Topics - Variance
The variance of a chromatographic peak is a measure of its dispersion (peak spreading). Due to the processes that cause peak dispersion being random in nature, the elution curve takes the form of a Gaussian function (and error function). The standard deviation of the Gaussian peak is equal to half the peak width measured at 0.6065 of the peak height. The variance of the peak is equal to the square of the standard deviation. The ultimate dispersion of a solute peak is the result of a number of individual dispersion processes that take place inside and outside the column. Quantitatively, the dispersion of the final peak in a chromatogram is the result of the combination of the effect of all these dispersion processes. Each dispersion process, being random, would produce a respective Gaussian profile of concentration versus time. Unfortunately, the dispersion of the final peak can not be obtained by adding the standard deviations resulting from all the individual dispersion processes. The variance of the final peak, however, can be obtained by adding the variances of all the individual dispersion process. Thus, by developing functions for the variances of each of the dispersion processes, they can be summed to produce an expression for the total variance of the eluted peak. The theory that achieves this is called the Rate Theory and the equation for the variance per unit length of a column, so produced, is called the HETP equation.