Constituent phases

Lamellar morphology variables in semicrystalline polymers can be estimated from the correlation and interface distribution fiinctions using a two-phase model. The analysis of a correlation function by the two-phase model has been demonstrated in detail before [30,11] The thicknesses of the two constituent phases (crystal and amorphous) can be extracted by several approaches described by Strobl and Schneider [32]. For example, one approach is based on the following relationship ... 

In order to solve the system of the above-described equations, and which are derived by applying the self-consistent model, applied for composites by Budiansky 7), it is necessary to evaluate experimentally the moduli of elasticity (tension, shear, bulk) and Poisson s ratios of the constituent phases and the composite. Thus, the only unknown are the radius r of the mesophase layer and its mechanical properties and thermal expansion coefficient, which are then derived. 

In order now to evaluate the exponent rp we make recourse to the law of mixtures, given by relation (21), which expresses the elastic modulus of the composite in terms of the moduli and the radii (or volume fractions) of the constituent phases. This relation yields the average elastic modulus for the mesophase Ef. Then, it is valid for the mesophase layer that ... 

Fig. 16. The variation of the moduli of the constituent phases and the composite versus the fiber volume content for a series of E-glass-epoxy fiber reinforced composites...

Disperse systems can be classified in various ways. Classification based on the physical state of the two constituent phases is presented in Table 1. The dispersed phase and the dispersion medium can be either solids, liquids, or gases. Pharmaceutically most important are suspensions, emulsions, and aerosols. (Suspensions and emulsions are described in detail in Secs. IV and V pharmaceutical aerosols are treated in Chapter 14.) A suspension is a solid/liquid dispersion, e.g., a solid drug that is dispersed within a liquid that is a poor solvent for the drug. An emulsion is a li-quid/liquid dispersion in which the two phases are either completely immiscible or saturated with each other. In the case of aerosols, either a liquid (e.g., drug solution) or a solid (e.g., fine drug particles) is dispersed within a gaseous phase. There is no disperse system in which both phases are gases. 

In colloid science, colloidal systems are commonly classified as being lyophilic or lyophobic, based on the interaction between the dispersed phase and the dispersion medium. In lyophilic dispersions, there is a considerable affinity between the two constituent phases (e.g., hydrophilic polymers in water, polystyrene in benzene). The more restrictive terms hydrophilic and oleophilic can be used when the external phase is water and a nonpolar liquid, respectively. In contrast, in lyophobic systems there is little attraction between the two phases (e.g., aqueous dispersions of sulfur). If the dispersion medium is water, the term hydrophobic can be used. Resulting from the high affinity between the dispersed phase and the dispersion medium, lyophilic systems often form spontaneously and are considered as being thermodynamically stable. On the other hand, lyophobic systems generally do not form spontaneously and are intrinsically unstable. 

The number of the constituent phases of a disperse system can be higher than two. Many commercial multiphase pharmaceutical products cannot be categorized easily and should be classified as complex disperse systems. Examples include various types of multiple emulsions and suspensions in which solid particles are dispersed within an emulsion base. These complexities influence the physicochemical properties of the system, which, in turn, determine the overall characteristics of the dosage forms with which the formulators are concerned. 

Hsieh and Plesset assumed that the two-phase homogeneous mixture can be represented as a uniform medium with physical properties synthesized from the constituent phases and weighted according to void fraction, a, and quality, X. Using such a model, they were able to show that the gas compression is essentially isothermal and the acoustic velocity can be approximated as... 

The observation under a light microscope may be complemented by examination under an electron microscope, possibly equipped with microanalysis devices to analyse point by point the composition of the sample and of its constituent phases. 

At the heart of impedance analysis is the concept of an equivalent circuit. We assume that any cell (and its constituent phases, planes and layers) can be approximated to an array of electrical components. This array is termed the equivalent circuit , with a knowledge of its make-up being an extremely powetfitl simulation technique. Basically, we mentally dissect the cell or sample into resistors and capacitors, and then arrange them in such a way that the impedance behaviour in the Nyquist plot is reproduced exactly (see Section 10.2 below on electrochemical simulation). 

Two important morphological parameters characterizing ball-milled powders are the particle and grain size of constituent phases within the powders. In our laboratory, the size measurement of the powder particles is carried out by attaching loose powder to sticky carbon tape and taking pictures under secondary electron (SE) mode in the SEM. The images are then analyzed by an image analysis software. The size of the powders is calculated as the particle equivalent circle diameter, ECD = AA/nf, where A represents the projected particle area. Usually from -300 to 700 particles are analyzed for each batch. 

Properties such as internal energy, volume and entropy are called extensive because their values for a given phase are proportional to the mass or volume of the phase. The value of an extensive property of an entire system is the sum of the values of each of the constituent phases. The molar value of an extensive property is that for a properly defined gram-molecular weight or mole of material. The specific value of an extensive property is that per unit weight (eg, one gram of material). A property is called intensive if its value for a given phase is independent of the mass of the phase. Temp and pressure are examples of such intensive properties... 

Eley BM, Garrett JR. 1983. Tissue reactions to the separate implantation of individual constituent phases of dental amalgam, including assessement by energy dispersive x-ray microanalysis. Biomaterials 4 73-80. 

Spanggord, R. J., Mabey, W. R., Mill, T., Chou, T.-W., Smith, J. H., Lee, S. and Roberts, D., Environmental fate studies on certain ammunition wastewater constituents Phase IV. Lagoon Model Studies , Report AD-A138550, US Army Medical Research and Development Command, Fort Detrick, Frederick, MD, 1984. 

The particles in a colloidal dispersion are sufficiently large for definite surfaces of separation to exist between the particles and the medium in which they are dispersed. Simple colloidal dispersions are, therefore, two-phase systems. The phases are distinguished by the terms dispersed phase (for the phase forming the particles) and dispersion medium (for the medium in which the particles are distributed) - see Table 1.1. The physical nature of a dispersion depends, of course, on the respective roles of the constituent phases for example, an oil-in-water (O/W) emulsion and a water-in-oil (W/O) emulsion could have almost the same overall composition, but their physical properties would be notably different (see Chapter 10). 

When selecting the processing method, differences between the properties of the two constituent phases of the FGM are of primary importance. In a compositional FGM, for example, the difference in heat resistance between... 

In addition to conventional sintering, reactive powder processing, also called combustion synthesis or self-propagating high-temperature synthesis (SHS), can be used if the target compounds can be synthezised from the starting powder mixture (Stangle and Miyamoto, 1995). This process comprises a rapid and exothermic chemical reaction to simultaneously synthesize some or all of the constituent phases in the FGM and density the component. 

We performed the addition reaction of z-Pr2Zn to pyrimidine-5-carbalde-hyde 11 in the presence of a constituent phase of the meteorite by appropriate treatments. Asymmetric autocatalysis with amplification of chirality gave pyrimidyl alkanol 12 with ee of detectable level. 

Calculation of Master Curves from Mechanical Models. The only way to obtain valid master curves for the thermorheologically complex systems (75/25 and 50/50 blends) is to calculate the moduli of the blends as a function of time, using an appropriate mechanical model. This method requires knowledge of the time and temperature dependence of the mechanical properties of the constituent phases. 

Alite is the most important constituent of all normal Portland cement clinkers, of which it constitutes 50-70%. It is tricalcium silicate (CajSiOj) modified in composition and crystal structure by incorporation of foreign ions, especially Mg ", AP and Fe. It reacts relatively quickly with water, and in normal Portland cements is the most important of the constituent phases for strength development at ages up to 28 days, it is by far the most important. 

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