Spherulites nucleation rate

Fig. 9.26 Plot of spherulite nucleation rate in poly(hexamethylene adipamide), Mn = 14 600, at indicated crystallization temperatures. (From McLaren (108))...

The overall rate of crystallization is determined by both the rate of nuclei formation and by the crystal growth rate. The maximum crystal growth rate lies at temperatures of between 170 and 190 °C [71, 72], as does the overall crystallization rate [51, 61, 75], The former is measured using hot stage optical microscopy while the latter is quantified by the half-time of crystallization. Both are influenced by the rate of nucleation on the crystal surface and the rate of diffusion of polymer chains to this surface. It has been shown that the spherulite growth rate decreases with increasing molecular weight due to the decrease in the rate of diffusion of molecules to this surface [46, 50, 55, 71, 74],... 

Both the rate of nuclei formation and the crystal growth rate can also be expected to influence the spherulite size. It has been reported (hat, in the temperature range 130-180 °C, the spherulite size increases with increasing temperature [74], This trend can be expected to extend to higher temperatures as the nucleation rate decreases. On the other hand, the presence of nucleating... 

The isothermal crystallization of PEO in a PEO-PMMA diblock was monitored by observation of the increase in radius of spherulites or the enthalpy of fusion as a function of time by Richardson etal. (1995). Comparative experiments were also made on blends of the two homopolymers. The block copolymer was observed to have a lower melting point and lower spherulitic growth rate compared to the blend with the same composition. The growth rates extracted from optical microscopy were interpreted in terms of the kinetic nucleation theory of Hoffman and co-workers (Hoffman and Miller 1989 Lauritzen and Hoffman 1960) (Section 5.3.3). The fold surface free energy obtained using this model (ere 2.5-3 kJ mol"1) was close to that obtained for PEO/PPO copolymers by Booth and co-workers (Ashman and Booth 1975 Ashman et al. 1975) using the Flory-Vrij theory. 

The isotherms obtained in dilatometric measurements of the crystallization rate could be fitted with an Avrami (3) type equation only by assuming the existence of a secondary crystallization process much slower than the rate of spherulitic growth observed microscopically, and by taking into account the experimentally determined form of the nucleation rate. The nucleation rate was found to be a first-order process. Assuming that the secondary crystalliza-... 

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. 

Fillers affect the nucleation rate as polypropylene crystalizes. The addition of 2.5 wt% titanium dioxide reduces the size of spherulite by a factor of 3 due to an in-... 

Plaris et al. [1993] investigated also the same blend system and reported that blending had a pronounced effect on the lamellar morphology. Furthermore, the isothermal crystallization experiments indicated that the spherulite growth rate, G, and the nucleation density of the PP phase were enhanced. The authors suggested that these observations could be related to the formation of additional nucleation sites, which arise from the polymer-polymer interfaces created by the blending. 

Once the supramolecular structure of a crystallizing polymer reaches a mature spherulitic shape, and the diameter is greater than 5 pm, the HSOM method (Figure 9.2) becomes particularly useful to monitor spherulitic growth and nucleation rate parameters in real-time. These measurements provide insights into crystallization phenomena, such as ... 

Table 8.1 shows the dependence of K and n on the mechanism of nucleation and growth. Measurements of n have shown that it decreases as crystallization proceeds. Mandelkem [28)] has considered the case of sporadic nucleation on predetermined nuclei that cause a decrease in as crystallization proceeds. However, n may also decrease when A cs is not constant but varies with time. A comparison of degree of crystallinity measurements with spherulitic growth rate measurements on the same polymer [29] shows this. The polymer continues to crystallize after the volume fills with spherulites. The value of n for this secondary crystallization is usually less than for the primary crystallization process. This difference gives rise to a change of n with time. Reference 30 treats this problem theoretically as do Hilliar [31] and Price [32]. 

The power n is postulated to have integral values between 1 and 4. The value of (n) correlates to the some of the number of crystallite dimensions (3 for a spherulite, 2 for a disc, and 1 for a needle shape) and the order of the nucle-ation step (0 for spontaneous heterogeneous process, and 1 for homogeneous nucleation rate which is proportional to time, t). 

The relative size of the spherulite can be predicted from what is known of the crystallization of monatomic solids. Low-temperature solidification leads to small spherulites because the nucleation rate is high and the growth rate low. Convetsety, high-temperature solidification leads to large spherulites because the nucleation rate is low relative to the growth rate. 

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... 

For neat PLA, information about the temperature dependence of the nucleation rate was gained by analysis of the spherulite density, as shown in Figure 5.5. The data suggest an increasing nucleation density with decreasing temperature in the analyzed temperature range between 95 and 140 C, to reach a plateau value around 90°C [14, 23, 48-50]. At temperatures lower than about 95 C, such analysis of the nucleation rate via measurement of the spherulite density fails because their number then is too high to be reliably analyzed. 

PP/LLDPE + EP blockpol. + SEBS triblock -1- SEBS-g-MA 72/18/10 Type of compatibilizer Nucleation density at Tc = 135 °C - tT with EP - J. with SEBS Spherulite growth rate upon compatibilization Interfacial free energy of PP crystal surfaces J, with compatibilization Compatibilization changes the int ace morphology = > Additional nucleation sites from interfaces Finer dispersion of LLDPE can cause more unidimraisional growth of crystals Flaris et al. (1993)... 

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