Influence of specimen thickness on isothermal crystallization kinetics. A theoretical analysis

Abstract

In the DSC technique, isothermal crystallization experiments are usually performed on thin flat specimens, but their interpretation generally uses theories developed for an unbounded volume. In this paper, isothermal crystallization of spherical entities in the volume limited by two parallel infinite planes is considered. Our model, derived from Avrami's theory, gives an analytical expression for the transformed volume fraction as a function of time. It is shown that the influence of thickness becomes important when thickness becomes of the order of or smaller than the average spherulite radius. The main effects of a decreasing thickness are a slower crystallization kinetics and a decrease in the Avrami exponent. These results can be used to interpret experimental data obtained in isothermal polymer crystallization.

Thermal dependence of nucleation and growth rate in polypropylene by non isothermal calorimetry

“…The observed differences may be due to truncation effects. In a recent paper [10], Escleine et al have shown that the truncation of spherulites by the specimen surfaces can induce a decrease of the Avrami exponent. This decrease, which can range from 0 (unbounded volume) to 1, is particularly important when the specimen thickness is of the order of or smaller than the final average spherulite radius.…”

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

“…While these phenomena do take place in most cases, spherulite impingement and spatial confinement are also responsible for a significant part of the Avrami exponent deviation as they are inherent in all polymers and do not depend on polymer chain properties. 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.…”

“…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.…”

A new methodology and model for characterization of nucleation and growth kinetics in solids

“…In addition, the growth velocity may be ascertained from fits of the model to data for prenucleated ''thin'' films whose phase change kinetics are expected to slow noticeably when the mean crystallite size is comparable to the film thickness. 13,14,[17][18][19] Finally, based upon these results and the transition kinetics of large, non-pre-nucleated specimens, the temperature dependence and rate of nucleation can be computed.…”

“…More typically, a large number of nucleation events occur during the course of phase change and hence the mean grain size is often far smaller than specimen dimensions. In this case, isothermal transformation kinetics can usually be described by the Kolmogorov-Johnson-Mehl-Avrami equation or its derivatives, [1][2][3][4][5][9][10][11][12][13][14][15][16] e.g.,…”