Phase volumes, defined

One of the most attractive roles of liquid liquid interfaces that we found in solvent extraction kinetics of metal ions is a catalytic effect. Shaking or stirring of the solvent extraction system generates a wide interfacial area or a large specific interfacial area defined as the interfacial area divided by a bulk phase volume. Metal extractants have a molecular structure which has both hydrophilic and hydrophobic groups. Therefore, they have a property of interfacial adsorptivity much like surfactant molecules. Adsorption of extractant at the liquid liquid interface can dramatically facilitate the interfacial com-plexation which has been exploited from our research. 

If 17 is defined to be the phase volume enclosed by the microcanonical energy surface, the exponential form, in the limit AE —> 0, becomes... 

Let E, E, and E denote the partial statistical integrals corresponding, respectively, to librational, precessional, and rotational subensembles, which are defined as integrals of the Boltzmann factor exp( h) over corresponding phase volumes ... 

For a given set of values for H, V, and n, values of n, n", and n " can be calculated if the molar enthalpies and molar volumes of the three phases can be determined. The molar volumes can be obtained experimentally, but the absolute values of the molar enthalpies are not known. In order to solve this problem, we make use of the concept of standard states. We choose one of the three phases and define the standard state to be the state of the system when all of the component exists in that phase at the temperature and pressure of the triple point. If we choose the triple-primed phase as the standard phase, we subtract nH " from each side of Equation (8.50) and obtain... 

Tk represents the rate of mass generation of phase k per unit volume. It is noted that the unit volume in this context is that of the gas-solid system. If a phase is defined in a physical sense such as the solid phase or the gas phase, Tk may be caused by chemical reactions or phase changes. On the other hand, when a phase is defined in a dynamic sense [Soo, 1965], Tk may result from the size change due to attrition or agglomeration in addition to the chemical reaction or phase change. From the mass balance of the mixture, we have... 

For the assessment of the extent of change of the phase ratio of a HPLC column system with temperature or another experimental condition, several different experimental approaches can be employed. Classical volumetric or gravimetric methods have proved to be unsuitable for the measurement of the values of the stationary phase volume Vs or mobile phase volume Vm, and thus the phase ratio ( = Vs/Vm). The tracer pulse method266,267 with isotopically labeled solutes as probes represents a convenient experimental procedure to determine Vs and V0, where V0 is the thermodynamic dead volume of the column packed with a defined chromatographic sorbent. The value of Vm can be the calculated in the usual manner from the expression Vm = Eo — Vs. In addition, the true value of Vm can be independently measured using an analyte that is not adsorbed to the sorbent and resides exclusively in the mobile phase. As a further independent measure, the extent of change of 4> with T can be assessed with weakly interacting neutral or... 

Let us introduce the VOF method in more detail. The phase volume function fi(r) is defined by/) = 1 in phase 1 and f x — 0 in phase 2 cf. Eq. (1). A discrete analog of the phase volume function fx is the scalar field tpi known as the volume fraction (or area fraction in spatially 2D cases). It represents the fraction of the volume of the voxel with size h and the coordinate of its center r filled with the phase 1,... 

The ratio between the volumes of the soft component and the polystyrene matrix is known as the phase volume ratio (where the soft component is defined as the rubber component including the occlusions). The volume ratio depends on the rubber content, the number and size of the occlusions and the degree of grafting. The importance of the phase volume ratio for the mechanical properties of the polymer was first recognized by Cigna, and was later confirmed in a series of investigations carried out by Bucknall. 

---