Crystallization nonisothermal

To characterize nonisothermal crystallization, the crystallization rate peak temperature is frequently used. The 

It must be mentioned that there are many reports on deviation of the Ozawa plots from linearity and also on M values that are different from those predicted theoretically. The analysis of nonisothermal crystallization encounters even more difficulties than that of isothermal crystallization. Additional problems result from the requirement to combine the results of several crystallization experiments performed at different cooling rates. The Ozawa theory is based on the assumption that the nucleation rate dependence on temperature f(T) is unaffected by a cooling rate. As a consequence, the validity of the Ozawa approach is limited to a narrow range of cooling rates that results in the crystallization in similar temperature intervals. Markedly different cooling rates cause variation of M, for instance as shown in Reference [64]. The same applies to other simplified approaches, for example, the Nakamura isokinetic model, in which nonisothermal crystallization is treated as a succession of isothermal processes. The results are reasonable as long as the nucleation process is not infiu- 

Similarly, as in the case of the Avrami analysis of isothermal crystallization, the discrepancies between experimentally determined curves and predictions of the Ozawa equation originate mainly from oversimplified assumptions concerning the polymer crystallization. Those discrepancies inspired some authors to search for other equations enabling a better description and analysis of nonisothermal crystallization. For instance, the classic isothermal Avrami analysis based on Equation (7.5) with E expressed by Equation (7.10) was applied to nonisothermal crystallization [65, 66]. Such an approach has no theoretical justification. Even if a straight line Avrami plot is obtained, the parameters k and n are, at best, two adjustable parameters without a clear physical meaning. The Jeziomy method [67] deserves similar criticism. Jeziomy proposed using Equation (7.5) and Equation (7.10) and characterizing the process with the parameter kc defined as  

Nonisothermal crystallization is frequently analyzed via calculation of the so-called energy of activation of crystallization according to the Kissinger method [69, 70]. The method is based on the simplifying assumption that a transformation rate during a reaction (crystallization in the present case) is a product of two functions, one depending solely on the transformed fraction,/( ), and the other depending solely on temperature, with an Arrhenius-type dependence  

In the view of equations describing the nonisothermal crystallization in detail, kc has no physical meaning. Liu et al. [68] combined isothermal Avrami equation (Eq. 7.10) with the nonisothermal Ozawa equation into a single equation  

Attention up to now has been focused on isothermal crystallization. This mode of crystallization is most amenable to theoretical analysis and comparison with experimental results. However, crystallization can also occur by coohng from the melt or heating from the glassy state. Nonisothermal crystallization has many practical applications. It is thus of interest to analyze such processes. There has been a great deal of theoretical and experimental activity in this area, which has been extensively summarized.(66,83,84) Therefore, focus here will be on the basic theoretical principles involved and pertinent experimental results. 

Underlying any theoretical development is the temperature, T(t), at time t. In general 

Here To is the initial melt temperature and V (r) is the time function for either cooling or heating. The simplest case to consider is a constant cooling rate where V (t) = (pt, t being a constant. Using the Evans approach to isothermal crystallization kinetics, Ozawa showed that when a sample is cooled from the equilibrium melting temperature to the temperature T, at a constant rate (p, the volume fraction of transformed material can be expressed as (85) 

In this formulation the fraction transformed will depend on the type of nucleation that is taking place. For instantaneous nucleation, the nucleation rate, N(9), is independent of time and cooling rate. It only depends on the temperature. Consequently, under these circumstances 

The constant Ci, termed the cooling crystallization function, is given by 

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Even though the nonisothermal crystallization leads to just small changes in the subsequent melting behavior of different types of triblock copolymers, isothermal experiments employed to calculate the equilibrium melting temperature, T, have shown that this parameter can exhibit significant changes depending on composition. It has been reported that in PS-fc-PB-fc-PCL tri-... 

Nonisothermal crystallization Guerra et al. [ 16] reported on sPS/PPE blends of various compositions, prepared by compression molding (T ax = 290°C and Wx = 10 min) and then cooled to room temperature at a rate of 10°C/min. Their DSC results show that, below 50wt%, sPS is completely amorphous. Moreover, WAXD spectra of the same samples indicate that the amount of the a form, which is 100wt% in neat sPS, decreases on increasing PPE and rmax (Figure 20.1a and b) in favor of the (3 form. The authors reported that the loss of the memory of the a form, which they suggested for melt-crystallized neat sPS, is more rapid for the same temperature and time when PPE is present [16]. 

In order to investigate the cocrystallization and phase segregation behaviors of the above-mentioned PE blend samples, we performed the experiments for both the isothermal and nonisothermal crystallizations. In the nonisothermal crystallization, the temperature is changed gradually and the WAXD, SAXS, or infrared spectra are collected as a function of temperature. In the isothermal crystallization, the... 

The present study has shown that low crystallinity ePP crystallizes from the melt into well-defined morphologies. This smdy presented definitive evidence that this class of materials, when crystallized isothermally from the melt, exhibits morphologies that are reminiscent of classical semicrystalline polymers. The presence of lamellae, crosshatching, and spherulites was revealed by high resolution tapping mode AFM and optical microscopy. The nonisothermally crystallized ePP specimens also display the hierarchical ordering as seen in the case of iPP. 

Isothermal and Nonisothermal Crystallization of Blends of Linear Low Density Polyethylene with a Semiflexible Liquid Crystalline Polymer... 

Table 21.5 Various Parameters of PP and PP/Epoxy Blends Obtained from the Nonisothermal Crystallization Exotherm at a Cooling Rate of 10°C min . ...

Run M, Song A, Wang Y, Yao C (2007) Melting, crysttillization behaviors, and nonisothermal crystallization kinetics of PET/PTT/PBT ternary blends. J Appl Polym Sci 104 3459-3468 Salaneck WR (1997) Conjugated polymer surfaces and interfaces. Philos Trans R Soc Lond A... 

The mass balance equations for the case of nonisothermal crystal is ... 

Finally, poly(a-PIN) was used in the nonisothermal crystallization of isotactic polypropylene from blends containing up to 30 per cent of this polyterpene [110-112]. 

Xu, W., Liand, G., Wang, W., Tang, S., He, R, and Pan, W.-P. 2003. Poly(propylene)-poly(propylene)-grafted maleic anhydride-organic montmoriUonite (PP-PP-g-MAH-Org-MMT) nanocomposites. II. Nonisothermal crystallization kinetics. 

Studies on a similar group of materials - polymeric composites reinforced with sisal fibers - were conducted by Manchado et al. [35]. They analyzed the presence of different fibers, such as sisal, on crystallization of polypropylene. The composites were prepared in special chamber for mixing where the matrix was plastified at 190°C. Obtained materials were subjected to thermal analysis by DSC. The analysis of thermograms allowed for a similar finding like in Joseph s studies [34], The presence of sisal fibers, as well as other fibers used in the study, accelerated crystallization of polypropylene. This was explained by the nucleating effect of sisal filler. Also, the half-time crystallization (ti/2) decrease was observed for polypropylene with the addition of sisal fibers in comparison with unfilled polypropylene. The analysis of nonisothermal crystallization showed that the degree of polypropylene crystallinity is higher for the composites filled with sisal fibers than for unfilled polymer. 

Khonakdar, H.A., Monemian, S.A., Hassler, R., and (ehnicehn, D. (2009) Nonisothermal crystallization kinetics and determination of surface-folding free energy of PP/EVA/OMMT nanocomposites. J. Polym. Sci. Part B Polym. Phys., 47, 674. 

Differential scanning calorimetry (DSC) is one of the routine methods used in polymer characterization and improves the knowledge of the microphase structure with other complementary methods. Lu et al. [149] investigated nonisothermal crystallization processes of Nylon/EVM (ethylene-vinyl acetate rubbers) blend using DSC and they found out that EVM rubber could act as heterogeneous nuclei acting more effective in Nylon/... 

Sodium benzoate, nucleating agerrt for a-form of iPP, increases the crystallization temperature of iPP by 15 C and decreases its isothermal and nonisothermal crystallization half-times at concentrations that approach its eqirilibrirrm solubihty in the molten poly-... 

The overall crystallization rate is used to follow the course of solidification of iPP. Differential scanning calorimetry (DSC), dilatometry, dynamic X-ray diffraction and light depolarization microscopy are then the most useful methods. The overall crystallization rate depends on the nucleation rate, 1(0 and the growth rate of spherulites, G(0. The probabilistic approach to the description of spherulite patterns provides a convenient tool for the description of the conversion of melt to spherulites. The conversion of melt to spherulites in the most general case of nonisothermal crystallization is described by the Avrami equation ... 

The analysis of the above equations is often applied for obtaining the nucleation data from isothermal and nonisothermal crystallization experiments. Several simplifications of the equations are developed and used for isothermal crystallization (with instantaneous or spontaneous nucleations only) and nonisothermal processes with a constant cooling rate. It was found that the crystallization of iPP follows the dependence log [1 — a(f)] t where n is around three for relatively low supercoolings which indicates instantaneous character of primary nucleation. 

To characterize the spherulitic nucleation during nonisothermal crystallization, the Ozawa equation is applied, which could be obtained by integrating twice by parts the Avrami equation and assuming cooling at the constant rate, a. The slope of the plot ln -ln[l - a(T)] versus In(fl) equals two or three for instantaneous nucleation, three or four for nucleation prolonged in time, in two- and three-dimensional crystallization, respectively. The values from three to four, depending on temperature range were obtained for iPP from DSC nonisothermal crystallization [4],... 

Recently the statistical approach was developed [5] for the description of the kinetics of conversion of melt to spherulites and the kinetics of formation of spherulitic pattern during both isothermal and nonisothermal crystallizations. The final spherulitic pattern can also be described. The rates of formation of spherulitic interiors and boundaries (boundary lines, surfaces and points) as well as the their final amounts could be predicted if spherulite growth and nucleation rates are known. Applied to iPP crystallized during cooling with various rates, the approach allowed for the predictions of tendencies in the kinetics of formation of spherulitic structure and its final form. 

Keywords entanglement, disentanglement, cross-hatching, lamellae, crystallization, nucleation, reptation, nucleation (crystallization) regimes, nucleation agents, nucleation rate, spherulitic growth rate, Avrami-equation, Ozawa-equation, isothermal crystallization, nonisothermal crystallization, secondary nucleation, supercooling. 

Li Z-M, Yang W, Li L B, Xie B H, Huang R and Yang M B (2004) Morphology and nonisothermal crystallization of in situ microfibrillar poly(ethylene terephthalate)/polypropylene blend fabricated trough slit-extrusion, hot-stretch quenching, J Polym Sci Part B Polym Phys 42 374-385. 

As a whole, the crystallization rate of iPP in MRCs is obviously faster than in PET/iPP common composite, and the PET/iPP common composite crystalhzes faster than neat iPP [35]. The PET phase in iPP acts as heterogeneous nuclei during the nonisothermal crystallization process hence, the crystallization rate of the iPP phase can be enhanced. When the PET is deformed into microfibrils during processing, its effect on iPP crystallization can be considerably enhanced. The PET concentration and its hot stretch ratio influence the crystallization kinetics of MRCs. 

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