Linear non-ideal chromatography

The mass balance of a solute in the infinitesimal volume of a chromatographic bed (column), delineated by two parallel sections of identical area A, drawn perpendicular to the direction of the mobile phase flow at distances z and z + dz from the beginning of the bed leads to the equation  

If K is the area of the phase interface in unit bed volume, then for the flow /(M S) it holds that 

Changes in the concentration of the solute in the stationary phase occur due to transfer of the solute across the phase interface and longitudinal diffusion in the stationary phase. Thus, it may be written 

Let us now define the initial and boundary conditions for the case of column elution chromatography. At the beginning no solute is present in the column, i.e. 

The solute is applied to the column in the form of a concentration pulse of the concentration Cj o duration fit, so that 

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The model of ideal linear non-equilibrium chromatography is sufficient to cover all cases of practical importance, in which rate constants were determined. 

In this way four combined models of chromatography may be postulated A, ideal linear B, non-ideal linear C, ideal non-linear and D, non-ideal non-linear. Whereas the models B and D are real, the models A and C are apparently hypothetical. In spite of this even the latter two models are very useful from the theoretical point of view. 

An exact solution of a completely general model of non-ideal linear chromatography has not yet been found. Therefore, approximate methods [15,16] which would make... 

H.C. Thomas (1948) Mathematical treatment of the model of non-ideal linear chromatography (neglecting the longitudinal solute diffusion)... 

The approximations involved in the determination of crystallinity by gas chromatography were evaluated in reference [189]. The non-ideality of the gas phase and the modification of the enthalpy of vaporization of the injected substance with temperature cause the retention diagrams at temperatures below T, to be not linear, but slightly convex against abscissa. Thus the FJ values obtained from linear extrapolation of data from temperatures higher than T, will give values lower than the true value for polymer crystallinity, especially at low temperatures. 

Nile Red was recently introduced as a solvatochromic dye for studying supercritical fluids (10). Although not ideal, Nile Red does dissolve in both nonpolar and polar fluids and does not lose its color in the presence of acids, like some previously used dyes. Major criticisms of Nile Red include the fact that it measures several different aspects of "polarity" simultaneously (polarizability and acidity (15)) yet it is insensitive to bases (10). However, in chromatography other single dimension polarity scales, like P, are routinely used. Measurements with Nile Red and other dyes indicate that the solvent strength of binary supercritical fluids is often a non-linear function of composition (10-14). For example, small... 

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