Ideal chromatography

Figure 1.10. Linear ideal chromatography. tQ=start of separation (point of sample injection) tfi=reten-tion time of component A tfi=retention time of component B tn=time for emergence of mobile phase from...

Figure 1.15. Isotherms for nonlinear ideal chromatography. Cg = cone, at surface or in stationary phase Cg = cone, in solution at equilibrium.

Artifacts in EE can also occur for peaks that are not fully resolved, as is often the case in enantiomer analysis of POPs. In this case, deconvolution of enantiomer peaks using least-squares fitting of chromatographic data to mathematical models accounting for non-ideal chromatography can provide more accurate and precise results than conventional integration techniques [340]. Of course, full chromatographic resolution of peaks is always desired, but this may not be possible or feasible. 

In ideal chromatography, we assume that the column efficiency is infinite, or in other words, that the axial dispersion is negligibly small and the rate of the mass transfer kinetics is infinite. In ideal chromatography, the surface inside the particles is constantly at equilibrium with the solution that percolates through the particle bed. Under such conditions, the band profiles are controlled only by the thermodynamics of phase equilibria. In linear, ideal chromatography, all the elution band profiles are identical to the injection profiles, with a time or volume delay that depends only on the retention factor, or slope of the linear isotherm, and on the mobile phase velocity. This situation is unrealistic, and is usually of little importance or practical interest (except in SMB, see Chapter 17). By contrast, nonlinear, ideal chromatography is an important model, because the profiles of high-concentration bands is essentially controlled by equilibrium thermodynamics and this model permits the detailed study of the influence of thermodynamics on these profiles, independently of the influence of the kinetics of mass transfer... 

The coherence theory of chromatography [9] is based on the use of the concept of coherence to explain the band profiles observed in ideal chromatography. A chromatographic coltunn subject to a disturbance will, after a period, settle into a "resolved " state, which consists of a series of composition waves, each of them being subject to the coherence condition... 

In Chapters 3 and 4, we discussed the numerical analysis procedure suggested by James et al. [35] and applied by Felinger et al. [36] to calculate solutions of the inverse problem of ideal chromatography and, more specifically, to derive the best possible estimates of the numerical coefficients of an isotherm model together with a figure of merit for any isotherm model selected. The main drawback of this approach is that it is based on the use of the equilibrium-dispersive model since... 

The relative importance of the contributions of the nonlinear thermodynamics of phase equilibrium and of the finite mass transfer kinetics to the band profile is evidenced and quantified by the numerical value of e. When e = 0, Cg = cjsiCm), and Eqs. 10.59a and 10.59b reduce to Eq. 10.58 by summing them up, which gives the equation of ideal chromatography. This asymptotic result can be justified in a few cases. On the other hand, the slower the mass transfer kinetics, the larger will be the value of e. 

This final expression linking the experimental parameters to the thermodynamic coefficient of distribution K, is valid for the ideal chromatography. 

Complete separation of the functionality fractions can be obtained, when the interaction of the terminal groups with the adsorbent is much stronger than that of the polymer chain (ideal chromatography at the critical point). 

Analogous to the models for a single column different model approaches exist. Here, only the approach for ideal chromatography will be explained. The more complex kinetic models result from this model in an analogous way as shown in Section 9.4.1. 

In ideal chromatography, it is assumed that the axial dispersion is negligibly small and the rate of the mass transfer kinetics is infinite in other words the column efficiency is infinite. In non-ideal chromatography the column efficiency is a defined and measurable value. 

In the second equality, W /2av is the average width at half-height, which is used more often than Wgv because W /2av is easier to measure. The better the resolution, the more complete the separation between neighboring peaks. Figure 21-4 shows peaks with a resolution of 0.50 and 1.00. For quantitative analysis, resolution >2 is desirable for negligible overlap. If you double the length of an ideal chromatography column, you will improve resolution by. ... 

Similarly, a decision must be made whether or not to take into account the influence on band profiles of such phenomena as axial dispersion (dispersion in the direction of the concentration gradient in the column) and resistance to mass transfer (i.e.. the fact that equilibration between mobile and stationary phases is not instantaneous). These phenomena are responsible for the finite efficiency of actual columns. Neglecting them and assuming the column to have infinite efficiency leads to a model of ideal chromatography. Taking them into account results in one of the models of nonideal chromatography. 

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