Ellipsoidal particles for liquid chromatography: Fluid mechanics, efficiency and wall effects

On the contribution of the top and bottom walls in micro-pillar array columns and related high-aspect ratio chromatography systems

We report on a steady-state based, and hence highly accurate numerical modelling study of the effect of the top and bottom wall in the current generation of micro-pillar array columns. These have a mesoporous retention layer that not only covers the pillar walls but also the bottom wall. Our results show that the performance of these columns can in general not be improved by also covering the top wall with the same layer, despite the increased column symmetry this approach would offer. The reason for this is that the local species retardation caused by a retentive layer is much stronger than the pure flow arresting effect of an uncovered wall. At least, this has a crucial impact in high aspect-ratio systems such as micro-pillar array columns because these require a small inter-pillar distance to promote mass transfer together with a large channel depth to enable a sufficiently high flow rate. On the other hand, a notable improvement could be made if micro-pillar array would be produced without having a retentive layer at the bottom. At Péclet number Pe = 50 and aspect ratio AR = 5 for flow-channels, this gain amounts up to about 4.5 h-units at a zone retention factor k'' = 2 and 1.75 h-units at k'' = 16 (gain scales almost linearly with Pe). To verify these results, we also considered another high aspect-ratio system with a simplified geometry: the open-tubular channel with a flat-rectangular cross-section. This led to very similar observations, thus confirming the findings for the micro-pillar array. The results produced in the present study also allow us to conclude that the classic modelling paradigm adopted in chromatography, which is based on the independency and hence additivity of the hCm- and hCs-contributions, can lead to large modelling errors in chromatographic systems with a high aspect-ratio, even when their geometry is so simple as that of a straight open-tubular channel with constant cross-section. Indeed, when both zones are treated independently, the analysis misses how the vertical diffusion through the retentive layer helps suppressing the vertical gradients in the mobile zone. The diffusion through this layer occurs in a ratio of k''Ds/Dm (Dm being the diffusion coefficient in mobile phase zone and Ds being the diffusion coefficient in stationary phase zone), such that at high retention factors this diffusion contribution even becomes the dominant one.

Theoretical computation of the band broadening in micro-pillar array columns

We have investigated the possibility to establish a theoretical plate height expression for the band broadening in the most widely used micro-pillar array column format, i.e., a cylindrical pillar array wherein the pillar walls and the channel bottom are coated with a thin layer of meso‑porous material. Assuming isotropic diffusion in the shell-layer, it was found that the vertical diffusive transport along the porous shell-layer covering the pillar walls significantly suppresses the band broadening originating from the vertical migration velocity gradients. As the vertical transport in the shell-layer increases linearly with the retention equilibrium constant K, this leads to an anomalous dependency on the retention factor. Indeed, instead of increasing with k'' and following the classic (1+ak''+bk''2)/(1 + k'')2-dependency governing a classic Taylor-Aris system, the variation of the mobile zone mass transfer resistance term hCm in a 3D pillar array with bottom-wall retention goes through a maximum (resp. factor 1.5 (k''=4) and 2 (k''=16) difference between observed and classic Taylor-Aris behaviour). This effect increases with increasing pillar heights and increasing reduced velocities. Because of this complex k''-dependency, it proves very cumbersome to establish a general plate height equation covering all conditions. Instead, a plate height expression was established that is limited up to k''=4, but remains accurate for higher k''-values for cases where the ratio of pillar height over inter-pillar distance remains below 5. It can however be anticipated the proposed analytical model is only valid in a rather limited range around the presently considered external porosity of ε=0.5.

Engineering the surface patchiness and topography of polystyrene colloids: From spheres to ellipsoids

HYPOTHESIS

Colloidal surface morphology determines suspension properties and applications. While existing methods are effective at generating specific features on spherical particles, an approach extending this to non-spherical particles is currently missing. Synthesizing un-crosslinked polymer microspheres with controlled chemical patchiness would allow subsequent thermomechanical stretching to translate surface topographical features to ellipsoidal particles.

EXPERIMENTS

A systematic study using seeded emulsion polymerization to create polystyrene (PS) microspheres with controlled surface patches of poly(tert-butyl acrylate) (PtBA) was performed with different polymerization parameters such as concentration of tBA monomer, co-swelling agent, and initiator. Thermomechanical stretching converted seed spheres to microellipsoids. Acid catalyzed hydrolysis (ACH) was performed to remove the patch domains. Roughness was characterized before and after ACH using atomic force microscopy.

FINDINGS

PS spheres with controlled chemical patchiness were synthesized. A balance between two factors, domain coalescence from reduced viscosity and domain growth via monomer absorption, dictates the final PtBA) patch features. ACH mediated removal of patch domains produced either golf ball-like porous particles or multicavity particles, depending on the size of the precursor patches. Patchy microspheres were successfully stretched into microellipsoids while retaining their surface characteristics. Particle roughness is governed by the patch geometry and increases after ACH. Overall, this study provides a facile yet controllable platform for creating colloids with highly adjustable surface patterns.

Basic Structure-Independent Equations of Kinetic Performance of Columns in Liquid Chromatography

The lowest dimensionless plate height (h_min) of the liquid chromatography (LC) column is a subjective metric that cannot be found from measurements of parameters of a column as a separation device and is not suitable for comparison of kinetic performance of differently structured columns. In some cases (monolithic, pillar-array columns), there is no correlation between h_min (as it is currently understood) and the column performance. The same is true for the flow resistance parameter (ϕ). Recently introduced measurable effective diameter and structural quality factor (q_max) of a column are objective replacements for ϕ and h_min. Metric q_max, the maximum of the flow-dependent kinetic performance factor (q), is suitable for comparison of differently structured columns. Structure-independent basic equations binding kinetic performance of LC column with its q and other parameters and operational conditions were developed. It has been shown that previously known and new equations of a column kinetic performance can be derived from the basic ones. An example of using the equations for solving a known practical problem of column selection is provided.

Practical limits to column performance in liquid chromatography - Optimal operations

Columns of different structures have different potential kinetic performance - the trade-off between separation, time, and pressure. However, the full potential of a structure cannot always be realized in practically existing columns. Each combination of column efficiency, time, and pressure requires certain cross-sectional dimensions of the column flow-through channels. However, there are limits to the narrowest flow-through channels that can be manufactured with current technology. As a result, columns of some structures cannot be optimized for providing the required efficiency in the shortest time. Additionally, the full potential of its structure can be realized only if a column can operate at the highest pressure available from liquid chromatography (LC) equipment, has sufficient loadability, and satisfies other practical requirements. Equations tailored for a systematic approach to evaluation of factors affecting performance of optimized LC columns (effects of column structure, column dimensions, operational conditions, etc.) were developed. Parameters quantifying the performance of a specific column at and below its largest acceptable pressure were identified. New objective performance parameters of columns and their structures were introduced. Among them are the apparent structural quality factor accounting for the effect of insufficiently high pressure acceptable for the column, the dimensionless plate duration - the parameter of a column structure affecting its performance when the pressure is not limited, - and others. Applying the theory developed herein to published data, the performance of several differently structured columns is evaluated, and the factors affecting their comparative performance are discussed. In the final count, not the quality of a column structure, but practical factors such as the narrowest manufacturable flow-through channels can dominate the choice of the kinetically most suitable column for a practical LC analysis.

Numerical Elucidation of Flow and Dispersion in Ordered Packed Beds: Nonspherical Polygons and the Effect of Particle Overlap on Chromatographic Performance

Spherical particles are widely considered as the benchmark stationary phase for preparative and analytical chromatography. Although this has proven true for randomly packed beds in the past, we challenge this paradigm for ordered packings, the fabrication of which are now feasible through additive manufacturing (3D printing). Using computational fluid dynamics (Lattice Boltzmann Method) this work shows that nonspherical particles can both reduce mobile-phase band broadening and increase permeability compared with spheres in ordered packed beds. In practice, ordered packed beds can only remain physically stable if the particles are fused to form a contiguous matrix, thus creating a positional overlap at the points of fusion between what would otherwise be discrete particles. Overlap is shown to decrease performance of ordered packed beds in all observed cases, thus we recommend it should be kept to the minimum extent necessary to ensure physical stability. Finally, we introduce a metric to estimate column performance, the mean deviated velocity, a quantitative description of the spread of the velocity field in the column. This metric appears to be a good indicator of mobile-phase dispersion in ordered packed bed media, including overlapped beds, and is a useful tool for screening new stationary-phase morphologies without having to perform computationally expensive simulations.

Simulation and theory of open-tube dispersion in short and long capillaries with slip boundaries and retention

Using random walk techniques, high resolution simulations of zone shape are conducted in open capillary tubes for short and long tube conditions. Finite size solutes are used as tracers in this treatment. Slip flow boundary conditions and wall retention are utilized as needed. These simulations are able to reproduce previous work in short and long tubes. For the short tube case where dispersion does not asymptotically approach the classic Taylor-Aris and Golay solutions, the effect of slip flow boundaries in the transient region shows zone shapes with abbreviated tails where the larger slip flow values cause zone compression. The use of slip flow to lower dispersion in capillary-based, wall-coated separations is shown to favor long tube behavior. This is because slip flow is relevant for cases where slip lengths are fractions of small capillary tube diameters. Incorporating slip flow into transport in capillaries favors a very small capillary radius where the cross-sectional diffusion length is very small and sampling times are fast. The purely convective zone shape with slip flow boundaries is derived analytically. Applications for this type of separation, guided by both analytical theory and simulation, show the potential for nano-sized capillary tubes less than 1 μm in diameter and favor very fast isocratic separations. Using long tube retention theory with slip boundaries shows that the dispersion-reducing region is most important in the range 0 ≤ k' ≤ 1, a relatively small retention window. Further discussion of the gradient elution technique and dispersion in packed beds suggests that the general usage of slip flow boundaries is restricted in liquid phase separation systems.