Measurement and modelling of the intra-particle diffusion and b-term in reversed-phase liquid chromatography

In an ongoing effort to better understand the underlying mechanisms of band broadening in particle-packed reversed-phase liquid chromatography columns, new models for intra-particle diffusion, representing an adsorption- and partition-type retention behavior, are proposed. These models assume the mesoporous zone inside the particles is subdivided in four distinct regions: a fraction f₁ filled with bulk mobile phase, a fraction f₂ enriched in pure organic modifier extending outside the stationary phase layer, a fraction f₃ comprising the liquid surrounding the alkyl chains and a fraction f₄ consisting of the stationary phase alkyl chains. Intra-particle diffusion is calculated as a residence time weighted average of the diffusion in these different regions. Experimental procedures and models are proposed to determine the volumes of these four regions and applied to three reversed-phase liquid chromatography columns with different pore sizes (80 Å versus 300 Å) and different stationary phase types (C₁₈ versus C₈). The newly proposed models are then applied to predict the intra-particle diffusion of butyrophenone across a wide range of retention factors (1 ≤ k" ≤ 40) in each of these columns. These predictions are compared to experimental data that are extracted from the effective diffusion coefficients of butyrophenone obtained via peak parking experiments. It is demonstrated that both adsorption- and partition-type models for intra-particle diffusion model the actual behavior of the test compound well, and require the determination of only one (partition) or two (adsorption) fitting factors: the obstruction to free movement the analytes experience from the alkyl chains in the retained state (partition and adsorption) and in the unretained state (adsorption). Finally, it is demonstrated that the major contributor to the intra-particle diffusion of retained compounds (k" > 2) is the diffusion these analytes undergo when retained in the organic-modifier enriched zone surrounding the alkyl chains (partition model) or when adsorbed onto the alkyl chains (adsorption model), confirming that surface diffusion plays an important role in the mass transfer of retained compounds in reversed-phase liquid chromatography columns.