The Golay Equation

Where (H) is the variance per unit length of the column for the given solute, (k) is the capacity factor of the eluted solute, 

If the solute is unretained (i.e. k-0 ) then the the Golay equation reduces to, 

Taking a value of 2.5 XIO 5 for Dm (the diffusivity of benzyl acetate in n-heptane) equation (8) can be employed to calculate the curve relating (H) and (u) for an uncoated capillary tube. The results are shown in figure (3). 

Graph of H against U for a Capillary Column ( Unretained Peak) 

It is seen that the Golay equation produces a curve identical to the Van Deemter equation but with no contribution from a multipath term. It is also seen that, the value of (H) is solely dependent on the diffusivity of the solute in the mobile phase and the linear mobile phase velocity, It is clear that the capillary column can, therefore, provide a simple means of determining the diffusivity of a solute in any given liquid. 

The Golay equation [9] for open tubular columns has been discussed in the previous chapter. It differs from the other equations by the absence of a multi-path term that can only be present in packed columns. The Golay equation can also be used to examine the dispersion that takes place in connecting tubes, detector cells and other sources of extra-column dispersion. Extra-column dispersion will be considered in another chapter but the use of the Golay equation for this purpose will be briefly considered here. Reiterating the Golay equation from the previous chapter. 

Marcel Dekker, Inc. 270 Madison Avenue, New York, New York 10016 

---

The silica dispersion showed the smallest retention volume. It should be noted, however, that the authors reported that the silica dispersion required sonicating for 5 hours before the silica was sufficiently dispersed to be used as "pseudo-solute". The retention volume of the silica dispersion gave the value of the kinetic dead volume, /.e., the volume of the moving portion of the mobile phase. It is clear that the difference between the retention volume of sodium nitroprusside and that of the silica dispersion is very small, and so the sodium nitroprusside can be used to measure the kinetic dead volume of a packed column. From such data, the mean kinetic linear velocity and the kinetic capacity ratio can be calculated for use with the Van Deemter equation [12] or the Golay equation [13]. 

Most sensor volumes, whether in LC (e.g., a UV absorption cell) or in GC (e.g., a katharometer cell), are cylindrical in shape, are relatively short in length and have a small length-to-diameter ratio. The small length-to-diameter ratio is in conflict with the premises adopted in the development of the Golay equation for dispersion in an open tube and, consequently, its conclusions are not pertinent to detector sensors. Atwood and Golay [12] extended the theory of dispersion in open tubes to tubes of small length-to-diameter ratio. The theory developed is not pertinent here as it will be seen that, with correctly designed cells, that dispersion from viscous sources can be... 

Now, it has been previously shown from the Golay equation (chapter 8) that the value of (H) is given by a function of the form,... 

The Golay equation is strictly applicable to open tubular columns with smooth walls but, with certain approximations, it can be extended to include support-coated (77) and whisker-walled (78)... 

Beginning with the most favorable case, band broadening in open tubul2u eoluams is satisfactoi..iy described by the Golay equation, extended to situations of appreciable pressure drop by Glddings, equation (1.34)... 

Reduced parameters (section 1.7.10) can -be used to compare the potential of open tubular and packed columns to deliver a certain separation potential in SFC [8,43,53-56]. The Golay equation, equation 6.1, can be rewritten as... 

It should be noted that the Golay equation for capillary columns will be discussed in detail in the next chapter.)... 

The Golay equation (equation 7) can be Dut in a simplified form in a similar manner to the equations for packed columns -... 

In the Golay equation, ef is the phase thickness, D, and Ds are diffusion coefficients in the mobile phase (m) and the stationary phase (i), respectively. 

The use of electroosmotic flow (EOF) to drive the mobile-phase flow results in plug flow in the channels between particles, thus reducing CMu by a factor which can be estimated by considering such a channel as an open tube diameter dc, for which CM can be related to dc and retention factor, k, by the Golay equation [8]... 

The approximate efficiency of a capillary column operated at its optimum velocity (assuming the inlet/outlet pressure ratio is small) is given by the Golay equation. 

The dispersion that takes place in an open tube is described by the Golay equation (5),(ref. chapter 8) under conditions where there is no stationary phase and thus, k =0. As a result,the variance due to an open tube (otu )will be... 

The Golay equation for open-tubular columns of circular geometry is given by ... 

C. The detector sensitivity was also found to be inadequate even when increeised by a factor of two beyond its maximum range with an external amplifier. At this sensitivity, the solute peaJc still fronted slightly, but the noise level wets approaching unacceptable levels and no further reduction in sample size (split ratio of 10,000 1) wets possible. Nevertheless, comparison with Hjjjjjj predicted by the Golay equation is... 

For a capillary column, the "A" term is zero and the column inner radius, r, replaces the particle diameter in the van Deempter equation, resulting in what is known as the Golay equation, so that... 

These calculations ignore the fact that for small column diameters the resultant significant pressure gradients require a more fundamental form of the Golay equation (8,9). Because the optimum linear velocity becomes increasingly more independent of the diameter as the number of plates increases for diameters of this size... 

As we will see in Chapter 20, capillary columns are the most widely used in gas chromatography because of their high efficiency due to large numbers of plates. These columns have no packing, and so the eddy diffusion term in the van Deempter equation disappears. For open tubular columns, the modification of the van Deempter equation, called the Golay equation, applies ... 

How does the Golay equation differ from the van Deemter equation ... 

---