Distribution ratio principles

The principle of solvent extraction is illustrated in Fig. 1.1. The vessel (a separatory funnel) contains two layers of liquids, one that is generally water (Sa,) and the other generally an organic solvent (S g). In the example shown, the organic solvent is lighter (i.e., has a lower density) than water, but the opposite situation is also possible. The solute A, which initially is dissolved in only one of the two liquids, eventually distributes between the two phases. When this distribution reaches equilibrium, the solute is at concentration [A]a, in the aqueous layer and at concentration [AJ g in the organic layer. The distribution ratio of the solute... 

The general principles established for extraction apply to stripping, although of course distribution ratios are sought that are significantly less than unity in order to accomplish the strip as efficiently as possible. 

Theoretically, any number of solutes can be separated in this manner and the method has been applied, for example, to the separation of fatty acids, amino acids, polypeptides and other biological materials with distribution ratios in some cases differing by less than 0.1. However, the procedure can be lengthy and consumes large volumes of solvents. It is frequently more convenient to use one of the chromatographic techniques described later in this chapter. These can be considered as a development of the principle of countercurrent distribution. 

According to the principles of extraction chromatography, the distribution ratios are related to the resin capacity factor k by the following expression ... 

Liquid-liquid extraction (LLE) is based on a simple principle that a compound will be partitioned between two immiscible solvents with concentration at a distribution ratio proportional to its solubility in each of the solvents. LLE is a common method of working up organic reaction mixtures. A conventional LLE application is to separate compounds between water and an organic solvent such as diethyl ether, ethyl acetate, or methylene chloride. Acidic or basic buffers are often used to control the distribution ratio of a certain substance. 

Often the ratio (or Q) - M /M (dispersity ) is used to describe the broadness of a molar mass distribution. In principle, each ratio of mean values can be used to characterize the dispersity of a distribution, e.g. which results from eq. (4.1.3). 

In solubilized systems in which the solubilizate has a significant water solubility it is of interest to know not only the distribution ratio of solubilizate between the micelles and water under saturation conditions but also at varying degrees of saturation of the system with solubilizate. Such information cannot, of course, be obtained using the solubility methods discussed in Section 5.2.1. A dialysis technique has been described by Patel and Kostenbauder [32] and with various modifications has become a widely used technique [33-41]. In principle, the surfactant solution is separated from an aqueous solution of the solubilizate by a membrane permeable to solubilizate but not to micelles. In a typical dialysis cell the membrane is clamped between two Perspex half cells of approximately 150cm capacity (see Fig. 5.2). Provision is made for stirring and pH control if... 

For preparative purposes batch fractionation is often employed. Although fractional crystallization may be included in a list of batch fractionation methods, we shall consider only those methods based on the phase separation of polymer solutions fractional precipitation and coacervate extraction. The general principles for these methods were presented in the last section. In this section we shall develop these ideas more fully with the objective of obtaining a more narrow distribution of molecular weights from a polydisperse system. Note that the final product of fractionation still contains a distribution of chain lengths however, the ratio M /M is smaller than for the unfractionated sample. 

In principle, the excitation energy would be expected to be distributed between ketones (5)and (6) in a ratio dependent on the substituent R, and the distribution would be expected to favor the ketone having the lowest triplet excitation energy. 

In principle, the velocities c and ti can be determined by taking a series of pictures at a very high frequency of the flow through a transparent plastic tube. Because of the particle size distribution, each particle moves at a different velocity, and this makes this method difficult to apply in practice. We have therefore used an indirect method, where we have measured the pressure losses of pneumatic conveying for two mixture ratios and then fit the parameters so that Eq, (14.126) coincides as accurately as possible with measured pressure losses. 

When a dilute solution of a polymer (c << c ) is equilibrated with a porous medium, some polymer chains are partitioned to the pore channels. The partition coefficient K, defined as the ratio of the polymer concentration in the pore to the one in the exterior solution, decreases with increasing MW of the polymer (7). This size exclusion principle has been used successfully in SEC to characterize the MW distribution of polymer samples (8). 

The arrangement of monomer units in copolymer chains is determined by the monomer reactivity ratios which can be influenced by the reaction medium and various additives. The average sequence distribution to the triad level can often be measured by NMR (Section 7.3.3.2) and in special cases by other techniques.100 101 Longer sequences are usually difficult to determine experimentally, however, by assuming a model (terminal, penultimate, etc.) they can be predicted.7 102 Where sequence distributions can be accurately determined Lhey provide, in principle, a powerful method for determining monomer reactivity ratios. 

While sequence distributions are usually subject to more experimental noise than composition data, this is often outweighed by the greater information content. In principle, reactivity ratios can be estimated from a single copolymer sample. The consistency in reactivity ratios estimated with eqs. 45 and 46 for copolymers prepared with different monomer feed compositions and/or obtaining the same result from cqs. 50 and 51 (4 aab—Ai ab) and cqs. 52 and 53 (r aba-Aiba) arc... 

An ordered distribution of spheres of different sizes always allows a better filling of space the atoms are closer together, and the attractive bonding forces become more effective. As for the structures of other types of compound, we observe the validity of the principle of the most efficient filling of space. A definite order of atoms requires a definite chemical composition. Therefore, metal atoms having different radii preferentially will combine in the solid state with a definite stoichiometric ratio they will form an inter-metallic compound. 

The difference is clearly seen for a spur initially containing two dissociations of AB molecules into radicals A and B (Pimblott and Green, 1995). Considering the same reaction radii for the reactions A + A, A + B, and B + B and the same initial distributions of radicals, the statistical ratio of the products should be 1 4 1 for A2 AB B2, since there is one each of A-A and B-B distances but there are four A-B distances. For n dissociations in the spur, this combinatorial ratio is n(n - l)/2 n2 n(n - l)/2, whereas deterministic kinetics gives this ratio always as 1 2 1. Thus, deterministic kinetics seriously underestimates cross-recombination and overestimates molecular products, although the difference tends to diminish for bigger spurs. Since smaller spurs dominate water radiolysis (Pimblott and Mozumder, 1991), many authors stress the importance of stochastic kinetics in principle. Stochasticity enters in another form in... 

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