Biphasic equilibrium

Biphasic coexistence is most conveniently treated by imposing the condition that the chemical potentials jXj and Pp (obtained as partial derivatives of the free energy) of the respective components in the two phases must be equal at equilibrium, i.e., that 

Characteristics of the biphasic equilibria calculated from the lattice theory are summarized in Table 1. Results obtained for the volume fractions Vp and v at coexistence, for their ratio Vp/Vp, for xVp and for y/x according to the 1956 approximate version of the theory are given in columns 2, 3 and 4 for the neat fluid, for rods with X = 20 and in the limit x = oo, respectively. Corresponding calculations from the exact version of the theory are given in the last three columns. The latter calculations yield somewhat lower volume fractions for the coexisting phases. The ratios Vp/Vp are smaller in the limit x - oo this ratio is 1.465 compared with 1.592 in the earlier approximation The differences are comparatively small, however. Hence, use of the 1956 treatment with its advantages of greater simplicity is vindicated for most purposes. 

The volume fraction at incipient separation of the nematic phase lies just beyond the volume fraction v at which exhibits critical behavior with respect to the disorder index y, according to the 1956 theory. The confusion of v calculated using Eq. (11) with Vp at incipience therefore has led to underestimation of the latter volume fraction according to that version of the theory. The improved theory leads to somewhat lower values of the volume fraction at incipient phase separation. Hence, the error attending misapplication of Eq. (11) is offset by inaccuracies of the original theory, with the fortuitous consequence that this equation offers a slightly better approximation for the threshold volume fraction than for vj, for which latter it was originally intended. The widespread misuse of Eq. (11) is therefore well justified. 

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First, the equilibrium constant for the reaction in the aqueous phase was determined, and it was found that the equilibrium of the reaction was shifted almost entirely toward the left = 2 X 10 ). The yield of the ester obtained for reaction in the aqueous phase was as low as 0.01%. Next, four different organic solvents (chloroform, benzene, carbon tetrachloride, and diethyl ether) were selected the partition coefficient was determined for each of the four solvent-water binaries. Then the biphasic equilibrium constant was found from Equation 18.7 and plotted as a function of a (Figure 18.3). 

Compositions between ErSe 33 and ErSe 43 were biphasic. Equilibrium conditions are established so slowly below 1200°C that the true homogeneity region may be masked, Guittard et al. [4], also see [2, 3]. Values a = 11.355, b = 8.095, c = 24.175 A for yellow Er2Se3 are determined from powder patterns, Klein Hanefeld, Jellinek [11]. 

A large number of Brpnsted and Lewis acid catalysts have been employed in the Fischer indole synthesis. Only a few have been found to be sufficiently useful for general use. It is worth noting that some Fischer indolizations are unsuccessful simply due to the sensitivity of the reaction intermediates or products under acidic conditions. In many such cases the thermal indolization process may be of use if the reaction intermediates or products are thermally stable (vide infra). If the products (intermediates) are labile to either thermal or acidic conditions, the use of pyridine chloride in pyridine or biphasic conditions are employed. The general mechanism for the acid catalyzed reaction is believed to be facilitated by the equilibrium between the aryl-hydrazone 13 (R = FF or Lewis acid) and the ene-hydrazine tautomer 14, presumably stabilizing the latter intermediate 14 by either protonation or complex formation (i.e. Lewis acid) at the more basic nitrogen atom (i.e. the 2-nitrogen atom in the arylhydrazone) is important. 

X(A1C13) = 0.5) to immobilize a ruthenium carbene complex for biphasic ADMET polymerization of an acyclic diene ester (Figure 7.4-2). The reaction is an equilibrium processes, and so removal of ethylene drives the equilibrium towards the products. The reaction proceeds readily at ambient temperatures, producing mostly polymeric materials but also 10 % dimeric material. 

Depicted in Fig. 2, microemulsion-based liquid liquid extraction (LLE) of biomolecules consists of the contacting of a biomolecule-containing aqueous solution with a surfactant-containing lipophilic phase. Upon contact, some of the water and biomolecules will transfer to the organic phase, depending on the phase equilibrium position, resulting in a biphasic Winsor II system (w/o-ME phase in equilibrium with an excess aqueous phase). Besides serving as a means to solubilize biomolecules in w/o-MEs, LLE has been frequently used to isolate and separate amino acids, peptides and proteins [4, and references therein]. In addition, LLE has recently been employed to isolate vitamins, antibiotics, and nucleotides [6,19,40,77-79]. Industrially relevant applications of LLE are listed in Table 2 [14,15,20,80-90]. 

Since the beginning of the 20th century, organic solvents have been used in enzymatic reaction media [30]. Biocatalytic reactions in water-organic biphasic media were first carried out by Cremonesi et al. [31] and by Buckland et al. [32] less than 30 years ago. Their work aimed at the conversion of high concentrations of poorly water soluble components, particularly steroids. Later, biphasic systems were used for enzyme-catalyzed synthesis reactions that were unfavored in water, changing the reaction equilibrium towards the higher yield of the product, such as esters or peptides. 

Several experiments using different organic solvents in different biphasic media are necessary to find the adequate distribution of the reaction components. A series of experiments are essential for the choice of a process and for scaling-up. Experiments using Lewis cells [44] may yield useful results for understanding equilibrium, kinetics, and interactions between organic solvent-substrate and/or organic solvent-biocatalyst. A study of two-liquid phase biotransformation systems is detailed below in Sections II-IX. 

The volumetric ratio of the two liquid phases (j6 = Forg/ Faq) can affect the efficiency of substrate conversion in biphasic media. The biocatalyst stability and the reaction equilibrium shift are dependent on the volume ratio of the two phases [29]. In our previous work [37], we studied the importance of the nonpolar phase in a biphasic system (octane-buffer pH 9) by varying the volume of solvent. The ratio /I = 2/10 has been the most appropriate for an improvement of the yield of the two-enzyme (lipase-lipoxygenase) system. We found that a larger volume of organic phase decreases the total yield of conversion. Nevertheless, Antonini et al. [61] affirmed that changes in the ratios of phases in water-organic two-phase system have little effect upon biotransformation rate. 

At equilibrium, in biphasic system, distribution of a chemical species (i) between the two phases is given by its partition coefficient ... 

Martinek et al. [28] defined the apparent reaction equilibrium in a biphasic system by the constant A),i. In their model, the ratio represents the equilibrium change when... 

The present section deals with the improvement in the performance of biocatalysis when carried out in organic-aqueous biphasic systems. Such systems are very useful in equilibrium reactions and conversion yield where substrates and products can be dissolved and drawn into different phases. Subsequently the synthesis in the reactive aqueous phase is allowed to continue. 

Lipophilicity is a molecular property expressing the relative affinity of solutes for an aqueous phase and an organic, water-immiscible solvent. As such, lipophilicity encodes most of the intermolecular forces that can take place between a solute and a solvent, and represents the affinity of a molecule for a lipophilic environment. This parameter is commonly measured by its distribution behavior in a biphasic system, described by the partition coefficient of the species X, P. Thermodynamically, is defined as a constant relating the activity of a solute in two immiscible phases at equilibrium [111,112]. By convention, P is given with the organic phase as numerator, so that a positive value for log P reflects a preference for the lipid phase ... 

Another type of biphase partition comprises equilibration of a crown ether-containing solution with a sparingly soluble solid salt. Assuming that the amount of free salt [M+.X in (1)] at equilibrium equals the solubility—which can be determined separately—one can calculate the association constant ATlp from the amount of solubilized salt. Reinhoudt et al. (1977) applied this technique using Zeise s salts. 

In the simplest binary system comprising two liquids (A and B), adding a small amount of either liquid to the other creates a single phase, as the one liquid dissolves completely in the other. As more of the second liquid is added, in this case B, the first liquid A becomes saturated with B and no more will dissolve. At this point, the system will consist of two phases in equilibrium with each other, one of liquid A saturated with B and the other of liquid B saturated with A. If B is continually added to A, there will come a point at which A becomes the minor component in the system and, ultimately, will dissolve completely in liquid B a single phase will be formed once more. The relative proportions of each liquid that are required to form single or biphasic systems depends both... 

In a biphasic system, the same rules as above apply, however, the rate of the reaction and the position of the equilibrium are determined by the concentration of the reactants and products in the phase where the reaction takes place, rather than their overall concentration in the system. Exactly where the reaction actually takes place is still a matter of debate, with two locations proposed, specifically, at the interfacial layer between the two phases (model 1) and in the bulk of the catalyst-containing phase (model 2), as shown in Figure 2.9. 

As for the rate of diffusion, the equilibrium constant for a reaction in a biphasic system is not determined by the overall concentration of each reagent, but by their concentrations in the reaction phase. In some cases this can drive the forward reaction to completion, and in other cases it can be inhibitory, depending on the relative concentrations of the reactants and products. In model 1, where the reaction takes place at the phase boundary, the effective concentration of the reactants and products will be that in phase 1, and assuming each has an equivalent solubility, the equilibrium position will approach that of a homogeneous system. Where the reaction takes place in the bulk solvent, as in model 2, the equilibrium position is very much dependent on the solubility of the reagents in phase 2. For example, if the product is less soluble in phase 2 than the reactant, as the product is formed it will diffuse back into phase 1, reducing its concentration in phase 2 where the reaction is occurring and therefore the reaction will... 

To understand the pharmacokinetic relevance of the proxibarbal-valofan equilibrium, the kinetics and thermodynamics of the reaction were carefully examined in aqueous and biphasic media. The various pseudo-first-order rate constants shown in Fig. 11.19 were determined in the pH range of 6.7 - 8.0... 

Gold nanoparticles from 2.5 to 5 nm sizes have also been prepared by using a biphasic Winsor II [126] (a water-in-oil microemulsion that is in equilibrium with the excess water phase) type microemulsion of diethyl ether/AOT/water. The surfactant, AOT, performs the dual role of forming a microemulsion and the transferring of charged metal ions from the aqueous to organic phase. This provides gold nanoparticles, which are readily dispersed in the nonpolar phase. 

A 53 mL hydrod5mamic CCC machine was equilibrated wifh fhe 40/20/40 biphasic liquid system. The resulfs af equilibrium and 830 rpm were = 15 mL and I/g = 53 15 = 38 mL of IL-rich liquid sfafionary phase... 

In case of ions, it is important to know the coordination environment to extract metals. UV-Vis spectroscopic measurements provide the respective information. There are systems in which both the biphasic extraction equilibrium and the metal coordination environment in an IL and a molecular organic solvent are the same [17]. 

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