AMS Special Topics II Batteries & Fuel Cells · (Hittdorf experiment negligible back-diffusion) ......

2012-05-22 AMS Battery & FC Lectures - Basics (Michele P. for Hubert G.).ppt p. 1

AMS Special Topics II – Batteries & Fuel Cells (3 1.5 hours: 22/05 10:00 -11:30 12:15 - 13:45 and 05/06 10:00 - 11:30)

Electrochemistry Basics

- electrochemical cells & ion transport

- electrochemical potential

- half-cell reactions

Lithium Ion Batteries (LiBs)

- battery materials

- application of batteries

- “post-LiBs”

Fuel Cell Basics & Applications

- fuel cell types and materials

- basic electrocatalysis

- H2 reduction & O2 reduction kinetics

- transport resistances

- cell-reversal & start-stop degradation

Michele Piana (for Prof. Hubert Gasteiger)

Technical Electrochemistry, Chemistry Dept., TUM


Electrochemical Cells

meta

l

meta

l

e- e-

Cl- H+

reduction (cathode)

2H+ + 2e- H2

oxidation (anode)

2Cl- Cl2 + 2e-

H2 Cl2

aqueous HCl

net reaction: 2HCl H2 + Cl2

charge transport: - electrons in external circuit

- ions in electrolyte

cations migrate to cathode

anions migrate to anode

electrolytic cell

( battery charging)

similar process for chlor-alkaline electrolysis

+ -


Thermodynamic Potential

where,

2HCl H2 + Cl2 ;

f

)HCl(

f

)Cl(

f

)H(R GGGG 222

0 RGcell reaction:

mol/kJ0GkPa101atClandHfor f

)Cl,H(22 22

mol/kJ1.131Gf

)HClM1(

standard states: -

-

mol/kJ2.262GR

need to add energy to drive the reaction

thermodynamic cell potential: Fn

GE R

rev,cell

where, n = number of electrons

F = Faraday constant = 96485 As/mol

= e0 NA = 1.60218 10-19 As/e- 6.0221 1023 e-/mol

V36.1mol/As964852

mol/kJ2.262E rev,cell

Ecell,rev < 0 for electrolytic cells


Electrochemical Cells

meta

l

meta

l

e- e-

Cl- H+

oxidation (anode)

H2 2H+ + 2e-

reduction (cathode)

Cl2 + 2e- 2Cl-

aqueous HCl

net reaction: H2 + Cl2 2HCl

charge transport:

- electrons in external circuit

- ions in electrolyte

(cations migrate to cathode, anions to anode)

galvanic cell ( battery discharge)

H2 Cl2

kJ/mol262.2

2 )()()( 22

f

Cl

f

H

f

HClR GGGG

V36.1E rev,cell

Ecell,rev > 0 for galvanic cells

+ -


Ionic Movement in Electrochemical Cells

meta

l

+ -

meta

l

e- e-

Cl- H+

2H+ + 2e- H2 2Cl- Cl2 + 2e-

H2 Cl2

electrolytic cell

meta

l

meta

l

e- e-

Cl- H+

H2 2H+ + 2e- Cl2 + 2e- 2Cl-

aqueous HCl

H2 Cl2

galvanic cell

x

fs

exce

ss C

l-

exce

ss H

+

+ -

+

- Cl-

H+

x

exce

ss C

l-

exce

ss H

+

+

- Cl-

H+

fs

fs increases Ecell

increases the energy needed

to drive electrolysis

fs decreases Ecell

lowers the energy obtained from

a galvanic cell (battery, fuel cell)

Ecell Ecell


Deviation from Equilibrium

Ecell [V]

i [A/cm2]

Ecell,rev

+ -

ele

ctr

ode

e- Ecell

ele

ctr

ode

Rext

Rinternal

iRexternal

iRint h (“overpotential”)

Ecell deviates from Ecell,rev as the current density (i) increases

simplified equivalent circuit:

Rinternal + Rexternal (load)

generated/consumed power (Pelectric) & thermodynamic efficiency (h)

rev,cell

cell

galvanicE

EhPelectric [W/cm2] = Ecell [V] i [A/cm2]

cell

rev,cell

icelectrolytE

Ehor

iRint h (“overpotential”)


Ionic Conductivity (k)

[mol+/(cm2s)]

vczvczNei A0

svu f [cm2/(Vs)]

suczuczFi f

defining ionic mobility as:

ionic conductivty can be defined by considering the flow of ionic charges

note: - anions flowing to the right positive current

- cations flowing to the left positive current

[mol-/(cm2s)] [As/mol]

(note: the minus sign is required to give the right sign of i)

kfk uczuczFwhere,i s

, where: c is the ionic molarity,

z is the ion charge

v is the ion velocity

[W-1cm-1 S/cm]

meta

l

++--

meta

l

e-e-

Cl-H+

2H+ + 2e- H2 2Cl- Cl2 + 2e-

H2 Cl2

x

fs

exce

ss C

l-

exce

ss H

+++

--Cl-

H+

Ecell


Simple Model for u

els0dyndrag Fezvr6F fh

at steady-state, electric force (Fel) and the drag force (Fdrag) of the ions are balanced

this can be illustrated using Stokes Law

u only depends on ion & electrolyte properties

(infinite dilute solution approximation)

where: - hdyn is the dynamic viscosity

(hdyn = rnkinematic ; for H2O at 20C: hdyn 1 mPas = 1 centiPoise)

- r is the hydrodynamic ion radius

- v is the ion steady-state velocity

h

f

r6

ezvu

dyn

0

s

from: A.J. Bard, L.R. Faulkner; Electrochemical Methods (1980), pg. 67


Ionic Conductivity Values

from: H.J. Gores et al.; Liquid Nonaqueous Electrolytes;

in: Handbook of Battery Materials (Eds.: C. Daniel & J.O.

Besenhard), Wiley: 2nd edition (2011), vol. 2, pp.525

for most lithium ion battery (LiB)

electrolytes, k 1-20 mS/cm at 20C

from: C.K. Mittelsteadt & H. Liu, in: Handbook of

Fuel Cells: Fund., Techn. & Appl. (eds: W. Vielstich,

H.A. Gasteiger, H. Yokokawa), Wiley (2009): vol. 5.

for proton exchange membranes,

k 100 mS/cm at fuel cell run conditions

k of Nafion

(perfluoro sulfonic acid ionomer)


Estimated Ohmic Losses

for quasi-1D geometry (x/y length >> telectrolyte):

si fk

areal

s

eelectrolyt

s

Rti

f

fk k /tR eelectrolytareal

battery & fuel cell geometry

+ - negative current collector

or negative bipolar plate

negative electrode positive electrode

positve current collector

or positive bipolar plate

10’s

of

cm

0.002 – 0.005 cm electrolyte thickness, telectrolyte

(“porous separator” or “membrane”)

battery: teff telectrolyte /(eelectrolyte)1.5 25mm/(0.5)1.5 70 mm & k 10 mS/cm

Rareal 0.7 Wcm2 or Eohmic 10 mA/cm2 0.7 Wcm2 7 mV

fuel cell: telectrolyte 20mm & k 100 mS/cm

Rareal 0.02 Wcm2 or Eohmic 1.5 A/cm2 0.02 Wcm2 30 mV


Transference Numbers

fk uczuczFi sfor binary electrolytes:

the total ionic current (i) is carried partially by anions (i-) and cations (i+)

the fraction of the i carried by each species is defined as transference number (t)

suczFi f suczFi f and

uczucz

ucz

ii

it

from: A.J. Bard, L.R. Faulkner; Electrochemical Methods (1980), pg. 67

the transference number of a given cation depends on all the other ions

1tt

iti and


Measurement of Transference Numbers

from: C.H. Hamann, A. Hamnett, W. Vielstich; Electrochemistry; Wiley (2007)

assuming a total charge of 1F 1 molelectrons (Hittdorf experiment negligible back-diffusion)

2H+ + 2e- H2 2Cl- Cl2 + 2e-

-1 molH+ for H2 evolution

+tH+ molH+ via H+-transport

iH+ = tH+ i

iCl- = tCl- i

-tCl- molCl- via Cl--transport

-tCl- molH+ net los

-tCl- molHCl net loss

-1 molCl- for Cl2 evolution

+tCl- molCl- via Cl--transport

-tH+ molH+ via H+-transport

-tH+ molCl- net los

-tH+ molHCl net loss

only 0.18 molHCl are lost in the cathode compartment

compared to 0.82 molHCl in the anode compartment

high tH+ due to Grotthuss mechanism

(H+ tunneling via H-bonding)

-

+

(discussion of Faraday’s Law on the blackboard)







- battery materials


- “post-LiBs”








Important Thermodynamic Relationships

thermodynamics of an arbitrary chemical reaction,

if the reaction consists of electrochemical processes, the reversible electrical work

(We,rev = nFErev) equates to GR :

nnnnnntstanreac

)i(i

products

)i(i)B(B)A(A)D(D)C(CR GGGGGGG

DCBA DCBA nnnn

where G0(i) is the standard chemical potential (298K, 101kPa)

- since often only H0 and S0 values are tabulated:

Fn

GE R

rev

where: - Erev is >0 for a galvanic cell (fuel cell, battery discharge)

- Erev is <0 for an electrolytic cell (electrolyzer)

(note: in electrolyzer R&D, usually Ecell is used)

RRR STHG

to obtain the temperature dependence: Fn

S

TG

Fn

1T

E )T(R

P

)T(R

P

)T(rev

note: follows closely the text book by C.H. Hamann, A. Hamnett, W. Vielstich; Electrochemistry; Wiley (2007)


Chemical Potential for Mixtures

chemical potential of mixtures

i0

ii alnTR mm where: - mi is the chemical potential of compound i

- ai is the chemical activity of compound i

- R is the gas constant (8.314 J/(molK))

- T is the temperature in K

- mi is defined as: T,P,nni

i

ij

nG

m

mnmnmtstanreac

ii

products

iiR

mnmntstanreac

ii

products

ii0

again:

in the chemical equilibrium:

change of the Gibbs free energy when one mole of i

is added an infinite amount of the mixture, so that

all other component concentrations stay “constant”

if two mixtures/solutions are in contact, each component i is exchanged between

the two phases (I and II) until: (II))I( ii mm


Electrochemical Potential

for an electrochemical reaction, e.g.,

charge separation between the electrolyte

phase (aq) and the metal phase (M)

creates an electrical potential

difference between the two phases

)M(e2)s(Cu)M(Cu 20

ndissolutio Cu

2CuCu

mm

plating Cu

2CuCu

mm

the energy term due to the electrical

potential difference must be included

f(s

)

f(M

)

f(s

)

f(M

)

)s(Fz)s()M(Fz)M( 22 CuCuiCu fmfm note:

We = QE [AsV]

if referenced to 1mol ions/e-

We = zFE [(As/mol)V]

where f(M,s) are referred to as Galvani Potentials

definition of the electrochemical potential:

fmfmm Fz)aln(TRFz~ii

0

iiii

with the equilibrium condition: mnmntstanreac

ii

products

ii~~0

from: C.H. Hamann, A. Hamnett, W. Vielstich;

Electrochemistry; Wiley (2007)


Electrochemical Double Layer Model fr

om

: C

.H. H

am

an

n, A

. H

am

ne

tt, W

. V

iels

tich

; E

lectr

oche

mis

try; W

iley (

200

7)

adsorption/accumulation of

anions and/or cations

dipole alignment of

water/solvent molecules

excess charge at the metal interface:

electrochemical metal/solution interface

resembles a capacitor

at an applied AC voltage/current signal,

capacitive behavior is observed

capacitor model for electrochemical

interfaces in AC impedance

(discussion on blackboard)







- battery materials


- “post-LiBs”








Nernst Equation – Metal Electrode

consider: )M(e2)s(Cu)M(Cu 20

)M(~2)s(~)M(~eCuCu 20 mmmin equilibrium

- assuming Cu0(M) in the metal to be neutral

(constant copper and electron concentration)

)M()M(~00 CuCu

mm

Me

0

esCu

0

CuCu

0

Cu F2)M)(aln(RT2)M(2F2)s)(aln(RT)s()M)(aln(RT)M( 22 fmfmm

=0 =0

)s)(aln(F2

RT

F2

)M()M(2)s(2

2

Cu

0

Cu

0

e

0

CusM

mmm

fff

)s)(aln(F2

RT2Cu

0ff

where:

- f = metal/solution Galvani Potential Difference

- f0 = f for aCu2+ = 1

note: fand f0 cannot be measured directly

would require a second electrode with its own unknown f

use of a reference electrode with (arbitrarily) defined fand f0


Galvani Potentials Drops (schematic) fr

om

: C

.H. H

am

an

n, A

. H

am

ne

tt, W

. V

iels

tich

; E

lectr

oche

mis

try; W

iley (

200

7)

fs

fs

fM(I)

fM(II)

fM(I)

fM(II)

f0(I)

f0(I)

f0(II)

f0(II)

E0 = f0(I) - f0(II)

E0 = f0(I) - f0(II) )II()II()I()II(E 00MM ffff

irrespective of fs :

note: E emf (electromotive force)


Nernst Equation – General

Nernst Equation for any half-cell reaction:

ff

n

n

reducedi

oxidizedi0

)a(

)a(ln

nF

RTi

i

example – the hydrogen electrode:

with ai defined as: - for solids: ai = 1

- for liquids: ai = gi ci (often approximated as ci )

- for ions: ai = g c (often approximated as ci )

- for gases: ai = fi pi (often approximated as pi )

- for H2O: aH2O = 1 in dilute aqueous electroytes

where:

- n = number of electrons exchanged

- ni = stoichiometric coefficients

)gas(H)M(e2)s(H2 2

f

ff

5.0

H

H0

)H,H(H

2

H0

)H,H()H,H( )p(

aln

F

RT

p

)a(ln

F2

RT

2

2

2

22

by arbitrarily defining f0(H2/H+) 0 V, the potentials of all half-cell reactions

can be measured vs. the Standard Hydrogen Electrode (SHE) potential


SHE Potential Measurements

in acidic solutions, platinum catalyzes: )gas(H)Pt(e2)s(H2 2

SHE potential defined for: aH+ = 1 (pH=0) and pH2 = 101 kPa

measuring E between any

half-cell reaction and the SHE

thermodynamic redox-potentials

can be determined

n

n

reducedi

oxidizedi

2/12/1)a(

)a(ln

nF

RTEE

i

i0

from: C.H. Hamann, A. Hamnett, W. Vielstich; Electrochemistry; Wiley (2007)


Half-Cell Potentials

fro

m: C

.H. H

am

an

n, A

. H

am

ne

tt, W

. V

iels

tich

; E

lectr

oche

mis

try; W

iley (

200

7) standard reduction potentials

referenced to SHE at 25C and

and standard activities

(1M solutions, 101 kPa gases)

redox couples at higher potential

can oxidize those a lower potential


Daniell Element

use of half-cell potentials to determine Erev (emf) of any electrochemical cell

Zn Zn++ + 2e- ; E0(Zn+2/Zn) -0.763 V

Cu++ + 2e- Cu ; E0(Cu2+/Cu) +0.34V

anode:

cathode:

cell: Zn + CuSO4 ZnSO4 + Cu ; Erev(cell) = 1.1 V

ZnSO4 CuSO4

electrolyte bridge

Zn Zn++

2e-

2e-

Cu++

Cu

SO4--

determination of Erev when standard reduction potentials are used

(equivalent to changing the sign of E0 when writing as oxidation reaction)

Erev = E0cathode – E0

anode = E0(Cu2+/Cu) – E0

(Zn2+/Zn)


O2 & H2 Reduction/Oxidation Potentials

Erev vs. pH and pgas :

n

n

reducedi

oxidizedi0

)a(

)a(ln

nF

RTEE

i

i

2

22

H

2

H0

)H/H(rev)H/H(rev a

)a(ln

F2

TREE

for the hydrogen electrode: H2 2 H+ + 2e- ; E0rev(H2/H+) 0 V

separating the ln-terms, converting to log10, and considering pH -log(aH+) :

kPa101plogF2

TR303.2pH

F

TR303.2EE

222H

0

)H/H(rev)H/H(rev

60mV at 25°C 30mV at 25°C

(Nernst equation)


O2 & H2 Reduction/Oxidation Potentials

n

n

reducedi

oxidizedi0

)a(

)a(ln

nF

RTEE

i

i

for the oxygen electrode:

separating the ln-terms, converting to log10, and considering pH -log(aH+) :

0.5O2 + 2 H+

+ 2e- H2O ; E0rev(O2/H2O) 1.23 V

OH

2

H

5.0

O0

)OH/O(rev)OH/O(rev

2

2

2222 a

)a()a(ln

F2

TREE

)ref(OHOHO

0

)OH/O(rev)OH/O(rev 2222222aalog

F2

TR303.2kPa101plog

F4

TR303.2pH

F

TR303.2EE

note: the partial pressure dependence on Erev is smaller for O2 than for H2

15mV at 25°C 60mV at 25°C

Erev vs. pH and pgas :

(Nernst equation)

1 in dilute aqueous

electrolytes


Erev / pH Diagram of H2 & O2 Reactions

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

-1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 pH

E v

s.

SH

E [

V]

0.5 O2 + 2 H+ + 2e

- H2O

H2 2 H+ 2e

-

25°C

pi =101kPa

H2O(liquid)

Erev(O2/H2O):

1.23V SHE

1.23V RHE

Erev(O2/H2O):

0.40V SHE

1.23V

RHE

Erev(cell) = Erev(O2/H2O) – Erev(H2/H+) (pH)

independent of electrolyte (pH)

Erev(O2/H2O) vs. SHE varies with pH,

but is constant vs. RHE

RHE-scale mostly used for FC’s

frequently operating H2-anode

is used as “RHE”-reference

(Dynamic H2 RE or DHE)

kPa101plogF2

TR303.2pH

F

TR303.2EE

222H

0

)H/H(rev)H/H(rev

kPa101plogF4

TR303.2pH

F

TR303.2EE

22222 O

0

)OH/O(rev)OH/O(rev

; assumption: aH2O

1


Reference Electrodes to measure the potential of a single electrode of interest (working electrode, WE)

generally requires the use of reference electrodes (RE) with defined potential:

note: RE’s are sensing electrodes;

they do not pass “any” current

common reference electrodes for aqueous electrolytes

type reaction ESHE [V]

SHE (std. hydrogen electrode) 2H+ + 2e

- H2 0.000

Pd-aH (Pd-hydride electrode) Pd + H+ + e

- Pd-aH +0.050

Silver-Silverchloride (KClsat) AgCl + e- Ag + Cl

- +0.197

SCE (saturated calomel electrode, KClsat) HgCl2 + 2e- Hg + 2Cl

- +0.241

Mercury-Mercurousoxide (0.1M NaOH) HgO + 2H+ + 2e

- Hg + H2O +0.926

e.g., measurement of E(O2/H2O) vs. i:

as current passes through the WE, its potential

is measured (current-less) against the RE

the counter electrode (CE), passes the current

via an appropriate reaction with the electrolyte

or species in the electrolyte

(for the shown configuration, oxygen evolution

occurs on the CE: H2O 0.5 O2 + 2 H+ + 2e- )

O2

Pt Pt

2H+

½ O2

2e-

H2SO4 H2O

CE WE

i

E

RE


Pourbaix Diagrams thermodynamic phase diagram for aqueous electrolytes

illustration of the thermodynamically most stable species vs. pH, E, and ci

)clog(0295.0277.0]V[E

e2CoCo

2CO

0

2

reaction 11:

pH260.12)clog(

H2OHCo

2CO

2

2

CoO

reaction 8:

)clog(030.0pH118.0612.1]V[E

e2H4OH2Co

2CO

0

2

2

2CoO

reaction 17:

convenient depiction of

thermodynamically stable species

(minimized Gibbs free energy)

(discussion of lines a and b)

AMS Special Topics II Batteries & Fuel Cells · (Hittdorf experiment negligible back-diffusion) ......

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Transcript of AMS Special Topics II Batteries & Fuel Cells · (Hittdorf experiment negligible back-diffusion) ......