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usual dispersion processes that take place in the column to provide a value for the ultimate peak variance. Consequently, if the column efficiency is not to be seriously reduced the maximum volume of sample that can be placed on the column must be limited. Consider a volume (Vi) of sample, injected onto a column. This sample volume will constitute a rectangular distribution on the front of the column. Now, (as discussed in Dispersion in Chromatography Columns of this series) the variance of the peak eluted from the column will be the sum of the variances of the injected sample plus the normal variance of the eluted peak. Thus:                                  where  s2  is the variance of the eluted peak, si2 is the variance of the eluted sample,          and sc2 is the variance due to column dispersion. The maximum increase in band width that can be accepted due to any (and all) extraneous

that can be placed on the column and thus, the ultimate sensitivity of the analysis. Now, summing the variances         where () is the overall variance of the eluted peak,            () is the variance of the sample volume,     and () is the variance due to column dispersion. It has been established that the variance of a rectangular distribution of sample volume (Vi) will be . It can again be assumed that the peak variance can be increased by 10% as a result of extra column dispersion without seriously denigrating column performance. Unfortunately, all the permitted extra column dispersion can not be assigned to the effect of a finite sample volume as some must be allocated to other dispersion sources. As an arbitrary judgment half of the permissible extension of peak width will be allotted to the effect of the sample volume (i.e., the variance can be increased by 5 %). This is a variable proportion as it

a variance  ,                 Hence,         where,  () is the variance of the solute band as sensed by the detector. The above equation is the algebraic enunciation of the principle of the summation of variances and is fundamentally important. If the individual dispersion processes that are taking place in a column can be identified, and an expression for the variance arising from each dispersion process evaluated, then the variance of the final band can be calculated from the sum of all the individual variances. This is how the Rate Theory provides an equation for the final variance of the peak leaving the column. The Alternative Axes of a Chromatogram An elution curve of a chromatogram can be expressed using parameters other than the volume flow of mobile phase as the independent variable. The Plate theory provides an equation that expresses

extra column dispersion (except for that from the finite sample volume), will be considered negligible.  It is now possible to apply the principle of the summation of variances to the effect of sample volume. Thus,                               s2 = si2 + sc2        where (s2) is the overall variance of the eluted peak,            (si2) is the variance of the sample volume,     and (sc2) is the variance due to column dispersion

To develop an HETP equation it is necessary to first identify the dispersion processes that occur in a column and then determine  the variance that will result from each process per unit length of column. The sum of all these variances will be (H), the Height of the Theoretical Plate, or the total variance per unit column length. There are a number of methods used to arrive at an expression for the variance resulting from each dispersion process and these can be obtained from the various references provided. However, as an example, the Random-Walk Model introduced by Giddings (3) will be employed here to illustrate the

Maximum Permissible Extra Column Dispersion The total variance of an eluted peak ()will be the sum of the variance due to column dispersion () and the variance from extra column dispersion ().                Thus,                    Now, the maximum increase in peak variance from extra column dispersion that can be tolerated while not significantly effecting the resolution is 10 %. This value was suggested by Klinkenberg (3) in 1960 and has been accepted as the criteria for extra column dispersion since that time