This review concerns the “termination of crystallization or ordering of flexible, linear macromolecules” before the transition from the amorphous phase reaches thermodynamic equilibrium. It makes use of the precision of hindsight in interpretation of old experiments and the back-integration of more recent experiments into the knowledge gained from the well-known older experiments which had led to the paradox: Once the semi-ordered sample is produced, its disordering frequently follows a zero-entropy-production path, i.e., its latent heat is linked to the free enthalpy of the non-equilibrium phase, while on ordering, there exists a metastable temperature region of the polymer melt which cannot be broken by nuclei of the ordered phase. The classic scheme of crystallization via nucleation and growth is used to set the stage for the discussion. This scheme has been used for many years to describe the motion of single motifs to crystallize small, rigid molecules and its slow-down when approaching the glass transition. For flexible macromolecules, the ordering mechanism needs to be expanded to the description of cooperative ordering schemes of more than one motif of the molecular segments and a more complicated, multiple-step slow down when approaching the much wider glass transition region. The structural features causing the incomplete ordering of flexible macromolecules are the three-dimensional defects created at the phase boundaries between ordered and disordered phases, initially called the amorphous defects. The matter contained in these amorphous defects possesses a much broader glass transition. If this glass transition lies above the glass transition of the unrestrained, amorphous phase, the amorphous defects represent a separate nanophase, called a rigid-amorphous fraction. Modern differential scanning calorimetry (DSC), temperature-modulated DSC, and differential fast scanning calorimetry permit the study of latent heats and heat-capacity changes involved in the liquid–solid transitions of amorphous phases, crystals, and mesophases. In this more complex framework, the “termination of crystallization of flexible, linear macromolecules” is described together with the possibility of molar mass segregation by long-range and local diffusion instead of a thermodynamic mechanism.
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