At the beginning of a chromatographic separation the solute occupies a narrow band of finite width. As the solute passes through the column, the width of its band continually increases in a process called band broadening. Column efficiency pro- vides a quantitative measure of the extent of band broadening.
In their original theoretical model of chromatography, Martin and Synge2 treated the chromatographic column as though it consists of discrete sections at which partitioning of the solute between the stationary and mobile phases occurs. They called each section a theoretical plate and defined column efficiency in terms of the number of theoretical plates, N, or the height of a theoretical plate, H; where
A column’s efficiency improves with an increase in the number of theoretical plates or a decrease in the height of a theoretical plate.
Assuming a Gaussian profile, the extent of band broadening is measured by the variance or standard deviation of a chromatographic peak. The height of a theoreti- cal plate is defined as the variance per unit length of the column
where the variance, σ2, has units of distance squared. Because retention time and peak width are usually measured in seconds or minutes, it is more convenient to ex- press the standard deviation in units of time, τ, by dividing by the mobile phase’s average linear velocity.
When a chromatographic peak has a Gaussian shape, its width at the baseline, w, is four times its standard deviation, τ.
w = 4τ …………………12.15
The number of theoretical plates in a chromatographic column is obtained by com- bining equations 12.12 and 12.16.
Alternatively, the number of theoretical plates can be approximated as
where w1/2 is the width of the chromatographic peak at half its height.
It is important to remember that a theoretical plate is an artificial construct and that no such plates exist in a chromatographic column. In fact, the number of theo- retical plates depends on both the properties of the column and the solute. As a re- sult, the number of theoretical plates for a column is not fixed and may vary from solute to solute.