Evaluation of the instantaneous nucleation density in the isothermal crystallization of polymers

An expression is established for the temperature dependence of the average density of nuclei, as well as a temperature-dependent relationship between the half-crystallization times, t50%, obtained from isothermal differential scanning calorimetry polymer crystallization experiments, and the linear spherulite growth rate, G, obtained by hot-stage optical microscopy. This relationship allows the evaluation of the mean number of nuclei per unit volume grown at a given crystallization temperature. For an athermal nucleation, the spatial density of nuclei is simply related to their surface density in a sampleʹs cross-section, and the experimentally observed mean number of nuclei is compared with the predicted value, at each crystallization temperature. It is also shown that the ratio between the temperature dependencies of ln(1/t50%) and ln(G) may be used as an indicator of the nucleation type and of the morphology developed.