Isothermal crystallization kinetics in a limited volume. A geometrical approach based on Evans' theory

A Monte Carlo Simulation of Homogeneous Crystallization in Confined Spaces: Effect of Crystallization Kinetics on the Avrami Exponent

“…At this moment, the existing analytical Equations take into account only a limited number of possible truncations per crystallizing body (no more than two) which by no means reflects all possible scenarios of crystallization. For example, equations, proposed by Billon et al, [14] yield an Avrami exponent varying from 3 to 4 depending on the plate thickness, clearly indicating some model deficiency. Only a comprehensive numerical simulation of crystallization taking into account all possible and statistically significant confinements could provide reliable crystallization kinetics data.…”

“…A complex dependence of overall crystallization kinetics on crystallizing volume geometry as well as crystallization parameters, especially growth and nucleation rates had been shown by Escleine et al [13] Several previous studies have revealed the influence of spatial confinement and spherulite impingement on observed crystallization kinetics. Mathematical formulations taking into account the influence of spatial confinement on crystallization kinetics were first proposed by Escleine et al [13] and Billon et al [14] Further development included adding probabilistic functions in order to attempt to describe the random nature of homogeneous nucleation. [15] These studies suggested a noticeable decrease in the Avrami exponent due to spatial confinement.…”

Transcrystallinity effects in high‐density polyethylene. II. Determination of kinetics parameters

“…To achieve this, it was first necessary to fit ␣ v and V sur with accurate mathematical expressions. We needed the estimate of nucleation parameters for the bulk polymer to use a rigorous model (e.g., those developed in previous articles 12,23,24 ). So, for convenience, and simplicity, we chose an Ozawa dependence 25 for ␣ v : where T p is the cooling rate, n is the so-called Avramiexponent, and is a function depending on temperature.…”

“…With regard to V sur , rigorous models have been developed 12,23,24 on the basis on Evans' approach 26 that enable us to predict the crystallization of a thin film of polymer. One of these models, combined with computer simulations and applied to the particular case of DSC analysis, 12,13 makes it possible to reproduce and understand crystallization traces as well as morphology development.…”

Fabrication and Structural Evaluation of Beaded Inorganic Nanostructures Using Soft‐Electron‐Beam Lithography

“…It is well known that crystallization rates measured in bulk samples (3D) are noticeably higher than those measured on thin films (2D) for a given material system. [28][29][30][31][32] This is usually explained by considering only retarded grain growth due to dimensional constraints: the growth of the crystalline-phase nuclei is truncated upon impingement with neighboring nuclei in the 3D case, whereas in 2D case they are in addition truncated upon impingement with the free surface-this results in an overall reduction in the crystallization rate. This argument could be further extended to the 1D case (lines), where growth will be truncated in the lateral dimension in addition to the thickness dimension.…”