Revisit the Gibbs-Thomson Equation Fitting of Poly(butylene succinate) Based on Oligomer Extended-Chain Crystals

Abstract

The equilibrium melting point (T_m⁰) is a crucial thermodynamic parameter for characterizing the crystallization and melting behavior of semi-crystalline polymers. However, the direct measurement of T_m⁰ poses a significant challenge because of the difficulty in physically fabricating fully-extended chain crystals of high-molecular-weight polymers. Therefore, various extrapolation equations for T_m⁰ have been proposed that utilize the thermal properties of ordinary folded-chain lamellae. Among these, the Gibbs-Thomson equation is one of the most commonly employed for modeling. Despite its widespread use, there are notable variations in the T_m⁰ values obtained by different research groups, even when based on similar samples. This raises questions about the validity and accuracy of using the Gibbs-Thomson equation to linearly extrapolate T_m⁰. In this study, we prepared a series of oligomer extended-chain crystals (ECCs) of poly(butylene succinate) (PBS) and used their properties for Gibbs-Thomson fitting. The results reveal a perfect linear relationship, with an extrapolated T_m⁰ value of 136.08 °C. The basal surface free energy of the oligomer ECCs was calculated as 0.084 J/m², which is approximately twice that of folded-chain lamellae. This difference is attributed to the aggregation of highly mobile free tails on the crystal surface. The two structural features of oligomer ECCs—large thickness and fixed surface—better fulfill the conditions for applying the Gibbs-Thomson equation, ensuring its validity and accuracy. Therefore, we believe that the Gibbs-Thomson fit can produce reliable results when sufficient high-quality data are used.