Determination of the Equilibrium Melting Temperature of Polymer Crystals: Linear and Nonlinear Hoffman−Weeks Extrapolations

Abstract

The applicability of the Hoffman−Weeks (HW) linear extrapolation for the determination of equilibrium melting temperatures of polymers is critically reviewed. In the first paper of this series, it is shown that the linear extrapolation of observed melting temperatures cannot, in general, provide a reliable estimate of the equilibrium melting temperature. A combination of the experimentally observed undercooling dependence of the initial lamellar thickness, l * = C 1 /Δ T + C 2, and the finite lamellar thickness dependent melting temperature depression, as described by the Gibbs−Thomson treatment, provides a venue to the general relationship between the crystallization and observed melting temperatures. It is further shown that, for a constant thickening coefficient, the observed melting temperature must vary nonlinearly with the crystallization temperature. The origin of this nonlinearity lies in the term C 2, which is neglected in the classical HW treatment. The principal implications of this study in the context of the Lauritzen−Hoffman theory are the following: (1) the linear extrapolation, when carried out for lamellar crystals exhibiting a constant thickening coefficient, invariably underestimates the equilibrium melting temperature; (2) the extent of the underestimation increases with a decrease in the lamellar thickening coefficient, with an increase in the magnitude of C 2 and with an increase in the range of undercoolings where the crystals are formed; (3) the linear extrapolation always leads to an overestimation of the lamellar thickening coefficient. Finally, a more accurate method is proposed for the determination of equilibrium melting temperatures in cases where the thickening coefficient can be assumed constant.