Spherulites radial growth

Spherulite radial growth continues at a constant rate, even after other portions of the spherulite have impinged with its neighbors — indicating that lamellae within a given spherulite grow independently... 

The measured T]/2 values of many polypropylene samples of high isotacticity are shown in Fig. 14 as a function of T. It is seen that tj/2 increases very rapidly with Jc whereas at any given T, no statistically significant correlation with molecular mass is found. The independence of Ti/2 with molecular mass agrees with the fact that nucleation density and spherulite radial growth rate were found to have no identifiable dependence on molecular mass. 

Lim and coworkers [183] proposed the following modification of the Hoffman and Lauritzen Eq. (8) to measure spherulite radial growth rate, as a function of T and cooling rate ... 

They therefore finally appear as polyhedra. Because of their radial growth the fibrillar or lamellar crystals have only little space-filling ability as they move away from the central nucleus. Typically for spherulitic structures, an irregular noncrystallo-graphic branching usually at small angles can be observed. 

Figure 5.9 shows the time evolution of the radii of selected 2D spherulites from Fig. 5.8. We observe that the process is non-linear and accelerated, (fR/df > 0. It is also interesting to notice that, at a given time, the radial growth velocity Ur = dR/dt (slope) is nearly the same for all spherulites, which implies that it depends on the deposition time and certainly not on the radius of the spherulites. In the case discussed here the thickness of the film is increasing with time because of continuous exposure to the molecular beam. The non-linearity is more pronounced at the beginning of the experiment (roughly between 250 and 350 s) and the velocity nearly tends towards an asymptotic value, so that 2D spherulites that are formed last show almost linear growth.

The observed non-linear radial growth of the spherulites can be described in terms of a thickness-dependent growth law given by the expression ... 

The primary crystallization process is characterized by three parameters. These are the rate of radial growth of the spherulite, G, the time constant for nucleation, t , and the time constant for the primary crystallization process, Tc, which is determined from the Avrami equation. All three parameters seem to depend on the stereoregularity of the polymer, but the nucleation rate seems to depend most strongly. 

Fig. 2 Visible light micrograph of spherulites from a crystalline diepoxide taken with a 5X lens and cross polarization. The observed maltese cross pattern arises from the spiral positioning of lamella along the radial growth direction. The high refractive index c-axis is tangential to the spherulite s radius.

For pure iPP and PB-1 homopolymers and their respective blends, the spherulite radius increases linearly with time t for all T, investigated. For all samples, the isothermal radial growth rate G was calculated at different as G = dR /dt. Generally, the G values decrease an increase in the values and with increase in the amount of noncrystallizable component in the blend. As shown in Fig. 6.1, where the relative G values of the iPP-based blends are reported for = 125°C, the depression of the G values was more pronounced for the blends prepared with HOCP as the second component. 

The spheruhte dimension, at constant T, increases with increasing concentration of noncrystallizable component. The spherulite radius R increases linearly with crystalhzation time for pure iPP and iPP/PB-l/HOCP blends for all investigated. For all samples, the isothermal radial growth rate, G = dR/dt, calculated at different Tc, is reported in Table 6.11. With the increase in the T, the G values appear to decrease for all investigated compositions. The blends prepared with the same fraction of iPP show G values that decrease with increasing of HOCP fraction at constant Tc value. 

FIGURE 11.1 Radial growth rate r of spherulites of isotactic polystyrene as a function of the crystallization temperature. 

The morphology and the isothermal radial growth rate of PEO spherulites in the blends were studied on thin films of these samples using a Reichert polarizing microscope equipped with a Mettler hot stage. The films were first melted at 85° C for 5 minutes, following which they were rapidly cooled to a fixed crystallization temperature T and the radius of the growing spherulites was measured as a function of time. 

Fig. 2, Radial growth rate G of spherulites in pure PEG and PEO/PMMA blends as a function of crystallization temperature.

Fig. 5.17 Early stages in the growth of spherulites (a) the sheaf-life stage in the growth of a polyethylene spherulite and (b) the beginnings of radial growth in a spherulite of poly(4-methylpentane). ((a) Reprinted by permission of Kluwer Academic Publishers (b) Cambridge University Press 1981.)...

FIC U RE 12 Plot of radial growth rate of PTT spherulites as a function of T as discussed in Hong et al., (2002) (modified from Hong and co-workers (2002)). 

Ozawa proposed to study the overall crystallization kinetics from several simple DSC scanning experiments (Ozawa 1971). Assuming that when the polymer sample is cooled from To with a fixed cooling rate a = dT/dt, both the radial growth rate v T) of the spherulites and the nucleation rate 1(T) will change with temperature. For a sphemlite nucleated at time t, its radius at time t will be... 

More importantly, the crystallization kinetics of all samples of different molar mass displays the characteristic discontinuity due to the different radial growth rates of a - and a-spherulites. Independent of the molar mass, the transition from growth of a -crystals to growth of a-crystals occurs at 100-120 C [28]. 

As mentioned above, PLA should be addressed as a random copolymer rather than as a homopolymer the properties of the former depend on the ratio between L-lactic acid and D-lactic acid units. A few studies describe the influence of the concentration of D-lactic acid co-units in the PLLA macromolecule on the crystallization kinetics [15, 37, 77-79]. The incorporation of D-lactic acid co-units reduces the radial growth rate of spherulites and increases the induction period of spherulite formation, as is typical for random copolymers. In a recent work, the influence of the chain structure on the crystal polymorphism of PL A was detailed [15], with the results summarized in Figure 5.13. It shows the influence of D-lactic acid units on spherulite growth rates and crystal polymorphism of PLA for two selected molar mass ranges. 

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