Shake theory

Aberg, T. Shake theory of multiple excitation processes. In Photoionization and other probes of many-electron interactions. Wuilleumier, F. (ed.), pp. 49-59. NATO Advanced Study Institute Series. New York Plenum Press 1976... 

According to the shake theory and the sudden approximation the probability of excitation of the j th final state l j(N-l) is given by33,34... 

If two pure, immiscible liquids, such as benzene and water, are vigorously shaken together, they will form a dispersion, but it is doubtful that one phase or the other will be uniquely continuous or dispersed. On stopping the agitation, phase separation occurs so quickly that it is questionable whether the term emulsion really should be applied to the system. A surfactant component is generally needed to obtain a stable or reasonably stable emulsion. Thus, if a little soap is added to the benzene-water system, the result on shaking is a true emulsion that separates out only very slowly. Theories of... 

The reaction mixture was then dissolved in methylene chloride, the amine was removed by shaking with dilute hydrochloric acid, the reaction product was extracted from the organic phase by means of dilute sodium hydroxide solution and the alkaline solution was acidified with acetic acid to a pH value of 6. The 1 -hvdroxv-4-methyl-6-cvclohexvl-2-pyridone precipitated in crystalline form. It was filtered off with suction, washed with water and dried. The yield was 1.05 g (49% of theory) melting point 143°C. 

However, as stated above, the partition coefficients measured by the shake-flask method or by potenhometric titration can be influenced by the potenhal difference between the two phases, and are therefore apparent values which depend on the experimental condihons (phase volume ratio, nature and concentrahons of all ions in the solutions). In particular, it has been shown that the difference between the apparent and the standard log Pi depends on the phase volume raho and that this relationship itself depends on the lipophilicity of the ion [80]. In theory, the most relevant case for in vivo extrapolation is when V /V 1 as it corresponds to the phase ratio encountered by a drug as it distributes within the body. The measurement of apparent log Pi values does not allow to differentiate between ion-pairing effect and partihoning of the ions due to the Galvani potential difference, and it has been shown that the apparent lipophilicity of a number of quaternary ion drugs is not due to ion-pair partitioning as inihally thought [80]. 

Theory The iodine monochloride method described earlier employing standard potassium iodate is the basis for the official assay of potassium iodide. Vigorous shaking is a prime requirement, as the end-point is approached in this assay, because of the fact that both iodine and iodate in different phases attribute a heterogeneous medium. However, the reaction involving the oxidation of KI by iodate may be designated as shown below ... 

Theory First and foremost the active ingredient i.e., glyceryl trinitrate is extracted completely from the tables by shaking with glacial acetic acid. To an aliquot of the resulting acetic acid solution an excess of phenoldisulphonic acid is added to produce a yellow colour which is subsequently intensified by adding an excess of ammonia. The following reactions take place ... 

In a 3-I. round-bottom flask are placed 410 g. of crude benzoin and 1 1. of nitric acid (sp. gr. 1.42), (2.5 cc. of nitric acid per gram of benzoin). The mixture is heated on a water bath for about one hour with occasional shaking, until the evolution of oxides of nitrogen ceases. The reaction mixture is then poured with stirring into four to five times its volume of cold water the benzil precipitates as small yellow lumps. The crude product is filtered and washed several times with water to remove the nitric acid. The yield after drying is 390 to 395 g. (96-97 per cent theory). Absolutely pure benzil may be obtained by crystallization from an alcohol solution. 390 g. of the crude benzil may be dissolved in about r 1. of boiling alcohol and since pure benzil is quite insoluble in cold alcohol, there is no difficulty in obtaining 370 g. of the pure product from the 390 g. used. 

We have already shown that excitation energies can be diagrammatically decomposed to yield simpler quantities such as ionization potentials and electron affinities plus some remaining diagrams. MB-RSPT permits the use of this treatment for even more complex processes. In this section, we present the applicability of the theory to double ionizations observed in Auger spectra as well as excitations accompanying photoionization (shake-up processes) observed in ESCA and photoelectron spectroscopy. A detailed description of this approach is given in Refs.135,136. Here we shall present only the formal description. 

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