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The possibilities of using multivariate determination of carbon nanotubes properties based on the dependence data of the normalized transmission logarithm on the sample displacement in the case of Z-scan with an open aperture as well as on the total pulse energy in the case of fixed sample position measurements are studied. The radiation transfer equation for the threshold dependence of the absorption coefficient on the intensity of a flat-top laser beam is used. The data of physical and computational experiments showed the sensitivity of the measured curves with respect to the values of the constants of the optical and threshold energy fluence, as well as the beam waist radius. The possibility of multivariate determination of the properties of liquid carbon nanotube-based dispersed media with a nonlinear optical threshold effect and beam waist radius inside such samples has been established. Keywords: optical limiting, multivariate analysis, carbon nanotubes, Z-scan

The effect of the vacancy edge defect (bonds breaking between carbon atoms) of a graphene sheet on the Raman spectrum was studied. The spectra were calculated using the density functional theory (DFT) using the Gaussian-09 program. Modeling of a graphene sheet fragment with a break of one bond between carbon atoms at the edge showed that changes in the Raman spectrum were common for the presence of nitrogen and oxygen atoms. In this case, the strongest D lines appear in functionalized graphene with oxygen atoms, and the Dʹ lines-in nitrogen-doped graphene. This is confirmed by the experimental Raman spectra as well as calculated ones. The strongest 2D line is characteristic of the graphene model without impurities; the presence of other oxygen or nitrogen atoms leads to a decrease in its intensity. Modeling of a graphene sheet fragment with a break of one bond between carbon atoms at the edge showed that changes in the spectrum are common for both cases of graphene nitrogen-doping and functionalization with oxygen atoms. A comparison of the experimental data with the simulation results showed good agreement between the data. Moreover, the vibrations of hydrogen atoms linked by covalent bonds with neighboring carbon atoms moved towards each other in disturbed hexagonal structures located on the edge of the graphene sheet. Such a steric effect led to a decrease in the frequency of the stretching vibration q(CH), which appeared in the region of ~2700 cm −1 and corresponded to the 2D vibration. The results of the vacancy edge defect modeling for the graphene sheet fragment being nitrogen-doped and functionalized by oxygen atoms were compared with experimental data.

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