Benford's law, its applicability and breakdown in the IR spectra of polymers

Infrared spectra of various polymers were treated statistically. It was established that for the absorbance spectra the Benford distribution of leading digits takes place, whereas the distribution of leading digits for transmittance spectra is random. This observation may be explained by the fact that the value of transmittance Tr is restricted 0 < Tr < 1, due to the physical reasons, whereas the value of absorbance is not. Moreover, the transmittance and absorbance A are interrelated by the logarithmic dependence A = -log Tr. This observation supplies the idea that the Benford law is valid in the situations, when logarithmic dependencies take place. Amalgamation of spectral data obtained for various polymers brings the distribution of the leading digits in the absorbance domain into proximity to the Benford Law. (C) 2015 Elsevier B.V. All rights reserved.