Spatial and temporal progressions of spatial statistical moments in linear chromatography

Quantitative comparison of performance of isothermal and temperature-programmed gas chromatography

As a basic metric of separation for comparing isothermal and temperature-programmed GC (gas chromatography), we used the separation measure. S (defined elsewhere). We used this metric as both a measure of separation of any two peaks, and a measure of separation capacity of arbitrary intervals where peaks can potentially exist. We derived several formulae for calculation of S for any pair of peaks regardless of their shape and the distance from each other in isothermal and temperature-programmed GC. The formulae for isothermal GC can be viewed as generalizations of previously known expressions while, in the case of temperature-programmed GC, no equivalents for the new formulae were previously known from the literature. In all formulae for S. we identified similar key component-metrics (solute separability, intrinsic efficiency of separation, specific separation measure, separation power) that helped us to identify and better understand the key factors affecting the separation process. These metrics also facilitated the quantitative comparison of separation capacities and analysis times in isothermal and temperature-programmed GC. Some of these metrics can be useful beyond GC. In the case of GC, we have shown that, if the same complex mixture was analyzed by the same column, and the same separation requirements were used then isothermal analysis can separate more peaks than its temperature-programmed counterpart can. Unfortunately, this advantage comes at the cost of prohibitively longer isothermal analysis time. The latter is a well know fact. Here, however, we provided a quantitative comparison. In a specific example, we have shown that a single-ramp temperature program with a typical heating rate yields about 25% fewer peaks than the number of peaks available from isothermal analysis of the same mixture using the same column. However, that isothermal analysis would last 1000 times longer than its temperature-programmed counterpart. Using twice as longer column in the case of a temperature-programmed analysis, allows one to recover the 25% disadvantage in the number of separated peaks, while still retaining a 500-fold advantage in the speed of analysis.