Evidence of absorption dominating over scattering in light attenuation by nanodiamonds

We show an experimental evidence of the domination of absorption over scattering in absorbance spectra of detonation nanodiamonds. We perform absorbance measurements on the UV-vis spectrophotometer equipped with an integrating sphere and compare them with conventional absorbance spectra. Additionally, we measure the scattering light intensity at the cuvette side wall (scattering at ${90}^{\circ }$ angle). The obtained experimental data were interpreted using photon random-walk simulations in turbid media and the Kubelka-Munk approach. The scattering cross sections and indicatrices were obtained by Mie theory. We discover that despite being very close to the ${\lambda }^{-4}$ power law (like Rayleigh scattering) the light extinction by the primary 4-nm diamond crystallites is due to absorption only and scattering can be neglected. That is the reason why previously absorption and scattering contributions were confused. The scattering is governed only by the agglomerates of 100 nm and larger in size remaining in the hydrosols and their fraction can be effectively controlled by centrifugation. Only Mie theory reproduces correctly the close to ${\lambda }^{-2}$ scattering by the agglomerates accounting for the weird interplay between their size, fractal dimension, and dielectric properties. Finally, using the obtained absorbance spectra we estimate the fraction of nondiamond phase in nanodiamonds and their agglomerates.

Figure 1

Absorbance spectra measurements on (a) the spectrophotometer equipped with IS and (b) the spectrophotometer without the sphere (conventional Abs measurements). For the experiment without the sphere, the forward-scattered light vanishes, whereas the sphere collects it and brings the additional intensity $I_{\mathrm{Diff}}$ into account.

Figure 2

(a) A ${90}^{\circ }$ scattering experiment on the Chirascan device giving $T_{90}\left(\lambda \right)$. (b) Reference measurement was carried out with water in the cuvette.

Figure 3

Distribution by scattered light intensity for $\mathrm{Z}+$ nanodiamond supernatant ($\mathrm{Z}+1$) and precipitate ($\mathrm{Z}+2$) obtained by DLS. One sees the trimodal size distribution.

Figure 4

Absorbance spectra for all the studied samples. Orange is for $\text{Z}-2$, pink is for the $\text{Z}-1$ sample, light green is for the $\mathrm{Z}+2$, dark green is for $\mathrm{Z}+1$, cyan is for Z02, and blue is for Z01. Solid curves are for ${\mathrm{Abs}}_{\mathrm{N}}\left(\lambda \right)$ (measurements without IS) and dashed curves are for ${\mathrm{Abs}}_{\mathrm{IS}}\left(\lambda \right)$ (measurements with IS). Also, the ${\lambda }^{-2}$ and ${\lambda }^{-4}$ functions are plotted with dotted black curves.

Figure 5

Scattering effectiveness for all samples in terms of $T_{\mathrm{Diff}}\left(\lambda \right)$ and $T_{90}\left(\lambda \right)$. Solid curves are for $T_{\mathrm{Diff}}\left(\lambda \right)$ obtained from Abs measurements without and with sphere substituted to Eq. (4). Dashed curves are for the results of the ${90}^{\circ }$ scattering experiment on the Chirascan device $T_{90}\left(\lambda \right)$ obtained with Eq. (5). Orange color is for the $\text{Z}-2$ sample, pink is for the $\text{Z}-1$ sample, light green is for $\mathrm{Z}+2$, dark green is for $\mathrm{Z}+1$, cyan is for Z02, and blue is for Z01.

Figure 6

The Abs spectra with and without sphere, obtained with photon random-walk simulation (depicted with markers) and the experimentally measured Abs spectra of $\mathrm{Z}+1$ (dashed curves) and $\mathrm{Z}+2$ (solid curves) samples with (black curves) and without (green curves) the integrating sphere. The predictions of the theory of light propagation in turbid media for Abs spectra with integrating sphere are shown with the blue markers. The red dashed curve shows the ${\lambda }^{-4}$ function corresponding to Rayleigh scattering and the blue dashed curve is for ${\lambda }^{-2}$.

Figure 7

The results of photon random-walk simulations for scattering efficiency in terms of $T_{\mathrm{Diff}}\left(\lambda \right)$ (green colors) and $T_{90}\left(\lambda \right)$ (orange colors) are shown with markers. Circles are for $\mathrm{Z}+1$ and squares are for the $\mathrm{Z}+2$ sample. The experimental spectra are given by dense points. Experimental $T_{\mathrm{Diff}}\left(\lambda \right)$ spectra were obtained on the basis of Abs measurements with and without sphere using Eq. (4) and experimental $T_{90}\left(\lambda \right)$ spectra were obtained from ${90}^{\circ }$ scattering experiment on the Chirascan device using Eq. (5). Blue markers denote the results of the theory of light propagation in turbid media.

Figure 8

Decomposition of the Abs spectra to scattering and absorption based on Eqs. (11) and (12). Solid curves are for $\mathrm{Z}+2$ and dashed curves are for the $\mathrm{Z}+1$ sample. Green color is for total Abs, gray color is for scattering, and black color is for absorption. For supernatant $\mathrm{Z}+1$, the contribution to absorption from primary crystallites (red color) and agglomerates (blue color) is given. For precipitate $\mathrm{Z}+2$, both scattering and absorption are governed mainly by agglomerates.