Basic Mechanisms and Analogies

This chapter covers separations that are strictly a segregation of well-defined phase materials, that is. gas, solid, or liquid. Excluded are separations involving equilibrium considerations or phase changes of any of the components. 

Separations of this type are always performed following some other contacting operation, often an equiliMum separation, such as, entrainment separatkn following distillation, filtration after crystallization, decantatioa after liquid-liquid extraction, and collection of solids from air exiting a dryer. Sometimes, the phase segregation is performed by the equilibrium separator hardware, but most frequently a separate piece of equi nent is used. 

These operations will be grouped by the phases that are to be separated gas-liquid, liquid-liquid, solid-gas, and solid-liquid. The fundamental mechamsms in each group ate similar. Ihere are four basic mechanisms that contribute to each group of separatioos  

Within each separation group there are variations and differences of effects, but most of the methods and equipment fall into one of these four cat mies. 

Gravity separations dqtend essentially on die density differences of the gas, solid, or liquids present in the mix. The particle size of the dispersed phase and the properties of the continuous phase are alw factors with the separation motivated by die acceleration of gravity. The simplest representation of this involves the assumption of a rigid spherical particle dispersed in a fluid with the terminal or free-settling velocity represented by 

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As demonstrated above, the heat current from D to S can be switched between different values. However, in many cases, like in an analog circuit, we need to continuously adjust the current Js and/or Jo in a wide range by adjusting the control temperature Tg. In Fig.11 we demonstrate this modulator/amplifier function of our transistor. The basic mechanism of such modulator/amplifier is the same as that of the switch but we consider here different parameter values. It is seen that in the temperature interval Tq (0.05,0.135), the heat current through the segment G remains very small ((—10-5 10-5), within the shadow strip in Fig. 10, while the heat currents Js and Jg continuously increase from 5 x 10-5 to 2 x 10-4. 

The transfer of mass from one point to the other may take place by two different modes, namely, diffusion and convection. The basic mechanisms for these modes of mass transfer are similar to those for heat transfer discussed in 4.2 and 4.3. Specifically, the mechanism for mass convection is analogous to heat convection and that for mass diffusion is analogous to heat conduction. 

A single step of the polymerization is analogous to a diastereoselective synthesis. Thus, to achieve a certain level of chemical stereocontrol, chirality of the catalytically active species is necessary. In metallocene catalysis, chirality may be associated with the transition metal, the ligand, or the growing polymer chain (e.g., the terminal monomer unit). Therefore, two basic mechanisms of stereocontrol are possible (145,146) (i) catalytic site control (also referred to as enantiomorphic site control), which is associated with the chirality at the transition metal or the ligand and (ii) chain-end control, which is caused by the chirality of the last inserted monomer unit. These two mechanisms cause the formation of microstructures that may be described by different statistics in catalytic site control, errors are corrected by the (nature (chirality) of the catalytic site (Bernoullian statistics), but chain-end controlled propagation is not capable of correcting the subsequently inserted monomers after a monomer has been incorrectly inserted (Markovian statistics). 

The reaction of aryl azides with excess alkenes in the presence of trifluoroacetic acid proceeds by an analogous mechanism and afforded, after basic hydrolysis, /5-hydroxy amines together with byproducts. A diastereoselective reaction was observed only with cyclic and acyclic (Z/-alkenes, e.g., 12 and 1388. From methyl ( )-2-butenoate, A-phenylthreonine methyl ester was similarly prepared in 30% yield88. 

The Amadori rearrangement has some features of the Lobry de Bruyn-Alberda van Ekenstein transformation, as can be seen from the ammono analogy to sugar enolization formulated in Part 2 of this Section. Both reactions occur in basic media, and each doubtless involves 1,2-enolization of the sugar. However, the Amadori rearrangement proceeds by acceptance of a proton from the acid catalyst, whereas the Lobry de Bruyn Alberda van Ekenstein transformation proceeds by delivery of a proton to the base catalyst. Aside from what may be argued as to the enolization mechanism, there are other important differences. 

The Bom-Oppenheimer theorem is a goexi starting point. The theorem basically. stales that electrons move in a stationary field of nuclei and therefore, the electron and nuclear motions can be considered separately. This approximation is valid in most cases of interest to medicinal chemists. since on the lime. scale of electron motion, the nuclei do not move. The difference in speed is a consequence of the differences in mass of the electron and the particles within the nucleus. It is analogous to speedboats circling a heavy aircraft carrier. On the lime scale of the speedboats, during a brief snapshot of time, the aircraft carrier is molion-lc.ss relative to the lighter craft. The.se facts, summari /cd in the Bom-Oppenheimer theorem, enable successful use of the various mathematical mcxlcls used in quantum mechanics and force field-based melhcxls. 

The details of hydrogen transfer from carbon are unclear. Analogy with other reactions of this type, particularly those of TEMPO, would suggest a cyclic transition state, characterised by primary hydrogen effects of 2, under basic conditions and a general base-catalysed process under acidic conditions, characterised by isotope effects around 5. However, the cyclic mechanism was also proposed for the standard oxidation conditions of aqueous acetic acid, originally on the basis of a rate decrease in aqueous acetic acid as sodium acetate was added, despite such an addition possibly deprotonating the... 

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