Enthalpic and entropic origins of nucleation barriers during polymer crystallization: the Hoffman-Lauritzen theory and beyond

In the search for a greater understanding of polymer crystallization, numerous experimental observations with regards to microscopic structures and macroscopic properties have been reported in the past half-century. There are generally two types of experimental results to provide information about the mechanisms of polymer crystal growth, i.e. molecular dynamic/scattering and structural/morphological. Since we cannot follow the trajectory of individual chain molecules when they undergo the transition from liquid to solid state during the crystallization process, structural/morphological analysis of polymer crystals reveal information recorded during this process. Namely, the final structure and morphology of polymer crystals have atomic, stem and global chain conformation information embedded in them during crystallization which provides evidence which can be used to deduce molecular aspects of the polymer crystallization process. It is commonly understood that polymer crystallization, from the thermodynamic perspective, is a first-order transition involving the relaxation of a metastable undercooled melt towards the equilibrium state which is rarely reached in polymer crystals. This process is controlled by a free energy barrier. A molecular model is required to describe the landscape of the free energy barriers and to provide an analytical explanation concerning and predictions about polymer crystallization. The Hoffman-Lauritzen (HL) theory, which was put forward more than 40 years ago, was one of the first analytical theories to illustrate how polymers crystallize. Since then, modifications to the HL theory and suggestions for new approaches have been reported, but the core physical picture of the HL theory has largely remained intact. This article consists of four major parts: (1) we will compare the crystallization of small molecules and long chain molecules, and the relationship between crystallization and crystal habits. The diversity of crystalline structures and morphologies of semi-crystalline polymers must be taken into account when studying the crystallization mechanism of polymers (2) this article also serves as a brief review of the HL theory and its importance in our understanding of polymer crystallization (3) we have tried to answer the question: what is the nucleation barrier? Specifically, we will illustrate that the nucleation barrier in polymer crystallization consists of both enthalpic and entropic components as deduced from experimental results. This barrier, from our perspective, consists of selection processes taking place in different length- and time-scales (4) finally, there is a brief discussion on what issues remain, in particular, in the areas of undercooled liquid structures and the initial stages of crystallization.