Harnessing an elastic flow instability to improve the kinetic performance of chromatographic columns.

Despite decades of research and development, the optimal efficiency of slurry-packed HPLC columns is still hindered by inherent long-range flow heterogeneity from the wall to the central bulk region of these columns. Here, we show an example of how this issue can be addressed through the straightforward addition of a semidilute amount (500 ppm) of a large, flexible, synthetic polymer (18 MDa partially hydrolyzed polyacrylamide, HPAM) to the mobile phase (1% NaCl aqueous solution, hereafter referred to as "brine") during operation of a 4.6 mm × 300 mm column packed with 10µm BEHTM 125 Å particles. Addition of the polymer imparts elasticity to the mobile phase, causing the flow in the interparticle pore space to become unstable above a threshold flow rate. We verify the development of this elastic flow instability using pressure drop measurements of the friction factor versus Reynolds number. In prior work, we showed that this flow instability is characterized by large spatiotemporal fluctuations in the pore-scale flow velocities that may promote analyte dispersion across the column. Axial dispersion measurements of the quasi non-retained tracer thiourea confirm this possibility: they reveal that operating above the onset of the instability improves column efficiency by greater than 100%. These experiments thereby suggest that elastic flow instabilities can be harnessed to mitigate the negative impact of trans-column flow heterogeneities on the efficiency of slurry-packed HPLC columns. While this approach has its own inherent limitations and constraints, our results lay the groundwork for future targeted development of polymers that can impart elasticity when dissolved in commonly used liquid chromatography mobile phases, and can thereby generate elastic flow instabilities to help improve the resolution of HPLC columns.

Theoretical predictions to facilitate the method development in slalom chromatography for the separation of large DNA molecules.

Slalom chromatography (SC) re-emerged in 2024 due to the availability of low adsorption ultra-high pressure liquid chromatography (UHPLC) packed columns/instruments and large modalities being investigated in the context of cell and gene therapies. The physico-chemical principles of SC retention combined with hydrodynamic chromatography (HDC) exclusion have been recently reported. In SC, DNA macromolecules are retarded because: (1) they can be stretched to lengths comparable to the particle diameter, and (2) their elastic relaxation time is long enough to maintain them in non-equilibrium extended conformations under regular UHPLC shear flow conditions. Here, a quantitative HDC-SC retention model is consolidated. A general plate height model accounting for the band broadening of long DNA biopolymers along packed beds is also derived for supporting method development and predicting speed-resolution performance in SC. For illustration, the chromatographic speed-resolution properties in SC are predicted for the separation of specific critical pairs (4.0/4.5, 10/11, and 25/27 kbp) of linear dsDNA polymers. The calculations are performed for two available custom-made particle sizes, dp= 1.7 and 2.5µm, at a constant pressure of 10,000 psi. The predictions are directly validated from experimental data acquired using low adsorption MaxPeakTM 4.6 mm i.d. Columns packed with 1.7µm BEHTM 45 Å (15 cm long column) and 2.5µm BEH 125 Å (30 cm long column) Particles, and by injecting six linear dsDNAs (λ DNA-Hind III Digest). The LC system is very low dispersion ACQUITYTM UPLCTM I-class PLUS System, and the mobile phase is a 100 mM phosphate buffer at pH 8. Maximum resolution is always achieved when the average extended lengths of linear dsDNAs are equal to a critical length, which is proportional to the particle diameter and to the square root of the applied shear rate. Most advantageously, the experimental results reveal that the relaxation times of linear dsDNAs observed under shear flow conditions are two orders of magnitude shorter than those expected in the absence of flow: this enables the detection of the longest linear dsDNAs up to 25 kbp without irremediable loss in column performance. Finally, the retention-efficiency model elaborated in this work can be used to rapidly anticipate and develop methods (selection of particle size, column length, and operating pressure) for any targeted DNA and time-resolution constraints.

Understanding retention and intra-particle diffusivity of alkylsulfobetaine-bonded Ethylene Bridged Particles with different mesopore sizes for hydrophilic interaction liquid chromatography applications.

The role of the average pore diameter (APD) of 1.7µm AtlantisTM Premier BEHTM Particles derivatized with a zwitterionic group (propylsulfobetaine) on the efficiency of their 2.1 × 50 mm hydrophilic interaction liquid chromatography (HILIC) packed columns is investigated experimentally. Van Deemter plots for toluene (neutral, hydrophobic), cytosine (neutral, polar), tosylate (negatively charged), bretylium and atenolol (positively charged) were measured on three HILIC columns packed with BEH Z-HILIC Particles having APDs of 95 Å, 130 Å, and 300 Å. The intraparticle diffusivities of the analytes across these three BEH Z-HILIC Particles were measured by the peak parking method. The experimental data reveal that the slope of the C-branch of the van Deemter plots can be reduced by factors of about 15 for toluene, 2.5 for cytosine, 6 for atenolol, 5 for tosylate, and 14 for bretylium with increasing the APD from 95 Å to 300 Å. This observation is explained by: (1) the reduced amount of the highly viscous water diffuse layer and subsequent increase of the amount of acetonitrile-rich eluent in the mesopores, (2) the localized electrostatic adsorption of the retained analytes onto the zwitterion-bonded BEH Particles, and (3) depletion/excess of the analytes into the water diffuse layer. A general model of intraparticle diffusivity was then proposed to account for the impact of the APD of Z-HILIC Particles on the solid-to-liquid mass transfer resistance of small molecules. The model highlights the relevance of the thickness of the water diffuse layer, the access of the bulk eluent into the mesopore, the localized electrostatic adsorption, and the partitioning constant of the retained analyte between the bulk eluent and the water diffuse layer.

Retention mechanism in combined hydrodynamic and slalom chromatography for analyzing large nucleic acid biopolymers relevant to cell and gene therapies.

Slalom chromatography (SC) was discovered in 1988 for analyzing double-stranded (ds) DNA. However, its progress was impeded by practical issues such as low-purity particles, sample loss, and lack of a clear retention mechanism. With the rise of cell and gene therapies and the availability today of bio-inert ultra-high-pressure liquid chromatography (UHPLC) columns and systems, SC has regained interest. In SC, the elution order is opposite to that observed in hydrodynamic chromatography (HDC): larger DNA molecules are more retained than small ones. Yet, the underlying SC retention mechanism remains elusive. We provide the physicochemical background necessary to explain, at a microscopic scale, the full transition from a HDC to a SC retention mechanism. This includes the persistence length of the DNA macromolecule (representing DNA stiffness), their relaxation time (τR) from the non-equilibrium contour length to the equilibrium entropic configuration, and the relationship between the mobile phase shear rate (〈γ̇〉) in packed columns and the DNA extended length. We propose a relevant retention model to account for the simultaneous impact of hydrodynamic chromatography (HDC) and SC on the retention factors of a series of large and linear dsDNAs (ranging from 2 to 48 kbp). SC data were acquired using bio-inert MaxPeakTM Columns packed with 1.7µm BEHTM 45 Å, 1.8µm BEH 125 Å, 2.4µm BEH 125 Å, 5.3µm BEH 125 Å, and 11.3µm BEH 125 Å Particles, an ACQUITYTM UPLCTM I-class PLUS System, and either 1 × PBS (pH 7.4) or 100 mM phosphate buffer (pH 8) as the mobile phase. SC is a non-equilibrium retention mode that is dominant when the Weissenberg number (Wi=〈γ̇〉τR) is much larger than 10 and the average extended length of DNA exceeds the particle diameter. HDC, on the other hand, is an equilibrium retention mode that dominates when Wi<1 (DNA chains remaining in their non-extended configuration). Maximum dsDNA resolution is observed in a mixed HDC-SC retention mode when the extended length of the DNA is approximately half the particle diameter. This work facilitates the development of methods for characterizing various plasmid DNA mixtures, containing linear, supercoiled, and relaxed circular dsDNAs which all have different degree of molecular stiffness.

Preparation and investigation of two-component silica-modified hydrophobic layer for minimizing retention loss of reversed-phase chromatographic columns using fully aqueous mobile phases.

Chromatographers often employ fully aqueous mobile phases to retain highly polar compounds in reversed-phase liquid chromatography (RPLC). However, when the flow rate is interrupted, either accidentally or intentionally, a substantial loss in retention occurs due to the spontaneous dewetting of water from the hydrophobic surface of conventional RPLC-C18 particles. Previous studies have shown that maintaining a low C18 surface coverage (approximately 1.5 µmol/m2) can mitigate water dewetting by increasing chain disorder, facilitating the intercalation of water clusters between the C18-bonded chains, and keeping the mesopores wetted. In this research, we explore the potential and additional benefits of using two-component surface bonding materials (C8/C18 and PhenylHexyl (PhHx)/C18) at a constant and low total surface coverage of 1.51 ± 0.15 µmol/m2. We synthesized seven one- and two-component modified silica particles with a volume average particle size of 5.22 µm and an average mesopore size of 104 Å. The surface coverage was increased from 0 to 0.54, 1.00, and to 1.66 µmol2 for C8 chains and from 0 to 0.52, 0.70, and to 1.65 µmol2 for PhHx ligands. To prevent interactions between water and any unreacted silanols, all seven derivatized particles were heavily endcapped with trimethylsilane (TMS) reagent. The fraction of the surface area remaining in contact with water was determined by measuring the retention times of weakly (thiourea) and strongly (thymine) retained compounds at intervals of 1, 2, 4, 8, 16, 32, and 64 minutes following the cessation of flow. Two distinct column temperatures, 24°C and 60°C, were employed in the experiments. Retention losses were found to be minimized in the presence of a small quantity of C8 chains (less than 40% of the total surface coverage). Additionally, it is essential to consider substantial fractions of PhHx chains, as long as the presence of the PhHx ligand does not significantly impact retention and selectivity. Combining mixed RPLC bondings with a low total surface coverage of approximately 1.5 µmol/m2 emerges as a viable solution for further minimizing retention loss in standard C18-bonded RPLC columns, particularly within the surface coverage range of 2.5-3.0 µmol/m2.

Physical origin of the peak tailing of monoclonal antibodies in size-exclusion chromatography using bio-compatible systems and columns.

The analysis of mixtures containing monoclonal antibody (mAb) (approximately 150 kDa molecular weight) and sub-unit impurities (approximately 100 kDa) is challenging, even when adopting the latest ultra-high-pressure liquid chromatography (UHPLC) columns (4.6 mm [Formula: see text] 150 mm coated hardware, 1.7 [Formula: see text]m 250 BEH[Formula: see text] Surface-modified Particles) and systems (ACQUITY[Formula: see text] UPLC[Formula: see text] I-class Bio Plus). The main issue still encountered is a persistent tail of the mAb peak. Here, the physical origin(s) of such peak tailing in size-exclusion chromatography (SEC) are investigated from both fundamental and practical approaches. Up to five relevant physical origins are analyzed: sample heterogeneity (glycoforms), UHPLC system dispersion, strong residual binding of the mAb to the SEC particles (via hydrophobic and/or electrostatic interactions) and to the stainless steel column/system hardware, slow escape kinetics of the mAb from the SEC particles, and flow heterogeneity caused by the non-ideal slurry packing of SEC columns. Experiments (testing sample heterogeneity, system dispersion, and strong residual interactions) and calculations (predicting the transient absorption/escape kinetics in a single SEC particle and the two-dimensional peak concentration profiles) altogether unambiguously demonstrate that the observed mAb peak tailing is caused primarily by the long-range velocity biases across the SEC column combined with the slow transverse dispersion of mAbs. Therefore, improvement in the resolution between mAb and sub-unit fragment impurities can only be achieved by increasing the column length, e.g., by applying recycling chromatography at acceptable pressures.

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.

Absorption and escape kinetics of spherical biomolecules from fully porous particles utilized in size exclusion chromatography.

The increasing demand for the characterization of large biomolecules such as monoclonal antibodies, double-stranded deoxyribonucleic acid (dsDNA), and virus-like particles (VLPs) is raising fundamental questions pertaining to their absorption (ingress) and escape (egress) kinetics from fully porous particles. The exact expression of their concentration profiles is derived as a function of time and radial position across a single sub-3 µm Bridge-Ethylene-Hybrid (BEHTM) Particle present in size exclusion chromatography (SEC) columns. The boundary condition at the external surface area of the particle is a rectangular concentration profile mimicking the passage of the chromatographic zone. Four different BEH Particles were considered in the calculations depending on the molecular size of the analyte: 2.0 µm 100 Å BEH Particles for small molecules, 2.0 µm 200 Å BEH Particles for monoclonal antibodies, 2.0 µm 300 Å BEH Particles for dsDNA (100 base pairs), and 2.5 µm 900 Å BEH Particles for virus-like particles (VLPs). The calculated concentration profiles of small molecules and monoclonal antibodies confirm that all BEH Particles present in the column reach quasi-instantaneously thermodynamic equilibrium with the bulk mobile phase during the passage of the chromatographic band. This is no longer the case for larger biomolecules such as dsDNA or VLPs, especially when the SEC particle is located near the column inlet and for high velocities. The kinetics of biomolecule egress is slower than its kinetics of ingress leading to pronounced peak tailing. The mean concentration of the largest biomolecules in the SEC particles remains always smaller than the maximum bulk concentration. This persistent and transient intra-particle diffusion regime has direct implications on the theoretical expressions of the observed retention factors and plate heights. Classical theories of chromatography assume uniform spatial distribution of the analyte in the particle volume: this hypothesis is not verified for the largest biomolecules. These results imply that non-porous particles or monolithic structures are the most promising stationary phases for the separation and purification of the largest biomolecules in life science.

Multiple-open-tubular column enabling transverse diffusion. Part 3: Simulation of solute dispersion along a real three dimensional-printed column with quadratic channels.

Multiple-open-tubular columns enabling transverse diffusion (MOTTD) consist of straight and parallel flow-through channels separated by a mesoporous stationary phase. In Part 1, a stochastic model of band broadening along MOTTD columns accounting for longitudinal diffusion, trans-channel velocity bias, and mass transfer resistance in the stationary phase was derived to demonstrate the intrinsic advantage of MOTTD columns over classical particulate columns. In Part 2, the model was refined for the critical contribution of the channel-to-channel polydispersity and applied to address the best trade-off between analysis speed and performance. In this Part 3, a MOTTD column with a square array of quadratic channels is fabricated by 3D-printing (combining polymer stereolithography with photolithography using photomasks) to deliver unprecedently small apparent channel diameters of 117.6 ± 5.0 µm. The colors in the microscopy photographs of the actual 3D-printed channels are binarized to delimitate the mobile phase volume from the stationary phase volume. The same numerical simulations as those in Part 2 are then performed for two MOTTD columns (external porosity ϵe=31.7%, same apparent channel diameter 117.6 µm): one containing 16 virtual perfect quadratic channels and the other 16 real 3D-printed channels. The reduced velocities (or Peclet numbers) are varied over a wide range from 0.2 to 5000 and the zone retention factors were fixed at k1=1.04, 5, and 25. The results demonstrate that smoothing the edges of the targeted quadratic channels by the 3D-printed technique is advantageous in terms of solute dispersion. It outperforms the negative effect of the channel-to-channel polydispersity which is mitigated by transverse diffusion of the analyte in the stationary phase. For Peclet numbers larger than 50, the HETP of the 3D-printed MOTTD column is found 7%, 15%, and 16% smaller than that of the MOTTD column consisting of a square array of perfect quadratic channels. This confirms the known effect of channel geometry on solute dispersion in microfluidic systems. Flow channels in fabricated MOTTD columns are preferred to be circular so that the distribution of transverse diffusion lengths across the open channels remains as tight as possible. Finally, the general theory of nonuniform columns of Giddings reveals that the polydispersity of the cross-sectional area (RSD 8.4%) along a single 3D-printed channel has no negative impact on solute dispersion in MOTTD columns. Overall, MOTTD columns could become a serious alternative technology to conventional particulate columns. This implies a novel fabrication process that delivers circular channel diameters smaller than 10 µm, cross-sectional area polydispersity no larger than 25%, external porosities in a range from 15% (high speed separations) to 75% (high performance separations), and conventional mesoporous silica as the stationary phase. It adresses new synthesis routes based on either organic fibers or tubular micelle templating agents in suspension with silica gel solutions.

Retention and mass transfer properties of the series of unbonded, amide-bonded, and alkylsulfobetaine-bonded ethylene bridged hybrid hydrophilic interaction liquid chromatography columns.

This work investigates the link between the retentivity and the stationary phase to mobile phase mass transfer resistance of hydrophilic interaction liquid chromatography (HILIC) columns packed with the same base ethylene-bridged hybrid particles (BEH). The retention volumes, the plate heights, and the volume of the adsorbed water layer were measured for the ACQUITYTM UPLCTM BEHTM 130 Å HILIC Column (unbonded BEH), ACQUITY UPLC BEH 130 Å Amide Column (amide group attached), and AtlantisTM Premier BEH 95 Å Z-HILIC (zwitterionic group attached) Column. The method of Guo (toluene retention volumes in pure acetonitrile and in the HILIC eluent) was validated from the UNIFAC group-contribution method and applied to measure accurately the water layer volumes in these columns. A strong correlation was found between the retention volumes of most neutral polar analytes and the volume of the water layer adsorbed in the HILIC column. The fraction of the pore volume occupied by the water layer increases significantly from the BEH HILIC Column to the BEH Amide Column, and to the BEH Z-HILIC Column. This is explained by the water solvation of the attached ligands in the pore volume of the BEH Particles and to the smaller average mesopore size of the BEH Z-HILIC Particles. A second and strong correlation is also observed between the water content in the HILIC particle and the stationary phase to mobile phase mass transfer resistance of the HILIC columns at high mobile phase linear velocities. The measured intra-particle diffusivity normalized to the bulk diffusion coefficient decreased from 0.33 (BEH HILIC Column) to 0.10 (BEH Amide Column) and to only 0.03 (BEH Z-HILIC Column) for comparable retention of cytosine. These results are fully consistent with the higher viscosity of the internal eluent (higher water content) and higher internal obstruction for diffusion (smaller mesopores and internal porosity) in the BEH Z-HILIC Particles. Still, in gradient elution mode, the peak capacity was found to be 18% higher for the BEH Z-HILIC Column than that on the BEH Amide Column because the retention factors at elution were smaller when maintaining the same analysis time and starting eluent composition.

Prediction of surface excess adsorption and retention factors in reversed-phase liquid chromatography from molecular dynamics simulations.

An alternative method to the classical fit of semi-empirical, statistical, or artificial intelligence-based models to retention data is proposed to predict surface excess adsorption and retention factors in liquid chromatography. The approach is based on a fundamental, microscopic description of the liquid-to-solid adsorption of analytes taking place at the interface between a bulk liquid phase and a solid surface. Molecular dynamics (MD) simulations are performed at T=300 K in a 100 Å wide slit-pore model (ß-cristobalite-C18 surface in contact with an acetonitrile/water mobile phase) to quantify a priori the retention factors of small molecules expected in reversed phase liquid chromatography (RPLC). Uracil is chosen as the reference "non-retained" marker, whereas benzyl alcohol, acetophenone, benzene, and ethylbenzene are four selected retained, neutral compounds. The MD simulations allow to determine the pore-level density profiles of these five compounds, i.e., the variation of the analyte concentration as a function of distance from the silica surface. The retention factors of the retained analytes are expressed using their respective calculated surface excess adsorption relative to uracil. By definition, the retention factors are proportional to the surface excess adsorbed and the proportionality constant is directly scaled to the retention time of the "non-retained" marker. Experimentally, a 4.6 mm × 150 mm RPLC-C18 column packed with 5 µm 100 Å High Strength Silica (HSS)-C18 particles is used and the retention times of these five compounds are measured. The volume fraction of acetonitrile in water increases from 20 to 90% generating a wide range of retention factors from 0.15 to 183 at T=300 K. The results demonstrate very good agreement between the MD-predicted surface excess adsorption data and measured retention factors (R2> 0.985). A systematic error is observed as the proportionality constant is not exactly scaled to the retention time of uracil. This is most likely caused by the differences between the chemical and morphological features of the slit-pore model adopted in the MD simulations and those of the actual HSS-C18 particles: the average surface coverage with C18 chains, the geometry of the mesopores, and the pore size distribution. Specifically, the impact on RPLC retention of slight, local variations in surface chemistry (e.g., functional group density and uniformity) and how this aspect is affected by the pore space morphology (e.g., pore curvature and size) is worth investigating by future MD simulations.

Modeling of the transient diffusion regime in fully porous particles-Application to the analysis of large biomolecules by ultra-high pressure liquid chromatography.

The transient diffusion regime of large biomolecules such as monoclonal antibodies, double-stranded (ds) DNA (base pair number ∼ 100), and virus-like particles is modeled in a single fully porous particle utilized as size exclusion chromatography (SEC) packing materials in ultra-high pressure liquid chromatography (UHPLC). The expression of the time and space dependent concentration profiles is derived for a step concentration change. Four different UHPLC particles were considered in the calculations depending on the size of the analyte : 2.0 µm 125 Å Bridge-Ethylene-Hybrid (BEH) XBridgeTM particles for small molecules (size: 4 Å), 2.0 µm 125 Å and 250 Å BEH particles for monoclonal antibodies (size: 55 Å), 2.0 µm 250 Å and 2.5 µm 450 Å BEH particles for dsDNA (size: 160 Å), and 2.5 µm 900 Å BEH particles for virus-like particles (size: 500 Å). The accessible porosities and the hindrance diffusion factors of these analytes were determined from the physical reconstruction of the internal structure of a 2.0 µm 130 Å BEH particle and from the simulation of the analyte mobility in the reconstructed mesopores. The analysis of the transient diffusion profiles reveals that there is insufficient time for the largest analytes to fully equilibrate the BEH particles in UHPLC. The dynamic capacity of the BEH particles is estimated to decrease from more than 99% for small molecules to 96% for monoclonal antibodies, 74% for 100 base pair dsDNA, and to less than 2% for virus-like particles. A full but reduced column capacity relative to fully porous particles can be recovered for monoclonal antibodies by considering superficially porous particles with a core-to-particle diameter ratio of about 0.8. In contrast, this is not possible for either large dsDNA (base pair number ≥ 100) or virus-like particles because the shell thickness would become smaller than the mesopore size required. The presented results open up two research avenues in order to analyze such large biomolecules by UHPLC: prepare ultra-high pressure-resistant sub-3 µm silica-based particles with pore sizes much larger than 1000 Å and design proper nonporous macrostructures to load, trap, separate, and elute rapidly by gradient UHPLC.

On the road toward highly efficient and large volume three-dimensional-printed liquid chromatography columns?

The current performance of commercially packed liquid chromatography columns is limited by the random structure of the packed bed and by the wall-to-center heterogeneity of its structure. The minimum reduced plate heights observed are not smaller than 1.4, whereas they could theoretically be as low as 0.1 for dense and perfectly ordered packings of spheres. To bridge this gap, a wide inner diameter column with an ordered macroporous structure is printed in three dimensions by stereolithography of poly(ethylene glycol diacrylate) resin. Feature sizes below 100 µm are achieved by combining conventional polymer stereolithography with photolithography using photomasks. A layer-by-layer polymerization is performed by alternating two distinct photomasks having horizontally and vertically oriented patterns. Despite the inevitable printing imperfections, minimum reduced plate heights around unity are measured for nonretained analytes. The next challenges for the successful printing of highly efficient and large volume liquid chromatography columns are threefold: reducing the feature size down to below 10 µm, keeping minimum the unevenness of the flow channel dimensions, and tackling additive manufacturing of silica aerogels at such small feature sizes for higher mechanical stability and broader range of retention/selectivity than those delivered by polymer materials.

Model of retention time and density of gradient peak capacity for improved LC-MS method optimization: Application to metabolomics.

A general and deterministic model is derived from the fundamentals of liquid chromatography to calculate retention time, peak width, peak capacity, and density of peak capacity in gradient liquid chromatography. The calculation of these chromatographic properties accounts for 1) the presence of initial (separation of the earliest eluters) and final (column wash) isocratic steps before and after the linear gradient, respectively, 2) the pre- (flow through needle and preheater tubes) and post-column (outlet and emitter tubes before MS detection) dispersion, 3) the compression of the chromatographic band, and 4) the retention of the organic modifier onto the RPLC column. The multiple and variable method parameters may include the column dimensions, particle size, flow rate, temperature, initial and final isocratic hold times, gradient time, gradient steepness, column conditioning/sample load time, and the pre- and post-column tube dimensions. The model enables the users to perform robust multi-dimensional optimization of UHPLC-MS methods and offers the possibility to predict the expected MS feature density for increased method performance. Method optimization can be further improved by matching the observed MS feature density (number of metabolites detected as function of time) to the predicted density of peak capacity. It is directly applied to the optimization of high-throughput RPLC separation methods specifically designed for large-scale urinary metabolic phenotyping.

Extraction of intrinsic column peak profiles of narrow-bore and microbore columns by peak deconvolution methods.

The intrinsic peak profiles (free from the delay and dispersion caused by state-of-the art UHPLC systems) generated by narrow-bore and microbore chromatographic columns used in liquid chromatography-mass spectrometry (LC-MS) proteomic analyses are extracted from two different deconvolution methods. The first method is based on the classical discrete Fourier transform (DFT) while the second method refers to the Taylor expansion of the continuous Fourier transform (FT). The two numerical methods are compared regarding the accurate determination of the intrinsic peak profiles of the non-retained compound (toluene) expected on a narrow-bore 2.1 mm × 100 mm column packed with 1.6 µm CORTECS-C18 superficially porous particles and installed on three different LC systems (ACQUITY i-class UPLC, ACQUITY H-class UPLC, and Arc LC systems). The DFT-based method is most relevant when the low-frequency band of the chromatographic peak does not overlap with the high-frequency bands related to the experimental baseline noise (pump/detector). The Taylor expansion-based method is successful for the extraction of the intrinsic peak profiles of narrow-bore 2.1 mm i.d. columns packed with sub-2 µm particles installed on standard UHPLC systems. When the LC system dispersion significantly exceeds that of the column, the DFT-based method is preferred over the Taylor expansion-based method and is successfully applied to extract the intrinsic peak profiles generated by a microbore 1.0 mm × 100 mm column packed with 1.8 µm HSS-C18 fully porous particles (volume variance ∼ 0.15 µL2 for the non-retained compound toluene) run on the low-dispersion ACQUITY i-class UPLC system (∼ 1 µL2 volume variance). This result opens up promising avenues for the development, quality control, and LC-MS analyses of microbore 1 mm i.d. columns using the state-of-the-art UHPLC instruments at flow rates larger than 0.1 mL/min.

Rebirth of recycling liquid chromatography with modern chromatographic columns : Extension to gradient elution.

Twin column recycling semi-preparative liquid chromatography (TCRLC) is revived to prepare small amount (∼ 1 mg) of a pure targeted compound, which cannot be isolated by conventional preparative liquid chromatography. In this work, TCRLC is extended to gradient elution. The first step of this modified process consists of a gradient step, which eliminates both early and late impurities. If not discarded, some late impurities could echo during the second isocratic recycling step of the process and compromise the purity level required for the targeted compound. Additionally, the entire gradient TCRLC (GTCRLC) process is automated regarding the eluent composition programmed and the actuation times of two valves: one two-position four-port divert valve enables to shave the targeted compound from early and late impurities during the initial gradient step. The second two-position six-port recycling valve ensures the complete baseline resolution between the band of the targeted compound and those of the closest impurities, which are not fully eliminated after the initial gradient step. The automation of the whole GTCRLC process is achieved by running four preliminary scouting gradient runs (at four different relative gradient times, tgt0= 2, 6, 18, and 54, where t0 is the hold-up column time) for the accurate determination of the thermodynamics (lnk versus φ plots of the retention factor as a function of the mobile phase composition) of the first impurity, the targeted compound(s), and of the last impurity. The automated GTCRLC process was successfully applied for the isolation of a polycyclic aromatic hydrocarbon (PAH), chrysene, from a complex mixture of PAHs containing two nearly co-eluting impurities (benzo[a]anthracene and triphenylene) and nine other early/late impurities (sample volume injected: 1 mL, 7.8 mm × 150 mm Sunfire-C18 column, acetonitrile/water eluent mixtures, T= 55 ∘C, 20 cycles, baseline separation in less than two hours). Additionally, the GTCRLC process is advantageously used to isolate and baseline separate the vitamins D2 and D3 initially present in a milk extract mixture (0.3 mL sample injection volume, 7.8 mm × 150 mm Sunfire-C18 column, methanol/water eluent mixtures, T= 65 ∘C, 14 cycles needed in 1.5 hours). These results open promising avenues toward an effective preparation of unknown targeted compounds before further physico-chemical characterization and unambiguous identification.

Theoretical framework for mixer design for noise reduction and gradient fidelity.

The mixing of two or more solvent streams to deliver a stable and accurate solvent composition is crucial to the performance, repeatability and reproducibility of a liquid chromatographic separation. We provide a theoretical treatment of axial mixing of a sequence of solvent packets with the framework of continuous stirred tank reactors (CSTRs) in series and investigate the tradeoffs presented between the primary goal of mixers (noise reduction) and it's necessary side-effects of gradient deformation and asymmetry. An experimental setup to mimic CSTR conditions was created using a stop-flow setup where the fluid flow was periodically paused and sonicated within pods of a certain volume. The effects of mixer volume relative to the volume of pump strokes and gradient volumes were investigated and discussed. A total mixer volume that is six-fold the pump stroke volume was found to be necessary to achieve sufficient (95%) noise reduction necessary for certain applications. A series of two or more CSTR elements was found to outperform a single CSTR element for larger mixer-to-pump stroke volume ratio in dampening baseline noise. For linear gradients, a gradient volume that is ten times larger than the mixer volume was found to sufficiently maintain gradient fidelity. For very small gradient volumes relative to the mixer volume, deformation of linear gradients was found to be significantly greater than predicted by the analytical solution. Furthermore, the nature of the solvent gradient deformation was asymmetric, with the latter half of the solvent gradient deforming significantly more than the first half. Combining analytically and numerically derived solutions for multiple CSTRs connected in series with experimental data, several suggestions can be made on mixer dimensions and design for a certain pump system and method transfer, given a pump stroke volume and gradient time.

Theoretical study of the efficiency of liquid chromatography columns with particle size gradient.

Modern analytical applications of liquid chromatography require more and more efficient columns. In this work, the possibility of utilizing particle size gradient in the chromatographic column was studied by a theoretical approach. In the course of our work three different scenarios of particle size gradients were considered with different shapes (linear, convex and concave). The evolution of bandwidth inside the column was plotted for each scenario. As a reference point, the bandwidth of the uniform column was used, which had the same pressure drop as the non-uniform column. According to our calculations, in isocratic elution mode, the non-uniform column does not offer any advantage compared to the uniform column, regardless the type of the particle size gradient. In gradient elution mode, however, extra band compression occurs was found. For negative particle size gradients, the final physical bandwidth was found to be approximately 1-4 % smaller than for uniform columns. This slight gain in efficiency in terms of bandwidth compression can be expanded to 5-8 % by the optimization of the limiting particle sizes. These optimized results are obtained when the final particle size is approximately 40% of the initial particle diameter.

Mitigation of analyte loss on metal surfaces in liquid chromatography.

The adsorptive loss of acidic analytes in liquid chromatography was investigated using metal frits. Repetitive injections of acidic small molecules or an oligonucleotide were made on individual 2.1 or 4.6 mm i.d. column frits. Losses were observed for adenosine 5'-(α,ß-methylene) diphosphate, 2-pyridinol 1-oxide and the 25-mer phosphorothioate oligonucleotide Trecovirsen (GEM91) on stainless steel and titanium frits. Analyte adsorption was greatest at acidic pH due to the positive charge on the metal oxide surface. Analyte recovery increased when a series of injections was performed; this effect is known as sample conditioning. Nearly complete recovery was achieved when the metal adsorptive sites were saturated with the analyte. A similar effect was achieved by conditioning the frits with phosphoric, citric or etidronic acids, or their buffered solutions. These procedures can be utilized to mitigate analyte loss. However, the effect is temporary, as the conditioning agent is gradually removed by the running mobile phase. Metal frits modified with hybrid organic/inorganic surface technology were shown to mitigate analyte-to-metal surface interactions and improve recovery of acidic analytes. Quantitative recovery of a 15-35 mer oligodeoxythymidine mixture was achieved using column hardware modified with hybrid surface technology, without a need for column conditioning prior to analysis.