One-phase region

Finally, we consider the isothennal compressibility = hi V/dp)y = d hi p/5p) j, along tlie coexistence curve. A consideration of Figure A2.5.6 shows that the compressibility is finite and positive at every point in the one-phase region except at tlie critical point. Differentiation of equation (A2.5.2) yields the compressibility along the critical isochore ... 

Figure A2.5.17. The coefficient Aias a fimction of temperature T. The line IRT (shown as dashed line) defines the critical point and separates the two-phase region from the one-phase region, (a) A constant K as assumed in the simplest example (b) a slowly decreasing K, found frequently in experimental systems, and (c) a sharply curved K T) that produces two critical-solution temperatures with a two-phase region in between.

The phase-diagram (temperature vs concentration) for a eutectic two-component alloy shows at low temperatures a central two-phase region and two solid one-phase regions at low and high relative concentrations. At the eutectic temperature the liquid phase at an intermediate concentration can all of a sudden coexist with the two solid phases. Upon further increase of temperature, the liquidus lines open up a V-shaped liquid... 

Recently, Chester has described (21) how a consideration of the phase diagram of the mobile phase shows that a one-phase region (Figure 1.1) is available for the selection of the mobile phase parameters, and that the boundaries separating... 

The heat capacity of the different one-phase regions obtained in this study can be integrated to give the following values. 

Below some critical surfactant concentration, the system is two-phase with excess oil or water depending on the oil/water concentration. On adding more surfactant, the system moves into a one-phase region with normal micelles forming in water-rich systems. The water constitutes the continuous phase, solvating the headgroups of the surfactant whose hydro-phobic tails solubilise oil in the core of the micelle. In oil rich systems, reverse-micelles form. With further increases in surfactant composition. 

In the one phase region, when the sample was seen to flow easily, it was said that the system was still a sol. When the meniscus was seen not to deform under it own weight, the system was considered a gel. The sol-gel transition was taken at the onset of meniscus deformation when the tube is held horizontal. Syneresis and precipitation were detected by the presence of water at the gel surface or by the existence of large turbid aggregates which could be centrifugated. 

Up to this point, we assumed that a system exists in a one-phase region over the range of densities and energies sampled. If a phase transition exists then in principle,... 

This system was examined up to 82 wt % lipid. l

phase region an Ltt phase. 2q> Two-phase region (La+ dilute aqueous lipid)... 

Figure 2.42. The Cu-Zn system phase diagram and microstructure scheme of the diffusion couple obtainable by maintaining Cu and Zn blocks in contact for several days at 400°C. Shading indicates subsequent layers, each one corresponding to a one-phase region. The two-phase regions are represented by the interfaces between the one-phase layers (adapted from Rhines 1956).

Fig.Z Adsorption isotherms of the lattice gas model with (a) nearest neighbor attractive interaction, and (b) nearest neighbor repulsion and next nearest neighbor attraction of the same strength. Only 0 < 1/2 is shown because the isotherms are antisymmetric around the point 0 = 0, + e = 0 in this case, (c) Adsorption isotherms of a lattice gas with non-additive interactions with P = 1.5 (cf. text) for fixed reduced temperature, T/T,. Dotted curve describes the two branches 0 of the coexistence curve separating the two-phase region from the one-phase region. Cases (a), (b) are taken from Binder and Landau, case (c) from Milchev and Binder. )...

Note A ringing gel is often a hydrogel with a surfactant as a third component and has a composition within an isotropic, one-phase region of its ternary phase diagram... 

One-phase regions may touch each other only at single points, never along boundary lines. Adjacent one-phase regions are separated from each other by two-phase regions involving the same two phases. 

To study the nature of this rapid polymer transport in detail, this section will be concerned with a series of experimental measurements on one particular system, namely a solution of dextran T10 (N5W 10 ) with a uniform concentration of 135 kg m-3 and an imposed gradient of a linear, flexible polyvinylpyrrolidone) (NTn 3 x 10s) (PVP 360). This gradient initially extended from 5 kg m3 to zero concentration. The choice of using the polymers at this concentration was based upon our earlier work441 in which it was shown that nearly maximal transport rates of PVP 360 occur in such a system. This system will be referred to as the standard system. The phase diagram of this PVP 360/dextran T10 mixture clearly demonstrates that the transport experiments were performed within the one-phase region 47). 

Figure 7.14 Complete phase diagram of the water + p-lactoglobulin + gum arabic system at 20 °C and pH = 4.2. Features indicated are , tie-lines , binodal points I, one-phase region II, two-phase region. Reproduced from Schmitt et al. (1999) with permission.

At 20°C, moving from left to right, we cross from a one-phase region (homogeneous micellar, O/W) into a two-phase region (oil plus homogeneous micellar, O/W). 

It should be emphasized that the criterion for macroscopic character is based on independent properties only. (The importance of properly enumerating the number of independent intensive properties will become apparent in the discussion of the Gibbs phase rule, Section 5.1). For example, from two independent extensive variables such as mass m and volume V, one can obviously form the ratio m/V (density p), which is neither extensive nor intensive, nor independent of m and V. (That density cannot fulfill the uniform value throughout criterion for intensive character will be apparent from consideration of any 2-phase system, where p certainly varies from one phase region to another.) Of course, for many thermodynamic purposes, we are free to choose a different set of independent properties (perhaps including, for example, p or other ratio-type properties), rather than the base set of intensive and extensive properties that are used to assess macroscopic character. But considerable conceptual and formal simplifications result from choosing properties of pure intensive (R() or extensive QQ character as independent arguments of thermodynamic state functions, and it is important to realize that this pure choice is always possible if (and only if) the system is macroscopic. 

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