Kinetic of isothermal crystallization

The temperature dependencies of K, a and Bo in Eq. (2.50) can be found from experimental data for the kinetics of isothermal crystallization. As a general rule, the temperature dependence of K can be represented by a double exponential function. 

Figure 9. Kinetics of isothermal crystallization at 20° C of the PTHF homopolymer and the ST-i, -2, -3, and -4 copolymers after quenching from 80°C...

K " and n can be extracted from the intercept and the slope of Avrami plot, lg[-ln(l-.A0] versus lg(f-f ), respectively. The prime requirement of Avrami model is the ability of spherulites of a polymer to grow in a free space. Besides, Avrami equation is usually only valid at low degree of conversion, where impingement of polymer spherulites is yet to take place. The rate of crystallization of polymer can also be characterized by reciprocal half-time (/ 5). The use of Avrami model permits the understanding on the kinetics of isothermal crystallization as well as non-isothermal crystallizatioa However, in this chapter the discussion of the kinetics of crystallization is limited to isothermal conditions. 

Mucha and Krolikowski [39], studying the kinetics of isothermal crystallization of polypropylene, noticed that addition of a filler, e.g., wood flour, efficiently reduces the time of crystallization. This is desirable in the processing of composites as it reduces the injection-forming cycle and forms small spherulites improving the mechanical properties of composites. Transcrystalline structures are formed during polymer crystallization in the presence of lignocellulosic filler. 

Figure 3.6. Kinetics of isothermal crystallization of propylene-ethylene copolymer. [Data from Dou, G Dou, Q, Thermochim. Acta, 614, 21-32, 2015.]...

Fig. 5.10. — The kinetics of isothermal crystallization for high density po yethy ene [16 1.

Figure 20.26 Polarized optical micrographs of isothermal crystallized (4h) melt blends (x400) (a) 210°C (b) 230°C (c) 210°C (d) 230°C [44], From Park, J. K Park, Y. H., Kim, D. J. and Kim, S. H., Crystallization kinetics of TLCP with polyester blends, J. Korean Fiber Soc., 37, 69-76 (2000). Reproduced with permission of The Korean Fiber Society...

Blaurock and Carothers (1990) and Blaurock and Wan (1990) described a simple way, valid for butteroil, of analyzing isothermal DSC data to characterize the kinetics of early crystallization in a supercooled oil. This approach yielded a single crystallization-temperature dependent combined nucleation/crystal growth constant (which they called NG). The temperature dependence of NG could be modeled with the Arrhenius equation. 

Metin, S., and R.W. Hartel, Thermal Analysis of Isothermal Crystallization Kinetics in Blends of Cocoa Butter with Milk Fat or Milk Fat Fractions, Ibid. 75 1617-1624 (1990). 

Crystallization Kinetics. Typical isothermal crystallization curves, which were measured using cast films of both types of copolymers, are presented in Figures 9 and 10. At the early stage of crystallization, the effect of the noncrystalline PS block on the rate curves was only shifts of the degree of crystallinity [1 — A(t)] vs. time curve along the time axis. However, the extent of shift does not correspond to PS content in the block copolymers. The change in crystallization temperature also causes the crystallization curves to shift. At the initial stage of crystallization, these rate curves could be superimposed on the rate curve of the homo-PTHF (Mn = 6 X 104), and an Avrami exponent... 

A mathematical phase-field model for the kinetics of isothermal polymorphic crystallization has recently been proposed [47], according to which crystallization involves rapid relaxation of the metastable state followed by nucleation and growth of the polycrystalline phase. Computer simulations were used to obtain results which could be tested experimentally using X-ray scattering experiments. Growth rates of different polymorphic polymers have also been investigated [48]. Simultaneous development of spherulites of different polymorphs occurs at different rates under isothermal conditions. From observation of interspherulitic boundaries between the a- and y-forms of polypivalolactone. 

The kinetics of melt-crystallization of PLA has been analyzed by a number of research groups [14, 35, 39, 71-75]. Isothermal bulk crystallization rates were determined in a wide temperature range from 70 to 165 C [71,72]. The maximum crystaUization rate is observed around 100 C, and the most peculiar behavior is a discontinuity in the phase change kinetics around 110-120°C, an example of which is shown in Figure 5.10. Figure 5.10a reports the half-time of crystallization of PLA as function of the isothermal crystallization temperature. The data set shows a broad minimum around 108 C and a step/discontinuity around 116-118°C, indicated by the arrow. The sudden variation in crystallization rate... 

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 ... 

Jabarin [31] in his study of isothermal crystallization kinetics of PET samples received from different manufacturers observed that molecular weight and polycondensation catalyst affect the crystallization mechanism and crystallization rate. 

Wellen, R.M.R., Rabello, M.S., 2005. The kinetics of isothermal cold crystallization and tensile properties of poly(ethylene terephthal-ate). J. Mater. Sci. 40, 6099—6104. 

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