To fairly compare columns characterized with different mobile phases, different particle sizes (packed-column chromatography) or different column diameters (open-tubular chromatography) it is important to use reduced parameters.
Reduced parameters are dimensionless values that essentially normalize the parameters in the plate-height equation. The relevant parameters are shown in Table 1.
Open-tubular chromatography #
In open-tubular (“capillary”) columns the reduced plate height (h) is the ratio of the absolute plate height (in length units, e.g. µm) and the column diameter (in he same length units as h). As a result, the reduced plate height is a dimensionless number.
The reduced linear velocity is also a dimensionless number (known by engineers as the Péclet number). It is the ratio of the product of the column diameter (in length units, such as m) and the linear velocity (m s-1), divided by the diffusion coefficient of the analyte in the mobile phase (m2 s-1).
For packed columns the characteristic diameter is the particle diameter instead of the column diameter. The essential idea behind this concept is that columns (of a given type; e.g. open-tubular columns or packed columns) behave the same if the reduced parameters are the same.
This is illustrated for some open-tubular columns in Figure 1. Figure 1A shows actual H vs. u (“van Deemter”) curves, calculated using the Golay equation (Section 1.7.7) with k = 1, \delta_{\text{f}} = 0.3 and D_{\text{m}} = 5×10-6 m2 s-1. The legend indicates the column internal diameter in µm.
The actual plate heights are highest and the optimum linear velocity is lowest for the 530-µm i.d. column, whereas the 250-µm i.d. column shows the lowest plate heights and the highest optimum linear velocity.
However, when plotting the reduced h vs. \nu curves all three lines coincide. For all three curves nu_{\text{opt}} = 5.7 and h_{\text{min}} = 0.7. This makes it easy to predict the actual minimum plate height and optimum velocity for a column with any diameter. For the 250-µm i.d. column the outcome is H_{\text{min}} = 0.7 × 250 = 175 µm, while u_{\text{opt}} = 5.7 × 5×10-6 / 5×10-6 = 0.11 m s-1. For a 100-µm i.d. column we obtain H_{\text{min}} = 70 µm and u_{\text{opt}} = 0.28 m×s-1, etc.
Open-tubular chromatography #
For packed columns, the concept of reduced parameters reveals, for example, that when replacing 5-µm HPLC particles by 1.7-µm UHPLC particles the actual plate height will be about 3 times lower and the optimal linear velocity three times higher.
Figure 2. Left: Effect of particle size on the plate height as a function of flow rate. Right) Reduced plate heights or the curves shown to the left. Adapted from Ref. [1], Copyright (2017), with permission from Elsevier.
SEE ALSO SECTION 1.7.3
Reduced Plate Height Parameters
References #
[1] M. M. Dittmann and X. Wang, in Handbook of Advanced Chromatography /mass Spectrometry Techniques, eds. M. Holçapek and W. C. Byrdwell, Elsevier, 2017, pp. 179–225.
