Dispersion in Chromatography Columns - The Golay Equation > Page 72

Taking  a value of 2.5 x10-5 for Dm (the diffusivity of benzyl acetate in n-heptane) equation (52) can be employed to calculate the curve relating (H) and (u) for an uncoated  capillary tube. The results  are shown in figure 17. 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 (equation (52)) can be put in a simplified form in a similar manner to the equations for packed columns:-

                                                                          (54)

Where,   and          

The form of the HETP curve for a capillary column is the same as that for a packed column and exhibits a minimum value for (H) at an optimum velocity.

Differentiating equation (54) with respect to (u),              

Thus, when      H = Hmin,    then,            

         and thus,                                                      (55)

Substituting for (B) and (C) in equation (55)

                 

or,                     (56)

It is seen that, in a similar manner to the packed column, the optimum mobile phase velocity is directly proportional to the diffusivity of the solute in the mobile phase. However, in the capillary column the radius (r) replaces the particle diameter (dp) of the packed column and consequently, (uopt) is inversely proportional to the column radius.