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LECTURER: Prof. Yung-Eun Sung ( 성영은 ) School of Chemical & Biological Engineering Office: 302-729, Phone: 880-1889, TEXTBOOK &

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Presentation on theme: "LECTURER: Prof. Yung-Eun Sung ( 성영은 ) School of Chemical & Biological Engineering Office: 302-729, Phone: 880-1889, TEXTBOOK &"— Presentation transcript:

1 LECTURER: Prof. Yung-Eun Sung ( 성영은 ) School of Chemical & Biological Engineering Office: , Phone: , TEXTBOOK & REFERENCES A.J. Bard, L. R. Faulkner, Electrochemical Methods, Wiley, H. B. Oldham, J. C. Myland, Fundamentals of Electrochemical Science, Academic, P. G. Bruce, Solid State Electrochemistry, Cambridge, Lecture Schedule 5/3 (Thurs): Basic & Principle of Electrochemistry 5/9 (Wed): Characterization Technique: Voltammetry 5/17 (Thurs): Electric Double Layer Structure

2 Basic & Principle of Electrochemistry

3 Information on Electrochemistry JOURNALS Electrochemical and Solid State Letters Electrochemistry Communications Electroanalysis Electrochimica Acta Fuel Cells - From Fundamentals to Systems Fuel Cells Bulletin Fuel Cell Review Ionics Interface International Journal of Hydrogen Energy Journal of The Electrochemical Society Journal of Power Sources Journal of Solid State Electrochemistry Journal of Applied Electrochemistry Journal of Electroceramics Journal of New Materials for Electrochemical Systems Journal of Electroanalytical Chemistry Journal of the Electrochemical Society of Japan Journal of the Korean Electrochemical Society Journal of the Bioelectrochemical Society Russian Journal of Electrochemistry (English Version) Solid State Ionics

4 REVIEW & PROCEEDINGS SERIES Current Topics in Electrochemistry, Electroanalysis, Electroanalytical Chemistry, Electrochemical Technology, The Electrochemical Society Frontiers of Electrochemistry, VCH Publishers Modern Aspects of Electrochemistry, Advances in Electrochemical Science and Engineering, Wiley-VCH Techniques of Electrochemistry Solid state ionics proceedings; MRS (Materials research Society) homepage The Electrochemical Society, proceedings; ECS homepage SOCIETIES The Electrochemical Society, Inc. (ECS) Electrochemical Society of Japan International Society of Electrochemistry (ISE) International Association for Hydrogen Energy (IAHE) Korean Electrochemical Society ( 한국전기화학회 ) International Battery Materials Association (IBA) International Society for Solid State Ionics National Hydrogen Association 공업화학회, 화학공학회, 화학회, 신재생학회, 부식학회 등등

5 HANDBOOKS Reference electrodes, theory and practice, D.J.G. Ives, NACE International, Encyclopedia of electrochemistry of the elements (15 volumes), A.J. Bard, Marcel Dekker, Atlas of electrochemical equilibria in aqueous solutions, M.J.N. Pourbaix, NACE, Kinetic parameters of electrode reactions of metallic compounds, R. Tamamushi, CRC handbook series in organic electrochemistry (6 volumes), L. Meites, CRC Press, Tables of standard electrode potentials, G. Milazzo and S. Caroli, Wiley, CRC handbook series in inorganic electrochemistry (8 volumes), L. Meites, CRC Press, Handbook of aqueous electrolyte solutions, A.L. Horvath, Chichester, Electrochemical synthesis of inorganic compounds, a bibliography, Z. Nagy, Plenum Press, Standard potentials in aqueous solutions, A.J. Bard, Marcell Dekker, Handbook of aqueous electrolyte thermodynamics, J.F. Zemaitis, AICE, Handbook of conducting polymers, 2 volumes, T.A. Skotheim (Ed), Marcel Dekker, Fuel cell handbook, A.J. Appleby, Krieger, Malabar, Handbook of electrolyte solutions (2 volumes), V.M.M. Lobo, Elsevier, Properties of aqueous solutions of electrolytes, I.D. Zaytsev, CRC Press, Boca Raton, CRC handbook of solid state electrochemistry, P.J. Gellings, CRC, Boca Raton, Handbook of organic conductive molecules and polymers (Vol. 1-4), H.S. Nalwa (Ed), Wiley, Handbook of conducting polymers (2nd ed), T.A. Skotheim, Marcel Dekker, Battery reference book (3rd ed), T.R. Crompton, Newnes, Uhlig's corrosion handbook (2nd ed), R.W. Revie (Ed), Wiley, Modern electroplating (4th ed), M. Schlesinger and M. Paunovic (Ed), Wiley, Handbook of batteries (3rd ed), D. Linden and T.B. Reddy (Ed), McGraw-Hill, Handbook of fuel cells: fundamentals, technology, applications, Vol. 1-4, W. Vielstich, Wiley, 03.

6 BOOKS A.J. Bard, L. R. Faulkner, Electrochemical Methods, Wiley, H. B. Oldham, J. C. Myland, Fundamentals of Electrochemical Science, Academic, D. B. Hibbert, Introduction to Electrochemistry, Macmillan, C. M. A. Brett, Electrochemistry, Oxford Univ. Press, D. T. Sawyer, A. Sobkowiak, J. L. Roberts, Electrochemistry for Chemists, Wiley, J. R. Macdonald, Impedance Spectroscopy, John Wiley & Sons, P. J. Gellings, H. J. M. Bouwmeester, Handbook of Solid State Electrochem., CRC, P. G. Bruce, Solid State Electrochemistry, Cambridge, Electrochemistry & Solid State Science, The Electrochemical Society, Koto, Solid State Electrochemistry & Its Applications to Sensors & Electronic Devices, Elsevier, H. Rickert, Electrochemistry of Solids, Springer-Verlag, N. Masuko, T. Osaka, Y. Ito, Electrochemical Technology, Gordon & Breach, D. Pletcher, F. C. Walsh, Industrial Electrochemistry, Blackie, 남종우 역, 현대의 전기화학, 청문각 T. Kudo, K. Fueki, Solid State Ionics, Kodansha/VCH, N. Sata, Electrochemistry at Metal & Semiconductor Electrodes, Elsevier, Other Electrochemical Information Electrochemical Science & Technology Information Resources:

7 Electronics: the transport of electrons (or positive holes) Optoelectronics: light + electronics Electrochemical system (electrodics + ionics) Electrochemistry: the coupling of chemical changes to the passage of electricity  ionic conduction (flow of ions) + electronic conduction (flow of electrons)  Electrochemical devices & electrochemical technologies  Materials & devices & processing What is electrochemistry?

8 Examples of Electrochemical devices/technologies Battery or Fuel cell: chemical state changes(electrochemistry)  electric power Photoelectrochemical cell (Solar cell): light + electrochemistry  electric power Photocatalysis: light  hydrogen or chemical reaction Electrochromic display: chemical state changes by electric signal  coloration Sensors: chemical state changes by mass  electric signal Electrolysis: electric power  chemical species by chemical state changes Electrodeposition: electric power  chemical change: thin film, Cu metallization Corrosion: potential difference  chemical change Etching Solid State Electrochemistry Solid electrolyte: solid substances which can conduct electric current by ionic motion as do electrolyte solutions  “solid state electrochemistry” or “solid state ionics”  “solid state device” Several distinct states may correspond to the same energy. That is, each energy level may be degenerate. Three energy levels are shown here, possessing one, three, and five distinct states.

9 Basic Concepts for Electrochemistry Electric charge & current Electric charge (=amount of electricity) Q (unit: Coulomb, C), time t Electric current (unit: ampere (A)): I = dQ/dt Q =  Idt Current density (unit: A/m2): i = I/A, A: surface of area Ammeter: measuring current Circuit: electric current flows in a closed path Electrical potential & electric field Electrical potential (unit; volts, V),  : the pressure of the electric fluid Voltage: the electrical potential difference (  ) Voltmeter: measuring an electrical potential difference Electric field strength (unit: V/m) X = -d  /dx

10 Ohm’s law: most conductors obey this law Current density is proportional to the field strength i  X i =  X = -  d  /dx  ; electrical conductivity (siemens/m, S = A/V), 1/  ; resistivity  = -RI R;resistance (unit of ohm), G; conductance, G = 1/R =  A/L = -I/  L; conductor length, A; cross section Ohm’s law does not have universal validity. It does not apply to electrochemical cells. Resistor: a device that is fabricated to have a stable and known resistance Power (watts) = I 2 R

11 Electrical quantities & their SI units QuantityUnit Current (I) Current density (i) Charge (Q) Charge density (  ) Potential (  ) Field strength (X) Conductivity (  ) Resistance (R) Conductance (G) Permittivity (  ) Energy of work (w) Power Capacitance (C) Ampere (A) Ampere per square meter (A/m 2 ) Coulomb (C = As) Coulomb per cubic meter (C/m 3 ) Volt (V = J/C) Volt per meter (V/m) Siemens per meter (S/m) Ohm (  =1/S = V/A) Siemens (S = A/V) Farad per meter (F/m = C/Vm) Joule (J = VC) Watt (W = J/s = AV) Farad (F = s/  = Ss), F = C/V

12 Classes of conductors Materials 1.Conductors Electronic conductors Ionic conductors 2. Insulators Conductors: metals Insulators: plastics, ceramics, gases No clear cut distinction between conductor and insulator Typical value of electrical conductivity S/m  x10 -2 for S/cm Material  /Sm -1 Ionic conductors Electronic conductors Ionic crystals Solid electrolytes Strong(liquid) electrolytes Metals Semiconductors Insulators – – – – 10 4 <10 -10

13 Material  /Sm -1 Charge carriers Electron pairs Electrons Pi electrons K + and Cl - H + and HSO 4 - Cations & anions Electrons and holes K + and Cl - H + and OH - Univalent cations ? Electrical conductivity of various materials (most at 298 K) Superconductors (low temp) Ag Cu Hg C (graphite) Doped polypyrrole Molten KCl (at 1043 K) 5.2 M H 2 SO 4 (battery acid) Seawater Ge 0.1 M KCl H 2 O Typical glass Teflon, (CF2)n Vacuum & most gases  6.3 x x x x x x x

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16 Electronically conductive polymers

17 Mobility: conduction from the standpoint of the charge carriers Electric current = rate at which charge crosses any plane = [number of carriers per unit volume][cross sectional area][charge on each carrier][average carrier speed] I = dQ/dt = (N A c i )(A)(Q i )( i ) i: particular charge carrier, c i ; concentration, Q i ; charge, i ; average velocity, N A ; Avogadro’s constant ( x mol -1 ), A; area z i ; charge number = Q i /Q e where Q e ( x C), e.g., electrons:-1, Mg 2+ ; +2 i  f i  X  d  /dx f i ; force exerted on the charge carrier, X; electric field strength

18 mobility of the carrier, u i (m 2 s -1 V -1 unit) = velocity to field ratio ( i / X) i =  u i X = - (z i /  z i  )u i d  /dx  z i  : absolute value of the charge number u e- of electrons: 6.7 x m 2 s -1 V -1 for Ag, less mobile in other metals mobility of ions in aqueous solution: smaller than the factor of 10 5 (factor 10 5 slower); u cu2+ o = 5.9 x m 2 s -1 V -1 in extremely diluted solution Current I, I = -A N A Q e  z i  u i c i d  /dx Faraday constant F = N A Q e = (6.02 x mol -1 )( x C) = Cmol -1

19 is numerically equal to the charge carried by one mole of univalent cations. (F is large. Small amount of chemicals higher electricity) If there are several kind of charge carriers, I = -AFd  /dx  z i  u i c i i = -Fd  /dx  z i  u i c i Transport number t i ; the fraction of the total current carried by one particular charge carrier t i = (  z i  u i c i )/  (  z i  u i c i ) From i =  X = -  d  /dx, conductivity   = F  z i  u i c i molar ionic conductivity ( i ); Fu i

20 Solid electrolyte: ions move under electric field without solvent → 전도도 존재 → batteries, fuel cells, and electrochemical devices Ionic mobilities at extreme dilution in aqueous solution at 298 K Grotthuss mechanism

21 Capacitance parallel conducting plate separated by a narrow gap containing air or insulator  Idt = Q   E Q = -C  E C; capacitance (unit; farads (F) = C/V) C = -Q/  E =  A/L A;cross-section area of the gap, L; width,  ; permittivity of the insulator Relative permittivity (  r ) or dielectric constant ( 유전상수 ) air: ~ 1 water: 78  Coulomb interaction energy is reduced by two orders of magnitudes from its vacuum value polar molecules:  r  refractive index: n r =  r 1/2 at the frequency Capacitor;  ; current integrator

22  /  0 ; relative permittivity or dielectric constant mylar; poly(ethylene glycol terephthalate), (CH 2 OOCC 6 H 4 COOCH 2 ) n Liquid > solid: large capacitance in electrochemical capacitor (supercapacitor) Material  /Fm -1 Material  /Fm -1 vacuum (  0 ) N 2 (g) Teflon(s), (CF 2 ) n CCl 4 (l) Polyethene (s) Mylar (s) SiO 2 (s) Typical glass (s) C 6 H 5 Cl(l) Neoprene ClC 2 H 4 Cl(l) CH 3 OH(l) C 6 H 5 NO 2 (l) CH 3 CN(l) H 2 O(l) HCONH 2 (l) TiO 2 (s) BaTiO 3 (s)  1500  Permittivity of various materials

23 Electricity flows either by electron motion or ion motion In both cases, the intensity of the flow (= current density)  electric field strength i =  X = -  d  /dx conductivity   = F  z i  u i c i determined by the concentration of charge carriers and their mobilities one form of Ohm’s law  E = -RI potential difference across resistor to the current flowing through it Resistor: dissipate energy Capacitor: store energy Summary

24 . Potential & Thermodynamics Introduction Electrochemistry: chemical change  electric force Electrodics: in which the reactions at electrodes are considered Ionics: in which the properties of electrolytes have the central attention  concentration of ions, their mobilities, interactions etc Basic laws were developed in systems with liquid electrolytes  “solid state” (same and different features of solid electrolyte system) Ionic solutions Most important ionic conductor e.g., aqueous solution of electrolyte Electrolyte; a substance that produces ions so enhance the electrical conductivity e.g., solid(NaCl), liquid(H 2 SO 4 ), gas(NH 3 ) cf) solid electrolyte

25 Electrode The junction between electronic conductor and ionic conductor that the chemistry of electrochemistry occurs Electrochemical cell Basic unit: an ionic conductor sandwiched between two electronic conductors e.g., aqueous solution of electrolyte between two pieces of metal, solid electrolyte between two metals

26 Cell voltage (E) or emf(electromotive force) electric potential difference between the two electronic conductors voltameter e.g., lead/acid cell (car battery) Electronic conductors: PbO 2, Pb Ionic conductor: concentrated aqueous solution of sulfuric acid

27 Electrochemical reaction Anode: Pb(s) + HSO 4 - (aq)  2e - + PbSO 4 (s) + H + (aq) Cathode: PbO 2 (s) + HSO 4 - (aq) + 3H + (aq) + 2e -  PbSO 4 (s) + 2H 2 O(l) Cell: PbO 2 (s) + Pb(s) + 2H + (aq) + 2HSO 4 - (aq)  2PbSO 4 (s) + 2H 2 O(l) Right-hand electrode: electrons produced: oxidation, “anode” Left-hand electrode: electrons consumed; reduction, “cathode” Energy is delivered by the cell into the load; ex) car: starting engine, lighting lamps Galvanic cell: a cell which provides energy in this way, “discharge”( 방전 ) 2.0 V without current flow, 1.8 V with current flow (load); “polarization”; voltages decrease in magnitude when energy is taken from them. the effect becomes greater if the current is increased.

28 “charge” ( 충전 ): current flow in the opposite direction by using an external source (ex. Battery); Electrolytic cell; opposite direction to its spontaneous motion PbO 2 : anode, Pb: cathode 2.0 V; perfect balance between the applied and cell voltages, no current flow  equilibrium cell voltage or reversible cell voltage or null voltage or rest voltage or “open-circuit voltage”(since no current flows, it makes no difference if the circuit is interrupted, as by opening the switch)

29 VVoltammogram A Plot of cell currents versus the cell voltages (volt + am(pere) + mogram) N O NNot linear  electrochemical cells do not obey Ohm’s law Notation of the structure of cells ZZn/Zn 2+, Cl - /AgCl/Ag HHg/Hg 2 Cl 2 /Cl - (aq)//Zn 2+ (aq)/Zn //: phase boundary, “,” or : two components in the same phase, ///: liquid junction (a salt bridge) lleft: oxidation (anode), right: reduction(cathode)

30 Thermodynamics Why is it that chemical reactions in electrochemical cells proceed spontaneously in one direction and furnish current? (thermodynamics: 평형상태에 대한 정보, kinetics: 전극반응속도에 대한 정보 ) : Cell potential of an electrochemical cell E cell = E right – E left or E cell = E cathode – E anode E obtained from the Nernst equation oO + …+ ne - = rR + …. (reduction) pP + …. = qQ + … + ne - (oxidation) oO + pP + … = qQ + rR + … E cell (cell reaction) E cell = E 0 – (RT/nF)ln[(a Q q a R r..)/(a O o a P p..)]

31 Gibbs free energy,  G = -nFE cell  G <0  spontaneous E 0 : standard electrode potential = E right 0 – E left 0 E right 0, E left 0,,: standard electrode potential of half reactions expresses as reductions vs. NHE(normal hydrogen electrode) with all species at unit activity (a i =1) (see the Table of Standard Potentials) e.g., MnO 2 + 4H + + 2e -  Mn H 2 O E 0 = V E = E 0 –(RT/2F)ln[(a H+ 4 )/a Mn2+ ], a MnO2, a H2O = unity  G = -nFE cf. RT/2F = [(8.314 JK -1 mol -1 )(298 K)/2(96485 JV -1 mol -1 )] = V

32 Several distinct states may correspond to the same energy. That is, each energy level may be degenerate. Three energy levels are shown here, possessing one, three, and five distinct states.

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34 ee.g., Zn/Zn 2+ (aq), Cu 2+ (aq)/Cu Ccell: Zn + Cu 2+  Zn 2+ + Cu Rright: Cu e -  Cu E 0 = V Left: Zn e -  Zn E 0 = V E cell 0 = – (-0.76) = V  G 0 = -2 x 1.10(V) x (JV -1 mol -1 ) = -212 kJmol -1 rreaction  spontaneous EE cell = E 0 – (RT/2F)ln(a Zn2+ /(a Cu2+ ) IIf we assume a Zn2+ = a Cu2+, E cell = 1.10 V HHg/Hg 2 Cl 2 /Cl - (aq)//Zn 2+ (aq)/Zn 2Hg + Cl - + Zn 2+  Hg 2 Cl 2 + Zn rright: Zn e -  Zn E 0 = V lleft: Hg 2 Cl 2 + 2e -  2Hg + 2Cl - E 0 = V EE cell 0 = –0.27 =-1.03 V,  G 0 = +199 kJmol -1, should be opposite direction

35 Measurement of E 0 : (i) experiment (ii) E 0 = (RT/nF)lnK, K; equilibrium constant of cell  K = exp(-  G 0 /RT) (iii) E 0 = E right 0 – E left 0 or E 0 = E cathode 0 – E anode 0 (from Table) (iv) E 0 = -  G 0 /nF Cell: PbO 2 (s) + Pb(s) + 2H + (aq) + 2HSO 4 - (aq)  2PbSO 4 (s) + 2H 2 O(l) From thermodynamics Table, Standard Gibbs Energy (kJmol -1 ): (PbSO 4 (s)), (H 2 O(l)), (PbO 2 (s)), (HSO 4 - (aq)), cf)  G 0 for element (Pb(s)) and H + (aq) = 0  G 0 = 2  G 0 (PbSO 4 (s)) + 2  G 0 (H 2 O(l)) – [  G 0 (PbO 2 (s)) + 2  G 0 (HSO 4 - (aq))] = -371 kJmol -1   G 0 = -nFE 0  E 0 = (Jmol -1 )/[2 x (JV -1 mol -1 )] = V battery acid: 5.2 M E cell = V – (RT/2F)ln[a H2O(l) 2 /(a H+(aq) 2 a HSO4-(aq) 2 )] = V – ln [1/(5.2) 2 ] = V

36 activity term: minor contribution to the cell voltage activity (a)  concentration (c); a =  c,  ; activity coefficient a i  1(solvent, pure solid, ideal solution) (Examples) 1. Indicate in the following reactions which are reductions and which are oxidations: (1) Fe e -  Fe (2) Cl -  1/2Cl 2 + e - (3) Fe 2+  Fe 3+ + e - (4) CrO e -  Cr 3+ (5) O 2 + 4e -  2O 2- (6) Br 2 + 2e -  2Br - 2. A Galvanic cell is constructed from a Cu 2+ /Cu electrode and an Ag + /Ag electrode. (1) Make a schematic drawing of the cell (2) Write the reactions at the electrode (3) Indicate the anode and the cathode 3. Assuming standard states for all reactants and products, determine the spontaneous direction of the following reactions by calculating the cell potential: (1) Cu + 2HCl = CuCl 2 + H 2 (2) Ag + FeCl 3 = FeCl 2 + AgCl

37 Definitions Two equal electrodes  interest in one electrode only Electrodes Working electrode(WE): electrode of interest Reference electrode(RE): second electrode, measure potential of WE with respect to RE Electrode potential E = E work –E ref Reference electrodes SHE (standard hydrogen electrode) or NHE(normal hydrogen electrode): universally accepted standard H + (aq, a=1) + e - = 1/2H 2 (g, 10 5 Pa) E = 0 V SCE (saturated calomel electrode) Hg 2 Cl 2 (s) + 2e - = 2Hg + Cl - E ref = V vs. NHE Ag/AgCl AgCl(s) + e - = Ag(s) + Cl - (aq) E ref = V with saturated KCl

38 Potentials of reference electrodes E(RHE) = E(NHE) pH E(SCE) = E(NHE) – E(Ag/AgCl) = E(NHE) – E(Ag/AgCl, sat.KCl) = E(NHE) – E(Hg/HgO 1M KOH) = E(NHE) – pH E(Hg/Hg 2 SO 4 ) = E(NHE) –

39 Potential vs. energy (vs. vacuum)

40 예 : Potential vs. energy (vs. vacuum)

41 Controlling potential of the working electrode with respect to the reference  controlling the energy of the electrons within the working electrode More negitive potential  energy of electrons is raised  reach a level to occupy vacant states (LUMO) on species in the electrolyte  flow of electrons from electrode to solution (a reduction current) More positive potential  electron flow from solution (HOMO) to electrode (oxidation current) Working electrode can act (i) as only a source (for reduction) or a sink (for oxidation) of electrons transferred to or from species in electrolyte (e.g., C, Au, Pt, Hg) or can (ii) take part in the electrode reaction, as in dissolution of a metal M (Zn  Zn e - )

42 Applying potential from its equilibrium (or its zero-current)

43 Polarization Voltammogram: historical one vs. new one E > 0  working electrode potential > 0 (positive: right of x-axis) I > 0  oxidation at the working electrode Polarization: the shift in the voltage across a cell caused by the passage of current Departure of the cell potential from the reversible(or equilibrium or nernstian) potential Ohmic polarization Activation polarization Concentration polarization Overvoltage (  ): the voltage shift caused by each kind of polarization Extent of potential measured by the overpotential:  = E - E eq E = E n +  ohm +  act +  conc

44 (i) ohmic polarization  ohm = IR sol, “IR drop” R sol = L/  A If free of activation & concentration polarization, slope = 1/R sol R sol = L/  A If free of activation & concentration polarization, slope = 1/R sol

45 Electrochemistry needs to minimize  ohm  (conductivity)   ohm  (by adding extra electrolyte: “supporting electrolyte”) three-electrode system two-electrode cell vs. three-electrode cell E appl = E + iR s = E eq +  + iR s IR s : ohmic drop in the solution (ohmic polarization)  should be minimized  short distance between working and reference electrode & three-electrode cell Two-electrode cell: iR s problem due to high current flow Three-electrode cell: current between WE and auxiliary electrode(or counter electrode) Potential measurement between WE and RE  almost no current to reference electrode  Potentiostat, etc electrochemical system: three electrode system

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47 (ii) activation polarization slow electrode reaction  activation polarization; slow kinetics  activation energy This can be overcome by increasing the temperature and by applying extra voltage (activation overvoltage (  act ))

48 (iii) concentration polarization from difference between the electrode surface and bulk concentration R  O + ne -  conc = E –E n = (RT/nF)ln[(c R b c O s )/c R s c O b ]] Limiting current Ideal polarizable electrode (totally polarized electrode): a very large change in potential upon small current Ideal nonpolarizable electrode: potential does not change upon passage of current (e.g., reference electrode)

49 Semiconductor electrode Semiconductor/electrolyte  space charge region due to space charge capacity, C sc, ~ 1  Fcm -2, (cf; C dl = 10 ~ 100  Fcm -2 )  band bending n-type SC when E F of SC lies above that in electrolyte  electron flow from SC (positively charged) to electrolyte (negatively charged)  bent upward by applying potential of  bulk =  surface, band bending & space charge region disappear  “flat band potential (  fb or E fb )”

50 space charge capacitance C sc  Mott-Schottly equation 1/C sc 2 = (2/e  0 N) 1/2 (-  - kT/e)  : dielectric constant, N: donor or acceptor densities, e: quantity of charge, -  = E-E fb A plot of 1/C sc 2 vs. potential E should be linear  E fb, doping level N

51 p-type p-type


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