Polymer crystallization, kinetic analysis

Ozawa extended the Avrami model to quantify polymer crystallization kinetics using noniso-thermal data [289]. It was reasoned that nonisothermal crystallization amounted to infinitesimal short crystallization times at isothermal conditions, given a crystallization temperature T [290]. This analysis led to the following equation ... 

Crystallization kinetics have been studied by differential thermal analysis (92,94,95). The heat of fusion of the crystalline phase is approximately 96 kj/kg (23 kcal/mol), and the activation energy for crystallization is 104 kj/mol (25 kcal/mol). The extent of crystallinity may be calculated from the density of amorphous polymer (d = 1.23), and the crystalline density (d = 1.35). Using this method, polymer prepared at —40° C melts at 73°C and is 38% crystalline. Polymer made at +40° C melts at 45°C and is about 12% crystalline. 

The stereosequence length also has a marked effect on the isothermal crystallization kinetics of the propylene oxide polymers. These studies and analysis of results on crystallization kinetics will be described in detail in another communication. Here we summarize briefly the main conclusions of the effect of stereosequence length on the isothermal crystallization rates. 

FIGURE 3.54 Crystallization kinetics for polypropylene fibers spun at high (sample A) and low (sample B) spin-line stress levels. (From Jaffe, M. In Thermal Methods in Polymer Analysis, Shalaby, S.W. ed., Franklin Institute Press, Philadelphia, 1977, p. 93. With permission.)... 

Differential thermal analysis (DTA) has also been exploited, mainly to determine polymer crystal melting temperatures but also (less frequently) to determine crystallization kinetics. Crystallite formation also changes the optical... 

The notoriously poor polymer crystals described in Chap. 5 and their typical microphase and nanophase separations in polymer systems have forced a rethit ing of the application of thermodynamics of phases. Equilibrium thermodynamics remains important for the description of the limiting (but for polymers often not attainable) equilibrium states. Thermal analysis, with its methods described in Chap. 4, is quite often neglected in physical chemistry, but unites thermodynamics with irreversible thermodynamics and kinetics as introduced in Chap. 2, and used as an important tool in description of polymeric materials in Chaps. 6 and 7. 

There are several methods for studying crystallization kinetics of polymers, which fall into two general categories bulk or volumetric analysis, and crystal growth analysis. The simplest experimental study is the bulk growth, but it is the most difficult to analyze in detail. However, it can be analyzed partially using the Avrami equation [1,2]. 

For PEIMs (n = odds), crystallization at temperatures above the liquid crystalline transition may result in spherulitic morphology development. Kinetics analysis of these PEIMs indicates that the phase transition is mainly determined by the number of methyl units in the spacers. The liquid crystallization formation can be either transport-controlled or nucleation-controlled, depending on how far apart the liquid crystalline transition is from the glass transition temperature of the polymer. As all of these PEIMs form a monoclinic system, the lifetime of mesophase may be very short (in seconds). Therefore, kinetics analysis may involve two stages mesophase formation followed by true crystallization (Table 3.2). 

The average values n are indicative of thermal and/or athermal nucleation followed by a three-dimensional crystal growth. Indeed, for spherulitic growth and athermal nucleation, n is expected to be 3. In the case of thermal nucleation, it is expected to be 4 [2], However, complications in the Avrami analysis often arise because several assumptions, not completely applicable to polymer crystallization, are involved in the derivation. A comparison of some crystallization kinetics parameters is summarized in Table 3.5 [70-80]. 

The overall nucleation and crystalhzation rates of PLA tmder heterogeneous conditions are relatively higher than in homogenous conditions. The nucleation and crystallization rates of propylene-ethylene copolymer are increased tmder isothermal conditions. Addition of nucleating agent accelerates crystallization. Avrami equation is in popular use in the analysis of isothermal crystallization kinetics of polymers ... 

Imai, M. Mori, K. Mizukami, T. Kaji, K. Kanaya, T. Structural formation of polyfethylene tere-phthalate) during the induction period of crystallization. 2. Kinetic analysis based on the theories of phase separation. Polymer 1992, 33, 4457-4462. 

Dhurandhar, H. Patel, A.T. Shanker-Rao, T.L. Lad, K.N. Pratap, A. (2010). Kinetics of crystallization of Co-based multi-component amorphous alloy. Journal of ASTM International, Vol. 7, pp. 1-15 978-0-8031-7516-7 Doyle, CD. (1961). Kinetic Analysis of Thermogravimetric Data, Journal cf Applied Polymer Science, Vol. 5, pp. 285-292 ISSN 1097-4628... 

Ideally, it would be preferable to operate Crystaf in conditions that fractionate the polymer chains according to their crystallizabilities at thermodynamic equilibrium in order to eliminate any crystallization kinetics effects. Practically, this idealized condition is imtenable because very long analysis times would be required. Recent investigations [29] have shown that the fractionation process in Crystaf is, in fact, very far from thermodynamic equilibrium. 

Ming Chen and Chia-Ting Chung. "Analysis of crystallization kinetics of poly(ether ether ketone) by a nonisothermal method." Journal of Polymer Science Part B Polymer Physics, pp. 2393-2399,1998. 

Bruk et al. [716] described the low-temperature radiation polymerization of crystalline TFE in detail. It has been established that three solid-phase postpolymerization reactions can take place when irradiated specimens are heated above the melting point low-temperature polymerization (in the interval 77 to IlOK), slow polymerization close to the melting point (in the interval 128 to 138 K), and rapid polymerization during melting of the crystal (142 K). Tabata et al. [717] have found that a significant post-polymerization takes place even in the liquid phase. Kinetic analysis has been made of the in-source and post-polymerizations [718,719]. Post-polymerization is explained by a long lifetime of polymer radicals in the hquid phase at —78 °C due to the slow combination rate of the polymer radicals caused by their rod-like shape. 

Due to length limitation of this chapter, many theoretical approaches on the phenomenological aspects of polymer crystallization have to be skipped. The isothermal and non-isothermal kinetic analysis of overall crystallization appears as technically important in the data treatment of DSC measurements. Some theoretical considerations on the metastable aspects of crystal morphologies and their evolution under various circumstances appear as practically important and case sensitive (see Chap. 1). In this sense, a combination of this chapter with other contributions of this book will provide reader a broad cutting-edge knowledge about our basic understanding of polymer crystallization. 

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