Basic chromatographic relationships

In the previous sections the thermodynamic theory of chromatographic retention was discussed . Here we will discuss how it is actually working in the real systems, and how the equations are related to the measurable parameters.

Dead volume

As we have seen, the dead volume (Vo) is present in all basic equations and calculated parameters. So, we have to discuss it deeper.

Dead volume is the total volume of the liquid phase in the chromatographic column.

It is obvious from the definition that Vo is the geometrical parameter, and it should not be dependent on the types of analytes and mobile phase. This definition is the most general and it is true if the stationary phase (adsorbent) used is rigid, nonsoluble and nonpermeable. This definition may not be applicable for some ion-exchange stationary phases based on the cross-linked semi-rigid polymers, which may swell or shrink depending on the mobile phase.

In adsorption (normal- or reversed-phase) chromatography and in size-exclusion chromatography, dead volume is a property of the column and it has to be measured independently. But, the question - how to measure it - is the most complicated one.

The most obvious way, is to inject a so called "nonretained" component in the column and measure its retention volume. But, what is the "nonretained component", and how is it found?

In the ideal situation, if we could some how mark eluent molecules in such a way that it will not change their properties, and inject them, then their retention will show a true dead volume. It was shown experimentally that even deuturated eluent molecules show some adsorption effect, and could not be used for dead volume measurement.

From the basic retention equation we can conclude that a compound is not retained if its derivative of the excess adsorption is equal to zero. We have to mention that in general, excess adsorption could be positive (preferential adsorption) and negative.

The simple and accurate method to measure dead volume does not exist. For analytical applications most of the suggested methods could be used:
Injection of one of the eluent components;
Injection of the uracil solution in reversed phase HPLC and benzene in normal phase.
For most of the modern columns a simple formula, based on the column and adsorbent geometry could be used:

All these methods may have a deviation from the real dead volume. A 10%  deviation is acceptable for analytical purposes.

In physico-chemical applications a true value of Vo should be used.

Two basic methods to measure thermodynamic dead volume have been suggested. All are based on the specific features of the excess adsorption isotherm: that the excess adsorption of the pure component is equal to zero.

If we fill the column with one solvent and displace it with another, than the inflection point of the resulting frontal chromatogram will have retention volume equal to dead volume.

Another method is based on the minor disturbance of the equilibrated chromatographic system. If we equilibrate the system at the certain binary eluent composition and inject a small amount of the same eluent with a small difference in the composition, then the injected "disturbance" will move through the column according to the basic retention equation. By measuring this at different equilibrium concentrations, we will finally have an experimental dependence of the retention volume on the eluent composition for the minor disturbance peaks for the total concentration range.

If we will integrate basic retention equation by concentration we will get:

          (17)
  

or

          (18)
  

As mentioned before, an excess adsorption of the pure component is equal to zero. Therefore, the rightmost term of the above expression is equal to zero, and the final expression for the dead volume will be:

          (19)
  

Which is, in fact, an integral average of the dependence of the retention volume on the concentration.