Investigating the equilibrium melting temperature of linear polyethylene using the non-linear Hoffman-Weeks approach

Abstract

The melting behavior of three linear polyethylene fractions with number average molecular weights of 11, 29, and 100.5 kg/mol was studied as a function of crystallization time with conventional and ultra-fast calorimetry. The initial melting temperatures of non-thickened lamellae formed under isothermal conditions over a range of crystallization temperatures were analyzed with the non-linear Hoffman-Weeks method to determine the equilibrium melting temperature. Tmeq values of 138.4±0.9°C, 139.7.4±0.9°C, and 140.9±0.8°C were estimated for PE 11K, PE 29K, and PE 100K, respectively, in close agreement with those reported in the literature for the melting of extended-chain crystals or with the Gibbs-Thomson analysis. The Lauritzen-Hoffman theory and the non-linear Hoffman-Weeks treatment were modified to account for the effect of the tilt angle, θ, of the crystallized stems of linear polyethylene on the initial average lamellar thickness. Accuracy of the non-linear Hoffman-Weeks method was examined using initial lamellar thickness, ℓg∗ , data reported for PE 29K in the literature at different crystallization temperatures. The equilibrium melting temperature obtained by the Gibbs-Thomson approach and the C2 value extracted from the ℓg∗vs.1/ΔT plot were similar within the limits of experimental error to those obtained here through the non-linear Hoffman-Weeks method. Using the Huggins equation, the equilibrium melting temperature of an infinitely long linear polyethylene chain is found to be equal to 141.4±0.8°C, the same value proposed by Wunderlich.