Volume Properties

Two volume properties of a closed system are defined as follows  

The cubic expansion coefQdent is also called the coefficient of thermal expansion and the expansivity coefficient. Other symbols for the isothermal compressibility are ff and 

These definitions show that a is the fractional volume increase per unit temperaffire increase at constant pressure, and kt is the fractional volume decrease per unit pressure increase at constant temperature. Both quantities are intensive properties. Most substances have positive values of and all substances have positive values of kt, because a pressure increase at constant temperature requires a volume decrease. 

If an amount n of a substance is in a single phase, we can divide the numerator and denominator of the right sides of Eqs. 7.1.1 and 7.1.2 by n to obtain the alternative expres- 

If we choose T and p as the independent variables of the closed system, the total differential of V is given hy 

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Depending on the context, we sometimes prefer the term interphase over interface because the latter refers to an infinitely sharp dividing plane between two phases. Organisms generally form boundary layers, e.g. the cell wall, that are characterised by a gradual transition from the biological phase to the medium phase, and if we discuss the volume properties of such layers the term interphase is more appropriate. 

This relation externally is very similar to Eq. (43) but includes only volume properties. 

A. One Atmosphere Densities. The densities or volume properties of solutions have been studied by a number of methods which are extensively reviewed elsewhere (4,5. 6,7) of all of the methods, only the magnetic float (7-14), the hydrostatic balance (3,15-20), the vibrating flow densimeter (21,22), and dilatometric (23,24,25) methods give data with sufficient precision to study the densities of dilute solutions. For more concentrated... 

The volume properties of crystalline mixtures must be related to the crystal chemical properties of the various cations that occupy the nonequivalent lattice sites in variable proportions. This is particularly true for olivines, in which the relatively rigid [Si04] groups are isolated by Ml and M2 sites with distorted octahedral symmetry. To link the various interionic distances to the properties of cations, the concept of ionic radius is insufficient it is preferable to adopt the concept of crystal radius (Tosi, 1964 see section 1.9). This concept, as we have already noted, is associated with the radial extension of the ion in conjunction with its neighboring atoms. Experimental electron density maps for olivines (Fujino et al., 1981) delineate well-defined minima (cf figure 1.7) marking the maximum radial extension (rn, ,x) of the neighboring ions ... 

Concerning the volume properties of the various polymorphs with respect to their chemical compositions, existing information on Pbca and P2 /c structures indicates linear dependence of mean Ml and M2 site dimensions on the ionic radii of the occupying cations (algebraic mean). As figure 5.21 shows, this linearity is more marked for Ml than for M2, which has distorted symmetry. 

Evaluation of the effects of chemistry on volume properties of amphiboles is comphcated by the high number of sites in which isomorphous substitutions take place. Limiting ourselves to the main structural classes C2lm, Pnma, and P2, m, we present the following evaluations. 

Based on equations 5.91 to 5.96, we may expect C2/m amphibole mixtures to have nearly ideal behavior in regard to volume properties. 

Volume properties in the system Mg7Si8022(OH)2-Fe7Si8022(OH)2 (cumming-tonite-grunerite) show well-defined linearity in the compositional range = 0.60 1.00 (Klein, 1964 Viswanathan and Ghose, 1965) Ve-... 

Most glasses can be made to crystallize if they are subjected io the right conditions of temperature and rate of cooling, which suggests that the glassy stale is like a supercooled liquid. This is not home out by measurements of density and other volume properties, which do not decrease in a linear manner as glass is cooled below its crystallization temperature. 

The two-dimensional drawing in Fig. I shows SiOy in the ordered, or crystalline, and in the random, or glassy, state to illustrate the difference on a submioroscopic scale. Figure 2 shows how the volume properties of a material would respond to temperature if they could be prepared as a glass, a supercooled liquid, or crystalline material.1... 

Fig 2, Volume properties of glass in comrast wilh crystalline solids as a function of temperature... 

The term property refers to a characteristic of a material and can be measured. Examples are pressure, temperature and volume. Properties may also be computed, such as, for example, internal energy, which cannot be measured directly. An extensive property is one whose value is the sum of each of the subsystems comprising the entire system. An example is a gas mixture, in which each constituent (or subsystem) has masses or volumes different from the original system. Thus, mass or volume is an extensive property. 

There are several indications that a crystalline solid is the most appropriate state to model the protein interior (Chothia, 1984). The very fact that protein structures can be determined to high resolution by X-ray diffraction is indicative of the crystalline nature of the protein. Additionally, the packing density and volume properties of amino acid residues in proteins are characteristic of amino acid crystals (Richards, 1974, 1977). In spite of the apparent crystallinity of the protein interior, most model compound studies have investigated either the transfer of compounds from an organic liquid into water (see, for example, Nozaki and Tanford, 1971 Gill et al., 1976 Fauch-ere and Pliska, 1983), or the association of solute molecules in aqueous solution (see, for example, Schellman, 1955 Klotz and Franzen, 1962 Susi et al., 1964 Gill and Noll, 1972). Both these approaches tacitly assume a liquidlike protein interior. 

The data on the volume properties of PMS liquids (i.e. coefficient of volumetric expansion, relative volume variation, coefficient of isothermal compressibility) are essential for the performance characteristics of oli-godimethylsiloxanes in hydraulic systems, hydraulic shocks and dampers they allow one to determine the working characteristics of these systems with some brands of PMS liquids at different temperatures and pressures. 

Thus, for this small ion, activation is not accompanied by significant reorganization of water in the solvent co-sphere as in the case of apolar solutes (p. 256). The volume of activation for the hydrolysis of t-BuEtMeS+ is positive, 6 cm3 mol-1 at 313 K (Brower and Wu, 1970) from which it has been concluded that the reaction involes breaking of a C—S bond. However, the complexity of volume properties of solutes in water indicates that AV values should be interpreted with caution. It would not be surprising if AV were controlled to a considerable extent by changes in the solvent co-sphere. 

The main volume properties of polymers are colour and transparency. Both may either be inherent to the polymer or caused by additions, e.g. dyes and other additives. Most polymers do not show differential absorption in visible light and are therefore colourless. The volume properties cover a wide range from glass clarity to full opaqueness. This is also the case for the surface properties they may vary from high gloss to full dullness (matt). 

A number of techniques have been employed to examine free volume properties of polymers. These include small angle x-ray scattering and neutron diffraction that have been used to determine denisty fluctuations to deduce free volume size distributions [4-7]. Photochromic labelling techniques by site specific probes have been developed to monitor the rate of photoisomerizations of the probes and from this deduce free volume distributions [8-11]. Additional probing methods used to probe voids and defects in materials such as scanning tunneling microscopy (STM) and... 

Liu, J., Jean, Y.C., Yang, H. (1995) Free volume properties of polymer blends by positron annihilation spectroscopy Miscibility . Macromolecules. 28, 5774. 

Since CP is governed by the heteronuclear dipolar interactions, the Tis time constant is related to the intemuclear distances and molecular mobility. The relaxation time describes the decay of intensity for longer contact times. Relaxation is mostly ensured by the Ft- lT homonuclear dipolar interactions. In contrast to the Tis time characteristic of the chemical group under study, relaxation time is a volume property averaged over the distance of ca. 

G.S. Kell, Precise representation of volume properties of water at one atmosphere, J. Chem. Eng. Data, 12 (1967) 66-89. 

Attempts to quantify electrocatalytic activities on the basis of correlation dependences that take into account the volume properties [79-81,97,98] made it necessary to obtain well-characterized experimental data, and thus stimulated the improvement of perovskite electrode construction. Methods were developed for determining the real surface area of disperse perovskites in the electrodes with polymer binders [99], and also for measurements on quasi-smooth, highly conductive ceramics [81, 82,100]. This experience was applied successfully later in the studies of HTSC electrodes. 

The phase equilibria and volume properties of the systems KF-K2TiF6 and KCl-K2TiFe were studied in detail by Danek and MatiaSovsky (1989). They found that in these binary systems, the compounds KsTiFy and KsTiFeCl are formed according to the reactions... 

The formation of KsTiFy and KsTiFeCl does not substantially affect the volume properties. This indicates that, either these compounds dissociate in the melt to a... 

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