Mass fraction crystallinity

From the mass balance, pV — pcVc + paVa, and volume additivity, Va — V—Vc, the volume and mass fraction crystallinities are written, respectively. 

The mass fraction crystallinity of molded PHB samples is typically around 60%. As shown in Table 3, PHB resembles isotactic polypropylene (iPP) with respect to melting temperature (175-180°C), Young s modulus (3.5-4 GPa) and the tensile strength (40 MPa). In addition, the crystallinity of iPP is approximately 65% [18]. Accordingly, the fracture behavior of PHB may be anticipated to be tough at room temperature. Molded PHB samples do indeed show ductile behavior, but over a period of several days at ambient conditions, they slowly become more brittle [82, 85, 86]. Consequently, the elongation to break of the ultimate PHB (3-8%) is markedly lower than that of iPP (400%). 

Solid PET feedstock for the SSP process is semicrystalline, and the crystalline fraction increases during the course of the SSP reaction. The crystallinity of the polymer influences the reaction rates, as well as the diffusivity of the low-molecular-weight compounds. The crystallization rate is often described by the Avrami equation for auto-accelerating reactions (1 — Xc) = cxp(—kc/"), with xc being the mass fraction crystallinity, kc the crystallization rate constant and n a function of nucleation growth and type. 

The most frequently used techniques (X-ray diffraction, density and calorimetry) give the degree of crystallinity as a mass fraction (Gedde, 1995). Conversion of volume fraction crystallinity into the mass fraction crystallinity Wc is straightforwardly given by multiplication of the former with the factor pc/fi. Pc being the crystal density. 

Calculate the mass fraction crystallinity of polyethylene samples of densities 926, 940, and 955 kgm", using values of and given in Section 2.4. (2) Calculate the crystallinity of a polyotymeth-ylene (POM) sample of density 1410 kgm , given that the densities of crystalline and amorphous phases are 1506 and 1250 kg/m, respectively. 

Next, the equation for the evaluation of the crystallized volume-fraction is derived in Eqs. (3-5) of Fig. 3.84. Equation (5) is also used to compute the volume fraction crystallinity of semicrystaUine polymers from dUatometric experiments (see Sect. 4.1). The more common mass-fraction crystallinity is derived in Sect. 5.3.1. Simple density determinations as a function of time can, according to Eq. (5), establish the overall progress of crystallization. 

The mass fraction crystallinity of PHB can be obtained from X-ray diffraction studies, density measurement or DSC thermal analysis. At 20°C the amorphous density is 1-177 gcm and the crystalline density 1-260 gcm". The heat of fusion of PHB has been estimated at 146 Whichever method is used, the mass fraction crystallinity... 

The heat of fusion of a polymer sample can be used to determine the mass fraction crystallinity (x). As a first approximation, the following relationship can be used ... 

After switching from fast cooling to isothermal conditions at time zero, the measured heat flow rate exponentially approaches a constant value (-10.3 mW) with a time constant of about 3 seconds for this DSC. The observed crystallization peak is often symmetric, and then the time of the peak maximum (nunimum) is a measure of crystallization half time. Integration of the peak yields the enthalpy change, which can be transformed into relative crystallinity by dividing by the limiting value at infinite time. To obtain development of absolute crystallinity (mass fraction) the curve has to be divided by the enthalpy difference between crystal and liquid at the crystallization temperature, which is available from ATHAS-DB [124], The commonly applied Kolmogorov-Johnson-Mehl-Avrami (KJMA) model for the kinetic analysis of isothermal crystallization data is based on volume fractions. Therefore, the mass fraction crystallinity, Wc, as always obtained from DSC, should be transformed into volume crystallinity. 

The crystalline density of polyethylene is 1000 kg m and the density of amorphous polyethylene is 865 kg m". Calculate the mass fraction crystallinity in a sample of linear polyethylene of density 970 kg m" and in a sample of branched polyethylene of density 917 kg m". Why do the two samples have considerably different crystallinities ... 

The corresponding result for the mass fraction crystallinity is given by... 

The simplest method of determining the mass fraction crystallinity X of an unfilled, semicrystalline homopolymer is to measure the density p of a representative sample. If the material is free of voids and impurities, the total volume V of unit mass of polymer is given by... 

Crystallization of PET proceeds in two distinct steps [97], i.e. (1) a fast primary crystallization which can be described by the Avrami equation, and (2) a slow secondary crystallization which can be described by a rate being proportional to the crystallizable amorphous fraction dXc/dt = (Xmax — tc)kc, with Xmax being the maximum crystallinity (mass fraction) [98], Under SSP conditions, the primary crystallization lasts for a few minutes before it is replaced by secondary crystallization. The residence time of the polymer in the reactor is of the order of hours to days and therefore the second rate equation can be applied for modelling the SSP process. 

Ammonium perchlorate (AP NH4CIO4) is a white, crystalline material, the crystal structure of which changes from orthorhombic to cubic at 513 K, which affects the decomposition process. AP is not hygroscopic in the atmosphere and the mass fraction of oxygen is 0.545. It is used as an oxidizer in various types of propellants and pyrolants. A rapid sublimation occurs between 670 K and 710 K at low pressures. Under slow heating, AP starts to decompose at about 470 K according to ... 

Ammonium nitrate (AN NH4NO3) is a white, crystalline material, the crystal structure of which varies with temperature.melting point is 442 K and its heat of fusion is 71.4 kj kg . Though the mass fraction of oxygen of AN is 0.5996, it is highly hygroscopic and absorbs moisture from the atmosphere to form liquid AN acid. This limits its application in propellants and pyrolants. However, AN is widely used as an oxidizer of explosives such as slurry explosives and ANFO (ammonium nitrate fuel oil) explosives. 

When the catalysts are in the form of crystalline solid particles, the characteristics of Efc are different compared to when liquid organoiron catalysts are used. As shown in Fig. 11.18, the critical friction energy is independent of the mass fraction of the catalysts SrCOj and FcjOj. Though Fe203 reduces the Ef similarly to the... 

Note 3 The degree of crystallinity may be expressed either as the mass fraction, Wc, or as the volume fraction, c, the two quantities being related by... 

The 2003 ACGIH threshold limit valuetime-weighted average (TLV-TWA) for particulate matter containing no asbestos and <1% crystalline silica is 3mg/m for respirable size fraction and lOmg/m for inhalable mass fraction. Exposure to any substance in the particulate mass that has a designated TLV should be controlled to that value. 

Here, H can be conveniently expressed as the deviation of the field from the center of the resonance in gauss units H=H —H0 yb,ym, and yn are the elementary spectra of the broad, the medium, and the narrow components, respectively. These are considered to be contributed from protons belonging to the crystalline region, and hindered-rotational and micro-Brownian mobile methylene groups in the amorphous region, respectively. pb,pm, and 0n determine the line-width and breadth of the respective elementary spectra wb, wm, and iv designate the respective mass fractions. Each elementary spectrum is normalized as... 

Figure 8 shows the relationship between the mass fraction wb of the broad component and the crystallinity (1 —X)[Pg.151]

Fig. 8. Mass fraction of broad component vs. crystallinity obtained from density measurements66. Solid circles indicate data of Mandelkern ef ai.68, 69 Straight line indicates the relation, (l-k)

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