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Two of these four factors promoting the broadening of the analyte band are influ-

enced by the flow rate of the eluent through the column. Longitudinal diffusion,

defined by Fick’s law, is inversely proportional to flow rate whilst equilibration time

due to the partitioning of the analyte is directly proportional to flow rate. These two

factors together with that of the multiple pathways factor determine the value of the

plate height for a particular column and, as previously stated, plate height determines

the width of the analyte peak. The precise relationship between the three factors and

plate height is expressed by thevan Deemter equation(equation 11.11) which is

shown graphically in Fig. 11.3:

H¼AþB

ux

þCux ð 11 : 11 Þ

whereuxis the flow rate of the eluent andA, BandCare constants for a particular

column and stationary phase relating to multiple paths, longitudinal diffusion and

equilibration time respectively.

Figure 11.3 gives a clear demonstration of the importance of establishing the

optimum flow rate for a particular column. Longitudinal diffusion is much faster in

a gas than in a liquid and as a consequence flow rates are higher in gas chromatog-

raphy than in liquid chromatography.

As previously stated, the width of an analyte peak is expressed in terms of the

standard deviations, which is half the peak width at the point of inflexion (0.607hp,

wherehpis the peak height, Fig. 11.1). It can be shown thats¼

p

2 PtRwherePis the

diffusion coefficient of the analyte that is a measure of the rate at which the analyte

moves randomly in the mobile phase from a region of high concentration to one of

lower concentration. It has units of m^2 s^1. Since the value ofsis proportional to the

square root oftRit follows that if the elution time increases by a factor of four the

Eluent flow rate

Column plate height

Plate height

Longitudinal

diffusion

Equilibration time

Multiple paths

Optimum

flow rate

Fig. 11.3Example of a van Deemter plot. The plot shows that the optimum flow rate for a given column is the

net result of the influence of flow rate on longitudinal diffusion, equilibration time and multiple pathways.

440 Chromatographic techniques