Si . solution

The D and E positions have 15 B near neighbors. The E position can be occupied by transition metals. The D hole is occupied except in the Si solution. The center of the D hole is poorly defined. Within this hole, Cu or Ge atoms are distributed on two separate positions, situated 40 pm and 80 pm apart, respectively. 

In this example, one solute is used on the column. The / b(BSi) and J(BSi) values control the afiinity of the Si solute for the stationary phase. The parameters are shown in the Parameter Setup 6.4. In the report, the position of each solute cell is recorded in groups of five rows from 0 to 100 after a certain... 

The goal of theory and computer simulation is to predict S i) and relate it to solvent and solute properties. In order to accomplish this, it is necessary to determine how the presence of the solvent affects the So —> Si electronic transition energy. The usual assmnption is that the chromophore undergoes a Franck-Condon transition, i.e., that the transition occurs essentially instantaneously on the time scale of nuclear motions. The time-evolution of the fluorescence Stokes shift is then due the solvent effects on the vertical energy gap between the So and Si solute states. In most models for SD, the time-evolution of the solute electronic stracture in response to the changes in solvent environment is not taken into accoimt and one focuses on the portion AE of the energy gap due to nuclear coordinates. 

Reference electrode salt bridge in solvent si solution S in solvent s H2 Pt (II)... 

This is the case of SI solutions discussed in the next chapter. 

We start by defining a symmetrical ideal (SI) solution as a system for which the chemical potential of each species has the form... 

Clearly, an ideal-gas mixture is a particular example of a SI solution, as we have seen in the previous section (particularly equation 5.18). Here we discuss a real mixture at normal liquid densities, consisting of interacting molecules. We shall examine first the conditions on the molecular properties (specifically on the intermolecular interactions) that lead to this particular form of the chemical potential. In section 5.2.2, we shall examine the local conditions under which relation (5.20) is achieved. 

Very similar components A sufficient condition for SI solutions... 

It is interesting to note that even mixtures of isotopes sometimes show measurable deviations from SI solutions. Examples are mixtures of 36Ar and 40Ar (Calado et al. 2000) and mixtures of CH4 and CD4 (Calado et al. 1994). However, mixtures of H20 and D20 do not show any significant deviations from SI solutions (Jancso and Jakli 1980). 

A classical example is a mixture of ethylene bromide (EB) and propylene bromide (PB). Figure 5.2a shows the partial and the total pressures of these mixtures as a function of the mole fraction of (PB) at 85 °C, Based on the work of von Zawidzki (1900) quoted by Guggenheim (1952). These two components clearly cannot be considered as being identical, or very similar. Yet, the fact that they form an SI solution in the entire range of compositions is equivalent... 

Clearly, (5.35) and (5.36) are equivalent conditions for SI solutions, in the sense that each one follows from the other. 

We note that the necessary and sufficient condition, Aab = 0, for SI was derived here and is valid for mixtures at constant P, T. The condition (5.38) is very general for SI solutions. It should be recognized that this condition does not depend on any model assumption for the solution. For instance, within the lattice models of solutions we find a sufficient condition for SI solutions of the form (Guggenheim 1952)... 

We have seen in section (5.17) that (5.41) is a sufficient condition for an SI solution. 

Since we have shown that condition (d) is a sufficient condition for SI solutions, any condition that precedes (d) will also be a sufficient condition. In general, the arrows in (5.43) may not be reversed. For instance, the condition (c) implies an equality of the integrals, which is a far weaker requirement than equality of the integrands gap. It is also obvious that (d) is much weaker than (c) i.e., the Gap may be quite different and yet fulfill (d). It is not clear whether relation (a) follows from (b). If we require the condition (b) to hold for all compositions, and all P, T it is likely that (a) will follow. 

We end this section by considering the phenomenological characterization of SI solutions in terms of their partial molar entropies and enthalpies. If one assumes that equation (5.35) is valid for a finite interval of temperatures and pressures, then, by differentiation, we obtain... 

The SI solutions are characterized by zero excess thermodynamic functions. Clearly, the phenomenological characterization of SI requires stronger assumptions than the condition (5.38). 

Finally, we note that the condition (5.38) for SI solutions applies only for systems at constant P, T. This condition does not apply to systems at constant volume. 

We have discussed in this section the condition for SI solutions for a two-component system. One can show that similar conditions for SI solutions apply to multicomponent systems. We can prove, based on the KB theory, and with a great deal of algebra, that in three- and four-component systems, a necessary and sufficient condition for SI solutions, in the sense of (5.35) for all a is... 

The symmetric ideal (SI) solution is obtained for similar components in the sense that Aab = 0 for all compositions 0 < xA < 1, which again leads to (5.69)... 

Note that some authors refer to the symmetrical convention as the limiting behavior ofy, — 1 as x, — 1, see, for example, Prausnitz et al. (1986). However, this limiting behavior is manifested for any mixture, when one of its mole fractions approaches unity. Similarly, for any mixture, when x, —> 0, we have ji —> 1. The concept of SI solution is very different from these limiting behaviors. 

In the phenomenological characterization of small deviations from SI solutions, the concepts of regular and athermal solutions were introduced. Normally, the theoretical treatment of these two cases was discussed within the lattice theories of solutions. Here, we discuss only the very general conditions for these two deviations to occur. First, when Pt ab does not depend on temperature, we can differentiate (6.19) with respect to T to obtain... 

This is the case of athermal solution, i.e., no excess enthalpy but finite excess entropy, both with respect to SI solutions. 

The term regular solutions was first coined by Hildebrand (1929). It was characterized phe-nomenoligically in terms of the excess entropy of mixing. It was later used in the context of lattice theory of mixtures mainly by Guggenheim (1952). It should be stressed that in both the phenomenological and the lattice theory approaches, the regular solution concept applies to deviations from SI solutions, (see also Appendix M). 

The second case, referred to as symmetric ideal (SI) solutions, occurs whenever the various components are similar to each other. There are no... 

Figure 6.1 shows such curves for mixtures of carbon disulphide and acetone, and the second for mixtures of chloroform and acetone. The first shows positive deviations from SI behavior in the entire range of compositions the second shows negative deviations from SI solution. 

This means that a mixture of A and B differing in size will always behave as an SI solution. Hence, the corresponding excess function is zero ... 

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