Avrami

J. MACROMOL. SCI.—PHYS., B39(2), 257–277 (2000)

Application of the Avrami, Tobin, Malkin, and Simultaneous Avrami Macrokinetic Models to Isothermal Crystallization of Syndiotactic Polypropylenes
PITT SUPAPHOL* and JOSEPH E. SPRUIELL† Center for Materials Processing and Department of Materials Science and Engineering University of Tennessee Knoxville, Tennessee

ABSTRACT
Various macrokineticmodels (the Avrami, Tobin, Malkin, and simultaneous Avrami models) were applied to describe the primary crystallization of syndiotactic polypropylene (sPP) under isothermal conditions. Analysis of the experimental data was carried out using a direct-fitting method such that the experimental data were fitted directly to each macrokinetic model using a nonlinear multivariable regression program.Comparison of the kinetics parameters obtained from the program to those obtained from the traditional analytical procedure suggested that applicability and reliability of the direct-fitting method are satisfactory. Prediction of the time-dependent relative evolution of crystallinity at other crystallization temperatures was demonstrated based on the bulk kinetics parameters obtained from the analysis.Key Words. Avrami analysis, Isothermal crystallization, Macrokinetic model, Malkin analysis, Syndiotactic polypropylene, Tobin analysis.

*Current address: Petroleum and Petrochemical College, Chulalongkorn University, Soi Chulalongkorn 12, Phyathai Road, Pathumwan, Bangkok 10330, Thailand. †To whom correspondence should be addressed at: 434 Dougherty Engineering Building, Knoxville, TN 37996-2000.E-mail: spruiell@utk.edu

257 Copyright © 2000 by Marcel Dekker, Inc. www.dekker.com

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SUPAPHOL AND SPRUIELL

INTRODUCTION
The overall crystallization process in semicrystalline polymers can be divided into two main processes: primary crystallization and secondary crystallization. The primary crystallization process is the macroscopic development of crystallinity as a resultof two consecutive microscopic mechanisms: primary nucleation and secondary nucleation (i.e., subsequent crystal growth). The secondary crystallization process is mainly concerned with the crystallization of interfibrillar melt, which was rejected and trapped between the fibrillar structure formed during the growth of crystalline aggregates (e.g., axialites, spherulites, etc.) [1–3]. It should benoted that, if the crystallization time becomes very long, other types of secondary crystallization (i.e., crystal perfection and crystal thickening) may become significant enough to increase the ultimate absolute crystallinity. For the purpose of describing the macroscopic evolution of crystallinity under quiescent isothermal conditions, a number of mathematical models [4–13] have been proposed,based primarily on the notion of primary nucleation and subsequent crystal growth microscopic mechanisms, over the past 60 years. Even though the contributions from Kolmogoroff [4], Johnson and Mehl [5], Avrami [6–8], and Evans [9] are essentially similar, it is the work of Avrami that has received the most attention. Therefore, these contributions are frequently referred to as the “Avramiequation.” Based on different approaches, Tobin [10–12] and Malkin et al. [13] arrived at different mathematical models, which are also different from the Avrami model. Consequently, the quiescent crystallization data of semicrystalline polymers at a constant temperature can be described mathematically by these three distinct models. Unlike the Avrami model, use of the Tobin and Malkin models to analyzethe isothermal crystallization data of semicrystalline polymers is scarce. Critical descriptive comparisons between the Avrami and Tobin models were performed on the isothermal crystallization data of poly(ethylene terephthalate) (PET), poly(phenylene sulfide) (PPS) [14], medium-density polyethylene (MDPE), and poly(oxymethylene) (POM) [15]. On the other hand, critical descriptive comparisons...