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.

Estimating angoricity and granular equations of state for monodisperse packings of frictional hard spheres in a wide range of densities.

In this paper, we study the granular equation of state (EOS) for computer-generated three-dimensional mechanically stable packings of frictional monodisperse particles over a wide range of densities (packing fractions), φ=0.56-0.72. As a statistical physics framework, we utilize the statistical ensemble for granular matter, specifically the "angoricity" ensemble, where the compressional component Σ_{p} of the force-moment tensor serves as granular energy and angoricity A_{p} is the corresponding granular "temperature." We demonstrate that the systems under study conform well to this statistical description, and the simple equation of state Σ_{p}=2.8NA_{p} holds very well, where N is the number of particles. We show that granular temperature exhibits a rapid drop around the random-close packing (RCP) limit φ≈0.64-0.65, and, hence, one can say that granular packings "freeze" at the RCP limit. We repeat these calculation for shear angoricity A_{sh} and shear component Σ_{sh} of the force-moment tensor and obtain a similar EOS, Σ_{sh}=0.85NA_{sh}. Additionally, we measure the so-called keramicity, an inverse temperature variable corresponding to the determinant of the force-moment tensor, while pressure angoricity corresponds to its trace. We show that inverse keramicity κ^{-1} and angoricity A_{p} conform to an EOS 1/A_{p}Σ_{p}/N+0.11κ(Σ_{p}/N)^{3}=1.2, whose form is predicted by mean-field theory. Finally, we demonstrate that the alternative statistical ensemble where Voronoi volumes serve as granular energy (and so-called compactivity serves as temperature) does not describe the systems under study well.

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.

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

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

Quantitative analysis of mesoporous structures by electron tomography: A phantom study.

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.

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.

Oxidative formation of bis-N-methylquinolinone from anti-head-to-head N-methylquinolinone cyclodimer.

The light-driven formation and cleavage of cyclobutane structural motifs resulting from [2 + 2]-pericyclic reactions, as found in thymine and coumarin-type systems, is an important and intensively studied photochemical reaction. Various applications are reported utilizing these systems, among others, in cross-linked polymers, light-triggered drug release, or other technical applications. Herein coumarin is most frequently used as the photoactive group. Quite often, a poor quantum yield for dimerization and cyclobutane-cleavage and a lack of reversibility are described. In this work, we present the identification of a heterogeneous pathway of dimer cleavage found in a rarely studied coumarin analog molecule, the N-methyl-quinolinone (NMQ). The monomer was irradiated in a tube flow-reactor and the reaction process was monitored using online HPLC measurements. We found the formation of a pseudo-equilibrium between monomeric and dimeric NMQ and a continuous rise of a side product via oxidative dimer splitting and proton elimination which was identified as 3,3'-bis-NMQ. Oxidative conversion by singlet oxygen was identified to be the cause of this non-conventional cyclobutane cleavage. The addition of antioxidants suppressing singlet oxygen enables achieving a 100% photochemical conversion from NMQ to the anti-head-to-head-NMQ-dimer. Using dissolved oxygen upon light activation to singlet oxygen limits the reversibility of the photochemical [2 + 2]-cycloaddition and cycloreversion of NMQ and most likely comparable systems. Based on these findings, the development of highly efficient cycloaddition-cycloreversion systems should be enabled.

Multiple-open-tubular column enabling transverse diffusion. Part 2: Channel size distribution and structure optimization.

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, 2, 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 k1 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 rc,1=(1-RSD) and rc,2=(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.

Insights into the intraparticle morphology of dendritic mesoporous silica nanoparticles from electron tomographic reconstructions.

HYPOTHESIS: Although many synthetic pathways allow to fine-tune the morphology of dendritic mesoporous silica nanoparticles (DMSNs), the control of their particle size and mesopore diameter remains a challenge. Our study focuses on either increasing the mean particle size or adjusting the pore size distribution, changing only one parameter (particle or pore size) at a time. The dependence of key morphological features (porosity; pore shape and pore dimensions) on radial distance from the particle center has been investigated in detail. EXPERIMENTS: Three-dimensional reconstructions of the particles obtained by scanning transmission electron microscopy (STEM) tomography were adapted as geometrical models for the quantification of intraparticle morphologies by radial porosity and chord length distribution analyses. Structural properties of the different synthesized DMSNs have been complementary characterized using TEM, SEM, nitrogen physisorption, and dynamic light scattering. FINDINGS: The successful independent tuning of particle and pore sizes of the DMSNs could be confirmed by conventional analysis methods. Unique morphological features, which influence the uptake and release of guest molecules in biomedical applications, were uncovered from analyzing the STEM tomography-based reconstructions. It includes the quantification of structural hierarchy, identification of intrawall openings and pores, as well as the distinction of pore shapes (conical vs. cylindrical).

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.

Multiple-open-tubular column enabling transverse diffusion. Part 1: Band broadening model for accurate mass transfer predictions.

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, qs, related to the specific geometry of the stationary phase in MOTTD columns. qs 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.

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.

Morphology-transport relationships in liquid chromatography: Application to method development in size exclusion chromatography.

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.

Olefin Metathesis in Confined Geometries: A Biomimetic Approach toward Selective Macrocyclization.

The synthesis of macrocycles is severely impeded by concomitant oligomer formation. Here, we present a biomimetic approach that utilizes spatial confinement to increase macrocyclization selectivity in the ring-closing metathesis of various dienes at elevated substrate concentration up to 25 mM using an olefin metathesis catalyst selectively immobilized inside ordered mesoporous silicas with defined pore diameters. By this approach, the ratio between macro(mono)cyclization (MMC) product and all undesired oligomerization products (O) resulting from acyclic diene metathesis polymerization was increased from 0.55, corresponding to 35% MMC product obtained with the homogeneous catalyst, up to 1.49, corresponding to 60% MMC product. A correlation between the MMC/O ratio and the substrate-to-pore-size ratio was successfully established. Modification of the inner pore surface with dimethoxydimethylsilane allowed fine-tuning the effective pore size and reversing surface polarity, which resulted in a further increase of the MMC/O ratio up to 2.2, corresponding to >68% MMC product. Molecular-level simulations in model pore geometries help to rationalize the complex interplay between spatial confinement, specific (substrate and product) interaction with the pore surface, and diffusive transport. These effects can be synergistically adjusted for optimum selectivity by suitable surface modification.

Faster dewetting of water from C8- than from C18-bonded silica particles used in reversed-phase liquid chromatography: Solving the paradox.

For comparable surface coverage of alkyl-bonded chains (∼3 µmol/m2), the dewetting of 100% aqueous mobile phases from the mesopores of octyl(C8)-bonded silica particles is found 70 times faster than that from the same but octadecyl(C18)-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 C8-bonded materials is 10-15 Šlarger than that of C18-bonded materials for the same unbounded silica gel and (2) the contact angle of water measured on smooth and planar C8-bonded surface is about 6° smaller than that on the same but C18-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-C8 than for silica-C18 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 C18- and C8-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 C8 and C18-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 C8-bonded silicas are found larger (by an average of +7° and +2°, respectively) than those measured for the same but C18-bonded silica (average of 112° and 92°). Finally, the calculated pore connectivity is decreasing by about 30% for 90 Šunbounded silica materials from C8 to C18-bonded RPLC phases. Overall, the observed and much faster dewetting of water from C8 column than that from C18 column is primarily explained by a higher internal pore connectivity due to the thinner thickness of the alkyl-bonded layer (7 Šversus 15 Å) and, to a lesser extent, by a higher extrusion Laplace pressure of water (≃+10 bar).

Quantifying Morphology and Diffusion Properties of Mesoporous Carbon From High-Fidelity 3D Reconstructions.

A reliable quantitative analysis in electron tomography, which depends on the segmentation of the three-dimensional reconstruction, is challenging because of constraints during tilt-series acquisition (missing wedge) and reconstruction artifacts introduced by reconstruction algorithms such as the Simultaneous Iterative Reconstruction Technique (SIRT) and Discrete Algebraic Reconstruction Technique (DART). We have carefully evaluated the fidelity of segmented reconstructions analyzing a disordered mesoporous carbon used as support in catalysis. Using experimental scanning transmission electron microscopy (STEM) tomography data as well as realistic phantoms, we have quantitatively analyzed the effect on the morphological description as well as on diffusion properties (based on a random-walk particle-tracking simulation) to understand the role of porosity in catalysis. The morphological description of the pore structure can be obtained reliably both using SIRT and DART reconstructions even in the presence of a limited missing wedge. However, the measured pore volume is sensitive to the threshold settings, which are difficult to define globally for SIRT reconstructions. This leads to noticeable variations of the diffusion coefficients in the case of SIRT reconstructions, whereas DART reconstructions resulted in more reliable data. In addition, the anisotropy of the determined diffusion properties was evaluated, which was significant in the presence of a limited missing wedge for SIRT and strongly reduced for DART.

Kinetics Studies on a Multicomponent Knoevenagel-Michael Domino Reaction by an Automated Flow Reactor.

The optimization of complex chemical reaction systems is often a troublesome and time-consuming process. The application of modern technologies, including automated reactors and analytics, opens the avenue for generating large data sets on chemical reaction processes in a short period of time. In this work, an automated flow reactor is used to present detailed kinetics and mechanistic studies about an amine-catalyzed Knoevenagel-Michael domino reaction to yield tetrahydrochromene derivatives. High-performance monoliths as catalyst supports and online coupled HPLC analysis allow for time-efficient data generation. We show that the two-step multicomponent domino reaction does not follow the kinetics of consecutive reaction steps proceeding independently from each other. Instead, the starting materials of both individual reactions compete for the active sites on the heterogeneous catalyst, which lowers the rate constants of both steps. This knowledge was used to implement a more efficient experimental setup which increased the turnover numbers of the catalyst, without adjusting common reaction parameters like temperature, reaction time, and concentrations.