Dissertation Vogler

8/10/2019 Dissertation Vogler

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E cell

cathode

O2 H

2

H2O

O2-

. .

e- e

-

electrolyte

anode



H2 + 1/2O2 H2O .

1/2O2 + 2e− O2− ,

H2 + O2− H2O + 2e− .

∆H

∆G = ∆H − T ∆S

ηFC = ∆G

∆H .

T 1

T 2

ηCarnot = T 1 − T 2

T 1.



80 C

OH−

H2

80 C 150 C

H+

H2

≤

80 C H+

200 C

H+

H2

650 C

CO2−3

H2

900 C

600 C

O2− H2

H2

O2

E th

cell

E thcell = −

1

zF ∆G ,

z

F

E thcell = −

∆G0

zF −

RT

zF · ln

aH2O

aH2 a0.5O2

,

∆G0

R

T

ai



H2

CO

H2





Y2xZr1−2xO2−x

x

Y2O3

ZrO2

ZrO2

Gd2xCe1−2xO2−x−δ

x

Gd2O3 CeO2

δ

La1−xSrxMnO3



E c e l l

[ V ]

i cell

00

E cell

OCV

a)

-0.5η [V]

0.5

l o g i c

e l l

[ A / c m ² ]

0

b)

cathodic branch

anodic branch

[A/cm²]

R pol

η = E th

cell

−E cell

η > 0

η < 0

i

E cell(i)

η(i) = E OCV

cell −E cell(i)



E c e l l

[ V ]

i cell

00

a)

f [Hz]

10-1

100

101

102

103

104

R e ( Z ) [

Ω / c m ² ]

b)

R pol

[A/cm²]

E(t)

i(t)

I m ( Z ) [ Ω

/ c m ² ]

0

200

100R pol

Rpol

i(t)

Z

Rpol

Rpol

Rpol = dη

di .



a)

100 μm

b)

YSZ

Ni



HNi

O2−YSZ

Hgas2

Ogas2

OXOYSZ

Hx

i Ni

e−



E

∆G = −zFE ,

∆G

F

z

E

H2 + 1/2O2 H2O .

Hgas2 + OX

OYSZ H2Ogas + V••OYSZ + 2 e− ,

1

2Ogas

2 + V••OYSZ + 2 e− O2−

YSZ .

V••

OYSZ

O2−YSZ

OX

OYSZ



y

I,E cell I,E cell

η

counter

electrolyte

work ref

porous anode

porous cathode

electrolyte

LE

a) b)

∆φequil

∆φequil,an = ∆Gan

2F −

RT

2F · ln

a(H2) · a(OX

OYSZ)

a(H2O) · a(V••OYSZ)

,

∆φequil,ca = ∆Gca

2F −

RT

2F · ln

a(OX

OYSZ)

a(O2)1/2 · a(V••OYSZ)

.

E equil = ∆φequil,ca − ∆φequil,an .

∆φ

∆φan = φelde,an − φelyt,an and ∆φca = φelde,ca − φelyt,ca ,

φelde

φelyt

i

E (i) = φelde,ca − φelde,an(i) .

E (i)

i



y

i

φelde,ca

∆φelde,ca = φelde,ca − φelyt,ca(y) and ∆φelde,an = φelde,an − φelyt,an(y) .

∆φca

∆φan φelyt

i

iV

F

iel

i = LE

y=0

iVF dy + iel .

iV

F

LE

i

η(i)

η(i) = φelde,work(i) − φelde,ref − iRelyt,

φelde,work(i)

φelde,ref

i

∆φelde,work = φelde,work−φelyt,work and ∆φelde,ref = φelde,ref −φelyt,ref .

i



i∈Rf

ν

i A

i + z e−

j∈Rr

ν

j A

j

A

A

ν

ν

z

∆φ = φelde − φelyt

kr/f

kf = k0f exp−

E actf

RT exp− (1 − α) zF

RT · ∆φ ,

kr = k0r exp

−

E actr

RT

exp

α

zF

RT · ∆φ

.

E act

α

F,R,T

i

si

si = ν i kf j∈Rf ,

Aν

j

j − kr j∈Rr,

Aν

j

j ,

si

Ai

si

ji = zF si .



∆φ = 0

si

∆G

∆G = ∆H − T ∆S ≡ 0 .

∆H

∆S

∆H =i∈Rf

ν i hi −i∈Rr

ν ihi ,

∆S =i∈Rf

ν i si −i∈Rr

ν isi .

k0

E act

E act

f − E act

r = ∆H ,

k0f

k0r

= exp

∆S

R

.

ρ

ctot = i ci

M = 1/ctot i ciM i

ci

X i = ci/ctot

Y i = M i/M X i M i

i

ρ = p M

RT ,

p

R

T

sV

i



ci

Γk

θi = ci · σi

Γ k,

σi

i

sA

i

i

ηact

i = i0

exp

β a

F

RT ηact

− exp

−β c

F

RT ηact

,



i0

β a

β c

β a

β c

i0an = i∗an exp

−

E actan

RT pan

H2

p∗H21/4

pan

H2O

101325 Pa3/4

1 +

panH2

p∗H2−1/2

,

β a = 1.5

β c = 0.5

i0ca = i∗ca exp

−

E actcath

RT

pca

O2

p∗O2

1/4 1 +

pcaO2

p∗O2

−1/2

,

β a = 0.5

β c = 0.5

i∗

p∗

lTPB

lA

TPB

lV

TPB

iF



iF,ct = zF lTPBkf ,ct j∈Rct

Aν

j

j − kr,ct j∈Pct

Aν

j

j .

iF

iF =

all CTRs

iF,ct .

•

•

•

•

•

F

V

V

F (t) =

V

f (x, t) dV .



F (t)

J f (x, t)

∂V

q f (x, t)

sf

dA

dV

J f n dA , q f dV , and sf dV .

n

dA

F

∂F

∂t = −

∂V

J f n dA +

V

q f dV +

V

sf dV .

∂F

∂t =

V

∂f

∂tdV

∂V V

∂f (x, t)

∂t = −div J f (x, t) + q f (x, t) + sf (x, t) .

∂φelde

∂y = 0 .



ielyt

ielyt = −σeff elyt

∂

∂yφelyt = −σelytf σ

∂

∂yφelyt ,

φelyt σeff elyt = σelytf σ

σelyt

f σ ≈ /τ

iF

∂ielyt

∂y

= iF .

∆φ = φelde−φelyt

∂

∂y

σelytf σ

∂

∂y∆φan

= −iF .

∂

∂y

σelyt

∂

∂yφelyt

= 0 .

σelyt = Aσ

T · exp

−

E σRT

,

Aσ

E σ

f σ

∂

∂yφelyt(dense) = f σ

∂

∂yφelyt(porous) ,



φelyt(dense) = φelyt(porous) .

η = φelde,ref = φelde,work .

φelyt,center = 0 , φca = 0.

•

•

pO2

pO2



iel = −ielyt

σeelyt( pca

O2, T )

σi

elyt

(T ) exp

ηcaF

RT · exp(EF /RT ) − 1

1 − exp (−ielytLelytF )/(

RT σi

elyt)

iel ielyt

σi

elyt σe

elyt

ηca

E

Lelyt

pca

O2

σeelyt( pcath

O2 , T ) =

pcathO2

p0

−1/4

· aelyt0

T · exp

belyt0

T

.

∂ (ρcPT )

∂t =

∂

∂y λq

∂T

∂y + sq ,

cP

T

ρ

λq

sq

sq = σielyt

∂φelyt

∂y

2

sqJoule

+

i∈S g,S s

sV i hi

sqchem

.

•

T ca = T an = T fluid .



•

T anode = T gas .

janodeq = j gas

q + σSB · anq

T 4anode − T 4ref ,an

σ

SB

an

q

T ref ,an = T burner .

jcathodeq = α (T cathode − T ref ) + σca

SB · caq

T 4cathode − T 4ref

,

α = N uλgas

q

L .

T ref = 293 K

∂ρ

∂t = −div (ρv)

J f

+ S m

qf

.



ρ

v

S m

ρi i

i

∂ρi

∂t = −div

ρiv + jdiff

i

J f

+ S i qf

.

jdiff i

jdiff i

S i

∂ (ρv)

∂t = −

∇ · ρvv

− grad p −

∇ · τ

−div J f

+ ρg

sf

.

J f ∇ · ρvv

ρvv

p

τ

ρg

h

∂ (ρh)

∂t = −

∇ · ρvh

−

∇ · jq

−

τ ∇ · v

+ ∂p

∂t + [v · grad p] + S q ,

jp

S q

p

T

ρ



pM = ρRT .

M

1

M =i∈S g

Y iM i

.

S g

M i

i

Y i

jdiff 1 = −ρD12

∂Y 1∂x

and jdiff 2 = −ρD21

∂Y 2∂x

.

∂ci

∂x =

j∈S g

X iJ diff

j − X jJ diff i

Dij.

jdiff i = −ρ

Y iX i

Di∂X i∂x

Di

Di = 1 − Y i j∈S g,j=i X j /Dij

.

Dij

i

j

Dij = D ji

i

ci

X i Y i

jdiff i



J diff

i

jdiff i = M i J diff

i und X i = Y iM

M i.

i∈S g

jdiff i = 0 .

jdiff , corri = j diff

i − Y i j∈S g

jdiff j .

jq

jq = −λ∂T

∂x +i∈S g

hi jdiff i

λi

λ = 1

2

i∈S g

X iλi +

i∈S g

X iλi

−1 ,

µi

µ = 1

2

i∈S g

X iµi +

i∈S g

X iµi

−1 .



ρvy

V = vr/r

Y i

Λ = 1/r · (d p/dr)

∂ρ

∂t = −

∂ (ρvy)

∂y − 2ρV

∂ (ρV )

∂t = −

∂ (ρvyV )

∂y −

∂

∂y

µ

∂V

∂y

− ρV 2 − Λ

∂ (ρY i)

∂t = −∂ (ρvyY i)

∂y − ∂j diff

i

∂y + sV i M i

∂ (ρcPT )

∂t = −

∂ (ρvycPT )

∂y +

∂

∂y

λq

∂T

∂y

−i∈S g

cP,i jdiff i

∂T

∂y −

i∈S g

sV i hi .

ρ

inv

in

T in

vStef = 1

ρ

i

M i siA ,



∂ (εci)

∂t = −

∂J diff i

∂y −

∂ J flowi

∂y + sV

i .

J diff i

i

J flowi

i

sVi

ε

sVi

sk

i AV

k

sVi = k∈S k

AVk sk

i .

Deff ij

Deff ij = Deff

ji = ε

2τ 2

DK

i Dij

DKi + Dij

+DK

j Dij

DK j + Dij

.

ε/τ 2

DK

i

rP

DKi =

2rP

3

8RT

πM i.

J flow

i

J flowi = −X icg B

µ

∂p

∂y ,

cg

µ

p

B



B = ε3d2

P

72τ 2 (1 − ε)2 ,

dP

J diff i + J flow

i = sgas ,

p (electrode) = p (gas) .

J diff i = J flow

i = 0 .

−→J i

i

ai

−→J i = −Di ·

−→∇ · ai ,

Di

i

ai

ai = θi = σi/Γici

ai = ci/ctot

θtot =i∈S

θi = 1 .



θ

−→J i = −θDi ·

−→∇θi .

−→∇ai = 0 .

ν at

D0

i

D0i = x2/2t = 1/s · ν at · l2 ,

x2

l2

1/t = ν at

E act

i

Di = D0 · e−Eact

R·T .

Hx

i Ni

H•

i YSZ





H2,gas + OXOYSZ H2Ogas + V••

OYSZ + 2e−Ni







YSZ Ni

YSZ Ni

YSZ Ni

H2O

OH-

OH

-

--

H2

H

YSZ Ni

Ni

a)

b)

c)

d)

e)

--OO

x

H1 H2

--

-- OO

x

-

OH

O

O5

O4

O2O1

O3

H2O

OH-

---

--

H2

OHOO

x

H2O

H2

Hi

*

Hi

xx

H-int

--OO

x

--

-

--



H2

H2O

O2−

YSZ

H2

H2O

OH−

YSZ

OH−

YSZ

H2

H2O



a)

b)

c)

½ d Ni

½ d YSZ

d)

Surface spillover reaction Bulk-bulk interchange

TPB

Edge

d Ni

Repeat unit d YSZ

1D surface transport 1D surface transport +2D bulk transport

Ni YSZ

d YSZ d

Ni

½ d YSZ

TPB½ d

Ni

y =0

z =0 z =0

Surface diffusion

Ni stripe

YSZ crystal

•



•

•

•

•

•

µm

Rpol

Rpol = dη

di .



si

J/(K·mol)

hi

kJ/mol

hi si hi si

H2Ogas OH−YSZ

H2,gas O2−YSZ

O2,gas H2OYSZ

YSZ

HNi

ONi

V••O YSZ

OHNi Hxi Ni

H2ONi H•i YSZ

Ni OXO YSZ

H2,gas

H2O,gas O2,gas

Ni

HNi

ONi OHNi

H2ONi Ni

O2−

YSZ OH−

YSZ H2OYSZ YSZ

OX

OYSZ V••

OYSZ H•

iYSZ Hx

i Ni



k0

f ,m

β m E act

f ,m

OX

OYSZ

O2−

YSZ

H2O

YSZ

k0 = ν at

Γ k

ν at

1013



H2O

TiO2

H

2O

OXOYSZ

Hxi Ni

H•i YSZ

YSZ

YSZ

ZrO2

TiO2

H2O

YSZ

YSZ

1.4 ·10−7 cm2/s



Γ Y S Z

=

1 . 3

·

1 0 − 9

m o l / c m 2

Γ N i =

6 . 1

·

1 0 − 9

m o l / c m 2

S i

k 0 i

k 0 i

E a c t

i

[ k J /

m o l ]

β i

Y S Z

H 2 O

g a s

+

Y S Z

H 2 O

Y s Z

6 . 6

·

1 0 1 1

c m

3 /

( m o l · s )

S

H 2 O

Y S Z +

O 2 −

Y S Z

2 ·

O H − Y

S Z

7 . 7

·

1 0 2 1

c m 2 /

( m o l · s )

H • i Y

S Z +

O H − Y

S Z

V Y S Z +

H 2 O

Y S Z

7 . 7

·

1 0 2 1

c m

2 /

( m o l · s )

O 2 − Y S

Z +

V • •

O Y S Z

O XO

Y S Z +

Y S Z

7 . 7

·

1 0 2 1

c m

2 /

( m o l · s )

H 2 O

g a s

+

N i

H 2 O

N i

1 . 4

·

1 0 1 0

c m

3 /

( m o l · s )

S

H 2 , g

a s +

2 ·

N i

2 ·

H N i

9 . 8

·

1 0 1 7

c m 5 /

( m o l · s )

S

H N i

+

O N i

O H

N i +

N i

5 . 0

·

1 0 2 2

c m

2 /

( m o l · s )

H 2 O

N i +

O N i

2 ·

O H

N i

5 . 4

·

1 0 2 3

c m

2 /

( m o l · s )

O H

N i +

H N i

H 2 O

N i +

N i

3 . 0

·

1 0 2 0

c m

2 /

( m o l · s )

H N i

+

V N i

H x i

N i +

N i

1 . 6

·

1 0 2 1

c m

2 /

( m o l · s )

H N i

+

O H − Y

S Z

H 2 O

Y S Z +

e N

i +

N i

α =

0 . 5

H N i

+

O 2 −

Y S Z

O H − Y

S Z +

e N

i +

N i

α =

0 . 5

O 2 − Y S

Z

O − Y

S Z +

e N

i

α =

0 . 5

O − Y S

Z +

N i

O N i +

e N

i +

Y S Z

α =

0 . 5

O 2 − Y S

Z +

N i

O − N

i +

e N

i +

Y S Z

α =

0 . 5

O − N i

O N i +

e N

i

α =

0 . 5

O 2 − Y S

Z +

N i

O N i +

2 ·

e N

i +

Y S Z

α =

0 . 5

O H − Y

S Z +

N i

O H

N i +

e N

i +

Y S Z

α =

0 . 5

V Y S

Z +

H x i

N i

V N i +

H • i

Y S Z +

e N

i

α =

0 . 5



D0

i

ν at = 1013Hz

lNi = 3.6·10−10m

lYSZ = 5.1 · 10−10m

E act

i

ZrO2

D0i

ˆcm2/s

˜ E acti [kJ/mol]

Di

ˆcm2/s

˜

HNi 3.7 · 10−3 9.2 · 10−4

2.8 · 10−3 2.7 · 10−4

6 · 10−3 1.0 · 10−3

6 · 10−3 1.2 · 10−3

4.6 · 10−3 7.8 · 10−4

ONi 7 · 10−3 8 · 10−5

3 · 10−5

6 · 10−3 6.6 · 10−6

6 · 10−3 3.0 · 10−9

6.3 · 10−3 3.2 · 10−6

OHNi 6 · 10−3 6.5 · 10−6

6 · 10−3 2.9 · 10−3

6.0 · 10−3

1.4 · 10−4

H2ONi 6 · 10−3 6 · 10−6

6 · 10−3 ∼ 0 6 · 10−3

6 · 10−3 1.8 · 10−4

Hxi Ni 7.6 · 10−2

4.7 · 10−4

O2−YSZ 5.5 · 10−7

8.1 · 10−12 ZrO2

CeO2

3 · 10−9 7.3 · 10−11 TiO2

5.5 · 10−7 8.1 · 10−12

H2OYSZ 1.3 · 10−2 1.5 · 10−5

OH−YSZ 1.3 · 10−2

1.5 · 10−5

H•i YSZ 5.6 · 10−3

1.4 · 10−7



∂∂t

θi = σiΓ k

sAi − ∂∂z

J surf i

sAi =

Xm

νi,m

0B@kf ,m

Yj∈Rf ,m

cν

jj − kr,m

Yj∈Rr,m

cν

jj

1CA

kf ,m = k0f ,m · T βm · exp

−Eactf ,mRT

!

kr,m = kf ,m · exp

„∆Gm

RT

«

∆Gm =X

i∈Rf ,m

ν

i,m (hi − T · si) −X

i∈Rr,m

ν

i,m (hi − T · si)

J surf i = −Dsurf i · θ ·

∂θi∂z

Dsurf i = D0

i · e−EactiRT .

D0i = 1

2 · νat · l

2 .

kf ,ct = k0f ,ct exp

−

Eactf ,ct

RT

!exp

„αzF

RT · ∆φ

«

kr,ct = kf ,ct exp

„∆Gm

RT

«exp

„− (1 − α)

zF

RT · ∆φ

«

∆φwork = φelde,work − φelyt,work

∆φref = φelde,ref − φelyt,ref

∂∂y

“σelyt

∂∂y φelyt

”= 0

Relyt = T AΣ

· exp“EσRT

”

η = φelde,work − φelde,ref

iAF,ct = zFlATPB

0B@kf

Yj∈Rf ,ct

θν

jj − kr

Yj∈Rr,ct

θν

jj

1CA

mTafel = α · z

iAF =X

allCTRs

iAF,ct



Rexp

pol

f s

lA

TPB

lATPB = 3.7 m/cm2

Rexppol [Ω/cm2] f s lA

TPB [m/cm2]

p(H2) = 2.5 · 104 − 7.5 · 104

p(H2O) = 4 · 101 − 2 · 103

T = 673 − 973

η = 0 − 200

H2

H2O

N2

H2

H2O

Rpol

mTafel

Rexp

pol

f s = lsTPB/lref

TPB = Rexp,ref pol /Rexp,s

pol

m/cm2

Si, Al

Na



pH2 2.5 · 104

pH2O 5 · 101

ptot

lATPB

m/cm2

dNi µm

dYSZ µm

η

T



k0

E act

pH2

pH2O T

H2

H2

H2O

pH2O



k 0 H 1 =

2 . 5 · 1 0 3 m

o l / ( c m · s )

E a c t

H 1

=

1 7 5 k J / m o l

D 0 H 2 O

Y S Z

=

6 . 3 · 1 0 + 3 c m 2 / s

D 0 O H

− Y S Z

=

3 . 3 · 1 0 + 3 c m 2 / s

O H − Y S Z

H 2 O

k 0 H 2 =

1 . 2 · 1 0 − 2

m o l / ( c m · s )

E a c t

H 2

=

1 1 3 k J / m o l

D 0 H 2 O

Y S Z

=

7 . 3 · 1 0 − 2 c m 2 / s

D 0 O H

− Y S Z

=

6 . 3 · 1 0 − 3 c m 2 / s

O H − Y S Z

H 2 O

∼

1

k 0 H 1 =

6 . 0 · 1 0 2 m

o l / ( c m · s )

E a c t

H 1

=

1 8 5 k J / m o l

k 0 H 2 =

8 . 0 m o l / ( c

m · s )

E a c t

H 2

=

1 6 7 k J / m o l

D 0 H 2 O

Y S Z

=

1 . 3 · 1 0 − 3 c m 2 / s

D 0 O H

− Y S Z

=

5 . 3 · 1 0 − 3 c m 2 / s

O H − Y S Z

H 2 O

H 2 O

k 0 H 1 =

2 . 0 · 1 0 2 m

o l / ( c m · s )

E a c t

H 1

=

1 7 4 k J / m o l

k 0 H 2 =

4 . 2 m o l / ( c

m · s )

E a c t

H 2

=

1 1 3 k J / m o l

D 0 H 2 O

Y S Z

=

3 . 3 · 1 0 + 3 c m 2 / s

D

0 O H − Y S Z

=

3 . 3 c m 2 / s

H 2 O

O H − Y S Z

H 2 O

H 2 O

k 0 O 1 =

2 . 4 · 1 0 − 2

m o l / ( c m · s )

E a c t

O 1

=

7 1 k J / m o l

k 0 O 2 =

2 . 5 · 1 0 − 5

m o l / ( c m · s )

E a c t

O 2

=

7 1 k J / m o l

D 0 O H N i =

1 . 0 · 1 0 − 1 c m 2 / s

D 0 O

N i =

8 . 0 · 1 0 − 1 c m 2 / s

O H N i

O N i

∼

2

k 0 O 3 =

7 . 3 · 1 0 − 5

m o l / ( c m · s )

E a c t

O 3

=

7 3 k J / m o l

k 0 = O 4 =

1 . 1 · 1 0 −

4 m o l / ( c m · s )

E a c t

O 4

=

7 3 k J / m o l

D 0 O

N i =

5 . 0 · 1 0 − 2 c m 2 / s

O N i

k 0 O H

=

4 . 5 · 1 0 − 4 m o l / ( c m · s )

E a c t

O H

=

7 3 k J / m o l

D 0 O H N i =

6 . 0 c m 2 / s

D 0 O H − Y S Z

=

5 . 3

c m 2 / s

O H N i

O H − Y S Z

k 0 O 5 =

4 . 0 · 1 0 − 4

m o l / ( c m · s )

E a c t

O 5

=

7 4 k J / m o l

D 0 O

N i =

1 . 0 · 1 0 + 1 c m 2 / s

O N i

H 2 O

k 0 H

− I n t =

4 . 5 · 1 0 − 4 m o l / ( c m · s )

E a c t

O H

=

7 3 k J / m o l

D 0 H • i Y S Z

=

0 . 6 c m 2 / s

H • i Y S Z



100

101

102

103

103

104

105

R p o l [ Ω c

m 2 ]

l o g i [ A / c m

2 ]

p H2 [Pa] p H2O [Pa] T [K] η [V]

O5

100

101

102

103

101

102

103

104

101

102

103

104

750 850 950-5

-4

-3

-2

-1

-0.5 0 0.5

100

101

102

103

103

104

105

R p o l [ Ω c

m 2 ]

l o g

i [ A / c m

2 ]

OH

100

101

102

103

101

102

103

104

101

102

103

104

750 850 950-5-4

-3

-2

-1

-0.5 0 0.5

100

101

102

103

103

104

105

R

p o l [ Ω c

m 2 ]

l o

g i [ A / c m

2 ]

O3+O4

100

101

102

103

101

102

103

104

101

102

103

104

750 850 950-5

-4

-3

-2

-1

-0.5 0 0.5

100

101

102

103

103

104

105

R p o l [ Ω c

m 2 ]

l o g i [ A / c m

2 ]

H1+H2

100

101

102

103

101

102

103

104

101

102

103

104

750 850 950-5

-4

-3

-2

-1

-0.5 0 0.5

100

101

102

103

103

104

105

R p o l [ Ω c

m 2 ]

l o g i [ A / c m

2 ]

H1

100

101

102

103

101

102

103

104 101

102

103

104

750 850 950-5

-4

-3

-2

-1

-0.5 0 0.5

100

101

102

103

103

104

105

R p o l [ Ω c

m 2 ]

l o g i [ A / c m

2 ]

H2

100

101

102

103

101

102

103

104

101

102

103

104

750 850 950-5

-4

-3

-2

-1

-0.5 0 0.5

100

101

102

103

103

104

105

R p o l [ Ω c

m 2 ]

l o g i [ A / c m

2 ]

O1+O2

100

101

102

103

101

102

103

104

101

102

103

104

750 850 950-5

-4

-3

-2

-1

-0.5 0 0.5

η=0 mV η=50 mV η=100 mV η=200 mV



100

101

102

103

103

104

105

p H2 [Pa]

R

p o l

[ Ω c

m 2 ]

l o g i [ A / c m

2 ]

H1+H2

100

101

102

103

101

102

103

104

p H2O [Pa]

101

102

103

750 850 950

T [K]

-5

-4

-3

-2

-1

-0.5 0 0.5

η [V]

η=0 mV η=50 mV η=100 mV η=200 mV

H2OYSZ

η = ±200

10−8

10−7 m



-10

-8

-6

-4

-2

0

-6 -7 -8 -9 -9 -8 -7 -6

l o g c

o v e r a g e

H1+H2 η = +200mV

HNi

ONi

H2ONi

OHNi

OH-YSZ

H2OYSZ

O2-

YSZ

-6 -7 -8 -9 -9 -8 -7 -6

H1+H2 η = -200mV

HNi

ONi

H2ONi

OHNi

OH-YSZ

H2OYSZ

O2-

YSZ

-10

-8

-6

-4

-2

0

-6 -7 -8 -9 -9 -8 -7 -6

l o g c

o v e r a g e

log dist. from TPB [m]

O1+O2 η = +200mV

HNi

ONi

H2ONi

OHNi

OH-YSZ

H2OYSZ

O2-

YSZ

O-YSZ

-6 -7 -8 -9 -9 -8 -7 -6

log dist. from TPB [m]

O1+O2 η = -200mV

HNi

ONi

H2ONi

OHNi

OH-YSZ

H2OYSZ

O2-

YSZ

O-YSZ

i

η = ±200

η = 0

P i

P 0i

P +i = 1.1 ·P 0i ∂i = (i+−i0)/i0

∂P i = (P +i −P 0i )/P 0i = 0.1

f rel = ∂i/∂P i

P i

f rel

f rel >



-1 -0.5 0 0.5 1-1 -0.5 0 0.5 1-1 -0.5 0 0.5 1

H2 + 2Ni = 2HNi

H2O + Ni = H2ONi

HNi + ONi = Ni + OHNi

H2O + ONi = 2OHNi

OHNi + HNi = Ni + H2ONi

H2O + YSZ = H2OYSZ

H2OYSZ + O2-YSZ = 2OH-

YSZ

HNi + OH-YSZ = H2OYSZ + Ni + e'Ni

HNi

OHNi

H2ONi

ONi

O2-YSZ

OH-YSZ

H2OYSZ

HNi

H2ONi

ONi

OH-YSZ

H2OYSZ

OHNi

O2-YSZ

O2-YSZ + VO,YSZ = OO,YSZ + YSZ

x

HNi + O2-YSZ = OH-

YSZ + Ni + e'Ni

k i

Di

μ i

η = -200 mV η = 0 mV η = +200 mV

CTR

Sensitivity of cuent !f e"

# Sensitivity of R ct

Sensitivity of cuent !f e"

#

1.$

10.%

-2.%

-&%

(

&.2

-5.1

-(.2

&.

-).&

-1.(

i

η = +200

η = −200

Rpol

η = 0

ki

Di

µi = hi − T · si

OH−

YSZ



OH−

YSZ

OH−

YSZ

OH−

YSZ

OH−

YSZ

OH−

YSZ

µi

∆G

µi

OH−

YSZ



a) b) c)

1 12 3 1+33

dist from TPB

c o v e r a g e



100

101

102

103

103

104

105

R p o l

[ Ω c

m 2

]

l o g i [ A / c m

2 ]


H1+H2

100

101

102

103

101

102

103

104

101

102

103

104

750 850 950

-5

-4

-3

-2

-1

-0.5 0 0.5

100

101

102

103

103

104

105

R p o l

[ Ω c

m 2 ]

l o g i [ A / c m

2 ]

O1+O2

100

101

102

103

101

102

103

104

101

102

103

104

750 850 950

-5

-4

-3

-2

-1

-0.5 0 0.5

η=0 mV η=50 mV η=100 mV η=200 mV

dYSZ = 60 nm dNi = 10 µm

dYSZ =

10 µm dNi = 70 nm

100

101

102

103

103

104

105

R p o l

[ Ω c

m 2 ]

l o g i [ A / c m

2 ]


H1+H2

100

101

102

103

101

102

103

104

101

102

103

104

750 850 950

-5

-4

-3

-2

-1

-0.5 0 0.5

100

101

102

103

103

104

105

R p o l [ Ω c

m 2 ]

l o g i

[ A / c m

2 ]

O1+O2

100

101

102

103

101

102

103

104

101

102

103

104

750 850 950

-5

-4

-3

-2

-1

-0.5 0 0.5

η=0 mV η=50 mV η=100 mV η=200 mV





TPB

Edge

y

z =0

Surface diffusion

Hxi, Ni

H•i, YSZ

z =½ d YSZ

½ hYSZ

d Ni

Repeat unit d YSZ

Ni stripe

YSZ crysta

a!

"!



z = 0

z = 1/sdYSZ

y = 1/2 (hYSZ + hNi)

k0

H−Int

D0H•

i YSZ

ai

±300

ai = ci/cmax



100

101

102

103

103

104

105

p H2 [Pa]

R p o l

[ Ω c

m 2 ]

l o g i [ A / c m

2 ]

H-int

100

101

102

103

101

102

103

104

p H2O [Pa]

101

102

103

104

750 850 950

T [K]

-5

-4

-3

-2

-1

-0.5 0 0.5

η [V]

η=0 mV η=50 mV η=100 mV η=200 mV

0 5 10 15 20

10-2

10-1

100

101

102

0 5 10

10-3

10-2

10-1

100

0 5 10

10-3

10-2

10-1

100 −4

1.56 10−4

1.58 10

−4

1.59 10

b)

d)

−4

a)

c)

activity at 300 mV activity at −300 mV

0 5 10 15 20

10-2

10-1

100

101

102

µ

[

m

]

y

µ

[

m

]

y

µz [ m ] µz [ m ]

1.58 10

YSZ

Ni

10

10 10

10

10

−6

−4 −6

−7

−5

±

y = 10 µm



10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

10-2

10-1

100

101

C o v e r a g e N i s u r f a c e

Dist from TPB [µm]

H(NI)

OH(NI)

H2O(NI)

O(NI)

10-3

10-2

10-1

100

10110

-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

C o v e r a

g e Y S Z

s u r f a c e

Dist from TPB [µm]

O2-

(YSZ)

H2O(YSZ)

OH-(YSZ)

y ≈ 1/2hYSZ

OH−YSZ

•

1 µm

•

•



10-4

10-3

10-2

10-1

100

101

0 5 10

Dist. from TPB [µm]

edge

H2 ads. on Ni

10-4

10-3

10-2

10-1

100

101

0 5 10


H2O desorp. from YSZ

10-4

10-3

10-2

10-1

100

101

0 5 10


CT reaction

a)

F l u x

[ m o l / m ² / s ]

c)b)

η = 300 mV

8 µm

z = 2 µm

•

•

H•

i YSZ



hYSZ

cm2

pmol/s

µA

H2

H2O

H2

β

β = 1/2



β = 1/2

β = 3/2

H2OYSZ

OH−

YSZ + O2−YSZ

H2OYSZ

β = 3/2 H2OYSZ

> 1/2 · (RT )/F

H2OYSZ

H2OYSZ

H2O



SiO2

SiO2

•

•

•



•

H2 H2O

•

<





•

C1

C2

•

•

•

•





glowing Ptwire

thermocouple

fuel cell

a) Experimental setup b) Modelling domain

y

flat-flameburner

45 mm

13 mm

mCH4 mair

φ

φ = r/rstoich

r = ˙mfuel/ ˙mOx rstoich

C3H4

N2 : O2 = 79 : 21

ptot,std = 1 bar



Ce0.8 Sm0.2 O2−δ

175 µm

13 mm

1300 C

500 − 770 K

Sm0.5 St0.5 CoO3

5 wt% Rh2O3

57 wt%

8 mol%

38 wt%



1200 C

lcon = 60 cm



∂ρ∂t = −

∂ (ρvy)∂y − 2ρV

∂ (ρV )∂t = −

∂ (ρvyV )∂y − ∂

∂y

“µ∂V

∂y

”− ρV 2 −Λ

∂ (ρY i)∂t

= −∂ (ρvyY i)

∂y −

∂jdiff i∂y

+ sV i M i

∂ (ρcPT )∂t =

−∂ (ρvycPT )

∂y + ∂ ∂y

“λq

∂T ∂y

”−P

i∈Sg

cP,i jdiff i

∂T ∂y −

Pi∈Sg

sV i hi

∂ Λ∂y = 0

sV i =Pm

ν i,m

kf ,mQ

j∈Rf ,m

cν

jj − kr,mQ

j∈Rr,mcν

jj!

∂ (ci)∂t = −

∂J diff i∂y −

∂J flowi∂y + sV i

J diff i = −ciDi

∂Xi∂x

J flowi = −X icg

Bµ

∂p∂y

Di = (1 − X i)

Pj∈Sg,j=i

Xj/Deff ij

!−1

Deff ij = Deff

ji = τ

12

„ 1

1/DKi +

1/Dij+ 1

1/DKj +

1/Dij

«

B =

2d2P

72·τ (1−)2

sV i =P

AV k si

A

k∈SN

∂ (ρcPT )∂t = ∂

∂y “λq ∂T ∂y ”+ sq

sq = σielyt

“∂φelyt

∂y

”2+

Pi∈Sg,Ss

sV i hi

α = N u · λair

q

Lchar

jelecq = α (T elec − T gas) + σSBq

`T 4elec − T 4ref



θi = ciΓk

sAi =

Xm

ν i,m

0@kf ,m

Yj∈Rf ,m

cν

j

j − kr,m

Yj∈Rr,m

cν

j

j

1A

kf ,m = k0f ,m · T βm · exp

„−

Eactf ,m

RT

«

kr,m = kf ,m · exp

„∆Gm

RT

«

∆Gm =X

i∈Rf ,m

ν

i,m (hi − T · si) −X

i∈Rr,m

ν

i,m (hi − T · si)

kf ,ct = k0f ,ct exp

−

E actf ,ct

RT

!exp

„α

zF

RT · ∆φan

«

kr,ct = kf ,ct exp

„∆Gm

RT

«exp

„− (1 − α)

zF

RT · ∆φan

«

iV tot =P

j∈CTRsiV j

iVCTR = zF lV

TPB

0@kf

Yj∈Rf ,ct

θνjj − kr

Yj∈Rr,ct

θνjj

1A

i0ca = i∗ca exp

„−

EactcathRT

«„pcaO2p∗O2

«1/4„1 +

pcaO2p∗O2

«−1/2

ica = i0ca ·

hexp

“β a

zF RT ηca

”− exp

“−β c

zF RT ηca

”i

E (i) = φelde,cath − φelde,an(i)

∆φan = φelde,an − φelyt,an

∆φcath = φelde,ca − φelyt,ca

η = ∆φ − ∆φequil

∂ ∂y φelde = 0



∂ ∂y

“σelyt

∂ ∂y φelyt

”= 0

∂ ∂y

“σelytf σ ∂

∂y ∆φan”

= −iVtot

i =R

iVtot dy + iel

ielyt = −σeff elyt

∂ ∂y φelyt = −σelytf σ

∂ ∂y φelyt

iel = −ielytσeelyt(pcaO2

,T )

σielyt

(T ) exp

“ηcaF RT

”·

exp(EF /RT )−1

1−exp“

(−ielytLelytF )/“RTσi

elyt

””

σeelyt( pcath

O2 , T ) =

pcath

O2

p0

!−1/4

·a

elyt0

T · exp

b

elyt0

T

!

σelyt = AσT · exp

“−Eσ

RT

”

Ra = ρcon · lcon

Acon

ρcon = ρ0con · (1 + αcon · (T − T 0))



T cath

φ

d

P max

T cath

φ

vinlet

d



φ vinlet [cm/s] d [cm]

φ vinlet [cm/s] d [cm]



200

400

600

800

1000

1200

1400

1600

1800

2000

0 0.25 0.5

SOFC

1 2 3 4 5 6 7 8 9 10

flame front

gas phase

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 20 40 60 80 100 120 140 160 180 0

10

20

30

40

U c e l l

[ V ]

I cell [mA/cm2]

P cell [mW/cm2]

U cell [V]

10-14

10-12

10-10

10-8

10-6

10-4

10-2

100

0.4 0.5

anode

1 2 3 4 5 6 7 8 9 10

flame front

gas phase

10-14

10-12

10-10

10-8

10-6

10-4

10-2

100

0.4 0.5

anode

1 2 3 4 5 6 7 8 9 10

gas phase

0

20

40

60

80

100

0 2 4 6 8 10 0

0.2

0.4

0.6

0.8

1

v rad [1/s]

v ax [m/s]

10-14

10-12

10-10

10-8

10-6

10-4

10-2

100

0.4 0.5

anode

1 2 3 4 5 6 7 8 9 10

flame front

gas phase

v

G a s v e l o c i t i e s

X

M o l e f r a c t i o n

X


X


b)a)

c)

f)e)

Dist. from cathode surface [mm] Dist. from cathode surface [mm]

Dist. from cathode surface [mm]

E

Exp

C A T e m p e r a t u r e [ K ]

d)

ExpSim Sim Exp

Dist. from cathode surface [mm]



10−10

10−5

H2O

H2

CO CO2

φ = 1.2



10-14

10-12

10-10

10-8

10-6

10-4

10-2

100

0 0.1 0.2

anode

1 2 3 4 5 6 7 8 9 10

flame front

gas phase

CH4 O2 CH H OH

10-2

10-1

0 0.1 0.2

anode

1 2 3 4 5 6 7 8 9 10

flame front

gas phase

H2 H2O CO CO2

Distance from cathode surface mm

M o l e f r a c t i o

n

CO2

H2

CO2

CO2



29.7

29.8

29.9

30

30.1

30.2

30.3

30.4

0 50 100 150 200

C o v e r a

g e [ % ]

H(Ni)

39.6

39.8

40

40.2 40.4

40.6

40.8

41

41.2

41.4

0 50 100 150 200

CO(Ni)

3.34 3.36 3.38

3.4 3.42 3.44 3.46 3.48

3.5 3.52 3.54

0 50 100 150 200

H2O(Ni)

2.21

2.22

2.23

2.24

2.25

2.26

2.27

2.28

0 50 100 150 200

Distance from dense electrolyte [µm]

C o v e r a g e [ ‰ ]

OCV 150 mA

CO2(Ni)

CO2

CO2



0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 50 100 150 200

U c e l l [ V

]

Current [mA/cm2]

ExpFull modelIV model

0

5

10

15

20

25

30

35

40

0 50 100 150 200

P [ m W / c m

2 ]

Current [mA/cm2]

ExpFull modelIV model

C3H7



Full model Thermal model

500

1000

1500

2000

2500

0 0.250.5

SOFC

1 2 3 4 5 6 7 8 9 10

flame front

gas phase

T e m p e r a t u r e [ K ]

Distance from cathode [mm]



∆T = T an − T cath

∆T

P max

φ

vinlet

φ = 1.1

vinlet = 0.1m/s

φ = 1.1 vinlet = 0.2m/s

φ = 1.2

vinlet = 0.1m/s

P max



0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3

φ =1.1 v =0.1

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3

φ =1.1 v =0.2

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3

φ =1.1 v =0.3

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3

φ =1.2 v =0.1

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3

φ =1.2 v =0.2

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3

φ =1.2 v =0.3

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3

φ =1.3 v =0.1

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3

φ =1.3 v =0.2

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3

φ =1.3 v =0.3

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3

φ =1.4 v =0.1

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3

φ =1.4 v =0.2

I mA I mA I mA

Exp

Sim

C e l l v o l t a g e [ V ]

C e l l v o l t a g e [ V ]



0.6

0.7

0.8

0.9

1

1.1

1.2

1 2 3 4 5 6 7 8 9 10 11

O C V

[ V ]

Flame condition

φ =1.1 φ =1.2 φ =1.3 φ =1.4

model experiment

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10 11

P m a x

[ m W / c m

2 ]

Flame condition

φ =1.1 φ =1.2 φ =1.3 φ =1.4

model experiment

v v

a

P max

φ



600

700

800

900

1000

1100

1 2 3 4 5 6 7 8 9 10 11

T

[ K ]

Flame condition

φ =1.1 φ =1.2 φ =1.3 φ =1.4

model experiment

OCVNernst



0

20

40

60

80

100

120

140

160

600 800 1000 1200 1400

P m a x

[ m W

/ c m

2 ]

Temperature [K]

Sim. flat-flameExp. porousExp. flat-flame

0.2

0.4

0.6

0.8

1

1.2

600 800 1000 1200 1400

O C V [ V ]

Temperature [K]

Exp. porousExp. flat-flameSim. flat-flameOCVNernst

a) b)

P max

T peak



0

10

20

30

40

50

600 800 1000 1200 1400

P o w e r l o s s [ m W / c m

2 ]

Temperature [K]

Cath.Elyt. ionicElyt. electronicAnodeRa

0

20

40

60

80

100

600 800 1000 1200 1400

R e l a t i v e p o w e r l o s s [ % ]

Temperature [K]

a) b)

•

Ra

•

•



•



0

50

100

150

200

250

0.5 1 1.5 2 2.5 3 3.5 4

P m a x

[ m W / c m

2 ]

Wire radius [mm]

standard

60

70

80

90

100

110

0 50 100 150 200 250 300 350

P m a x

[ m W / c m

2 ]

Electrolyte thickness [µm]

standard

60

70

80

90

100

110

0 50 100 150 200 250 300 350 400

P m a x

[ m W / c m

2 ]

Anode thickness [µm]

standard

60

70

80

90

100

110

0 50 100 150 200 250 300 350 400

P m a x

[ m W / c m

2 ]

Cathode thickness [µm]

standard

a) b)

c)

T = T peak



H2

CO

P max



mW/cm2

mW/cm2

dan µm β

an E actcath

kJmol

τ an i∗ca 5.9 · 1017 A

m3

dcath µm p(O2)

cath lV,an

TPB 1 · 1012 m/m3

τ cath

k0H1 135 mol

s

E actH1 185 kJmol

Acell cm2 E actel

kJmol

aelyt0 7.3 · 1011 K

(Ω·m·Pa1/4)

pO2cath 4.9 · 108

belyt0 2.7 · 10−4

E σ Lchar

Aσ 5.2 · 107 1/K Nu

delyt µm λairq

W/(mK)

lcon λelytq

W/(mK)

Acon mm2 λan

q

W/(mK)

αcon 3.8 · 10−3 1/K λcatq

W/(mK)

ρ0con 110

(Ω·mm2)m ca

q

anq







H2











H•

iYSZ

H2Ogas + V••OYSZ 2 H•

i YSZ + OXOYSZ ,

H•

iYSZ

exp−∆G

RT =

a (H•iYSZ)2 · a OX

OYSZa H2Ogas · a (V••

OYSZ) .

H•

iYSZ

a (H•iYSZ) =

exp

−

∆G

RT

· a (V••

OYSZ)

a (OXOYSZ)

· a

H2Ogas

.

∆G

∆G = 2 · ∆G (H•iYSZ) + ∆G OX

OYSZ− ∆G (H2O) − ∆G (V••OYSZ) .



∆G

∆G (H•iYSZ) = −

RT

2

· lna (H•

i YSZ)2 · a

OX

OYSZ

a H2Ogas · a (V••

OYSZ)

+1

2 ·

∆G

H2Ogas

+ ∆G (V••

OYSZ) − ∆G

OXOYSZ

.

a (H•

iYSZ)

∆S (H•

iYSZ)

∆H (H•iYSZ)

∆G = ∆H − T · ∆S .

∆S (H•iYSZ) = 64.5 J

mol

∆H (H•iYSZ) = 16.4

kJ

mol .

∆H

OX

OYSZ

≡ 0

ZrO2

YO3

CaF2

csat

H•i YSZ

H•iYSZ

csatH•

i YSZ=

1

4 · ρYSZ ,

ρYSZ = 0.05 mol/cm3

ρH•i YSZ

= 1.25 · 104 mol

m3 .

Hx

i Ni

vNi = 6.59 cm3/mol



Hx

i Ni

csatHx

i Ni= 3.8 · 104 mol

m3 .

Hxi Ni

H2,gas 2 Hxi Ni ,

−∆G = RT · lna (Hx

i Ni)2

a (H2,gas)

.

Hx

i Ni H2,gas

∆S Hxi Ni

= 43 J

mol ; ∆HHx

i Ni= 36

kJ

mol .





10-6

10-5

10-4

10-3

10-2

10-1

0.8 1 1.2 1.4 1.6 1.8 2

σ

[ K / c m ]

1000/ T [1/K]

Fit: σ T =a * exp(-E act /R/T )

a =5.17e+05 [K*S/cm]

E act=80.2 [kJ/mol]

FitExp Jung et al.

Exp Shinko

C3



k0 β E act



k0 β E act



k0 β E act



k0 β E act



k0 β E act

H2

H2O CO2

CH4 O2

k0 β E act







T wall

A T fluid

∂

∂tQwall = A · α · (T wall − T fluid) ,

α

α = N u · λ

L ,

N u

L

λ

Nu = 1

∂

∂tQwall = −λ ·

A

L · (T wall − T fluid)

λ ≈ 5.848 · 10−2 W

m·K

L ≈ 1.2 · 10−2m

T





AVk

m2/m3

Acell cm2

Aσ K/Ω m

ai i

aelyt0

K/(Ω·m·Pa1/4)

B m2

belyt0

1/K

ci mol/m2

i

ci mol/m3

i

cg mol/m3

cq J/K·kg

d

d

dP

Di m2/s

i

Di m2/s

i

Dij m2/s

i

j

Deff ij

m2/s

DKi

m2/s

i

delyt



E actf ,r

J/mol

E

E σ J/mol

F C/mol

f

f σ

∆G J/mol

g m/s2

hi J/mol

i

∆H J/mol

hNi

i0 A/m3

i∗ A/m3

icell A/m2

iel A/m2

iAF

A/m2

i

V

F

A

/m3

itot A/m2

J diff i

mol/m2s i

J flowi

mol/m2s i

jdiff i

kg/m2s i

jq J/m2s

k0ct

mol/m s

k0 mol/mns

lVTPB

m/m3

lATPB

m/m2

lcon

M kg/mol

M i kg/mol i

P cell W/m2



p

pi i

p0O2

R J/Kmol

R Ω

Rpol Ω cm2

S g

∆S J/Kmol

sAi

mol/m2s

sVi

mol/m3s

T

t

U th V

V m3

v m/s

vStef m/s

X i i

Xi i

Y i iy

z

z

α

α W/m2K

αcon 1/K

β

Γ mol/m2

ε

q

η

θi i

λq W/K m

i

µi kg/s m

i



µ kg/s m

ν i i

ν at

ρi kg/m3

i

ρcon (Ωmm2)/m

σi i

σelyt 1/Ω m

σeff elyt

1/Ω m

τ

τ w

φ V

∆φ V

Λ kg/m3s2

V••OYSZ

Hxi Ni

H•iYSZ

OXOYSZ





2 2

H2

H2

H2

H2O

Ni

YSZ



2

2 3



H2/H2O/Ni/YSZ



H2

H2 − H2O

Y2O3 ZrO2

2 2

OYSZ





Y2O3

ZrO2

18O2

16O

SiO2

Al2O3

ZrO2

CeO2

CeO2

Al2O3

TiO2





µ

Documents

Dissertation Vogler