On the Multiplicity of Resolution Equations in the Chromatographic Literature

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Abstract
It is shown that, in spite of the multiplicity of resolution equations in the literature, there are only three basic relations: the Purnell, Knox, and Said equations of resolution. The Giddings equation for peak capacity in its differential form may also be extended to include resolution, leading to an alternative definition for it in which the width log mean average is used instead of the width arithmetic average. This definition is based on the continuity of peak width variation along the column and leads to numerical answers practically identical with those based on the original definition. This new definition of resolution, which is not an approximation of the original one but stands on its own merits, gives strength to an already deduced and simple peak capacity equation, which was thought to be approximate, as being exact. This eliminates the necessity of lengthy algebraic derivations leading to complicated equations which give no more than the results obtained by the simple peak capacity equation. Alternate resolution equations which are simple and exact were derived and a chart for the separation efficiency 1:1 as a function of the number of theoretical plates N and the separation factor α was prepared. The resolution Rs can be read on an extra scale in the plot. This chart may be used as a substitute for the controversial Glueckauf chart. The average plate number N used in the resolution equation was studied when N 1 # N 2. The study leads to the conclusion that due to the large uncertainties in both the experimental and theoretical determination of N, any suggestion for Nav other than the simple arithmetic average cannot be justified. Some erroneous equations and conclusions in the literature concerning resolution and peak capacity are pointed out.