The resolution equation

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Page ID: 61059

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Nico Vonk, Avans+, Breda, The Netherlands

Abstract:

A simulation shows how the resolution factor changes when we change the three parameters k, N and α.

Level: Basic

We can combine all the equations concerning efficiency, selectivity, retention and resolution mathematically to obtain the so called resolution equation:

\[R_s=\dfrac{1}{4}\times\dfrac{α-1}{α}\times\dfrac{k}{k+1}\times\sqrt{N_{th}}\]

In qualitative terms, this equation tells us that:

The sample components must be retained by the stationary phase in order to become separated (k > 0).
Separation also depends on different degrees of retention, i.e. the k values must be different from each other so that the selectivity α is greater than unity. The greater the difference, the greater is the chance of separation.
The column plate number N must be high enough in order to produce sufficiently narrow peaks that are baseline separated. When N is not sufficiently high, peaks will overlap and the separation will be incomplete.

With this equation we can explain and/or predict the effect of any change in chromatographic parameters on the separation. This equation is, therefore, an important tool in method optimization. The simulation shows how the resolution factor changes when we change the three parameters α, k and Nth:

CHROMEDIA PROGRAM

A resolution value smaller than 1.5 leads to incomplete separation: the peaks overlap. The overlap can sometimes be so large that the individual components cannot be distinguished at all. One peak then "contains" two compounds. With a resolution value between 1.25 and 1.5, the extent of separation depends on peak symmetry (discussed later). With a R_s smaller than 1.25 we can never obtain baseline separation.