Spherulites determination

The model described above was applied to the crystallization of y-POP at 15°C, because y-POP was observed to occur exclusively as spherulites [39]. Four cases were simulated with different nucleation laws. The first case (SI) supposes an instantaneous nucleation, with a density of nuclei equal to the final number of spherulites determined experimentally. The three other simulations suppose nucleation at constant rate /q. Case S2 estimates 7o based on the final crystal density and the growth rate measured experimentally, using the formula of Mei-jering [40] ... 

This influx coverage parameter /, can be used to characterize both intra and inter-spherulitic influxes and combinations of the two.The maximum force Fj, required to cohesively break an influx is determined by... 

Usually, crystallization of flexible-chain polymers from undeformed solutions and melts involves chain folding. Spherulite structures without a preferred orientation are generally formed. The structure of the sample as a whole is isotropic it is a system with a large number of folded-chain crystals distributed in an amorphous matrix and connected by a small number of tie chains (and an even smaller number of strained chains called loaded chains). In this case, the mechanical properties of polymer materials are determined by the small number of these ties and, hence, the tensile strength and elastic moduli of these polymers are not high. 

These concepts have to be correlated with the inherent helical form of the starch molecule, and attempts which have been made to determine the orientation of the portions of the molecules in the crystallites will be dealt with later (in the Section on x-ray diffraction studies—see p. 376). In this connection, the work on the orientation of synthetic crystalline polymers into spherulites containing helically arranged molecules23 may be important. 

It is of course important to note that the overall rate of crystallization is not only determined by the growth rate of the spherulites, but also by the amount of nuclei being present in the system. This possibility is used as an effective method to influence the total crystallization rate of commercial polymeric materials in a controlled manner and to influence the size of spherulites and thus the physical properties of finished articles made from semicrystalline polymers. 

The overall rate of crystallization is determined by both the rate of nuclei formation and by the crystal growth rate. The maximum crystal growth rate lies at temperatures of between 170 and 190 °C [71, 72], as does the overall crystallization rate [51, 61, 75], The former is measured using hot stage optical microscopy while the latter is quantified by the half-time of crystallization. Both are influenced by the rate of nucleation on the crystal surface and the rate of diffusion of polymer chains to this surface. It has been shown that the spherulite growth rate decreases with increasing molecular weight due to the decrease in the rate of diffusion of molecules to this surface [46, 50, 55, 71, 74],... 

Video microscopy with crossed polarizers permits the direct and non-invasive observahon of the nucleahon and growth process for many substances, and thus the study of the hme evoluhon of the spherulite radius R t). When the growth is controlled by diffusion the radius of the spherulites increases as R t) a while when the growth is determined by a nucleation-controlled process (incorporahon of atoms or molecules to the surface of the crystalline part) the radius increases linearly with hme, R t) a t. 

The crystalline melting point is determined by heating a crystallized sample on the Kofler heating stage of a polarizing microscope. The samples are crystallized by heating at 180° to 190°C. until spherulites appear. 

---