Theory of Band Broadening and Column Efficiency

Column efficiency is affected by the amount of band broadening that occurs as the sample passes through the column. Rate theory describes the shapes of the peaks in quantitative terms and is based upon the infinite number of paths that the sample may take in order to elute out of the column. Some molecules will travel through the column quickly due to their accidentally inclusion in the mobile phase while other molecules will severely lag behind because of their accidental inclusion in the stationary phase. The result of these effects is a typical Gaussian shaped chromatographic band with a spread of velocities around the mean value. Furthermore, the width of the peak increases as it move down the column because of the increased opportunity for spreading.

Two additional, undesirable chromatographic features are fronting and tailing. With fronting, the front of the peak is drawn out and the tali is steepened. The opposite is true for tailing. Both effects can be cause by distribution constant that varies with the concentration. These non-ideal effects are unwanted because of they lead to poor separations.

The two terms used to measure column efficiency are plate height, H , and plate count, N. These two terms related by the following equation where L is the length of the column:

Greater column efficiency is characterized by a large plate count N and a small plate height H. Both H and N can be determined experimentally using the following two equations:

where L is the length of the column packing, W is the width of the magnitude of the base of the triangle and tR is the retention time of the analyte. Using the theory of band broadening, the efficiency of chromatographic columns can be approximated by the van Deemter equation:

where H is the plate height in centimeters and u is the linear velocity of the mobile phase in centimeters per second. The term A describes the multiple path effect, or eddy diffusion, B describes the longitudinal diffusion coefficient and CSu and CMu are the mass-transfer coefficients for the stationary and mobile phases, respectively.