Fall 4582 608 4582-608
Electrochemical Energy Engineering 전기화학에너지공학
전기화학에너지공학
LECTURER: Yung-Eun Sung (성영은) LECTURER: Yung-Eun Sung (성영은)
Office: Rm #729, Phone: 880-1889, E-mail: ysung@snu.ac.kr homepage: http://pin.snu.ac.kr/~peel p g p p p
OUTLINE
Thi l d l i h l h i l i i l f h l h i l
This class deals with electrochemical principles of the electrochemical energy devices and systems such as fuel cells, batteries & solar cells
and so on It teaches the electrode electrolyte and electrode/electrolyte and so on. It teaches the electrode, electrolyte, and electrode/electrolyte interfaces, double-layer structure & adsorption, electroactive layers &
modified electrodes, electrochemical instrumentation, scanning probe g p
techniques, spectroelectrochemistry, and photoelectrochemistry.
TEXTBOOK & REFERENCES
A J Bard L R Faulkner Electrochemical Methods Wiley 2001 A.J. Bard, L. R. Faulkner, Electrochemical Methods, Wiley, 2001.
SCHEDULES
B i t f l t h i t
Basic concept of electrochemistry
Principles of electrochemistry: thermodynamics, kinetics, mass transfer Double-layer structure & adsorption
Double layer structure & adsorption
Electroactive layers & modified electrodes Scanning probe techniques
Spectroelectrochemistry Photoelectrochemistry
GRADING
Midterm Exam 40%
Final Exam 40%
Homework & Attendance 20 %
LECTURE: Rm #302-620, 11:00-12:15 Tue. & Thurs.
Electrochemical Energy Engineering, Fall 2011
Fall, 2011
Basic concept of electrochemistry
Basic concept of electrochemistry
El t i th t t f l t ( iti h l )
What is electrochemistry?
• Electronics: the transport of electrons (or positive holes) Optoelectronics: light + electronics
• Electrochemical system: electrodics + ionics
• Electrochemistry:
th li f h i l h t th f l t i it
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 & process
• Examples of Electrochemical devices/technologies Examples of Electrochemical devices/technologies
Battery or Fuel cell: chemical state changes(electrochemistry) → electric power Supercapacitor: double layer phenomena → electric power
Photoelectrochemical cell (Solar cell): light + 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
S h i l t t h b → l t i i l
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 Electrochemical synthesis: electric power → chemical change
Corrosion: potential difference → chemical change Etching
• Solid State Electrochemistry
Solid electrolyte: solid substances which can conduct electric current by ionic y y
motion as do electrolyte solutions → “solid state electrochemistry” or “solid state ionics” → “solid state device”
Basic concepts for electrochemistry
Electric charge & current
Electric charge (=amount of electricity), q (unit: Coulomb, C), time t Electric c rrent I ( nit: ampere (A)):
Electric current, I (unit: ampere (A)):
I = dq/dt q = ∫ Idt
Current density (unit: A/cm2): i = I/A, A: surface of area Ammeter: measuring current
Circuit: electric current flows in a closed pathp Electrical potential & electric field
Electrical potential (unit; volts V) φ: the pressure of the electric fluid Electrical potential (unit; volts, V), φ: the pressure of the electric fluid Voltage: the electrical potential difference (Δφ)
Voltmeter: measuring an electrical potential difference Electric field strength X (unit: V/m)
Electric field strength, X (unit: V/m)
X = -dφ/dx
Ohm’s law: most conductors obey this law
Current density is proportional to the field strength Current density is proportional to the field strength
i ∝ X
i X dφ/d
i = κX = -κ dφ/dx
κ; electrical conductivity (siemens/m, S = A/V), 1/κ; resistivity Δφ = -RI
R; resistance (unit of ohm), G; conductance,
G = 1/R = κA/L = -I/Δφ G 1/R κA/L I/Δφ L; conductor length, A; cross section
Ohm’s law does not have universal validity It does not apply to electrochemical 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) = I2R
Electrical quantities & their SI unitsq
Quantity Unit
Quantity Unit
Current (I) Current density (i)
Ampere (A)
Ampere per square meter (A/m2) Current density (i)
Charge (q) Charge density (ρ)
P t ti l (φ)
Ampere per square meter (A/m2) Coulomb (C = As)
Coulomb per cubic meter (C/m3) V lt (V J/C)
Potential (φ) Field strength (X)
Conductivity (κ)
Volt (V = J/C) Volt per meter (V/m) Siemens per meter (S/m) Resistance (R)
Conductance (G) Permittivity (ε)
Ohm (Ω =1/S = V/A) Siemens (S = A/V)
Farad per meter (F/m = C/Vm) y ( )
Energy of work (w) Power
Capacitance (C)
p ( )
Joule (J = VC) Watt (W = J/s = AV)
Farad (F = s/Ω = Ss), F = C/V Capacitance (C) Farad (F s/Ω Ss), F C/V
Classes of conductors
Materials 1 Conductors Electronic 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 conductivityyp y
Material κ/Sm-1
Ionic conductors Ionic crystals Solid electrolytes
Strong(liquid) electrolytes
10-16 – 10-2 10-1 – 103 10-1 – 103
Electronic conductors Metals
Semiconductors Insulators
103 – 107 10-3 – 104
<10-10
S/m → x10-2 for S/cm
Electrical conductivity of various materials (most at 298 K)
Material κ/Sm-1 Charge carriers
Electron pairs Electrons
Electrons Superconductors (low temp)
Ag Cu
∞ 6.3 x 107
6 0 x 107 Electrons
Electrons Pi electrons Pi electrons Cu
Hg
C (graphite)
Doped polypyrrole
6.0 x 107 1.0 x 106 4 x 104
6 x 103 Pi electrons K+ and Cl- H+ and HSO4- C i & i Doped polypyrrole
Molten KCl (at 1043 K) 5.2 M H2SO4 (battery acid) Sea water
6 x 10 217
82
5.2 Cations & anions Electrons and holes K+ and Cl-
Sea water Ge
0.1 M KCl H2O
5.2 2.2 1.3 5.7 x 10-6
H+ and OH-
Univalent cations
?
2
Typical glass Teflon, (CF2)n
Vacuum & most gases
3 x 10-10 10-15
0 g
S/m → x10-2 for S/cm
Electronically conductive polymers
Mobilities: 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 = (Nq ( AA ici)(A)(q)( )(qii)(ν)( ii))
i: particular charge carrier ci; concentration qi; charge νi; average velocity i: particular charge carrier, ci; concentration, qi; charge, νi; average velocity, NA; Avogadro’s constant (6.02 x 1023 mol-1), A; area
zi; charge number = qi/qe where qe(1.6022 x 10-19 C), e g electrons: 1 Mg2+; +2
e.g., electrons:-1, Mg2+; +2
νi ∝ fi ∝ X ∝ dφ/dx
fi; force exerted on the charge carrier, X; electric field strength
mobility of the carrier, ui (m2s-1V-1 unit) = velocity to field ratio (νi / X) mobility of the carrier, ui (m s V unit) velocity to field ratio (νi / X)
νi = ±uiX = - (zi/⏐zi⏐)uidφ/dx
⏐zi⏐: absolute value of the charge number
f l t 6 7 10-3 2 -1V-1 f A l bil i th t l ue- of electrons: 6.7 x 10-3 m2s-1V-1 for Ag, less mobile in other metals
mobility of ions in aqueous solution: smaller than the factor of 105 (factor 105
8 2 1 1
slower); ucu2+o = 5.9 x 10-8 m2s-1V-1 in extremely diluted solution Current I,
I = -A NAqe⏐zi⏐uicidφ/dx Faraday constant
F = N q = (6 02 x 1023 mol-1)(1 6022 x 10-19 C) = 96485 Cmol-1 F NAqe (6.02 x 10 mol )(1.6022 x 10 C) 96485 Cmol
Faraday constant 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 = -AFdφ/dxΣ⏐z ⏐u c I -AFdφ/dxΣ⏐zi⏐uici
i = -Fdφ/dxΣ⏐zi⏐uici
Transport number ti; the fraction of the total current carried by one particular charge carrier
(⏐ ⏐ )/Σ(⏐ ⏐ ) ti = (⏐zi⏐uici )/Σ(⏐zi⏐uici) From i = κX = -κdφ/dx, conductivity κ
κ = FΣ⏐zi⏐uici molar ionic conductivity (λi); Fui
Ion mobilities at extreme dilution in aqueous solution at 298 K Ion mobilities at extreme dilution in aqueous solution at 298 K
/ 2 1 1
Ion uo/m2s-1V-1
H+ 362.5 x 10-9
K+ Ag+ Cu2+
76.2 x 10-9 64.2 x 10-9 58.6 x 10-9 Na+
Li+ OH-
51.9 x 10-9 40.1 x 10-9 204.8 x 10-9 OH
SO42- Cl- ClO -
204.8 x 10 82.7 x 10-9 79.1 x 10-9 69 8 x 10-9 ClO4
C6H5COO-
69.8 x 10 9 33.5 x 10-9 cf u of electrons: 6 7 x 10-3 m2s-1V-1 for Ag
cf. ue- of electrons: 6.7 x 10 3 m2s 1V1 for Ag
Capacitance
parallel conducting plate separated by a narrow gap containing air or insulator parallel conducting plate separated by a narrow gap containing air or insulator
∫ Idt = q ∝ ΔE q = -CΔE C; capacitance (unit; farads (F) = C/V)
C = -q/ΔE = εA/L
A; cross-section area of the gap, L; width, ε; permittivity of the insulator
• Relative permittivity (εp y ( rr) or dielectric constant (유전상수)) ( ) air: ~ 1
water: 78 → Coulomb interaction energy is reduced by two orders of magnitudes from its vacuum value
from its vacuum value polar molecules: εr↑
refractive index: nr = εr1/2at the frequency Capacitor; ⎯⏐⏐⎯ ; current integrator
P itti it f i t i l
Material 1012 ε/Fm-1 Material 1012 ε/Fm-1
Permittivity of various materials
vacuum (ε0) 8.85419 Neoprene 58
vacuum (ε0) N2(g)
Teflon(s), (CF2)n CCl (l)
8.85419 8.85905 18
19 7
Neoprene ClC2H4Cl(l) CH3OH(l) C H NO (l)
58 91.7 288.9 308 3 CCl4(l)
Polyethene (s) Mylar (s)
SiO ( )
19.7 20 28 38 1
C6H5NO2(l) CH3CN(l) H2O(l)
HCONH (l)
308.3 332 695.4 933 SiO2(s)
Typical glass (s) C6H5Cl(l)
38.1 44 49.8
HCONH2(l) TiO2(s)
BaTiO3(s)
933≤1500
≤110000 ε/ε0; relative permittivity or dielectric constant
mylar; poly(ethylene glycol terephthalate), (CH22OOCC66H44COOCH22 n)n
Liquid > solid: large capacitance in electrochemical capacitor (supercapacitor)
Electricity flows either by electron motion or ion motion
Summary
Electricity flows either by electron motion or ion motion In both cases,
the intensity of the flow (= current density) ∝ electric field strength i = κX = -κdφ/dx
conductivity κ
κ = FΣ⏐zi⏐uici
determined by the concentration of charge carriers and their mobilities one form of Ohm’s law
ΔE = -RI
potential difference across resistor to the current flowing through it potential difference across resistor to the current flowing through it Resistor: dissipate energy
Capacitor: store energy Capacitor: store energy
. Potential & Thermodynamics
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”
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
El t l t b t th t d i h th l t i l
Electrolyte; a substance that produces ions so enhance the electrical conductivity
e.g., solid(NaCl), liquid(H2SO4), gas(NH3) cf) solid electrolyte
Electrode
The junction between electronic conductor and ionic conductor that the chemistry of electrochemistry occursy y
Electrochemical cell
Basic unit: an ionic conductor sandwiched between two electronic conductors 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
Cell voltage (E) or emf(electromotive force)
electric potential difference between the two electronic conductors electric potential difference between the two electronic conductors voltameter
l d/ id ll ( b )
e.g., lead/acid cell (car battery) Electronic conductors: PbO2, Pb
Ionic conductor: concentrated aqueous solution of sulfuric acid
Electrochemical reaction Electrochemical reaction
Anode: Pb(s) + HSO4-(aq) → 2e- + PbSO4(s) + H+(aq)
Cathode: PbO (s) + HSO -(aq) + 3H+(aq) + 2e- → PbSO (s) + 2H O(l) Cathode: PbO2(s) + HSO4 (aq) + 3H (aq) + 2e → PbSO4(s) + 2H2O(l) Cell: PbO2(s) + Pb(s) + 2H+(aq) + 2HSO4-(aq) → 2PbSO4(s) + 2H2O(l)
Ri ht h d l t d l t d d id ti “ d ”
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”;, ( ); p ; voltages decrease in magnitude when energy is taken from them. the effect becomes greater if the current is increased.
“charge” (충전): current flow in the opposite direction by using an external
( B ) El l i ll i di i i
source (ex. Battery); Electrolytic cell; opposite direction to its spontaneous motion
PbO2 : 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)
Voltammogram
Plot of cell currents versus the cell voltages (volt + am(pere) + mogram) Plot of cell currents versus the cell voltages (volt + am(pere) + mogram)
Not linear → electrochemical cells do not obey Ohm’s law
Notation of the structure of cells
Zn/Zn2+ Cl-/AgCl/Ag Zn/Zn2 , Cl /AgCl/Ag
Hg/Hg2Cl2/Cl-(aq)//Zn2+(aq)/Zn
/: phase boundary, “,” or : two components in the same phase, // li id j ti ( lt b id )
//: liquid junction (a salt bridge)
left: oxidation (anode), right: reduction(cathode)
Thermodynamics
Why is it that chemical reactions in electrochemical cells proceed spontaneously in one direction and furnish current?
(thermodynamics: 평형상태에 대한 정보, kinetics: 전극반응속도에
( y
대한 정보) :
Cell potential of an electrochemical cell Cell potential of an electrochemical cell
Ecell = Eright – Eleft
or E = E – E
or Ecell = Ecathode – Eanode E obtained from the Nernst equation
oO + …+ ne- = rR + …. (reduction) pP + …. = qQ + … + ne- (oxidation)
oO + pP + … = qQ + rR + … Ecell (cell reaction)
Ecell = E0 – (RT/nF)ln[(aQqaRr..)/(aOoaPp..)]
Gibbs free energy, ΔG = -nFEcell ΔG <0 → spontaneous
E0: standard electrode potential = Eright0 – Eleft0
E 0 E 0 : standard electrode potential of half reactions expresses as reductions Eright0, Eleft0,,: standard electrode potential of half reactions expresses as reductions vs. NHE(normal hydrogen electrode) with all species at unit activity (ai =1)
( th T bl f St d d P t ti l ) (see the Table of Standard Potentials)
e.g., MnO2 + 4H+ + 2e- → Mn2+ + 2H2O E0 = + 1.23 V
E = E0 –(RT/2F)ln[(aH+4)/aMn2+], aMnO2, aH2O = unity ΔG = -nFE
cf. RT/2F = [(8.314 JK-1mol-1)(298 K)/2(96485 JV-1mol-1)] = 0.01285 V
e.g., Zn/Zn2+(aq), Cu2+(aq)/Cu Cell: Zn + Cu2+ → Zn2+ + Cu
Right: Cu2+ + 2e- → Cu E0 = +0.34 V Left: Zn2+ + 2e- → Zn E0 = -0.76 V
Ecell0 = +0.34 – (-0.76) = +1.10 V
ΔΔG0 = -2 x 1.10(V) x 96485 (JV( ) ( -1mol-1) = -212 kJmol) -1 reaction → spontaneous
EEcell = E0 – (RT/2F)ln(aZn2+/(aCu2+) If we assume aZn2+= aCu2+, Ecell = 1.10 V
---
Hg/Hg Cl /Cl-(aq)//Zn2+(aq)/Zn Hg/Hg2Cl2/Cl (aq)//Zn (aq)/Zn 2Hg + Cl- + Zn2+ → Hg2Cl2 + Zn
i ht Z 2+ + 2 → Z E0 0 76 V right: Zn2+ + 2e- → Zn E0 = -0.76 V
left: Hg2Cl2 + 2e- → 2Hg + 2Cl- E0 = +0.27 V
0 0 1
Ecell0 = -0.76 –0.27 =-1.03 V, ΔG0 = +199 kJmol-1, should be opposite direction
Measurement of E0:
(i) i t
(i) experiment
(ii) E0 = (RT/nF)lnK, K; equilibrium constant of cell ← K = exp(-ΔG0/RT) (iii) E0 = Eright0 – Eleft0 or E0 = Ecathode0 – Eanode0 (from Table)
0 0
(iv) E0 = -ΔG0/nF
Cell: PbO22(s) + Pb(s) + 2H+(aq) + 2HSO44-(aq) → 2PbSO44(s) + 2H22O(l) From thermodynamics Table,
Standard Gibbs Energy (kJmolgy ( -1): -813.76 (PbSO) ( 44(s)), -237.13 (H( )), ( 22O(l)), -218.96( )), (PbO2(s)), -755.91 (HSO4-(aq)), cf) ΔG0 for element (Pb(s)) and H+(aq) = 0
ΔG0 = 2ΔG0 (PbSO (s)) + 2ΔG0 (H O(l)) – [ΔG0 (PbO (s)) + 2ΔG0 (HSO -(aq))]
ΔG 2ΔG (PbSO4(s)) + 2ΔG (H2O(l)) [ΔG (PbO2(s)) + 2ΔG (HSO4 (aq))]
= -371 kJmol-1
→ ΔG0 = -nFE0
→ E0 = 371000(Jmol-1)/[2 x 96485 (JV-1mol-1)] = 1 923 V
→ E0 = 371000(Jmol 1)/[2 x 96485 (JV1mol 1)] = 1.923 V battery acid: 5.2 M
Ecell = 1.923 V – (RT/2F)ln[aH2O(l)2/(aH+(aq)2aHSO4-(aq)2)]
1 923 V 0 01285l [1/(5 2)2] 2 008 V
= 1.923 V – 0.01285ln [1/(5.2)2] = 2.008 V
activity term: minor contribution to the cell voltage
activity (a)y ( ) → concentration (c); a = γc, γ; activity coefficient( ); γ , γ; y ai ≅ 1(solvent, pure solid, ideal solution)
(Examples) (Examples)
1. Indicate in the following reactions which are reductions and which are oxidations:
(1) Fe2+ + 2e- → Fe (2) Cl- → 1/2Cl2 + e- (3) Fe2+ → Fe3+ + e- (4) CrO42- + 3e- → Cr3+ (5) O2 + 4e- → 2O2- (6) Br2 + 2e- → 2Br-
( ) 4 ( ) 2 ( ) 2
2. A Galvanic cell is constructed from a Cu2+/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
di i f h f ll i i b l l i h ll i l
direction of the following reactions by calculating the cell potential:
(1) Cu + 2HCl = CuCl2 + H2
(2) Ag + FeCl3 = FeCl2 + AgCl
Two equal electrodes → interest in one electrode only Electrodes
Electrodes
Working electrode(WE): electrode of interest
Reference electrode(RE): second electrode, measure potential of WE with respect to RE
to RE
Electrode potential E = Ework –Eref
R f l t d
Reference electrodes
SHE (standard hydrogen electrode) or NHE(normal hydrogen electrode):
universally accepted standard
H+(aq, a=1) + e- = 1/2H2(g, 105 Pa) E = 0 V SCE (saturated calomel electrode)( )
Hg2Cl2(s) + 2e- = 2Hg + Cl- Eref = 0.244 V vs. NHE Ag/AgCl
AgCl(s) + e- = Ag(s) + Cl-(aq) E f = 0.199 V with saturated KCl AgCl(s) e Ag(s) Cl (aq) Eref 0.199 V with saturated KCl
Potentials of reference electrodes E(RHE) = E(NHE) + 0 05916pH E(RHE) E(NHE) + 0.05916pH E(SCE) = E(NHE) – 0.2444
E(Ag/AgCl) = E(NHE) – 0.2223
E(Ag/AgCl sat KCl) = E(NHE) 0 196 E(Ag/AgCl, sat.KCl) = E(NHE) – 0.196
E(Hg/HgO 1M KOH) = E(NHE) – 0.1100 + 0.05946pH E(Hg/Hg2SO4) = E(NHE) – 0.6152
Potential vs energy (vs vacuum) Potential vs. energy (vs. vacuum)
예: Potential vs energy (vs vacuum) 예: Potential vs. energy (vs. vacuum)
Controlling potential of the working electrode with respect to the reference → Controlling potential of the working electrode with respect to the reference → controlling the energy of the electrons within the working electrode
M iti t ti l f l t i i d h l l t
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 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 → Zn2+ + 2e-)
Applying potential from its equilibrium (or its zero-current)
Polarization
V l hi i l
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 Departure of the cell potential from the reversible(or equilibrium or nernstian) potential
Ohmic polarization Activation polarization Activation polarization Concentration polarization
O lt ( ) th lt hift d b h ki d f l i ti
Overvoltage (η): the voltage shift caused by each kind of polarization Extent of potential measured by the overpotential: η = E – Eeq
E = En + ηohm + ηact + ηconc
(i) ohmic polarization
( ) p
ηohm = IRsol, “IR drop”
If free of activation & concentration polarization slope = 1/R
Rsol= L/κA If free of activation & concentration polarization, slope = 1/Rsol
Rsol = L/κA
If free of activation & concentration polarization, slope = 1/R l If free of activation & concentration polarization, slope 1/Rsol
Electrochemistry needs to minimizey ηηohmohm
κ (conductivity) ↑→ ηohm ↓ (by adding extra electrolyte: “supporting electrolyte”)
three-electrode system three electrode system
two-electrode cell vs. three-electrode cell
Eappl = E + iRs = Eeq + η + iRs
IR h i d i th l ti ( h i l i ti ) h ld b i i i d
IRs: ohmic drop in the solution (ohmic polarization) → should be minimized → short distance between working and reference electrode & three-electrode cell Two-electrode cell: iRs 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
(ii) activation polarization
slow electrode reaction → activation polarization; slow kinetics ∝ activation slow electrode reaction → activation polarization; slow kinetics ∝ activation energy
This can be overcome by increasing the temperature and This can be overcome by increasing the temperature and
by applying extra voltage (activation overvoltage (ηact))
(iii) concentration polarization
( ) p
from difference between the electrode surface and bulk concentration R → O + ne-
η = E –E = (RT/nF)ln[(cRbcOs)/cRscOb]]
ηconc E En (RT/nF)ln[(cR cO )/cR cO ]]
Limiting current
Ideal polarizable electrode (totally polarized electrode): a very large change in 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
( f l t d )
(e.g., reference electrode)
D bl l
Double layer
Electrode-solution interface → capacitor “double layer”
Same concept as capacitor (two metal sheets separated with q (coulomb)/E = C(farad)) ))
qM = -qS
qM: charge from electrons in metal electrode qS: charge from ions in solution qM: charge from electrons in metal electrode, qS: charge from ions in solution charge density σM =qM/A (μC/cm2)
double layer capacitance, cd: 10 ~ 40 μF/cm2
l d l H l h l G Ch S G h d l
several models: Helmholtz, Gouy-Chapman, Stern, Grahame model etc
Grahame model: IHP (inner Helmholtz plane, specifically adsorbed anion) + OHP (outer HP solvated cation) + diffuse layer
OHP (outer HP, solvated cation) + diffuse layer
Electrochemical systems in terms of circuit elements Electrochemical systems in terms of circuit elements e.g.,) Hg/K+, Cl-/SCE, Hg: ideal polarized electrode
CSCE, Cd: capacitances of SCE and double layer, Rs: solution resistor CT = CSCECd/(CSCE + Cd), CSCE>> Cd → CT ≈ Cd → RC circuit
) l i l ( i l)
e.g.,) applying voltage (or potential) step:
potential step: E, EC of capacitor, ER of resistor q = CdEC
E = ER + EC = iRs + q/Cd i = dq/dt
dq/dt = -q/(Rq q ( ssCdd) + E/R) ss
q =0 at t = 0 → q = ECd[1 – exp(-t/RsCd)]
By differentiating,
I = (E/R )exp(-t/R Cd) I (E/Rs)exp( t/RsCd)
At time constant τ = RsCd → current for charging the double layer capacitance drops to
37 % at τ = t 5 % at τ = 3t 37 % at τ = t, 5 % at τ = 3t
e g ) R = 1 Ω C = 20 μF τ = 20 μsec → double layer charging is 95 % e.g.,) Rs 1 Ω, Cd 20 μF, τ 20 μsec → double layer charging is 95 % complete in 60 μsec
Double layer charging process: “non-faradaic process”
Cf) oxidation /reduction) → electron transfer ; governed by Faraday’s law (the; g y y ( amount of chemical reaction caused by the flow of current is proportional to the amount of electricity passed) → “faradaic process” or “charge transfer process”
Semiconductor electrode Semiconductor electrode
Semiconductor/electrolyte → space charge region due to space charge capacity, Csc, 0.001 ~ 1 μFcm-2, (cf; Cdl = 10 ~ 100 μFcm-2 ) → band bending
n-type SC
when EF of SC lies above that in electrolyte → electron flow from SC (positively when EF of SC lies above that in electrolyte → electron flow from SC (positively charged) to electrolyte (negatively charged) → bent upward
by applying potential of φbulk = φsurface, band bending & space charge region disappear → “flat band potential (φ or E )”
disappear → flat band potential (φfb or Efb)
space charge capacitance C → Mott-Schottly equation space charge capacitance Csc → Mott Schottly equation
1/Csc2 = (2/eεε0N)1/2(-Δφ - kT/e)
ε: dielectric constant, N: donor or acceptor densities, e: quantity of charge, -Δφ = E-Efb
A plot of 1/Csc2 vs. potential E should be linear → Efb, doping level N
M S h k l f d I P
Mott-Schottky plots for n- and p-type InP in 1 M KCl + 0.01 M HCl
p-type