Resolution

Resolution $R_{\text{S}}$ is a measure of the extent of separation of two peaks $j$ and $i$ in a chromatogram.

1. Absolute definition for symmetrical peaks #

The mathematical definition is

Equation 1.35: $R_{\text{S},j,i}=\frac{t_{\text{R},j}-t_{\text{R},i}}{2(\sigma_{\text{t},i}+\sigma_{\text{t},j})}\approx \frac{\Delta t_{\text{R},j,i}}{4 \sigma_{\text{t}}}$

Here, $t_{\text{R},j}$ and $t_{\text{R},i}$ are the retention times for peaks $j$ and $i$ , respectively, and \sigma_{\text{t},j} and \sigma_{\text{t},i} the peak standard deviations.

Equation 1.35 compares the distance between the two peaks with their widths and is always valid for two symmetrical peaks of equal height. The equation is also valid for

when the conditions are constant during the run (such as isothermal conditions in gas chromatography, GC, or isocratic conditions in liquid chromatography, LC); and
when the vary (such as in temperature-programmed GC or gradient-elution LC).

Figure: Schematic example of two peaks pairs with identical selectivity yet different degrees of resolution.

2. Method development #

Only in case of isocratic elution, the following equation may be derived (where it is assumed that the plate count is the same for the two peaks).

Equation 1.39: $R_{\text{S},j,i}=\frac{\sqrt{N}}{2} \cdot \frac{\alpha_{j,i}-1}{\alpha{j,i}+1} \cdot \frac{\bar{k}}{1+\bar{k}}$

This equation illustrates that there are three ways to improve resolution in method development, viz. (i) to ensure that there is sufficient retention, (ii) to increase the selectivity, and (iii) to increase the plate count.

Analytical Separation Science by B.W.J. Pirok and P.J. Schoenmakers

SEE SECTION 1.5.1

RESOLUTION

3. Purnell equation #

Equation 1.40 is often used in stead of Equation 1.39 although it is approximate and not exact such as Equation 1.39. Equation 1.40 is also known as the Purnell equation:

Equation 1.40: $R_{\text{S},j,i} \approx \frac{\sqrt{N}}{4} \cdot \frac{\alpha_{j,i}-1}{\alpha{j,i}} \cdot \frac{\bar{k}}{1+\bar{k}}$