Chromatographic processes Gaussian profile

The standard deviation chromatographic zone with (approximately) a Gaussian profile is related to the width of the zone at the inflection points. As in any error process, the square of the standard deviation (the variance) accumulates and hence Equation 22.9 follows. It is useful to keep in mind that in column-chromatographic methods, a is a volume element and that increasing extra-column dead volume (for example) will increase and decrease the total number of plates. 

In this model, each step of the chromatographic process is analyzed in detail [16]. Separate mass-balance equations are written for the mobile phase that flows through the bed and for the stagnant mobile phase inside the particles. Separate kinetic equations are then written for the kinetics of adsorption/desorption and for mass transfer. Again, if these kinetics are not unduly slow, the band profile tends toward a Gaussian shape (in which case a simpler model is actually more suitable). 

This expression will predict the movement of a solute whose adsorption is in equilibrium with the surrounding strata. This equilibrium chromatographic motion will result in the migration of a band of activity whose concentration profile is gaussian and whose deviation will be a function of the hydrodynamic dispersion, T (due to statistical variations in path length) and absorptive dispersion T (due to statistical variations in the absorption and desorption process). While these dispersions are interactive and do not sum in a simple fashion they both depend on path length. 

Fig. 14. The calculated concentration profile for bovine trypsin undergoing dynamic interconversion whilst chromatographed on a reversed phase column. It is assumed that the interconversion processes occur by a two-state reversible transition with overall forward conversion and reverse conversion rates r /t = r /t =1.25X10 sec and that at / = 0 and equilibrium mixture of two inteiconverting components of equivalent mole fractions is initially loaded onto the column. It is further assumed that the migrating zone for each component generates a Gaussian distribution profile with a = 0.1 and that the effective diffusion coefficients of both forms are the same. From (23].

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