Chromatography plate dispersion

Bismethylaminoanthraquinone (Disperse Blue 14) [2475-44-7] M 266.3, A,max 640 (594)nm. Purified by thin-layer chromatography on silica gel plates, using toluene/acetone (3.1) as eluent. The main band was scraped off and extracted with MeOH. The solvent was evapd and the dye was dried in a drying pistol [Land, McAlpine, Sinclair and Truscott J Chem Soc, Faraday Trans I 72 2091 7976]. 

There are two fundamental chromatography theories that deal with solute retention and solute dispersion and these are the Plate Theory and the Rate Theory, respectively. It is essential to be familiar with both these theories in order to understand the chromatographic process, the function of the column, and column design. The first effective theory to be developed was the plate theory, which revealed those factors that controlled chromatographic retention and allowed the... 

In a chromatographic separation, the individual components of a mixture are moved apart in the column due to their different affinities for the stationary phase and, as their dispersion is contained by appropriate system design, the individual solutes can be eluted discretely and resolution is achieved. Chromatography theory has been developed over the last half century, but the two critical theories, the Plate Theory and the Rate Theory, were both well established by 1960. There have been many contributors to chromatography theory over the intervening years but, with the... 

Column efficiency (number of theoretical plates) As in batch chromatography, one needs to determine the efficiency of the column in order to evaluate the dispersion of the fronts due to hydrodynamics dispersion or kinetics limitations. The relationship of N proportional to L can be expressed in terms of the equation for height equivalent to a theoretical plate (HETP) as ... 

As in chromatography, the most common variable to describe dispersion in FFF is the plate height (H), defined as the ratio between the spatial variance (Oj) of the band and its mean position (s) as it migrates inside the separation medium of length (L) ... 

Given a certain relative dispersion in flow velocities, Eq. 9.12 shows that the plate height increases with the mean velocity V of the solute. Clearly then, H can be reduced by decreasing the flowrate. However a reduction in flow will lead to longer retention times and slower separation. Therefore the choice of flow velocity requires a compromise between separation speed and efficiency. This subject has been treated in some detail for chromatography [2] we will say more about it in Chapter 12. 

Equation 11.18 shows that the plate height in partition chromatography is reduced by dispersing the stationary phase into extremely fine units or as a very thin film so that the average depth d is small. Other aspects of optimization will be discussed in the next chapter. 

What is H anyway The original interpretation, taken from distillation theory, was height equivalent to a theoretical plate, or HETP. We have seen that this concept was inadequate, and the preceding discussion of the van Deemter equation has presented it as a measure of the extent of spreading of an analyte zone as it passes through a column. Thus, a more appropriate term might be column dispersivity. In fact, another, independent approach to the theory of chromatography defines H as... 

The well-known parameters of chromatography, such as the number of theoretical plates, N, have been adapted to describe the zone dispersion in CE. Analogous to chromatography, the plate numbers are calculated from the migration time t and peak width b in half height ... 

For the solution of sophisticated mathematical models of adsorption cycles including complex multicomponent equilibrium and rate expressions, two numerical methods are popular. These are finite difference methods and orthogonal collocation. The former vary in the manner in which distance variables are discretized, ranging from simple backward difference stage models (akin to the plate theory of chromatography) to more involved schemes exhibiting little numerical dispersion. Collocation methods are often thought to be faster computationally, but oscillations in the polynomial trial function can be a problem. The choice of best method is often the preference of the user. 

A very detailed study of the combined effects of axial dispersion and mass-transfer resistance under a constant pattern behavior has been conducted by Rhee and Amundson [10]. They used the shock-layer theory. The shock layer is defined as a zone of a breakthrough curve where a specific concentration change occurs (i.e., a concentration change from 10% to 90%). The study of the shock-layer thickness is a new approach to the study of column performance in nonlinear chromatography. The optimum velocity for minimum shock-layer thickness (SLT) can be quite different from the optimum velocity for the height equivalent to a theoretical plate (HETP) [9]. 

The rate theory examines the kinetics of exchange that takes place in a chromatographic system and identifies the factors that control band dispersion. The first explicit height equivalent to a theoretical plate (HETP) equation was developed by Van Deemter et al. in 1956 [1] for a packed gas chromatography (GC) column. Van Deemter et al. considered that four spreading processes were responsible for peak dispersion, namely multi-path dispersion, longitudinal diffusion, resistance to mass transfer in the mobile phase, and resistance to mass transfer in the stationary phase. 

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