Simulation of the Light Transmittance in Macroporous Silica
Abstract
:1. Introduction
2. Generation of Porous Silica Models
- -
- A certain amount of seeding points are created first, corresponding to the cells of the final structure. A Random Sequential Absorption Algorithm [33] is imposed to make the equal-sized spheres (centred at the created seeding points) distributed in the given space without overlapping for the random structures.
- -
- The space is partitioned into polyhedral regions with the seeding points by Voronoi diagram [34].
- -
- The resulting structure is optimized by Surface Evolver [35] for energy stability.
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- Polygonal struts are created with the final skeleton.
- (1)
- Porosity, p, indicates the proportion of the gas phase. In this paper, the porosities of models are limited in the range , corresponding to the products prepared by sol-gel method in experiments.
- (2)
- Coefficient of variation, , figures the dispersion of cell size distribution of random structures, where and are the standard deviation of cell diameter and the average equivalent cell diameter respectively. In this paper, the Gaussian unimodal distribution with different standard deviations is used for different cell size distributions.
- (3)
- Diameter ratio, , represents the ratio of the cross section diameter between the middle and the end of a strut, where and are the minimum and maximum diameter. Table 1 shows the illustration of the struts with different diameter ratios.
- (4)
- Normalized curvature, , governs the shape of the cross section of a strut, where stands for the curvature radius of the circumcircle of the cross section and is the curvature radius of the sides of the cross section. Table 2 exhibits the illustration of the cross sections with different normalized curvatures.
3. Numerical Simulation
3.1. Mesh Sensitivity
3.2. Boundary Value Problem
4. Results and Discussion
4.1. Analysis of Light Propagation
4.2. Influences of the Morphological Parameters
4.2.1. Porosity p
4.2.2. Coefficient of Variation
4.2.3. Diameter Ratio t
4.2.4. Normalized Curvature k
4.3. Influence of the Wavelength
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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t | 1 | ||
---|---|---|---|
Struts | | | |
k | 0 | 1 | ||
---|---|---|---|---|
Struts | | | | |
Variable | Range |
---|---|
Porosity p | (, , , , ) |
Coefficient of variation | (0.0, 0.1, 0.2, 0.3, 0.4) |
Diameter ratio t | (0.33, 0.40, 0.50, 0.67, 1.00) |
Normalized curvature k | (-0.3, 0.0, 0.3, 0.6, 1.0) |
Wavelength | (400 nm, 500 nm, 600 nm, 700 nm, 770 nm) |
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Zhu, W.; Guo, X.; Wu, L.; Yang, H. Simulation of the Light Transmittance in Macroporous Silica. Materials 2020, 13, 1635. https://doi.org/10.3390/ma13071635
Zhu W, Guo X, Wu L, Yang H. Simulation of the Light Transmittance in Macroporous Silica. Materials. 2020; 13(7):1635. https://doi.org/10.3390/ma13071635
Chicago/Turabian StyleZhu, Wenqi, Xingzhong Guo, Lan Wu, and Hui Yang. 2020. "Simulation of the Light Transmittance in Macroporous Silica" Materials 13, no. 7: 1635. https://doi.org/10.3390/ma13071635