Ternary systems derivation

The expressions for the KBIs of ternary systems derived from the general KB equations (in volume per mole) have the following form ... 

Among the investigated catalysts in PO-AGE copolymerization, the most productive systems, considering both copolymer yield and molecular mass, proved to be the ternary systems deriving from TIBA and water, and having as a third component Zn(acac)2 (Cat 8) or Zn(DIPS)2 (Cat 9). For molar ratios TIBA H20 Zn = 1 0.5 0.25, the isolated yields were 94.5% and 83.7%, respectively, after 6 h reaction time (entry 8 and 9, Table 2). 

Selected physical properties of various methacrylate esters, amides, and derivatives are given in Tables 1—4. Tables 3 and 4 describe more commercially available methacrylic acid derivatives. A2eotrope data for MMA are shown in Table 5 (8). The solubiUty of MMA in water at 25°C is 1.5%. Water solubiUty of longer alkyl methacrylates ranges from slight to insoluble. Some functionalized esters such as 2-dimethylaniinoethyl methacrylate are miscible and/or hydrolyze. The solubiUty of 2-hydroxypropyl methacrylate in water at 25°C is 13%. Vapor—Hquid equiUbrium (VLE) data have been pubHshed on methanol, methyl methacrylate, and methacrylic acid pairs (9), as have solubiUty data for this ternary system (10). VLE data are also available for methyl methacrylate, methacrylic acid, methyl a-hydroxyisobutyrate, methanol, and water, which are the critical components obtained in the commercially important acetone cyanohydrin route to methyl methacrylate (11). 

Metal-induced reductive dimerization of carbonyl compounds is a useful synthetic method for the formation of vicinally functionalized carbon-carbon bonds. For stoichiometric reductive dimerizations, low-valent metals such as aluminum amalgam, titanium, vanadium, zinc, and samarium have been employed. Alternatively, ternary systems consisting of catalytic amounts of a metal salt or metal complex, a chlorosilane, and a stoichiometric co-reductant provide a catalytic method for the formation of pinacols based on reversible redox couples.2 The homocoupling of aldehydes is effected by vanadium or titanium catalysts in the presence of Me3SiCl and Zn or A1 to give the 1,2-diol derivatives high selectivity for the /-isomer is observed in the case of secondary aliphatic or aromatic aldehydes. 

The densities and volumetric heat capacities of the binary systems, which are required for the calculation of the transfer functions, were measured at the same time as those of the ternary systems. The derived apparent molar quantities of the binaries were In excellent agreement with those In the literature (11,16). 

His procedure was used for the calculation of the activity coefficients in the aqueous solution of two electrolytes with a common ion from isopiestic data (3). Kelly, Robinson, and Stokes (4) proposed a treatment of isopiestic data of ternary systems with two electrolytes by a procedure based on the assumption that at all values of molal concentrations, mi,m2, the partial derivatives may be expressed by a sum of two functions in their differential form as follows ... 

Scheffe [5] suggested to describe mixture properties by reduced polynomials obtainable from Eq. (3.11), which is subject to the normalization condition of Eq. (3.2) for a sum of independent variables. We shall demonstrate below how, for instance, such a reduced second-degree polynomial is derived for a ternary system. The polynomial has the general form ... 

Table 3.38 tabulates the D-optimal design for the derivation of a ternary system third-degree polynomial. Following this design the coefficients are obtained for a third-degree polynomial having the same form as that from a conventional simplex lattice ... 

After one or the other design of Draper-Lawrence has been constructed for a ternary system, first-degree polynomials are derived in two independent variables Zi and Z2 (ri [=l for n2=2). 

As is evident from the foregoing paragraphs, the interaction of the components in the ternary R-M-Sb systems have not been adequately studied. The isothermal sections (over all concentration region or partially) have been constructed for the limited number of ternary systems (22), and in other systems only the samples of specific compositions were synthesized and investigated structurally with respect to the formation of isotypic compounds. This paucity of data complicates the pursuance of a proper analysis and the derivation of regularities. 

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]. 

Several alkali metal (M) derived ate complexes have been prepared (Table 8). Again, the formation of such ternary systems is preferred. Even Sm(II) derivatives were readily available [89], A common feature of the observed molecular structures are close inter- and intramolecular M - C as well as close Ln-- Si van der Waals contacts which ensure steric saturation of the metal centers. Depending on the size of the alkali metal, different types of solid state structures are generated (Fig. 15). A comparison to the ammonia derived species in Sect. 2.1 can be drawn. 

Although LiPor-precursors are involved in the synthesis, ate complexes of type MI[LnPor2] have not been isolated, in contrast to the pyrrol derivatives [197] or charge related M [Ln(COT)2] complexes [240]. However, ternary systems are readily available by reaction of the protonated form HLnPor2 with, e.g., M OR (Eq. 16). Structural evidence has been given for the thallium complex Tl[Pr(OEP)2] [228]. 

The ternary system of peroxidase/nitrite/hydrogen peroxide can also be advantageously used for nitration of indole derivatives. Several nitro derivatives, together with the /V-nitro and /V-nitroso adducts, are formed in this reaction. Interestingly, the composition of the product mixture depends on the enzyme used (LPO or HRP) and on nitrite concentration [109]. By changing the enzyme and the reaction conditions, it is possible to drive the reaction toward the N-nitroso derivative or the nitro-derivatives (Fig. 6.9c). 

Initially, an attempt was made to develop original global rate expressions for Reactions 14 to 16 from these rate data. It soon became clear, however, that the number of experimental points was too few to allow the attainment of this goal. Moreover, since a ternary system was being analyzed, the concentration profiles had an intricate form which made numerical differentiation to retrieve the rates somewhat inaccurate. It was therefore decided to use these rate data to check the overall rate expressions derived by other authors and used in the present model. 

The mutual solubility of cellulose (CELLOHO CTA, PCT and PMMA in TFA-CH2CI2 offers the opportunity to determine if Flory s prediction applies to ternary systems consisting of cellulose or a cellulose derivative and a synthetic polymer. 

Table HI shows the values for the kinetic and statistical parameters obtained by analyzing the data for all ternary systems according to the phenomenological model of Hall [5]. A comparison of the values of the various parameters (cf. Table II and Table III) obtained from analyses employing these two models show, generally, that larger values are obtained with the Hall model however, the trends in the derived parameters are similar. The values of the rate constants for the alcohol exchange process in the Hall model were obtained by extrapolating C —> 0 to avoid any concentration dependence of k. Using the extrapolated value of k, it was shown [5] that kj is given by...

In such ternary systems comprising a solute and a mixed stationary phase (polymers 2 and 3), the polymer-polymer interaction is derived through the interactions of the solute with the mixed and the pure stationary phases. Note that in ternaiy systems index 3, formerly applied to the carrier gas [Eq. (5)], is now given to a polymer. 

In terms of the amounts produced, sheet and container glass is clearly the most widely produced type whose composition is derived from the ternary system Na O —CaO — — S1O2. 

These are the general equations defining the critical phases in a ternary system they were first derived by Gibbs. ... 

Reverse micellar systems were used for the polymerization of phenol derivatives. HRP-catalyzed polymerization of p-ethylphenol in the ternary system composed of a bis(2-ethylhexyl) sodium sulfosuccinate (AOT)—water—isooctane system produced spherical polyphenol particles having 0.1—2 /tm diameters quantitatively.21 Similar particles were obtained by pouring the solution of enzymatically prepared polyphenol into a nonsolvent containing AOT.22... 

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