Near-equilibrium conditions

Under near-equilibrium conditions the shape of this curve is related to two contributions, the compositional dependence of the configurational entropy of the guest ions, and the contribution to the chemical potential from the electron gas [31]. 

In the near-equilibrium conditions, the coverage at each temperature is close to its equilibrium value. Thus... 

NaCl-KCl-PuCl3-MgCl2, under near-equilibrium conditions. Virtually all of the impurities concentrate in the anode. Of the impurities usually present in plutonium, only americium concentrates in the salt. 

Experiments were conducted in a large (-26 m3) radon/thoron test facility (RTTF) designed for calibration purposes and simulation studies (Bigu, 1984). A number of different materials were exposed in the RTTF to a radon/radon progeny or thoron/thoron progeny atmosphere. Exposure of the materials was carried out under laboratory-controlled conditions of radiation level, aerosol concentration, air moisture content and temperature. The materials used were in the form of circular discs of the same thickness (-0.5 mm) and diameter (-25 mm), and they were placed at different locations on the walls of the RTTF at about 1.6 m above the floor. Other samples were placed on horizontal trays. Samples (discs) of different materials were arranged in sets of 3 to 4 they were placed very close to one another to ensure exposure under identical conditions. Exposure time was at least 24 hours to ensure surface activity equilibrium, or near equilibrium, conditions. 

Fig. 3.42. Depletion below solar abundances of elements in the H I gas towards f Ophiuchi plotted against atomic mass number in (a) and condensation temperature in (b), based in part on the curve of growth shown in Fig. 3.11. Vertical boxes indicate error bars. The dotted curve in the left panel represents an A-1/2 dependence expected for non-equilibrium accretion of gas on to grains in the ISM. The condensation temperature gives a somewhat better, though not perfect, fit, suggesting condensation under near-equilibrium conditions at a variety of temperatures either in stellar ejecta or in some nebular environment. Note the extreme depletion of Ca ( Calcium in the plane stays mainly in the grain ). After Spitzer and Jenkins (1975). Copyright by Annual Reviews, Inc.

As shown in Section 3.3.13, near equilibrium conditions can be obtained by choosing an arbitrarily high value for the mass transfer capacity constant KLa. 

Highly structured, 3-D nanoparticle-polymer nanocomposites possess unique magnetic, electronic, and optical properties that differ from individual entities, providing new systems for the creation of nanodevices and biosensors (Murray et al. 2000 Shipway et al. 2000). The choice of assembly interactions is a key issue in order to obtain complete control over the thermodynamics of the assembled system. The introduction of reversible hydrogen bonding and flexible linear polymers into the bricks and mortar concept gave rise to system formation in near-equilibrium conditions, providing well-defined stmctures. 

In the absence of secondary effects as part of the RPC distribution process(es), i.e., when no temperature- or ligand-mediated conformational effects, slow chemical equilibrium, or pH-dependent ionization events occur, then the resolution, Rsi, between two adjacent peptides separated under equilibrium or near-equilibrium conditions can be expressed as... 

It may seem from the above discussion that it is impossible to use even batch isotherm measurements to design HPLC (or SPE) separations. This is not so, however, at least when the HPLC separation occurs under near-equilibrium conditions. Nonlinear chromatographic peaks can be simulated [38] once the corresponding isotherms have been measured. In this case one does not need a physical interpretation of the isotherm equation s constants they can be regarded merely as interpolation factors. Separately measured isotherms of the two compounds are satisfactory in many cases because - as mentioned above - competition often has only minor influence on the separated peaks position and shape. 

The experimental data, Cbi vs time, were compared to the model predictions by choosing the parameters m0smi and m, that gave the best fit with the competitive adsorption data. A nonlinear parameter estimation package was used [39] which employed a weighting factor for the residuals proportional to 2 so that the information obtained near equilibrium conditions was highlighted. 

Two unit operations are used in the equilibration of the salt and metal phases (1) intermixing of salt and metal, and (2) disengagement of salt and metal. Because this is a batch extraction, both operations (intermixing and disengagement of phases) occur sequentially in the same vessel. For practical operation of the molten salt extraction process, attainment of equilibrium or near-equilibrium conditions (when the value of F approaches 1) in a relatively short period of time is essential. 

Note that at equilibrium wr - Ar - 0 however, situations may arise where (i) wr - 0, Ar 0, corresponding to inhibited reactions that may be remedied by introduction of a suitable catalyst, (ii) wr 0, Ar - 0, as in thought experiments in which a reaction is carried out under near-equilibrium conditions. 

Storage modulus measurements. All measurements were taken at temperatures near 45 °C above the network Tg s. Representative network true stress versus strain curves from the tensile experiments are shown in Fig. 2. The ordinate axis, true stress, is normalized by 3eRT to account for the different test temperatures employed. The resultant curves are thereby directly comparable for structural differences, since the instantaneous slopes are proportional to l/M, after Eq. (2). The curves of all five networks are linear and reversible up to strains of around 10 percent. The reversibility suggests that the measurements were performed under near-equilibrium conditions and that the networks were stable at the high test temperatures employed. 

Perhaps most prominent of these materials are the organic conducting and superconducting salts based on the so-called ET compounds, in which BEDT-TTF 3-X is the donor (cation in the salt), generally in a 2 1 ratio with the acceptor (anion in the salt) (Williams et al. 1991). One of the most widely studied of these salts is (ET)2l3, for which at least 14 different phases have been reported (Carlson et al. 1990 Williams et al. 1991), although the a and phases tend to dominate (Carlson et al. 1990 Shibaeva et al. 1990). It has been shown that a is the kinetically favoured product (>90 per cent) under conditions of high current density and a small amount of water or oxidant added to the crystallization medium. Under more nearly equilibrium conditions (i.e. much lower current density) and dry solvent (tetrahydrofuran), pure phase can be obtained, suggesting that it is the thermodynamically preferred form. Intermediate conditions apparently lead to concomitant crystallization of the two forms (Carlson et al. 1990 Williams et al. 1991). 

Zuddas P., Seimbille F., and Michard G. (1995) Granite-fluid interaction at near-equilibrium conditions experimental and theoretical constraints from Sr contents and isotopic ratios. Chem. Geol 121, 145-154. 

Under equilibrium or near-equilibrium conditions, the distribution of volatile species between gas and water phases can be described in terms of Henry s law. The rate of transfer of a compound across the water-gas phase boundary can be characterized by a mass-transfer coefficient and the activity gradient at the air—water interface. In addition, these substance-specific coefficients depend on the turbulence, interfacial area, and other conditions of the aquatic systems. They may be related to the exchange constant of oxygen as a reference substance for a system-independent parameter reaeration coefficients are often known for individual rivers and lakes. 

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