Influence of the Particle Size Distribution on Hydraulic Permeability and Eddy Dispersion in Bulk Packings

Development of a particle packed bed model for homogeneity evaluation of liquid chromatography column

Particle packed columns used for liquid chromatography (LC) can suppress a column internal band broadening (hereinafter referred to as band broadening) by packing monodisperse particles homogenously. However, a quantitative evaluation for the effects of particle shape and packed state on band broadening needs to be more investigated. In this study, we fabricated a model of particle packed bed using microfluid LC columns that have pillar array structure prepared by microfabrication technology, evaluating how structural factors inside of a column affect its band broadening. At first, microfluid LC columns was prepared using Si-quartz glass (Si-Q column) for the optimization of LC measurement system. Through the evaluation, it showed 11.6 times higher pressure tolerance compared to that of PDMS-soda lime glass (PDMS-g column). Then, an optimized LC measurement system was constructed using a microfluidic LC column made of Si-Q column, and it was confirmed that the measurement error was small enough and the LC measurement could be performed with high repeatability. Additionally, the effect of a distribution of structural size on band broadening was evaluated. It was confirmed that wide distribution of the structural size provided large band broadening in actual measurements. Comparing two columns having different structural log-normal distributions of 0 and 0.22 showed approximately 1.8 times difference in both real LC measurement. Lastly, the relationship between packed state and band broadening was evaluated. As packed state, we employed void arrangement and structural arrangement in the columns. Different location arrangements of 50 and 100 µm pillar sizes afforded different band broadening. Well-homogenized array showed approximately two times worse band broadening compared to that of delocalized array. Based on these results, the developed packed bed of particles model was able to evaluate the relation between structural factors and band broadening.

Reversed-Phase Liquid Chromatography of Peptides for Bottom-Up Proteomics: A Tutorial

The performance of the current bottom-up liquid chromatography hyphenated with mass spectrometry (LC-MS) analyses has undoubtedly been fueled by spectacular progress in mass spectrometry. It is thus not surprising that the MS instrument attracts the most attention during LC-MS method development, whereas optimizing conditions for peptide separation using reversed-phase liquid chromatography (RPLC) remains somewhat in its shadow. Consequently, the wisdom of the fundaments of chromatography is slowly vanishing from some laboratories. However, the full potential of advanced MS instruments cannot be achieved without highly efficient RPLC. This is impossible to attain without understanding fundamental processes in the chromatographic system and the properties of peptides important for their chromatographic behavior. We wrote this tutorial intending to give practitioners an overview of critical aspects of peptide separation using RPLC to facilitate setting the LC parameters so that they can leverage the full capabilities of their MS instruments. After briefly introducing the gradient separation of peptides, we discuss their properties that affect the quality of LC-MS chromatograms the most. Next, we address the in-column and extra-column broadening. The last section is devoted to key parameters of LC-MS methods. We also extracted trends in practice from recent bottom-up proteomics studies and correlated them with the current knowledge on peptide RPLC separation.

Mass Transfer in Hierarchical Silica Monoliths Loaded With Pt in the Continuous-Flow Liquid-Phase Hydrogenation of p-Nitrophenol

Sol-gel-based silica monoliths with hierarchical mesopores/macropores are promising catalyst support and flow reactors. Here, we report the successful preparation of cylindrically shaped Pt-loaded silica monoliths (length: 2 cm, diameter: 0.5 cm) with a variable mean macropore width of 1, 6, 10, or 27 μm at a fixed mean mesopore width of 17 nm. The Pt-loaded monolithic catalysts were housed in a robust cladding made of borosilicate glass for use as a flow reactor. The monolithic reactors exhibit a permeability as high as 2 μm2 with a pressure drop below 9 bars over a flow rate range of 2–20 cm3 min−1 (solvent: water). The aqueous-phase hydrogenation of p-nitrophenol to p-aminophenol with NaBH4 as a reducing agent was used as a test reaction to study the influence of mass transfer on catalytic activity in continuous flow. No influence of flow rate on conversion at a fixed contact time of 2.6 s was observed for monolithic catalysts with mean macropore widths of 1, 10, or 27 µm. As opposed to earlier studies conducted at much lower flow velocities, this strongly indicates the absence of external mass-transfer limitations or stagnant layer formation in the macropores of the monolithic catalysts.

Effect of the polydispersity on the dispersion of polymers through silicas having different morphologies (fully porous and core-shell particles and monoliths)

The effect of the polydispersity of polystyrenes on the dispersion through silicas having different morphologies (fully porous, core-shell particles and monoliths) was investigated. The heights equivalent to a theoretical plate (HETP) of those columns were measured for a small molecule (toluene) and a series of polystyrenes of different sizes in non-adsorbing conditions. The different contributions to the total HETP including polydispersity were determined experimentally. The longitudinal diffusion and the mass transfer resistance term were obtained from peak parking experiments. The eddy dispersion was obtained from models and experiments. The effect of polydispersity on the HETP values (H_poly) can thus be calculated from the total HETP by substraction of the other contributions. The results were compared to the Knox model which surestimates the H_poly values for porous and core-shell particles which is usually explained by an overestimation of the polydispersity index (PDI) given by the manufacturer. The PDI of two polymers (P02, M_w= 690 g.mol^-1 and P03, M_w=1380 g.mol^-1) was verified by liquid chromatography by separating each fraction of the polymer on the silica columns by using adsorbing conditions which are obtained with a mixture of heptane and THF. The PDI obtained are comparable to the PDI given by the manufacturer meaning that the assumptions made by Knox are not entirely valid. A direct method is proposed in this paper in order to determine H_poly. In this method the excess of spreading as compared with a polymer with only one size corresponding to the average size is studied assuming the polymer size distribution is gaussian. The H_poly values obtained by the direct method are comparable to the experimental values.

The theory and practice of ultrafast liquid chromatography: A tutorial

Modern high-throughput experimentation and challenging analytical problems of academic/industrial research have put the responsibility on separation scientists to develop new fast separation approaches. With the availability of high-pressure pumps, small particles with hydrolytically stable surface chemistries, reduced extra-column band broadening, and low volume detectors with fast signal processing, it is now feasible to do sub-minute to sub-second chromatography. Herein, the fundamental theoretical principles of ultrafast chromatography, along with practical solutions, are reviewed. Approaches for rapid separations in packed beds, narrow open tubular columns, and monoliths are demonstrated, along with the challenges that were faced. The instrumentation requirements (pumps, injection systems, detectors, column packing process) for using short columns ranging from 0.5 to 5 cm are examined, followed by real applications. One of the main problems in ultrafast chromatography is partial or complete peak overlap. As per Gidding's statistical overlap theory, peak overlap cannot be avoided for a completely random sample for a column with a given peak capacity. Signal processing techniques based on Fourier transform deconvolution of band broadening, power laws, derivatives, and iterative curve fitting are explained to help improve the chromatographic resolution. An example of ten peaks separated in under a second is shown and discussed. Other ultrafast separations in supercritical fluid chromatography or capillary electrophoresis are briefly mentioned to provide a complete understanding of this emerging field.

Pyrolytic remediation of crude oil-contaminated soil

Deterioration of our terrestrial environment due to decreasing soil quality brought on by crude oil spills and leakages is a major issue. In this study, soil samples were prepared by mixing clay (bentonite) and sand contaminated with 5 and 10 wt% crude oil (in order to study the effect of oil concentration), and weathered in a laboratory to simulate actual contaminated soil. Volatilization of light oil was inhibited in clay rich-soil, resulting in higher contamination after weathering. The efficiency of the pyrolytic treatment was evaluated by comparing the weight change and n-hexane extractable material (HEM) content of the soil samples. The working temperature influenced pyrolysis efficiency more than the reaction time. A residual amount of 0.29-0.61 wt% (below the soil pollution standard) was observed in the samples with high clay content and pollution level (by pyrolysis for 30 min at 400 °C). Infrared analysis of treated soil samples showed a reduction in alkyl functionality (CH), confirming a decrease in hydrophobicity and an improvement in water holding capacity (WHC). Seed germination and plant growth were relatively better in the pyrolyzed soil. The field applicability of the pyrolytic treatment process was confirmed at laboratory and pilot scale, as well as by treating soil samples collected from actual polluted sites.

Numerical Elucidation of Flow and Dispersion in Ordered Packed Beds: Nonspherical Polygons and the Effect of Particle Overlap on Chromatographic Performance

Spherical particles are widely considered as the benchmark stationary phase for preparative and analytical chromatography. Although this has proven true for randomly packed beds in the past, we challenge this paradigm for ordered packings, the fabrication of which are now feasible through additive manufacturing (3D printing). Using computational fluid dynamics (Lattice Boltzmann Method) this work shows that nonspherical particles can both reduce mobile-phase band broadening and increase permeability compared with spheres in ordered packed beds. In practice, ordered packed beds can only remain physically stable if the particles are fused to form a contiguous matrix, thus creating a positional overlap at the points of fusion between what would otherwise be discrete particles. Overlap is shown to decrease performance of ordered packed beds in all observed cases, thus we recommend it should be kept to the minimum extent necessary to ensure physical stability. Finally, we introduce a metric to estimate column performance, the mean deviated velocity, a quantitative description of the spread of the velocity field in the column. This metric appears to be a good indicator of mobile-phase dispersion in ordered packed bed media, including overlapped beds, and is a useful tool for screening new stationary-phase morphologies without having to perform computationally expensive simulations.

Fabrication of Demineralized Bone Matrix/Polycaprolactone Composites Using Large Area Projection Sintering (LAPS)

Cadaveric decellularized bone tissue is utilized as an allograft in many musculoskeletal surgical procedures. Typically, the allograft acts as a scaffold to guide tissue regeneration with superior biocompatibility relative to synthetic scaffolds. Traditionally these scaffolds are machined into the required dimensions and shapes. However, the geometrical simplicity and, in some cases, limited dimensions of the donated tissue restrict the use of allograft scaffolds. This could be overcome by additive manufacturing using granulated bone that is both decellularized and demineralized. In this study, the large area projection sintering (LAPS) method is evaluated as a fabrication method to build porous structures composed of granulated cortical bone bound by polycaprolactone (PCL). This additive manufacturing method utilizes visible light to selectively cure the deposited material layer-by-layer to create 3D geometry. First, the spreading behavior of the composite mixtures is evaluated and the conditions to attain improved powder bed density to fabricate the test specimens are determined. The tensile strength of the LAPS fabricated samples in both dry and hydrated states are determined and compared to the demineralized cancellous bone allograft and the heat treated demineralized-bone/PCL mixture in mold. The results indicated that the projection sintered composites of 45–55 wt %. Demineralized bone matrix (DBM) particulates produced strength comparable to processed and demineralized cancellous bone.

Fundamental Properties of Packing Materials for Liquid Chromatography

The high performance of chemically-modified silica gel packing materials is based on the utilization of pure silica gels. Earlier silica gels used to be made from inorganic silica; however, nowadays, silica gels are made from organic silanes. The surface smoothness and lack of trace metals of new silica gels permits easy surface modifications (chemical reactions) and improves the reproducibility and stability. Sharpening peak symmetry is based on developing better surface modification methods (silylation). Typical examples can be found in the chromatography of amitriptyline for silanol testing and that of quinizarin for trace metal testing. These test compounds were selected and demonstrated sensitive results in the measurement of trace amounts of either silanol or trace metals. Here, we demonstrate the three-dimensional model chemical structures of bonded-phase silica gels with surface electron density for easy understanding of the molecular interaction sites with analytes. Furthermore, a quantitative explanation of hydrophilic and hydrophobic liquid chromatographies was provided. The synthesis methods of superficially porous silica gels and their modified products were introduced.

Detailed efficiency analysis of columns with a different packing quality and confirmation via total pore blocking

We report on a systematic study involving columns with a clearly different efficiency (4 distinct quality groups) obtained by packing the columns that were C₁₈ bonded and endcapped with a different carbon loading. Using B-term analysis (via peak parking) and theoretical models to estimate the magnitude of the C_m- and C_s-term contributions, it could be concluded that the difference in efficiency among the groups was entirely due to a difference in eddy dispersion. As such, the columns provided an ideal testing ground to verify how well the total pore blocking (TPB)-method can be used to probe differences in packing heterogeneity. In agreement with earlier literature observations, it turns out the TPB-method is much more sensitive to packing heterogeneities than the eddy dispersion (H_eddy)-contribution measured under open-pore conditions via B- and C- term subtraction. Typically, differences in H_eddy on the order of 0.1-0.5μm translate into a difference on the order of 0.5-2μm in the TPB mode. This confirms the TPB as a powerful technique to make very sensitive measurements of the homogeneity of packed beds.

Ultra-High Pressure (>30,000 psi) Packing of Capillary Columns Enhancing Depth of Shotgun Proteomic Analyses

Extreme sample complexity is an inherent challenge in shotgun proteomics that positions quality of chromatographic separations as one of the key determinants of attainable proteome coverage. In search of better separations, macroscopic physical characteristics of capillary columns, i.e., length and properties of stationary phase particles, are typically considered and optimized, while significance of packing bed morphology is frequently underappreciated. Here, we describe a technology that enables packing of capillary columns at excess of 30,000 psi and demonstrate that such columns exhibit reduced backpressure and remarkably reproducible chromatographic performance, improved on average by 23%. These enhancements afford up to 35% increase in the depth of commonplace bottom-up proteomic analyses, owning to augmented sensitivity and resolution of peptide separations and improvements in spectral quality. Our findings strongly corroborate advantages of ultra-high pressure packing of capillary columns for diverse shotgun proteomic workflows.

Pore-scale statistics of flow and transport through porous media

Flow in porous media is known to be largely affected by pore morphology. In this work, we investigate the effects of pore geometry on the transport and spatial correlations of flow through porous media in two distinct pore structures arising from three-dimensional assemblies of overlapping and nonoverlapping spheres. Using high-resolution direct numerical simulations (DNS), we perform Eulerian and Lagrangian analysis of the flow and transport characteristics in porous media. We show that the Eulerian velocity distributions change from nearly exponential to Gaussian distributions as porosity increases. A stretched exponential distribution can be used to represent this behavior for a wide range of porosities. Evolution of Lagrangian velocities is studied for the uniform injection rule. Evaluation of tortuosity and trajectory length distributions of each porous medium shows that the model of overlapping spheres results in higher tortuosity and more skewed trajectory length distributions compared to the model of nonoverlapping spheres. Wider velocity distribution and higher tortuosity for overlapping spheres model give rise to non-Fickian transport while transport in nonoverlapping spheres model is found to be Fickian. Particularly, for overlapping spheres model our analysis of first-passage time distribution shows that the transport is very similar to those observed for sandstone. Finally, using three-dimensional (3D) velocity field obtained by DNS at the pore-scale, we quantitatively show that despite the randomness of pore-space, the spatially fluctuating velocity field and the 3D pore-space distribution are strongly correlated for a range of porous media from relatively homogeneous monodisperse sphere packs to Castlegate sandstone.

Recent advances in capillary ultrahigh pressure liquid chromatography

In the twenty years since its initial demonstration, capillary ultrahigh pressure liquid chromatography (UHPLC) has proven to be one of most powerful separation techniques for the analysis of complex mixtures. This review focuses on the most recent advances made since 2010 towards increasing the performance of such separations. Improvements in capillary column preparation techniques that have led to columns with unprecedented performance are described. New stationary phases and phase supports that have been reported over the past decade are detailed, with a focus on their use in capillary formats. A discussion on the instrument developments that have been required to ensure that extra-column effects do not diminish the intrinsic efficiency of these columns during analysis is also included. Finally, the impact of these capillary UHPLC topics on the field of proteomics and ways in which capillary UHPLC may continue to be applied to the separation of complex samples are addressed.

Statistical characterization of microstructure of packings of polydisperse hard cubes

Polydisperse packings of cubic particles arise in several important problems. Examples include zeolite microcubes that represent catalytic materials, fluidization of such microcubes in catalytic reactors, fabrication of new classes of porous materials with precise control of their morphology, and several others. We present the results of detailed and extensive simulation and microstructural characterization of packings of nonoverlapping polydisperse cubic particles. The packings are generated via a modified random sequential-addition algorithm. Two probability density functions (PDFs) for the particle-size distribution, the Schulz and log-normal PDFs, are used. The packings are analyzed, and their random close-packing density is computed as a function of the parameters of the two PDFs. The maximum packing fraction for the highest degree of polydispersivity is estimated to be about 0.81, much higher than 0.57 for the monodisperse packings. In addition, a variety of microstructural descriptors have been calculated and analyzed. In particular, we show that (i) an approximate analytical expression for the structure factor of Percus-Yevick fluids of polydisperse hard spheres with the Schulz PDF also predicts all the qualitative features of the structure factor of the packings that we study; (ii) as the packings become more polydisperse, their behavior resembles increasingly that of an ideal system-"ideal gas"-with little or no correlations; and (iii) the mean survival time and mean relaxation time of a diffusing species in the packings increase with increasing degrees of polydispersivity.

Larger voids in mechanically stable, loose packings of 1.3μm frictional, cohesive particles: Their reconstruction, statistical analysis, and impact on separation efficiency

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

Topological analysis of non-granular, disordered porous media: determination of pore connectivity, pore coordination, and geometric tortuosity in physically reconstructed silica monoliths

Different approaches are applied and compared, which are universally applicable to quantify pore coordination, pore and pore-throat connectivity, and geometric tortuosity.

Evaluation of preparative hydrodynamic chromatography of silica stationary phase supports

Reducing the particle size distribution (PSD) of sub-2 μm chromatographic packing materials can improve the performance of capillary UHPLC columns, but several size refinement methods are only partially effective in this size range. To this end, a preparative scale hydrodynamic chromatography (HDC) method was developed to size-refine C18 functionalized sub-2 μm particles, but suffered from poor reproducibility and particle aggregation issues. Presented here are improvements based on the use of an ammonium hydroxide as the mobile phase. This mobile phase makes the method reproducible, decreases column conditioning requirements, and focuses on the preparation of bare silica material which allows for a wider variety of stationary phase bondings. Additionally, particle recovery for both non-porous silica size standards and bridged-ethyl hybrid (BEH) particles are detailed to highlight the advantages of this method. The data presented demonstrates the capability of this method to reduce the relative standard deviation (RSD) of the PSD of BEH particles by 33% in under 2 h with sufficient yield to pack several capillary columns.