Linear ideal chromatography

As already mentioned in paragraph 1.4, the concept of ideal linear chromatography is based on the model [13] which should have the following properties (i) infinitely fast setting of equilibrium between the solute concentrations in the mobile and stationary phases (ii) zero longitudinal diffusion of the solute in both phases (iii) 

When the terms representing the longitudinal diffusion of the solute in the mobile phase in equation 1 is neglected and equation 5 is substituted by the following equation 

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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...

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... 

Using these two sets of conditions, we can then describe four chromatographic systems (a) linear ideal chromatography, (b) linear nonideal chromatography, (c) nonlinear ideal chromatography, and (d) nonlinear nonideal chromatography. 

FIGURE 2.11 Isotherms for linear ideal chromatography Cs = concentration at surface or in stationary phase Cq = concentration in solution at equihbrium. 

Zhong G., Guioehon G. (1996) Analytieal Solution for the Linear Ideal Model of Simulated Moving Bed Chromatography, Chem. Eng. Sci. 51 4307-4319. 

This description is based on the differential equation for the transport velocity of a substance in the ideal linear gas chromatography [3] ... 

The model of ideal linear gas chromatography (Equation 1) [12] also describes the transport of a chemical species in the temperature gradient of a vacuum tube. At molecular flow conditions the linear velocity of the carrier gas, which is identical to the transport velocity of the adsorbate in the gas phase, has to be substituted by the fraction of the column length over the average retention time of the species in the column ... 

Zhong, G., Guiochon, G. Analytical solution for the linear ideal model of simulated moving bed chromatography, Chem. Eng. Sci., 1996, 51(18), 4307 1-319. 

There are simple algebraic solutions for the linear ideal model of chromatography for the two main coimter-current continuous separation processes. Simulated Moving Bed (SMB) and True Moving Bed (TMB) chromatography. Exphcit algebraic expressions are obtained for the concentration profiles of the raffinate and the extract in the columns and for their concentration histories in the two system effluents. The transition of the SMB process toward steady state can be studied in detail with these equations. A constant concentration pattern can be reached very early for both components in colimm III. In contrast, a periodic steady state can be reached only in an asymptotic sense in colunms II and IV and in the effluents. The algebraic solution allows the exact calculation of these limits. This result can be used to estimate a measure of the distance from steady state rmder nonideal conditions. 

In ideal chromatography, frontal analysis results in the gradual extension of a band of adsorbate at constant concentration down the column, assuming constant column temperature and constant partial pressure of adsorbate in the gas entering the column. By equating total adsorbate introduced to the column to the amount present in the gas phase plus adsorbent phase in a band of length on the column, one arrives at f = (qL/P (CG + vA/P ) t, where t is total time of flow in minutes. In the case of a linear isotherm this is just = AF t, as one intuitively expects. ven if the isotherm is nonlinear, (v/P is constant everywhere in the band, for P constant. This... 

Principles and Characteristics As mentioned already (Section 3.5.2) solid-phase microextraction involves the use of a micro-fibre which is exposed to the analyte(s) for a prespecified time. GC-MS is an ideal detector after SPME extraction/injection for both qualitative and quantitative analysis. For SPME-GC analysis, the fibre is forced into the chromatography capillary injector, where the entire extraction is desorbed. A high linear flow-rate of the carrier gas along the fibre is essential to ensure complete desorption of the analytes. Because no solvent is injected, and the analytes are rapidly desorbed on to the column, minimum detection limits are improved and resolution is maintained. Online coupling of conventional fibre-based SPME coupled with GC is now becoming routine. Automated SPME takes the sample directly from bottle to gas chromatograph. Split/splitless, on-column and PTV injection are compatible with SPME. SPME can also be used very effectively for sample introduction to fast GC systems, provided that a dedicated injector is used for this purpose [69,70],... 

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