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

journal contribution

posted on 24.01.2019, 00:00 by Gérard Audran, Sylvain R. A. Marque, Maurice SantelliAfter
quantum calculations of absolute free energies of polyatomic
sulfur derivatives or hydrocarbon oligomer compounds, we have studied
the variations of

*G*_{n}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,*G*_{n}=*An*+*B*(A and B, constants), with a high accuracy which enables an extrapolation for higher values of*n*, and (b) a power law:, δ*G*=*G*_{n}/*n*–*G*_{(n–1)}/(*n*– 1)*=**C*/*n*^{d}(*C*and*d*, constants). From comparison of variations of the C–C bond lengths, we show that the conjugation of*trans*-polyenes (up to C_{60}H_{62}) is more important than for polyynes (up to C_{60}H_{2}).