Spatial point statistics for quantifying TiO2 distribution in paint

Elton, N. J.; Legrix, A.

doi:10.1007/s11998-013-9564-5

Cited by 5 publications

(5 citation statements)

References 18 publications

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“…Interestingly, for high‐refractive index, anisotropic systems outperform ensembles of optimized isotropic particles only for aspect ratios larger than 40 (more details in Section S5, Supporting Information). The predicted optimal values of radius ( r 0 = 100nm) and filling fraction (ff = 0.3) for isotropic systems with n = 2.60 are in agreement with those reported in theoretical and experimental studies regarding scattering optimization for titanium‐dioxide particles . Moreover, Figure S2d in the Supporting Information shows that, after exhibiting a strong growth in function of the aspect ratio, between c = 400 and c = 1400, the integrated reflectance shows a less marked dependence on c , with a maximum value at c = 500.…”

Section: Resultssupporting

confidence: 87%

Role of Anisotropy and Refractive Index in Scattering and Whiteness Optimization

Jacucci

Bertolotti

Vignolini

2019

Advanced Optical Materials

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structure factor) and their specific characteristics (form factor and refractive index). [1][2][3][4] Therefore, most efforts to control light propagation in random systems have been focused upon the optimization of isotropic spatial correlations in highrefractive index systems. These studies had a remarkable impact in many fundamental [5][6][7][8][9][10][11][12][13][14][15][16] and applied phenomena. [17][18][19][20][21] However, the role of anisotropy in multiple scattering systems has been overlooked. In fact, despite the well-known analytical solution for the single scattering, [4,22] the response of an ensemble of randomly arranged anisotropic particles has not been theoretically investigated. The same is valid for the presence of anisotropic structural correlations. Similarly, recent experimental works focused on the fabrication and optical characterization of anisotropic, disordered materials but without proving the role of anisotropy in scattering optimization. [23][24][25][26][27][28][29][30] Here, we study the effect of structural and single-particle anisotropy on the opacity of a material and identify the criteria to improve scattering over a large parameter space, including filling fraction and refractive index. Our work proves that ensembles of uncorrelated, anisotropic particles outperform their isotropic counterpart both for low-and high-refractive indices. In addition, anisotropic, low-refractive index systems not only require a lower amount of material to maximize scattering than isotropic media, but they also exhibit a whiteness comparable to those of high-refractive index materials.Our results showcase how to exploit natural resources (e.g., biopolymers) to replace commercially available white enhancers, made from inorganic high-refractive materials (e.g., TiO 2 ), which have recently raised safety concerns. [31,32] Moreover, our work unveils why anisotropy is an evolutionary-chosen mechanism to optimize scattering in biological systems. Results and DiscussionTo establish a comparison between different disordered materials, we numerically investigated the optical properties of 2D media (see Sections S1 and S2 in the Supporting Information). Exploiting a 2D numerical approach allows to independently vary the structural and form factors of a system, and therefore to disentangle their role in scattering optimization, while avoiding computational burden. In particular, we systematically The ability to manipulate light-matter interaction to tailor the scattering properties of materials is crucial to many aspects of everyday life, from paints to lighting, and to many fundamental concepts in disordered photonics. Light transport and scattering in a granular disordered medium are dictated by the spatial distribution (structure factor) and the scattering properties (form factor and refractive index) of its building blocks. As yet, however, the importance of anisotropy in such systems has not been considered. Here, a systematic numerical survey that disentangles and quantifies the role of different kinds...

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Section: Resultssupporting

confidence: 87%

Role of Anisotropy and Refractive Index in Scattering and Whiteness Optimization

Jacucci

Bertolotti

Vignolini

2019

Advanced Optical Materials

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“…The refractive index is set to 2.67 and 1.5 for the particles and host matrix, respectively, in accordance with typical values used in the literature to describe paint film components [29,32]. All cylindrical configurations have a diameter/height ratio strictly above 4 to avoid finite-size effects [40].…”

Section: A Design Of Sample Configurationsmentioning

confidence: 99%

“…A typical example is related to the use of titanium dioxide (TiO 2 ) nanoparticles in coating and paint applications, which we will use as a reference test case in this work due to its generality, technologic relevance, and long-standing research efforts on the topic [23][24][25][26][27]. Indeed, while there is general agreement on the fact that scattering nanoparticles for an optimal white paint formulation should have a diameter of roughly 200 nm [18,28,29], little else is agreed upon when it comes to the optimal density, spatial correlations, and degree of clustering. The latter is another exemplary issue of debate: while flocculation and particle clustering is typically seen as a detrimental factor [29][30][31][32][33], numerical and experimental evidence exist showing that light scattering is either insensitive to clustering [34] or even enhanced by it [35].…”

Section: Introductionmentioning

confidence: 99%

“…Indeed, while there is general agreement on the fact that scattering nanoparticles for an optimal white paint formulation should have a diameter of roughly 200 nm [18,28,29], little else is agreed upon when it comes to the optimal density, spatial correlations, and degree of clustering. The latter is another exemplary issue of debate: while flocculation and particle clustering is typically seen as a detrimental factor [29][30][31][32][33], numerical and experimental evidence exist showing that light scattering is either insensitive to clustering [34] or even enhanced by it [35]. Similarly, even the onset of the so-called "dependent" scattering regime is often questioned, being generally set around 1% volume fraction [18][19][20]36] with experimental evidence suggesting values well above that [28,37], possibly up to 20% [38].…”

Section: Introductionmentioning

confidence: 99%

“…Adding to this, conflicting interests between industrial players fostering an increased use of either scatterering particles or inter-particle spacers also seem to bias findings and claims in part of the literature [33]. Finally, even when spatial correlations are explicitly considered, e.g., exploiting either steric or electrostatic repulsion between particles, the actual effect on the three-dimensional (3D) point statistics is hard to evaluate or quantify, being at best only indirectly inferred by time-consuming analysis of twodimensional (2D) micrographs [29]. As can be imagined, similar inconsistencies affect the optical characterization of all discrete random media beyond the illustrative case of TiO 2 in paint coatings.…”

Section: Introductionmentioning

confidence: 99%

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Role of packing density and spatial correlations in strongly scattering 3D systems

Pattelli¹,

Egel²,

Lemmer³

et al. 2018

Optica

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Discrete random media have been investigated extensively over the past century due to their ability to scatter light. Even so, the link between the three-dimensional (3D) spatial distribution of the scattering elements and the resulting opacity is still lively debated to date due to different experimental conditions, range of parameters explored, or sample formulations. On the other hand, a unified numerical survey with controlled parameters has been impractical up to date due to the sheer computational power required to address samples with representative size. In this work, we exploit a graphics processing unit implementation of the T -matrix method to investigate the complete range of particle volume concentration and packing-induced spatial correlations, allowing us to reveal and elucidate a twofold role played by spatial correlations in either enhancing or suppressing opacity. By applying these findings to the illustrative case of white paint, we determine the optimal combination of density and spatial correlations corresponding to the highest opacity.

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Wavelength dependence of Kubelka–Munk scattering spectra for studies of TiO2 microstructure and aggregation in paints

Elton

Legrix²

2014

J Coat Technol Res

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Spatial point statistics for quantifying TiO2 distribution in paint

Cited by 5 publications

References 18 publications

Role of Anisotropy and Refractive Index in Scattering and Whiteness Optimization

Role of Anisotropy and Refractive Index in Scattering and Whiteness Optimization

Role of packing density and spatial correlations in strongly scattering 3D systems

Wavelength dependence of Kubelka–Munk scattering spectra for studies of TiO2 microstructure and aggregation in paints

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