for Electrochemical Cells Electrochemical Cells A salt bridge has three functions: 1) It allows electrical contact between the two half-cells 2) I prevents mixing It i i off the h electrode l d solutions l i 3) It maintains electrical neutrality in each halfcell as ions flow into and out of the salt bridge CHEMICAL CHANGE ---> ---> ELECTRIC CURRENT Zn metal With time, Cu plates out onto Zn metal strip, and Zn strip p “disappears.” pp Cu2+ ions •Zn is oxidized and is the reducing agent 2eZn(s) ---> ---> Zn2+(aq) + 2e•Cu2+ is reduced and is the oxidizing agent 2e-- -----> > Cu(s) Cu2+(aq) + 2e Electrochemical Cell: An Atomic‐Level View Cell potential QuickTime Movie • Water only spontaneously flows one way in a waterfall. • Likewise, electrons only spontaneously y p y flow one way in a redox reaction—from higher to lower potential energy. Some Electrochemical Terms Electrochemical Cells e– QuickTime Movie Voltaic cell Load • Voltaic: spontaneous chemical reaction produces electrical energy • Electrolytic: electrical energy forces a nonspontaneous reaction to occur Galvanic Cells Cathode Electrolyte • Electrode: surface where redox reaction occurs Anode: oxidation Cathode: reduction Active: part of redox Inert: does not react • Electrolyte: conducting solution (has ions) • Electric current due to electron and ion flow A Voltaic Cell: The Daniell (Zn (Zn--Cu) Cell CHEMICAL CHANGE Æ CHEMICAL CHANGE Æ ELECTRIC CURRENT anode Oxidation negative electrode Power Anode Electrolyte Voltaic V lt i cell ll Electrolytic El t l ti cell ll • An apparatus that allows a redox reaction to occur by transferring electrons through an external connector. Electrolytic cell e– cathode Reduction Positive electrode spontaneous p redox reaction •To obtain a useful current, we separate the oxidizing and reducing agents so that electron transfer occurs thru an external wire. This is accomplished in a GALVANIC or VOLTAIC cell. A group of such cells is called a battery battery.. Electrolytic Cell Battery Anode (+): 4OH– Electrochemistry Two broad areas QuickTime Movie Water (aq) → O2(g) + 2H2O(l) + 4e– Galvanic Cells Rechargeable Electrolysis Cells batteries Cathode (– (–): 4H2O(l) + 4e 4e-- → 2H2(g) + 4OH– Overall: 2H2O(l) → O2(g) + 2H2(g) Voltaic Cell Diagram Electrolytic vs Voltaic Cells The Cu‐Ag Cell } • spontaneous reaction generates electricity • Oxidation: anode Reduction: cathode l d l i • Electrode Polarity: Anode: negative Cathode: positive • e–flow: anode to cathode • Ion flow: anions to anode; cations to cathode } • nonspontaneous reaction forced to occur • Oxidation: anode Reduction: cathode • Electrode Polarity: l d l i Anode: positive Cathode: negative • e–flow: anode to cathode • Ion flow: anions to anode; cations to cathode The Daniell cell: Zn(s) + Cu2+(aq) → Zn2+(aq) + Cu(s) may be represented by a cell diagram: Zn | Zn2+(1.0 M) || Cu2+(1.0 M) | Cu Oxidation half--cell half R d ti Reduction half--cell half ¾The ANODE is described before the CATHODE. ¾Concentrations of ions are indicated in brackets. ¾A vertical line represents a phase boundary. ¾A double vertical line represents the salt bridge. A Comparison of Cell Potentials • Zn‐Cu cell potential: 1.10 V Zn(s) + Cu 2+(aq) → Zn2+(aq) + Cu(s) • Cu‐Ag cell potential: 0.46 V Cu(s) + 2Ag+(aq) → Cu 2+(aq) + 2Ag(s) • Oxidizing power: Ag+ > Cu 2+ > Zn 2+ • Cell potential (voltage) depends on: nature of electrodes and ions concentrations of ions temperature of cell The Cell Potential • The magnitude of the cell potential, Ecell, is a measure of the spontaneity of a redox reaction • The more positive the cell potential, the greater the driving force for the redox reaction to proceed as written g p • The standard cell potential, Eocell, is for a cell operating under standard conditions Standard Electrode Potentials: Standard Electrode Potentials: • The standard electrode potential, Eohalf‐cell, is the potential of a given half‐cell when all components are in their standard states • Byy convention,, the standard electrode potential refers to a half‐reaction written as a reduction • The more positive the potential, the greater the tendency for the reaction to proceed forward Standard Electrode Potentials • The E°cell calculated is for the cell operating under standard state conditions • For electrochemical cell standard conditions are: -solutes l t att 1 M concentrations n ntr ti n - gases at 1 atm partial pressure - solids and liquids in pure form • The potential of a half‐cell is referenced with respect to the standard hydrogen electrode (SHE) By convention: • By convention: SHE Half‐Reaction Eohalf‐cell H2 → 2H+ + 2e– 0.00 V 0.00 V 2H+ + 2e– → H2 • All at some specified temperature, usually 298 K Standard Hydrogen Electrode (SHE) SHE - the reference electrode Reference Electrode Standard ReductionPotentials (The Electromotive Series) Acidic Solution Li+(aq) + e– → Li(s) Al3+(aq) + 3e– → Al(s) Cr2+(aq) + 2e– → Cr(s) ( ) + 2e () Zn2+(aq) + 2e– → Zn(s) Cr3+(aq) + 3e– → Cr(s) Cr3+(aq) + e– → Cr2+(aq) 2H+(aq) + 2e– → H2(g) Cu2+(aq) + e– → Cu+(aq) Cu2+(aq) + 2e– → Cu(s) F2(aq) + 2e– → 2F–(aq) SRP, Eo(volts) –3.045 –1.66 –0.91 0.91 –0.763 –0.74 –0.41 0.00 0.153 0.337 2.87 Relative Oxidizing & Reducing Strengths To determine which is a stronger oxidizing agent between Cl2 and Pb2+: • Compare their reduction potentials Eo = 1.360 V Cl2 + 2e– → 2Cl– Pb2++ 2e– → Pb Eo = –0.126 V • The stronger oxidizing agent is more easily reduced; i.e., has more positive Eo ⇒ Cl2 is the stronger oxidizing agent Table of Standard Reduction Potentials Things to Remember about Eo • The more positive the Eo, the greater the tendency for the reaction to occur in the forward direction • The more negative the Eo for a reaction, the greater the tendency for the reaction to occur in the reverse direction • If a reaction is reversed, the sign of its Eo is reversed • If a reaction is multiplied by a factor, its potential stays the same; Eo is not multiplied by the factor • If half-reactions are summed up to give an overall reaction, potentials can be summed up to give an overall cell potential Table Of Standard Reduction Potentials oxidizing ability of ion Eo (V) Cu2+ + 2e- Cu +0.34 2 H+ + 2e- H2 0.00 Zn2+ + 2e- Zn -0.76 To determine an oxidation from a reduction table, just take the opposite sign of the reduction! reducing ability of element Oxidizing and Reducing Agents • The strongest oxidizers have the most positive reduction potentials. • The strongest reducers have the most negative reduction potentials. Cell Potentials Predicting Reaction Spontaneity • Diagonal Rule for the Electromotive Series: Any species on the left half‐cell reaction will react spontaneously with a species on the right half‐cell reaction located above it 2+ + 2e Zn2+ + 2e–→ Zn Eo = – = 0.76 V 0 76 V 2+ – Cu + 2e → Cu Eo = 0.34 V • Spontaneous if Eocell is positive Eo = 0 .76 V Zn → Zn2+ + 2e– 2+ – Eo = 0. 34 V Cu + 2e → Cu 2+ 2+ Eo = 1.10 V Zn + Cu → Zn + Cu Determination of Cell Potentials Determination of Cell Potentials • Choose appropriate half‐reactions from the Table of Standard Potentials • Write half‐reaction with more positive Eohalf‐cell as a reduction • Write less positive half‐reaction as an oxidation; re erse sign of Eohalf‐cell reverse • Balance number of electrons; do not multiply Eohalf‐cell by factors used to multiply electrons • Sum up reactions and potentials to give Eocell • If Eocell > 0: reaction is spontaneous The Cell Potential Cr3+ (aq) + 3eAnode ((oxidation): ) Cd (s) E0 = -0.40 V Cd is the stronger oxidizer E0 = -0.74 V Cr (s) Cathode (reduction): 2e- + Cd2+ (1 M) 2Cr (s) + 3Cd2+ (1 M) Cd will oxidize Cr Cr3+ ((1 M)) + 3e- x 2 Cr ((s)) Cd (s) x3 3Cd (s) + 2Cr3+ (1 M) 0 = E0 0 Ecell cathode + Eanode 0 = -0.40 + (+0.74) Ecell 0 = 0.34 V Ecell • 3Fe3+(aq) + 3e → 3Fe2+(aq); Ered= +0.771 V (2) Subtraction of reduction (or oxidation) potentials of half-reactions having g the same number of electronics. • Cl2(g) +2e → 2Cl-(aq); Ered= +1.36 V • Zn2+(aq) +2e → Zn(s); • • Therefore for Cl2(g) +Zn(s) → 2Cl-(aq) +Zn2+(aq); Ecell= +2.123 Ered= -0.763 V Electron Transfer Reactions What is the standard potential of an electrochemical cell made of a Cd electrode in a 1.0 M Cd(NO3)2 solution and a Cr electrode in a 1.0 M Cr(NO3)3 solution? Cd2+ (aq) + 2e- (1) A half-reaction can be multiplied through by any number without affecting the reduction (or oxidation) potential • Fe3+(aq) + e → Fe2+(aq); Ered= +0.771 V • Electron transfer reactions are Electron transfer reactions are oxidation oxidation‐‐reduction or redox or redox reactions. • Results in the generation of an electric current ( l (electricity) or be caused by imposing an electric i i ) b db i i l i current. • Therefore, this field of chemistry is often called ELECTROCHEMISTRY. Thermodynamics Electrochemistry The Gibbs free energy is defined as: G = H − TS Where H = U + PV • Deals with the inter‐conversion between electrical energy and chemical energy • Involves oxidation‐reduction reactions in electrochemical cells (redox) U is the internal energy (SI unit: J) P is pressure (SI unit: Pa) V is volume (SI unit: m3) T is the temperature (SI unit: K) S is the entropy (SI unit: J/K) H is the enthalpy (SI unit: J) Gibbs energy is the capacity of a system to do non-mechanical work and ΔG measures the non-mechanical work done on it. The Gibbs free energy is the maximum amount of non-expansion work that can be extracted from a closed system; this maximum can be attained only in a completely reversible process. G is a thermodynamic properties. G is a state function G is NOT a path function. http://en.wikipedia.org/wiki/Gibbs_free_energy Thermodynamics Thermodynamics of Chemical Reactions The change in the Gibbs free energy of the system that occurs during a reaction is: Any reaction for which If the reaction is run at constant temperature, this equation can be : If the data are collected under standard-state conditions, the result is the standard-state free energy of reaction, Standard-state conditions: • The partial pressures of any gases involved in the reaction is 0.1 MPa. • The concentrations of all aqueous solutions are 1 M. • Measurements are also generally taken at a temperature of 25 oC (298 K) This equation is to determine the relative importance of the enthalpy and entropy terms as driving forces behind a particular reaction. The change in the free energy of the system that occurs during a reaction measures the balance between the two driving forces that determine whether a reaction 51 is spontaneous. Thermodynamics of Chemical Reactions For a chemical reaction, Standard-State Free Energy of Formation Any reaction for which The Gibbs free energy is the maximum amount of non-expansion work that can be extracted from a closed system; this maximum can be attained only in a completely reversible process. Go < 0 is positive is therefore unfavorable. Unfavorable or non‐spontaneous reactions: Go > 0 Reactions can be classified according to the change in enthalpy (heat): <0 A larger amount of the energy released in the reaction is subtracted from a smaller amount of the energy used for the reaction. 52 Thermodynamics of Chemical Reactions For a reaction: aA+ bB →c C +d D Chemical quotient (reaction quotient) is defined as: Q= The standard-state free energy of reaction can be calculated from the standard-state free energies of formation as well. It is the sum of the free energies of formation of the products minus the sum of the free energies of formation of the reactants is negative should be favorable, or spontaneous Favorable, or spontaneous reactions: [C ]c [ D] d [ A] a [ B]b In a chemical process, chemical equilibrium is the state in which the chemical activities or concentrations of the reactants and products have no net change over time. If Q correspond d to t equilibrium ilib i concentrations, t ti then th the th above b expression i iis called the equilibrium constant and its value is denoted by K (or Kc or Kp.) K is thus the special value that Q has when the reaction is at equilibrium If K > Q, a reaction will proceed forward. If K < Q, the reaction will proceed in the reverse direction, converting products into reactants. If Q = K then the system is already at equilibrium Thermodynamics of Chemical Reactions Thermodynamics of Chemical Reactions Example: 0.035 moles of SO2, 0.5 moles of SO2Cl2, and 0.08 moles of Cl2 are combined in an evacuated 5 L flask and heated to 100 oC. What is Q before the reaction begins? Which direction will the reaction proceed in order to establish equilibrium? For any chemical process, the free-energy change under any conditions, ΔG, is given by: R is the ideal-gas constant, 8.314 J/mol · K; T is the absolute temperature; and Q is the reaction quotient When a system (a reaction) is at equilibrium: ΔG = 0, and K=Q Thus, at equilibrium, the equation above can be rewritten as Solution: The relationship between ΔGo and K can be summarized as follows <0: K>1 0.078 (K) > 0.011 (Q) = 0: K>1 Since K >Q, the reaction will proceed in the forward direction in order to increase the concentrations of both SO2 and Cl2 and decrease that of 55 SO2Cl2 until Q = K. >0: K<1 56 http://www.chem.purdue.edu/gchelp/howtosolveit/equilibrium/Reaction_Quotient.htm Thermodynamics of Chemical Reactions Electrolysis and Mass Changes Thermodynamics of Electrochemical Cells Free Energy charge (Coulombs) = current (Amperes) x time (sec) 1 mole e- = 96,500 C = 1 Faraday Mols of metal dissolved are obtained by dividing the mols of electron by n: Faraday’s Law: M = It (mol) nF ΔG for a redox reaction can be found by using the equation ΔG = −nFE where n is the number of moles of electrons transferred, and F is a constant, the Faraday. 1 F = 96,485 C/mol = 96,485 J/V-mol I –current (A); t –time (s); n- number of electrons transferred; F –Faraday constant (96500 C) Thermodynamics of Electrochemical Cells Thermodynamics of Electrochemical Cells The Cell Potential : Work done in a redox reaction = - n FEcell Nernst Equation Units: Joules = moles x (coul/mole) x volts = coul x volt = J – 1 coulomb x 1 volt = 1 joule or Joule / Coulomb = volt – Since a spontaneous redox rxn does work on the surroundings, the sign is “-”: W = - nFEcell = ΔG Free Energy, ΔG = maximum useful work done ¾ ΔG = - nFEcell ¾ At 1M concentrations, 1 atm pressure & 25 oC: ΔG = ΔGo ¾ ΔGo = - nFEocell • Remember that ΔG = ΔG° + RT ln Q • This means −nFE = −nFE° + RT ln Q 59 Thermodynamics of Electrochemical Cells The Nernst Equation: • At nonstandard conditions, the cell potential may be calculated using the Nernst equation: S Standard cell potential Faraday, 96,500 J/Vmol e- ΔG = -nFEcell 0 ΔG0 = -nFEcell n = number of moles of electrons in reaction F = 96,500 J = 96,500 C/mol V • mol 0 ΔG0 = -RT ln K = -nFEcell o E = E – 2.303 RT log Q nF Reaction quotient mol electrons transferred Thermodynamics of Electrochemical Cells Absolute temperature 0 = Ecell ( (8.314 J/K•mol)(298 )( K)) RT l K= ln ln K n (96,500 J/V•mol) nF 0 Ecell = 0.0257 V ln K n 0 = Ecell 0.0592 V log K n Gas constant, 8.314 J/mol K Thermodynamics of Electrochemical Cells Thermodynamics of Electrochemical Cells The Cell Potential and the Progress of a Reaction The Nernst Equation • For the reaction: Zn + Cu2+ → Zn2+ + Cu • the cell potential is given by: • Substitution of the values for the gas constant R and the Faraday into the Nernst equation at 25oC gives: 0.0592 E = Eo– n 2+ log Q z z z Thermodynamics of Electrochemical Cells The Cell Potential and the Reaction Quotient Q E = E o – 2.303 RT log Q nF 0.0592 o E =E – log Q n • When: Q < 1: [reactant] > [product], Ecell > Eocell Q = 1: [reactant] = [product], Ecell = Eocell Q > 1: [reactant] < [product], Ecell < Eocell E = E o – 2.303 RT log [ Zn 2+ ] nF [ Cu ] At standard conditions: conditions: Ecell = Eocell As cell operates operates:: Zn2+ increases, Cu2+ decreases, log Q increases, Ecell decreases When Ecell = 0 (equilibrium); cell “runs down” Thermodynamics of Electrochemical Cells The Relationships Between Eocell, ΔGo and Keq • Eocell, is related to ΔGo by: ΔGo = –nFEocell • Since ΔGo = –2.303 RTlog K: –nFEocell = –2.303 RTlog K • Solving for Eocell or for K: E o = 2.303 RT log K nF E o = 0.0592 log K n nFE o 2.303 RT nE o log K = 0.0592 log K = Thermodynamics of Electrochemical Cells Thermodynamics of Electrochemical Cells Eocell, ΔGo and K: A Summary ΔGo – 0 + Forward Reaction S Spontaneous t Equilibrium Nonspontaneous Eocell + 0 – K >1 =1 <1 Calculating Equilibrium Constants • When an electrochemical cell operates, the concentrations of the ions change until Q = K . • When the cell reaches equilibrium, Ecell = 0. • Combining these facts with the Nernst equation gives: Ecell = 0 = Eo − RT ln (K ) nF Alkaline Battery • Calculate K for the reaction that occurs at 25 oC when Mg is added to a solution of AgNO3. • The net reaction is: Mg + 2 Ag+ ' Mg2+ + 2 Ag RT l (K ) ln nF • Rearranging, we can derive an equation to calculate the equilibrium constant for a redox reaction: Eo = Calculating K for a Redox Reaction Eo = RT ln (K ) nF 3.17 V = (8.314)(29 8 K) ln (K ) (2 mol)(96500 C/mol) 247 = ln (K) so K = e247 = HUGE QuickTime Movie Anode ((-): Zn + 2 OH- -----> > ZnO + H2O + 2e 2e-2e-- -----> > Mn2O3 + 2 OHCathode (+): 2 MnO2 + H2O + 2e Corrosion QuickTime Movie Sacrificial Anode Corrosion Prevention Because since is a stronger reducing agent ( i.e. more easily oxidized) than Fe, it will act as a “sacrificial” anode in place of Fe, therefore preventing the iron metal from corroding. Polarization Faraday’s Law: M = Kinetics of Electrochemical Reaction I t n F It nF (mol) – current (A); – time (s); - number of electrons transferred; – Farady constant (96500 C) The mass dissolution rate: r= Exchange Current Density At equilibrium in a reaction such as Electron flow must be the same in both directions (forward and reverse), i,e., so at equilibrium: r f = rr = I0 nF where io = exchange current density, related to the current flow in an q situation equilibrium • At the equilibrium potential of a reaction, a reduction and an oxidation reaction occur, both at the same rate. • For example, H ions are converted gas and released from the gas at the same rate • The net reaction rate and net current density are zero M I M = t nF Polarization exchange current density, related to the current flow in an equilibrium situation Polarization Polarization • Electrode reactions deviates from the equilibrium state due to the flow of an electrical current through an electrochemical cell causing a change in the electrode potential. This electrochemical phenomenon is referred to as polarization. • The deviation from equilibrium causes an electrical potential difference between the polarized and the equilibrium (unpolarized) electrode potential known as overpotential Polarization Ecorr = corrosion potential or mixed potential corrosion rate: icorr = ia = rate of anodic dissolution in a system equilibrium Equilibrium potential for cathodic reaction = Eoc Cathodic Overpotential: ηc = E – Eoc < 0 Real potential = E anodic Overpotential: Equilibrium potential for anodic reaction = Eoa ηa = E – Eoa > 0 Polarization • Depending on the type of resistance that limits the reaction rate, we are talking about three different kinds of polarization • activation polarization • concentration polarization and • resistance (ohmic) polarization or IR Drop Zn in acidic water Activation Polarization activation polarization: • An electrochemical reaction may consist of several steps Activation Polarization activation polarization: • The overpotential due to the activation polarization is determined by Tafel equation • The slowest step determines the rate of the reaction which requires activation energy to proceed • Subsequent shift in potential or polarization is termed activation polarization β= 2.3RT αnF whenever η = zero (i.e. no polarization), i = io, exchange current Concentration Polarization Activation Polarization Hydrogen Overpotential: • Sometimes the mass transport within the solution may be rate determining – in such cases we have concentration polarization • Hydrogen evaluation at a platinum electrode: – H+ + e‐ → Hads – 2Hads → H → H2 • Concentration Concentration polarization polarization implies either there is a shortage of reactants at the electrode or that an accumulation of reaction product occurs • Step 2 is rate limiting step and its rate determines the value of hydrogen overpotential on platinum O 2 + 4H − + 4e − → 2H 2 O Source: K. B. Kabir Concentration Polarization • Fick’s Law: dc dM = − D ×10 −3 dt dx (1) • where dM/dt is the mass transport in x direction in mol/cm2s, D is the diffusion coefficient in cm2/s, and c is the concentration in mol/m3 • Faraday’s law: d ’ l M I i = = AΔt AnF nF (2) • Under steady state, mass transfer rate = reaction rate i = DnF C B − C0 δ Source: K. B. Kabir Concentration Polarization • Maximum transport and reaction rate are attained when C0 approaches zero and the current density approaches the limiting current density: iL = DnF C δ (4) • The most typical concentration polarization occurs when there is a lack of reactants, and (in corroding systems) therefore most a lack of reactants, and (in corroding systems) therefore most often for reduction reactions • This is the case because reduction usually implies that ions or molecules are transported from the bulk of the liquid to the electrode surface, while for the anodic (dissolution) reaction, mass is transported from the metal, where there is a large reservoir of the actual reactant (3) Where δ is the width of the depletion zone Source: K. B. Kabir Concentration Polarization • Equations (1) to (4) are valid for uncharged particles, as for instance oxygen molecules • If charged particles are considered, migration will occur in addition to the diffusion and the previous occur in addition to the diffusion and the previous equation must be replaced by i L = DnF C δN (5) where N is the transference number of all ions in solution except the ion getting reduced Overpotential due to concentration polarization • If copper is made cathode in a solution of dilute CuSO4 in which the activity of cupric ion is represented by (Cu2+ ), then the potential in absence of external current, is given by the Nernst equation: E1 = 0.337 − 2.3RT 1 2.3RT log = 0.337 + log(Cu 2 + ) nF (Cu 2+ ) nF • When current flows, copper is deposited on the electrode, thereby decreasing surface concentration of copper ions to a level at (Cu2+)s. The potential of the electrode becomes: E2 = 0.337 − 2.3RT 1 2.3RT log = 0.337 + log(Cu 2+ )S nF (Cu 2+ )S nF Source: K. B. Kabir Overpotential due to concentration polarization • Since (Cu2+ )s is less than (Cu2+ ), the potential of the polarized cathode is less noble, or more active, than in the absence of external current. The difference of potential, E2 − E1 , is the concentration polarization , equal to: E2 − E1 = (Cu 2+ )S 2.3RT log nF (Cu 2+ ) Overpotential due to concentration polarization i L = DnF C (5) δN ( Cu 2 + ) S = ( Cu 2 + ) − ( Cu C 2+ ) = iδ N DnF iLδN DnF η Conc = E 2 − E 1 = ⎛ i ⎞ 2 . 3 RT log ⎜⎜ 1 − ⎟⎟ nF iL ⎠ ⎝ Source: K. B. Kabir Source: K. B. Kabir IR Drop Concentration Polarization • When polarization is measured with a potentiometer and a reference electrode-Luggin probe combination, the measured potential includes the potential drop due to the electrolyte resistance and possible film formation on the electrode surface • The drop in potential between the electrode and the tip of Luggin probe equals iR. • If l is the length of the electrode path of cross sectional area s, k is the specific conductivity, and i is the current density then resistance l R= • iR drop in volts = Combined Polarization k il k Third electrode • Total polarization of an electrode is the sum of the individual contributions: ηT = ηa + ηc + ηr A voltage or potentiostat current source V RE WE RE CE ηohm WE ηact WE ηconc RE ηconc RE ηact E − En = η = ηact + ηconc + IRu Typical polarization curve http://www.electrochem.org/dl/interface/fal/fal04/IF8-04-Pages17-19,45.pdf cab Current/A Constant--Potential Coulometry Constant Time after application of potential at which species is electrolyzed Voltammetry Measurement of (Faradaic) current as a function of applied potential Charge/C ∫ I dt Analyte concentration is related to peak or limiting current Linear--Sweep Voltammetry Linear Linear--Sweep Voltammetry Linear Stirred Solutions Unstirred Solutions EApplied > E1/2 IL ≡ Limiting Current = KCA E1/2 ≡ Half Half--wave Potential = E E°° EApplied < E1/2 Electrode surface is depleted of reactants after prolonged reaction times (Non--Hydrodynamic) Linear(Non Linear-Sweep Cyclic Voltammetry For a reversible (Nernstian) couple: Ipc = –Ipa Epa - Epc = 0.0592/n E° = (Epa + Epc)/2 Start Ip = KCA IF = IDL = Diffusion Diffusion--limited current For an irreversible couple: Ipc ≠ –Ipa Epa - Epc > 0.0592/n E° = (Epa + Epc)/2 Voltammogram is non non--symmetric Used mainly for qualitative analysis Electrochemical Impedance Spectroscopy Electrochemical Impedance Spectroscopy • Ohms Law: V R= I Electrochemical Impedance Spectroscopy • Impedance is a general expression for resistance under the • Where V is the applied voltage and I is the current • R is a resistor. It follows Ohm’s Law at all current and voltage levels • The resistance value is independent of frequency • AC current and voltage signals through a resistor are in phase with each other L A A C=ε L R: resistance, unit: Ω ρ: resistivity, Ω cm C: capacitance, F ε: permittivity, F cm‐1 R =ρ alternating current (AC) excitation signal • For a sinusoidal current, the voltage is expressed by E = E0 sin ωt t: time f: frequency ω: angular frequency = 2πf ωt: phase angle The current is I = I0 sin (ωt + θ) θ: phase shift Electrochemical Impedance Spectroscopy Electrochemical Impedance Spectroscopy Impedance can be given with an expression analogous to Ohm's Law as: The expression for Z(w) is composed of a real and an imaginary part. If the real part is plotted on the Z axis and the imaginary part on the Y axis of a chart, we get a "Nyquist plot". N ti that Notice th t in i this thi plot l t the th yaxis is negative and that each point on the Nyquist plot is the impedance at one frequency. With Eulers relationship, Then the potential is described as and the current response as The impedance is then represented as a complex number, The impedance is composed of a real and an imaginary part Electrochemical Impedance Spectroscopy Electrical Circuit Elements EIS data is commonly analyzed by fitting it to an equivalent electrical circuit model. Most of the circuit elements in the model are common electrical elements such as resistors, capacitors, and inductors. To be useful, the elements in the model should have a basis in the physical electrochemistry of the system. Component Current Vs. Voltage Impedance resistor E= IR Z=R inductor E = L dI/dt Z = jωL capacitor I = C dE/dt Z = 1/j ωC Nyquist Plot (or Cole-Cole plot) of Impedance low frequency data are on the right side of the plot and higher frequencies are on the left. This is true for EIS data where impedance usually falls as frequency rises (this is not true of all circuits). Electrochemical Impedance Spectroscopy Electrical Circuit Elements • An alternating current can be phase shifted with respect to the voltage • The phase shift depends on what kind of sample the current ppasses • To describe the response from a sample on the alternating current, we introduce 3 passive circuit elements (R, C and L) • The current and voltage through a resistor, R, is not phase shifted Æ the impedance is not dependant on frequency • A resistor only contributes to the real part of the impedance Electrochemical Impedance Spectroscopy • The inductor is an ideal conductor, and an ideal isolator • The inductor only contributes to the imaginary part of the impedance • The impedance of an inductor increases as frequency increases. An inductor's current is phase shifted 90 degrees with respect to the voltage 0 -6 6 L = 10 H -X / Ω -2 Increasing frequency -6 2 4 6 • The capacitor (C ) can store electrical charge: C =ε A A = ε 0ε r L L ε: permittivity ε0: permittivity of free space εr: relative dielectric e at e d e ect c constant A capacitor only contributes to the imaginary part of the impedance. A capacitor's impedance decreases as the frequency is raised. -4 0 Electrochemical Impedance Spectroscopy 8 a pure capacitor Nyquist plot R/Ω a pure inductor Nyquist plot Souce: H. Fjeld Electrochemical Impedance Spectroscopy • Capacitors often do not behave ideally. Instead, they act like a constant phase element (CPE) as defined below [ Souce: H. Fjeld Electrochemical Impedance Spectroscopy Impedance of Constant Phase Element (CPE) CPE ] Z Q = Y ( jω) n −1 Rct • The Th CPE is i very versatile: il -Z” If n = 1, CPE represents an ideal capacitor Cdl If n = 0, CPE represents a resistor If n = -1, CPE represents an inductor If n = 0.5, CPE represents a Warburg element Bode plot CPE Rct 2 Rct Z’ Electrochemical Impedance Spectroscopy Simplified Randles Cell The Simplified Randles cell is one of most common cell models. It includes a solution resistance, a double layer capacitor and a charge transfer (or polarization resistance). Another common plot format of impedance spectra is the Bode plot. In general it depicts two curves. The x-axis shows the logarithm of the frequency. The left axis gives th llogarithm the ith off the th impedance, while the right axis gives the phase angle. equivalent circuit for a Simplified Randles Cell Bode plots of Impedance Source: Gamry.com Electrochemical Impedance Spectroscopy Simplified Randles Cell The polarization resistance was calculated to be 250. A capacitance of 40 μF/cm2 and a solution resistance of 20 Q were also assumed Nyquist plot of The Simplified Randles cell Electrochemical Impedance Spectroscopy Warburg impedance of Diffusion Diffusion can create an impedance known as the Warburg impedance. At high frequencies the Warburg impedance is small since diffusing reactants don't have to move very far. At low frequencies the reactants have to diffuse farther, thereby increasing the Warburg impedance. The equation for the "infinite" Warburg impedance is: Where is the Warburg Constant. On a Nyquist plot the infinite Warburg impedance appears as a diagonal line with a slope of 0.5. On a Bode plot, the Warburg impedance exhibits a phase shift of 45°. Electrochemical Impedance Spectroscopy Impedance of electrochemical reaction at the electrode with infinite diffusion Electrochemical Impedance Spectroscopy Simplified Randles Cell Nyquist plot of The Simplified Randles cell Source: Gamry.com Electrochemical Impedance Spectroscopy Warburg impedance of Diffusion Warburg impedance is only valid if the diffusion layer has an infinite thickness. Quite often this is not the case. If the diffusion layer is bounded, the impedance at lower frequencies no longer obeys the equation above. Instead, we get the form: with, δ = Nernst diffusion layer thickness D = an average value of the diffusion coefficients of the diffusing species Electrochemical Impedance Spectroscopy Impedance of electrochemical reaction at the electrode with infinite diffusion Or CPE In case a charge transfer is also influenced by diffusion to and from the electrode, the Warburg impedance will be seen in the impedance plot. The Warburg element is easily recognized by a line with an angle of 45 ° in the lower frequency region. The equivalent of this electrochemical cell Or CPE is called Randles' circuit. circuit showing the solution resistance, double layer capacitance (or CPE), charge transfer resistance and Warburg impedance Complex plane plots for the circuit of Fig 5 with an ideal double layer capacitance (which means n=1) (a) and a CPE (b) with n = 0.88. Electrochemical Impedance Spectroscopy Impedance of electrochemical reaction at the electrode with infinite diffusion Peak frequency: ω0 = (RC)-1 Electrochemical Impedance Spectroscopy

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