Crystalline phase density

The dimensional stability of molded components benefits from several unique aspects of SPS. First, the amorphous and crystalline phases have equivalent density, and this tends to minimize the crystalline gradients that are typical of semicrystalline, thermoplastic materials. A comparison of the amorphous phase density with the crystalline phase density of SPS and other semicrystalline thermoplastics is shown in Table 15.3. 

Density. Density of LLDPE is measured by flotation in density gradient columns according to ASTM D1505-85. The most often used Hquid system is 2-propanol—water, which provides a density range of 0.79—1.00 g/cm. This technique is simple but requires over 50 hours for a precise measurement. The correlation between density (d) and crystallinity (CR) is given hy Ijd = CRj + (1 — Ci ) / d, where the density of the crystalline phase, ify, is 1.00 g/cm and the density of the amorphous phase, is 0.852—0.862 g/cm. Ultrasonic methods (Tecrad Company) and soHd-state nmr methods (Auburn International, Rheometrics) have been developed for crystallinity and density measurements of LLDPE resins both in pelletized and granular forms. 

The density of vitreous sihca is lower than those of the low pressure crystalline phases of sihcon dioxide (121), especially that of quartz. 

Crystallization kinetics have been studied by differential thermal analysis (92,94,95). The heat of fusion of the crystalline phase is approximately 96 kj/kg (23 kcal/mol), and the activation energy for crystallization is 104 kj/mol (25 kcal/mol). The extent of crystallinity may be calculated from the density of amorphous polymer (d = 1.23), and the crystalline density (d = 1.35). Using this method, polymer prepared at —40° C melts at 73°C and is 38% crystalline. Polymer made at +40° C melts at 45°C and is about 12% crystalline. 

Figure 5 Electron density distributions along the bilayer normal from an MD simulation of a fully hydrated liquid crystalline phase DPPC bilayer. (a) Total, lipid, and water contributions (b) contributions of lipid components in the interfacial region.

The amorphous phase differs from the mesophase and the crystalline phase by a clearly lower value of density. The amorphous phase density depends on the internal orientation of the fiber. Us value is in the range 1.335-1.357 g/cm. In the case of a very high orientation, it can even reach the value 1.363 g/cm-. ... 

The cost/performance factor of individual surfactants will always be considered in determining which surfactants are blended in a mixed active formulation. However, with the recent advent of compact powders and concentrated liquids, other factors, such as processing, density, powder flowability, water content, stabilization of additives, dispersibility in nonaqueous solvents, dispersion of builders, and liquid crystalline phase behavior, have become important in determining the selection of individual surfactants. 

A polymorph is a solid crystalline phase of a compound resulting from the possibility of at least two different crystal lattice arrangements of that compound in the solid state [42], Polymorphs of a compound are, however, identical in the liquid and vapor states. They usually melt at different temperatures but give melts of identical composition. Two polymorphs of a compound may be as different in structure and properties as crystals of two different compounds [43,44], Apparent solubility, melting point, density, hardness, crystal shape, optical and electrical properties, vapor pressure, etc. may all vary with the polymorphic form. The polymorphs that are produced depend upon factors such as storage temperature, recrystallization solvent, and rate of cooling. Table 2 suggests the importance of polymorphism in the field of pharmaceutics [45],... 

It has also been inferred that differences found between crystallinities measured by density and those from heat of fusion by DSC area determination, as given for polyethylenes in the example of Figure 4 [72], may be related to baseline uncertainties, or not accounting for the temperature correction of AHc. Given that similar differences in crystallinity from density and heat of fusion were reported for isotactic poly(propylene) [43] and polyfaryl ether ether ketone ketone), PEEKK [73], other features of phase structure that deviate from the two-phase model may be involved in the crystallinity discrepancy. 

The Phenomenon. In existing materials the electron density is not even constant inside a single phase. This is obvious for the liquid structure of amorphous regions. Nevertheless, even in crystalline phases lattice distortions and grain boundaries result in variations of the electron density about its mean value. In analogy to the sunlight scattered from the fluctuations of air density, X-rays are scattered from the fluctuations of electron density. 

Lines 21 -40. Physical data. The usual crystalline shape, density (note two values reported.), sublimation notation, boiling point data, and so on. K at 25° is the ionization constant of the acid the pH of the saturated solution (2.8 at 25°C) is given. The solubility data (Soly) is very complete, including water solutions at various temperatures, a bit about the phase diagram of the compound, and solubility in other solvents. Note that numerical data is given where possible. 

It is quite likely to find dense quark matter inside compact stars like neutron stars. However, when we study the quark matter in compact stars, we need to take into account not only the charge and color neutrality of compact stars and but also the mass of the strange quark, which is not negligible at the intermediate density. By the neutrality condition and the strange quark mass, the quarks with different quantum numbers in general have different chemical potentials and different Fermi momenta. When the difference in the chemical potential becomes too large the Cooper-pairs breaks or other exotic phases like kaon condensation or crystalline phase is more preferred to the BCS phase. 

Density functional theory has been extensively used to calculate vibrational properties of minerals and other crystalline phases in addition to molecules and molecule-like substances. This method has recently begun to be used to calculate isotope fractionation factors (Schauble et al. in press Anbar et al. in press), and shows great potential for future research. Programs such as ABINIT (Gonze et al. 2002), pwSCF (Baroni et al. 2001)—both freely available—and the commercial package CASTEP (Accelrys, Inc.) can be used to calculate vibrational properties of crystals. 

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