Dispersion in Chromatography Columns - Alternative Equations for Peak Dispersion > The Knox Equation > Page 69

Employing the reduced parameters the equation of Knox takes the following form,

                                                            (50)

It should be noted that the constants of the equation were arrived at by a curve fitting procedure and not derived theoretically from a basic dispersion model; as a consequence the Knox equation has limited use in column design. It is, however, extremely valuable in accessing the quality of the packing. This can be seen from the diagram shown in figure 16.

 

Figure  16. Graph of Log. Reduced Plate height against Log. Reduced Velocity for Poor and Well Packed Columns

The curves represent a plot of Log.(h ),(Reduced Plate height)against Log.(n ), (Reduced Velocity). The lower the Log.(h ) versus the Log.(n )  curve the better the column is packed. At low velocities the (B) term dominates and at high velocities the (C) term dominates as in the Van Deemter equation. The best column efficiency is achieved when the minimum is about 2 particle diameters and thus, Log (h ) is about 0.35. The minimum value for (H) as predicted by the Van Deemter equation has also been shown to be about two particle diameters. The optimum reduced velocity is in the range of 3 to 5 that is Log.(n) takes values between 0.3 and 0.5. The Knox equation is a simple and effective method of examining the quality of a given column but, as stated before, is not nearly so useful in column design due to the empirical nature of the constants.