2. Contents
Contents
• Motivation
• Overview over different FC types
• Net reactions and ideal potentials (Nernst Equation)
• Actual performance and energy losses
• Atomistic view of electrodes
– Double layer models
– Potentials
– Capacity model
– Charge distribution
• Problems for fuel cell modeling:
– Electrode / Interface
– Membrane
– H2 storage
2
3. First Fuel Cell
First Fuel Cell
3
In 1839, William Grove, a British jurist and amateur physicist,
In 1839, William Grove, a British jurist and amateur physicist, first
first
discovered the principle of the fuel cell. Grove utilized four c
discovered the principle of the fuel cell. Grove utilized four cells,
ells,
each containing hydrogen and oxygen, to produce electric power
each containing hydrogen and oxygen, to produce electric power
which was then used to split the water in the smaller upper cell
which was then used to split the water in the smaller upper cell into
into
hydrogen and oxygen
hydrogen and oxygen
4. 4
Why Fuel Cells?
Why Fuel Cells?
• Limitation of
fossile energy
resources
• Increasing
CO2 emission
• Global warming
• Transport problems
• .....
5. Pros – Cons (Ideal Situation)
Pros – Cons (Ideal Situation)
+
• Direct energy conversion (no combustion)
• Low emissions
• No moving part in the energy converter
• Quiet
• High availability of lower temperature units
• Siting ability
• Fuel flexibility
• Remote/unattended operation
• Small size
—
• High market entry cost, production cost
• Unfamiliar technology to the power industry
• Almost no infrastructure
• Still at level of development
5
8. 8
Fuel Cell types
Fuel Cell types
η
η 50
50-
-65%
65% 50
50-
-80
80%
% 35
35-
-45%
45% 45
45-
-60%
60% 50
50-
-60%
60%
Applications
Applications Transport,
Transport,
space
space,
, ships
ships
transport
transport,
,cars
cars,
,
space
space,
,houses
houses,
,
ships
ships,mobile
,mobile
appl
appl.
.
100 MW
100 MW plants
plants
50
50-
-500 kW
500 kW
block
block heating
heating
plants
plants
100 MW
100 MW plants
plants
50
50-
-500 kW
500 kW
block
block heating
heating
plants
plants
100 MW
100 MW plants
plants
50
50-
-500 kW
500 kW
block
block heating
heating
plants
plants
Status quo
Status quo 50
50-
-100 kW,
100 kW,
can be bought
can be bought,
,
expensive
expensive
20 kW, high
20 kW, high
efficiency
efficiency
100 kW
100 kW
prototype
prototype
25 kW
25 kW prototype
prototype
9. Fuel Cell Overview
Fuel Cell Overview
9
Electrode
catalysis:
•Make more
efficient
•Reduce
overpotential
Electrolyte:
•Less expensive
•More efficient
•Wide operation
temperature range
H2 storage:
•Carbon Nanotubes
•Metal Hydrides
10. 10
Pros – Cons (specific)
Pros – Cons (specific)
•
• PEMFC:
PEMFC: + Solid electrolyte Æ excellent
resistance to gas crossover
– Low CO tolerance (~ppm level)
– low temperature
+ working temperature ~80C
Æ short startup time
– unefficient to use rejected heat
for cogeneration of additional
power
+ can work at high current
densities compared to other cells
– difficult heat and water
management limit the operating
power densities
CF2
CF2
CF CF2
O CF2
CF O CF2
CF2
SO3
x y
CF3
z H
Nafion
Nafion®
®
11. Pros – Cons (specific)
Pros – Cons (specific)
•
• AFC
AFC:
: + Excellent performance on H2 and
O2 compared to other cells due to
active O2 electrode kinetics
(70% efficiency)
+ relatively low temperatures
(~80C)
– very clean fuel required, since
small contaminations dissociate
alkaline base,
– CO2 poisoning
+ wide range of possible
electrocatalysts
– significant pressure difference
across the membrane is required
– large Pt quantity is needed
because of harsh conditions
11
ISS
ISS
KOH
KOH
in matrix
in matrix
Pt
Pt
Pt
Pt
12. Pros – Cons (specific)
Pros – Cons (specific)
•
• PAFC:
PAFC:
12
+ CO2 (of reformed fuel gas stream)
resistent electrolyte
– lower performance due to slow
cathode reaction (37-42%)
+ low working temperatures
(~200C)
+ water boiling point is not limiting
– fuel from external hydrocarbon
reformation
+ less complex fuel conversion
(no membrane and attendent
pressure drop)
– high cost catalysts
– harsh conditions
– CO poisoning
(water gas shift reaction required)
H
H3
3PO
PO4
4 Pt
Pt
Pt
Pt
Timesquare
Timesquare
13. 13
Pros – Cons (specific)
Pros – Cons (specific)
• MCFC : + higher temperatures (~650C)
less sensitive reactions and less
expensive materials
+ Ni as catalyst
– very corrosive and mobile
electrolyte
– source of CO2 is required at
cathode to form carbonate ions
+ reforming within the cell
+ CO can directly be used as fuel
+ heat exhaust can be used with
external gas turbine (η~80%)
– low sulfur tolerance
– high temperatures
(~650C)
– stainless steel as cell hardware
– complex working procedure
Li
Li2
2CO
CO3
3
K
K2
2CO
CO3
3
Ni
Ni
Ni
Ni
14. 14
Pros – Cons (specific)
Pros – Cons (specific)
• SOFC + ceramic construction
Æ no hardware corrosion
Æ no gas crossover due to
absence of liquid
+ fast kinetics
– incoming air has to preheated
– high temperature (~1000C)
Æ thermal expansion mismatch
Æ sealing between cells is
difficult
+ fast kinetics
+ CO is directly usable
+ no CO2 is required at cathode
(as in MCFC)
– constraints on material collection
– difficult fabricate process
– high electrical resistivity in the
electrolyte Æ low performance
+ high temperature (~1000C)
Æ fuel can be reformed within
the cell
– high cost catalysts
Anode: Ni
Anode: Ni
Cathode: LaMnO
Cathode: LaMnO3
3
Electrolyte: YSZ
Electrolyte: YSZ
ZrO
ZrO2
2[Y
[Y2
2O
O3
3]
]
18. Nernst Equation
Nernst Equation
Temperature
Temperature
dependence of H
dependence of H2
2/O
/O2
2
Ideal Potential
Ideal Potential
Ideal voltage (for oxidation of hydrogen) as a function of cell
Ideal voltage (for oxidation of hydrogen) as a function of cell temperature
temperature
18
20. Actual Performance
Actual Performance
20
•
•Concentration Polarization
Concentration Polarization Æ
Æ reactions reduce educt concentrations
reactions reduce educt concentrations η
ηconc
conc
•
•Activation Polarization
Activation Polarization Æ
Æ Rates of electrochemical reactions
Rates of electrochemical reactions η
ηact
act
•
•Ohmic Polarization
Ohmic Polarization Æ
Æ resistance of ion flow
resistance of ion flow η
ηohm
ohm
21. 21
Concentration Polarization
Concentration Polarization
Rate of mass transport to an electrode surface can be described
Rate of mass transport to an electrode surface can be described by Fick’s first law of
by Fick’s first law of
diffusion:
diffusion:
(
(D
D: diffusion coefficient,
: diffusion coefficient, c
ci
i: concentration,
: concentration, δ
δ: thickness of diffusion layer
: thickness of diffusion layer
The limiting current (
The limiting current (i
iL
L) is a measure of the maximum rate at which reactants can be
) is a measure of the maximum rate at which reactants can be
supplied to an electrode and occurs at
supplied to an electrode and occurs at c
csurface
surface=0:
=0:
Nernst equation for
Nernst equation for reactant species
reactant species at equilibrium is
at equilibrium is
When current flows
When current flows c
csurface
surface is less than
is less than c
cbulk
bulk and
and
Potential difference produced by a concentration change:
Potential difference produced by a concentration change:
22. 22
Activation Polarization
Activation Polarization
The activation polarization is customarily expressed by a semi
The activation polarization is customarily expressed by a semi-
-
empirical equation, called Tafel equation:
empirical equation, called Tafel equation:
Here
Here α
α is the electron transfer coefficient of the reaction at the
is the electron transfer coefficient of the reaction at the
electrode, and
electrode, and i
i0
0 is the exchange current density.
is the exchange current density.
The usual form is given by
The usual form is given by
where a = (
where a = (−
−2.3
2.3RT
RT/
/α
αν
νF)
F)·
·log
logi
i0
0 and b=
and b= 2.3
2.3RT
RT/
/αν
ανF.
F.
B is called the Tafel slope
B is called the Tafel slope
23. Actual Performance
Actual Performance
23
Sum of electrode polarization:
Sum of electrode polarization: η
ηanode
anode=
= η
ηact,a
act,a+
+ η
ηconc,a
conc,a
η
ηcathode
cathode=
= η
ηact,c
act,c+
+ η
ηconc,c
conc,c
The effect is to shift the potential of an electrode (
The effect is to shift the potential of an electrode (Φ
Φelectrode
electrode):
):
Φ
Φ’
’cathode
cathode=
= Φ
Φcathode
cathode −
− |
| η
ηcathode
cathode|
|
Φ
Φ’
’anode
anode=
= Φ
Φanode
anode + |
+ | η
ηanode
anode|
|
Φ
Φcell
cell=
= Φ
Φcathode
cathode − |
− | η
ηcathode
cathode| − (
| − (Φ
Φanode
anode + |
+ | η
ηanode
anode|) − I
|) − I·
·R
R
Φ
Φcell
cell=
=∆
∆Φ
Φ − |
− | η
ηcathode
cathode| − |
| − | η
ηanode
anode| − I·R
| − I·R
Φ
Φcell
cell= − |
= − | η
ηcathode
cathode| − |
| − | η
ηanode
anode| − I·R
| − I·R
Current flow reduces cell voltage due to electrode and ohmic pol
Current flow reduces cell voltage due to electrode and ohmic polarization
arization
Goal: Minimize the polarization
Goal: Minimize the polarization
25. Atomistic View of Electrode
Atomistic View of Electrode
Steps
Steps of
of electrochemical reaction
electrochemical reaction:
:
1.
1. Transport of
Transport of reactants
reactants to
to electrode
electrode
2.
2. Adsorption of
Adsorption of reactants
reactants at
at electrode
electrode (
(maybe dissociative ads
maybe dissociative ads.)
.)
e.g. H
e.g. H2
2 H
H2,
2,ads
ads; H
; H2,
2,ads
ads 2H
2Hads
ads; H
; H2
2 H
H+
+ + A
+ A–
–
3.
3. Electron transfer through phase boundary
Electron transfer through phase boundary
e.g. H
e.g. H+
+ + e
+ e–
– H
Hads
ads
4.
4. Follow
Follow-
-reactions
reactions at
at electrode
electrode surface and desorption
surface and desorption
e.g. 2H
e.g. 2Hads
ads H
H2
2(g)
(g)
5.
5. Removing reaction products
Removing reaction products to
to solution
solution
25
26. Electron Transfer
Electron Transfer
E
EF
F:
: Fermi
Fermi-
-level
level of metal
of metal
a
a: Tunnel distance
: Tunnel distance
Φ
Φ:
: Work function
Work function of metal
of metal
EA
EA:
: Electron affinity
Electron affinity
EA
EA >
> Φ
Φ for reduction
for reduction
Φ
Φ–
–EA
EA should be small
Metal
Metal
Electrolyte
Electrolyte
should be small
Open
Open circuit
circuit:
: Reaction takes place until equilibrium
Reaction takes place until equilibrium at
at electrode
electrode
equilibrium
equilibrium potential
potential φ
φ0
26
Opposite charge distribution
Opposite charge distribution
in metal and
in metal and electrolyte
0
electrolyte
27. Double-Layer
Double-Layer
Metal
Metal Electrolyte
Electrolyte (
(solution
solution)
)
x
x
solution
solution Electroneutral
Electroneutral!
!
Potential
Potential is
is a
a result
result of
of
the charge distribution
the charge distribution
27
•
•Equilibrium
Equilibrium:
: dynamic equilibrium
dynamic equilibrium of
of charge transfer
charge transfer in
in both
both
directions
directions of
of phase boundary
phase boundary
•
•Electrochemical process only if coupled with reduction
Electrochemical process only if coupled with reduction (
(oxidation
oxidation)
)
at
at opposite
opposite electrode
electrode
•
•open
open circuit
circuit: EMK =
: EMK = φ
φ0
0 of
of galvanic cell
galvanic cell
28. PSZ-Potential of Zero Charge
PSZ-Potential of Zero Charge
28
Negative
Negative
charging current
charging current
Positive
Positive
charging current
charging current
At a
At a certain electrode
certain electrode potential (potential of
potential (potential of zero
zero charge
charge)
) the
the
electrode
electrode surface
surface charge vanishes
charge vanishes:
: q
q = 0,
= 0, σ
σ = 0
= 0
This can be measured polarographically
This can be measured polarographically
measuring
measuring I
I for
for different
different φ
φ
I
I
29. Potential Convention
Potential Convention
29
ψ (outer potential)
χ
φ (inner potential)
Remove electrolyte without changing the charge distribution
Remove electrolyte without changing the charge distribution of
of the
the
metal (surface)
metal (surface)
1
1
2
2
3
3
Region 1: Test
Region 1: Test charge feels Coulomb
charge feels Coulomb potential at far
potential at far distances
distances
Region 2: Surface
Region 2: Surface charge is not
charge is not a point
a point charge
charge
Region 3: Test
Region 3: Test charge feels
charge feels surface
surface charges
charges
vacuum
vacuum
E
E
30. Detailed view of Double-Layer
Detailed view of Double-Layer
Physisorption
Physisorption:
:
-
- electrostatic interaction between
electrostatic interaction between
charges
charges
-
- charge
charge-
-dipol interaction
dipol interaction
-
- polarisation
polarisation of
of molecules
molecules and
and ions
ions
-
- dispersion forces
dispersion forces,
, vdW forces
vdW forces
-
- Attachment
Attachment of
of opposite charged
opposite charged
ions
ions and
and molecule
molecule-
-dipols
dipols
Chemisorption
Chemisorption:
:
-
- chemical interaction between
chemical interaction between
particles
particles and metal
and metal
30
31. Detailed view of Double-Layer
Detailed view of Double-Layer
31
Inner Helmholtz Plane:
Inner Helmholtz Plane:
plane of
plane of adsorbed species
adsorbed species
(
(direct electrode contact
direct electrode contact)
)
Inner Helmholtz
Inner Helmholtz Layer
Layer:
:
Area
Area of
of reactions with desolvated
reactions with desolvated
particles
particles
Outer
Outer Helmholtz Plane:
Helmholtz Plane:
plane of
plane of closest possible solvated
closest possible solvated
particles
particles
Outer Hemholtz Layer
Outer Hemholtz Layer:
:
Area
Area of
of redoxreaction between
redoxreaction between
solvated particles
solvated particles
32. Condensator Model of Double-Layer
o.H.p. model
Condensator Model of Double-Layer
o.H.p. model
32
Charge
Charge density
density on metal surface:
on metal surface:
equivalent charge density
equivalent charge density in o.H.p.
in o.H.p. Æ
Æ electric
electric double
double layer
layer
Integral double
Integral double layer capacity
layer capacity (relative to
(relative to psz level
psz level):
):
Differential double
Differential double layer capacity
layer capacity:
:
Measurement
Measurement of differential
of differential capacity with
capacity with DC
DC methods
methods,
, electrocapillar
electrocapillar-
-experiments
experiments
33. Condensator Model of Double-Layer
o.H.p. model
Condensator Model of Double-Layer
o.H.p. model
33
Double
Double layer capacity
layer capacity
Electrolyte resistance
Electrolyte resistance
Capacity
Capacity of
of
reference electrode
reference electrode
(
(usually neglected
usually neglected)
)
Measurement by
Measurement by potential drop
potential drop method
method:
:
Solving Diff
Solving Diff.
. Eq
Eq.
. for
for q,
q, then integrate over
then integrate over t:
t:
Evaluate
Evaluate I:
I:
34. Models for electric double layer
Models for electric double layer
34
Helmholtz (1853)
Helmholtz (1853)
static
static double
double layer
layer
Gouy
Gouy (1910) and
(1910) and
Chapman
Chapman (1913)
(1913)
diffuse double
diffuse double layer
layer
Stern (1924)
Stern (1924) static
static
and diffuse double
and diffuse double
layer
layer (
(combination
combination)
)
New
New model
model also
also include
include:
:
•
•Specific adsorption
Specific adsorption at
at electrode
electrode
•
•Ion
Ion-
-metal,
metal, molecule
molecule-
-metal
metal
interaction
interaction and
and catalytic effects
catalytic effects
•
•Structure
Structure of
of conduction bands
conduction bands
•
•Overlap between valence
Overlap between valence band and
band and
conduction
conduction band at
band at phase boundary
phase boundary
•
•Dielectric filling
Dielectric filling of double
of double layer
layer
•
•Deformation of
Deformation of conduction
conduction band
band
35. Stern Model
Stern Model
Double
Double layer without adsorption
layer without adsorption of
of ions
ions (
(charges
charges)
) within the
within the i.H.l.
i.H.l.
35
o.H.l.:
o.H.l.: static
static double
double layer
layer,
, free
free of
of charges
charges
Poisson equation with conditions
Poisson equation with conditions:
:
Zeta
Zeta-
-Potential at
Potential at the boundary between
the boundary between
static
static Helmholtz
Helmholtz layer
layer and diffuse
and diffuse layer
layer
Æ
Æ Distance
Distance-
-dependency
dependency of potential:
of potential:
Diffuse double
Diffuse double layer
layer:
: Electrolyte beyond the
Electrolyte beyond the o.H.l. (
o.H.l. (bulk solution
bulk solution)
)
Poisson equation
Poisson equation:
:
36. Stern Model
Stern Model
Diffuse double
Diffuse double layer
layer
36
Conditions
Conditions:
:
Boltzmann
Boltzmann-
-Ansatz
Ansatz for the charge
for the charge
distribution within the electrolyte
distribution within the electrolyte Insert into Poisson equation
Insert into Poisson equation:
:
If
If Æ
Æ small concentrations
small concentrations Æ
Æ Taylor
Taylor expansion
expansion
Solution of
Solution of the
the partial differential
partial differential equation
equation:
:
37. Stern Model
Stern Model
Diffuse double
Diffuse double layer
layer
37
Conditions
Conditions:
:
1. Condition:
1. Condition:
2. Condition:
2. Condition:
Debye
Debye-
-distance:
distance: κ
κ-
-1
1
center
center of
of charge
charge in
in the
the
diffuse double
diffuse double layer
layer
For x =
For x = κ
κ-
-1
1:
:
Charge
Charge-
-density
density
38. Stern Model
Stern Model
Diffuse double
Diffuse double layer
layer
Small
Small κ
κ Æ
Æ broad
broad double
double layer extends into electrolyte region
layer extends into electrolyte region
Æ
Æ ς
ς of
of the
the o.H.p.
o.H.p. can be replaced by the electrode
can be replaced by the electrode potential
potential
Electric
Electric Field
Field:
:
38
Continous transition
Continous transition at
at x
x =
= a
a:
:
Charge
Charge density as
density as a
a function
function of
of the electrolyte concentration
the electrolyte concentration and
and electrode
electrode potential:
potential:
39. Stern Model
Stern Model
Diffuse double
Diffuse double layer
layer
39
Low concentrations
Low concentrations:
: Potential
Potential-
-drop
drop within the
within the o.H.l.
o.H.l. is almost zero
is almost zero
High
High concentrations
concentrations:
:
Potential
Potential-
-drop
drop within the
within the o.H.l.
o.H.l. increases with increasing concentrations
increases with increasing concentrations,
, linearisation
linearisation
of
of Poisson equation may be critical
Poisson equation may be critical!
!
Charge of
Charge of the
the diffuse
diffuse layer
layer
Capacity
Capacity of
of static
static double
double layer
layer:
: Capacity
Capacity of diffuse double
of diffuse double layer
layer:
:
Plate condensator
Plate condensator at distance
at distance κ
κ
40. Problems
Problems for Fuel Cell
for Fuel Cell
Modeling
Modeling
Electrodes
Electrodes /
/ Interfaces
Interfaces
40
41. 41
Current problems for modeling I
Current problems for modeling I
•
• Morphology
Morphology of
of the catalyst
the catalyst
In order to
In order to provide
provide a
a large surface area for simultaneous catalysis
large surface area for simultaneous catalysis
Pt
Pt nanoparticles
nanoparticles are used instead
are used instead of (semi
of (semi-
-) infinite systems
) infinite systems
However
However:
:
–
– Nanoparticles have structural
Nanoparticles have structural and
and
electronical properties
electronical properties,
, which might
which might
strongly depend
strongly depend on
on size
size and
and shape
shape
(e.g. Quantum
(e.g. Quantum Size Effects
Size Effects)
)
–
– Nanoparticles combine
Nanoparticles combine a
a variety
variety of
of
different
different functional groups
functional groups: different
: different
surfaces
surfaces,
, steps
steps,
, kinks
kinks,
, tips
tips,
, vacancies
vacancies, ...),
, ...),
having
having different
different properties
properties
Eb=0.49eV Eb=1.10eV
42. Current problems for modeling II
Current problems for modeling II
42
•
• Influence
Influence of
of the support
the support
– Pt nanoparticles are attached to
larger Carbon particles (~50nm),
which will change their structures.
Smaller particles Æ less deformation, close to spherical
structure
Larger particles Æ strong deformation, ellipsoidal shape
– Pt nanoparticles are assumed to be 2-5nm in diameter.
However, due to relatively low diffusion
barriers agglomeration may occur to create
larger particles.
(again having modified properties)
– Supporting material:
Pd particles on Au have ~10 times
higher reactivity than Pd particles on Cu
43. Current problems for modeling III
Current problems for modeling III
43
•Bulk region should have
structural properties (density,
distribution, …) of bulk Nafion,
otherwise system need to be
expanded
•Water layer forms between
electrode and membrane
(will be different in presence of
E-field)
after 2ns
44. Current problems for modeling IV
Current problems for modeling IV
•
• Reactive
Reactive Environment
Environment
–
– Cathode
Cathode is
is surrounded
surrounded by
by a
a variety
variety of different
of different compounds
compounds:
:
•
• H
H2
2O of
O of the
the electrolyte
electrolyte, and
, and reaction
reaction product
product
•
• H
H3
3O
O+
+
as
as proton
proton carrier
carrier (
(surrounded
surrounded by
by water
water molecules
molecules)
)
•
• O
O2
2 gas as
gas as reaction
reaction component
component
•
• Different
Different reaction
reaction intermediates
intermediates
(e.g. O, H, OH, OOH, HOOH,...)
(e.g. O, H, OH, OOH, HOOH,...)
•
• Impurities
Impurities in
in the
the fuel
fuel (e.g. CO,
(e.g. CO, No
Nox
x, ...)
, ...)
Æ
ÆThe
The environment
environment might
might influence
influence the
the structure
structure,
, stability
stability, and
, and
composition
composition of
of the
the Pt
Pt nanoparticles
nanoparticles (
(or
or certain
certain functional
functional
groups
groups).
).
Æ
ÆThis
This may
may vary
vary for
for different
different T
T and
and p
p conditions
conditions
44
45. Current problems for modeling V
Current problems for modeling V
45
•
• Solvation
Solvation effects
effects due
due to solvent in
to solvent in the
the electrolyte
electrolyte
–
– In
In case
case of
of PEM
PEM-
-FCs
FCs the
the electrolyte
electrolyte is
is hydrated
hydrated
–
– At
At the
the cathode
cathode water
water is
is generated
generated
Æ
ÆThe
The electrode
electrode is
is surrounded
surrounded by
by water
water
molecules
molecules,
, which
which influence
influence adsorption
adsorption
energies
energies and
and structures
structures.
.
This
This might
might change
change the
the reaction
reaction
mechanism
mechanism,
, but
but also
also stabilize
stabilize or
or
destabilize
destabilize certain
certain structures
structures
(e.g.
(e.g. electrode
electrode,
, adsorbates
adsorbates)
)
Æ
ÆSolvation
Solvation can
can be
be treated
treated by
by a
a two
two-
- or
or
three
three-
-shell
shell model
model
46. Current problems for modeling VI
Current problems for modeling VI
46
•
• Electrode
Electrode potential
potential
–
– Besides
Besides T
T and
and p
p,
, the
the electrode
electrode potential
potential φ
φ is
is another
another parameter
parameter,
, which
which
influences
influences structures
structures and energetics
and energetics
Example
Example: Au(100)
: Au(100) surface
surface in 0.01M HClO
in 0.01M HClO4
4-
-solution
solution
φ
φ<0.25V quasi
<0.25V quasi-
-hexagonal
hexagonal reconstruction
reconstruction
φ
φ>0.25V
>0.25V unreconstructed
unreconstructed surface
surface (H.
(H. Ibach
Ibach et al., Surf.
et al., Surf. Sci
Sci. 375, 107
. 375, 107
(1997))
(1997))
–
– Distribution of negative and positive
Distribution of negative and positive
charges
charges within
within the
the solution
solution changes
changes
–
– Counter
Counter charges
charges will
will be
be on
on the
the surface
surface
of
of the
the metal
metal electrode
electrode
(
(whole
whole interface
interface is
is electroneutral
electroneutral)
)
Æ
Æ electric
electric double
double layer
layer establishes
establishes
Æ
Æ potential drop (
potential drop (strong
strong E
E-
-field
field) on
) on
the
the electrode
electrode surface
surface
47. Current problems for modeling VII
Current problems for modeling VII
•
• All
All previous
previous problems
problems deal
deal with
with the
the system in
system in equilibrium
equilibrium.
.
However
However,
, under
under steady
steady state
state conditions
conditions structures
structures,
, compositions
compositions, and
, and
reaction
reaction mechanisms
mechanisms might
might be
be significantly
significantly different?
different?
Æ
Æ Use
Use kinetic
kinetic simulations
simulations to
to study
study exactly
exactly these
these influences
influences.
.
However
However, in order to
, in order to get
get reliable
reliable results
results all
all significant
significant processes
processes should
should
be
be studied
studied and
and the
the corresponding
corresponding parameters
parameters extracted
extracted:
:
Adsorptions
Adsorptions,
, desorptions
desorptions,
, diffusions
diffusions,
, reactions
reactions, …
, …
47
49. Ions exert dielectric
friction on H+ mobility
Sensitive parameter for
conductivity and
permeation
Each level has
implications on
membrane
performance
Width of water domains
affected by electrostatic
repulsions and polymer
elasticity
Coarseness of the
surface affects viscous
movement of the ion
Connectivity of water
domains determines
transport
Mechanical properties of
the matrix
wate
r
polymer
Stochastic & Analytical
Modeling
Nafion Microstructure
Atomistic & Coarse Grain
Simulations
Nanosegregation
5 nm
3.5 nm 1 nm
Atomistic Simulations
Interface analysis
Hydrated Nafion is a
multiscale
heterogenous
material
SO
3
Nanostructure & Dynamics of Polyelectrolyte Membranes
Nanostructure & Dynamics of Polyelectrolyte Membranes
Rational approach to the study of PEM: experiments and simulation are
complementary
Backbone flexibility
Backbone hydrophobicity
Equivalent weight
Charge localization
Side chain flexibility
Side chain polarity
Confinement 49
Blockiness of polymer
Side chain length
Acidity of ionomer
Counter ion
Water content
Temperature
Architecture of side chain
Microphase segregation
Water diffusion
Mechanical properties
Water’s electroosmotic drag
Maximum water uptake
Water evaporation
Extent of ionomer solvation
Mechanism of gas diffusion
Counter ion migration
Hydronium transport
Patchiness of the water/PE
interface
Interfacial free volume
Degree of crystallinity
T of glass transition(s)
Water percolation
50. Membrane structure
Membrane structure
Nafion 117
CF2
CF2
CF CF2
O CF2
CF O CF2
CF2
SO3
x y
CF3
z M
50
=
ALTERNATED POLYMER
SMALL PATCHES
=
BLOCKY POLYMER
BIG SEGREGATED
PATCHES
Effect of polymer sequence
Blockiness affects the extent of nanophase
segregation (is better for the blocky polymer) and
water-polymer interface heterogeneity.
We compute a water percolation threshold that is in
agreement with the one inferred from conductivity
The percolation of the hydrophilic phase is
necessary for proton conductivity. 0
Edmondson et al.
Solid State Ionics
(2002)
152: 355-361
Effect of water content
All the ions of the polymer contact the water nanophase.
Water domain is far from spherical
Non perco. percolated
Non perco.
Water diffusion is ~25% faster in the more segregated
structure. Experimental results between blocky and random.
Vehicular diffusion of hydronium is comparable for both
sequences (no exp). Activation energies of water diffusion in
agreement with experiment.
51. Membrane characteristics
Membrane characteristics
Characteristics of water mobility in
Characteristics of water mobility in
(a) Pure water, (b) neutral and ionized nafion, (c)
(a) Pure water, (b) neutral and ionized nafion, (c)
hydrophobic slabs, (d) hydrophilic slabs, (e) neutral and
hydrophobic slabs, (d) hydrophilic slabs, (e) neutral and
ionized
ionized homogeneous solution
homogeneous solution of nafion fragments
of nafion fragments
(a) (b) (c) (d) (e)
51
53. Doped Carbon-Based Materials
Doped Carbon-Based Materials
MD/MC
MD/MC studies
studies:
:
3
4
5
6
7
8
6 7 8 9 10 11 12
Interlayer distance (Å)
H
ydrogen
uptaking
m
ass%
57
67
77
37
47
27
H
ydrogen
density
(kg/m3)
hydrogen density
mass%
50 bar
100 bar
100 bar
50 bar
target line
3.5
4.5
5.5
6.5
7.5
6 7 8 9 10 11 12
Inter-tube distance (Å)
Hydrogen
uptaking
mass%
62
72
52
32
42
Hydrogen
density
(kg/m3)
hydrogen density
mass%
50 bar
100bar
100 bar
50 bar
target line
53
W. Deng, W. A. Goddard
W. Deng, W. A. Goddard
