Dispersion in Chromatography Columns - Alternative Equations for Peak Dispersion > The Giddings Equation > Page 65

Alternative Equations for Peak Dispersion

The Van Deemter equation remained unquestioned as the established equation for describing the peak dispersion that took place in a packed column until about 1961. However, as column performance was improved, it was found that when experimental data was fitted to the Van Deemter equation there was often very poor agreement between theory and experiment (particularly for data measured at high linear mobile phase velocities). In retrospect, this poor agreement between theory and experiment appeared to be due largely to the presence of experimental artifacts (such as those caused by extra column dispersion, large detector sensor and detector electronic time constants etc.) than any inadequacies of the Van Deemter equation. Nevertheless, it was the poor agreement between theory and experiment at the time, that provoked a number of workers in the field to develop alternative HETP equations. This work was carried out in the hope that a more exact relationship between HETP and linear mobile phase velocity could be obtained that would be compatible with experimental data.

The Giddings Equation

In 1961, Giddings (16) developed an HETP equation of which the Van Deemter equation was shown to be a special case. Giddings work was not provoked by poor agreement between theory and experiment but because he was dissatisfied with the Van Deemter equation inasmuch that it predicted a finite contribution to dispersion, independent of the solute diffusivity, in the limit of zero mobile phase velocity. This concept, not surprisingly, appeared to him unreasonable and unacceptable. Giddings developed the following equation to avoid this irregularity.

                                                       (46)

It is seen that when u >> E, equation (46) reduces to the Van Deemter equation,

                             

It is also seen that at very low velocities, where u << E, the first term tends to zero, thus meeting the requirements that there is no multipath dispersion at zero mobile phase velocity. Giddings also suggested that there was a coupling term that accounted for an increase in the 'effective diffusion' of the solute between the particles. The increased 'diffusion' resulted from the tortuous path followed by the molecules as they twisted and turned through the interstices of the packing. This process was considered to produced a form of microscopic turbulence that induced extremely rapid transfer of solute in the inter particulate spaces. However, again at  velocities where u >> E , this mixing effect could be considered complete and the resistance to mass transfer in the mobile phase between the particles becomes very small and the equation again reduces to the Van Deemter equation.