The variance and the quantity 2Dt in capillary zone electrophoresis

The variance is generally used as a measure of dispersion of zones in capillary zone electrophoresis (CZE). It is a quantitative measure of the separation power of a system and different causes of dispersion can be rated by their partial variances, which can be summed up to total variance. However, the additivity is only valid for independent dispersion sources, a fact that often seems to be ignored. The ubiquitous dispersion source diffusion is taken into consideration by the Einstein term 2Dt. Other sources of dispersion are, e.g., injection, detection, thermal gradients, adsorption, and hydrodynamic flow. For each of these sources various variance expressions have been derived. The origin of the term 2Dt and its relation to the variance is explained and the calculation of variance in general is discussed. The equivalence of the diffusion variance and the term 2Dt is verified with some simple initial forms of sample zone and the additivity of variances in ideal zone electrophoresis is demonstrated. The change of conductivity in zones results in asymmetrical zone forms which is an indication of nonideality of a system. It is shown that in such cases the term 2Dt is no longer valid and its use as an additive variance component leads to an erroneous total variance. Because in zone electrophoresis conductivity in a zone always changes more or less, the additivity of variances is never perfectly valid. However, in many cases the nonideality may be so small that the additivity in practice is still applicable. A generally valid way to calculate theroretically the total variance of a zone is to derive a functional representation of the distribution and then calculate the variance from it. This is possible only in the simplest cases. Usually the distribution must be calculated by numerical methods.