Chromatographic peaks longitudinal diffusion

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. 

Obviously, the aim is for a chromatographic separation in which peak width is narrow relative to the time of elution (wi/Vr is minimized), i.e., the number of theoretical plates is maximized. There are three main factors that give rise to band broadening (1) multiple path effect (eddy diffusion), (2) axial (longitudinal) diffusion, and (3) mass transfer—slow transfer/equilibration between mobile and stationary zones. 

Many workers have discussed the first time moment or centre of gravity of a chromatographic peak undergoing elution. In the absence of longitudinal or eddy diffusion this property has been shown to be equal to the ideal thermodynamic retention time for zero-pressure-drop columns. More recently, theories regarding the first time moment have been extended by Hicks and by Buffham to include pressure-drop columns and the first time moment has been related to thermodynamic properties. Buflfham used the mean residence time t which is equivalent to the first time moment ... 

Figure 1 illustrates the s)unmetrical nature of a chromatographic peak and S5urunetrical broadening. Figure 2 illustrates the mutiple-path, longitudinal diffusion and mass transfer effects. 

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