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On the existence of macro- and nanostructures with phonon spectra of low fractal dimensions

V. M. Kuznetsov, V. I. Khromov

D. Mendeleev University of Chemical Technology of Russia

Abstract: It is shown that structures possessing predominantly low-frequency vibrational spectra and phonon spectra of low fractal dimensions $d_f<$ 1, which have been predicted previously by the fractal theory of heat capacity, can exist among natural objects representing the cluster state of matter. This conclusion is based on an analysis of the frequency spectra of molecular vibrations in water clusters containing 10–22 molecules, which have been obtained using ab initio numerically simulations. It has been found that fractal dimensions of the corresponding phonon spectra fall within $d_f$ = 0.3–0.5. The temperature dependence of the heat capacity $C(T)$ of these clusters differs from that of bulk samples of the same chemical composition (e.g., macroscopic samples of ice with $d_f\approx$ 1.4). These differences are even more pronounced in comparison to substances that obey the traditional Debye law ($d_f$ = 3).

Received: 27.09.2011

 English version: Technical Physics Letters, 2012, 38:3, 207–210

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