Separation selectivity expression

The type of anion and cation, pH, ionic strength, concentration, addition of modifiers such as complexing agents, organic solvents, surfactants, etc., all are parameters of the bulk electrolyte in the capillary that can affect the selectivity of separation. Selectivity may be expressed in terms of mobility differences (A/i) or in mobility ratios (a) ... 

Equation (1) shows another important advantage of CE. As already mentioned, the separation selectivity in chromatographic techniques very closely relates to the thermodynamic selectivity of recognition (ar), in that the thermodynamic selectivity of recognition, which is the ratio of the binding constants, is the upper limit of separation selectivity. In contrast, the separation selectivity (as) in CE may be expressed by the equation... 

For reactions that occur with different selectivities or kinetics on the induced sites, the implications are far more complex. Teichner has found that the selectivities for the isomerization of methylcyclopropane and for cracking of benzene and cyclohexadienes may be substantially different on activated silica or alumina than on the normal oxides (see above). In these cases, a separate rate expression may need to be included. Depending on the rate constants and relative kinetics, this can substantially change the reaction-rate expression. Further, differences in the activation energies may affect the contribution at different temperatures. If the reaction temperature is sufficient, the activation of the support may be able to occur during the course of the experiment. 

In summary, one can see that separation selectivity for gas and vapor molecules depends on the category of pores (mesopores, supermicropores, and ultramicropores) and on the related transport mechanisms. Either size effect or preferential adsorption effect (irrespective of molecular dimension) is involved in selective separation of multicomponent mixtures. The membrane separation selectivity for two gases is usually expressed either as the ratio between the two pure gas permeation fluxes (ideal selectivity) or between each gas permeation flux measured from the mixture of the two gases (real selectivity). More detailed information on gas and vapor transport in porous ceramic membranes can be found in Ref. [24]. 

The membrane is the most important part in separation processes since its performance controls the efficiency and the selectivity of the process. Both flux and selectivity expressed in terms of separation or retention factors determine the process economics and usability, and finally the costs of the installation. 

The effect of the EOF on migration time and selectivity depends on the mutual signs of the mobilities of analytes and EOF, respectively. Concerning the change in separation selectivity, we refer to the expression of the selectivity term in the resolution equation. The difference between the mobilities of the two separands, i and j, will not be influenced by the EOF. However, the mean mobility is larger for the case of comigration. This means that the selectivity term in the expression for the resolution is always reduced in this case. In practice, selectivity is lost for cation separation when the EOF is directed, as is usual in uncoated fused-siUca capillaries, toward the cathode. For this reason, cationic additives are applied in the BGE to reverse the EOF direction. 

In column chromatography, the separation selectivity is often expressed by selectivity factor, a, of a critical pair of sample components ... 

The number of adjacent peaks, m, in which selectivity factor is higher than a threshold value, a > au .es, may be used to express overall separation selectivity of the chromatographic system for multicomponent sample separation ... 

In Section 3.3.7.1, we were introduced to gas-liquid equilibrium relations describing how one can quantify the distribution of a volatile solute between a gas phase and a liquid phase characterized as the absorbent phase. The solute i was a gas or a vapor under the operating conditions. In Section 4.1.1, we developed expressions for the selective absorption of one gas species 1 over the other gas species 2 in a liquid similarly, we developed the separation factor expression for absorption between two condensable... 

Thus, resolution can be increased by increasing the difference in retention time and decreasing the peak widths. The resolution Equation 9.14 may be expressed in a more useful form by introducing a separation (selectivity) factor a (similar to relative volatility in distillation) ... 

Electronic spectra are almost always treated within the framework of the Bom-Oppenlieimer approxunation [8] which states that the total wavefiinction of a molecule can be expressed as a product of electronic, vibrational, and rotational wavefiinctions (plus, of course, the translation of the centre of mass which can always be treated separately from the internal coordinates). The physical reason for the separation is that the nuclei are much heavier than the electrons and move much more slowly, so the electron cloud nonnally follows the instantaneous position of the nuclei quite well. The integral of equation (BE 1.1) is over all internal coordinates, both electronic and nuclear. Integration over the rotational wavefiinctions gives rotational selection rules which detemiine the fine structure and band shapes of electronic transitions in gaseous molecules. Rotational selection rules will be discussed below. For molecules in condensed phases the rotational motion is suppressed and replaced by oscillatory and diflfiisional motions. 

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