HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
A Mathematical Model for Hydrogen Productionof a Proton Exchange Membrane
Photoelectrochemical Cell
Bryan Van Scoy, Josh Adams, Robert MoserDr. Young, Dr. Clemons, Dr. Kreider
University of Akron
April 7, 2011
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Benefits of Hydrogen
Little or no emissions
Hydrogen engines more efficient than gasoline
Fuel cells available
Many ways to produce
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Ways to Produce Hydrogen
Natural gas
Coal
Biomass
Waste
Wind
Nuclear power
Sunlight
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Basic Cell Operation
Anode Water ChannelMembrane (PEM)Proton Exchange
+ −
Anode CL Cathode CL
Cathode Water Channel
H2OH2O
H+
hν
H2O2
e−
Vcell
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Basic Cell Operation
Anode Water ChannelMembrane (PEM)Proton Exchange
+ −
Anode CL Cathode CL
Cathode Water Channel
H2OH2O
H+
hν
H2O2
e−
Vcell
&%'$
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Nafion Membrane
Hydration Shell
Water Region
Polymer Backbone
x
SO−3 Charge
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Delta Functions
-800
-600
-400
-200
0
200
400
600
800
0 10 20 30 40 50 60
15 45C
harg
e D
ensi
ty (
C/m
3 )
Length (µm)
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Basic Cell Operation
Anode Water ChannelMembrane (PEM)Proton Exchange
+ −
Anode CL Cathode CL
Cathode Water Channel
H2OH2O
H+
hν
H2O2
e−
Vcell
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Basic Cell Operation
Anode Water ChannelMembrane (PEM)Proton Exchange
+ −
Anode CL Cathode CL
Cathode Water Channel
H2OH2O
H+
hν
H2O2
e−
Vcell
&%'$
&%'$
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Electrode Nanowire Array Assembly
Current ConductingSupport Scaffold
SiliconGermanium
Proton ExchangeMembrane (PEM)Silicon
Electrocatalyst (Pt)
Germanium
Electrocatalyst (Pt)
Anode Catalyst Layer Cathode Catalyst Layer
-
e−
Vcell
+
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Photograph of Nanowire Arrays
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Electrode Nanowire Array Assembly
Cathode
1 cm
1 cm
Mem
bran
e
Pitch (P)
ScaffoldThickness
Anode
(Pscaffold)
Default Lengths:LA = 15 µmLM = 30 µmLC = 15 µm
LM LCLA
y
x
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Symbol Description Symbol Description
A Surface area/volume ratio [m−1] pos Position of point-chargesc Speed of light [m/s] q Charge of a proton [C]D Diffusivity of protons [m2/s] R Gas constant [J/K·mol]Dw Diffusivity of water [m2/s] S Source/Sink termE Activation energy [J/mol] T Temperature [K]EW Equivalent weight of electrolyte
[kg/mol]W Molecular weight [kg/mol]
F Faraday constant [C/mol] V Volume [m3]h Planck constant [m2
·kg/s] V0 Equilibrium potential [V]Iν Radiant intensity [W/m2] η Overpotential [V]j Current density [A/m3] µ Mobility of protons [m2/V·s]J Flux ρ Density [kg/m3]kB Boltzmann constant [J/K] κ Thermal conductivity [W/m·K]L Length [m] σ Ionic conductivity [S/m]m Mass of an electron [kg] ǫ Permittivity [F/m]NA Avogadro constant [mol−1] ν Frequency of sunlight [Hz]
NSO
−
3
Number of SO−
3 charges χ Surface potential difference [J]
n Concentration of protons [mol/m3] φmetal Work function of metal [J]
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Governing Equation
Concentration of H+ 0 = ∇ · (D ∇n + µn ∇Φ) + S
Potential (CLs) 0 = ∇ · (σ ∇Φ) + S
Potential (Membrane) 0 = ∇ · (ǫ ∇Φ) + S
Water Content 0 = ∇ ·
(
ρmem
EWDmemw ∇λ
)
−∇ ·
(
ndjF
)
+ S
Temperature 0 = ∇ · (κ ∇T ) + S
D - Diffusivity of protons Dmemw - Diffusivity of water
n - Concentration of protons λ - Water contentµ - Mobility of protons nd - Electro-osmotic dragσ - Electrical conductivity j - Current densityΦ - Electric potential F - Faraday constantǫ - Permittivity κ - Thermal conductivityρmem - Density of membrane T - TemperatureEW - Equiv. weight of dry membrane
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Governing Equation
Concentration of H+ 0 = ddx(D dn
dx+ µn dΦ
dx) + S
Potential (CLs) 0 = ddx(σ dΦ
dx) + S
Potential (Membrane) 0 = ddx(ǫdΦ
dx) + S
Water Content 0 = ddx
(
ρmem
EWDmemw
dλdx
)
−ddx
(
ndjF
)
+ S
Temperature 0 = ddx(κdT
dx) + S
D - Diffusivity of protons Dmemw - Diffusivity of water
n - Concentration of protons λ - Water contentµ - Mobility of protons nd - Electro-osmotic dragσ - Electrical conductivity j - Current densityΦ - Electric potential F - Faraday constantǫ - Permittivity κ - Thermal conductivityρmem - Density of membrane T - TemperatureEW - Equiv. weight of dry membrane
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Current Density
jν =FIν
NA
mc2
h2ν2
(
1−φmetal + χ
hν
)
(Light)
japplied = iA0
[
exp
(
FηA
RT
)
− exp
(
−FηA
RT
)]
(Anode)
japplied = iC0
[
n
nrefexp
(
−FηC
RT
)
−n
nrefexp
(
FηC
RT
)]
(Cathode)
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Overpotentials
ηA =RT
Fsinh−1
(
japplied
2iA0
)
(Anode)
ηC = −RT
Fsinh−1
(
japplied
2iC0
nref
nC
)
(Cathode)
ηM =LM
σj (Membrane)
ηI = .05V0 (Interface)
V0 = 1.23− .9× 10−3(T − 298.15) (Equilibrium Potential)
φ0 = V0 + ηA − ηC + ηM + ηI (Cell Voltage)
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Other Equations
σ = (.5139λ− .326) exp
[
1268
(
1
303−
1
T
)]
(Conductivity)
D = 8× 10−10λ− 3.1× 10−9 (Diffusivity)
µ =Dq
kBT(Mobility)
RH2 =nC
nref
j
F
[
mol
m2 s
]
=nC
nref
j
F
WH2
ρH2
VC
P+ Pscaffold
[
L
s
]
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Electric Potential - Governing Equation
0 = (σΦx)x + S
0 = σΦxx + σxΦx + S
0 =σ
∆x2[Φi−1 − 2Φi +Φi+1] +
1
4∆x2[σi+1 − σi−1] [Φi+1 − Φi−1] + S
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
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EquationsResults
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Electric Potential - Matrix Equation
[1] Φi−1
+ [−2] Φi = −∆x2
σiS −
1
4σi(σi+1 − σi−1)(Φi+1 − Φi−1)
+ [1] Φi+1
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
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EquationsResults
Conclusions
Electric Potential - Boundary Conditions
Left Boundary Anode/Membrane Membrane/Cathode Right Boundaryx = xA = 0 x = xAM x = xMC x = xC
ΦA = V0 + ηA − ηC ΦA = ΦM + ηI2 ΦM = ΦC + ηI
2 ΦC = 0+ηM + ηI ǫA∇ΦA · n̂ ǫM∇ΦM · n̂
= ǫM∇ΦM · n̂ = ǫC∇ΦC · n̂
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Electric Potential - Boundary Conditions
ǫ1dΦ1
dx= ǫ2
dΦ2
dx
ǫ1
2∆x[Φi−2 − 4Φi−1 + 3Φi ] =
ǫ2
2∆x[−3Φi + 4Φi+1 − Φi+2]
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Electric Potential - Boundary Conditions
[ǫ1] Φi−2
+ [−4ǫ1] Φi−1
+ [3(ǫ1 + ǫ2)] Φi = 0
+ [−4ǫ2] Φi+1
+ [ǫ1] Φi+2
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Concentration of Hydrogen - Governing Equation
nt = (Dnx + µnΦx)x + S
1
∆t[nk+1
i − nki ] =Di
2∆x2[(nki−1 − 2nki + nki−1) + (nk+1
i−1 − 2nk+1i + nk+1
i−1 )]
+1
8∆x2[Di+1 − Di−1][(n
ki+1 − nki−1) + (nk+1
i+1 − nk+1i−1 )]
+µi
2∆x2[nk+1
i − nki ][Φi−1 − 2Φi +Φi+1]
+µi
8∆x2[(nki+1 − nki−1) + (nk+1
i+1 − nk+1i−1 )][Φi+1 − Φi−1]
+1
8∆x2[µi+1 − µi−1][n
k+1i − nki ][Φi+1 − Φi−1]
+ Ski
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Concentration of Hydrogen - Matrix Equation
[
−r̃
2Di +
r̃
8(Di+1 + Di−1) +
r̃
8µi (Φi+1 − Φi−1)
]
nk+1i−1
+
[
1 + r̃Di −r̃
2µi (Φi+1 − 2Φi +Φi−1)−
r̃
8(µi+1 − µi−1)(Φi+1 − Φi−1)
]
nk+1i
+
[
−r̃
2Di −
r̃
8(Di+1 − Di−1)−
r̃
8µi (Φi+1 − Φi−1)
]
nk+1i+1
= nki +r̃
2Di (n
ki−1 − 2nki + nki−1) +
r̃
8(Di+1 − Di−1)(n
ki+1 − nki−1)
+r̃
2µin
ki (Φi−1 − 2Φi +Φi+1) +
r̃
8µi (Φi+1 − Φi−1)(n
ki+1 − nki−1)
−r̃
8nki (µi+1 − µi−1)(Φi+1 − Φi−1) + ∆t Sk
i
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
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EquationsResults
Conclusions
Concentration of Hydrogen - Boundary Conditions
Left Boundary Anode/Membrane Membrane/Cathode Right Boundaryx = xA = 0 x = xAM x = xMC x = xCnA = n0 nA = nM nM = nC
~JA · n̂ = ~JM · n̂ ~JM · n̂ = ~JC · n̂ ~JC · n̂ = KMT [nC − n0]
~J = D ∇n − µn ∇Φ
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
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EquationsResults
Conclusions
Concentration of Hydrogen - Boundary Conditions
D1dn1
dx+ µ1n1
dΦ1
dx= D2
dn2
dx+ µ2n2
dΦ2
dx
D1
2∆x[ni−2 − 4ni−1 + 3ni ] +
µ1ni
2∆x[Φi−2 − 4Φi−1 + 3Φi ]
=D2
2∆x[−3ni + 4ni+1 − ni+2] +
µ2ni
2∆x[−3Φi + 4Φi+1 − Φi+2]
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Concentration of Hydrogen - Boundary Conditions
[D1] ni−2
+ [−4D1] ni−1
+ [3(D1 + D2) + µ1(Φi−2 − 4Φi−1 + 3Φi )
−µ2(−3Φi + 4Φi+1 − Φi+2)] ni = 0
+ [−4D2] ni+1
+ [D2] ni+2
[Di ] ni−2
+ [−4Di ] ni−1
+ [3Di + µi (Φi−2 − 4Φi−1 + 3Φi )− 2KMT∆x ] ni = −2KMTn0∆x
+ [−4D2] ni+1
+ [D2] ni+2
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
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EquationsResults
Conclusions
Temperature - Governing Equation
0 = (κTx)x + S
0 = κTxx + S
0 =κ
∆x2[Ti−1 − 2Ti + Ti+1] + S
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
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Temperature - Matrix Equation
[κ] Ti−1
+ [−2κ] Ti = −∆x2 S
+ [κ] Ti+1
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
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EquationsResults
Conclusions
Temperature - Boundary Conditions
Left Boundary Anode/Membrane Membrane/Cathode Right Boundaryx = xA = 0 x = xAM x = xMC x = xCTA = T0 TA = TM TM = TC TC = T0
∇TA · n̂ = ∇TM · n̂ ∇TM · n̂ = ∇TC · n̂
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
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Conclusions
Temperature - Boundary Conditions
κ1dT1
dx= κ2
dT2
dx
κ1
2∆x2[Ti−2 − 4Ti−1 + 3Ti ] =
κ2
2∆x2[−3Ti + 4Ti+1 − Ti+2]
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Temperature - Boundary Conditions
[κ1] Ti−2
+ [−4κ1] Ti−1
+ [3(κ1 + κ2)] Ti = 0
+ [−4κ2] Ti+1
+ [κ2] Ti+2
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Water Content - Governing Equation
0 =
(
ρmem
EWDw λx
)
x
−
(
ndj
F
)
x
+ S , nd =2.5
22λ
0 =ρmem
EW
Dwi
∆x2[λi−1 − 2λi + λi+1]
+ρmem
EW
1
4∆x2
[
Dwi+1 − Dwi−1
]
[λi+1 − λi−1]
−2.5
22
i
F
1
2∆x[λi+1 − λi−1]
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
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Conclusions
Water Content - Matrix Equation
[
ρmem
EW
(
Dwi−
Dwi+1 − Dwi−1
4
)
+∆x2.5
22
i
F
]
λi−1
+
[
−2ρmem
EWDwi
]
λi = −∆x2 S
+
[
ρmem
EW
(
Dwi+
Dwi+1 − Dwi−1
4
)
−∆x2.5
22
i
F
]
λi+1
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Water Content - Boundary Conditions
Left Boundary Anode/Membrane Membrane/Cathode Right Boundaryx = xA = 0 x = xAM x = xMC x = xCλA = λ0 λA = λM λM = λC λC = λ0
DwA∇λA · n̂ DwM
∇λM · n̂
= DwM∇λM · n̂ = DwC
∇λC · n̂
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
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Water Content - Boundary Conditions
Dw1
dλ1
dx= Dw2
dλ2
dx
Dw1
4 ∆x[λi−2 − 4λi−1 + 3λi ] =
Dw2
4 ∆x[−3λi + 4λi − λi+2]
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
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Water Content - Boundary Conditions
[Dw1 ] λi−2
+ [−4Dw1 ] λi−1
+ [3(Dw1 + Dw2)] λi = 0
+ [−4Dw2 ] λi+1
+ [Dw2 ] λi+2
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
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Conclusions
BC3 BC4 BC5
A2 A3 A4 A5
A1 A2 A3 A4 A5
A1 A2 A3 A4 A5 0
. . .. . .
. . .. . .
. . .
A1 A2 A3 A4 A5
BC1 BC2 BC3 BC4 BC5
A1 A2 A3 A4 A5
. . .. . .
. . .. . .
. . .
A1 A2 A3 A4 A5
BC1 BC2 BC3 BC4 BC5
0 A1 A2 A3 A4 A5
. . .. . .
. . .. . .
. . .
A1 A2 A3 A4
BC1 BC2 BC3
x1
x2
x3
x4
...
xA−1
xA
xA+1
...
xM−1
xM
xM+1
...
xC−1
xC
=
b1
b2
b3
b4
...
bA−1
bA
bA+1
...
bM−1
bM
bM+1
...
bC−1
bC
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
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Default Electric Potential
0
0.5
1
1.5
2
2.5
0 10 20 30 40 50 60
15 45P
oten
tial (
V)
Length (µm)
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
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Default Hydrogen Concentration
0
5
10
15
20
25
30
0 10 20 30 40 50 60
15 45H
+ C
once
ntra
tion
(mol
/m3 )
Length (µm)
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
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Default Temperature
352.98
353
353.02
353.04
353.06
353.08
353.1
353.12
353.14
353.16
353.18
0 10 20 30 40 50 60
15 45T
empe
ratu
re (
K)
Length (µm)
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
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Conclusions
Default Water Content
19.5
20
20.5
21
21.5
22
0 10 20 30 40 50 60
15 45W
ater
Con
tent
(m
ol S
O3- /m
ol H
20)
Length (µm)
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
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Effects of Temperature
0
0.5
1
1.5
2
2.5
0 10 20 30 40 50 60
15 45P
oten
tial (
V)
Length (µm)
T = 353KT = 333KT = 303K
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
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Conclusions
Effects of Temperature
16
17
18
19
20
21
22
0 10 20 30 40 50 60
15 45W
ater
Con
tent
(m
ol S
O3- /m
ol H
20)
Length (µm)
T = 353KT = 333KT = 303K
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
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Effects of Charges in Membrane
25.8
26
26.2
26.4
26.6
26.8
27
27.2
27.4
15 20 25 30 35 40 45
H+ C
once
ntra
tion
(mol
/m3 )
Length (µm)
NSO3- = 30
NSO3- = 100
NSO3- = 300
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
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Effects of Charges in Membrane
25
25.5
26
26.5
27
27.5
28
15 20 25 30 35 40 45
H+ C
once
ntra
tion
(mol
/m3 )
Length (µm)
pos = 0.5 pos = 0.25pos = 0.1
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Effects of Water Content
0
10
20
30
40
50
60
70
0 10 20 30 40 50 60
15 45
H+ C
once
ntra
tion
(mol
/m3 )
Length (µm)
λ0 = 22λ0 = 18λ0 = 12
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Effects of Mobility
0
20
40
60
80
100
120
140
160
180
0 10 20 30 40 50 60
15 45
H+ C
once
ntra
tion
(mol
/m3 )
Length (µm)
Full MobilityHalf MobilityNo Mobility
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Effect of Mass Transfer Coefficient
0
50
100
150
200
250
300
350
400
46 48 50 52 54 56 58 60
H+ C
once
ntra
tion
(mol
/m3 )
Length (µm)
KMT = .01KMT = 0KMT = ∞
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Hydrogen Production (Part I)
Test Case H2 Production[ml/min] % of Default
Default 5.9531 100.0 %Low Temperature (T = 333K) 5.8859 98.9 %Low Temperature (T = 303K) 6.0412 101.5 %λ0 = 18 6.8881 115.7 %λ0 = 12 9.4656 159.0 %100 SO−
3 and H+ Charges 5.9714 100.3 %300 SO−
3 and H+ Charges 6.0240 101.2 %pos = .25 6.0044 100.9 %pos = .1 6.0345 101.4 %KMT = 0 12.1445 204.0 %KMT = ∞ 5.5605 93.4 %
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Hydrogen Production (Part I)
Test Case H2 Production[ml/min] % of Default
Default 5.9531 100.0 %Low Temperature (T = 333K) 5.8859 98.9 %Low Temperature (T = 303K) 6.0412 101.5 %λ0 = 18 6.8881 115.7 %λ0 = 12 9.4656 159.0 %100 SO−
3 and H+ Charges 5.9714 100.3 %300 SO−
3 and H+ Charges 6.0240 101.2 %pos = .25 6.0044 100.9 %pos = .1 6.0345 101.4 %KMT = 0 12.1445 204.0 %KMT = ∞ 5.5605 93.4 %
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Hydrogen Production (Part II)
Test Case H2 Production[ml/min] % of Default
Default 5.9531 100.0 %Half Mobility 7.5597 127.0 %No Mobility 1.6420 27.6 %Iν = 0.6 mW/cm2 5.9869 100.6 %Iν = 1.2 mW/cm2 6.0556 101.7 %P = 5µm 9.6349 161.8 %P = 3µm 17.9736 301.9 %LA = LC = 10µm 2.4909 41.8 %LA = LC = 30µm 22.5301 378.5 %LM = 20µm 5.3653 90.1 %LM = 40µm 6.4290 108.0 %
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Hydrogen Production (Part II)
Test Case H2 Production[ml/min] % of Default
Default 5.9531 100.0 %Half Mobility 7.5597 127.0 %No Mobility 1.6420 27.6 %Iν = 0.6 mW/cm2 5.9869 100.6 %Iν = 1.2 mW/cm2 6.0556 101.7 %P = 5µm 9.6349 161.8 %P = 3µm 17.9736 301.9 %LA = LC = 10µm 2.4909 41.8 %LA = LC = 30µm 22.5301 378.5 %LM = 20µm 5.3653 90.1 %LM = 40µm 6.4290 108.0 %
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Significant Factors
Electrode surface area
Mass transfer coefficient between cathode and water channel
Input water concentration
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Significant Factors
Electrode surface area
Mass transfer coefficient between cathode and water channel
Input water concentration
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Significant Factors
Electrode surface area
Mass transfer coefficient between cathode and water channel
Input water concentration
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Future Work
Inclusion of water channels
Multi-dimensional
Non-linear channel flow
Optimal mobility and diffusivity
Transient response
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Future Work
Inclusion of water channels
Multi-dimensional
Non-linear channel flow
Optimal mobility and diffusivity
Transient response
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Future Work
Inclusion of water channels
Multi-dimensional
Non-linear channel flow
Optimal mobility and diffusivity
Transient response
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Future Work
Inclusion of water channels
Multi-dimensional
Non-linear channel flow
Optimal mobility and diffusivity
Transient response
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
Future Work
Inclusion of water channels
Multi-dimensional
Non-linear channel flow
Optimal mobility and diffusivity
Transient response
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
HydrogenPhotoelectrochemical Cells
EquationsResults
Conclusions
References
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membrane fuel cell, Journal of Power Sources 194 (2009), no. 1, Sp. Iss. SI, 423–432 (English), 10thSymposium on Fast Ionic Conductors, Grybow, POLAND, SEP 14-17, 2008.
Y. Akinaga, S. Hyodo, and T. Ikeshoji, Lattice Boltzmann simulations for proton transport in 2-D model
channels of Nafion, Physical Chemistry Chemical Physics 10 (2008), no. 37, 5678–5688 (English).
J.A. Elliott and S.J. Paddison, Modelling of morphology and proton transport in PFSA membranes, Physical
Chemistry Chemical Physics 9 (2007), no. 21, 2602–2618 (English).
K. Kang and H. Ju, Numerical modeling and analysis of micro-porous layer effects in polymer electrolyte
fuel cells, Journal of Power Sources 194 (2009), no. 2, Sp. Iss. SI, 763–773 (English).
K.D. Kreuer, On the development of proton conducting polymer membranes for hydrogen and methanol fuel
cells, Journal of Membrane Science 185 (2001), no. 1, Sp. Iss. SI, 29–39 (English).
J. Nie, Y. Chen, R.F. Boehm, and S. Katukota, A photoelectrochemical model of proton exchange water
electrolysis for hydrogen production, Journal of Heat Transfer-Transactions of the ASME 130 (2008), no. 4(English).
J.M. Ogden, Hydrogen: The fuel of the future?, Physics Today 55 (2002), no. 4, 69–75 (English).
J.M. Spurgeon, S.W. Boettcher, M.D. Kelzenberg, B.S. Brunschwig, H.A. Atwater, and N.S. Lewis,
Flexible, Polymer-Supported, Si Wire Array Photoelectrodes, Advanced Materials 22 (2010), no. 30, 3277+(English).
Bryan Van Scoy, Josh Adams, Robert Moser Dr. Young, Dr. Clemons, Dr. KreiderA Mathematical Model for Hydrogen Production of a Proton Exchange
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