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![Page 1: Paper-67Ad (v4) (Supporting Information) · 2020-02-24 · ^ r í o } v ] ^ µ o u v Ç / v ( } u ] } v Z o ] Ì ] } v } ( , ] P Z rY µ o ] Ç K ] o E v } } } µ ' ] v r/ v Æ &](https://reader036.pdfslide.us/reader036/viewer/2022080717/5f784546c5a3a60c852cc68e/html5/thumbnails/1.jpg)
S-1
Electronic Supplementary Information
Realization of High-Quality Optical Nanoporous Gradient-Index Filters
by Optimal Combination of Anodization Conditions Cheryl Suwen Lawa,b,c, Siew Yee Lima,b,c, Lina Liua,d,e, Andrew D. Abell*b,c,f, Lluis F. Marsal*g and Abel Santos*a,b,c
aSchool of Chemical Engineering and Advanced Materials, The University of Adelaide, Adelaide, South Australia 5005, Australia. bInstitute for Photonics and Advanced Sensing, The University of Adelaide, Adelaide, South Australia 5005, Australia. cARC Centre of Excellence for Nanoscale BioPhotonics, The University of Adelaide, Adelaide, South Australia 5005, Australia. dState key Laboratory of High-Efficiency Utilization of Coal and Green Chemical Engineering, Ningxia University, Yinchuan 750021, P. R. China. eCollege of Chemistry and Chemical Engineering, Ningxia University, Yinchuan 750021, P. R. China. fDepartment of Chemistry, The University of Adelaide, Adelaide, South Australia 5005 Adelaide, Australia. gDepartment of Electronic, Electric, and Automatics Engineering, University Rovira i Virgili, Tarragona, Tarragona 43007, Spain.
*E-Mails: [email protected] ; [email protected] ; [email protected]
Electronic Supplementary Material (ESI) for Nanoscale.This journal is © The Royal Society of Chemistry 2020
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Realization of High-Quality Optical Nanoporous Gradient-Index Filters by Optimal Combination of Anodization Conditions
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Table of Contents
Fig. S1: Effective medium assessment of NAA-GIFs as a function of J and tan.……………………………..S-3
Fig. S2: Transmission spectra of NAA-GIFs produced by SPA under various Tan and [H2SO4] for tan = 10
h.…………………………………………………………………………………………………………………..……………..….…..……S-4
Fig. S3: Transmission spectra of NAA-GIFs produced by SPA under various Tan and [H2SO4] for tan = 15
h.…………………………………………………………………………………………………………………..……………..……...……S-4
Fig. S4: Transmission spectra of NAA-GIFs produced by SPA under various Tan and [H2SO4] for tan= 20
h.……………………………………………………………………………….…………………………………..…………...……....……S-5
Fig. S5: FEG-SEM images of NAA films produced with varying anodization current density (J) and
anodization time (tan)…………………………………………………………………………………..…………………………..…….S-9
Table S1: Equations of different parameters for ANOVA table…………………………………….…………………S-7
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Realization of High-Quality Optical Nanoporous Gradient-Index Filters by Optimal Combination of Anodization Conditions
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Fig. S1. Assessment of effective medium of NAA films produced with varying J and tan. (a) Schematic illustration showing the correlation between nanopore geometry and effective medium in NAA films, with FEG-SEM images showing top and cross-sectional views of a representative NAA film (scale bar = 500 nm – top and scale bar = 1 µm – cross-section). (b) Schematic of set-up used to acquire the reflection spectrum of NAA films. (c) Effective optical thickness (OTeff) of NAA films produced with varying J = 0.280–1.120 mA cm–2 and tan = 0–20 h at varying angle of incidence (θ = 15o, 25o, 35o and 45o).
![Page 4: Paper-67Ad (v4) (Supporting Information) · 2020-02-24 · ^ r í o } v ] ^ µ o u v Ç / v ( } u ] } v Z o ] Ì ] } v } ( , ] P Z rY µ o ] Ç K ] o E v } } } µ ' ] v r/ v Æ &](https://reader036.pdfslide.us/reader036/viewer/2022080717/5f784546c5a3a60c852cc68e/html5/thumbnails/4.jpg)
Realization of High-Quality Optical Nanoporous Gradient-Index Filters by Optimal Combination of Anodization Conditions
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Fig. S2. Full transmission spectra and magnified views of the characteristic photonic stopband (PSB) of NAA-GIFs produced by SPA with varying Tan = –2–2 oC and [H2SO4] = 1.0–2.5 M for tan = 10 h.
Fig. S3. Full transmission spectra and magnified views of the characteristic photonic stop band (PSB) of NAA-GIFs produced by SPA with varying Tan = –2–2 oC and [H2SO4] = 1.0–2.5 M for tan = 15 h.
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Realization of High-Quality Optical Nanoporous Gradient-Index Filters by Optimal Combination of Anodization Conditions
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Fig. S4. Full transmission spectra and magnified views of the characteristic photonic stop band (PSB) of NAA-GIFs produced by SPA with varying Tan = –2–2 oC and [H2SO4] = 1.0–2.5 M for tan = 20 h.
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Realization of High-Quality Optical Nanoporous Gradient-Index Filters by Optimal Combination of Anodization Conditions
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Fig. S5. SEM images of NAA films produced with varying anodization current density (J) and anodization time (tan). (a) Cross-sectional view of NAA films showing the length of pore grown at different J (0.280–1.120 mA cm–2) (scale bar = 1 µm) (b) Top view of NAA films produced as a function of J and tan (0–20 h) (scale bar = 500 nm).
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S-7
The ANOVA table (Table 3) was calculated using the equations outlined in Table S1, where SS is the
sum of squares of the corresponding source, DF is the degree of freedom of such source, MS is the
mean square of corresponding source, F0 is the test statistic of that source, a, b and c are the total
number of levels corresponding to tan, Tan and [H2SO4], respectively, and n is the total number of
replications.
The hypotheses H0, H1, H2, H3, H4, H5 and H6 were evaluated based on the comparison between F0 value
calculated from ANOVA table and the value of F-distribution for a significance level of 95% (i.e. 0.05)
with the correspoding value of DF (Source) and DF (Error) (i.e. F(0.05, DF (Source), DF (Error)). In this way, the
tested null hypothese (i.e. H0, H1, H2, H3, H4, H5 and H6) associated with cases i–vii were rejected if:
i) H0: F0-tan ≥ F(0.05, DF (tan), DF (Error)
ii) H1: F0-Tan ≥ F(0.05, DF (Tan), DF (Error)
iii) H2: F0-[H2SO4] ≥ F(0.05, DF ([H2SO4]), DF (Error)
iv) H3: F0-tan.Tan ≥ F(0.05, DF (tan.Tan), DF (Error)
v) H4: F0-tan.[H2SO4] ≥ F(0.05, DF (tan.[H2SO4] ), DF (Error)
vi) H5: F0- Tan.[H2SO4] ≥ F(0.05, DF (Tan.[H2SO4]), DF (Error)
vii) H6: F0-tan.Tan.[H2SO4] ≥ F(0.05, DF (tan.Tan.[H2SO4]), DF (Error)
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S-8
Considering three-factor analysis of variance model in general form:
𝑦 = 𝜇 + 𝛼 + 𝛽 + 𝛾 + (𝛼𝛽) + (𝛼𝛾) + (𝛽𝛾) + (𝛼𝛽𝛾) + 𝜖
𝑖 = 1, 2, … , 𝑎𝑗 = 1, 2, … , 𝑏𝑘 = 1, 2, … , 𝑐𝑙 = 1, 2, … , 𝑛
In this study, α, β and γ represent tan, Tan, [H2SO4], respectively.
Table S1. Equations of different parameters for ANOVA table.
Source SS DF MS F0
tan 𝑆𝑆 =
1
𝑏𝑐𝑛𝑦 … −
𝑦….
𝑎𝑏𝑐𝑛
𝑎 − 1 𝑀𝑆 =
𝑆𝑆
𝑎 − 1 𝐹 =
𝑀𝑆
𝑀𝑆
Tan 𝑆𝑆 =
1
𝑎𝑐𝑛𝑦. .. −
𝑦.…
𝑎𝑏𝑐𝑛
𝑏 − 1 𝑀𝑆 =
𝑆𝑆
𝑏 − 1 𝐹 =
𝑀𝑆
𝑀𝑆
[H2SO4] 𝑆𝑆[ ] =
1
𝑎𝑏𝑛𝑦.. . −
𝑦.…
𝑎𝑏𝑐𝑛
𝑐 − 1 𝑀𝑆[ ] =
𝑆𝑆[ ]
𝑐 − 1 𝐹 [ ] =
𝑀𝑆[ ]
𝑀𝑆
tan.Tan 𝑆𝑆 .
=1
𝑐𝑛𝑦 … −
𝑦….
𝑎𝑏𝑐𝑛− 𝑆𝑆 − 𝑆𝑆
= 𝑆𝑆 ( . ) − 𝑆𝑆 − 𝑆𝑆
(𝑎 − 1)(𝑏 − 1) 𝑀𝑆 . =
𝑆𝑆 .
(𝑎 − 1)(𝑏 − 1) 𝐹 . =
𝑀𝑆 .
𝑀𝑆
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Realization of High-Quality Nanoporous Gradient-Index Filters by Optimal Combination of Anodization Conditions
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tan.[H2SO4] 𝑆𝑆 .[ ]
=1
𝑏𝑛𝑦 . . −
𝑦….
𝑎𝑏𝑐𝑛− 𝑆𝑆 − 𝑆𝑆[ ]
= 𝑆𝑆 ( .[ ]) − 𝑆𝑆 − 𝑆𝑆[ ]
(𝑎 − 1)(𝑐 − 1) 𝑀𝑆 .[ ]
=𝑆𝑆 .[ ]
(𝑎 − 1)(𝑐 − 1)
𝐹 .[ ]
=𝑀𝑆 .[ ]
𝑀𝑆
Tan.[H2SO4] 𝑆𝑆 .[ ]
=1
𝑎𝑛𝑦. . −
𝑦….
𝑎𝑏𝑐𝑛− 𝑆𝑆 − 𝑆𝑆[ ]
= 𝑆𝑆 ( .[ ]) − 𝑆𝑆 − 𝑆𝑆[ ]
(𝑏 − 1)(𝑐 − 1) 𝑀𝑆 .[ ]
=𝑆𝑆 .[ ]
(𝑏 − 1)(𝑐 − 1)
𝐹 .[ ]
=𝑀𝑆 .[ ]
𝑀𝑆
tan.Tan.[H2SO4] 𝑆𝑆 . .[ ]
=1
𝑛𝑦 . −
𝑦.…
𝑎𝑏𝑐𝑛− 𝑆𝑆 − 𝑆𝑆
−𝑆𝑆[ ] − 𝑆𝑆 . − 𝑆𝑆 .[ ]
−𝑆𝑆 .[ ]
= 𝑆𝑆 ( . .[ ]) − 𝑆𝑆 − 𝑆𝑆
−𝑆𝑆[ ] − 𝑆𝑆 . − 𝑆𝑆 .[ ]
−𝑆𝑆 .[ ]
(𝑎 − 1)(𝑏 − 1)(𝑐 − 1) 𝑀𝑆 . .[ ]
=𝑆𝑆 . .[ ]
(𝑎 − 1)(𝑏 − 1)(𝑐 − 1)
𝐹 . .[ ]
=𝑀𝑆 . .[ ]
𝑀𝑆
Total 𝑆𝑆 = 𝑦 −
𝑦.…
𝑎𝑏𝑐𝑛
𝑎𝑏𝑐𝑛 − 1
Error 𝑆𝑆 = 𝑆𝑆 − 𝑆𝑆 ( . .[ ]) 𝑎𝑏𝑐 (𝑛 − 1) 𝑀𝑆 =
𝑆𝑆
𝑎𝑏𝑐(𝑛 − 1)
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