Separation factor definition

Hint Use mole ratios to convert separation factor definitions to Xn( ) =... 

Equation 11 when manipulated according to the definitions of Rj, yields an expression for the separation factor ... 

Figure 1.7—Separation factor (or selectivity factor) between two adjacent components, a alone does not determine if the separation is, in fact, possible. Here, the separation factor is in the order of 1.3. For two non-adjacent peaks, the relative retention factor can be obtained and it is designated by r. By definition, neither a nor r can be less than one.

In this equation i represents the first eluting peak of a peak pair and j the last eluting peak. Hence, by definition a is always larger than unity. Sometimes a is called the separation factor, which is somewhat unfortunate terminology because separation is influenced by other factors than just a (see section 1.3). a is the chromatographic parameter that is most directly related to the selectivity of the phase system. In this book, therefore, the word selectivity will often be associated with a. Using eqns.(1.7) and (1.10) we can write two other equations for a, . 

Sample size, maximum, 223 Sensitivity (detector), 95 Separation, definition of, 4 Separation factor, 20-22, 77 Separation number, 18 Sieving, molecular sieves, 45-47. See also Size exclusion chromatography Silica, surface of, 166, 167, 236, 237 Simulated distillation, 150... 

Designated by the term a and refers to the relative affinity of two components for a chromatographic matrix and related to the resolution. By definition the separation factor is larger than one and could be described by the following expression a = t2lti, where t2 is the elution time for the apex of the more slowly moving solute, and is the elution time for the apex of the more rapidly moving solute. See Chen, Y, Kele, M., Quinones, L,... 

The definition of the separation factor, Equation 7, when combined with infinite reflux condition. Equation 11, gives... 

The competitive Langmuir isotherm has some important properties. First, we observe that the separation factor is constant, independent of the relative composition of the mixture. The separation factor for a binary mixtiue is by definition ... 

The application of the z-transform and of the coherence theory to the study of displacement chromatography were initially presented by Helfferich [35] and later described in detail by Helfferich and Klein [9]. These methods were used by Frenz and Horvath [14]. The coherence theory assumes local equilibrium between the mobile and the stationary phase gleets the influence of the mass transfer resistances and of axial dispersion (i.e., it uses the ideal model) and assumes also that the separation factors for all successive pairs of components of the system are constant. With these assumptions and using a nonlinear transform of the variables, the so-called li-transform, it is possible to derive a simple set of algebraic equations through which the displacement process can be described. In these critical publications, Helfferich [9,35] and Frenz and Horvath [14] used a convention that is opposite to ours regarding the definition of the elution order of the feed components. In this section as in the corresponding subsection of Chapter 4, we will assume with them that the most retained solute (i.e., the displacer) is component 1 and that component n is the least retained feed component, so that... 

Membrane characteristics such as permeation, selectivity and separation factor are given throughout this chapter. The definitions for these characteristics are given in the appendix. 

Here Xa, Ya are strictly equilibrium mole fractions for component A in the adsorbed phase and adsorbate (fluid) phase, respectively as are Xb, Fb for component B. For equilibrium-based adsorptive separation process, the adsorbent selectivity is the same as the separation factor as defined in Eq. (1). Apparently, this definition is not applicable to other processes based on kinetic and steric effects. In a kinetically controlled adsorption process, the adsorbent selectivity depends on both equilibrium and kinetic effects. A simplified definition for adsorbent separation factor is given by Ruthven et al. ... 

According to Table III, the contribution of the silicone layer to the flow of the less permeable carbon monoxide Is only 1.2% and can be neglected, but it does contribute remarkably to the flow of the more permeable hydrogen by approximately 20%. Correspondingly, the H /CO separation factor of the selective polysulfone skin-layer is reduced by 20% from 40 to 33, because the ideal separation factor is by definition the ratio of the permeability rates or - vice versa - the reciprocal of the ratio of the flow resistances. With this invention, Henis and Tripodi discovered a simple and ingenious solution to the problem of surface porosity. They found a limiting value for the surface porosity. If it exceeds the value of 10, ... 

From the definition of a separation factor (Equation (2.9)), one can write... 

As each of the above contributes to the total function of the pack, the separate factors included in the definition are expanded below. 

Because of the definition of separation factor (12.15), abundance ratios on adjacent stages at total reflux are related by... 

The definition of the separation factor, equation (9-10), can be used to eliminate y from equation (9-22). After some algebraic manipulation, we have... 

Column effects. In order to establish optimal operating conditions, it is useful to consider the effects of system parameters on the resolution characteristics of an HDC system. HDC has been described as a chromatographic method with very low capacity but very high efiBciency. For example, the calibration curves show that the spectrum of sizes from less than 100 nm to greater than 300 nm is encompassed in less than about 5% of the column void volume. On the other hand, the theoretical plate count corresponding to the marker peak is typically in the range of several thousand per foot. Comparisons in terms of the specific resolution factor, enable a more precise analysis, since both the separation factor and peak dispersion are included in its definition. A simple form for the specific resolution between two particle populations of diameter Dpi and Dp2 is [11]. 

This equality between products can be recast into an equality between ratios, allowing the definition of a dipole separability factor Sq as their common value ... 

FIGURE 7.7 Schemes of the relationships between basic quantities of the poles (bottom axes) and the dipole (top axis) in the cases of an asymmetric dipole (left) and of a symmetric one (right). The filled polygons indicate the two definitions of the dipole extrema (Eqnation 7.85) and the numbered arrows indicate the correspondences set by relationships in Eqnations 7.83 and 7.86. (Numbers by the arrows refer to these relationships.) The separability factor is set to 1/2 so the dipole scale is twice the pole scales. 

The first step consists of setting the extrema of the dipole basic quantity. This is done by setting all differences with respect to the references as proportional through the separability factor Sq. The definition of the dipole limits and q " " (more exactly, their difference with the dipole reference g°) is determined by relating the dipole minimum to the first pole and the dipole maximum to the second one ... 

Another useful definition is that of the separation factor, SFab> between the elements A and B in a liquid—liquid system. It is simply defined as... 

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