Non-invasive measurement of eddy diffusion in very efficient liquid chromatography columns packed with sub-3μm shell particles

A logarithmic law for the velocity- and retention-dependency of the eddy dispersion in chromatographic columns

Applying the recently introduced patchwork model for porous media, we present a new step forward in the modelling of eddy dispersion in chromatographic columns. The logarithmic law describing the velocity dependency emerging from this patchwork model is supplemented with a retention factor dependency via first principles modelling of the variations in flow resistance and retention capacity caused by the packing disorder. Furthermore, it is shown the derived expression is also able to fit the eddy dispersion originating from the wall effect on the packing. When applied to literature data of eddy dispersion, the newly introduced logarithmic law has a goodness of fit that is at least equal to that of Knox' empirical power law (R2>0.98). The main difference is that, whereas Knox' power law requires a separate fit for each component due to the retention factor dependency, the present model simultaneously fits all plate height curves measured on one chromatographic column, using only two parameters with a clear physical meaning.

Temperature Effects on Retention and Separation of PAHs in Reversed-Phase Liquid Chromatography Using Columns Packed with Fully Porous and Core-Shell Particles

Effects of temperature on the reversed-phase chromatographic behavior of PAHs were investigated on three columns. The first was the recent C18column (250 mm × 4.6 mm) packed with 5 µm core-shell particles while the others were more conventional C18columns (250 mm × 4.6 mm) packed with fully porous particles. Among the 16 PAHs studied, special attention has been paid to two pairs of PAHs, fluorene/acenaphthene and chrysene/benzo[a]anthracene, which often present coeluting problems. Due to the low surface area of the core-shell particles, lowest retention time of each PAH was highlighted and effects of the temperature on the separation of PAHs were negligible in regard to those using columns packed with fully porous particles. For each PAH studied, it was demonstrated that peaks were symmetrical and may be considered as Gaussian peaks when the column packed with core-shell particle was employed. In the best condition, the separation of PAHs was conducted at 16°C under very low pressure values (670–950 psi = 46–65 bars). Depending on PAHs, the limit of detection ranged from 0.88 to 9.16 μg L−1. Analysis of spiked acetonitrile samples with PAHs at 10 and 50 µg L−1and tap water at 10 µg L−1gave very good recoveries (94%–109.3%) and high precision (1.1%–3.5%).

The rationale for the optimum efficiency of columns packed with new 1.9μm fully porous Titan-C18 particles-a detailed investigation of the intra-particle diffusivity

In a previous report, it was reported that columns packed with fully porous 1.9μm Titan-C18 particles provided a minimum reduced plate height as small as 1.7 for the most retained compound (n-octanophenone) under RPLC conditions. These particles are characterized by a relatively narrow size distribution with a relative standard deviation (RSD) of only 10%. A column packed with classical 5μm Symmetry-C18 particles, used as a reference RPLC column, generated a minimum reduced plate height of 2.1 for the same retained compound. This work demonstrates that this was due to an unusually low intra-particle diffusivity across these particles, which leads to a small longitudinal diffusion coefficient along the column. The demonstration is based on the combination of accurate measurements of the height equivalent to a theoretical plate (HETP), inverse size exclusion chromatography (ISEC), peak parking (PP), and minor disturbance method (MDM) experiments. The experimental results show that the reduced eddy dispersion HETP term (A=0.8 for a reduced velocity of 5), the internal particle porosity (ϵp=0.35), and the enrichment of acetonitrile in the pore volume (75% acetonitrile in the bulk, 85% inside the mesoporous volume) are identical on both the Titan-C18 and Symmetry-C18 columns. The difference between the internal structures of these two brands of RPLC-C18 fully porous particles lies in the values of the internal obstruction factor γp, which is 0.42 for the Symmetry-C18 but only 0.26 for the Titan-C18 particles. This is in part related to the diffusion hindrance due to the small average pore size of the Titan-C18 particles, around 59Å versus 77Å for Symmetry-C18 particles. A simple model of constriction along diffusion paths having the shape of a truncated cone suggests that the width of the pore size distribution (RSD of 30% and 20% for Titan-C18 and Symmetry-C18 particles) is mostly responsible for the difference in their obstruction factors.

Geometrical and topological measures for hydrodynamic dispersion in confined sphere packings at low column-to-particle diameter ratios

At low column-to-particle diameter (or aspect) ratio (d(c)/d(p)) the kinetic column performance is dominated by the transcolumn disorder that arises from the morphological gradient between the more homogeneous, looser packed wall region and the random, dense core. For a systematic analysis of this morphology-dispersion relation we computer-generated a set of confined sphere packings varying three parameters: aspect ratio (d(c)/d(p)=10-30), bed porosity (ɛ=0.40-0.46), and packing homogeneity. Plate height curves were received from simulation of hydrodynamic dispersion in the packings over a wide range of reduced velocities (v=0.5-500). Geometrical measures derived from radial porosity and velocity profiles were insufficient as morphological descriptors of the plate height data. After Voronoi tessellation of the packings, topological information was obtained from the statistical moments of the free Voronoi volume (V(free)) distributions. The radial profile of the standard deviation of the V(free) distributions in the form of an integral measure was identified as a quantitative scalar measure for the transcolumn disorder. The first morphology-dispersion correlation for confined sphere packings deepens our understanding of how the packing microstructure determines the kinetic column performance.

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.

The current revolution in column technology: how it began, where is it going?

This work revisits the exceptionally rapid evolution of the technology of chromatographic columns and the important progress in speed of analysis and resolution power that was achieved over the last ten years. Whereas columns packed with 10 and 5 μm fully porous particles dominated the field for nearly thirty years (1975-2000), it took barely six years to see the commercialization of monolithic silica rods (2000), their raise to fame and decay to oblivion, the development of finer fully porous particles with size down to 1.7 μm (2006), and of sub-3 μm superficially porous particles (2006). Analysis times and plate heights delivered by columns packed with these recent packing materials have then been improved by more than one order of magnitude in this short period of time. This progress has rendered practically obsolete the age-old design of LC instruments. For low molecular weight compounds, analysts can now achieve peak capacities of 40 peaks in about 15s with a hold-up time of the order of 1.5s , in gradient elution, by operating columns packed with sub-3 μm shell particles at elevated temperatures, provided that they use optimized high pressure liquid chromatographs. This is the ultimate limit allowed by modern instruments, which have an extra-column band broadening contribution of 7 μL² at 4.0 mL/min and data acquisition rate of 160 Hz. The best 2.1 mm × 50 mm narrow-bore columns packed with 1.7 μm silica core-shell particles provide peaks that have a variance of 2.1 μL² for k=1. Finally, this work discusses possible ways to accelerate separations and, in the same time perform these separations at the same level of efficiency as they have today. It seems possible to pack columns with smaller particles, probably down to 1 μm and operate them with current vHPLC equipments for separations of biochemicals. Analyses of low molecular weight compounds will require new micro-HPLC systems able to operate 1mm I.D. columns at pressures up to 5 kbar, which would eliminate the heat friction problems, and providing extra-column band broadening contributions smaller than 0.1 μL². Alternatively, a new generation of vHPLC systems with minimal extra-column contributions of less than 0.5 μL² could run 2.1mm I.D. columns if these latter were to be packed with high heat conductivity materials such as core-shell particles made with an alumina or gold core.

Kinetic investigation of narrow-bore columns packed with prototype sub-2 μm superficially porous particles with various shell thickness

The recent successful breakthrough of sub-3 μm shell particles in HPLC has triggered considerable research efforts toward the design of new brands of core-shell particles. We investigated the mass transfer mechanism of a few analytes in narrow-bore columns packed with prototype 1.7 μm shell particles, made of 1.0, 1.2, and 1.4 μm solid nonporous cores surrounded by porous shells 350, 250, and 150 nm thick, respectively. Three probe solutes, uracil, naphthalene, and insulin, were chosen to assess the kinetic performance of these columns. Inverse size exclusion chromatography, peak parking experiments, and the numerical integration of the experimental peak profiles were carried out in order to measure the external, internal, and total column porosities, the true bulk diffusion coefficients of these analytes, the height equivalent to a theoretical plate, the longitudinal diffusion term, and the trans-particle mass transfer resistance term. The residual eddy diffusion term was measured by difference. The results show the existence of important trans-column velocity biases (7%) possibly due to the presence of particle multiplets in the slurry mixture used during the packing process. Our results illustrates some of the difficulties encountered by scientists preparing and packing shell particles into narrow-bore columns.