On the relationship between band broadening and the particle-size distribution of the packing material in liquid chromatography: theory and practice

The influence of the particle size distribution (PSD) on the band broadening and the efficiency of packed columns is investigated on both theoretical and practical viewpoints. Each of the classical contributions to mass transfer kinetics, those due to longitudinal diffusion, eddy dispersion, and solid-liquid mass transfer resistance are measured and analyzed in terms of their expected and observed intensity as a function of the PSD of mixtures of the commercially available packing materials, 5 and 3 μm Luna-C₁₈ particles (Phenomenex, Torrance, CA, USA). Six 4.6 mm × 150 mm columns were packed with different mixtures of these two materials. The efficiencies of these columns were measured for a non-retained and a retained analytes in a mixture of acetonitrile and water. The longitudinal diffusion coefficient was directly measured by the peak parking method. The solid-liquid mass transfer coefficient was measured from the combination of the peak parking method, the best model of effective diffusion coefficient and the actual PSDs of the different particle mixtures measured by Coulter counter experiments. The eddy diffusion term was measured according to a recently developed protocol, by numerical integration of the peak profiles. Our results clearly show that the PSD has no measurable impact on any of the coefficients of the van Deemter equation. On the contrary and surprisingly, adding a small fraction of large particles to a batch of small particles can improve the quality of the packing of the fine particles. Our results indirectly confirm that the success of sub-3 μm shell particles is due to the roughness of their external surface, which contributes to eliminate most of the nefarious wall effects.