Binary mixtures 19 coordination number

Lattice coordination numbers (2) and the cell volumes (vjj) for both the pure components and mixture lattices are assumed to have the same value. The partition function for this ensemble can be formulated following Equation 2. It is assumed now that the partition function, far from the binary critical point can be approximated by its largest term. Since molecule segments and holes can distribute themselves non-randomly, the partition function must incorporate terms to account for this effect. The nonrandomness correction rjj... 

In a binary mixture of solvents Si and S2, a cation M with a coordination number k and charge z forms k+ ) cations of the type [M(Si)i(S2)a - ]" with i = 0.. .k, differently solvated in the first solvation shell. These differently solvated species have been called solvatomers [254]. For example, with octahedrally coordinated cations k = 6), k + + 2 = solvatomers are to be expected (including three cisitrans isomeric solvatomers with i = 2, 3, or 4). In favourable cases, the concentrations of all solvatomers have been obtained as a function of the solvent mole fraction by NMR measurements [254]. 

On the assumptions that (F )i and (F J2 differ insignificantly from the respective values in the pure solvents and that the coordination number remains unaltered, the relaxation rate was calculated for several binary solvent mixtures. (48,49). In the numerical results it was further assumed that the solvent composition in the solvation sheath is... 

More recently the solvation of AP in binary mixtures of DMF and DMSO (126) and nitromethane and DMF (127) was investigated. For the former solvent system all possible mixed solvates Al(DMF) (DMSO)g were found to give rise to separate Al resonances. In the presence of nitromethane as a diluent the distribution of solvates follows the bulk solvent composition, and the coordination number is retained at all mixing ratios. In the undiluted binary system, however, AP is preferentially solvated by DMSO. 

The /z-transf orm method was also applied to the calculation of the breakthrough curve for the separation of a binary mixture on a charcoal bed by Tien et al. [36]. By using the li-transform, the course of the separation can be calculated by transforming the concentration variable via the /i-transform into a coordinate system in which algebraic equations describe the process for any number of components. 

The NRTL equation was developed by Renon and Prausnitz.54 The expression for the excess energy function gl (see Table 14-12) was developed on the basis of a two-liquid theory. In the theoretical development, the A,/s are the Gibbs interaction energies and the a,/s are the reciprocals of the lattice coordination numbers. In practice, the quantities (Ajt - A ), (A0 — A ), and atj are taken to be three adjustable parameters per binary pair in the mixture and are obtained by a regression of the equilibrium data. The NRTL equation has been used extensively. It is superior to the Wilson equation in that it can be used to represent liquid-liquid systems (al7 < 0.426). However, the NRTL equation requires three parameters per binary pair, whereas the Wilson equation requires only two parameters per binary pair. 

The of P= Na in mixtures of A=EG and B=MeCN was interpreted in terms of the stepwise replacement of B in 1B + by A, taking into account the nonideality of the Ah-B system. Quantitative evidence for the preferential solvation of sodium ions by ethylene glycol was obtained by Chuang et al. [52]. The 5. , of of the carbonyl group in 1M solutions of LiPF in binary solvent mixtures involving esters and amides was interpreted in terms of preferential coordination of the solvents to Li with a constant total coordination number of 4. In isomolar mixtures of A=methyl propionate and B = ethyl methyl carbonate Xg = 0.39, of A=MA -dimeth-ylacetamide and B=propylene carbonate Xg =0.40, and of A=methyl propionate and B = ethyl propionate Xg = 0.43 according to Matsubara et al. [53]. In all these cases Xg < 0.50, and hence it is solvent A that preferentially solvates the ion. 

The replacement of one solvent of a binary solvent mixture A+B in the solvation shell of an ion P by the other, yielding the set of reactions (6.6a-6.6b), can be described explicitly by the QL(JC method. The coordination number Af is set equal to the lattice parameter Z and equilibrium quotients depending on the preferential solvation parameter result ... 

We consider a binary mixture containing Na molecules A and Nb molecules 5 on a lattice of N — Na + b) sites with a coordination number z. Each molecule has z closest neighbours and there are in all I zN pairs of closest neighbours. Such pairs are of three kinds namely AA, AB, BB. We shall denote their respective numbers by Naa, Nab, NbB Slimming all neighbours of the Na molecules, we have... 

A sufficiently rarefied gas, or a mixture of gases, consists of a number of neutral molecules of species 1 and 2 (which may or may not be the same). We may assume a distribution of velocities (measured in the laboratory frame), fi ( ) d3u, that may be modeled by a Maxwellian distribution function, with i = 1 or 2, as long as the duration of the average collision is short compared to the time between collisions. For binary collisions, one usually transforms from laboratory coordinates, Vj, to relative ( >12) and center-of-mass (1>cm) velocities,... 

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