Bonded Phases - The Derivation of the Langmuir Adsorption Isotherm for Reverse Phases

For example, if the intercept and slope of a curve relating (1/V') to (Cm) is (A) and (B) respectively,

Then,

or, .......................................... (6)

and ................................................. (7)

Scott and Simpson (29) took some accurate measurements of (V') and (Cm) for several different aliphatic alcohols and two aliphatic acids in an attempt to measure their adsorption-desorption coefficients and the unique surface area of the reverse phase that was available to each solvent. Unfortunately, in practice, the method suggested above suffers from one severe drawback. In order to measure (V') the corrected retention volume accurately, it is necessary to obtain a precise value for the effective dead volume. Dead volume measurement has been studied extensively (32-37) and the problems associated with the accurate measurement of the dead volume has been discussed generally in the literature. There is still much disagreement on the best method of measurement and in their work, Scott and Simpson, employed sodium chloride as the dead volume marker. In subsequent review by other workers in the field, this solute was not considered appropriate and thus, many of their conclusions were considered in error. However, their data can be used very effectively without knowing the column dead volume. The following method, circumvents the uncertainties that arise from dead volume measurement but still provides values for the adsorption-desorption coefficients and the surface area of the reverse phase that is available to each solvent.

Restating equation (5)

Now, as, V' = Vr - Vo , then, substituting for (V') in equation (5)

................ (8)

To aid in algebraic manipulation equation (8) can be put in the simple form,

..................... (9)

where, as defined before and

Now, when the solvent is chromatographed as the solute in pure water as the mobile phase, (i.e. Cm = 0, and Vr = Vr(0) ), then,

Re-arranging, ...................................... (10)

Substituting for (Vo) from equation (10) into equation (9),

..... . . (11)

Where (Vr(n)) is the retention volume of the solvent when eluted as a solute in a mobile phase containing the solvent at a concentration (Cm(n)). Equation (11) relates the retention volume of the solvent (as opposed to the corrected retention volume) to the solvent concentration in the mobile phase and thus, the need to determine the column dead volume is eliminated.