Another approach to the Gibbs–Thomson equation and the melting point of polymers and oligomers

The common Gibbs–Thomson equation, widely used to explain the melting temperature of lamella crystals, is based on a given heat of fusion and a given surface free energy and the size (thickness) of the crystal. With this equation it is not possible to explain the, compared to the thickness of the crystals, very high melting temperature of cyclic alkanes and ultra-high molar mass polyethylene (UHMMPE). Another thermodynamic approach to the Gibbs–Thomson equation, starting from an incremental composition of enthalpy and entropy of the chain molecule, is presented. This describes the melting temperature of (lamella) crystals of linear, folded and cyclic alkanes as well as UHMMPE, all forming crystals of the same lattice type, with only one set of parameters. The essential variable turns out to be the number of CH2-groups of the respective molecule, incorporated into the crystallite, rather than its thickness. This may be explained if we assume the melting process caused by conformation dynamics which are more restricting the greater number of CH2-groups that are involved in the chain movement. In a lamella crystal of a certain thickness, a cyclic alkane ‘feels’ longer than an n-alkane, as well as a linear molecule with adjacent or tight folds feels longer than one with randomly distributed chains and large loops in the amorphous. This approach helps to understand the melting behavior of polymers forming folded-chain crystals. It enables the cyclic and folded ultra-long alkanes to serve as model substances for the folded-chain crystals of polyethylene without further assumptions concerning the surface energy and fits all findings smoothly into one picture.