Crystalline volume fraction

Since polymers are never completely crystalline, it is of importance to know, how big, in a certain case, the crystalline fraction is. The crystalline volume fraction, specific mass, p, if the densities of the amorphous fraction, pa, and of the crystal, pc, are known, since ... 

Because diffusion is limited to the amorphous phase of semicrystalline polymers, and the crystalline phase can additionally restrict chain motion in the amorphous phase, the value of D is dependent on the degree of crystallinity of the polymer. To a first approximation, this effect may be expressed by equation 7, where x is the crystalline volume fraction and D is the diffusion coefficient of the totally amorphous polymer. For example, diffusion coefficients for high density polyethylene are lower than for low density polyethylene (3). 

This relation corresponds to exchange-coupled crystallites diluted in an ideally soft magnetic matrix. The only modification made over the original single phase model is the inclusion of the crystalline volume fraction xcr. It should be noted that is scaling with the volume fraction in the same way as with the crystalline volume 1f. 

Vieth and Wuerth (2Ji) found negative deviations from the simple two phase model for semicrystalline polypropylene suggesting that the presence of crystallites in some way reduces the sorptive capacity of the amorphous phase. However, analysis of samples using x-ray diffraction revealed the presence of a less stable crystalline phase having a lower density. Since the crystalline volume fraction is commonly determined from density measurements, the presence of a second, less dense (however, still impermeable) crystalline phase would seem... 

It is well known that chitin is a semicrystalline polymer. Consequently, it is necessary to verify whether chitin s crystalline volume fraction changes with heat treatment and its influence on relaxation behaviors. The diffraction pattern of purified a-chitin powder is shown in Figure 2.8. The five characteristic crystalline reflections for a-chitin are present [51]. They are indexed as (020), (110), (120),... 

The estimation of crystalline volume fraction was based on the standard approach that assumes the fact that the experimental intensity curve is a linear combination of intensities of crystalline and amorphous phases. For bulk a-chitin, the crystalline volume fraction is about 30% and about 10% for film samples. A similar behavior was found for CS acetate after dissolution into acid solutions [54]. 

The films crystalline volume fraction does not change after anneaiing at 120 °C, and so the amorphous phase volume fraction is constant during the dielectric measurements at the annealing temperature employed. In subsequent analyses, we make the usual assumption that crystalline units are immobile relative to amorphous units and do not contribute to relaxations. 

Because of the usual experimental ranges of crystallinity, the appearance of the baselines in the study of semicrystalline polymers is not very frequent [36, 37]. Therefore, the crystalline volume fraction should be obtained by other alternative techniques such as, for example, differential scanning calorimetry. In this way, if the crystallinity in volume is known, it is possible to obtain the lost baseline [37, 38]. However, if the crystallinity is either low or high, it is possible to directly obtain the baseline for which it is foreseen that the morphology is solved [36]. For example, Vonk and Pijpers and Vonk and Koga worked at high crystallinities and they observed the aforementioned baselines [39]. 

One can observe experimentally the crystalline volume fraction, f, and the void volume fraction, e, defined by... 

The solubility S of a semicrystalline polymer containing a crystalline volume fraction of a. and with an amorphous phase solubility is given by ... 

Calculate Young s modulus of a sample with the same average crystalline and amorphous moduli and crystalline volume fraction as in example 6.2 but assuming that there is uniform strain throughout the sample. 

Fig. 16. a. Kinetics constant versus temperature for a and mesomorphic phase b. Crystallinity volume fraction as a function of cooling rate for various values of n (Avrami index) and K0 D (crystallizability). 

The onset of crystallization in the Vitreloy 1 alloy shown in Fig. 1.3 was based on the detection of a crystalline volume fraction of 10 " by conventional methods. There are two different curves for the onset of crystallization in Fig. 1.3. For the solid curve, which was obtained using classical nucleation theory, the effective diffusion constant was taken to be proportional to the reciprocal of the viscosity, which was considered to be of the VFT form. The dotted curve was obtained by the use of an Arrhenius form of expression for the effective diffusion constant, which was found to fit better at lower temperatures near Tg (Masuhr et al. 1999). This discussion shows that for understanding the kinetics of crystallization in multi-component alloys considerable improvisation becomes necessary. 

The rate of change of crystalline volume fraction is given by the equation ... 

In recent research, Al-Hussein et al. [25] prepared an oriented low-density polyethylene with a parallel lamellar stack morphology where the c axes of the crystalline lamellae were parallel to the lamellar plane normals. For this structure, explicit equations can be obtained for the elastic constants in terms of the crystalline volume fraction and the elastic constants of the crystalline lamellae (cji, C33, C44, etc.) and the amorphous layer (cji, cfj, c, etc.). 

---