GC026 The Golay Equation: Capillary columns – Part 2

A figure is used to describe the mass transfer in the stationary phase. We have a mid-horizontal line representing the interface. Above, we have the mobile phase and below, the stationary phase. At a given moment, an equilibrium is stablished, and two peaks with the base in the mid-horizontal line, but pointing to the top and to the bottom are depicted. An instant later the mobile gas moves the upper curve downstream, which gives rise to a situation of base size increase and the broadening of the overall zone of molecules. The solute molecules that moved ahead now participate in another partition between both phases, and vice versa for those that are in the stationary phase. The band broadening is inversely proportional to the speed of this process.

The Cs term in the Golay equation is:

Cs = (2*k*df) / (3*(1+k)^2*Ds)

Where df is the average film thickness of the liquid stationary phase, Ds is the diffusion coefficient of the solute in the stationary phase and k is the retention factor. If the contribution of this term should be minimized, the film thickness should be small and the diffusion coefficient large. Rapid diffusion through thin films produces less separation of the molecules. Thin films can be prepared by coating small amounts of liquid on the capillary walls and diffusion coefficients can only be controlled by selecting low viscosity stationary liquids.

An analogy for this process would a person jumping into and out a swimming pool; in shallow waters, the process is done quickly; if it is deep, it requires more time. Now consider the pool is filled with a viscous liquid as molasses or honey, the process would be much slower.

The ratio k/(k+1)^2 is also present in the Cs term. If the solute has high solubility in the stationary phase, it has a large value of k. The ratio is minimized at large values of k. However very little decrease occurs beyond a k of 20 and since analysis times increase with larger values of k, is no good to have k values greater than 20.

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