Crystallinity quantifying

One can quantify the pseudopotential by writing the total crystalline potential for an elemental solid as... 

To assess homogeneity, the distribution of chemical constituents in a matrix is at the core of the investigation. This distribution can range from a random temporal and spatial occurrence at atomic or molecular levels over well defined patterns in crystalline structures to clusters of a chemical of microscopic to macroscopic scale. Although many physical and optical methods as well as analytical chemistry methods are used to visualize and quantify such spatial distributions, the determination of chemical homogeneity in a CRM must be treated as part of the uncertainty budget affecting analytical chemistry measurements. 

Major determinants of membrane fluidity may be grouped within two categories [53] (1) intrinsic determinants, i.e., those quantifying the membrane composition and phase behavior, and (2) extrinsic determinants, i.e., environmental factors (Table 1). In general, any manipulation that induces an increase in the molal volume of the lipids, e.g., increase in temperature or increase in the fraction of unsaturated acyl chains, will lead to an increase in membrane fluidity. In addition, several intrinsic and extrinsic factors presented in Table 1 determine the temperature at which the lipid molecules undergo a transition from the gel state to liquid crystalline state, a transition associated with a large increase in bilayer fluidity. 

Solid-state NMR can be applied equally well to both crystalline and amorphous solids (10-17), and can be used to distinguish and quantify the crystalline and amorphous components of multi-component solids. Here we describe the... 

Materials that do not compress well produce soft tablets. In addition, brittle crystalline materials will yield brittle tablets. Hiestand was the first pharmaceutical scientist to quantify rationally the compaction properties of pharmaceutical powders [23-28], The results... 

The interfacial zone is by definition the region between the crystallite basal surface and the beginning of isotropy. Due to the conformationally diffuse nature of this region, quantitative contents of the interphase are most often determined by indirect measures. For example, they have been computed as a balance from one of the sum of the fractional contents of pure crystalline and amorphous regions. The analysis of the internal modes region of the Raman spectrum of polyethylene, as detailed in the previous section of this chapter, was used to quantify the content of the interphase region (ab). 

If one has a priori knowledge of the types of structural order relevant to a system of interest, one can then generally construct metrics that are capable of detecting and quantifying that order. Such metrics are often designed to report the deviation of a structure from a reference arrangement of particles. This information can be especially useful for studying the behavior of supercooled liquids and related systems that exhibit transient structural precursors of the stable crystalline phase.34 The structural order... 

Another possibihty to improve the temperature homogeneity is to introduce an additional polysiHcon plate in the membrane center. The thermal conductivity of polysilicon is lower than that of crystalline siHcon but much higher than the thermal conductivity of the dielectric layers, so that the heat conduction across the heated area is increased. Such an additional plate constitutes a heat spreader that can be realized without the use of an electrochemical etch stop technique. Although this device was not fabricated, simulations were performed in order to quantify the possible improvement of the temperature homogeneity. The simulation results of such a microhotplate are plotted in Fig. 4.9. The abbreviations Si to S4 denote the simulated temperatures at the characteristic locations of the temperature sensors. At the location T2, the simulated relative temperature difference is 5%, which corresponds to a temperature gradient of 0.15 °C/pm at 300 °C. 

P.E. Luner, S. Majuru, J.J. Seyer and M.S. Kemper, Quantifying crystalline form composition in binary powder mixtures using near-infrared reflectance spectroscopy, Pharm. Dev. Tech., 5, 231-246 (2000). 

The crystallization process can be illustrated by a phase diagram that shows which state (liquid, crystalline, or amorphous solid [precipitate]) is stable under a variety of crystallization parameters. It provides a means of quantifying the influence of the parameters such as the concentrations of protein, precipitant(s), additive(s), pH, and temperature on the production of crystals. Hence phase diagrams form the basis for the design of crystal growth conditions (McPherson, 1999 Ducruix and Giege, 1992 Ducruix and Giege, 1999 Chayen et ah, 1996 and references therein). 

PVDF is mainly obtained by radical polymerisation of 1,1-difluoroethylene head to tail is the preferred mode of linking between the monomer units, but according to the polymerisation conditions, head to head or tail to tail links may appear. The inversion percentage, which depends upon the polymerisation temperature (3.5% at 20°C, around 6% at 140°C), can be quantified by F or C NMR spectroscopy [30] or FTIR spectroscopy [31], and affects the crystallinity of the polymer and its physical properties. The latter have been extensively summarised by Lovinger [30]. Upon recrystallisation from the melted state, PVDF features a spherulitic structure with a crystalline phase representing 50% of the whole material [32]. Four different crystalline phases (a, jS, y, S) may be identified, but the a phase is the most common as it is the most stable from a thermodynamic point of view. Its helical structure is composed of two antiparallel chains. The other phases may be obtained, as shown by the conversion diagram (Fig. 7), by applying a mechanical or thermal stress or an electrical polarisation. The / phase owns ferroelectric, piezoelectric and pyroelectric properties. 

Metal sulfide powder samples were weighed and placed in a glass desiccator containing an open vial of metallic mercury. The desiccator was placed in a laboratory oven at 70 or 90°C for up to 24 days. The concentration of Hg(0) in the desiccator was calculated to be -1500 ppm 70°C and -2500 ppm 90°C. During the exposure period, the desiccator was periodically removed, cooled, and the metal sulfide samples weighed. The period of time that the samples were out of the oven was taken into account when reporting the Hg(0) exposure duration. XRD and quantitative data analysis, Rietveld analysis, was used to identify and quantify the post-reaction crystalline-phase constituents. 

The use of Cl to represent the percentage of the crystalline component is unjustified among such a diversity of cellulosic materials, whose lignin components vary from 0 to about 30%. Cl, as used here, is not intended to represent the proportion of the crystalline component. Rather, Cl provides a means of quantifying the characteristics of the x-ray diffraction patterns. When applied to a set of similar samples, Cl is a convenient measure of the degree of lateral order. 

Savolainen et al. investigated the role of Raman spectroscopy for monitoring amorphous content and compared the performance with that of NIR spectroscopy [41], Partial least squares (PLS) models in combination with several data pre-processing methods were employed. The prediction error for an independent test set was in the range of 2-3% for both NIR and Raman spectroscopy for amorphous and crystalline a-lactose monohydrate. The authors concluded that both techniques are useful for quantifying amorphous content however, the performance depends on process unit operation. Rantanen et al. performed a similar study of anhydrate/hydrate powder mixtures of nitrofurantoin, theophyllin, caffeine and carbamazepine [42], They found that both NIR and Raman performed well and that multivariate evaluation not always improves the evaluation in the case of Raman data. Santesson et al. demonstrated in situ Raman monitoring of crystallisation in acoustically levitated nanolitre drops [43]. Indomethazine and benzamide were used as model... 

Under constant experimental conditions, the number of Raman scattered photons is proportional to analyte concentration. Quantitative methods can be developed with simple peak height measurements.5 Just as with IR calibrations, multiple components in complex mixtures can be quantified if a distinct wavelength for each component can be identified. When isolated bands are not readily apparent, advanced multivariate statistical tools (chemometrics) like partial least squares (PLS) can help. These work by identifying all of the wavelengths correlated to, or systematically changing with, the levels of a component. Raman spectra can also be correlated to other properties, such as stress in semiconductors, polymer crystallinity, and particle size because these parameters are reflected in the local molecular environment. 

Conclusions. "R-factors" calculated between pairs of structure-factor sets determined by three different laboratories varied between 16 and 22%, and these large inaccuracies were the dominant contributor to errors in the parameters of the crystalline structure. Thus if the accuracy with which the structure of polymeric fibres is determined is to be improved, it is essential both to increase the accuracy of intensity measurement, and to quantify its errors. 

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