Plate Theory and Extensions - Vacancy Chromatography > Page 71

Vacancy chromatography can be considered theoretically using the equations derived from the plate theory for the elution of positive concentration profiles. If a mobile phase contains a solute at a concentration (Xo), then, after equilibrium, the eluent from the column will also contain the solute at a concentration (Xo). Let a sample containing the same solute at a concentration (Xi) be injected onto the column under where either (Xo<Xi) or (Xo>Xi),but (XoXi). Such an injection will produce a transient change in the concentration (Xo) of solute in the mobile phase. From the plate theory, this transient concentration change will be eluted through the column as a concentration difference and will be sensed as a negative or positive peak by the detector. The equation describing the resulting concentration profile of the eluted peak, from the plate theory will be,

 

                                                     

  

where X(n) is the concentration of the solute in the mobile phase leaving the (n)th plate,
(v) is the volume passed through the column in plate volumes,
and (n) is the number of theoretical plates in the column.

 

If the sample consisted of pure  mobile phase containing no solute, then Xi = 0 and