Band broadening (column efficiency)

After injection, a narrow chromatographic band is broaden during its movement through the column. The higher the column band broadening, the smaller the number of components that can be separated in a given time. In other words, the sharpness of the peak is an indication of how good, or efficient a column is.

The peak width is an indication of peak sharpness and, in general, an indication of the column efficiency . However, the peak width is dependent on a number of parameters (column length, flow rate, particle size). Flow rate is the only parameter which can be changed from run to run on the same column. Thus, it is better to consider a relative value to express column efficiency.

In absence of the specific interactions or sample overloading, the chromatographic peak can be represented by a Gaussian curve with the standard deviation (s). The ratio of standard deviation to the peak retention time (s/tR) is called the relative standard deviation, which is independent on the flow rate.

In practice, the square of the reciprocal value is normally used . This has become the accepted expression of column efficiency. The reason for using the second power has come from statistics, and it is related to the fact that not the standard deviation , but its square, the variance , is the basic measure of normal distribution. The value N is called the plate number or the number of theoretical plates. Term "theoretical plate" comes form the analogy with the distillation theory.

In practice, it is more convenient to measure peak width either at the base line, or at the half height, and not at 0.609 of the peak height, which actually correspond to .

             (2)
 
         (3)
 

The plate number depends on column length: the longer the column, the larger the plate number. Therefore, the plate height term has been introduced to measure how efficiently column has been packed, h = L/N .

The lower the plate height and the higher the plate number, the more efficient the chromatographic column.