전기화학에너지공학

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 i}c_i)(A)(q)( )(q_ii)(ν)( _ii))

i: particular charge carrier c_i; concentration q_i; charge ν_i; average velocity i: particular charge carrier, c_i; concentration, q_i; charge, ν_i; average velocity, N_A; Avogadro’s constant (6.02 x 10²³ mol^-1), A; area

z_i; charge number = q_i/q_e where q_e(1.6022 x 10^-19 C), e g electrons: 1 Mg²⁺; +2

e.g., electrons:-1, Mg²⁺; +2

ν_i ∝ f_i ∝ X ∝ dφ/dx

f_i; force exerted on the charge carrier, X; electric field strength

mobility of the carrier, u_i (m²s^-1V^-1 unit) = velocity to field ratio (ν_i / X) mobility of the carrier, u_i (m s V unit) velocity to field ratio (ν_i / X)

ν_i = ±u_iX = - (z_i/⏐z_i⏐)u_idφ/dx

⏐z_i⏐: absolute value of the charge number

f l t 6 7 10^{-3 2 -1}V^-1 f A l bil i th t l u_e- 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); u_cu2+^o = 5.9 x 10^-8 m²s^-1V^-1 in extremely diluted solution Current I,

I = -A N_Aq_e⏐z_i⏐u_ic_idφ/dx Faraday constant

F = N q = (6 02 x 10²³ mol^-1)(1 6022 x 10^-19 C) = 96485 Cmol^-1 F N_Aq_e (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⏐z_i⏐u_ic_i

i = -Fdφ/dxΣ⏐z_i⏐u_ic_i

Transport number t_i; the fraction of the total current carried by one particular charge carrier

(⏐ ⏐ )/Σ(⏐ ⏐ ) t_i = (⏐z_i⏐u_ic_i )/Σ(⏐z_i⏐u_ic_i) From i = κX = -κdφ/dx, conductivity κ

κ = FΣ⏐z_i⏐u_ic_i molar ionic conductivity (λ_i); Fu_i

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 u^o/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

SO₄^2- 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. u_e- 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: ε_r↑

refractive index: n_r = ε_r^1/2at 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), (CH₂₂OOCC₆₆H₄₄COOCH_{22 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⏐z_i⏐u_ic_i

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

E_cell = E_right – E_left

or E = E – E

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 = E⁰ – (RT/nF)ln[(a_Q^qa_R^r..)/(a_O^oa_P^p..)]

Gibbs free energy, ΔG = -nFE_cell ΔG <0 → spontaneous

E⁰: standard electrode potential = E_right⁰ – E_left⁰

E ⁰ E ⁰ : standard electrode potential of half reactions expresses as reductions E_right⁰, E_left⁰,,: standard electrode potential of half reactions expresses as reductions vs. NHE(normal hydrogen electrode) with all species at unit activity (a_i =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[(a_H+⁴)/a_Mn2+], a_MnO2, a_H2O = 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

E_cell⁰ = +0.34 – (-0.76) = +1.10 V

ΔΔG⁰ = -2 x 1.10(V) x 96485 (JV( ) ( ^-1mol^-1) = -212 kJmol) ^-1 reaction → spontaneous

EE_cell = E⁰ – (RT/2F)ln(a_Zn2+/(a_Cu2+) If we assume a_Zn2+= a_Cu2+, E_cell = 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

E_cell⁰ = -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 = E_right⁰ – E_left⁰ or E⁰ = E_cathode⁰ – E_anode⁰ (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

E_cell = 1.923 V – (RT/2F)ln[a_H2O(l)²/(a_H+(aq)²a_HSO4-(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 a_i ≅ 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) CrO₄^2- + 3e^- → Cr³⁺ (5) O₂ + 4e^- → 2O^2- (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 = E_work –E_ref

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^- E_ref = 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) E_ref 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 – E_eq

E = En + η_ohm + η_act + η_conc

(i) ohmic polarization

( ) p

η_ohm = IR_sol, “IR drop”

If free of activation & concentration polarization slope = 1/R

R_sol= L/κA If free of activation & concentration polarization, slope = 1/R_sol

R_sol = L/κA

If free of activation & concentration polarization, slope = 1/R _l If free of activation & concentration polarization, slope 1/R_sol

Electrochemistry needs to minimizey ηη_ohmohm

κ (conductivity) ↑→ η_ohm ↓ (by adding extra electrolyte: “supporting electrolyte”)

three-electrode system three electrode system

two-electrode cell vs. three-electrode cell

E_appl = E + iR_s = E_eq + η + iR_s

IR h i d i th l ti ( h i l i ti ) h ld b i i i d

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

(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 (η_act))

(iii) concentration polarization

( ) p

from difference between the electrode surface and bulk concentration R → O + ne^-

η = E –E = (RT/nF)ln[(c_R^bc_O^s)/c_R^sc_O^b]]

η_conc E E_n (RT/nF)ln[(c_R c_O )/c_R c_O ]]

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)) ))

q^M = -q^S

q^M: charge from electrons in metal electrode q^S: charge from ions in solution q^M: charge from electrons in metal electrode, q^S: charge from ions in solution charge density σ^M =q^M/A (μC/cm²)

double layer capacitance, c_d: 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

C_SCE, C_d: capacitances of SCE and double layer, R_s: solution resistor C_T = C_SCEC_d/(C_SCE + C_d), C_SCE>> C_d → C_T ≈ C_d → RC circuit

) l i l ( i l)

e.g.,) applying voltage (or potential) step:

potential step: E, E_C of capacitor, E_R of resistor q = C_dE_C

E = E_R + E_C = iR_s + q/C_d i = dq/dt

dq/dt = -q/(Rq q ( _ssC_dd) + E/R) _ss

q =0 at t = 0 → q = EC_d[1 – exp(-t/R_sC_d)]

By differentiating,

I = (E/R )exp(-t/R C_d) I (E/R_s)exp( t/R_sC_d)

At time constant τ = R_sC_d → 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.,) R_s 1 Ω, C_d 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, C_sc, 0.001 ~ 1 μFcm^-2, (cf; C_dl = 10 ~ 100 μFcm^-2 ) → band bending

n-type SC

when E_F of SC lies above that in electrolyte → electron flow from SC (positively 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 φ_bulk = φ_surface, band bending & space charge region disappear → “flat band potential (φ or E )”

disappear → flat band potential (φ_fb or E_fb)

space charge capacitance C → Mott-Schottly equation space charge capacitance C_sc → Mott Schottly equation

1/C_sc² = (2/eεε₀N)^1/2(-Δφ - kT/e)

ε: dielectric constant, N: donor or acceptor densities, e: quantity of charge, -Δφ = E-E_fb

A plot of 1/C_sc² vs. potential E should be linear → E_fb, 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

p-type