Radial growth rate

In conclusion, it can be said that the model depicted in Fig. 17.7 gives a good description of the observed results. A numerical analysis based on the same model is seen from Fig. 17.10 to also allow the radial growth rate dependence to be predicted and the agreement with experimental observations is reasonable. 

Cimmino et al. [25] reported that the radial growth rates of crystallization G, measured in sPS/PPE blends, decrease strongly with increase in PPE content (Figure 20.3). This effect might arise from an increase in the transport free energy of crystalline segments in the melt, due the larger Tg of the blend compared with pure sPS, or to a decreased capability of sPS to nucleate, induced by its dilution in PPE. 

In Equation 5 the index of the crystallization reaction, n, and z, are calculated from its linear format (Eq. 6) as the slope and intercept at Ln(f) = 0, respectively. The F values to calculate by linear regression (Eq. 6) n and z are, most of the time, between F < 0.25 and F S 0.75. These F values are considered to assure constant radial growth rate and no crystal impingement. 

The radial growth rate can also be related to the homogenity of the process. The following relative growth rates for particles has been established (consult Reference 25 for size distributions) ... 

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. 

FIGURE 11.18 Radial growth rates for pure isotactic polystyrene (PS) (M = 60,000 g mol" ) and two samples blended with atactic PS of molecular weight 41,700 and 247,000. (From Keith, H.D. and Padden, F.J., J. Appl. Phys., 35, 1286, 1964. With permission.)... 

Fig. 6. Radial growth rate, GxlO (cm/min), vs. elastomer content...

Fig. 7. Radial growth rate, GxlO (cm/min), vs. elastomer content at different undercooling AT(T - T ) a) iPP/EPDM blends b) iPP/PiBL]yj blends c) iPP/PiBj blends, d) iPP/PiB j blends.

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.

FIGURE 11 Radial growth rate of sphemlite of ( ) PHB (Cimmino et al., 1998) and (o) PHB8V (Peng et al., 2003) isothermally crystallized at different crystallization temperatures. 

Arrhenius activation energy Differential scanning calorimeter (DSC) Hoffman-Arrhenius model Radial growth rates Semicrystalline polymers... 

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. 

The different dependence of k and /c2 s is shown in Fig. 5.37. With increasing s, the density of the colonies, which depends on the branching rate /c25 decreases faster than the radial growth rate this can be interpreted in connection with the regulation of transport of metabolites within the hyphae. Cellular differentiation and the connection to product formation in molds was elaborated from Megee et al. (1970). 

The Avrami parameter, n, is computed as a function of temperature, and their values are summarized in Table 3.8. All the n values are in the low range of 0.2 to 0.5, which may be due to the fact that each crystal does not grow with a constant radial growth rate. 

A plot of 2 versus l/(TcATf) results in a straight line and from the slope, values of (Tg can be obtained. In Table 3.8 and Fig. 3.21, the free energy of folding, cr, for some PEG/PEMA and PEG/PMMA blends, respectively, derived from the overall kinetics of crystallization (Eq. 3.23), is compared with the values obtained from the radial growth rate data (Eq. 3.11). The compositional dependence of cr derived from both methods is similar, although higher values were obtained using Eq. 3.23 (overall kinetics of crystallization). 

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