Pore-size Dependence of Ion
Diffusivity in Dye-sensitized Solar
Cells
Yiqun Ma
SUPERVISOR: Dr. Gu Xu
1
Outline
• Background and introduction
I.
II.
III.
Dye-sensitized solar cells
Mass transport in electrolyte
Problem: pore-size dependence of ion diffusivity
• Experimental
I.
II.
Device fabrication and pore-size variation
DC polarization measurement
• Results and discussion
I.
II.
III.
Unification of two opposite views
Unexpected surface diffusion
Significance of results
• Conclusion
2
Introduction to Dye-sensitized Solar Cells
• Electrochemical cells utilizing dye molecules to
harvest sunlight
• First published in Nature in 1991
• 7% overall power conversion efficiency was
achieved, now has exceeded 12%
• New generation solar cell with possible low cost and
high stability
Oregan, B.; Gratzel, M., Nature 1991, 353 (6346), 737-740
3
Mesoporous TiO2 Thin Film
• Monolayer Dye molecules for light absorption  High surface
area required  mesoporous structure gives rise of 700 times
of nominal surface area
• Working electrochemical Junction formed at the interface
TiO2
Dye
I-/I3-
4
Device Physics of Dye-sensitized Solar Cells
FTO
Mass transport of ions
 Bottleneck of performance
5
Three Possible Mechanisms of Mass Transport
Diffusion
• Concentration gradient
Migration
• Electric field
Convection
dominant
mechanism in DSSCs
• Mass movement
• Due to temperature
difference etc.
 In standard DSSCs, the mass transport rate is determined by the
diffusion of minority ions (I3-) i.e. [I3-] <<[I-]
Kalaignan, G. P.; Kang, Y. S., J. Photochem. Photobiol. C-Photochem. Rev. 2006, 7 (1), 17-22.
6
Two Conflicting Views from Literature:
A) Pore-size Independent Diffusion
• Diffusion is pore-size independent when λ<0.1 (λ = rmolecule/rpore)
- Based on the short mean free path of inter-molecular collision in
liquid :
1
𝑙𝑡𝑜𝑡𝑎𝑙
=
1
𝑙𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒
• 𝐷𝑚𝑎𝑡𝑟𝑖𝑥 = 𝐷𝑏𝑢𝑙𝑘 ×
ε
τ
+
1
𝑙𝑝𝑜𝑟𝑒
(ε: porosity; τ:tortuosity)
• Tortuosity: ratio of the length of the curve (L) to the distance
between the ends of it (C)
A
C
B
𝑳
𝝉=
𝑪
L
Karger, J.; Ruthven, D. M., Diffusion in zeolites and other microporous solids. : Wiley: New York, 1992; pp 350-365.
7
Two Conflicting Views from Literature:
B) Pore-size Dependent Diffusion
• Frequently observed impeded diffusion in much larger
pores (λ ≈ 0.01)
• In this case ion diffusivity heavily depends on pore diameter
• Possibly due to the surface
interaction or bonding
mechanisms
• Decreases effective free
pore volume
Mitzithras, A.; Coveney, F. M.; Strange, J. H., J. Mol. Liq. 1992, 54 (4), 273-281.
40nm
8
Debating in Dye-sensitized Solar Cells
• Remains controversial in dye-sensitized solar cells
• Yet critical in estimation of the limiting current and
design of efficient devices
• Because various fabrication processes lead to pore
shrinking
I.
Dye loading
II. TiCl4 post-treatment
9
Experimental:
Device Fabrications
 To focus on ion diffusion, a modified version of DSSC is fabricated
1.
Injection hole
Coating of Pt on FTO glass by heat
treatment of chloroplanitic acid
(H2PtCl6)
2.
Deposition of TiO2 thin film by
screen printing process
3.
Sealing the cell with Surlyn film as
spacer(25μm)
4.
Injecting electrolyte (I-/I3- redox
couple in acetonitrile) from the hole
at the top
10
Pore-size Variation by
TiCl4 Treatment
• TiCl4 post-treatment is widely used in DSSC fabrication
• Chemical bath which forms TiO2 on top of TiO2
mesoporous film by epitaxial growth – growing overlayer
with the same structure
• Reduce recombination rate and improve charge injection
from dye molecules to the CB of TiO2
• Also reduce average pore size of TiO2 film
11
Pore-size Variation by
TiCl4 Treatment
1. Immerse for 30 mins
2. Rinse with DI water
3. Anneal at 450oC for 30 mins
TiCl4 treated TiO2 film
with smaller pores
TiO2 film on FTO/Pt glass
0.1M TiCl4
aqueous solution
at 70 oC
TiCl4 + 2 H2O → TiO2 + 4 HCl
Hot Plate
Ito, S.; Murakami, T. N.; Comte, P.; Liska, P.; Gratzel, C.; Nazeeruddin, M. K.; Gratzel, M., Thin Solid Films
2008, 516 (14), 4613-4619.
12
BET Characterization
Sample
Number of TiCl4
treatments
Average pore
diameter (nm)
Porosity ε
A
0
20.91±1.83
0.616±0.018
B
1
16.92±2.32
0.497±0.010
C
2
11.33±2.57
0.404±0.014
D
3
7.97±1.7
0.339±0.008
E
4
5.7±1.35
0.287±0.006
13
BET Characterization
14
Pore-size Distribution
 Curves follow more or less the
normal distribution
 Distribution shape remains
almost unchanged after
treatments
 Average pore diameter
decreases
 Error bars of pore diameters are
Sample A, C and E underwent 0, 2 and 4
times of TiCl4 treatments respectively
obtained from the FWHM values
15
DC Polarization Measurement
• The DC measurement was conducted in Dark
• Mass transport limited current
-
In this case, diffusion limited current
• IV curve will reach plateau at limiting
I
Charge injectio
starts
current value
• In this case, the current will increase
Ilim
after the plateau
-
Charge injection from the TiO2 to electrolyte
Ionic diffusion
V
VT
16
Model Construction
• First consider neat electrolyte between two electrodes
• Assuming diffusion layer thickness = cell thickness, and
𝑑2 𝑐
𝑑𝑥 2
=0
(since the current flow is independent of x)
• General equation of diffusion limited current
𝐼𝑙𝑖𝑚
2𝑛𝐹𝑐𝐷
=
𝑑
• F is the Faraday constant, c is the I3- concentration and n is the
stoichiometry constant which equals to 2 for I-/I3- redox couple
17
Model Construction
• Continuity of current in the device:
I=
𝐶 𝑡 −𝐶 0
2F𝐷𝑇𝑖𝑂2
𝑡
• The conservation of
c[εt + (l – t)] =
𝐶 𝑙 −𝐶 𝑡
= 2FDbulk
𝑙−𝑡
I3- ions:
𝐶 𝑡 +𝐶 0
ε
2
t+
𝐶 𝑡 +𝐶 𝑙
2
(l – t)
(1)
(2)
• Combine (1) and (2) with boundary condition c0=0:
𝑰𝒍𝒊𝒎 = 4Fc
𝑫𝑻𝒊𝑶𝟐 𝑫𝒃𝒖𝒍𝒌 (𝜺𝒕−𝒕+𝒍)
𝑫𝑻𝒊𝑶𝟐 (𝒍−𝒕)𝟐 +𝑫𝒃𝒖𝒍𝒌 (𝜺𝒕−𝟐𝒕+𝟐𝒍)
(3)
t = 12 μm; 𝒍= 25 μm
Kron, G.; Rau, U.; Durr, M.; Miteva, T.; Nelles, G.; Yasuda, A.; Werner, J. H., Electrochem. Solid State Lett.
2003, 6 (6), E11-E14.
18
DC Measurement Results
a) IV characteristic of control
sample without TiO2 thin film;
b) Typical IV curves of samples A to E
after 0 to 4 times of TiCl4 treatments
respectively
19
DC Measurement Results
Sample
Ilim
(mAcm-2)
DTiO2
(10-5cm2s-1)
Deff
(10-5cm2s-1)
Tortuosity
(τ)
A
35.25±1.25
0.747±0.038
1.22±0.09
1.05±0.09
B
24.80±0.60
0.513±0.016
1.03±0.05
1.24±0.06
C
21.10±0.45
0.437±0.012
1.08±0.07
1.18±0.08
D
16.67±0.35
0.343±0.009
1.01±0.05
1.26±0.06
E
10.33±0.50
0.207±0.011
0.721±0.055
1.78±0.13
DTiO2: ion diffusivity in matrix
Deff: effective ion diffusivity normalized with porosity
ε
τ
τ : tortuosity calculated from 𝐷𝑇𝑖𝑂2 = 𝐷𝑏𝑢𝑙𝑘 × , expected to range from 1.2 to 1.8*
20
Surprising Pore-size Dependence
A
C
D
D – E:
Pore-size dependent region, Deff
heavily depends on pore
diameters;
B
B – D:
Pore-size independent region,
almost forms a platform;
E
Transition:
Critical point of transition is
located at 5 – 7 nm;
A – B:
? What is going on here?
21
Two Opposite Views Are Now Unified……
Distinctive Regions of each diffusion
mode
Pore-size
dependent
E
C
D
B
Pore-size
independent
I.
Pore-size dependent region
•
•
< 5 – 7 nm
Significant steric hindrance
effect of pore walls.
II. Pore-size independent region
•
•
> 5 – 7 nm
Negligible collision between
liquid molecules and pore walls
Observed in DSSCs for the first time!
22
……by the Critical Point of Transition
• λ value at the transition ≈ 0.1 (550pm/5nm), which bears
remarkable agreement to the theoretical prediction
• The range of pore-size independent region(>5-7nm)
suggests fabrication processes of DSSCs will NOT cause
transition of diffusion behavior
• Not likely those processes will impede ion diffusivity
significantly
23
Significance of Our Results
Smaller
• Large interfacial
Area for efficient
light harvesting
• May impede mass
transport rate
Larger
Pore Size
• High mass
transport
limiting current
• Not enough
interfacial area
 Our results suggest the minimum pore-size without
hindering the diffusion.
 The balance between mass transport of electrolyte and
interfacial area can be optimized
24
Unexpected Rise from B to A
• The tortuosity in A ≈ 1(unrealistic)  Other
diffusion mechanism is involved
• Surface diffusion
⁻ Hopping mechanism of surface-adsorbed
molecules between adsorption sites.
⁻ Suppressed by the surface modification after
TiCl4 treatments
⁻ Act as a passivation process and decrease the
number of available adsorption sites
I3 -
A
B
Surface
diffusion
I3 -
TiO2
25
Conclusion
• Both pore-size dependent and independent diffusion were
observed under the same scheme by altering the average poresize of TiO2 matrix.
• The critical point of transition was located in the range of 5 – 7
nm. Thus standard fabrication processes will not cause
transition of diffusion mode.
• Surface diffusion mechanism was observed in untreated TiO2
and suppressed after the surface modification of TiCl4 posttreatment.
26
Acknowledgements
• Dr. Gu Xu
• Dr. Tony Petric and Dr. Joey Kish
• Dear group mates: Cindy Zhao, Lucy Deng
• Mr. Jim Garret
• Dr. Hanjiang Dong
• NSERC
27
Thanks for the attention!
Any questions?
28