Retention factor separation number

According to Equation 3, the resolution of two peaks in column separation is controlled by three major variables retention defined in terms of the retention factor k column efficiency expressed as the number of theoretical plates N and selectivity characterized by the selectivity factor a [48] ... 

In order to illustrate the critical process parameters of SMB process validation, we will consider the separation of the racemic drug as described in Process design. The study represents the effect of the influence of feed concentration, number of plates and retention factor on the second eluting enantiomer. The simulation of the process for different values of feed concentration is performed and the variations of the extract and raffinate purities are shown in Fig. 10.10. 

The resolution can be improved by increasing the column plate number, N, and/ or the separation factor, a (a = the ratio of the retention factors of the two compounds). N is the physical parameter and a is the chemical parameter for the separation. Higher N and a values give a better separation. 

FIGURE 4.1 Effect of the plate number (N), the separation factor (a ), and the retention factor (k) on resolution (Rs). (Adapted from Sandra, P.J. 1989. High Resolut. Chromatogr. 12 82-86. With permission.)... 

Equation (2) shows that the resolution is a function of three different factors (1) the resolving power of the column as measured by the plate number that expresses the relative width of bands (2) the relative retention of the two compounds that measures how far apart the bands are from each other and (3) the magnitude of retention, as separation is a result of retention. The relative influence of these factors has been discussed by Snyder (72,13) in a form very easy to use in practice. 

A great number of stationary phases are listed in catalogues and it is sometimes difficult to choose the best column for a particular analysis. The chemical nature of the phases and their polarities do not always allow one to predict which column will be optimal for a given separation. Therefore, a technique called the retention index system has been developed with the use of reference compounds whose retention factors differ with different stationary phases. Using retention indices obtained on columns of different stationary phases, it is possible to characterise a compound and facilitate its identification. 

Speed of separation Column capacity Retention factor, k Selectivity factor a Effective plate number, N... 

The main conclusion from Fig. 1 is that the well-known ideas of linear chromatography cannot be used when the isotherm is not linear. For example, the position of the peak maximum should not be used for the determination of a retention factor k. As Fig. 1 shows, such a k value would depend on the sample concentration and thus it might not be used for characterizing the retention of the analyte independently from its concentration. The width of the peak also has little to do with the number of plates. It will also be shown later in this chapter that the separation of two analytes cannot be simply characterized by a selectivity factor a, which is calculated as the ratio of the corresponding k values. 

Here, N is the column efficiency expressed in term of plate number, zu = A /Ai is the separation factor, which characterises the selectivity of separation, and k is the average retention factor of the two sample compounds 1 and 2 (or. to first approximation, the retention factor of the earlier-eluted compound 1). This expression is convenient for separation development and optimisation, as the three terms contributing to the resolution depend on many experimental conditions and the conditions can be adjusted to control each term more or less independently of the other two. (This does not fully apply for the last two terms, as the retention usually changes to some extent when the selectivity is manipulated.)... 

The value of Sp depends on several parameters, including the hydrodynamic properties of the channels, the centrifugal force (Sp increases to reach a maximum with the centrifugal force), the mobile-phase flow rate (Sp decreases linearly with the mobile-phase flow rate), the physical properties of the solvent system (such as viscosity, density, interfacial tension), the sample volume, the sample concentration, and the tensioactive properties of solutes to separate [2,3]. It is necessary to precisely monitor Sp because various chromatographic parameters depend on it, in particular the efficiency, the retention factor, and the resolution. Foucault proposed an explanation for the variation of Sp with the various parameters previously described. He modeled the mobile phase in a channel as a droplet and applied the Stokes law which relies on the density difference between the two phases, the viscosity of the stationary phase, and the centrifugal force. Then, he applied the Bond number, derived from the capillary wavelength which was formerly introduced for the hydrodynamic mode [4] and which relies on the density difference between the two phases the interfacial tension and the centrifugal force [3]. 

The retention of polar compounds (mono-, di-, and tri-substituted benzenes) on PGC, silica-based, and apolar copolymer supports was performed using unbuffered methanol water as eluent. The relationship between log k and the volume fraction of methanol was calculated separately for each solute. It was found that porous graphitic carbon retains polar compounds fairly well under reversed-phase conditions, while the retention factor increased with an increase in the number of polar substituents. In particular, the retention behavior of polar solutes on PGC supports is mainly governed by several polarity parameters (Hammett s constant, proton-donor capacity, and steric effects of substituents) and is quite different from that observed with other reversed-phase supports. Thus it was concluded that charge-induced interactions between the graphite surface as well as steric... 

Equation 31 -2 tells us that we can achieve faster separations by using short columns, higher-than-usual carrier gas velocities, and small retention factors. The price to be paid is reduced resolving power, caused by increased band broadening and reduced peak capacity (that is, the number of peaks that will fit in the chromatogram). 

In isocratic elution, resolution depends on the column efficiency or plate number N, the selectivity a, and the retention factor k, all of which can be experimentally influenced through systematic changes in individual chromatographic parameters. In the isocratic mode of separation, resolution is determined from... 

Equations 17.51 and 17.52 define a sufficient number of criteria to allow the correct choice of the operating conditions in an SMB operating rmder linear conditions. This set of conditions is equivalent to the one derived by Storti et al. [16] (see later. Subsection 17.6.5), the so called Triangle Method. However, both sets of conditions are based on the assumption that all columns have identical characteristics and an infinite efficiency. In practice, the different columns of an SMB separator cannot be identical. Their individual average porosity, permeability, retention factors, and efficiency are more or less different, however slightly. The influence of the possible differences between the colunms of an SMB imit on its performance is discussed later (Subsection 17.7.1.5)... 

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