Pairing phase

The liquid-liquid extraction of uranium(VI) from acetate aqueous solution employing the ion-pair phase separation of perfluorooctanoate ion with tetrabutylammonium ion has recently been reported [1]. Arsenazo 111 was used to determine U in the obtained extracts. 

The calculation of the perturbed radial distribution function g(2) for steady-state viscous flow is carried out using Eq. 34 for continuity in molecular pair phase space. The development is by no means simple but it is carried out without the introduction of additional assumptions beyond the formulation of appropriate boundary conditions. Those used by Kirkwood and co-workers27 38 make use of the following ... 

We consider the description of the general bimolecular reaction A-t-B =i C-hD. The primary variables of interest are now the reactive pair phase-space densities 6/j b(x,X2) and 5 cd( i 2)- These two fields are coupled by the reaction, but because of the diluteness of the solute species they are not coupled to other pair fields by the action of the pseudo-Liouville operator. In the present formulation singlet fields are not included in the description. Thus the pair fields do not have to be orthogonalized to the singlet fields and are simply given by, for example. 

The reactive pair phase-space correlation functions can be constructed from these fields as... 

The general pair phase-space kinetic equation is given in (7.32). Letting... 

Before concluding this section on the implications of the pair kinetic theory for configuration space descriptions, we show that the kinetic equation may also be used to obtain the kinetic theory result for the rate kernel. This can be accomplished by projecting out the position and velocity dependence of the pair phase-space correlation function ab,ab( 2> 1 2 /) to obtain an equation for... 

The interaction parameters for the hydrocarbon-hydrocarbon pairs are considerably less than those for the nonhydrocarbon—hydrocarbon pairs. To evaluate the need for the interaction parameter for hydrocarbon-hydrocarbon pairs, phase equilibria has been predicted both with and without interaction parameters for ternary systems for which experimental data are available. The ternary systems used and the results of the study are given in Table III. These results indicate that there is no significant advantage for using hydrocarbon-hydrocarbon interaction parameters in predictions for ternary systems. Therefore, for general calculations, hydrocarbon-hydrocarbon interaction parameters are set at zero, but nonzero interaction parameters are used for nonhydrocarbon-hydrocarbon pairs. 

Schreiber and Luo exploited domino sequences in both the coupling and pairing phases [25]. A gold-catalyzed cyclization of alkyne 157 was employed to obtain molecules that could subsequently be used in the pairing reaction. Activation of the alkyne by a gold(I) complex yielded the cydized cationic species 160,... 

Figure 10.27 shows the structure of a type II network (the almost pairing phase) found in the Monte Carlo simulation using bead-spring model chains [72]. In addition to the H-bonding energy e, the simulation incorporates the interaction Ae=0.3e between neighboring H-bonds. 

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