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sca.
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The treatment of core-shell particles as homogeneous effective medium assumes that the particle size is small enough to neglect interference contributions (typically d|n/nm, 1|/λ ≪ 1/20, When feature sizes are sufficiently large for interference effects to become significant, finite particle scattering will be present even for index-matched conditions; however, the effective medium approximation will still yield a low-scattering composition
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m) - 1|/λ ≪ 1/20). When feature sizes are sufficiently large for interference effects to become significant, finite particle scattering will be present even for index-matched conditions; however, the effective medium approximation will still yield a low-scattering composition.
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37549038367
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Several effective medium models (such as Maxwell-Garnett, Bruggeman, Bergman, etc.) have been postulated that differ by the underlying assumptions about the systems' morphology, as well as the approximation used to capture interactions between the inclusions. For the case of discrete particle inclusions in a homogeneous medium. Maxwell-Garnett theory is generally considered to be most appropriate. In the quasi-static limit (i.e., for particle diameters much smaller than the wavelength of light) Maxwell-Garnett theory presents an analytically accurate solution to the effective dielectric constant of a core-shell particle (see reference 14).
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Several effective medium models (such as Maxwell-Garnett, Bruggeman, Bergman, etc.) have been postulated that differ by the underlying assumptions about the systems' morphology, as well as the approximation used to capture interactions between the inclusions. For the case of discrete particle inclusions in a homogeneous medium. Maxwell-Garnett theory is generally considered to be most appropriate. In the quasi-static limit (i.e., for particle diameters much smaller than the wavelength of light) Maxwell-Garnett theory presents an analytically accurate solution to the effective dielectric constant of a core-shell particle (see reference 14).
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16
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37549067474
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The effective refractive index is calculated assuming that the solvent does not interpenetrate the polymer brush grafted to the particle surface, i.e, the polymer is in the dry-brush regime valid in the limit of high grafting densities
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The effective refractive index is calculated assuming that the solvent does not interpenetrate the polymer brush grafted to the particle surface, i.e., the polymer is in the dry-brush regime (valid in the limit of high grafting densities).
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37549007711
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The assumption of the refractive index of the grafted polymer shell being constant (as indicated in Fig. 1) implies constant polymer density and thus only approximately describes the realistic scenario involving solvent penetration (that results in a continuous variation of the refractive index throughout the shell). This simplification docs not compromise the application of effective medium theory to determine the index-matching condition because only the integral of the polarizability over the total particle is considered. Rather, swelling will affect the angle-dependence of the scattered light that explicitly probes the spatial distribution of the particle's polarizability. This, however, is of no concern for the design of null-scattering particle additives.
-
The assumption of the refractive index of the grafted polymer shell being constant (as indicated in Fig. 1) implies constant polymer density and thus only approximately describes the realistic scenario involving solvent penetration (that results in a continuous variation of the refractive index throughout the shell). This simplification docs not compromise the application of effective medium theory to determine the index-matching condition because only the integral of the polarizability over the total particle volume is considered. Rather, swelling will affect the angle-dependence of the scattered light that explicitly probes the spatial distribution of the particle's polarizability. This, however, is of no concern for the design of null-scattering particle additives.
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37549038771
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The molecular weight of the particles is calculated assuming uniform particle diameter d = 20 nm and grafting densities and molecular weights of the grafted PS as provided in Table 1. With respect to the conclusions drawn from the experimental data this value provides an appropriate estimate since deviations (e.g., arising from the finite disparity of particle sizes) will affect all samples similarly.
-
The molecular weight of the particles is calculated assuming uniform particle diameter d = 20 nm and grafting densities and molecular weights of the grafted PS as provided in Table 1. With respect to the conclusions drawn from the experimental data this value provides an appropriate estimate since deviations (e.g., arising from the finite disparity of particle sizes) will affect all samples similarly.
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eff is robust with respect to particle size disparity.
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eff is robust with respect to particle size disparity.
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