Quasi-binary systems

The solid curves in the figure represent the molecular weight dependence of r)0 for quasi-binary system consisting of a fractionated xanthan sample and 0.1 mol/1 aqueous NaCl. The circles for quasi-ternary solutions almost follow them at the same c, except at small 2. Thus, to a first approximation, r)o of stiff polymer solutions is independent of molecular weight distribution, and may be treated as a function of Mw or Mv and c. 

In binary systems of a light gas and members of the n-alkane homologuous series in almost all cases type II phase behaviour is found for the lower members of the n-alkane series. With increasing carbon number type IV phase behaviour is found followed by type HI phase behaviour at high carbon numbers. Systems of CO2 + n-alkanes show type II phase behaviour for n-alkane carbon numbers 12, type IV phase behaviour for =13 and type HI phase behaviour for n S14 [11, 12]. This transition from type II to type HI phase behaviour via type IV phase behaviour seems to be the rule, allthough in most binary families type IV phase behaviour is only found at broken values of n in so-called quasi-binary systems [13, 14]. 

We deal in this section with quasi-binary systems in which more than one product phase A, B forms between the reactants A(=AX) and B(=BX) (Fig. 6-9). The more interfaces separating the different product phases, the more likely it is that deviations from local equilibrium occur (the interfaces become polarized during transport as indicated in Fig. 6-9, curve b). Polarization of interfaces is the theme of Chapter 10. If, however, we assume that local equilibrium is established during reaction, the driving force of each individual phase (p) in the product is inversely... 

Chapters 6 and 7 dealt with solid state reactions in which the product separates the reactants spatially. For binary (or quasi-binary) systems, reactive growth is the only mode possible for an isothermal heterogeneous solid state reaction if local equilibrium prevails and phase transitions are disregarded. In ternary (and higher) systems, another reactive growth mode can occur. This is the internal reaction mode. The reaction product does not form at the contacting surfaces of the two reactants as discussed in Chapters 6 and 7, but instead forms within the interior of one of the reactants or within a solvent crystal. 

In practice, it is often feasible to reduce the multicomponent crystal in respect of its transport behavior to a quasi-binary system. Let us assume that the diffusion coefficients are DA>DB>DC, Dd, etc. The quasi-binary approach considers C, D, etc. as practically immobile, which means that A and B are interdiffusing in the im-... 

Figure 11-17. a) Phase diagram of the quasi-binary system AX-BX with an extended miscibility gap. b) Schematic electrolysis cell A/AX/BX/B. Cation vacancy drift and the mechanism of interface motion are indicated. 

In respect to Si3N4 ceramics the quasi-binary system Si3N4-Si02 is of greatest importance (Fig. 5). However, if the vapour phase is included in the... 

As can be concluded from Eq. (1), the decomposition will be significantly reduced with increasing N2 pressure. Therefore at high N2 pressure, the condensed phases can be treated as a quasi-binary system up to higher temperatures. 

Fig. 5. Temperature-concentration section (isopleth) through the Si-N-0 phase diagram from Si02 to Si3N4 [69]. Below 2114 K it is a quasi-binary system. G = gas phase LS = oxide nitride liquid LM = metallic liquid...

Fig. 2. The composition dependence of Ariij (mol/mol) around a methanol molecule for the (a) binary system methanol-water and for the quasi-binary system MA -dimethylformamide-methanol-water (b) jcp = 0.04 (c) jcp = 0.08 (d) jcp = 0 lb Zm = (- M + - w)) ...

Fig. 8. The composition dependence of (mol/mol) around a water for the quasi-binary system...

Xu and xi(23) represent the free energy parameter of the binary systems solvent 1/polymer i (i=2 and 3), and the quasi-binary system solvent 1/blend 23. Consequently, X23 describes the polymer 2/polymer 3 interaction energy, which cannot be directly measured. Yet, Xi(23) Xi2> and X13 are experimentally accessible quantities, and X23 may be calculated from Equation 1. 

Only solid solutions were present under the conditions of the investigation of the Fe-Co [242], Ni-Cu [250], and SnTe-PbSe [262] systems given in Table 7. The thermodynamic activities, excess Gibbs energies, mixing enthalpies and excess entropies were determined by the use of the ion intensity ratio method for the Fe-Co and Ni-Cu systems as described for the melts. The partial pressure of the molecules SnTe, SnSe, PbTe, and PbSe were obtained for different compositions of the quasi-binary system SnTe-PbSe using the isothermal evaporation technique. 

Table 20. Summary of mass spcctrometric Knudsen effusion studies since about the year 1980 of quasi-binary systems of metal halides. (The gaseous species or solid compounds are underlined if enthalpies of dissociation or formation are given)... 

The data for the hetero-complexes in Table 24 were obtained by a second-law evaluation. The accuracy of these data is checked by the computation of second-law dissociation enthalpies of dimer homo-complexes additionally present in the vapor of the quasi-binary systems. The dissociation enthalpies obtained in this way in general agree very well with the data in Table 23 resulting by vaporizing pure metail halides (cf e.g. Ref 61). 

In the field of metal halides there has been a particularly large increase of our knowledge of gaseous metal iodide homo- and hetero-complexes. Thermodynamic data of gaseous species and condensed phases of quasi binary systems with mixed anions have been determined. 

Figure 4.22 Phase diagram of the quasi-binary system Ca0-P205-H20 at a water partial pressure of 65.5 kPa. (After Riboud (1973).) Note that incongruent melting of hydroxyapatite (HAp) occurs at 1570°C under formation of a -C3P (a -TCP) and C4P (TTCP).

In a quasi-binary system, interdiffusion of ions also results in a so-called interdiffusion diffusion that is also rate-limited by the diffusivity of the slower of the two ions. This process occurs, e.g., when solid-state reactions between ceramics or ion-exchange experiments are carried out. Solid electrolytes can be used as sensors to measure thermodynamic data, such as activities and activity coefficients. The voltage generated across these solids is directly related to the activities of the electroactive species at each electrode. 

Figure 3.2 Volume fraction of diluent and DVB concentration (wt%) for the incipience of phase separation in copolymerization of styrene and DVB. Diluent 1) toluene (a quasi binary system, x = 0.46) 2) isooctane xfstyrene-polymer) = 0.46, xOsooctane-polymer) = 1.40, xbtyrene-isooctane) = 0.40 3) polystyrene mol.wt. 50,000...

First level every constituent is considered as monodisperse. For a modi-fied-thermosetting polymer undergoing polycondensation, this approximation level leads to a quasi-binary system consisting of... 

Other multicomponent polymer solutions of interest consist of chemically different polymers dissolved in a solvent or a single polymer in a mixture of different solvents. Their phase equilibrium behavior is important in relation to many practical problems, but it is much more complex and difficult to tinalyze and predict than that of quasi-binary systems. 

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