Statistical analysis of packed beds, the origin of short-range disorder, and its impact on eddy dispersion

Resolution limits of size exclusion chromatography columns identified from flow reversal and overcome by recycling liquid chromatography to improve the characterization of manufactured monoclonal antibodies

The flow reversal (FR) technique consists of reversing the flow direction along a chromatographic column. It is used to reveal the origin (such as poor column packing, active sites, or slow absorption/escape kinetics) for the resolution limit of 4.6 mm × 150 mm long columns packed with 1.7 μm 200 Å Bridge-Ethylene-Hybrid (BEHTM) Particles. These columns are used to separate manufactured monoclonal antibodies (mAb, ∼ 150 kDa) from their close impurities (or IdeS fragments, ∼ 100 kDa) by size exclusion chromatography (SEC). FR unambiguously demonstrates that the resolution limit of these SEC columns is primarily due to long-range flow velocity biases covering distances of at least 500 μm across the column diameter. This confirms the existence of center-to-wall flow heterogeneities which cause undesirable tailing for the mAb peak. Because the transverse dispersion coefficient (Dt=1.1 × 10-6 cm2/s) of mAbs across the column diameter is intrinsically low, the bandspreading of the mAb in a single flow direction is in part reversible upon reversing the flow direction. For the very same residence time in the column, the column efficiency is found to increase by +85% relative to that observed under conventional elution mode. The observed peak tailing of the mAb and its sub-units is not caused by active surface sites or by slow absorption/escape from the BEH Particles. Therefore, the most critical mAb impurities (hydrolytic degradation Fab/c and IdeS [Formula: see text] fragments) can only be successfully separated and quantified with acceptable accuracy by adopting alternate pumping recycling liquid chromatography (APRLC). APRLC enables the full baseline separation of the mAb and 100 kDa mAb fragments and partial separation of Fab/c and [Formula: see text] fragments after increasing the number of cycles to ten. It was made possible to accurately measure the relative abundances of the mAb (99.0 ± 0.1%), [Formula: see text] fragment (0.88 ± 0.03%), and Fab/c immunogenic fragment (0.13 ± 0.02%) in less than 45 min for a total mAb sample load of only 5 μg. Still, further improvements are needed to increase the sensitivity of the APRLC method and to reduce the solvent consumption by adopting narrow-bore 2.1 mm i.d. SEC columns.

Mobile-Phase Contributions to Organic-Solvent Excess Adsorption and Surface Diffusion in Reversed-Phase Liquid Chromatography

Fast transport of retained analytes in reversed-phase liquid chromatography occurs through surface diffusion in the organic-solvent (OS)-enriched interfacial "ditch" region between the hydrophobic stationary phase and the water (W)-OS mobile phase. Through molecular dynamics simulations that recover the OS excess adsorption isotherms of a typical C₁₈-stationary phase for methanol and acetonitrile, we explore the relation between OS properties, OS excess adsorption, and surface diffusion. The emerging molecular-level picture attributes the mobile-phase contribution to surface diffusion to the hydrogen-bond capability and the eluting power of the OS. The higher affinity of methanol for the formation of W-OS hydrogen bonds at the soft, hydrophobic surface presented by the bonded-phase (C₁₈) chains reduces the OS excess and the related viscosity drop in the ditch. The lower eluting power of methanol, however, translates to increased bonded-phase contacts for analytes, which can increase their mobility gain from surface diffusion above the gain observed with acetonitrile.

Prediction of the performance of pre-packed purification columns through machine learning

Pre-packed columns have been increasingly used in process development and biomanufacturing thanks to their ease of use and consistency. Traditionally, packing quality is predicted through rate models, which require extensive calibration efforts through independent experiments to determine relevant mass transfer and kinetic rate constants. Here we propose machine learning as a complementary predictive tool for column performance. A machine learning algorithm, extreme gradient boosting, was applied to a large data set of packing quality (plate height and asymmetry) for pre-packed columns as a function of quantitative parameters (column length, column diameter, and particle size) and qualitative attributes (backbone and functional mode). The machine learning model offered excellent predictive capabilities for the plate height and the asymmetry (90 and 93%, respectively), with packing quality strongly influenced by backbone (∼70% relative importance) and functional mode (∼15% relative importance), well above all other quantitative column parameters. The results highlight the ability of machine learning to provide reliable predictions of column performance from simple, generic parameters, including strategic qualitative parameters such as backbone and functionality, usually excluded from quantitative considerations. Our results will guide further efforts in column optimization, for example, by focusing on improvements of backbone and functional mode to obtain optimized packings.

Effect of the polydispersity on the dispersion of polymers through silicas having different morphologies (fully porous and core-shell particles and monoliths)

The effect of the polydispersity of polystyrenes on the dispersion through silicas having different morphologies (fully porous, core-shell particles and monoliths) was investigated. The heights equivalent to a theoretical plate (HETP) of those columns were measured for a small molecule (toluene) and a series of polystyrenes of different sizes in non-adsorbing conditions. The different contributions to the total HETP including polydispersity were determined experimentally. The longitudinal diffusion and the mass transfer resistance term were obtained from peak parking experiments. The eddy dispersion was obtained from models and experiments. The effect of polydispersity on the HETP values (H_poly) can thus be calculated from the total HETP by substraction of the other contributions. The results were compared to the Knox model which surestimates the H_poly values for porous and core-shell particles which is usually explained by an overestimation of the polydispersity index (PDI) given by the manufacturer. The PDI of two polymers (P02, M_w= 690 g.mol^-1 and P03, M_w=1380 g.mol^-1) was verified by liquid chromatography by separating each fraction of the polymer on the silica columns by using adsorbing conditions which are obtained with a mixture of heptane and THF. The PDI obtained are comparable to the PDI given by the manufacturer meaning that the assumptions made by Knox are not entirely valid. A direct method is proposed in this paper in order to determine H_poly. In this method the excess of spreading as compared with a polymer with only one size corresponding to the average size is studied assuming the polymer size distribution is gaussian. The H_poly values obtained by the direct method are comparable to the experimental values.

Enantioselective adsorption dynamics of leucyl-leucine in a Chirobiotic R column

The dynamics of adsorption of the Leu-Leu stereoisomers in a chromatographic column packed with the Chirobiotic R chiral stationary phase bearing grafted antibiotic ristocetin A was studied by means of measurement and analysis of van Deemter plots. Similar measurements were carried out with weakly retained Gly-Gly for the sake of comparison. The bulk diffusion coefficients of the investigated dipeptides were also determined. It is found that the van Deemter plots of both the Leu-Leu stereoisomers and Gly-Gly have an uncommon convex-upward shape. Besides, the van Deemter B coefficients for the Leu-Leu stereoisomers, but not for Gly-Gly, have unusually high values. It is suggested that a high transcolumn contribution to eddy dispersion, which turned out to be enantioselective, accounts for these findings. Adsorption kinetics of all the dipeptides considered is relatively slow, the adsorption rate constant (k_ads) being of order of magnitude 20-60 s^-1. k_ads does not depend on the configuration of Leu-Leu stereoisomers, although their affinity toward the chiral selector depends on this factor. This supports the above hypothesis that eddy dispersion is mainly responsible for the observed peculiarities in the dynamic behavior of dipeptides, and adsorption kinetics has secondary importance in this phenomenon.

The checkerboard model for the eddy-dispersion in laminar flows through porous media. Part I: Theory and velocity field properties

The additivity assumption underlying Giddings' coupling model for the eddy-dispersion in laminar flows through heterogeneous media is critically analyzed and a potential solution for its non-additivity in the high velocity limit is presented. Whereas the unit cell in Giddings' model only consists of a single velocity bias step, the unit dispersion cell of the newly proposed model comprises two consecutive velocity bias steps. Consequently, the unit cell of this new model allows to account for the occurrence of an internal velocity bias rectification at high reduced velocities and is therefore additive in both the low and high velocity limit. First, a mathematical expression for the velocity- and diffusion-dependency of the model's dispersion characteristics has been established. Subsequently, the physical behavior of the model is discussed. It is shown the relation between the eddy-dispersion plate height h and the reduced velocity ν can be expected to display a local maximum in systems where the transversal dispersion purely occurs by molecular diffusion, as is the case in perfectly ordered flow-through media. In disordered media, where the transversal dispersion also contains a significant advective component, the model predicts a velocity-dependency that is qualitatively similar to that described by Giddings' coupling model but, all other conditions being equal, converges to a significantly smaller horizontal asymptote at high reduced velocity. The latter might shed new light on earlier eddy-dispersion studies pursuing a quantitative agreement between experimental data and the Giddings model.

Unusual van Deemter plots of optical isomers on a chiral brush-type liquid chromatography column

Unusual dynamic behavior of the enantiomers of 9-bromo-11b-(tert-butyl)-2,3,6,11b-tetrahydrooxazolo[3',2':1,5]pyrrolo[3,4-b]quinoline-5,11-dione (I) was observed on a Nautilus-R column packed with silica grafted with antibiotic ristocetin. It consisted in (i) antibatic behavior of the van Deemter plots of the enantiomers and (ii) high and strongly enantiomer dependent values of the A- and B-terms of the van Deemter equation. Although rare, such a pattern has been found earlier in chiral chromatography, with all reported cases limited to brush-type chiral stationary phases. Adsorption dynamics in this system was studied by means of the moment method and the peak parking technique; hydrodynamic properties of the column were explored by using unretained tracers. It was shown that the peculiar shape of the van Deemter curves for the enantiomers of I is conditioned by imperfect packing of the stationary phase, which result in high transcolumn eddy dispersion, and by slow adsorption/desorption kinetics. It was proven that the whole void volume of the column available to an eluent is not accessible to the studied analyte because it cannot penetrate the space between neighboring grafted ligands. Its mass transfer in pores is also affected by the fact that the stagnant layer of the binary water-acetonitrile mobile phase differs in composition from the bulk liquid due to preferential adsorption of water that influences the apparent molecular diffusivity of solutes. An effect of the structures of analyte and chiral selector on the adsorption kinetics is also briefly discussed.

Kinetic Accessibility of Porous Material Adsorption Sites Studied through the Lattice Boltzmann Method

We present here a computational model based on the lattice Boltzmann scheme to investigate the accessibility of active adsorption sites in hierarchical porous materials to adsorbates in a flowing liquid. By studying the transport and adsorption of tracers after they enter the pore space of the virtual sample, we characterize their kinetics as they pass through the pore space and adsorb on the solid-liquid interface. The model is validated on simple geometries with a known analytical solution. We then use it to investigate the influence of regular grooves or disordered roughness on the walls of a slit pore geometry, looking at the impact on adsorption and transport. In particular, we highlight the importance of adsorption site accessibility, which depends on the shape and connectivity of the pore space as well as the fluid flow profile and velocity.

Experimental characterization of the nanoparticle size effect on the mechanical stability of nanoparticle-based coatings

We present an experimental investigation of the mechanical stability of silica nanoparticle-based coatings as a function of the size of the nanoparticles. The coatings are built following a layer-by-layer procedure, alternating positive and negative surface charges. The mechanical stability of the multilayers is studied in water, on the basis of an ultrasonic cavitation test. The resistance of the coating to cavitation is found to remarkably increase with decreasing the size of the nanoparticles, indicating an increase of the cohesive energy density. The relative contribution of van der Waals and electrical double-layer interactions to the stability of the multilayer is discussed toward their size dependence.

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.

Random-close packing limits for monodisperse and polydisperse hard spheres

We investigate how the densities of inherent structures, which we refer to as the closest jammed configurations, are distributed for packings of 10(4) frictionless hard spheres. A computational algorithm is introduced to generate closest jammed configurations and determine corresponding densities. Closest jamming densities for monodisperse packings generated with high compression rates using Lubachevsky-Stillinger and force-biased algorithms are distributed in a narrow density range from φ = 0.634-0.636 to φ≈ 0.64; closest jamming densities for monodisperse packings generated with low compression rates converge to φ≈ 0.65 and grow rapidly when crystallization starts with very low compression rates. We interpret φ≈ 0.64 as the random-close packing (RCP) limit and φ≈ 0.65 as a lower bound of the glass close packing (GCP) limit, whereas φ = 0.634-0.636 is attributed to another characteristic (lowest typical, LT) density φLT. The three characteristic densities φLT, φRCP, and φGCP are determined for polydisperse packings with log-normal sphere radii distributions.

Longitudinal and transverse dispersion in flow through random packings of spheres: a quantitative comparison of experiments, simulations, and models

Pulsed field gradient nuclear magnetic resonance was used to determine the intrinsic longitudinal and transverse dispersivity of random packings of nearly monodisperse spheres in experiments covering 3.5 orders of magnitude in reduced velocity Pe, from the diffusion dominated regime Pe < 1 to the high velocity regime Pe > 1000. Additionally, using lattice-Boltzmann simulations with tracer tracking, the dispersivities of random packings were determined numerically. Experimental and simulation results are shown to agree to within a few percent over the full velocity range. The velocity dependence of transverse and longitudinal dispersion in packed spheres is described by heuristic models with three parameters each. The simulations were extended to regimes not accessible to experiments, dispersing tracers in flows through random "packings" of floating spheres, for comparison with results obtained using jammed packings in which spheres touch. In the regime of fast flows, the jammed packings' longitudinal dispersivities scale with hydrodynamic length. This no longer holds true in the packings with floating spheres, highlighting the role of zones of slow flow or no flow surrounding sphere-sphere contacts.

3D printed porous media columns with fine control of column packing morphology

In this paper we demonstrate, for the first time, the use of 3D printing (also known as additive manufacturing or rapid prototyping) to create porous media with precisely defined packing morphologies, directly from computer aided design (CAD) models. We used CAD to design perfectly ordered beds with octahedral beads (115 μm apothem) packed in a simple cubic configuration and monoliths with hexagonal channels (150 μm apothem) in parallel and herringbone arrangements. The models were then printed by UV curing of acrylonitrile-butadiene-styrene powder layers. Each porous bed was printed at 1.0, 1.5 and 2.0 mL volumes, within a complete column, including internal flow distributors and threaded 10-32 flow connectors. Close replication of CAD models was achieved. The resultant individual octahedral beads were highly uniform in size, with apothems of 113.6±1.9 μm, while the monolith hexagonal cross-section channels had apothems of 148.2±2.0 μm. Residence time distribution measurements show that the beds largely behaved as expected from their design void volumes. Radial and fractal flow distributor designs were also tested. The former displayed poor flow distribution in parallel and herringbone pore columns, while the fractal distributors provided uniform flow distribution over the entire cross section. The results show that 3D printing is a feasible method for producing precisely controlled porous media. We expect our approach to revolutionize not only fundamental studies of flow in porous media but methods of chromatography column production.