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We performed multiscale simulations of analyte sorption and diffusion in hierarchical porosity models of monolithic silica columns for reversed-phase liquid chromatography to investigate how the mean mesopore size of the chromatographic bed and the analyte-specific interaction with the chromatographic interface influence the analyte diffusivity at various length scales. The reproduced experimental conditions comprised the retention of six analyte compounds of low to moderate solute polarity on a silica-based, endcapped, C 18 stationary phase with water‒acetonitrile and water-methanol mobile phases whose elution strength was varied via the volumetric solvent ratio. Detailed information about the analyte-specific interfacial dynamics received from molecular dynamics simulations was incorporated through appropriate linker schemes into Brownian dynamics diffusion simulations in three hierarchical porosity models received from physical reconstructions of silica monoliths with a mean macropore size of 1.23 µm and mean mesopore sizes of 12.3, 21.3, or 25.7 nm. The mean mesopore size was found to have a similar influence on the effective mesopore diffusivity as the analyte polarity and the mobile-phase elution strength, which together determine the analyte residence time on a column. A smaller mesopore size attenuated the increase of the effective mesopore diffusivity with increasing mobile-phase elution strength significantly. The effective bed diffusivity was limited by the analyte residence time rather than by morphological details of the mesopore space. The stronger an analyte was retained by the chromatographic interface inside the mesopores, the slower became the mass transfer between the pore space hierarchies and the lower was the effective bed diffusivity. The B-terms of the plate height equation were finally generated with the bed diffusivities and phase-based retention factors derived from the hierarchical porosity models using additional information about the stationary-phase limit obtained from the analysis of analyte-bonded phase contacts. The B-terms highlight analyte- and mobile phase-specific behavior relevant to isocratic and gradient elution conditions in chromatographic practice. In particular, U-shaped B-term curves are observed due to the dominating contribution of the retention factor and the bed diffusivity to the B-term at low and high elution strength of the mobile phase, respectively., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 The Author(s). Published by Elsevier B.V. All rights reserved.)

In liquid chromatography (LC), discrepancies in liquid properties such as elution strength and viscosity lead to a mismatch between the sample diluent and mobile phase. This mismatch can result in peak deformation, including peak splitting or even breakthrough, particularly when large sample volumes are injected. The formation of a T-junction between sample solution and mobile phase flow stream, a technique previously used in supercritical fluid chromatography, is the key enabler of feed injection in LC. This T-junction allows the injection needle to infuse the sample directly into the mobile phase. It ensures that the diluent is continuously mixed with the mobile phase before introduced onto the column, thereby reducing the initial solvent mismatch. The degree of dilution depends on the ratio between mobile phase flow rate (Q mp ) and feed rate (Q feed ) at which the sample is infused. Our study examined the effect of several parameters on the feed injection of large sample volumes from purely organic diluents in reversed-phase LC. These parameters included the type of diluent, compound retention factor (k), injected sample volume (V inj ), and Q mp . With varied Q feed , all compounds revealed a similar range of optimal values for Q r = (Q mp -Q feed )/Q feed between 2 and 5, a range unaffected by V inj and Q mp . For Q r > 5, the slope of the plate height curves (H vs. Q r ) decreases with increasing k, potentially extending the range of optimal Q r -values. However, the best Q r -value for a separation is determined by the compound with the smallest k, simplifying optimization. Using feed injection, we were able to reduce plate heights by up to a factor of 8 compared to classic flow-through injection of large sample volumes., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 The Author(s). Published by Elsevier B.V. All rights reserved.)

Mass transport through the mesopore space of a reversed-phase liquid chromatography (RPLC) column depends on the properties of the chromatographic interface, particularly on the extent of the organic-solvent ditch that favors the analyte surface diffusivity. Through molecular dynamics simulations in cylindrical RPLC mesopore models with pore diameters between 6 and 12 nm we systematically trace the evolution of organic-solvent ditch overlap due to spatial confinement in the mesopore space of RPLC columns for small-molecule separations. Each pore model of a silica-based, endcapped, C 18 -stationary phase is equilibrated with two mobile phases of comparable elution strength, namely 70/30 (v/v) water/acetonitrile and 60/40 (v/v) water/methanol, to consider the influence of the mobile-phase composition on the onset of organic-solvent ditch overlap. The simulations show that, as the pore diameter decreases from 9 to 6 nm, the bonded-phase density extends and compacts towards the pore center, which leads to increased accumulation of organic-solvent excess and thus enhanced organic-solvent diffusivity in the ditch. Because the acetonitrile ditch is more pronounced than the methanol ditch, acetonitrile ditch overlap sets in at less severe spatial confinement than methanol ditch overlap. The pore-averaged methanol and acetonitrile diffusivities are considerably raised by ditch overlap in the 6 nm-diameter pore, but also benefit from the ditch (without overlap) in the 7 to 12 nm-diameter pores, whereby local and pore-averaged effects are generally larger for acetonitrile than methanol., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024. Published by Elsevier B.V.)

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 ϵ e =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 k 1 =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., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 Elsevier B.V. All rights reserved.)

Electron tomography (ET) has attracted significant attention for a quantitative analysis of mesoporous materials, especially for complex disordered pore structures, as no priori assumption on the pore shape is needed, which is normally inevitable when using traditional bulk characterization techniques. However, a reliable quantification of such pore structures from ET critically depends on the fidelity of the segmented reconstruction, which can be significantly affected, e.g. by the raw data quality, the limited tilting range, artifacts introduced during alignment and further depends on the reconstruction algorithm. Therefore, we systematically investigated the reconstruction reliability of three main-stream algorithms including simultaneous iterative reconstruction technique (SIRT), total variation minimization (TVM) and discrete algebraic reconstruction technique (DART) for mesoporous materials using different imperfect (realistic) tilt-series based on a set of phantom simulations. We found that DART outperforms the other two methods in reliably revealing small pores and narrow channels, especially when the number of projections is strongly constrained. The accurately segmented reconstruction from DART makes it possible to achieve reliable quantification of the pores structure, which in turn leads to reliable evaluation of effective diffusion coefficients. We discuss the influence of different acquisition and reconstruction parameters on the reconstructed 3D volume and the quantitative analysis of pore features. We aim to provide a practical guideline for optimizing acquisition and reconstruction parameters and how to evaluate the accuracy when describing the mesoporous structure., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022. Published by Elsevier B.V.)

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 (β-cristobalite-C 18 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-C 18 column packed with 5 μm 100 Å High Strength Silica (HSS)-C 18 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 (R 2 > 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-C 18 particles: the average surface coverage with C 18 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., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022 Elsevier B.V. All rights reserved.)

Multiple-open-tubular columns enabling transverse diffusion (MOTTD) are made of straight, parallel, and cylindrical flow channels separated by a mesoporous stationary phase. In Part 1, a model of band broadening along MOTTD columns accounting for longitudinal diffusion, the trans-channel velocity bias, and mass transfer resistance in the stationary phase was proposed and validated. In this Part 2, the model is completed by considering the impact of short-range inter-channel velocity biases on the MOTTD plate number. These velocity biases are caused by the wide distribution of the channel diameters. Different ratios, ρ, of the average inner diameter, 2c >, of the flow channels to their closest center-to-center distance d (d= 5 μm, ρ= 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9) with a relative standard deviation (RSD) increasing from 0 to 50% are considered. The zone retention factor k 1 was increased from 1 to 25. The complete model of band broadening is validated after adjustment to dispersion data obtained by 1) the lattice-Boltzmann method for modeling fluid flow, 2) a random-walk particle-tracking (RWPT) technique to address advective-diffusive transport, and 3) by considering two distinct populations of flow channels (inner radii r c,1 =c >(1-RSD) and r c,2 =c >(1+RSD)) arranged at the nodes of a hexagonal compact array. The completed model of band broadening in MOTTD columns reveals that the RSD of the channel diameters has only a moderate impact on the optimum plate number of MOTTD columns: the relative increase of the minimum plate height do not exceed 30% even for the largest RSDs. However, when the mass transfer of the analyte is governed by its slow rate of transverse diffusion across the MOTTD column, the plate height can be increased by up to 100% at high average velocities. Regarding the best trade-off between analysis speed and column performance at a fixed pressure drop of 400 bar, irrespective of the zone retention factor and RSD of the distribution of the channel diameters, the fastest analyses are recommended for MOTTD columns having a small structural parameter ρ. In contrast, for the longest analysis times, the largest values of ρ are required to maximize the performance of MOTTD columns., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2021 Elsevier B.V. All rights reserved.)

Among the most popular compounds to estimate the hold-up time in reversed-phase liquid chromatography (RPLC) are acetone and uracil, which are considered as too small and too polar, respectively, for retention by the hydrophobic stationary phase, although their observed elution behavior does not fully support this assumption. We investigate how acetone and uracil as solutes interact with the chromatographic interface through molecular dynamics simulations in an RPLC mesopore model of a silica-supported, endcapped, C 18 phase equilibrated with a water (W)‒acetonitrile (ACN) mobile phase. The simulation results provide a molecular-level explanation for the observed elution behavior of acetone and uracil, but also question whether true dead time markers for RPLC exist. Both solutes have a density maximum in the interfacial region in addition to a low presence in the bonded-phase region, but these density peaks clearly differ from the adsorption and partitioning peaks of true analytes. Acetone partially behaves like a co-solvent of ACN and partially like the analyte acetophenone. Like ACN, acetone can be found in the first and second layer of solvent molecules at the silica surface; like acetophenone, acetone adsorbs to the bonded-phase chains by orienting its polar group to the bulk region to sustain hydrogen bonds with W molecules. Uracil behavior is governed by a need for extensive hydrogen-bond coordination by W molecules. Uracil adsorbs to the very edge of the bonded-phase chains, on the bulk-region side of the ACN density maximum in the interfacial region. Further penetration into the chains is prevented by the absence of W molecules, which are not found deeper in the bonded phase, except at the silica surface. Contrary to true analytes, accumulation of uracil and acetone in the interfacial region ceases at an equimolar presence of W and ACN in the mobile phase (at 70‒80% ACN volume fraction). Uracil achieves a closer approximation of the stationary-phase limit than acetone, but carries the risk of HILIC retention at high ACN fraction in the mobile phase., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2021 Elsevier B.V. All rights reserved.)

We derive a model of band broadening in multiple-open-tubular columns enabling transverse diffusion (MOTTD). In MOTTD columns, the flow channels are straight, parallel, cylindrical tubes arranged in a hexagonal compact array. A mesoporous material or stationary phase (130 Å bridged-ethyl hybrid (BEH) silica support) is filling the volume between the flow channels. The model is based on Giddings' random-walk theory of non-equilibrium chromatography. It is calibrated for the unknown configuration factor, q s , related to the specific geometry of the stationary phase in MOTTD columns. q s values are found based on the best fit of the model to simulated dispersion data obtained by the lattice-Boltzmann method for modelling fluid flow and a random-walk particle-tracking technique to address advective-diffusive transport of the analytes. For the model calibration, simulations are performed for different ratios, ρ, of the average inner diameter of the flow channels to their closest center-to-center distance under retained and non-retained conditions. The model is successfully validated (average relative errors below 10%) under both retained and non-retained conditions. For the same column format (4.6 mm i.d.  ×  150 mm), external porosity, zone retention factor, and relative standard deviation of the distribution of the inner diameters of the flow channels, the derived model reveals the intrinsic advantage of MOTTD columns (center-to-center distance between flow channels of 5 µm and ρ = 0.62) over a conventional column packed with 5 µm 130 Å BEH silica particles and the same multiple porous-layer open-tubular column (MPLOT) disabling transverse dispersion. MOTTD columns are weakly affected by the polydispersity of the inner diameter of the flow channels. Provided MOTTD columns could be prepared at a small feature size of 5 µm or less, they are expected to deliver a significant improvement in column technology relative to current particulate and silica monolithic columns., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2020. Published by Elsevier B.V.)

We present relationships between the multiscale structure and the separation properties of size exclusion chromatography (SEC) columns. Physical bed reconstructions of wall and bulk regions from a 2.1 mm i.d. column packed with fully porous 1.7 µm bridged-ethyl hybrid (BEH) particles, obtained by focused ion-beam scanning electron microscopy, serve as geometrical models for the packing microstructure in wall and central regions of a typical narrow-bore SEC column. In addition, the intraparticle mesopore space morphology of the BEH particles is reconstructed using electron tomography, to ultimately construct a realistic multiscale model of the bed morphology from mesopore level via interparticle macropore space to transcolumn scale. Complemented by the results of eddy dispersion simulations in computer-generated bulk packings, relationships between packing microstructure and transchannel, short-range interchannel, as well as transcolumn eddy dispersion are used to analyze the fluid dynamics in the interparticle macropore space of the model. Further, we simulate hindered diffusion and accessible porosity for passive, finite-size tracers in the intraparticle mesopore space, to finally determine the effective particle and bed diffusion coefficients of these tracers in the hierarchical (macro-mesoporous) bed. Retention and transport properties of polystyrene standards with hydrodynamic diameters from 5 to 95 Å in tetrahydrofuran are subsequently predicted without introducing bias from arbitrary models. These properties include the elution volumes of the polystyrene standards, the global peak capacity (over the entire separation window), and the rate of peak capacity at any fixed elution volume. Optimal flow rates yielding maximal global peak capacity and a nearly uniform rate of peak capacity over the entire separation window are close to 0.04 and 0.20 mL/min, respectively. SEC column performance obtained for fully porous and superficially porous particles is compared by varying the core-to-particle diameter ratio ρ from 0 to 0.95. Because the separation window is narrowing more rapidly than the rate of peak capacity is growing with increasing ρ, core-shell particles always provide smaller global peak capacity; they still can be advantageous but only for simple sample mixtures. The presented morphology-performance approach holds great promise for method development in SEC., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2020. Published by Elsevier B.V.)

For comparable surface coverage of alkyl-bonded chains (∼3 μmol/m 2 ), the dewetting of 100% aqueous mobile phases from the mesopores of octyl(C 8 )-bonded silica particles is found 70 times faster than that from the same but octadecyl(C 18 )-bonded silica particles. This observation was made in this work for both fully porous (5 μm Symmetry) and superficially porous (2.7 μm CORTECS) particles. This experimental result is paradoxical because (1) the average pore size of C 8 -bonded materials is 10-15 Å larger than that of C 18 -bonded materials for the same unbounded silica gel and (2) the contact angle of water measured on smooth and planar C 8 -bonded surface is about 6° smaller than that on the same but C 18 -bonded surface (104° versus 110°). The equilibrium Laplace pressure is then expected to be smaller and the kinetics of water dewetting to be slower for silica-C 8 than for silica-C 18 stationary phases used in RPLC. The solution to this riddle is investigated based on (1) the calculation of the dewetting time assuming that the pores are monosized and the process is driven by the Laplace pressure, (2) the measurement of the advancing and receding contact angles of three different C 18 - and C 8 -bonded silica gels (4 μm NovaPak, 5 μm Symmetry, and 2.7 μm CORTECS) from the water porograms measured in a range of water pressure from normal pressure to 500 bar, and (3) on the calculation of the pore connectivity for both C 8 and C 18 -bonded silica. First, the experimental results show that the observed dewetting times are of the order of minutes or even hours instead of millisecond as predicted by the dewetting model. Secondly, the advancing and receding contact angles of water onto the C 8 -bonded silicas are found larger (by an average of +7° and +2°, respectively) than those measured for the same but C 18 -bonded silica (average of 112° and 92°). Finally, the calculated pore connectivity is decreasing by about 30% for 90 Å unbounded silica materials from C 8 to C 18 -bonded RPLC phases. Overall, the observed and much faster dewetting of water from C 8 column than that from C 18 column is primarily explained by a higher internal pore connectivity due to the thinner thickness of the alkyl-bonded layer (7 Å versus 15 Å) and, to a lesser extent, by a higher extrusion Laplace pressure of water (≃+10 bar)., (Copyright © 2019 Elsevier B.V. All rights reserved.)

We analyse a relationship between the bulk microstructure of randomly packed beds, which we quantify through chord length distribution (CLD) analysis of the interparticle void space, and the associated flow heterogeneity, as expressed by the longitudinal dispersion coefficient at a Péclet number of Pe = 10. A random collection of physically reconstructed packings is complemented with a systematic set of computer-generated packings of monosized spheres, for which the packing-generation algorithm has been carefully adjusted to realize a monotonic variation of the bed porosity and microstructural heterogeneity. The most relevant difference in the morphology between these computer-generated and the physically reconstructed packings are structural defects present in the real packings, such as particle oligomers and larger voids as well as contaminations and particle debris. These defects influence the pore space morphology and introduce additional structural heterogeneity. Hydrodynamic dispersion coefficients for all packings are derived by implementing the lattice-Boltzmann method to simulate fluid flow and a random-walk particle tracking technique to record the transport of passive, point-like tracers in the flow fields. We propose a morphological descriptor, σ/μ, based on statistical parameters of a CLD (standard deviation σ and mean chord length μ) that can be used to predict the dispersion coefficient in packed beds, independent from the underlying particle size distribution, packing-generation protocol, bed porosity, and the occurrence of structural defects., (Copyright © 2019 Elsevier B.V. All rights reserved.)

We evaluate the effective diffusion coefficient in the interparticle pore space of eight physically reconstructed chromatographic packings of fully porous and core-shell particles, employing an analytical formula that involves the three-point microstructural parameter calculated from two-point and three-point correlation functions through an approach based on sampling templates. Diffusivities calculated by the approximate analytical formula are close to those obtained from pore-scale simulations in the reconstructions using a random-walk particle-tracking technique. Diffusivities are affected, apart from the interparticle porosity, by the actual bed microstructure and packing defects like particle oligomers, spalled shells, larger voids, and debris. Importantly, the data for the microstructural parameter and effective diffusion coefficient over the porosity range spanned by the individual packings (0.363-0.444) reveals non-monotonic behavior. Our analysis demonstrates that the three-point microstructural parameter reflects this morphological specificity of the packings and, as a result, Eq. (3) provides accurate estimates of the effective diffusion coefficients. The presented numerical approach can therefore be applied to evaluate diffusivities in packed beds with all their salient features just from the geometrical information embodied in the bed porosity and the three-point microstructural parameter., (Copyright © 2018 Elsevier B.V. All rights reserved.)

We study axial heterogeneities in capillary ultrahigh pressure liquid chromatography (UHPLC) columns through kinetic performance and bed morphological analysis. Two columns are used in this work, a 75 μm i.d. × 100 cm column packed with 1.3 μm C18-silica particles and a 75 μm i.d. × 45 cm column packed with 1.9 μm C18-silica particles. The long column is chromatographically characterized and is afterwards sectioned into three segments, each analyzed individually. The column packed with the 1.9 μm particles is subjected to a bed morphological analysis using confocal laser scanning microscopy near the inlet, center, and outlet of the column. Chromatographic and morphological characterizations reveal highest separation efficiency and most homogeneous bed microstructure towards the column outlet. Kinetic performance data for inlet and central packing segments indicate enhanced contributions from wall effects to a transcolumn flow heterogeneity. Bed morphological data reveal systematic changes in geometrical and frictional wall effects along the bed: from inlet to outlet, bed morphologies increasingly reflect packing microstructures associated with concentrated slurries. Variations in separation efficiency and bed morphology can be related to the constant-pressure packing mode; the decrease in packing rate along the bed leaves fewer chances for particle rearrangement and bed consolidation from inlet to outlet. It explains the relatively uniform bed morphology towards the outlet and also the relatively loose wall region near the inlet. Bed microstructural features are discussed in a context of previous observations made in the characterization of capillary UHPLC columns., (Copyright © 2018 Elsevier B.V. All rights reserved.)

Column wall effects are well recognized as major limiting factor in achieving high separation efficiency in HPLC. This is especially important for modern analytical columns packed with small particles, where wall effects dominate the band broadening. Detailed knowledge about the packing microstructure of packed analytical columns has so far not been acquired. Here, we present the first three-dimensional reconstruction protocol for these columns utilizing focused ion-beam scanning electron microscopy (FIB-SEM) on a commercial 2.1mm inner diameter×50mm length narrow-bore analytical column packed with 1.7μm bridged-ethyl hybrid silica particles. Two sections from the packed bed are chosen for reconstruction by FIB-SEM: one from the bulk packing region of the column and one from its critical wall region. This allows quantification of structural differences between the wall region and the center of the bed due to effects induced by the hard, confining column wall. Consequences of these effects on local flow velocity in the column are analyzed with flow simulations utilizing the lattice-Boltzmann method. The reconstructions of the bed structures reveal significant structural differences in the wall region (extending radially over approximately 62 particle diameters) compared to the center of the column. It includes the local reduction of the external porosity by up to 10% and an increase of the mean particle diameter by up to 3%, resulting in a decrease of the local flow velocity by up to 23%. In addition, four (more ordered) layers of particles in the direct vicinity of the column wall induce local velocity fluctuations by up to a factor of three regarding the involved velocity amplitudes. These observations highlight the impact of radial variations in packing microstructure on band migration and column performance. This knowledge on morphological peculiarities of column wall effects helps guiding us towards further optimization of the packing process for analytical HPLC columns., (Copyright © 2017 Elsevier B.V. All rights reserved.)

Column wall effects and the formation of larger voids in the bed during column packing are factors limiting the achievement of highly efficient columns. Systematic variation of packing conditions, combined with three-dimensional bed reconstruction and detailed morphological analysis of column beds, provide valuable insights into the packing process. Here, we study a set of sixteen 75μm i.d. fused-silica capillary columns packed with 1.9μm, C18-modified, bridged-ethyl hybrid silica particles slurried in acetone to concentrations ranging from 5 to 200mg/mL. Bed reconstructions for three of these columns (representing low, optimal, and high slurry concentrations), based on confocal laser scanning microscopy, reveal morphological features associated with the implemented slurry concentration, that lead to differences in column efficiency. At a low slurry concentration, the bed microstructure includes systematic radial heterogeneities such as particle size-segregation and local deviations from bulk packing density near the wall. These effects are suppressed (or at least reduced) with higher slurry concentrations. Concomitantly, larger voids (relative to the mean particle diameter) begin to form in the packing and increase in size and number with the slurry concentration. The most efficient columns are packed at slurry concentrations that balance these counteracting effects. Videos are taken at low and high slurry concentration to elucidate the bed formation process. At low slurry concentrations, particles arrive and settle individually, allowing for rearrangements. At high slurry concentrations, they arrive and pack as large patches (reflecting particle aggregation in the slurry). These processes are discussed with respect to column packing, chromatographic performance, and bed microstructure to help reinforce general trends previously described. Conclusions based on this comprehensive analysis guide us towards further improvement of the packing process., (Copyright © 2017 Elsevier B.V. All rights reserved.)

Slurry packing capillary columns for ultrahigh pressure liquid chromatography is complicated by many interdependent experimental variables. Previous results have suggested that combination of high slurry concentration and sonication during packing would create homogeneous bed microstructures and yield highly efficient capillary columns. Herein, the effect of sonication while packing very high slurry concentrations is presented. A series of six, 1m×75μm internal diameter columns were packed with 200mg/mL slurries of 2.02μm bridged-ethyl hybrid silica particles. Three of the columns underwent sonication during packing and yielded highly efficient separations with reduced plate heights as low as 1.05., (Copyright © 2016 Elsevier B.V. All rights reserved.)

Lateral transcolumn heterogeneities and the presence of larger voids in a packing (comparable to the particle size) can limit the preparation of efficient chromatographic columns. Optimizing and understanding the packing process provides keys to better packing structures and column performance. Here, we investigate the slurry-packing process for a set of capillary columns packed with C18-modified, 1.3μm bridged-ethyl hybrid porous silica particles. The slurry concentration used for packing 75μm i.d. fused-silica capillaries was increased gradually from 5 to 50mg/mL. An intermediate concentration (20mg/mL) resulted in the best separation efficiency. Three capillaries from the set representing low, intermediate, and high slurry concentrations were further used for three-dimensional bed reconstruction by confocal laser scanning microscopy and morphological analysis of the bed structure. Previous studies suggest increased slurry concentrations will result in higher column efficiency due to the suppression of transcolumn bed heterogeneities, but only up to a critical concentration. Too concentrated slurries favour the formation of larger packing voids (reaching the size of the average particle diameter). Especially large voids, which can accommodate particles from>90% of the particle size distribution, are responsible for a decrease in column efficiency at high slurry concentrations. Our work illuminates the increasing difficulty of achieving high bed densities with small, frictional, cohesive particles. As particle size decreases interparticle forces become increasingly important and hinder the ease of particle sliding during column packing. While an optimal slurry concentration is identified with respect to bed morphology and separation efficiency under conditions in this work, our results suggest adjustments of this concentration are required with regard to particle size, surface roughness, column dimensions, slurry liquid, and external effects utilized during the packing process (pressure protocol, ultrasound, electric fields)., (Copyright © 2016 Elsevier B.V. All rights reserved.)

In recent years, chromatographic columns packed with core-shell particles have been widely used for efficient and fast separations at comparatively low operating pressure. However, the influence of the porous shell properties on the mass transfer kinetics in core-shell packings is still not fully understood. We report on results obtained with a modeling approach to simulate three-dimensional advective-diffusive transport in bulk random packings of monosized core-shell particles, covering a range of reduced mobile phase flow velocities from 0.5 up to 1000. The impact of the effective diffusivity of analyte molecules in the porous shell and the shell thickness on the resulting plate height was investigated. An extension of Giddings' theory of coupled eddy dispersion to account for retention of analyte molecules due to stagnant regions in porous shells with zero mobile phase flow velocity is presented. The plate height equation involving a modified eddy dispersion term excellently describes simulated data obtained for particle-packings with varied shell thickness and shell diffusion coefficient. It is confirmed that the model of trans-particle mass transfer resistance of core-shell particles by Kaczmarski and Guiochon [42] is applicable up to a constant factor. We analyze individual contributions to the plate height from different mass transfer mechanisms in dependence of the shell parameters. The simulations demonstrate that a reduction of plate height in packings of core-shell relative to fully porous particles arises mainly due to reduced trans-particle mass transfer resistance and transchannel eddy dispersion., (Copyright © 2015 Elsevier B.V. All rights reserved.)

We propose an original model of effective diffusion along packed beds of mesoporous particles for HILIC developed by combining Torquatos model for heterogeneous beds (external eluent+particles), Landauers model for porous particles (solid skeleton+internal eluent), and the time-averaged model for the internal eluent (bulk phase+diffuse water (W) layer+rigid W layer). The new model allows to determine the analyte concentration in rigid and diffuse W layer from the experimentally determined retention factor and intra-particle diffusivity and thus to distinguish the retentive contributions from adsorption and partitioning. We apply the model to investigate the separation of toluene (TO, as a non-retained compound), nortriptyline (NT), cytosine (CYT), and niacin (NA) on an organic ethyl/inorganic silica hybrid adsorbent. Elution conditions are varied through the choice of a third solvent (W, ethanol, tetrahydrofuran (THF), acetonitrile (ACN), or n-hexane) in a mobile phase (MP) of ACN/aqueous acetate buffer (pH 5)/third solvent (90/5/5, v/v/v). Whereas NA and CYT retention factors increase monotonously from W to n-hexane as third solvent, NT retention reaches its maximum with polar aprotic third solvents. The involved equilibrium constants for adsorption and partitioning, however, do not follow the same trends as the overall retention factors. NT retention is dominated by partitioning and NA retention by adsorption, while CYT retention is controlled by adsorption rather than partitioning. Our results reveal that the relative importance of adsorption and partitioning mechanisms depends in a complex way from analyte properties and experimental parameters and cannot be predicted generally., (Copyright © 2014 Elsevier B.V. All rights reserved.)

The morphology of silica monoliths determines their mass transport properties. While eddy dispersion can be related to the size and structural heterogeneity of the macropores, longitudinal diffusion and trans-skeleton mass transfer resistance are influenced by the physical appearance of the mesopore space. We used two small analytes (uracil, naphthalene) and a large one (lysozyme) to characterize the column performance of a set of six second-generation analytical silica monoliths with systematically varied mean mesopore size from 5.5 to 25.7nm. Within this set of sample columns, the mean macropore size was conserved at about 1.2μm. Longitudinal diffusion and trans-skeleton mass transfer resistance were derived from peak parking experiments. Both contributions to the overall plate height are affected by the structural hindrance in the mesopores, which increases with smaller mesopore size. For the weakly retained naphthalene, this effect is counteracted by surface diffusion, which increases with the surface area of the mesopore space. Additivity of individual plate height contributions allows for the determination of eddy dispersion by subtraction of the other terms from the overall plate height curves. Column performance for lysozyme is limited by mass transfer resistance, which increases strongly with smaller mesopore size until lysozyme becomes totally excluded from the smallest (5.5nm) pores., (Copyright © 2014 Elsevier B.V. All rights reserved.)

Transcolumn dispersion limitations on the separation efficiency of chromatographic columns suggest the need for packing methods that increase bed homogeneity and minimize potential wall effects. Here we address the influence of the slurry concentration in the slurry packing process on the resulting morphology and separation efficiency of ultrahigh-pressure liquid chromatography capillary columns.30–75 μm i.d. capillaries were packed with fully porous 0.9, 1.7, and 1.9 μm bridged-ethyl hybrid particles and 1.9 μm Kinetex core–shell particles. Capillaries prepared with higher slurry concentrations(20–100 mg/mL) showed higher separation efficiencies than those prepared using a low slurry con-centration (2–3 mg/mL). The effect is explained by an analysis of transcolumn bed heterogeneities in three-dimensional reconstructions acquired from the packed capillaries using confocal laser scanning microscopy. The three-dimensional analysis of porosity distributions and local particle size illustrates that beds packed with higher slurry concentrations suppress particle size segregation, however, at the expense of a larger amount of packing voids. In core–shell packings, where only few packing voids were found, the higher slurry concentration allowed for an additional densification of the bed’s wall region, as revealed by a radial analysis of the mean particle distances. Overall, wall effects are attenuated in packed columns prepared with both wide and narrow particle size distributions, which will allow for improved chromatographic performance.

Shrinking the structural elements of a particulate bed or monolith (i.e., the particle or domain size) yields more efficient columns only when the homogeneity of the bed can be conserved in that process. We investigate this complex issue for a set of 2nd generation analytical silica monoliths with macropores reaching submicron dimensions using chromatographic methods, mercury intrusion porosimetry, scanning electron microscopy, and confocal laser scanning microscopy (CLSM), and present eddy dispersion simulations and a chord length distribution analysis for the CLSM-based physical reconstructions at macropore resolution. The combined results allow us to identify relevant morphological advances made from 1st to 2nd generation monoliths and additionally highlight the current limitations to a direct morphology-efficiency scaling with respect to the performance that can be accomplished in HPLC practice with these columns. Whereas the improvement in radial homogeneity from 1st to 2nd generation silica monoliths is represented by a dramatic increase in column efficiency, the further reduction of macropore size in the 2nd generation monoliths does not lead to the expected improvement of plate height data, although these monoliths realize submicron macropores at a simultaneously conserved bulk macropore space homogeneity and negligible radial heterogeneity. Our study implies that limitations to further improved column efficiency arise from the intrinsic border effects of the used 4.6mm i.d. analytical columns. This includes the sample distribution onto the monoliths and asynchronous sample collection through the endfittings at the column inlet and outlet, respectively. Only when these effects are reduced will additionally improved 2nd generation monoliths live up to column efficiencies, which are envisioned for them based on their morphological properties., (Copyright © 2013 Elsevier B.V. All rights reserved.)

We present the first quantitative comparison of eddy dispersion in the bulk macropore (flow-through) space of 1st and 2nd generation analytical silica monoliths. Based on samples taken from the bulk region of Chromolith columns, segments of the bulk macropore space were physically reconstructed by confocal laser scanning microscopy to serve as models in pore-scale simulations of flow and dispersion. Our results cover details of the 3D velocity field, macroscopic Darcy permeability, transient and asymptotic dispersion behavior, and chromatographic band broadening, and thus correlate morphological, microscopic, and macroscopic properties. A complete set of parameters for the individual eddy dispersion contributions in the bulk was obtained from a Giddings analysis of the simulated plate height data. The identified short-range structural heterogeneities correspond to the average domain size of the respective monoliths. Our plate height curves show that structural improvements in the bulk morphology of 2nd generation monoliths play only a minor role for the observed improvement in overall column efficiency. The results also indicate a topological dissimilarity between 1st and 2nd generation analytical silica monoliths, which raises the question how the domain size of silica monoliths can be further decreased without compromising the structural homogeneity of the bed., (Copyright © 2013 Elsevier B.V. All rights reserved.)

We comment on a recently published paper by Loh and Vasudevan [J. Chromatogr. A 1274 (2013) 65], which reported the physical reconstruction of the bulk macropore space of an analytical silica monolith by X-ray computed microtomography and the subsequent computational fluid dynamics simulations of flow and mass transport in the reconstructed monolith model. Loh and Vasudevan claim that their combined reconstruction and simulation approach offers a significant reduction of computational expenses without significant loss in accuracy in characterizing the macropore space heterogeneity of the monolith and predicting its transport properties. We challenge their claim and question the validity and validation of their results by discussing the employed scanning resolution, the characterization of macropore space heterogeneities, the interpretation of the simulated dispersion data, as well as the comparison of computational expenses with previous work., (Copyright © 2013 Elsevier B.V. All rights reserved.)

Analytical columns (4.6 mm i.d.) packed with core-shell particles have shown a significantly reduced eddy dispersion contribution to band broadening compared to conventional fully porous particles. It has been speculated if this is caused by the narrow particle size distribution (PSD) of the core-shell particles, as an intrinsic advantage, or by an improved packing structure that specifically reduces the transcolumn velocity biases caused by wall effects. A recent simulation study has pointed against the former proposition [A. Daneyko et al., Anal. Chem. 83 (2011) 3903]. It is more likely that the slurry packing process for core-shell particles results in bed morphologies with reduced wall effects compared to the fully porous particles with a wide PSD. To access the latter proposition experimentally we slurry packed capillary columns (100 μm i.d.) with different fully porous (wide PSDs) and core-shell (narrow PSDs) particles and imaged their bed structures three-dimensionally using confocal laser scanning microscopy. This allowed us to resolve and analyze the bed morphology in these columns locally on all length scales contributing to eddy dispersion. On the transcolumn scale we observed a systematic difference between core-shell and fully porous particles: In the vicinity of the column wall the core-shell particles packed denser (closer to the bulk packing densities) and with a higher regularity than the fully porous particles. The bulk regions of all packings were effectively indistinguishable. This provides experimental evidence that the reduced eddy dispersion contribution with core-shell packings should be attributed to a higher transcolumn homogeneity rather than to an improved bed morphology on smaller length scales, e.g., to a reduced short-range disorder., (Copyright © 2012 Elsevier B.V. All rights reserved.)

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., (Copyright © 2012 Elsevier B.V. All rights reserved.)

We study the impact of microscopic order on transverse dispersion in the interstitial void space of bulk (unconfined) chromatographic beds by numerical simulations of incompressible fluid flow and mass transport of a passive tracer. Our study includes polydisperse random sphere packings (computer-generated with particle size distributions of modern core-shell and sub-2 μm particles), the macropore space morphology of a physically reconstructed silica monolith, and computer-generated regular pillar arrays. These bed morphologies are analyzed by their velocity probability density distributions, transient dispersion behavior, and the dependence of asymptotic transverse dispersion coefficients on the mobile phase velocity. In our work, the spherical particles, the monolith skeleton, and the cylindrical pillars are all treated as impermeable solid phase (nonporous) and the tracer is unretained, to focus on the impact of microscopic order on flow and (particularly transverse) hydrodynamic dispersion in the interstitial void space. The microscopic order of the pillar arrays causes their velocity probability density distributions to start and end abruptly, their transient dispersion coefficients to oscillate, and the asymptotic transverse dispersion coefficients to plateau out of initial power law behavior. The microscopically disordered beds, by contrast, follow power law behavior over the whole investigated velocity range, for which we present refined equations (i.e., Eq.(13) and the data in Table 2 for the polydisperse sphere packings; Eq.(17) for the silica monolith). The bulk bed morphologies and their intrinsic differences addressed in this work determine how efficient a bed can relax the transverse concentration gradients caused by wall effects, which exist in all confined separation media used in chromatographic practice. Whereas the effect of diffusion on transverse dispersion decreases and ultimately disappears at increasing velocity with the microscopically disordered chromatographic beds, it dominates in the pillar arrays. The pillar arrays therefore become the least forgiving bed morphology with macroscopic heterogeneities and the engendered longitudinal dispersion in chromatographic practice. Wall effects in pillar arrays and the monolith caused by their confinement impact band broadening, which is traditionally observed on a macroscopic scale, more seriously than in the packings., (Copyright © 2012 Elsevier B.V. All rights reserved.)

The heterogeneous morphology of current silica monoliths hinders this column type to reach its envisioned performance goals. We present a new generation of analytical silica monoliths that deliver a substantially improved separation efficiency achieved through several advances in monolith morphology. Analytical silica monoliths from the 1st and 2nd Chromolith generation are characterized and compared by chromatographic methods, mercury intrusion porosimetry, scanning electron microscopy, and confocal laser scanning microscopy. The latter method is instrumental to quantify morphological differences between the monolith generations and to probe the radial variation of morphological properties. Compared with the 1st generation, the new monoliths possess not only smaller macropores, a more homogeneous macropore space, and a thinner silica skeleton, but also radial homogeneity of these structural parameters as well as of the local external or macroporosity. The 66.5% reduction in minimum plate height observed between silica monoliths of the 1st and 2nd Chromolith generation can thus be attributed to two key improvements: a smaller domain size at simultaneously increased macropore homogeneity and the absence of radial morphology gradients, which are behind the considerable peak asymmetry of the 1st generation., (Copyright © 2011 Elsevier B.V. All rights reserved.)

Flow and mass transport in bulk and confined chromatographic supports comprising random packings of solid, spherical particles and hexagonal arrays of solid cylinders (regular pillar arrays) are studied over a wide flow velocity range by a numerical analysis scheme, which includes packing generation by a modified Jodrey-Tory algorithm, three-dimensional flow field calculations by the lattice-Boltzmann method, and modeling of advective-diffusive mass transport by a random-walk particle-tracking technique. We demonstrate the impact of the confinement and its cross-sectional geometry (circular, quadratic, semicircular) on transient and asymptotic transverse and longitudinal dispersion in random sphere packings, and also address the influence of protocol-dependent packing disorder and the particle-aspect ratio. Plate height curves are analyzed with the Giddings equation to quantify the transcolumn contribution to eddy dispersion. Confined packings are compared with confined arrays under the condition of identical bed porosity, conduit cross-sectional area, and laterally fully equilibrated geometrical wall and corner effects on dispersion. Fluid dispersion in a regular pillar array is stronger affected by the macroscopic confinement and does not resemble eddy dispersion in random sphere packings, because the regular microstructure cannot function as a mechanical mixer like the random morphology. Giddings' coupling theory fails to preserve the nature of transverse dispersion behind the arrays' plate height curves, which approach a linear velocity-dependence as transverse dispersion becomes velocity-independent. Upon confinement this pseudo-diffusive behavior can outweigh the performance advantage of the regular over the random morphology., (Copyright © 2011 Elsevier B.V. All rights reserved.)

The mass transport properties of bulk random sphere packings depend primarily on the bed (external) porosity ε, but also on the packing microstructure. We investigate the influence of the packing microstructure on the diffusive tortuosity τ=D(m)/D(eff), which relates the bulk diffusion coefficient (D(m)) to the effective (asymptotic) diffusion coefficient in a porous medium (D(eff)), by numerical simulations of diffusion in a set of computer-generated, monodisperse, hard-sphere packings. Variation of packing generation algorithm and protocol yielded four Jodrey-Tory and two Monte Carlo packing types with systematically varied degrees of microstructural heterogeneity in the range between the random-close and the random-loose packing limit (ε=0.366-0.46). The distinctive tortuosity-porosity scaling of the packing types is influenced by the extent to which the structural environment of individual pores varies in a packing, and to quantify this influence we propose a measure based on Delaunay tessellation. We demonstrate that the ratio of the minimum to the maximum void face area of a Delaunay tetrahedron around a pore between four adjacent spheres, (A(min)/A(max))(D), is a measure for the structural heterogeneity in the direct environment of this pore, and that the standard deviation σ of the (A(min)/A(max))(D)-distribution considering all pores in a packing mimics the tortuosity-porosity scaling of the generated packing types. Thus, σ(A(min)/A(max))(D) provides a structure-transport correlation for diffusion in bulk, monodisperse, random sphere packings., (Copyright © 2011 Elsevier B.V. All rights reserved.)

We report an experimental study on the structural (especially radial) heterogeneity of eleven 100 μm i.d. capillary tetramethoxysilane-methyltrimethoxysilane hybrid silica monoliths with different pore and skeleton sizes, which were imaged by an optimized confocal laser scanning microscopy method. This method allows the optical sectioning of the monoliths, which is a prerequisite for quantitative morphological image analysis. Both radial porosity profiles and chord length distributions were calculated in the macropore domain for each column from at least 100 complete cross-sectional views along the column axis. The statistical approach visualized radial heterogeneities on different length scales in the monolithic structures. Chord length distributions followed a simplified k-gamma function, and a structural parameter obtained from this function is introduced to provide a scalar measure of column heterogeneity. It enables the comparison of monoliths with different pore sizes and helps to establish correlations between the microscopic properties of a column, eddy dispersion, and its separation efficiency., (Copyright © 2011 Elsevier B.V. All rights reserved.)

We report a fast, nondestructive, and quantitative approach to characterize the morphology of packed beds of fine particles by their three-dimensional reconstruction from confocal laser scanning microscopy images, exemplarily shown for a 100μm i.d. fused-silica capillary packed with 2.6μm-sized core-shell particles. The presented method is generally applicable to silica-based capillary columns, monolithic or particulate, and comprises column pretreatment, image acquisition, image processing, and statistical analysis of the image data. It defines a unique platform for fundamental comparisons of particulate and monolithic supports using the statistical measures derived from their reconstructions. Received morphological data are column cross-sectional porosity profiles and chord length distributions from the interparticle macropore space, which are a descriptor of local density and can be characterized by a simplified k-gamma distribution. This distribution function provides a parameter of location and a parameter of dispersion which can be correlated to individual chromatographic band broadening processes (i.e., to transchannel and short-range interchannel contributions to eddy dispersion, respectively). Together with the transcolumn porosity profile the presented approach allows to analyze and quantify the packing microstructure from pore to column scale and therefore holds great promise in a comparative study of packing conditions and particle properties, particularly for characterizing and minimizing the packing process-specific heterogeneities in the final bed structure., (Copyright © 2011 Elsevier B.V. All rights reserved.)

Changes in mobile phase composition during high performance liquid chromatography (HPLC) gradient elution coupled to mass spectrometry (MS) sensitively affect electrospray operation modes. In this work, we identify the influences of dynamic changes in bulk conductivity on the cone-jet stability island for aqueous acetonitrile and aqueous methanol mobile phases commonly used in reversed-phase HPLC. Bulk conductivities of the mobile phases were varied by adding different amounts of formic acid. A commercial microchip-HPLC/ESI-MS configuration was modified to enable in situ electrospray diagnostics by frequency analysis of the microchip emitter current and spray imaging. This approach facilitated the detection of different spray modes together with their onset potentials. The established spray modes are described and the differences in onset potentials and stability regions explained by the physicochemical properties of the electrosprayed liquid., (Copyright © 2011 Elsevier B.V. All rights reserved.)

We quantified the microstructural disorder of packed beds and correlated it with the resulting eddy dispersion. For this purpose we designed a set of bulk (unconfined) monodisperse random sphere packings with a systematic, protocol-dependent degree of microstructural heterogeneity, covering a porosity range from the random-close to the random-loose packing limit (ε = 0.366-0.46). With the precise knowledge of particle positions, size, and shape we conducted a Voronoiï tessellation of all packings and correlated the statistical moments of the Voronoiï volume distributions (standard deviation and skewness) with the porosity and the protocol-dependent microstructural disorder. The deviation of the Voronoiï volume distributions from the delta function of a crystalline packing describes the origin of short-range disorder of the investigated random packings. Eddy dispersion was simulated over a wide range of reduced velocities (0.5 ≤ ν ≤ 750) and analyzed with the comprehensive Giddings equation. Transient dispersion was found to correlate with the spatial scales of heterogeneity in the packings. The analysis of short-range disorder based on the Voronoiï volume distributions revealed a strong correlation with the short-range interchannel contribution to eddy dispersion, whereas transchannel dispersion was relatively little affected. The presented approach defines a strictly scientific route to the key morphology-transport relationships of current and future chromatographic supports, including their morphological reconstruction, statistical analysis, and the correlation with relevant transport phenomena. It also guides us in our understanding, comparison, and optimization of the diverse packing algorithms and protocols used in simulations and experimental studies.

This work presents an approach towards resolving hydrodynamic flow in real porous media by carrying out direct numerical simulations in the reconstructed macroporous (flow-through) domain of a silica monolith. The macroporous domain of a 60 microm x 60 microm x 12 microm segment of a 100 microm i.d. capillary silica monolith was reconstructed by confocal laser scanning microscopy. A 60 microm x 12 microm x 12 microm segment of the reconstructed domain was then used as the 3D matrix for simulation of fluid flow by the lattice-Boltzmann method on a high-performance computing platform. Excellent agreement is observed between the experimental and simulated Darcy permeabilities without any assumptions or further adjustments on the monolith morphology. The flow velocity field is analyzed in detail, including longitudinal and transverse velocity distributions, the occurrence of negative longitudinal velocities, as well as the beginning transition to the viscous-inertial flow regime. The presented methodology promises great potential for resolving the key relationships between morphology and band broadening in monolithic columns for HPLC applications., (Copyright 2010 Elsevier B.V. All rights reserved.)

Interparticle void volumes and porosities of packed capillaries have been determined using intraparticle Donnan exclusion of a small, unretained, co-ionic tracer (nitrate ions). The operational domain of this approach has been characterized for bare silica, reversed-phase, and strong cation-exchange materials (with different particle sizes and intraparticle pore sizes) in dependence of the mobile phase ionic strength. Interparticle porosities agree well with those analyzed by inverse size-exclusion chromatography (ISEC). Limitations to the use of Donnan exclusion (electrostatic exclusion) and ISEC (mechanical exclusion) arise as either type of exclusion becomes noticeable also in the cusp regions between the particles, or as the intraparticle pores are so large that complete electrostatic and size-exclusion are difficult to realize. Our data confirm that intraparticle Donnan exclusion presents a most simple, fast, and reliable approach for the analysis of packing densities., (Copyright (c) 2009 Elsevier B.V. All rights reserved.)

HPLC microchips are investigated experimentally with respect to packing density, pressure drop-flow rate relation, hydraulic permeability, and separation efficiency. The prototype microchips provide minimal dead volume, on-chip UV detection, and a 75 mm long separation channel with a ca. 50 microm x 75 microm trapezoidal cross-section. A custom-built stainless-steel holder allowed to adopt optimized packing conditions. Separation channels were slurry-packed with 3, 5, and 10 microm-sized spherical, porous C8-silica particles. Differences in interparticle porosity, permeability, and plate height data are analyzed and consistently explained by different microchannel-to-particle size (particle-aspect) ratios and particle size distributions.

This review is concerned with the analysis of flow regimes in porous media, in particular, in fixed beds of spherical particles used as reactors in engineering applications, or as separation units in liquid chromatography. A transition from creeping via viscous-inertial to turbulent flow is discussed based on macro-scale transport behaviour with respect to the pressure drop-flow rate dependence, in particular, the deviation from Darcy's law, as well as direct microscopic data which reflect concomitant changes in the pore-level hydrodynamics. In contrast to the flow behaviour in straight pipes, the transition from laminar to turbulent flow in fixed particulate beds is not sharp, but proceeds gradually through a viscous-inertial flow regime. The onset of this steady, nonlinear regime and increasing role of inertial forces is macroscopically manifested in the failure of Darcy's law to describe flow through fixed beds at higher Reynolds numbers. While the physical reasons for this failure still are not completely understood, it is not caused by turbulence which occurs at Reynolds numbers about two orders of magnitude above those for which a deviation from Darcy's law is observed. Microscopic analysis shows that this steady, nonlinear flow regime is characterized by the development of an inertial core in the pore-level profile, i.e., at increasing Reynolds number velocity profiles in individual pores become flatter towards the center of the pores, while the velocity gradient increases close to the solid-liquid interface. Further, regions with local backflow and stationary eddies are demonstrated for the laminar flow regime in fixed beds. The onset of local fluctuations (end of laminar regime) is observed at superficial Reynolds numbers on the order of 100. Complementary analysis of hydrodynamic dispersion suggests that this unsteady flow accelerates lateral equilibration between different velocities in fixed beds which, in turn, reduces spreading in the longitudial (macroscopic flow) direction.

We have investigated the basic dependence of electroosmotic flow (EOF) velocity and hydrodynamic dispersion in capillary electrochromatography (CEC) on the variation of applied field and mobile phase ionic strengths employing silica-based particulate and monolithic fixed beds. These porous media have a hierarchical structure characterized by discrete intraparticle (intraskeleton) mesoporous and interparticle (interskeleton) macroporous spatial domains. While the macroporous domains contain quasi-electroneutral electrolyte solution, the ion-permselectivity (charge-selectivity) of the mesoporous domains determines the co-ion exclusion and counter-ion enrichment at electrochemical equilibrium (without superimposed electrical field) which depends on mesopore-scale electrical double layer (EDL) overlap and surface charge density. This adjustable, locally charge-selective transport realized under most general conditions forms the basis for concentration polarization (CP) induced by electrical fields superimposed in CEC. CP characterizes the formation of convective diffusion boundary layers with reduced (depleted CP zone) and increased (enriched CP zone) electrolyte concentration, respectively, at the anodic and cathodic interfaces in fixed beds containing the cation-selective, silica-based particles (or monolith skeleton). CP originates in the electrical field-induced coupled mass and charge transport normal to the charge-selective interfaces and has consequences for the EOF dynamics, hydrodynamic dispersion, and analyte retention in CEC. A secondary EDL with mobile counter-ionic space charge can be induced in the depleted CP zone leading to induced-charge EOF in the macroporous domains. It is characterized by a nonlinear dependence of the average EOF velocities on applied field strength and strong local velocity components tangential to the surface which enhance lateral pore-scale dispersion, thereby decreasing (axial) zone spreading. Differences in the pore space morphology of random-close sphere packings and monoliths criticially affect the intensity of CP and induced-charge EOF in these materials. CP is identified as a key phenomenon in CEC which also influences effective migration and the retention of charged analytes because the local intensity of CP inherently depends on applied field and mobile phase ionic strengths.

The influence of Joule heating on electroosmotic flow velocity, the retention factor of neutral analytes, and separation efficiency in capillary electrochromatography was investigated theoretically and experimentally. A plot of electrical current against the applied electrical field strength was used to evaluate the Joule heating effect. When the mobile phase concentration of Tris buffer exceeded 5.0 mM in the studied capillary electrochromatography systems using particulate and monolithic columns (with an accompanying power level of heat dissipation higher than 0.35 W/m), the Joule heating effect became clearly noticeable. Theoretical models for describing the variation of electroosmotic flow velocity with increasing applied field strength and the change of retention factors for neutral analytes with electrical field strength at higher Tris buffer concentrations were analyzed to explain consequences of Joule heating in capillary electrochromatography. Qualitative agreement between experimental data and implications of the theoretical model analysis was observed. The decrease of separation efficiency in capillary electrochromatography with macroporous octadecylsilica particles at high buffer concentration can be also attributed to Joule heating mainly via the increased axial diffusion of the analyte molecules and dispersion of solute bands by a nonuniform electroosmotic flow profile over the column cross-section. However, within a moderate temperature range, the contribution of the macroscopic velocity profile in the column arising from radial temperature gradients is insignificant.

Monolithic chromatographic support structures offer, as compared to the conventional particulate materials, a unique combination of high bed permeability, optimized solute transport to and from the active surface sites and a high loading capacity by the introduction of hierarchical order in the interconnected pore network and the possibility to independently manipulate the contributing sets of pores. While basic principles governing flow resistance, axial dispersion and adsorption capacity are remaining identical, and a similarity to particulate systems can be well recognized on that basis, a direct comparison of sphere geometry with monolithic structures is less obvious due, not least, to the complex shape of theskeleton domain. We present here a simple, widely applicable, phenomenological approach for treating single-phase incompressible flow through structures having a continuous, rigid solid phase. It relies on the determination of equivalent particle (sphere) dimensions which characterize the corresponding behaviour in a particulate, i.e. discontinuous bed. Equivalence is then obtained by dimensionless scaling of macroscopic fluid dynamical behaviour, hydraulic permeability and hydrodynamic dispersion in both types of materials, without needing a direct geometrical translation of their constituent units. Differences in adsorption capacity between particulate and monolithic stationary phases show that the silica-based monoliths with a bimodal pore size distribution provide, due to the high total porosity of the material of more than 90%, comparable maximum loading capacities with respect to random-close packings of completely porous spheres.