Multipath term

In 1967, Huber and Hulsman [2] introduced yet another HETP equation having a very similar form to that of Giddings. Their equation included a modified multipath term somewhat similar in form to that of Giddings and a separate term describing the resistance to mass transfer in the mobile phase contained between the particles. The form of their equation was as follows ... 

In order to relate the value of (H) to the solute diffusivity and, consequently, to the molecular weight according to equation (11), certain preliminary calculations are necessary. It has already been demonstrated in the previous chapter (page 303) that the dynamic dead volume and capacity ratio must be used in dispersion studies but, for equation (11) to be utilized, the value of the multipath term (2Xdp) must also be... 

It is seen that the composite curve obtained from the Huber equation is indeed similar to that obtained from that of Van Deemter but the individual contributions to the overall variance are different. Although the contributions from the resistance to mass transfer in the mobile phase and longitudinal diffusion are common to both equations, the (A) term from the Huber equation increases with mobile phase flow-rate and only becomes a constant value, similar to the multipath term in the Van Deemter equation, when the mobile velocity is sufficiently large. In practice, however, it... 

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. 

In a similar manner to the design process for packed columns, the physical characteristics and the performance specifications can pe calculated theoretically for the open tubular columns Again, the procedure involves the use of a number of equations that have been previously derived and/or discussed (1). However, it will be seen that as a result of the geometric simplicity of the open tubular column, there are no packing factors and no multipath term and so the equations that result are far less complex and easier to manipulate and to understand. 

A multipath term in van Deemter equation As surface area... 

Martin equation, 235 Mass transfer, 28, 29, 32 Mesh sizes, 115 Micellar LC, 224 Microbore columns in LC, 200 Molecular sieves, 46, 47, 117 Molecular weight chromatograph, 83 Multipath term in rate equation, 31... 

The A term, which was known as the eddy diffusion effect, does not exist in Hawkes s equation as a separate term. The effect is better called a multipath term it is flow-dependent, contrary to the original van Deem-ter equation, and is included in the C term. An exact equation would be very complicated and is inappropriate because of the negligible contri-... 

The open-tubular column or capillary column is the one most commonly used in gas chromatography (GC) today. The equation that describes dispersion in open tubes was developed by Golay [1], who employed a modified form of the rate theory, and is similar in form to that for packed columns. However, as there is no packing, there can be no multipath term and, thus, the equation only describes two types of dispersion. One function describes the longitudinal diffusion effect and two others describe the combined resistance to mass-transfer terms for the mobile and stationary phases. 

The multipath term A arises, as in other forms of chromatography, from the different pathways the analyte molecule can follow in permeating the absorbent layer. 

Multipath term (Wf). Broadening of a chromatographic zone as it passes through the column arises from the variable channels which the... 

The multipath term (A) This term applies to columns packed with support particles. It becomes zero for open tubular columns when the mobile phase velocity is slow enough for the flow to be laminar (i.e., without mrbulent eddies). In a packed column, the paths of individual analyte molecules will differ as they take different routes through the spaces between the particles. Thus they will travel varying distances before they exit the column, and the difference between these distances contributes to band broadening. The relative magnitude of the multipath term depends on the particle and column dimensions. If Fig. 11.3 depicted a packed column, A would be a constant value for all values of u, and would appear as a horizontal line raising the curve by a constant amount. The multipath process is illustrated in Fig. 11.4. 

Figure 11.4 Mechanism of origin of multipath term A of Van Deempter equation.

Here H is the theoretical plate height, a parameter that characterizes the effectiveness of the chromatographic separation. The smaller the H the more powerful is the separation. A is the Eddy diffusion term (or multipath term), B relates to longitudinal diffusion, C represents the resistance of sorption processes (or kinetic term), and u is the linear flow rate. For a given chromatographic system. A, B, and C are constants, so the relationship between H and u can be plotted as shown in Fig. 6. 

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