Radius of spherulites

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. 

Fig. 4.25. A plot of the radius of spherulites of isotactic poly(styrene) as a function of time. From [153].

The ordered polymer chains are consistently oriented perpendicularly to the radius of the spherulite. 

Video microscopy with crossed polarizers permits the direct and non-invasive observahon of the nucleahon and growth process for many substances, and thus the study of the hme evoluhon of the spherulite radius R t). When the growth is controlled by diffusion the radius of the spherulites increases as R t) a while when the growth is determined by a nucleation-controlled process (incorporahon of atoms or molecules to the surface of the crystalline part) the radius increases linearly with hme, R t) a t. 

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.

Andrews76 gave results of the work of Reed and Martin on cis-polyisoprene specimens crystallized from a strained cross linked melt and on solid state polymerized poly-oxymethylene respectively, explaining the results by simple two phase models. He also summarized the studies of Patel and Philips775 on spherulitic polyethylene which showed that the Young s modulus increased as a function of crystallite radius by a factor of 3 up to a radius of about 13 n and then decreased on further increasing spherulite size. 

Morphology changes were observed by optical microscopy and small-angle light scattering. The pure components exhibit spherulitic structures, each with different orientation of the optic axis with respect to the spherulite radius. Spherulites become disordered and larger with the introduction of small amounts of the second component. Larger amounts of the second component result in a loss of spherulitic order. 

Fig. 15.4. Real-time observations of the formation of AP(l-40) spherulite. Realtime observations of AfJfl 40) amyloid fibril growth on PEI/PVS at pH 7.5 and 37°C. Concentrations of AP(l-40) monomers, seeds, and ThT were 50 pM, 5 pg ml-1, and 5pM, respectively. White arrows in panels of 0-20 min indicate the hazy area detected before clear images of spherical amyloid fibrils were obtained. At time zero, large clusters were not observed on the surface. At 10 min, hazy globular objects were identified. At 15 min, fibrils emerged. Fibrils grew both in size and number with time, forming huge spherical amyloid assemblies with a radius of more than 20 pm at 120 min. Reproduced from [15] with permission...

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.

The average spherulite size depends (among factors including the extent of approach to equilibrium during crystallization) on the extent of nucleation. When more nuclei are present, more spherulites will form, but the typical spherulite will be smaller. For ideal spherulitic crystallization where spherulites of identical radius pack as efficiently as possible into the crystalline fraction, Equation 6.36, based on geometrical considerations, can be used to relate the maximum possible spherulite radius (Rmax) to the density (number/cc) of nuclei (pn). Since many fabrication processes will result in a distribution of spherulite sizes which can be rather broad if different parts of a specimen experience significantly different thermal histories (as usually happens, for example, in injection molding), Equation 6.36 is obviously an idealization. 

Figure 9.7 Growth curves of spherulite radius R at 403K for (a) iPP/EHR33 and (b) iPP/EHR51. (From Reference 24 with permission from John Wiley Sons, Inc.)...

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. 

The value of R found in this way is heavily weighted towards larger spherulites, because the intensity scattered by a spherulite is proportional to its volume. The method is useful for comparing samples or following the growth of spherulites, since the rate of increase of radius is usually independent of the size of spherulite. The theory has also been worked out for more complicated forms of spherulites, for truncated spherulites and for other non-spherulitic types of crystalline aggregates. 

G = the growth rate of crystalline phase nuclei r = the radius of the sphere growing from the crystalline nuclei Fs(0 = the volume of spherulites at time (t) lFs(0 = the weight of spherulites at time (t)... 

Figure 4. Variation of spherulite radius growth rate with temperature. Notice that the data can be fitted to equation (5) using tlie appropriate characteristic constants.

Figure 2.21 shows the crystallization during the polycondensation reaction of 50/50 (mole ratio) AAA/IA. After nucleation, the radius of the spherulite increases with time almost linearly before the spherulite contacts other spherulites. 

The erystal growth proeess is normally studied by measuring the spherulite radius (r) as a function of the erystallization time (t). The spherulite radius inereases linearly with crystallization time at constant temperature unless the molten polymer experienees diffusion problems to the growth front (an unusual occurrenee). The spherulite growth rate (G) is simply equal to the slope of the r vs. t curve. Therefore, G is a constant value at a given crystallization temperature. Figure 3.7 shows plots of spherulite... 

PET branching accelerated the process of crystallization, although prolonged the induction time. Branching reduced the number of nucleation sites. Therefore, more perfect geometric growth of crystallization and greater radius of sphenrlites could develop in branched PET due to less tnmcation of spherulites ... 

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