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Power Law Distribution Concerning Absolute Free Energies of Linear Sulfur Chains, Polythiazyls, Polyisoprenes, Linear trans-Polyenes, and Polyynes

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journal contribution
posted on 24.01.2019, 00:00 by Gérard Audran, Sylvain R. A. Marque, Maurice Santelli
After quantum calculations of absolute free energies of polyatomic sulfur derivatives or hydrocarbon oligomer compounds, we have studied the variations of Gn as a function of the number of repeating units n (sulfur atoms or hydrocarbon units, n = 2 to about 60), and observed that these values can be correlated by (a) a nearly perfect linear relationship, Gn = An + B (A and B, constants), with a high accuracy which enables an extrapolation for higher values of n, and (b) a power law:, δG = Gn/nG(n–1) /(n – 1) = C/nd (C and d, constants). From comparison of variations of the C–C bond lengths, we show that the conjugation of trans-polyenes (up to C60H62) is more important than for polyynes (up to C60H2).