Organic-solvent ditch overlap in reversed-phase liquid chromatography: A molecular dynamics simulation study in cylindrical 6-12 nm-diameter pores.

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, C18-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.

The Solvation Shell of Small Solutes in Aqueous-Organic Solvent Mixtures and Its Implications for Reversed-Phase Liquid Chromatography.

Reversed-phase liquid chromatography (RPLC) operates with water-organic solvent (W-OS) mobile phases where preferential solvation (PS) of solutes is likely. To investigate the relevance of the solute solvation shell in the mobile phase for RPLC retention, we combine data from molecular dynamics simulations of small, neutral solutes (six analytes and two dead time markers) in W-methanol (MeOH) and W-acetonitrile (ACN) mixtures with corresponding retention data obtained on an RPLC column over a wide range of W/OS ratios. Data derived from Kirkwood-Buff integrals show PS by the OS for analytes vs low or negative PS for dead time markers. W-ACN mixtures generate a higher amount of PS than W-MeOH mixtures, which contributes to the higher eluent strength of ACN in RPLC. Difference spatial distribution functions reveal anisotropic solvation shells with OS excess at hydrocarbon elements and W excess at functional groups, predicting that retention by the hydrophobic stationary phase is favored by hydrocarbon elements and limited by functional groups. Analysis of solute-solvent hydrogen bonds pinpoints the hydrogen-bond requirements toward W as the retention-limiting factor. The relation between the solute solvation shell and retention confirms the importance of W-OS and solute-W hydrogen bonding for RPLC retention.

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

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

Prediction of 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.

Confinement Effects on Distribution and Transport of Neutral Solutes in a Small Hydrophobic Nanopore.

Molecular dynamics simulations are used to study confinement effects in small cylindrical silica pores with extended hydrophobic surface functionalization as realized, for example, in reversed-phase liquid chromatography (RPLC) columns. In particular, we use a 6 nm cylindrical and a 10 nm slit pore bearing the same C18 stationary phase to compare the conditions inside the smaller-than-average pores within an RPLC column to column-averaged properties. Two small, neutral, apolar to moderately polar solutes are used to assess the consequences of spatial confinement for typical RPLC analytes with water (W)-acetonitrile (ACN) mobile phases at W/ACN ratios between 70/30 and 10/90 (v/v). The simulated data show that true bulk liquid behavior, as observed over an extended center region in the 10 nm slit pore, is not recovered within the 6 nm cylindrical pore. Instead, the ACN-enriched solvent layer around the C18 chain ends (the ACN ditch), a general feature of hydrophobic interfaces equilibrated with aqueous-organic liquids, extends over the entire pore lumen of the small cylindrical pore. This renders the entire pore a highly hydrophobic environment, where, contrary to column-averaged behavior, neither the local nor the pore-averaged sorption and diffusion of analytes scales directly with the W/ACN ratio of the mobile phase. Additionally, the solute polarity-related discrimination between analytes is enhanced. The consequences of local ACN ditch overlap in RPLC columns are reminiscent of ion transport in porous media with charged surfaces, where electrical double-layer overlap occurring locally in smaller pores leads to discrimination between co- and counterionic species.

Consequences of Cylindrical Pore Geometry for Interfacial Phenomena in Reversed-Phase Liquid Chromatography.

The interfacial phenomena behind analyte separation in a reversed-phase liquid chromatography column take place nearly exclusively inside the silica mesopores. Their cylindrical geometry can be expected to shape the properties of the chromatographic interface with consequences for the analyte density distribution and diffusivity. To investigate this topic through molecular dynamics simulations, we introduce a cylindrical pore inside a slit pore configuration, where the inner curved and outer planar silica surface bear the same bonded phase. The present model replicates an average-sized (9 nm) mesopore in an endcapped C18 column equilibrated with a mobile phase of 70/30 (v/v) water/acetonitrile. Simulations performed for ethylbenzene and acetophenone show that the surface curvature shifts the bonded phase and analyte density toward the pore center, decreases the solvent density in the bonded-phase region, increases the acetonitrile excess in the interfacial region, and considerably enhances the surface diffusivity of both analytes. Overall, the cylindrical pore provides a more hydrophobic environment than the slit pore. Ethylbenzene density is decidedly increased in the cylindrical pore, whereas acetophenone density is nearly equally distributed between the cylindrical and slit pore. The cylindrical pore geometry thus sharpens the discrimination between the apolar and moderately polar analytes while enhancing the mass transport of both.

Insights from molecular simulations about dead time markers in reversed-phase liquid chromatography.

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, C18 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.

Morphology-transport relationships for SBA-15 and KIT-6 ordered mesoporous silicas.

Quantitative morphology-transport relationships are derived for ordered mesoporous silicas through direct numerical simulation of hindered diffusion in realistic geometrical models of the pore space obtained from physical reconstruction by electron tomography. We monitor accessible porosity and effective diffusion coefficients resulting from steric and hydrodynamic interactions between passive tracers and the pore space confinement as a function of λ = dtracer/dmeso (ratio of tracer diameter to mean mesopore diameter) in SBA-15 (dmeso = 9.1 nm) and KIT-6 (dmeso = 10.5 nm) silica samples. For λ = 0, the pointlike tracers reproduce the true diffusive tortuosities. For 0 ≤λ < 0.5, the derived hindrance factor quantifies the extent to which diffusion of finite-size tracers through the materials is hindered compared with free diffusion in the bulk liquid. The hindrance factor connects the transport properties of the ordered silicas to their mesopore space morphologies and enables quantitative comparison with random mesoporous silicas. Key feature of the ordered silicas is a narrow, symmetric mesopore size distribution (∼10% relative standard deviation), which engenders a sharper decline of the accessible-porosity window with increasing λ than observed for random silicas with their wide, asymmetric mesopore size distributions. As support structures, ordered mesoporous silicas should offer benefits for applications where spatial confinement effects and molecular size-selectivity are of prime importance. On the other hand, random mesoporous silicas enable higher diffusivities for λ > 0.3, because the larger pores carry most of the diffusive flux and keep pathways open when smaller pores have closed off.

Morphological Properties of Methacrylate-Based Polymer Monoliths: From Gel Porosity to Macroscopic Inhomogeneities.

Shaping chemical interfaces of hard and soft matter materials into physical morphologies that guarantee excellent transport properties is of central importance for technologies relying on adsorption, separation, and reaction at the interface. Polymer monoliths with a hierarchically structured pore space, for example, are widely used in flow-driven processes, whose efficiency depends on the morphology of the support material over several length scales. Compared with alternative support structures, particularly silica monoliths, polymer monoliths yield lower efficiency, which suggests a suboptimal morphology. Based on physical reconstruction by serial block-face scanning electron microscopy we evaluate the structural features of a methacrylate-based polymer monolith from the pore scale to the column scale. The morphological data reveal a homogeneous polymer skeleton with a solute-impenetrable core-porous shell architecture and a heterogeneous macropore space that suffers from inhomogeneities at the short-range and the transcolumn scale. Although the morphology of the polymer phase is favorable to efficient mass transport, the performance of the polymer monolith is limited by severe transcolumn gradients in macroporosity and macropore size. We propose to overcome these morphological limitations by pursuing a preparation strategy that involves active rather than passive shaping of the macropore space, for example, by using silica monoliths as templating structures for polymer monolith preparation.

Assessing structural correlations and heterogeneity length scales in functional porous polymers from physical reconstructions.

A general, model-free, quantitative approach to the key morphological properties of a porous polymer monolith is presented. After 3D reconstruction, image-based analysis delivers detailed spatial and spatially correlated information on the structural heterogeneities in the void space and the polymer skeleton. Identified heterogeneities, which limit the monolith's performance in targeted applications, are traced back to the preparation process.

The relative importance of the adsorption and partitioning mechanisms in hydrophilic interaction liquid chromatography.

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.

Morphological analysis of disordered macroporous-mesoporous solids based on physical reconstruction by nanoscale tomography.

Solids with a hierarchically structured, disordered pore space, such as macroporous-mesoporous silica monoliths, are used as fixed beds in separation and catalysis. Targeted optimization of their functional properties requires a knowledge of the relation among their synthesis, morphology, and mass transport properties. However, an accurate and comprehensive morphological description has not been available for macroporous-mesoporous silica monoliths. Here we offer a solution to this problem based on the physical reconstruction of the hierarchically structured pore space by nanoscale tomography. Relying exclusively on image analysis, we deliver a concise, accurate, and model-free description of the void volume distribution and pore coordination inside the silica monolith. Structural features are connected to key transport properties (effective diffusion, hydrodynamic dispersion) of macropore and mesopore space. The presented approach is applicable to other fixed-bed formats of disordered macroporous-mesoporous solids, such as packings of mesoporous particles and organic-polymer monoliths.

How ternary mobile phases allow tuning of analyte retention in hydrophilic interaction liquid chromatography.

An attractive yet hardly explored feature of hydrophilic interaction liquid chromatography (HILIC) is the tuning of analyte retention through the addition of an alcohol to the water (W)-acetonitrile (ACN) mobile phase (MP). When retention times increase sharply between 10/90 and 5/95 (v/v) W/ACN, intermediate retention values are stepwise accessible with a ternary MP of 5/90/5 (v/v/v) W/ACN/alcohol by switching from methanol to ethanol to isopropyl alcohol. We investigate the physicochemical basis of this retention tuning by molecular dynamics simulations using a model of a 9 nm silica pore between two solvent reservoirs. Our simulations show that alcohol molecules insert themselves neatly into the retentive W-rich layer at the silica surface, without disrupting the layer's structure or altering its essential properties. With the decreasing tendency of an alcohol (methanol > ethanol > isopropyl alcohol) to move toward the silica surface, the contrast between the W-rich layer and the bulk MP sharpens as the latter becomes more organic, while the W density near the silica surface remains high. Analyte retention increases with the ratio between the W mole fraction in the diffuse part of the W-rich layer and that in the bulk MP. We predict that tuning of HILIC retention is possible over a wide range through the choice of the third solvent in a W/ACN-based ternary MP, whereby the largest retention values can be expected from W-immiscible solvents that fully remain in the bulk MP.

Comparison of first and second generation analytical silica monoliths by pore-scale simulations of eddy dispersion in the bulk region.

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.

Comments on "hydrodynamic and dispersion behavior in a non-porous silica monolith through fluid dynamic study of a computational mimic reconstructed from sub-micro-tomographic scans".

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.

Reconstruction and characterization of a polymer-based monolithic stationary phase using serial block-face scanning electron microscopy.

Porous, polymer-based materials are increasingly used as stationary phases in separation science and catalysis, yet their morphology remains largely unknown. The main difficulty lies in reconciling their soft matter nature with the demands of microscopic imaging techniques. We analyze the morphology of a hyper-cross-linked poly(styrene-divinylbenzene) monolith in capillary column format from a sample volume of 60.5 × 60.5 × 19.9 µm(3) reconstructed by serial block-face scanning electron microscopy. To obtain a suitable specimen, the polymer skeleton was stained with tetraphenyllead and the void space filled with resin before the whole monolith was resin-embedded after removing the fused-silica capillary. Chord length distribution analysis revealed characteristic lengths of 7.32 and 0.73 µm, corresponding to two distinct macropore types. The macroporosity (77% on average) was found to increase systematically from the wall to the center. Our results provide valuable insights into the formation process of the monolith and its stationary-phase properties.

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

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

Morphology and separation efficiency of a new generation of analytical silica monoliths.

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.

From random sphere packings to regular pillar arrays: effect of the macroscopic confinement on hydrodynamic dispersion.

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.