Ternary systems probabilities

The effect of adding a surfactant, (NaDDS), was also investigated. One such case only is shown in Fig. 6 where BE is replaced by a 5 1 mixture of BE-NaDDS. The main effect of NaDDS is to increase the miscibility range of the oil in water. Various ratios of BE-NaDDS were used and, as a first approximation, the change in the phase diagram is directly proportional to the concentration of NaDDS. The addition of a surfactant probably stabilizes the microstructures which were already present in the ternary system BE-DEC-H O and decreases the quantity of BE needed to solubilize DEC. Therefore the presence of a surfactant is useful but not essential to the stability of microemulsions. 

Thermodynamic optimisation is probably the largest single area of reported work m die jotmial CALPHAD. It invariably concerns binary and ternary systems and can... 

The ternary systems, Cr(VI)/GSH/sugars, have been studied in detail by Kozlowski and coworkers.60 EPR signals were observed for the reactions of Cr(V) with biological reductants (such as GSH) in the presence of various sugars that possess 1,2-diol moieties [such as D-glucose (11) or D-ribose].72 Compound 11 is a probable candidate ligand responsible for Cr(V) coordination in the giso= 1.979 species in Cr (VI)-exposed animal tissues.19... 

The ternary systems display a variety of structural chemistry depending on the sizes of the alkaline and lanthanide metals (Scheme 3 Fig. 3 [43, 45-57]). The smaller alkali cations determine the expected coordination structures as found in salt-like compounds, e.g., Na3Y (NH2)6 or KY(NH2)4. Layer structures are observed in alkali metal poor systems like MLa2(NH2)7 while cesium derivatives, apart from the lanthanum compounds, form perowskit-like arrangements as in CsEu(NH2)3 and Cs3Ln2(NH2)9. The mono ammoniates of some Cs-systems are probably metastable. Preparation of analogous ternary systems with Li were unsuccessful in contrast to, e.g., LiAl(NH2)4 [58]. 

Figure 3.22 (right) represents the three-phase temperature intervals for Q2E4 and Q2E5 vs the number n of carbon atoms of n-alkanes (for the phase behaviour of ternary systems see Section 3.4.2, Figure 3.26). The left part of Figure 3.22 shows the detergency of these surfactants for hexadecane. Both parts of Figure 3.22 indicate that the maximum oil removal is in the three-phase interval of the oil used (n-hexadecane) [22]. This means that not only the solubilisation capacity of the concentrated surfactant phase, but probably also the minimum interfacial tension existing in the range of the three-phase body is responsible for the maximum oil removal. Further details about the influence of the polarity of the oil, the type of surfactant and the addition of salt are summarised in the review of Miller and Raney [23].

Ham assumes that the formation probability of the sequence MjMj, M2M3) is equal to the formation probability of the opposite sequence M2M j" ( M3M], M3M2)t. In a ternary system, the probability of monomer M2 addition to the active centre will be given by the ratio of this addition rate to the sum of the rates of all possible addition types... 

Numerical calculations have been carried out for (i) ternary systems consisting of rods of two lengths x and x and a diluent with x = 1 (ii) solutions of polydisperse rods having a most probable distribution (iii) a Poisson distribution of rods in solution and (iv) various Gaussian distributions of rods in a diluent In all cases longer rods are preferentially partitioned into the nematic phase. For Xa = 2xb in case (i) the ratio of the concentration of either of the species in one of... 

At this point, the question is is the picture of SAS conditioning thermodynamic behaviors complete Probably not. Indeed, very complex interactions are possible in ternary systems. The approach proposed is encouraging from another point of view. Even if a very complex behavior develops in the ternary systems, a systematic analysis of VLEs can allow the identification of the regions in which effective precipitation can be obtained. 

From a more recent investigation by Smits and de Leeuw, it would, however, appear probable that the acetaldehyde-paraldehyde system is not so simple as was found by Hollmann, but that we have here a case of a pseudo-ternary system in which are present not only the simple acetaldehyde molecules (CH3. CHO), but also the molecules of paraldehyde, (CH3. CHO)3, and of metaldehyde, (CHg. CHO)4. 

According to Menger a simple nucleophilic catalysis is considered to occur in methanolysis of tetrachlorophthalic anhydride ia the presence of pyridine, and charge-transfer complex formation has been confirmed neither by kinetic studies nor by spectrometry. Also, the conductivity of a binary solution anhydride-tertiary amine is much lower than that of the ternary system containing an epoxide and does not change with time. Antoon and Koenig also reject the formation of zwitterions. Hence, the first modification of Fischer s mechanism performed by Tanaka and Kakiuchi is not appropriate, which was later admitted by the authors The formation of ionic species probably proceeds by the anionic mechanism... 

Litvinov [26] evolved a graphical method for determining the probability that azeotropy occurs in ternary systems. He shows that ternary azeotropes may occur even when the system in question has no binary azeotropes. The e.xistence of a quaternary azeotrope, however, is associated with the occurrence of binar - and ternary azeotropes. Marinichev and Susarev [56a] elaborated an extensive system of equations in order to infer physical properties of quaternary azeotropes. 

Carbides, Silicides, and Germanides. The standard heat of formation and the dissociation energy of TiCjCg) have been determined as — 730 9 and 160 + 8 kJ mol , respectively, using the mass spectrometric Knudsen effusion technique. The standard heat and entropy of formation of TijSijis) have been reported as — 580 kJ moP and 272 e.u., respectively. A thermodynamic analysis of the co-reduction of TiOj with Si02 by carbon at elevated temperatures has shown that the formation of TiSi is more probable than TiSij. Phase equilibria in the Ti-Nb-Ge ternary system have been investigated. ... 

The functional (15) determines via the Boltzmann weight exp(—/ o[d>]) the probability of each configuration of the order parameter field (r) to occur in thermal equilibrium. In the ternary system under consideration, the order parameter field d>(r) is identified with the local concentration difference of oil and water. The local amphiphile concentration is considered to be integrated out in this model [41]. 

How many ways can columns be coupled for multiconponent distillation Lots For exanple. Figure 11-9 illustrates nine ways in which columns can be coupled for a ternary system that does not form azeotropes. With more conponents, the number of possibilities increases geometrically. Figure 11-9A shows the normal sequence, where the more volatile conponents are removed in the distillate one at a time. This is probably the most commonly used sequence, particularly in older plants. Scheme B shows an inverted sequence, where products are removed in the bottoms one at a time. With more conponents, a wide variety of combinations of these two schemes are possible. The scheme in Figure 11-9C is similar to the... 

W-Ti-C and W-Ta-C Systems.Pl The ternary system tungsten titanium carbide is an important material system with applications in cemented carbides for cutting tools. The solubility of WC in the TiC lattice is a function of temperature. It is 60 wt.% at 1500, reaches 90 wt.% at 2400°C, and is probably complete above 2600"C. WC is also soluble in TaC but to a lesser degree. In both systems, WC crystals precipitate upon cooling from sintering temperature and, as a result, these systems should be considered as mixed crystals or as a ceramic/ceramic composite. 

The phase diagram of the ternary system KF-KCI--KBF4 was measured in [3]. It was found that all three binaiy systems and the ternary system are simple eutectic ones. The calculated co-ordinates of the eutectic point in the ternary system is 19.2 mole % KF, 18.4 mole % KCl, 61.4 mole % KBF4 and the temperature of the eutectic crystallization 422 C. The probable inaccuracy in the calculated ternary phase diagram is 6.9 X,... 

The Sc-Nb Si isothermal section at 800"C presented in fig. 61 has been reported by Kotur (1986). Solid solution of substitution Sc5 1.5Nbo-3.5Si3 occurs in the system. The variation of the lattice parameters show negative deviation from Vegard s rule. Other binary scandium and niobium silicides do not dissolve the third component. T vo ternary compounds exist in the system. Probably Sco.4Nb4.6Si3 is a solid solution of the binary... 

Perhaps because of its polyfunctionality and complex molecular structure, C12MG (and probably also its analogs) displays a high level of complexity in its physical behavior. Polymorphism exists in the dry material three different crystalline polymorphs that vary widely in their kinetic stabilities have been discovered. Nonequuilibrium phenomena exist in unary and in binary aqueous systems. The likelihood that similar complexity also exists in ternary systems is very high. Unfortunately, one cannot be sure that this behavior is unique to these molecules because few other systems have been studied in the depth that C12MG has been. It would have been desirable to have studied in depth one or two other analogs, but time did not allow this. 

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