DETERMINATION OF THE EQUILIBRIUM MELTING TEMPERATURE OF POLYMER CRYSTALS - LINEAR AND NONLINEAR HOFFMAN-WEEKS EXTRAPOLATIONS

The applicability of the Hoffman-Weeks (HW) linear extrapolation for t he determination of equilibrium melting temperatures of polymers is cr itically 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 temper ature. A combination of the experimentally observed undercooling depen dence of the initial lamellar thickness, l = C-1/Delta T + C-2, and t he 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 coef ficient, the observed melting temperature must vary nonlinearly with t he crystallization temperature. The origin of this nonlinearity lies i n the term C-2, which is neglected in the classical HW treatment. The principal implications of this study in the context of the Lauritzen-H offman theory are the following: (1) the linear extrapolation, when ca rried out for lamellar crystals exhibiting a constant thickening coeff icient, invariably underestimates the equilibrium melting temperature; (2) the extent of the underestimation increases with a decrease in th e lamellar thickening coefficient, with an increase in the magnitude o f C-2 and with an increase in the range of undercoolings where the cry stals are formed; (3) the linear extrapolation always leads to an over estimation of the lamellar thickening coefficient. Finally, a more acc urate method is proposed for the determination of equilibrium melting temperatures in cases where the thickening coefficient can be assumed constant.