Crystallinity, analysis volume fraction

Analysis of Fractions. Surface areas and pore size distributions for both coked and regenerated catalyst fractions were determined by low temperature (Digisorb) N2 adsorption isotherms. Relative zeolite (micropore volume) and matrix (external surface area) contributions to the BET surface area were determined by t-plot analyses (3). Carbon and hydrogen on catalyst were determined using a Perkin Elmer 240 C instrument. Unit cell size and crystallinity for the molecular zeolite component were determined for coked and for regenerated catalyst fractions by x-ray diffraction. Elemental compositions for Ni, Fe, and V on each fraction were determined by ICP. Regeneration of coked catalyst fractions was accomplished in an air muffle furnace heated to 538°C at 2.8°C/min and held at that temperature for 6 hr. 

The interest in multicomponent materials, in the past, has led to many attempts to relate their mechanical behaviour to that of the constituent phases (Hull, 1981). Several theoretical developments have concentrated on the study of the elastic moduli of two-component systems (Arridge, 1975 Peterlin, 1973). Specifically, the application of composite theories to relationships between elastic modulus and microstructure applies for semicrystalline polymers exhibiting distinct crystalline and amorphous phases (Andrews, 1974). Furthermore, as discussed in Chapter 4, the elastic modulus has been shown to be correlated to microhardness for lamellar PE. In addition, H has been shown to be a property that describes a semicrystalline polymer as a composite material consisting of stiff (crystals) and soft, compliant elements. Application of this concept to lamellar PE involves, however, certain difficulties. This material has a microstructure that requires specific methods of analysis involving the calculation of the volume fraction of crystallized material, crystal shape and dimensions, etc. (Balta Calleja et al, 1981). 

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... 

In any case one speaks about the degree of crystallinity of the materials, being a measure of the volume fraction of the crystalline part of the material. This parameter is, however, not uniquely defined, but varies considerably with the method used for its determination. The degree of crystallinity determined by means of x-ray diffraction is often call the x-ray crystallinity, Xc- In the spirit of Ruland analysis [36]... 

Data on the development of crystallinity, obtained by adiabatic calorimetry are depicted in Fig. 3.99. Note, that for the Avrami analysis the crystallinity must be calculated in volume fraction, v, while the heat of fusion is usually expressed in weight-fraction, w, as displayed in Figs. 3.84 and derived in Fig. 5.80, respectively. The correlation between the two crystallinities is given by ... 

A technique that leads to quantitative data for the determination of the volume-fraction crystallinity is the infrared analysis. As an example, in Fig. 5.84 one can see the two areas in the IR spectrum of polyethylene where amorphous and crystalline samples are largely different (frequencies A and C). The equation in the upper right-hand comer permits now a quantitative evaluation, as is documented in Fig. 5.85 for... 

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. 

Gas-chromatographic analysis (column PEG-6000, 2 meters, column temperature 180°C., carrier gas, He) of the residue showed that it consisted of three main products. The first peak was identified as bicyclohexyl, the second as 3-cyclohexylcyclohexene, and the third as 3,3 -bicy-clohexenyl. The residue was distilled, and a fraction boiling at 90°-122°C./20 mm. Hg was collected. This fraction was poured into 10 times its volume of acetic acid. The solution was cooled to 0°C., and bromine was added. Colorless needle crystals and a red viscous oily liquid were obtained. The crystalline material was recrystallized from acetic acid and melted at 157.5°-160°C. (decomp.) [literature, 158°C. (6)]. A mixed melting point with an authetic tetrabromide of 3,3 -bicyclohexenyl was not depressed. 

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