fundamentals of...

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Fundamentals of Electrochemistry

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1. Distinctive Concepts in Electrochemistry 2. Thermodynamics and Kinetics

in Electrochemistry

3. Electrode potentials

4. Ions in solution: electrolytes

5. Electrochemical kinetics

6. Electrochemical cells

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Heterogeneous charge transfer reaction; Electron tunneling at electrode/solution interface

Cu2+ + 2e → Cu0 (electrochemical reduction)

Fe2+ → Fe3+ + e (electrochemical oxidation)

Anode (산화전극): electrochemical oxidation Cathode (환원전극): electrochemical reduction

Electrochemical reactions

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Heterogeneous charge transfer (전하전달)

Cu2+ + 2e → Cu

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1. Electrode potential is an expression of electron energy 2. Many things can happen at once 3. Electrochemical system is not homogeneous 4. Current is an expression of reaction rate 5. E and I can not be controlled simultaneously 6. Current passes through a “closed loop”

Distinctive Concepts in Electrochemistry

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Electrode potential is an expression of electron energy

Electrode potential (전극전위)↔ Electron energy (전극 내 전자의 에너지)

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Electrode potential is tunable by potentiostat 일정전위기

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Electrode potential is an expression of electron energy

FeCp2+

FeCp2+ + e → FeCp2

LUMO; Lowest un-occupied molecular orbital HOMO; highest occupied molecular orbital

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Many things can happen at once

Mass transfer: (물질전달) Diffusion (확산) Migration (이동) Convection (대류)

Electrochemical reactions: Mass transfer + Charge transfer

Rate-determining step

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Electrochemical system is not homogeneous

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Electrochemical system is not homogeneous

General chemical reactions: Homogeneous Electrochemical reactions: only within diffusion layer

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Current is an expression of reaction rate

PSV

FeCp2+

FeCp2

R’

O’

ee

e e

Ref CtrWk

전류 (i) ∝ 반응속도

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How to control reaction rate (current) ?

E and I can not be controlled simultaneously !!

과전압

Charge transfer limited

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Current vs. rate-limiting step

Charge transfer limited

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Current passes through a “closed loop” (닫힌고리)

- electrode + electrode

ic: cathodic current

ia : anodic current

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Cathode area >> Anode area, but ic = |ia |, what happens?

Current passes through a “closed loop”

1) Cathode 2) Anode 3) Electrolyte 4) Circuit

Crevice corrosion (틈새 부식)

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“closed loop” in redox-flow battery

Vanadium redox-flow cell

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Shutdown mechanism in lithium ion batteries

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Anode Dye Electrolyte Cathode

R O

Ecell

Do/D+

Mediator

D*

eLoad

e

e

e

e

hv

“closed loop” in dye-sensitized solar cells

염료감응 태양전지

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Thermodynamics and Kinetics in Electrochemistry

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Thermodynamics vs. Kinetics

FeCp2+ Faradaic current

Non-faradaic current

Thermodynamics: 가능성

Kinetics: 속도(전류)

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Thermodynamics vs. Kinetics

Equivalent circuit (등가회로)

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Ideally polarized electrodes (이상 분극전극)

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Ideally polarized electrodes (이상 분극전극)

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1) Always double-layer charging current with E change 2) Ideally polarized electrodes: Rct → ∞ 3) Ideally non-polarizable electrodes: Rct → 0 (이상 비분극 전극) 4) EDLC; electric double-layer capacitors (전기이중층 커패시터)

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Electrode potentials 1. Standard electrode potential

2. Equilibrium potential

3. Formal potential

4. Mixed potential

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1. Electrical potential is defined by difference (차이) 2. Electrical potential : charge separation at

interfaces (계면에서 전하 분리) 3. Infinitesimally small (극소량) charge separation 4. Potential difference must be defined at

equilibrium or steady-state (평형 또는 일정 상태)

Electrode Potentials (전극전위)

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Electrode Solution

Electron Cation

r

Infinitesimally small charge separation

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Potential difference at interfaces

Potential difference must be defined at equilibrium (평형) or steady-state (일정 상태)

Ag+ + e (in Ag) → Ag

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Chemical Potential (화학전위)?

Escaping tendency (이탈 경향)

∂∂

=i

i nGαµ

jnPT ,,

iα

(a)

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Electrochemical Potential (전기화학전위)?

αααφµµ ⋅+= Fziii

iα

αφ ( ions)

Additional energy

(b)

Q x V = energy

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Conditions for Equilibrium

Potential-determining equilibrium (전위결정 평형식)

Ag+ + e (in Ag) = Ag

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Potential difference at equilibrium state

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Inert electrode/redox pair or gas

PtFe3+

Fe2+

X-

(a)

PtH2

2H+

X-

(b)

모든 반쪽전지 (half-cell)는 1개의 전위결정 평형식을 가짐

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Standard electrode potential (표준 전극전위)

HCl

H2

Pt electrode

Fe2+ Fe3+

Pt wire

Salt bridge

V

NHE (SHE)를 기준으로 반쪽전지의 전압(V) 측정

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Standard electrode potential (E0)

V

PtH2

H+

Fe2+

Fe3+

X- X-

Pt

H2/H+Fe2+/Fe3+

Vljφ∆

Pt

Pt

1φ∆

2φ∆

Potential 차이는 상(phase)과 상의 계면에서 !!

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Nernst equation

전위결정 평형식 (potential-determining equilibrium)에서 이온들의 활동도(activity)만으로 표시

Fe3+ + e = Fe2+

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Standard electrode potential (E0) Half-cell에 관여된 potential-determining equilibrium에서 모든 이온의 activity = 1인 경우 Eeq

평형상태의 값이다 (thermodynamic parameter) 모든 반쪽전지는 고유한 E0을 갖는다 NHE (normal hydrogen electrode)를 기준으로 한 250C에서 값

Fe3+ + e = Fe2+

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Li+ + e = Li E0 = - 3.04 V (vs. NHE)

2H+ + 2e = H2 E0 = 0.0 V (vs. NHE)

Cl2 + 2e = 2Cl- E0 = 1.36 V (vs. NHE)

← More negative More positive →

← 산화경향 증가 환원경향 증가 →

금속의 이온화 경향:

Li> K> Ca> Na> Mg> Al> Zn> Fe> Ni> Sn> Pb> Cu> Au

← ← ← ← E0 more negative

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Practical reference electrodes(기준전극)

E (vs. NHE)

0.2412 V

0.197 V

0.0 V

Hg/Hg2Cl2(s), KCl(sat’d)

Ag/AgCl(s), KCl(sat’d)

Pt/H2/H+ (NHE)

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Formal potential

E0 ≈ E0’

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Mixed potentials (혼성전위 )

Zn

Zn2+

( =1)

Zn2+

AnodeCathodeX-

2H+

H2(g)

e ea

For a Galvanic cell 1) Cathode 2) Anode 3) Electrolyte 4) Circuit

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Mixed potentials; Zn corrosion

2H++ 2e H2(g)ic

ia

0.0 -0.76

Mixed potential

E (-) (vs. NHE)

Zn Zn2++ 2e

icia

(ic = |ia|)

Zn의 용해(부식)과 수소의 발생

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Mixed potentials; Zn corrosion

2H++2e H2(g)ic

ia

0.0 -0.76 E (-) (vs. NHE)

Zn Zn2++2e

pH

Mixed potentialDecrease in ic and ia

pH dependence

Eeq = Constant - 0.059 V x pH

(at 298K)

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H2 and O2 evolution as a function of pH

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Alkaline battery

Negative cover

Seal

Steel can

Cathode (MnO2)

Separator

Anode (Zn)

Currentcollector

Electrolyte: concentrated KOH Negative electrode; Zn powder Positive electrode: MnO2 (EMD) Mercury-free cells

Addition of mercury (Hg)

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Metal - log I0 (A/cm2)

Metal - log I0 (A/cm2)

Ru 2.1 Fe 6.0

Pd 2.3 Cu 6.7

Rh 2.8 W 7.0

Pt 3.6 Cr 7.4

Co 5.2 Zn 10.5

Ni 5.2 Cd 11.0

Ag 5.4 Pb 12.2

Au 5.5 Hg 12.5

Exchange current density for H2 evolution 1.0 M H2SO4

- Large overpotential for H2 evolution - Large Rct

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Ion-ion interactions Ion-solvent interactions

Ions in solution : electrolyte

1) Activity coefficient; Debye-Hückel theory

2) Migration of ions

3) Molar conductivity

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(Salt Conc.)1/2 (Salt Conc.)1/2

log

0.0

Λ±γ

Λ̊

Activity coefficient and transport property

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Debye-Hückel theory

Ionic atmosphere

Ionic concentration ↑; Ionic strength ↑; Debye length ↓; More stabilized; γj↓

δ−

δ+ = δ−

δ−δ−

δ−

I1

∝Debye length

+

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Activity coefficient vs ionic strength

0.0

log

DHL

EDHL

Real

R-S

I

γj

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Li+ Na+ K+

Crystal radius a /Å 0.60 0.95 1.33

Hydrated radius b/Å 2.4 1.8 1.3

Hydration number 2-22 2-13 1-6

Li+, Na+, K+ 이온의 결정학적 반경, 수화된 반경, 수화 수

a From x-ray diffraction analysis, b Using Stokes’ law

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Fe3+

H

H

OH

H

O

H

H

OH

H

OO

HH

OHH O

HH

OHH

OHH

OHH

OHHO

HH

OHH

OH

H

OH

H

OHH

O

HH

O

HH

O

HH

O

HH

O

HH

O

HH

O

HH

O

HH

Bulk solution

Innerhydration

shellOuterHydration

shell

Ion-solvent interaction

Ion-solvent interactions

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Ionic conductivity

A A

l

V

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Molar conductivity

NiSO4 (weak electrolyte)

Ideal

KCl (strong electrolyte)

Λ

Λ

˚

(Salt Conc.)1/2

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Relaxation effect and electrophoretic effect

Eexternal

Erelaxation

Ionic atmosphere

Decrease in mobility

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1. Charge transfer kinetics

Butler-Volmer equation

Tafel plot

2. Mass transfer kinetics

Electrochemical kinetics

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Activated complex theory

Reaction coordinate

Free

ene

rgy

∆G‡

∆G‡

Reactant Product

Activated complex

b

f

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Activation energy by potential control

Reaction coordinate

Free

ene

rgy

nF(E - Eo’) αnF(E - Eo’)

(1-α)nF(E - Eo’)

O + ne R

∆G‡ ∆G‡

∆G‡

oc oa

oc

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Butler-Volmer equation

ηc

ic

Eeq = - 0.11 V

E (vs. SCE)

= 2.2 ia

= 2.2 µA

µA

ic

ia

io

io

inet

Charge transfer rate

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Linear relationship: i vs. E

inet

ic

ia

ic

ia

E (-)

Slope

(−η)

nF i0= RT

= 1Rct

=

inet =

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Tafel plot

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Tafel plot

log │inet│

- 0.10.10.2η (V)

log i0

Slope (1-α)nF=

2.3RTSlope αnF

=2.3RT

- 0.2

η = a + b log inet

Tafel equation

Tafel behavior

Tafel region

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Electrochemical cells 1. Electrolytic cells

2. Galvanic cells

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Electrolytic cells (전해셀)

Brine (NaCl/H2O) electrolysis (소금물 전기분해 (또는 전해))

RT aO Eeq = E0 + — ln —— nF aR

Nernst equation

E0 : Standard electrode potential (표준전극전위) at 298 K NHE: Normal hydrogen electrode

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Electrolytic cells

1) Cathode 2) Anode 3) Electrolyte 4) Power supply

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Electrolytic cells; charge transfer limited

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Electrolytic cells; charge transfer limited

Eappl: 전해를 위해 두 전극 사이 걸어주어야 하는 전압

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ic

ia

E

ηa

1.36 V

Electrode A

ηa

Electrode B

( - )

Electrolytic cells

Electrode selection Rsolution

Electrode gap Separator (분리막)

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Galvanic cells (갈바니 셀)

2H2 + O2 → 2H2O (∆G

0

<< 0 ; spontaneous, 자발적)

Electrochemical pathway (전기화학 경로) Anode: 2H2 → 4H+ + 4e Cathode: O2 + 4H+ + 4e → 2H2O Overall: 2H2 + O2 → 2H2O (∆G < 0 ; spontaneous)

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Galvanic cells

Fuel cell (연료전지)

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Galvanic cells

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Galvanic cells

Ewk: 갈바니 셀의 작동 전압

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Secondary batteries (이차전지)

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Secondary batteries (이차전지)

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Cathode vs. anode

Cathode: emit electrons Anode: accept electrons

Cathode: Cu2+ + 2e → Cu0

(emit electrons)

Anode: Fe2+ → Fe3+ + e

(accept electrons)

Cathode ray tube

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Cathode vs. anode

Hollow Cathode Lamp

Ar → Ar+ + electrons electrons; to anode (accept electrons) Ar+ ; attack cathode (accept positive charges = emit negative charges (electrons)

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