Near-critical region, definition

Local density enhancements, being by definition short-ranged, are not peculiar to the highly compressible near-critical region. Very close to the solute molecule, the local environment differs markedly from the bulk (for example, the local density in the first solvation shell at bulk near-critical conditions is p (R) = 1.43 pc when p = 0.31 and T/Tc = 1.02). However, even this region does not appear to have a liquid-like character, as suggested by other spectroscopic experiments (35-36),... 

For most experimental conditions, the p-V-T data of adsorptive gases are available [42,44]. Updated p-V-T data are published in Journal of Physical and Chemical Reference Data from time to time. However, all of the published data are also calculated by an equation of state and arranged in tables. To obtain the data for a specified experimental condition, one has to estabhsh a functional relationship between molar volume V and T for a specified p first, and between and p for a specified T afterward. Although the readers are warned that any interpolation is unreliable for the near-critical region [44], an interpolated entry yielded by a locally smooth curve does make sense. For every molar volume that is calculated from the above-established correlation under the experimental condition, there is a definite value for the compressibility factor z as calculated by... 

The other major difference between fluid metals and semiconductors concerns the phase behavior and the electronic character in various regions of the temperature-density plane. The low-temperature liquid-vapor equilibrium of semiconducting liquids involves two nonmetallic phases whereas the vapors of metallic elements are, by definition, in equilibrium with a liquid metal phase. The metallic state develops in fluid semiconductors when the temperature and pressure are high enough to disrupt the structural order responsible for semiconducting electronic structure. If this occurs near the critical region, there exists the possibility of rapid MNM transitions and strong interplay between the electronic properties and critical density fluctuations. In this respect, fluid metals and semiconductors behave similarly under extreme conditions whereas they are markedly different near their respective triple points. 

Whenever a system has a composition that lies in the polyphasic region, it will generally separate (at equilibrium) into two phases, the representative points of which are located at the two extremes of the tie-line (see Fig. 3). In most cases the tie-hne is inchned i.e., one of the phases is rich in surfactant because it is located relatively near A or far from the OW side. If it is also located far from the AW and AO sides, then it contains both W and O in sizable amounts and fits the definition of a microemulsion (shaded region). Near the upper end of the tie-line in Fig. 3, it is an O/W type microemulsion. The other extreme of the tie-line is located near the OW side and near one of the component vertices (O in Rg. 3) and thus contains essentially one of the components. It is called an excess phase, in this case an oil excess phase. In most cases, particularly with ionic surfactant, the excess phase does contain a very small concentration of amphiphile, about the critical micelle concentration (cmc). In other words, the excess phase does not contain micelles, and as a consequence no micellar solubilization of the other phase can occur in the excess phase, an important feature when the mass balance is to be discussed. 

As in Section 2.7 we now formulate as a condition for the onset of the limit cycle that the oscillator in (6.24) is not damped but amplified, i.e., x < 0, but still A > 0. We expect that x as defined in (6.23) is some function of the external parameters of the network such that at least near the thermodynamic equilibrium we have X > 0 and only for sufficiently strong nonequilibrium conditions for the external parameters X becomes negative. This behaviour is typically reflected by the conditions (2.75) and (2.76) for our model in Section 2.7. At the critical point, the so-called bifurcation point, which separates the damped region from the amplifying one, we have X = 0 and thus from the definition of x in (6.23) opposite signs of and 2 2 2 2 other hand we... 

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