Hindrance Factor Expression for Diffusion in Random Mesoporous Adsorbents Obtained from Pore-Scale Simulations in Physical Reconstructions

Pore structure reconstruction to reveal the adsorption capacity limitation of current oligo-dT resins and guide new resin design

In-depth knowledge of the pore structure of chromatographic resins is instrumental for better mechanistic understanding of adsorption performance, which can be translated into strategies to guide the design of new resins. Aiming to reveal the underlying reasons of low mRNA adsorption capacities of commercial oligo-dT resins, three-dimensional (3D) pore structure reconstruction was applied to relate key pore properties to the adsorption performance. The static 3D pore analysis revealed that the amount and connectivity of the accessible pores for 100 nm-sized mRNA reduced by over 90% and 46% compared with initial pore structure of resins, respectively, which led to discontinuous transport paths for mRNA. The dynamic simulations revealed that the strong hindrance of the firstly bound mRNA to the following mRNA molecules led to less than 10% of mRNA being able to penetrate into the resins with a depth of only 1-2 μm. Based on the digital material model, a virtual nanofiber-based macroporous resin was designed to explore its potential. Simulation results demonstrated that due to large pores and high connectivity, the new resin could allow over 91% of mRNA diffusion into the resin interior, showing great potential to improve the adsorption capacity of mRNA. This work provided a new method to evaluate the limitations of commercial oligo-dT resins and obtained some valuable guidance for the structure design of next-generation resins.

Development and Application of an Advanced Percolation Model for Pore Network Characterization by Physical Adsorption

Physical adsorption is one of the most widely used techniques to characterize porous materials because it is reliable and able to assess micro- and mesopores within one approach. Challenges and open questions persist in characterizing disordered and hierarchically structured porous materials. This study introduces a pore network model aimed at enhancing the textural characterization of nanoporous materials. The model, based on percolation theory on a finite-sized Bethe lattice, includes all mechanisms known to contribute to adsorption hysteresis in mesoporous pore networks. The model accounts for delayed and initiated condensation during adsorption as well as equilibrium evaporation, pore blocking, and cavitation during desorption. Coupled with dedicated nonlocal-density functional theory kernels, the proposed method provides a unified framework for modeling the entire experimental adsorption-desorption isotherm, including desorption hysteresis scans. The applicability of the method is demonstrated on a selected set of nanoporous silica materials exhibiting distinct types of hysteresis loops (types H1, H2a, H1/H2a, and H5), including ordered mesoporous silica networks (KIT-6 and SBA-15/MCM-41 hybrid silica with plugged pores) and disordered mesoporous silica networks (hierarchical meso-macroporous monolith and porous Vycor glass). For all materials, a good correlation is found between calculated and experimental primary isotherms as well as desorption scans. The model allows us to determine key pore network characteristics such as pore connectivity and pore size distributions as well as a parameter correlated with the impact of pore network disorder on the adsorption behavior. The versatility and enriched textural insights provided by the proposed novel network model allow for a comprehensive characterization previously inaccessible and hence will contribute to further advancement in the textural characterization of novel nanoporous materials. It has the potential to provide important guidance for the design and selection of porous materials for optimizing various applications, including separation processes such as chromatography, heterogeneous catalysis and gas and energy storage.

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

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

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, C18 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.

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

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

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.

Gas Sorption Characterization of Porous Materials Employing a Statistical Theory for Bethe Lattices

In the present work, a recently developed statistical theory for adsorption and desorption processes in mesoporous solids, modeled by random Bethe lattices, has been applied to obtain pore size distributions and interpore connectivity from sorption isotherms in real random porous materials, employing a robust and validated methodology. Using the experimental adsorption-desorption N2 isotherms at 77.4 K on Vycor glass, a porous material with random pore structure, we demonstrate the solution of the inverse problem resulting in extracted pore size distribution and interpore connectivity, notably different from the predictions of earlier theories. The results presented are corroborated by the analysis of 3D digital images of reconstructed Vycor porous glass, showing excellent agreement between the predictions of geometric analysis and the new statistical theory.

Development, characterization and application of 3D printed adsorbents for in situ recovery of taxadiene from microbial cultivations

Microbial cell factories are an attractive alternative to produce high-value natural products using sustainable processes. However, product recovery is one of the main challenges to reduce production cost and make these technologies economically interesting. In this work, new resins were formulated to 3D print hydrophobic adsorbents for the recovery of biologics from microbial cultivations. Benzyl methacrylate (BEMA) and butyl methacrylate (BUMA) were selected as functional monomers suitable for the adsorption of hydrophobic compounds. Pore morphology was tailored through the inclusion of pore forming agents (porogens) in the resin. Different porogens and porogen concentrations were evaluated resulting in materials with different porous networks. Sudan 1 and the anticancer drug paclitaxel were employed as model compounds to test the adsorption performance of hydrophobic and terpene molecules onto the developed 3D printed materials. The material with greatest adsorption capacity was obtained using BEMA monomer with 40 % (v/v) porogen (BEMA40). The performance of BEMA40 to recover taxadiene from small-scale (5 mL) Saccharomyces cerevisiae cultivations was tested and compared with commercial Diaion HP-20 beads. Taxadiene titres on BEMA40 (46 ± 2 mg/L) and Diaion HP-20 (54 ± 4 mg/L) were comparable, with no taxadiene detected in the cells and cell-free media, suggesting near 100 % taxadiene partition on the adsorbents. Compared to commercial beads, 3D printed adsorbents can be customized with adjustments in the resin formulation, are well adaptable to diverse bioreactor types, do not clog sampling ports and columns and are easier to handle during post processing. The results of this work demonstrate the potential of 3D printing to fabricate hydrophobic interaction adsorbent materials and their application in the recovery of biological products.

On the contribution of the top and bottom walls in micro-pillar array columns and related high-aspect ratio chromatography systems

We report on a steady-state based, and hence highly accurate numerical modelling study of the effect of the top and bottom wall in the current generation of micro-pillar array columns. These have a mesoporous retention layer that not only covers the pillar walls but also the bottom wall. Our results show that the performance of these columns can in general not be improved by also covering the top wall with the same layer, despite the increased column symmetry this approach would offer. The reason for this is that the local species retardation caused by a retentive layer is much stronger than the pure flow arresting effect of an uncovered wall. At least, this has a crucial impact in high aspect-ratio systems such as micro-pillar array columns because these require a small inter-pillar distance to promote mass transfer together with a large channel depth to enable a sufficiently high flow rate. On the other hand, a notable improvement could be made if micro-pillar array would be produced without having a retentive layer at the bottom. At Péclet number Pe = 50 and aspect ratio AR = 5 for flow-channels, this gain amounts up to about 4.5 h-units at a zone retention factor k'' = 2 and 1.75 h-units at k'' = 16 (gain scales almost linearly with Pe). To verify these results, we also considered another high aspect-ratio system with a simplified geometry: the open-tubular channel with a flat-rectangular cross-section. This led to very similar observations, thus confirming the findings for the micro-pillar array. The results produced in the present study also allow us to conclude that the classic modelling paradigm adopted in chromatography, which is based on the independency and hence additivity of the hCm- and hCs-contributions, can lead to large modelling errors in chromatographic systems with a high aspect-ratio, even when their geometry is so simple as that of a straight open-tubular channel with constant cross-section. Indeed, when both zones are treated independently, the analysis misses how the vertical diffusion through the retentive layer helps suppressing the vertical gradients in the mobile zone. The diffusion through this layer occurs in a ratio of k''Ds/Dm (Dm being the diffusion coefficient in mobile phase zone and Ds being the diffusion coefficient in stationary phase zone), such that at high retention factors this diffusion contribution even becomes the dominant one.

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

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

Influence of the Mesoporosity of Hierarchical ZSM-5 in Toluene Alkylation by Methanol

Among the different strategies to design highly shape-selective ZSM-5 to obtain para-xylene through toluene alkylation with methanol, the introduction of mesopores to increase reactant and product diffusion has been proposed but barely studied. In this study, we prepared mesoporous ZSM-5 catalysts, named ZSM5-MT(x), from commercial ZSM-5 (Si/Al = 15), using a two-step micelle-templating procedure with octadecyltrimethylammonium bromide as a surfactant in basic medium (x = NaOH/Si). These materials were used as catalysts for the alkylation of toluene by methanol at a low contact time to avoid thermodynamic equilibrium of the xylene isomers. Compared to the parent ZSM-5, the mesoporous ZSM5-MT(x) catalysts did not improve the para-xylene selectivity, revealing that the strategy of increasing diffusion in the catalyst is not a good strategy to follow. However, ZSM5-MT(0.5) showed less deactivation on stream than the parent ZSM-5. Therefore, introducing mesopores to ZSM-5 could be interesting to explore, combined with another strategy of shape selectivity, such as the passivation of the external surface acidity.

Resolution limits of size exclusion chromatography columns identified from flow reversal and overcome by recycling liquid chromatography to improve the characterization of manufactured monoclonal antibodies

The flow reversal (FR) technique consists of reversing the flow direction along a chromatographic column. It is used to reveal the origin (such as poor column packing, active sites, or slow absorption/escape kinetics) for the resolution limit of 4.6 mm × 150 mm long columns packed with 1.7 μm 200 Å Bridge-Ethylene-Hybrid (BEHTM) Particles. These columns are used to separate manufactured monoclonal antibodies (mAb, ∼ 150 kDa) from their close impurities (or IdeS fragments, ∼ 100 kDa) by size exclusion chromatography (SEC). FR unambiguously demonstrates that the resolution limit of these SEC columns is primarily due to long-range flow velocity biases covering distances of at least 500 μm across the column diameter. This confirms the existence of center-to-wall flow heterogeneities which cause undesirable tailing for the mAb peak. Because the transverse dispersion coefficient (Dt=1.1 × 10-6 cm2/s) of mAbs across the column diameter is intrinsically low, the bandspreading of the mAb in a single flow direction is in part reversible upon reversing the flow direction. For the very same residence time in the column, the column efficiency is found to increase by +85% relative to that observed under conventional elution mode. The observed peak tailing of the mAb and its sub-units is not caused by active surface sites or by slow absorption/escape from the BEH Particles. Therefore, the most critical mAb impurities (hydrolytic degradation Fab/c and IdeS [Formula: see text] fragments) can only be successfully separated and quantified with acceptable accuracy by adopting alternate pumping recycling liquid chromatography (APRLC). APRLC enables the full baseline separation of the mAb and 100 kDa mAb fragments and partial separation of Fab/c and [Formula: see text] fragments after increasing the number of cycles to ten. It was made possible to accurately measure the relative abundances of the mAb (99.0 ± 0.1%), [Formula: see text] fragment (0.88 ± 0.03%), and Fab/c immunogenic fragment (0.13 ± 0.02%) in less than 45 min for a total mAb sample load of only 5 μg. Still, further improvements are needed to increase the sensitivity of the APRLC method and to reduce the solvent consumption by adopting narrow-bore 2.1 mm i.d. SEC columns.

Disclosing the leaching behaviour of Pd@CMK3 catalysts in formic acid decomposition by electron tomography

Supported nanocatalysts exhibit different performances in batch and fixed bed reactors for a wide range of liquid phase catalytic reactions due to differences in metal leaching. To investigate this leaching process and its influence on the catalytic performance, a quantitative 3D characterization of the particle size and the particle distribution is important to follow the structural evolution of the active metal catalysts supported on porous materials during the reaction. In this work, electron tomography has been applied to uncover leaching and redeposition of a Pd@CMK3 catalyst during formic acid decomposition in batch and fixed bed reactors. The 3D distribution of Pd NPs on the mesoporous carbon CMK3 has been determined by a quantitative tomographic analysis and the determined structural changes are correlated with the observed differences in activity and stability of formic acid decomposition using batch and fixed bed reactors.

Diffusion in liquid mixtures

The understanding of transport and mixing in fluids in the presence and in the absence of external fields and reactions represents a challenging topic of strategic relevance for space exploration. Indeed, mixing and transport of components in a fluid are especially important during long-term space missions where fuels, food and other materials, needed for the sustainability of long space travels, must be processed under microgravity conditions. So far, the processes of transport and mixing have been investigated mainly at the macroscopic and microscopic scale. Their investigation at the mesoscopic scale is becoming increasingly important for the understanding of mass transfer in confined systems, such as porous media, biological systems and microfluidic systems. Microgravity conditions will provide the opportunity to analyze the effect of external fields and reactions on optimizing mixing and transport in the absence of the convective flows induced by buoyancy on Earth. This would be of great practical applicative relevance to handle complex fluids under microgravity conditions for the processing of materials in space.

New Perspectives for Evaluating the Mass Transport in Porous Catalysts and Unfolding Macro- and Microkinetics

In this article we shed light on newly emerging perspectives to characterize and understand the interplay of diffusive mass transport and surface catalytic processes in pores of gas phase metal catalysts. As a case study, nanoporous gold, as an interesting example exhibiting a well-defined pore structure and a high activity for total and partial oxidation reactions is considered. PFG NMR (pulsed field gradient nuclear magnetic resonance) measurements allowed here for a quantitative evaluation of gas diffusivities within the material. STEM (scanning transmission electron microscopy) tomography furthermore provided additional insight into the structural details of the pore system, helping to judge which of its features are most decisive for slowing down mass transport. Based on the quantitative knowledge about the diffusion coefficients inside a porous catalyst, it becomes possible to disentangle mass transport contributions form the measured reaction kinetics and to determine the kinetic rate constant of the underlying catalytic surface reaction. In addition, predictions can be made for an improved effectiveness of the catalyst, i.e., optimized conversion rates. This approach will be discussed at the example of low-temperature CO oxidation, efficiently catalysed by npAu at 30 °C. The case study shall reveal that novel porous materials exhibiting well-defined micro- and mesoscopic features and sufficient catalytic activity, in combination with modern techniques to evaluate diffusive transport, offer interesting new opportunities for an integral understanding of catalytic processes.

Graphical Abstract

A prediction model for nanoparticle diffusion behavior in fibrous materials considering steric and hydrodynamic resistances

Precise prediction of the hindered diffusion behavior of electroneutral particles in fibrous media plays a critical role in the development of drugs, polymer membranes, and porous electrodes. However, the random microstructure and unknown coupling relationship of multiple resistance mechanisms lead to the lack of a universal prediction model. In this work, a dual-resistance model is proposed by reconstructed pore-scale simulations, which presents the coexistence of steric and hydrodynamic resistances in the multiplication form. The simulation results show that the relationship between steric resistance and structural parameters (porosity, fiber radius, and particle radius) is exponential, while that for hydrodynamic resistance is polynomial. The dominant diffusion resistance is found to change from hydrodynamic to steric resistance with a decrease in porosity. The fluorescent polystyrene microsphere diffusivity in a series of SiO₂ fibrous media is determined by single-particle tracking experiments, quantitatively confirming the dual-resistance model. The present model can be used for rapid diffusivity prediction and fibrous membrane and drug design.

Adsorption and Catalytic Activity of Gold Nanoparticles in Mesoporous Silica: Effect of Pore Size and Dispersion Salinity

The assembled state of nanoparticles (NPs) within porous matrices plays a governing role in directing their biological, electronic, and catalytic properties. However, the effects of the spatial confinement and environmental factors, such as salinity, on the NP assemblies within the pores are poorly understood. In this study, we use adsorption isotherms, spectrophotometry, and small-angle neutron scattering to develop a better understanding of the effect of spatial confinement on the assembled state and catalytic performance of gold (Au) NPs in propylamine-functionalized SBA-15 and MCM-41 mesoporous silica materials (mSiO2). We carry out a detailed investigation of the effect of pore diameter and ionic strength on the packing and spatial distribution of AuNPs within mSiO2 to get a comprehensive insight into the structure, functioning, and activity of these NPs. We demonstrate the ability of the adsorbed AuNPs to withstand aggregation under high salinity conditions. We attribute the observed preservation of the adsorbed state of AuNPs to the strong electrostatic attraction between oppositely charged pore walls and AuNPs. The preservation of the structure allows the AuNPs to retain their catalytic activity for a model reaction in high salinity aqueous solution, here, the reduction of p-nitrophenol to p-aminophenol, which otherwise is significantly diminished due to bulk aggregation of the AuNPs. This fundamental study demonstrates the critical role of confinement and dispersion salinity on the adsorption and catalytic performance of NPs.

Quantitative 3D Characterization of Nanoporous Gold Nanoparticles by Transmission Electron Microscopy

Quantitative structural characterization of nanomaterials is important to tailor their functional properties. Corrosion of AgAu-alloy nanoparticles (NPs) results in porous structures, making them interesting for applications especially in the fields of catalysis and surface-enhanced Raman spectroscopy. For the present report, structures of dealloyed NPs were reconstructed three-dimensionally using scanning transmission electron microscopy tomography. These reconstructions were evaluated quantitatively, revealing structural information such as pore size, porosity, specific surface area, and tortuosity. Results show significant differences compared to the structure of dealloyed bulk samples and can be used as input for simulations of diffusion or mass transport processes, for example, in catalytic applications.

Visualizing defects and pore connectivity within metal-organic frameworks by X-ray transmission tomography

Metal-Organic Frameworks (MOFs) have the potential to change the landscape of molecular separations in chemical processes owing to their ability of selectively binding molecules. Their molecular sorting properties generally rely on the micro- and meso-pore structure, as well as on the presence of coordinatively unsaturated sites that interact with the different chemical species present in the feed. In this work, we show a first-of-its-kind tomographic imaging of the crystal morphology of a metal-organic framework by means of transmission X-ray microscopy (TXM), including a detailed data reconstruction and processing approach. Corroboration with Focused Ion Beam-Scanning Electron Microscopy (FIB-SEM) images shows the potential of this strategy for further (non-destructively) assessing the inner architecture of MOF crystals. By doing this, we have unraveled the presence of large voids in the internal structure of a MIL-47(V) crystal, which are typically thought of as rather homogeneous lattices. This challenges the established opinion that hydrothermal syntheses yield relatively defect-free material and sheds further light on the internal morphology of crystals.

Comprehensive Characterization of a Mesoporous Cerium Oxide Nanomaterial with High Surface Area and High Thermal Stability

In the present study, the pore space of a mesoporous cerium oxide material is investigated, which forms by the self-assembly of primary particles into a spherical secondary structure possessing a disordered mesopore space. The material under study exhibits quite stable mesoporosity upon aging at high temperatures (800 °C) and is, thus, of potential interest in high-temperature catalysis. Here, different characterization techniques were applied to elucidate the structural evolution taking place between heat treatment at 400 °C and aging at 800 °C, i.e., in a water-containing atmosphere, which is usually detrimental to nanoscaled porosity. The changes in the mesoporosity were monitored by advanced physisorption experiments, including hysteresis scanning, and electron tomography analysis coupled with a 3D reconstruction of the mesopore space. These methods indicate that the 3D spatial arrangement of the primary particles during the synthesis under hydrothermal conditions via thermal hydrolysis is related to the thermal stability of the hierarchical mesopore structure. The assembly of the primary CeO₂ particles (∼4 nm in size) results in an interparticulate space constituting an open 3D mesopore network, as revealed by skeleton analysis of tomography data, being in conformity with hysteresis scanning. At elevated temperatures (800 °C), sinter processes occur resulting in the growth of the primary particles, but the 3D mesopore network and the spherical secondary structure are preserved.

Theoretical performance of multiple size-exclusion chromatography columns connected in series

The fundamental relationships are derived for the retention, peak width, and peak capacity of non-retained polymers eluting from multiple standard size-exclusion chromatography (SEC) columns connected in series. The standard SEC columns may have different dimensions and are packed with particles having distinct average particle diameters (APDs) and average mesopore sizes (AMSs). The performances (peak capacity, local resolution power, and sensitivity) of three standard SEC columns connected in series (called a tri-SEC column) packed with bridged-ethylene-hybrid (BEH) fully porous particles (FPPs) having three different APDs (1.7, 2.5, and 3.5 μm) and AMSs (200, 450, and 900 Å, respectively) are calculated as a function of the applied flow rate and size of polystyrene standards. Irrespective of the APD and AMS, the present investigation assumes isomorphological materials relative to the mesopore space of the three different BEH particles. The advantage of a 15 cm long tri-SEC column over a single reference SEC column (APD=3.5 μm, AMS=900 Å), which generates the same back pressure and separation window as those of the tri-SEC column, is expected at flow rates larger than the optimum flow rate generating the maximum peak capacity. The calculations predict a significant relative increase of the peak capacity (from +25% to +85%), resolution of small molecules (from +75% to +225%), and of the detection limit of intermediate size (from +15% to +70%) and largest polymers (from +25 to +110%). This is explained by 1) the exclusion of the largest polymers from the internal volume of the particles having the smallest mesopores (restricted access media) and 2) the minimum dispersion along the columns packed with the smallest particle sizes in the tri-SEC column. The main benefit of multi-SEC columns is to easily adjust the desired pore size distribution by properly selecting the lengths of each individual SEC column. The user can then control the pore size distribution for any specific separation problem. A potential application is theoretically demonstrated for the fast purification of monoclonal antibodies from metabolites, host cell proteins, aggregated forms, and from virus-like particles.

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

Retention loss of reversed-phase chromatographic columns using 100% aqueous mobile phases from fundamental insights to best practice

This work deals with experimental investigations pertaining to the impact of chemical (electrolyte concentration from 0 to 100 mM, dissolved nitrogen gas from 0 to 6.7  ×  10^-4 M in water; surface chemistry including hexylphenyl, polyphenyl, C₃₀, C₁₈, and C₈; surface coverage in C₁₈-bonded chains from 1.5 to 3.5 µmol/m²; presence of surface dopant), physical (hydrostatic pressure of water from 50 to 500 bar; temperature from 27 ^∘C to 75 ^∘C), and structural parameters (average pore size from 50 Å to 400 Å; pore connectivity) on the dewetting kinetics of water from the hydrophobic mesopores of particles packed in RPLC columns. The results are explained from physico-chemical viewpoints involving intrusion and extrusion Laplace pressures, advancing and receding contact angles, surface tension of water, vapor pressure of water, 3D reconstruction of the actual mesoporous structure, pore connectivity, and the hysteresis in nitrogen adsorption and desorption isotherm onto reversed-phase chromatographic materials. A model of water dewetting consistent with the observations and the physical interpretations is then proposed. Finally, the most relevant practical solutions (pressurizing the column in absence of flow, pore size enlargement, using phenyl-bonded phase, polar embedded or surface doped C₁₈-bonded phases, reducing the C₁₈ surface coverage, doping the silica surface, lengthening of the alkyl-bonded chains, applying low temperatures, purging and degassing the mobile phase with helium gas) are suggested in order to eliminate or at least minimize the retention loss of RPLC columns when using fully aqueous mobile phases.

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.

Morphology of Fluids Confined in Physically Reconstructed Mesoporous Silica: Experiment and Mean Field Density Functional Theory

Three-dimensional physical reconstruction of the random mesopore network in a hierarchically structured, macroporous-mesoporous silica monolith via electron tomography has been used to generate a lattice model of amorphous, mesoporous silica. This geometrical model has subsequently been employed in mean field density functional theory (MFDFT) calculations of adsorption and desorption. Comparison of the results with experimental sorption isotherms for nitrogen at 77 K shows a good qualitative agreement, with both experiment and theory producing isotherms characterized by type H2 hysteresis. In addition to the isotherms, MFDFT provides the three-dimensional density distribution for the fluid in the porous material for each state studied. We use this information to map the phase distribution in the mesopore network in the hysteresis region. Phase distributions on the desorption boundary curve are compared to those on the adsorption boundary curve for both fixed pressure and fixed density, revealing insights into the relationship between phase distribution and hysteresis.

Hierarchical silica monoliths with submicron macropores as continuous-flow microreactors for reaction kinetic and mechanistic studies in heterogeneous catalysis

The proposed scheme enables academic laboratories to prepare hierarchical silica monoliths as continuous-flow microreactors for kinetic studies in heterogeneous catalysis.