The Basic Equations Describing Chromatographic Separations

We will state or derive a bare minimum of the equations most useful for understanding and describing how the most easily measured or controlled variables affect separations in chromatography. Many of the factors in these equations can be derived or calculated from more fundamental parameters, such as diffusion coefficients of analytes in the two chromatographic phases, column dimensions, or variables defined in the statistical theory of random variation. Such details are covered in more advanced texts. 

Manufacmrers of open tubular GC columns often specify column radius Tc and stationary phase film thickness (df), which is usually much smaller. Simple geometry enables us to calculate the phase ratio  

For packed GC columns one might have weighed the stationary phase applied to the particulate support, calculated its volume knowing its density, and measured the gas flow rate through the column, and combined it with the time for an unretained component to transit the column to get the mobile phase volume. In the case of LC columns where a molecular scale layer of stationary phase is bonded to an unknown surface area of support, stationary phase volume is very difficult to estimate. 

How much a component is retained by the stationary phase is better described by (fr — fiji) = 4, which is defined as the adjusted retention time (i.e., we count time from the introduction on the column, and then adjust it by subtracting the time it would take to flow through the column if no stationary phase interaction occurred). The capacity or retention factor described in Eq. (11.1) can be calculated from these time measurements using Eq. (11.3) 

The amount by which we can separate two components as peaks in time, or bands in distance, on a chromatographic system is determined by the selectivity of the stationary phase. It is defined for specific conditions namely, temperature in GC, or mobile phase composition in LC. Selectivity, a, is related to the ratio of partition constants of components A and B, or their more easily measured adjusted retention times, as illustrated in Fig. 11.2 and calculated from Eq. (11.4). 

---