Spherulitic growth rates

It has been reported that the overall rate of crystallization of pure PHB is relatively low compared to that of common synthetic polymers, showing a maximum in the temperature range of 55-60°C [23]. The spherulite growth rate kinetics have been evaluated [59] in terms of the theory by Hoffmann et al. [63], At about 90 °C, the spherulite growth rate displayed a maximum, which is not excessively low compared to that of common synthetic polymers. Therefore it was stated that the low overall crystallization rate of PHB centers on the nuclea-tion process rather than the subsequent crystal growth. Indeed, it has been shown that PHB has an exceptionally low level of heterogeneous nuclei [18]. 

Fig. 8 a Spherulitic growth rates for PPDX and the PPDX block within D7732C2310 diblock copolymer. Solid lines are fits to Lauritzen and Hoffman theory, b Lauritzen and Hoffman kinetics theory plot for PPDX (K = 17.2 x 104 K2) and the PPDX block within D7732C2310 diblock copolymer (K = 46 x 104 K2). (From [103]. Reproduced with permission of the Royal Society of Chemistry)... 

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],... 

The spouting bed temperature is generally in the range of 150-170 °C, which is close to the maximum spherulite growth rate, and therefore ensures quick completion of the primary crystallization. The material temperature at the outlet of the pulsed fluid bed is usually <180°C. 

Tant, M. R. and Culberson, W. T., Effect of molecular weight on spherulite growth rate of poly(ethylene terephthalate) via real-time small angle light scattering, Polym. Eng. Sci., 33, 1152-1156 (1993). 

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. 

This equation has been widely used although the validity of applying the WLF equation to spherulitic growth rate is merely a repetitive assertion (Hoffman et al., 1959 Hoffman and Weeks, 1962), not involving any direct proof of substantiation, as Mandelkern has stated. 

Figure 20.3 Spherulite growth rate (G) for sPS/PPE and sPS/PVME blends as a function of the crystallization temperature Tci ( ) sPS ( ) sPS/PPE 90 10 ( ) sPS/ PPE 80 20 (A) sPS/PVME 80 20 ( ) sPS/PVME 70 30 ( ) sPS/PVME 50 50. Reprinted from Polymer, vol. 34, Cimmino S., Di Pace E., Martuscelli E., Silvestre C., sPS based blends crystallization and phase structure , p. 2799, Copyright 1993, with permission from Elsevier Science.

Figure 4. Computed distributions for samples partly crystallized at 125°C and quenched. DL = diffusion coefficient of additive in liquid pm2 sec"1 DS = back diffusion coefficient G = spherulite growth rate pm sec"1.

Spherulite Growth Rate in Miscible Polymer Blends... 

Figure 3,4. Spherulitic growth rate in iPS and iPS/PS blends (the values represent the percentage of atactic PS present in the blend) [Keith and Padden, 1964].

Table 3.4. Spherulite growth rate measurements in miscible polymer blends (G versus T).

The influence of the SAN copolymer composition on the spherulitic growth rate of PCL has been studied at a hxed crystallization temperature by Kressler et al. [1992, 1993]. A minimum has been observed at about 20 wt% AN in SAN for several compositions (see Figure 3.9), due to a minimum in the value of the interaction parameter, at the same copolymer composition that is responsible for a reduced chain mobility. 

Figure 3.9. Dependence of the spherulite growth rate G on the copolymer composition of SAN in PCL/SAN blends at 45°C [Kressler et a/., 1992, 1993].

The first value is calculated from the spherulitic growth rate data of PEG(10)/PMMA. The second one from the overall crystallization data of PEG(10)/PMMA. The third one from the spheruhtic growth rate data of PEG(2)/PMMA [Martuscelli and Demma, 1980] (the value between brackets refers to the molecular weight of PEG in kg/mol)... 

The discussion on the crystallization behavior of neat polymers would be expected to be applicable to immiscible polymer blends, where the crystallization takes place within domains of nearly neat component, largely unaffected by the presence of other polymers. However, although both phases are physically separated, they can exert a profound influence on each other. The presence of the second component can disturb the normal crystallization process, thus influencing crystallization kinetics, spherulite growth rate, semicrystalline morphology, etc. 

For homopolymers, the temperature dependence of the isothermal spherulite growth rate, G, is described by Eq 3.1 [Turnbull and Fischer, 1949] ... 

Phenomena Affecting the Spherulite Growth Rate Energetic Considerations... 

The spherulite growth rate depression is proportional to the type of energy barrier that has to be overcome, and can be quantitatively expressed by a modified equation of the spherulite growth rate [Martuscelli, 1984] ... 

Table 3.19. Expressions for the dissipation energy terms and corresponding spherulite growth rates in a crystalline/amorphous polymer blend system [Martuscelli, 1984 Baitczak et al., 1984]...

The temperature dependence of the spherulitic growth rate has been theoretically treated [Wenig et al., 1990], for several blends composed of a PP matrix in which PS droplets were dispersed. This temperature dependence could be calculated based on the work done by Hoffmann [1983] and by Suzuki and Kovacs [1970], and is defined as follows (Figure 3.38a) ... 

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