Interpretation of dynamic frontal analysis data in solid/supercritical fluid adsorption systems. I: theory

A theory is proposed to relate the elution times of the adsorption front shocks of breakthrough curves recorded during classical dynamic frontal analysis (FA) experiments with selected compounds and their adsorption isotherms in solid/supercritical fluid adsorption systems. The actual density and viscosity of binary mixtures of CO2 and methanol were obtained from the NIST REPPROP software. Diluted solutions of S-naproxen were considered (<2% in mass) but the possible effects of the analyte concentration on the viscosity and the density of the eluent percolating through the column were neglected. This allows the determination of the excess adsorption isotherm (or Gibbs excess isotherm) of the adsorbed analyte in the whole column at constant mass and volumetric flow rate of pure CO2 and of the modifier solution. A local Langmuir adsorption isotherm and a constant saturation capacity were assumed in the calculations. The variation of the adsorption-desorption constant with the eluent density was taken from the experimental variation of the retention factor of S-naproxen on a chiral column packed with Whelk-O1 particles. The results show that the isotherm parameters obtained from the best adjustment of the Langmuir model to the SFC excess adsorption data deviates by less than 7% from the assumed saturation capacity and from the average of the equilibrium constant along the chromatographic column. In practice, this conclusion holds true provided that the precision of the measurement of elution times of front shocks of breakthrough curves is better than 1% and that the maximum surface coverage qexp,max/qS is at least equal to 20%.