Crystallinity, analysis weight fraction

If an amorphous phase is present in the sample, it is still possible to perform the quantitative analysis by introducing a small amount of crystalline powder with the known weight fraction 1 that will be the iV+ 1 phase in the sample, so the equation becomes ... 

In a mixture of crystalline materials, each species will be characterized by its distinctive series of scattering peaks, and the observed powder pattern will consist of a sum of the individual components. The intensities of the peaks associated with each component are proportional to its weight fraction in the mixture, so the performance of a quantitative analysis is based on the accurate and reproducible measurement of peak intensities. The analysis can be performed either with or without an international standard, and the theory associated with each approach has been set forth by Suryanarayanan12 and others.18-21... 

Quantitative analysis can be done to determine relative amounts of compounds or phases in a sample of compound/phase mixtures. Quantitative analysis of a diffraction spectrum is based on the following factor. The intensity of the diffraction peaks of a particular crystalline phase in a phase mixture depends on the weight fraction of the particular phase in the mixture. Thus, we may obtain weight fraction information by measuring intensities of peaks assigned to a particular phase. Generally, we may express the relationship as the following. 

We often want to know not only the identity of chemical elements but also their concentrations in a specimen. Thus, quantitative elemental analysis is often required. The concentrations of elements must relate to their peak intensities in the spectrum, similar to the relationship between weight fractions of crystalline phases and their peak intensities in the XRD spectrum. Chemical compositions should be calculated by comparing the ratios of integrated peak intensities among elements in the specimen. In general, the weight fraction (C) of an element in relation to the relative intensities of its peaks (Ir) is mainly affected by the instrument factor (K), and the matrix factor of specimen (M). 

The reaction mechanism of this system involved the transfer of phases across the solid liquid interface. Hence, quantification using Equation (22) produced values that were overestimated. To determine the absolute phase abundances, powdered diamond was selected as an inert internal standard and was weighed into the starting solids. Acid was then added to this mixture and the standard concentration taken as its weight fraction of the sample in its entirety, i.e., solids and liquids in total. For each dataset the results of the quantitative phase analysis were adjusted according to the known amount of standard present in the system [Equation (16)]. This allowed the determination of variation in the amorphous content of the system to be assessed via Equation (17)] as well as the formation and consumption of crystalline phases. The amorphous content... 

The chemical analysis of the [Zn-Cr-Cl] phase so obtained confirms the definite ratio Zn/Cr = 2, previously proposed by Boehm, Steinle, and Vieweger 1977. Attempts to vary the Zn/Cr ratio in this way were unsuccessful. The relatively low weight fraction of ZnO (2-5 wt % range) and the slow addition of the CrCls solution or long aging time in contact with the mother liquor greatly improve the crystallinity of the double hydroxide (Figure 7-14). 

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 ... 

For quantitative analysis of largely amorphous composites, an analysis based on the diffraction-absorption method was also developed. In this approach, the intensity scale factor and the microabsorption parameter are obtained by a calibration procedure based on the diffraction data of different samples of pure crystalline and mixtures. This information is used to calculate the crystalline weight fraction. 

Probably the most widely used technique for determining degrees of crystallinity is differential scanning calorimetry (see Thermal Analysis). This is due to the ready availability of such instrumentation, rapid turn around time, and apparent simplicity. The heat of fusion is measured experimentally and the weight-fraction degree of crystallinity defined as ... 

Although polymers in-service are required to be resistant toward hydrolysis and solar degradation, for polymer deformulation purposes hydrolysis is an asset. Highly crystalline materials such as compounded polyamides are difficult to extract. For such materials hydrolysis or other forms of chemolysis render additives accessible for analysis. Polymers, which may profitably be depolymerised into their monomers by hydrolysis include PET, PBT, PC, PU, PES, POM, PA and others. Hydrolysis occurs when moisture causes chain scissions to occur within the molecule. In polyesters, chain scissions take place at the ester linkages (R-CO-O-R ), which causes a reduction in molecular weight as well as in mechanical properties. Polyesters show their susceptibility to hydrolysis with dramatic shifts in molecular weight distribution. Apart from access to the additives fraction, hydrolysis also facilitates molecular characterisation of the polymer. In this context, it is noticed that condensation polymers (polyesters, -amides, -ethers, -carbonates, -urethanes) have also been studied much... 

Molecular Weight Dependence of Phase Structure. Similar line shape analysis was performed for samples with molecular weight over a very wide range that had been crystallized from the melt. In some samples, an additional crystalline line appears at 34.4 ppm which can be assigned to trans-trans methylene sequences in a monoclinic crystal form. Therefore the spectrum was analyzed in terms of four Lorentzian functions with different peak positions and line widths i.e. for two crystalline and two noncrystalline lines. Reasonable curve fitting was also obtained in these cases. The results are plotted by solid circles on the data of the broad-line H NMR in Fig. 3. The mass fractions of the crystalline, amorphous phases and the crystalline-amorphous interphase are in good accord with those of the broad, narrow, and intermediate components from the broad-line NMR analysis. 

Polymeric addition compounds (16) of furan and ethylene, where n is a whole number from 1 to 50, have been prepared (58) by addition of >2 mole furan to 1 mole ethylene at 120 °C to 250 °C and high pressures followed by fractional extraction of the solid product formed. These polymers have interesting physical and chemical properties. They appear to be highly crystalline on analysis by X-ray. As a consequence, the polymers show good thermal stability, which increases directly with molecular weight. The presence of ether bridges makes possible conversion (Scheme 4) to other compounds that retain the double hydrocarbon chain (ladder) structure and may bear various func-... 

Fig. 3. Mass fractions of crystalline, rubbery, and crystalline-amorphous interfacial phases of bulk polyethylene as a function of molecular weight Mv O data by broad-line H NMR analysis. data by high-resolution NMR analysis...

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