The melting temperatures of the n-paraffins and the convergence temperature for polyethylene

Abstract

The extrapolation of the melting points, Tm, of the n-paraffins to large chain lengths (n ? 8) is reexamined in order to resolve the differences in the proposed values of the convergence temperature T0 = lim n ? 8 Tm. Experimental liquid entropies can be made consistant with a term, R In n, proposed by Flory and Vrij. This term effectively replaces the well-known expression Tm = T0 (n + a)/(n + b) with an expression Tm = T0 (n + a)/(n + ln n + b); thus, slowing the convergence rate and increasing T0 from 141.1 ?C to 144.7 ?C. Independent estimates of the parameters in the melting relationship were obtained from thermodynamic data and the least squares estimate of T0 = 144.7 ?C (calculated from 33 melting points with a standard deviation of Tm = 0.3 ?C) could not be altered by more than ?0.5 ?C by any reasonable variation of the parameters. A simplified melting expression is obtained for polyethylene which includes both the chain end and fold surface energies, and it is shown that chain end effects partly account for the discrepancy between the 144.7 ?C convergence temperature and experimental melting temperatures (~139 ?C) of extended chain polyethylene crystals.