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

The number of molecules will strike and adhere to the exposed surface (N2) will be proportional to the concentration of solvent in mobile phase, the unexposed area of surface and another constant (a),


Now, under equilibrium conditions,

N1 = N2



or, .......................(3)

where (K) is the distribution coefficient of the solvent between the stationary phase and a solution of the solvent in water at a concentration (Cm).

Actually, this means that if a neat sample of solvent is injected on to a column as a solute, when the mobile phase consists of an aqueous solution of the solvent at concentration (Cm), then the magnitude of its retention volume will be determined by the magnitude of the distribution coefficient (K).

Thus, ............... ...... (4).

where g = b/a = the desorption-adsorption coefficient of the adsorbing solvent

Now, if the reverse phase is packed into a column and used with a mobile phase having a solvent concentration of (Cm) in water, the corrected retention volume (V') is given by the equation derived from the Plate Theory (30),

V' = Kj where (j) is the total chromatographically available surface area of the reverse phase in the column.

Substituting for (K) from equation (3),

or, ............................(5)

It is seen that equation (5) shows that there will be a linear relationship between the reciprocal of the corrected retention volume and the concentration of solvent in the mobile phase. It follows, that if retention data is measured over a range of solvent concentrations, using the solvent itself as a solute, a linear relationship should be obtained by plotting (1/V') against (Cm). It also follows, that from the intercept and slope of the graph, numerical values for the (j), (g) and (K) can be calculated.