Effect of a Nucleating Agent on Polymer Crystallization Analyzed Using the Original Avrami Model

Abstract

The historically renowned original treatments of Avrami predicted the continuous change in the Avrami index between 3 and 4 with a time-dependent effective nucleation rate I for the nucleation and subsequent linear growth process of spherical domains under isothermal conditions. The nucleation rate I is determined by the number density N 0 of tiny germ-nuclei at t = 0 and the transformation rate r of a germ nucleus to the active nucleus. This model is applied to the crystallization of poly(butylene terephthalate) (PBT), which reveals a continuous change in the Avrami index with temperature when a nucleating agent (NA) talc is added. In particular, for crystallization with NA, N 0 corresponds to the number density of NA particles, and the rate r represents the formation rate of an active nucleus from an NA particle. The product of N 0 and crystal growth rate G, i.e., N 0 1/3 G, and the rate r are independently evaluated from the time-dependent behavior of crystallization with the Avrami index between 3 and 4. The efficiency of NA is evaluated from the rate r and its temperature dependence, which is determined by the thermal activation barrier for the transformation and is characterized by an excess surface free energy Δσ evaluable using the current analysis method. The dispersibility of NA is assessed by the relative increase of N na /N wo in N 0 , with the addition of NAs N na from the number density without agents N wo . The applicability and usability of the analysis method were confirmed for PBT crystallization with talc, using fast-scanning calorimetry. The evaluated rate r exhibited a stronger temperature dependence than the crystal growth rate G, and the relative increase N na /N wo was more than 100 times in the sample with well-dispersed talc.

Vitrification of the Entire Amorphous Phase during Crystallization of Poly(butylene terephthalate) near the Glass-Transition Temperature

“…In correspondence with these changes, the Avrami index of PBT in a previous report underwent a characteristic change, as schematically shown in Figure b. Schawe reported a similar behavior for isotactic polypropylene (iPP), although the low-temperature peak of iPP represents the nodular growth of a mesophase .…”

“…Therefore, if both modes of crystal nucleation and growth undergo crossover change, the exponent range expands to 1.5. The crossover change of the nucleation mode from sporadic nucleation to a fixed number of nuclei with the increase in nucleation rate at lower temperatures is conceivable, as confirmed when a nucleating agent is added …”

“…PBT ( M w = 5.86 × 10 4 g mol –1 and M w / M n = 2.25) was provided by the Chemicals Research Laboratories, Toray Industry, Inc. The crystallization and melting behaviors of the same PBT were examined in prior works by using FSC and T-M FSC. ,− FSC was performed with a Flash DSC 1 (Mettler-Toledo, Greifensee, Switzerland) using a UFS 1 chip sensor with a refrigerated cooling system. Dry nitrogen gas was purged through the cell at a flow rate of 30 mL min –1 .…”

“…In the crystallization of polymers, the crystallization half-time t half , which is the time required for the total crystallinity to reach 1/2, is regarded as an index of the rate of total crystallization. As shown in Figure a, many crystalline polymers including poly­(butylene terephthalate) (PBT) − possess a double peak that is not due to polymorphism . The high-temperature peak represents the crystallization starting from athermal nucleation on foreign heterogeneities, and the low-temperature peak is due to homogeneous thermal nucleation from the bulk melt.…”

Ethylene Comonomer-Directed Epitaxial Nucleation and Growth of β-Nucleated Isotactic Polypropylene

“…Crystallization of polymers is described in terms of nucleation and growth, where the primary nuclei exceeding a critical size are formed by density and structure fluctuations, and the subsequent secondary nucleation and growth on the surface of existing nuclei govern the crystallization process. − Heterogeneous nucleation, as a predominant nucleation pathway, frequently initiates on a foreign surface. , This surface generally lowers the nucleation barrier by reducing interfacial free energy and thus modifies the nucleation kinetics and polymorph selection. , The subsequent crystal growth can be described as a homoepitaxial process, which involves the deposition of a succession of incoming polymer chains to the surface of an existing crystal plane, followed by a perfect crystallographic registry. − The different polymorphs vary substantially by molecular conformations and/or packing arrangements in a unit cell . Therefore, the structural features of growing crystal planes determine the growth rates of polymorphic forms …”