A mathematical method to estimate the equilibrium melting temperature from growth rate data

Abstract

The regime transitions analysis is subject to all the limitations of the ordinary least squares method which is generally applied to the linearized form of the Lauritzen-Hoffman equation. Therefore, polymers growth rate has to be measured in a sufficiently wide temperature range to ensure a reliable kinetic analysis based on the secondary nucleation theory. Furthermore, an accurate value of the equilibrium melting temperature has to be used in order to achieve trustworthy thermodynamics outcomes, although this quantity may be affected by a high uncertainty. Here a method is proposed in order to verify directly from growth rate data the use of the most reliable value of the equilibrium melting temperature. The method is based on the comparison between the derivatives of the growth rate functions calculated by the Lauritzen-Hoffman equation using the outcomes of the regime analysis.