Supporting Information for:
High Temperature Structural Stability of Ceria Based Inverse Opals
Danielle C. Casillas,‡ Dan C. Wilkinson,‡ Chun-Han Lai,‡ Michael Ignatowich,‡‡ Stephen K. Wilke,ζ
Sossina M. Haile,§,¶,ζ,‡‡ and Bruce S. Dunn‡,†
‡
Department of Materials Science and Engineering, University of California, Los Angeles, Los
Angeles, California 90095
§
Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208
¶
Applied Physics, Northwestern University, Evanston, Illionis 60208
ζ
‡‡
Materials Science, California Institute of Technology, Pasadena, California 91125
Chemical Engineering, California Institute of Technology, Pasadena, California 91125
FFT Image Analysis:
The fast Fourier transform (FFT) is described by equation 1:
𝑁1 −1 𝑁2 −1
𝑋(𝑘𝑥 , 𝑘𝑦 ) = ∑ ∑ 𝑥(𝑛1 , 𝑛2
𝑘 𝑛 𝑘𝑦 𝑛2
)
−2𝜋𝑖( 𝑥 1 +
𝑁1
𝑁2
)𝑒
(1)
𝑛1 =0 𝑛2 =0
where 𝑥 (𝑛1 , 𝑛2 ) is the array of brightness values and 𝑘/𝑁 is the spatial frequency. In order to
compute the FFT, the fft2(X) function in Matlab was implemented. The image is converted to
grayscale, a threshold applied, and cropped to remove the information bar. The one-dimensional
discrete Fourier transform (DFT) is computed first for each column, and subsequently computed
for the row of each result. This results in a circular convolution, and the FFT data has the same
dimensions as the original image.
Next, Y=fftshift(x) is used to move the zero frequency
component to the center, and the absolute value is taken in order to remove the imaginary values
from the analysis. The absolute value is the intensity value seen in the final FFT image:
𝐼(𝑘𝑥 , 𝑘𝑦 ) = |𝑋(𝑘𝑥 𝑘𝑦 )|
(2)
If the image contains spatial order, this will result in an array of spots similar to a diffraction
pattern. The pixels comprising the spot at the center of the FFT image represent the average
brightness of the image. Additionally, the nearest neighbor spots to the zeroth frequency value
represent the lowest frequency occurring order. For this study, these are the data of interest. The
sum of the FFT along an axis of symmetry is taken by rotating the image and summing the
columns of the resulting FFT (Fig. S1).
(a)
(b)
(c)
(d)
Fig. S1 (a) Typical ZSC20 1µm inverse opal SEM image with threshold applied, (b) FFT image before
rotation, (c) FFT image after rotation, (d) sum of FFT image brightness along x-axis (matrix columns).
The spatial order parameter extracted from these FFT analyses is defined as the ratio of
the normalized first order FFT sum peak and the full width at half maximum (FWHM) of the
peak normalized by the total width of the image in pixels.24
In order to calculate the raw spatial order parameter, γ, the peak intensity and full width
at half maximum (FWHM) must be extracted. The findpeaks function in Matlab was used, and
the standard deviation of each peak was taken to estimate the FWHM. The peak minimum was
subtracted from the peak maximum to find the height.
These results correlate well with those of the FFT analysis. Here, γr > 0.4 indicates
complete retention of ordered porosity, while 0.2 < γr < 0.4 denotes a gradual loss of ordered
porosity, and materials with γr < 0.2 have random porosity. ZSC20 inverse opals retain ordered
porosity at 1000 °C for 12 hours, while ZSC30 and ZSC40 inverse opals maintain their
structures at 1100 °C for 12 hours.
X-Ray Diffraction
Powder XRD patterns for ZSC20, 30, and 40 after annealing at 1100 °C for 12 hours
(Fig. S2 (a)) show peak splitting, indicating formation of a second phase with smaller lattice
parameter for zirconia content greater than 20 at%.46 The shift of the (100) reflection at 29˚to
lower 2θ and the appearance of a shoulder at 30˚ point to a segregation of material into
zirconium-rich tetragonal, and zirconium-deficit cubic oxides. For Zr substitution greater than
20%, the tetragonal phase becomes apparent upon annealing. Tetragonal phase formation is
suppressed (or perhaps undetectable due to peak broadening) in nano-sized grains. However, as
shown here, upon annealing at high temperatures significant grain growth occurs. Powder X-ray
diffraction (XRD) also shows the emergence of a tetragonal, zirconium-rich phase. In Fig. S2,
the XRD patterns ZSC30 and ZSC40 annealed at 1100 ˚C contain extra reflections indicative of
the tetragonal phase. Consequently, for extended use of these materials at high temperatures, Zr
additions should remain around 20 atomic percent in order to achieve a highly defective lattice
without tetragonal phase formation.
In Fig. S2(b), the dependence of γ on crystallite size is shown for as-prepared samples
with nominal pore size of 1 m, and for identical materials annealed at 1100 ˚C for 12 hours. All
compositions in the as-synthesized state display an initial γ of 10-11 and an initial crystallite size
of 5-15 nm, and the two parameters are relatively uncorrelated. The post-annealed materials
show a stronger correlation between these two parameters, indicating that the processes leading
to grain growth also result in loss of pore ordering. The retention of order and small grain size
with increasing Zr content suggests that the mixed cation compositions have lower mean cation
mobility.
(b)
(a)
2θ (degree)
Fig. S2 (a) Powder XRD patterns for ZSC20, ZSC30, and ZSC40 inverse opals as-synthesized and
annealed at 1100°C for 12 hours. Lines indicate peak locations for tetragonal Ce0.86Zr0.14O2 reference
JCPDS 00-038-1437). (b) γ as a function of zirconium dependent grain size for ZSC as-synthesized
(closed symbols) and annealed at 1100˚C (open symbols). Crystallite size for ZSC10 from reference 35.
Raman Spectroscopy
Raman spectroscopy (Renishaw, 514nm) was used to verify subtle changes in the oxygen
sublattice such as vacancy formation and pseudo-cubic (t”) phase emergence. Fig. S3 shows the
Raman spectra of ZSC20 inverse opals annealed at 1100°C for 0.5 and 12 hours. The main cubic
phase vibrational mode peak occurs at 464 cm-1 for pure ceria, whereas the defect band (oxygen
vacancy) is at 600 cm-1, and a band at 307 cm-1 is characteristic of a tetragonal distortion. Peak
positions are designated by 2, 3 and 1 in Fig. S3, respectively.39 The cubic peak position is
slightly shifted due to the addition of zirconia, and shift of the cubic peak to higher wavenumbers
with annealing occurs due to crystallite growth. This phenomenon is likely due to phonon
confinement in small nanoparticles, in addition to lattice expansion, and these effects disappear
as the nanocrystals grow.47,48 The defect band is indicative of oxygen vacancy concentration,
and is associated with the pseudocubic phase. In this phase, cation positions remain unchanged
and oxygen positions are slightly shifted
rom their locations in the cubic lattice.
Fig. S3 Raman spectra of ZSC20 1µm inverse opal (a) assynthesized, and annealed at 1100 °C for (b) 0.5 hours and
(c) 12 hours. Pseudocubic phase, cubic phase, and oxygen
vacancy vibrational modes locations are indicated by 1, 2,
and 3, respectively.
None of the ZSC samples annealed at 1000 °C showed evidence of tetragonal t phase
formation, which would be indicated by peaks in addition to 1, 2 and 3, defined in Fig. S3. The
Raman spectra of ZSC30 and ZSC40 did, however, contain small broad peaks at 307 cm-1 and
600 cm-1, indicating the emergence of the defective pseudocubic t” phase (Fig. S4). ZSCX
Inverse opals annealed at 1100 °C for 1 hour are shown to contain defective pseudocubic phase
when X>10. However, undesired tetragonal phases (t and t’) begin to emerge where X>20, as
indicated by the presence of additional peaks ~260 cm-1.
The amount of Zr is the key parameter which determines the relation between coarsening
and the ability of inverse opals to maintain their structures. Large grains allow facile crack
propagation along grain boundaries, and thus make inverse opals more susceptible to fracture
and loss of order, in addition to the coarsening effects of long term high temperature
exposure.49,50
Fig. S4 Raman spectra of ZSC inverse opals annealed at 1000 °C and 1100 °C for 1 hour with (a) 0, (b)
10, (c) 20, (d) 30, (e) 40 atomic percent zirconia.
Pore Size Estimation for Facile Gas Transport
An effort towards the fabrication of large (> 1µm) pore ceria based inverse opals was
motivated by potential mass transport improvements. The small pore radii typical of catalyst
materials dictates the fluid flow regime. Within the molecular flow regime, the mean free path
of the fluid is much less than the diameter of the pore, and particle-particle interactions dominate
flow. In contrast, within the Knudsen flow regime the mean free path of the gas is greater than
the pore diameter, and particle-pore wall interactions dominate. For gases, typical diffusion
coefficients within the molecular regime and Knudsen regime are 10-1 cm2/s, and 10-5 to 10-2
cm2/s, respectively.51,52
To determine the diffusion regime within the pores it is useful to compare the mean free
path of the gas molecule to the pore diameter, which results in Knudsen number:51
𝐾𝑛# =
𝜆
𝑘𝐵 𝑇
=
𝑑 √2𝜋𝜎 2 𝑝𝑑
(3)
where d is the pore diameter, λ is the mean free path, kB is the Boltzmann constant, T is the
temperature, σ is the hard sphere diameter of a gas molecule, and p is the pressure. When
Knudsen number is much smaller than unity, molecular flow is dominant.52
The hard sphere radius can be estimated using the second coefficient of the virial
expansion, which simplifies to the second parameter of the Van der Waals equation of state (Eq.
4). This parameter, the Van der Waals volume, takes into account the volume exclusion of gas
molecules.53 For a rough approximation, the hard sphere radius is determined from the Van der
Waals volume of the gas using the relation:
4 𝜎 3
𝑏 = 𝑁𝑎 ∗ 𝜋 ( )
3 2
(4)
Where b is the Van der Waals volume [m3/mol] and Na is Avogadro’s number.
To estimate the minimum pore radius which ensures flow within the molecular regime,
the Knudsen number is set to 0.5 at atmospheric pressure, and the pore window diameter can be
determined. From visual inspection of pores, the window diameter is ~1/3 of the pore diameter.
Table S1 outlines the minimum pore diameters for the gases in this system using tabulated b
values.53 A minimum pore diameter of ~4.5µm should guarantee molecular flow.
Table S1 Estimated minimum pore diameters for flow within the molecular regime.
Gas
Min. Pore Diameter (μm)
b/10-5
3
(m /mol) 800°C
Water
3.1
4.2
Oxygen
3.2
4.2
Hydrogen 2.7
4.8
BET Analysis
Brunauer-Emmett-Teller (BET) surface area and pore size distribution analysis were
carried out at 77 K using a gas adsorption analyzer (Micromeritics ASAP 2010) with N2
adsorption isotherms. Before analysis, 200 mg test samples were outgassed at 110 °C under
vacuum overnight to ensure complete drying. The nitrogen adsorption isotherms were taken from
a pressure range between 5 μm Hg and 960 μm Hg. Table S2 shows that values of BET surface
area typically fall between ~ 25 m2 g-1 and 50 m2 g-1 for different ZSC20 inverse opals and
powders.
Table S2 BET surface area for ZSC20 powders and inverse opals of different pore sizes.
Inverse opal samples
Surface area (m2 g-1)
Control
powders
300 nm
650 nm
1 μm
51.8 ± 3.7 36.2 ± 8.8 31.3 ± 1.2 25.1 ± 1.4
Hydrogen Production Rate (mL/min/g)
Hydrogen production by ZDC20:
4.0
3.5
3.0
300 nm
650 nm
1000 nm
Control Powder
2.5
2.0
1.5
1.0
0.5
0.0
0
1
2
3
4
5
6
7
8
9
10
Time (min)
Fig. S5: Hydrogen production profiles for different ZDC20 inverse opal microstructures and control
powder.
Chemically reduced ZSC20 inverse opals having 300 nm, 650 nm and 1 µm nominal pore
sizes were evaluated for hydrogen production efficacy as follows. Samples 400 mg in mass were
placed in a horizontal tube furnace and heated at rate of 10 ˚C/min in air to 800 ˚C. After purging
with Ar gas, the samples were reduced by exposure to a mixture of 3% H2 and 20% H2O in Ar
for 20 minutes at a flow rate of 200 sccm (standard cubic centimeters per minute, implying a gas
velocity at the sample of 18 cm/s and reaction zone flush time of less than 1 s). The reactor was
then purged with Ar for 5 minutes (1000 sccm and gas velocity of 92 cm/s) to remove residual
hydrogen, following which, the inverse opals were oxidized using a wet Ar stream for 20
minutes (20% H2O, 200 sccm). The reactor was then purged again with Ar for 5 minutes before
beginning another cycle. The process was repeated 12 times. Representative hydrogen
production profiles obtained during the inverse opal oxidation step are presented in Figure S5.
The integrated hydrogen production (area under the curves) is similar between structures, an
expected result because the total production reflects the thermodynamic properties of the
material. The minimal influence of pore size on the features of the hydrogen evolution profiles is
tentatively assigned to competing effects of (slightly) decreasing surface area and presumably
increasing gas diffusion with increasing pore size.
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