Modeling solute transport in micellar liquid chromatography

To better understand the causes of reduced efficiencies in micellar liquid chromatography (MLC), a mathematical model that includes both solute-stationary phase and solute-micelle interactions has been developed. Solute mass transfer between mobile and stationary phases and kinetic limitations within the stationary phase are incorporated in the model equations. Equilibrium is assumed between the micelles and the surfactant monomer in the bulk solvent of the mobile phase as well as for the solute distributed between the micelles and the mobile phase solvent. It is also assumed that only free surfactant is found in the pores of the alkyl-bonded phase since the micelles are larger than the typical stationary phase pore sizes. The increase in mobile phase dispersion due to partitioning of the solute between the micelle and the bulk solvent is incorporated in this model. Solution of the solute mass balance equations developed for the mobile phase, the pores of the silica gel, and the surface of the stationary phase yields an explicit expression for the number of plates as a function of the physical and chemical parameters governing the kinetics and transport in MLC separations. An examination of changes in predicted plate numbers with different mobile phase conditions helps to understand the observed efficiencies with MLC systems. Model predictions were compared to experimental observations from a series of vanillin compounds injected onto a BDS-C-18 column with mobile phases containing different concentrations of sodium dodecyl sulfate. This comparison showed that an equilibrium model provides a reasonable prediction of the number of plates for all of the solutes considered. However, the experimental results for vanillin, isovanillin, and coumarin indicate that stationary phase kinetics also play a minor role in column efficiency. The results from this analysis suggest that it is the secondary equilibrium between micellar and bulk mobile phases, which is the primary contributor to band broadening in MLC.