Golay’s equation

The term A is related to the flow profile of the mobile phase as it traverses the stationary phase. The size of the stationary phase particles, their dimensional distribution, and the uniformity of the packing are responsible for a preferential path and add mainly to the improper exchange of solute between the two phases. This phenomenon is the result of Eddy diffusion or turbulent diffusion, considered to be non-important in liquid chromatography or absent by definition in capillary columns, and WCOT (wall coated open tubular) in gas phase chromatography (Golay s equation without term A, cf. 2.5). 

Table 2.2 Order of magnitude comparison of the contribution to band broadening by non-uniform local mobile phase velocities, the flow profile (i /Dm) in capillary columns (the Cq term in Golay s equation)...

As correctly stated by Ettre [13], the idea of making a column with a porous sorbent layer on the inner capillary walls was implied in an early version of Golay s equation describing chromatographic zone broadening in an open capillary column, depending on the carrier gas velocity (the Amsterdam Symposium, 1958). 

Data in agreement with Golay s equation for ALOT columns [41]. 

In 1957 Marcel Golay published a paper entitled Vapor Phase Chromatography and the Telegrapher s Equation [Anal. Chem., 29 (1957) 928]. His equation predicted increased number of plates in a narrow open-tubular column with the stationary phase supported on the inner wall. Band broadening due to multiple paths (eddy diffusion) would be eliminated. And in narrow columns, the rate of mass transfer is increased since molecules have small distances to diffuse. Higher flow... 

Others have defined rate equations that would serve both GC and LC [8]. An interesting discussion summarizing much of this work has been published by Hawkes [9]. His summary equation is in the same form as Golay s, but it is less specific. The references can be consulted for more information. 

Figure 2 Chromatographic efficiency (A) and a chromatogram (B) obtained using an end-column electrochemical detector coupled to an OTLC column. (A) Experimentally measured data of the OTLC system (plotted points) is compared to the theoretical efficiency as predicted by the Golay equation (solid eurve) for a column diameter of 14 pm and diffusion coefficient of 10 cmVs. (B) Chromatogram obtained for an injection of 0.76 pg hydroquinone onto a 14 pm x 1.2 m column operated at 6 mm/s. (Adapted from Ref. 13.)...

The Dq values used in Equations 5.5 and 5.8 are specified for the column outlet pressure. When a vacuum pump is used to reduce the column outlet pressure, the Dq values at the outlet pressure are found as the product of the atmospheric-pressure values and the ratio of atmospheric pressure to the column outlet pressure. Figure 5.4 shows column efficiency (Golay) plots for 5-m-long, thin-fihn columns operated with hydrogen carrier gas at 50°C and assuming a Dq value of 0.4 cm /s at atmospheric pressure. Broken-line plots are for an outlet pressure of 1.0 atm, and the solid-line plots are for an outlet pressure of 0.01 atmosphere. The top pair of plots is for a 0.1-mm-i.d. column, the center pair for a 0.25-mm-i.d. column, and the bottom pair for a 0.53-mm-i.d. (megabore) column. 

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