The Knox Equation During 1972 and 1973 Knox and his co-workers (18), (19), and (20) carried out a considerable amount of work on different packing materials with particular reference to the effect of particle size on the reduced plate height of a column. The concept of reduced plate height (h ) and reduced velocity  (n) was introduced by Giddings (21) and (22) in 1965 in an attempt to form a basis for the comparison of different columns packed with particles of different diameter. The reduced plate height is defined as,                                             &

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

of the sample valve) to about 6000 p.s.i. Thus, if the pressure is limited, then to utilize longer columns the particle diameter must be increased to reduce the flow impedance and allow the longer column to be operated at the optimum mobile phase velocity. The use of larger particles to reduce flow impedance and thus permit the use longer column is possible because, at the optimum velocity, the inlet pressure decreases as the square of the particle diameter but the efficiency is only reduced approximately linearly with the particle diameter (thids is true for packed columns only). Thus, doubling the particle diameter allows the column length to be increased by a factor of four and as the plate height will be increased by a factor 2 the net result will be to double the number of theoretical plates