Absence of Definite Scaling Laws in Raman Scattering from Fractals

TL;DR

This paper demonstrates through numerical calculations that Raman scattering from fractals does not follow universal scaling laws and is highly sensitive to microscopic details, complicating the extraction of macroscopic parameters.

Contribution

It reveals the absence of universal scaling laws in Raman scattering from fractals and highlights the dependence on microscopic structural details.

Findings

No general scaling law in Raman coupling coefficient $C()$

Sensitivity of $C()$ to microscopic cluster details

Difficulty in deriving macroscopic parameters from Raman data

Abstract

The frequency dependence of the Raman coupling coefficient $C(\omega)$ is calculated numerically for square and cubic percolation clusters. No general scaling law in terms of the macroscopic parameters such as the fractal dimension $D$ or the spectral dimension $\overline d$ is found. $C(\omega)$ is sensitive to the microscopic structure of the clusters and depends on: site- or bond-percolation, presence or absence of dangling bonds, scattering mechanism and polarization, presence or absence of polarizability disorder. This situation makes the derivation of macroscopic parameters from Raman experiments unreliable.