Lattice models for the description of partitioning/ adsorption and retention in reversed-phase liquid chromatography, including surface and shape effects

Abstract

The retention mechanism in reversed-phase liquid chromatography (RPLC) with silica particles modified with surface-grafted alkyl chains cannot be fully understood unless the specific properties of the surface layers, such as the configurational constraints of terminally attached chains, are taken into account. The commonly accepted view that the main factor governing RPLC retention behaviour is constituted by solute—solvent interactions in the bulk mobile phase is supported by useful but simplified theories based on solvation as in bulk liquids. Solvation in bulk liquids depends on the free energy to create “cavities” for solute molecules in mobile and stationary phases. This paper first reviews possibilities and shortcomings of regular solution theories, where the partition coefficient is expressed in terms of the Flory—Huggins (FH) interaction parameters for the solute. Where enthalpic effects dominate, these parameters can be obtained from experimental data or from generalized thermodynamic functions expressed as Hildebrand's solubility parameter, δ, representing the square root of the cohesive energy density. In RPLC with terminally attached chains on the support, entropy effects arising from the molecular organization of chains are also important, and entropic expulsion of solute molecules from the stationary phase is expected to take place. RPLC practice indicates that the nature of the grafted layer [ e.g., flexibility of grafted chains and “phase transitions”, geometrical effects, chain length effects, chain branching and surface effects (coverage and hydroxyls)] indeed influences the “adsorptive” and retentive capacity of the bonded stationary layer. Theories specially designed for grafted layers are reviewed starting with (oversimplified) rod-like chain models, followed by several, more recent, lattice theories, which are based on extensions of the Flory—Huggins lattice theory for polymers in solution. These theories, when applied to the RPLC retention mechanism, take into account some aspects of the molecular organization in the grafted layer, but are still subject to simplifying assumptions. A more general approach is based on the self-consistent field theory for adsorption (SCFA) originally developed by Scheutjens and Fleer to describe the polymer adsorption, where in essence the segment density distribution is found resulting from minimization of free energy. Extending the SCFA theory to allow for RPLC conditions provides insight into the effects of the solvent quality (modifier content), collapse of the chain phase, the grafted and the solute's chain lengths and the grafting density (surface coverage) on the segment density profile. Both aliphatic and amphiphilic solute molecules appear to be distributed non-uniformly in the grafted layer and are accumulated in the boundary region near the interface between chain phase and bulk solvent. Using the related theory by Leermakers and Scheutjens [self-consistent anisotropic field (SCAF) theory], shape selectivity is shown for flexible chain, star- and rod-like solutes, chain length effects and alignment are also being found. In the presence of a specific affinity for the silica surface, due to residual hydroxyls, for both polar solvent molecules and solute molecules for polar groupa, both the SCFA and the SCAF theories predict an accumulation of polar segments near the silica surface with is fairly pronounced, displacing most of the (unattached) non-polar segments more towards the chain phase surface.