Multiscale simulation of liquid chromatography: Effective diffusion in macro-mesoporous beds and the B-term of the plate height equation.

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 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.

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, C-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 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.

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 C-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.

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 (β-cristobalite-C 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).

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 C 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).

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.

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, C 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.

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 = d/d (ratio of tracer diameter to mean mesopore diameter) in SBA-15 (d = 9.1 nm) and KIT-6 (d = 10.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Structure-transport correlation for the diffusive tortuosity of bulk, monodisperse, random sphere packings.

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.

Transient and asymptotic dispersion in confined sphere packings with cylindrical and non-cylindrical conduit geometries.

We study the time and length scales of hydrodynamic dispersion in confined monodisperse sphere packings as a function of the conduit geometry. By a modified Jodrey-Tory algorithm, we generated packings at a bed porosity (interstitial void fraction) of ε=0.40 in conduits with circular, rectangular, or semicircular cross section of area 100πd(p)(2) (where d(p) is the sphere diameter) and dimensions of about 20d(p) (cylinder diameter) by 6553.

Influence of the particle size distribution on hydraulic permeability and eddy dispersion in bulk packings.

The narrow particle size distribution (PSD) of certain packing materials has been linked to a reduced eddy dispersion contribution to band broadening in chromatographic columns. It is unclear if the influence of the PSD acts mostly on the stage of the packing process or if a narrow PSD provides an additional, intrinsic advantage to the column performance. To investigate the latter proposition, we created narrow-PSD and wide-PSD random packings based on the experimental PSDs of sub-3 μm core-shell and sub-2 μm fully porous particles, respectively, as determined by scanning electron microscopy.

Composition, structure, and mobility of water-acetonitrile mixtures in a silica nanopore studied by molecular dynamics simulations.

To investigate the effect of the nanoscale confinement on the properties of a binary aqueous-organic solvent mixture, we performed molecular dynamics simulations of the equilibration of water-acetonitrile (W/ACN) mixtures between a cylindrical silica pore of 3 nm diameter and two bulk reservoirs. Water is enriched, and acetonitrile is depleted inside the pore with respect to the bulk reservoirs: for nominal molar (~volumetric) ratios of 1/3 (10/90), 1/1 (25/75), and 3/1 (50/50), the molar W/ACN ratio in the pore equilibrates to 1.5, 3.