By analyzing TEM images of the composites (Figure 2), which are obtained by means of treatment with H2S of Zn-siloxane mixtures with poly-(dimethyl)-block-(phenyl)siloxanes, one can see that the nanoparticles appear only after treatment of Zn-siloxanes with H2S. Such behavior assumes formation of ZnS nanoparticles, which is favorable at elevated temperatures, migration of Zn ions, and formation of clusters (nanoparticles) of ZnS. It is interesting to note that it does not happen in the case of oxygen, and ZnO nanoparticles do not form in oxygen media at elevated temperatures, so one can assume that sulfides are easier to form in a cluster form than oxides. Particle size was determined basing on TEM images. It was found that the particle size is approximately 3 nm with broad distribuiton around the mean value, and with the increase of ZnS concentration, it increases slightly up to 5 nm - mean value. It can be seen from the optical transmission spectra (Figure 4) that composites with smaller ZnS loading (up to 14 wt.% of Zn) possess very high optical transparency, combined with elevated values of refraction coefficient.
At the same time, for the nanocomposites with smaller ZnS loadings (A11S, A12S), we see no particles both in the TEM images and in the XRD spectra, but these compositions possess higher refractive index than pure polymer matrix. This is due to the fact, from our point of view, that for such small loadings, we have smaller clusters of ZnS, which have an amorphous structure and thus are not visible in the XRD spectra or in the HR-TEM or TEM images.
High optical transparency of samples is due to the fact that there is no Mie scattering for the particles with a size less than λ
/2, and the Rayleigh scattering intensity is expressed by a well-known formula:
where I is the intensity of the Rayleigh scattering; I
, the initial intensity of light; θ, the angle between the falling and the scattering ray; R, the distance to the nanoparticle; d, the diameter of the nanoparticle; n, the refraction coefficient; and λ, the wavelength of radiation. I depends on the particle size as d6. Thus, for very small particles with d approximately 2 to 3 nm, we obtain almost negligible Rayleigh scattering, thus providing optical transparency of the composites which reached 92% to 93% (Figure 4).
Nevertheless, the composites with higher ZnS loading show much higher scattering, which makes them opaque and shadow-like; thus, for the Zn concentrations of more than 12 wt.%, the compositions become highly scattering. This is probably due to the fact that the agglomeration takes place with the increase of ZnS concentration, and for high ZnS concentrations, the agglomerate size becomes comparable with λ/ 2. Also, for the compositions with high loadings, RI drops down drastically. This reflects, from our point of view, the fact that if the agglomerate of particle size is bigger than approximately 5λ, the light starts to refract at the interface between particle agglomerates and the polymer.
The values of the refractive index of nanocomposites up to A12S and from A16S to A18S do fit well using effective media theory prediction, which assumes that
where x is the volume rate of the component in the mixture, RIZnS = 2.39, and RImatrix = 1.55. Thus, for the A12S (1.96 vol.%), calculated according to effective media prediction, RI should have been 1.576, and in fact, it was measured to be 1.57.
We foresee three ranges of agglomerates in particle length scales, which differ in interaction with light: (1) d < < λ/2 - Rayleigh regime, which has ultra low scattering and high transparency; RI is fitted well with effective media approximation; (2) d = λ/2 to 5λ - Rayleigh scattering + Mie scattering, which has an average value of scattering and still has high transparency; some discrepancies from effective media theory predictions are observed; and (3) d > 5λ - geometry optics range, which has a lot of scattering; effective media approxiation works. Thus, we believe that for the nanocomposites with Zn of more than 12 wt.% (ZnS of 5.5 vol.%), nanoparticle aggregation in big clusters takes place (we measured XRD for these samples, and still there are no peaks of ZnS, which provides evidence of small nanoparticles but joined in the big aggregates); effective media approximation still works; we obtain composites where big nanoparticle aggregates work as scatterers; and the light is refracted at the polymer-aggregate interface. It is also anticipated that samples A14S and especially A15S are in the Mie scattering range since scattering becomes high, especially for A15S, and the effective media theory gives big discrepancies of RI in comparison with the experimentally observed ones.
Analyzing the dependencies of refractive indices of nanocomposites on ZnS content (Figure 6), it can be seen that the dependence is linear and is fitted with effective media approximation, except for nanocomposites A13S, A14S, and A15S. These nanocomposites are in the Mie scattering mode, according to our assumption, and their refractive indices are well above the values, predicted by effective media theory. The reason of these phenomena is unknown to the authors.
Also, it is necessary to note that the agglomeration of nanoparticles and growth of film inhomogeneity at higher ZnS content reflect the fact that ZnS nanocrystals tend to agglomerate if the concentration is higher than some critical one, minimizing the free surface energy. This provides some insight into the ability to disperse nanoparticles homogeneously in siloxane matrices without agglomeration.