High-performance computing of flow and transport in physically reconstructed silica monoliths

Shedding light on mechanisms leading to convex-upward van Deemter curves on a cellulose tris(4-chloro-3-methylphenylcarbamate)-based chiral stationary phase

An unusual convex-upward van Deemter curve was observed for the more retained enantiomer of a chiral sulfoxide (2-(benzylsulfinyl)benzamide) on a cellulose tris(4-chloro-3-methylphenylcarbamate)-based chiral stationary phase (CSP), prepared on silica particles of 1000 Å pore size. In contrast, the firstly eluted enantiomer of the same molecule exhibited the traditional convex-downward van Deemter curve. A detailed kinetic and thermodynamic investigation has revealed that this unusual phenomenon, which however has already been observed in chiral chromatography, originates when the adsorption of the compound is very strong and the solid-phase diffusion negligible. Experimentally, the intraparticle diffusion of the more retained enantiomer of the sulfoxide was found to be one order of magnitude smaller than that of the first eluted one. Overall, this translates into very little longitudinal diffusion (b-term of van Deemter curve) accompanied by high solid-liquid mass transfer resistance (c-term). Finally the comparison with another, differently-substituted chiral sulfoxide (whose enantiomers both exhibit traditional van Deemter curve behavior) has allowed to correlate these findings to the specific characteristics of the molecule.

From a Protein's Perspective: Elution at the Single-Molecule Level

Column chromatography is a widely used analytical technique capable of identifying and isolating a desired chemical species from a more complicated mixture. Despite the method's prevalence, theoretical descriptions have not advanced to accommodate today's common analyte, proteins. Proteins are increasingly used as biologics, a term that refers to biological pharmaceuticals, and present new complexities for chromatographic separation. Large variations in surface charge, chemistry, and structure among protein analytes expose the limits in the current theoretical framework's ability to predict the efficiency of a column without empirical data. The bottleneck created by empirical optimization is a strong motivation for a renewed effort to achieve an in-depth understanding of the range of interactions that occur between a protein analyte and the stationary phase that together enable its selective separation from other constituents of a mixture. The physical and chemical processes that dictate the amount of time an analyte spends in the column are often abstracted by theory and treated as statistical distributions. Until recently, these distributions could not be mapped experimentally as traditional experimental techniques could not reveal underlying heterogeneity in structure, charge, and dynamics. Aligning the latest experimental and theoretical advances is thus a hurdle to be overcome so that significant progress can be made toward a predictive chromatographic theory. In this Account, we detail the work of the Landes Lab in developing single-molecule techniques that refine the stochastic theory of chromatography as a first step toward predictive chromatographic column design. We provide a brief review of the development of stochastic theory and establish a mathematical framework to put the discussed physical chemistry in context. We describe our investigations of three pertinent phenomena: mobile/stationary phase exchange, adsorption/desorption kinetics, and hindered diffusion. We highlight experimental evidence that points to nonuniform behavior. Then, we describe our work in developing single-molecule techniques that can evaluate these effects on a protein-by-protein basis. We highlight two developments: fast imaging via super temporal-resolved microscopy (STReM) and visualizing diffusion within pores via a combination of fluorescence correlation spectroscopy and super-resolution optical fluctuation imaging (fcsSOFI). Both methods offer new ways to study chromatographic elution at the single-protein level. Such methods can identify the rare heterogeneities that prevent efficient separations and advance the field closer to predictively optimized protein separations.

Impact of diffusion on transverse dispersion in two-dimensional ordered and random porous media

Solute dispersion in fluid flow results from the interaction between advection and diffusion. The relative contributions of these two mechanisms to mass transport are characterized by the reduced velocity ν, also referred to as the Péclet number. In the absence of diffusion (i.e., when the solute diffusion coefficient D_{m}=0 and ν→∞), divergence-free laminar flow of an incompressible fluid results in a zero-transverse dispersion coefficient (D_{T}=0), both in ordered and random two-dimensional porous media. We demonstrate by numerical simulations that a more realistic realization of the condition ν→∞ using D_{m}≠0 and letting the fluid flow velocity approach infinity leads to completely different results for ordered and random two-dimensional porous media. With increasing reduced velocity, D_{T} approaches an asymptotic value in ordered two-dimensional porous media but grows linearly in disordered (random) structures depending on the geometrical disorder of a structure: a higher degree of heterogeneity results in a stronger growth of D_{T} with ν. The obtained results reveal that disorder in the geometrical structure of a two-dimensional porous medium leads to a growth of D_{T} with ν even in a uniform pore-scale advection field; however, lateral diffusion is a prerequisite for this growth. By contrast, in ordered two-dimensional porous media the presence of lateral diffusion leads to a plateau for the transverse dispersion coefficient with increasing ν.

Kinetic Accessibility of Porous Material Adsorption Sites Studied through the Lattice Boltzmann Method

We present here a computational model based on the lattice Boltzmann scheme to investigate the accessibility of active adsorption sites in hierarchical porous materials to adsorbates in a flowing liquid. By studying the transport and adsorption of tracers after they enter the pore space of the virtual sample, we characterize their kinetics as they pass through the pore space and adsorb on the solid-liquid interface. The model is validated on simple geometries with a known analytical solution. We then use it to investigate the influence of regular grooves or disordered roughness on the walls of a slit pore geometry, looking at the impact on adsorption and transport. In particular, we highlight the importance of adsorption site accessibility, which depends on the shape and connectivity of the pore space as well as the fluid flow profile and velocity.

Synthesis and morphological characterization of phenyl-modified macroporous–mesoporous hybrid silica monoliths

We present a comprehensive approach to characterize the one-pot synthesis, macropore space morphology, and chromatographic performance of phenyl-modified macro–mesoporous silica monoliths.

Correlation of chromatographic performance with morphological features of organic polymer monoliths

Monoliths are considered to be a low pressure alternative to particle packed columns for liquid chromatography (LC). However, the chromatographic performance of organic monoliths, in particular, has still not reached the level of particle packed columns. Since chromatographic performance can be attributed to morphological features of the monoliths, in-situ characterization of the monolith structure in three dimensions would provide valuable information that could be used to help improve performance. In this work, serial sectioning and imaging were performed with a dual-beam scanning electron microscope for reconstruction and quantitative characterization of poly(ethylene glycol) diacrylate (PEGDA) monoliths inside a capillary column. Chord lengths, homogeneity factors, porosities and tortuosities were calculated from three-dimensional (3D) reconstructions of two PEGDA monoliths. Chromatographic efficiency was better for the monolith with smaller mean chord length (i.e., 5.23μm), porosity (i.e., 0.49) and tortuosity (i.e., 1.50) compared to values of 5.90μm, 0.59 and 2.34, respectively, for the other monolithic column. Computational prediction of tortuosity (2.32) was found to be in agreement with the experimentally measured value (2.34) for the same column. The monoliths were found to have significant radial heterogeneity since the homogeneity factor decreased from 5.39 to 4.89 (from center to edge) along the column radius.

Analytical silica monoliths with submicron macropores: current limitations to a direct morphology-column efficiency scaling

Shrinking the structural elements of a particulate bed or monolith (i.e., the particle or domain size) yields more efficient columns only when the homogeneity of the bed can be conserved in that process. We investigate this complex issue for a set of 2nd generation analytical silica monoliths with macropores reaching submicron dimensions using chromatographic methods, mercury intrusion porosimetry, scanning electron microscopy, and confocal laser scanning microscopy (CLSM), and present eddy dispersion simulations and a chord length distribution analysis for the CLSM-based physical reconstructions at macropore resolution. The combined results allow us to identify relevant morphological advances made from 1st to 2nd generation monoliths and additionally highlight the current limitations to a direct morphology-efficiency scaling with respect to the performance that can be accomplished in HPLC practice with these columns. Whereas the improvement in radial homogeneity from 1st to 2nd generation silica monoliths is represented by a dramatic increase in column efficiency, the further reduction of macropore size in the 2nd generation monoliths does not lead to the expected improvement of plate height data, although these monoliths realize submicron macropores at a simultaneously conserved bulk macropore space homogeneity and negligible radial heterogeneity. Our study implies that limitations to further improved column efficiency arise from the intrinsic border effects of the used 4.6mm i.d. analytical columns. This includes the sample distribution onto the monoliths and asynchronous sample collection through the endfittings at the column inlet and outlet, respectively. Only when these effects are reduced will additionally improved 2nd generation monoliths live up to column efficiencies, which are envisioned for them based on their morphological properties.

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

We comment on a recently published paper by Loh and Vasudevan [J. Chromatogr. A 1274 (2013) 65], which reported the physical reconstruction of the bulk macropore space of an analytical silica monolith by X-ray computed microtomography and the subsequent computational fluid dynamics simulations of flow and mass transport in the reconstructed monolith model. Loh and Vasudevan claim that their combined reconstruction and simulation approach offers a significant reduction of computational expenses without significant loss in accuracy in characterizing the macropore space heterogeneity of the monolith and predicting its transport properties. We challenge their claim and question the validity and validation of their results by discussing the employed scanning resolution, the characterization of macropore space heterogeneities, the interpretation of the simulated dispersion data, as well as the comparison of computational expenses with previous work.

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

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

Modeling of dispersion in a polymeric chromatographic monolith

Dispersion in a commercial polymeric monolith was simulated on a sample geometry obtained by direct imaging using high-resolution electron microscopy. A parallelized random walk algorithm, implemented using a velocity field obtained previously by the lattice-Boltzmann method, was used to model mass transfer. Both point particles and probes of finite size were studied. Dispersion simulations with point particles using periodic boundaries resulted in plate heights that varied almost linearly with flow rate, at odds with the weaker dependence suggested by experimental observations and predicted by theory. This discrepancy resulted from the combined effect of the artificial symmetry in the velocity field and the periodic boundaries implemented to emulate macroscopic column lengths. Eliminating periodicity and simulating a single block length instead resulted in a functional dependence of plate heights on flow rate more in accord with experimental trends and theoretical predictions for random media. The lower values of the simulated plate heights than experimental ones are attributed in part to the presence of walls in real systems, an effect not modeled by the algorithm. On the other hand, analysis of transient dispersion coefficients and comparison of lateral particle positions at the entry and exit hinted at non-asymptotic behavior and a strong degree of correlation that was presumably a consequence of preferential high-velocity pathways in the raw sample block. Simulations with finite-sized probes resulted in particle trajectories that frequently terminated at narrow constrictions of the geometry. The amount of entrapment was predicted to increase monotonically with flow rate, evidently due to the relative contributions to transport by convection that carries particles to choke-points and diffusion that dislodges these entrapped particles. The overall effect is very similar to a flow-dependent entrapment phenomenon previously observed experimentally for adenovirus.

Kinetic investigation of narrow-bore columns packed with prototype sub-2 μm superficially porous particles with various shell thickness

The recent successful breakthrough of sub-3 μm shell particles in HPLC has triggered considerable research efforts toward the design of new brands of core-shell particles. We investigated the mass transfer mechanism of a few analytes in narrow-bore columns packed with prototype 1.7 μm shell particles, made of 1.0, 1.2, and 1.4 μm solid nonporous cores surrounded by porous shells 350, 250, and 150 nm thick, respectively. Three probe solutes, uracil, naphthalene, and insulin, were chosen to assess the kinetic performance of these columns. Inverse size exclusion chromatography, peak parking experiments, and the numerical integration of the experimental peak profiles were carried out in order to measure the external, internal, and total column porosities, the true bulk diffusion coefficients of these analytes, the height equivalent to a theoretical plate, the longitudinal diffusion term, and the trans-particle mass transfer resistance term. The residual eddy diffusion term was measured by difference. The results show the existence of important trans-column velocity biases (7%) possibly due to the presence of particle multiplets in the slurry mixture used during the packing process. Our results illustrates some of the difficulties encountered by scientists preparing and packing shell particles into narrow-bore columns.

Modeling of flow in a polymeric chromatographic monolith

The flow behavior of a commercial polymeric monolith was investigated by direct numerical simulations employing the lattice-Boltzmann (LB) methodology. An explicit structural representation of the monolith was obtained by serial sectioning of a portion of the monolith and imaging by scanning electron microscopy. After image processing, the three-dimensional structure of a sample block with dimensions of 17.8 μm × 17.8 μm × 14.1 μm was obtained, with uniform 18.5 nm voxel size. Flow was simulated on this reconstructed block using the LB method to obtain the velocity distribution, and in turn macroscopic flow properties such as the permeability and the average velocity. The computed axial velocity distribution exhibits a sharp peak with an exponentially decaying tail. Analysis of the local components of the flow field suggests that flow is not evenly distributed throughout the sample geometry, as is also seen in geometries that exhibit preferential flow paths, such as sphere pack arrays with defects. A significant fraction of negative axial velocities are observed; the largest of these are due to flow along horizontal pores that are also slightly oriented in the negative axial direction. Possible implications for mass transfer are discussed.

Monolithic phases for ion chromatography

Monolithic media are continuing to increase in popularity in chromatographic applications, and the ongoing use of commercially available materials in ion chromatography (IC) has made monoliths a viable alternative to packed-bed columns for routine use. We discuss different strategies for the synthesis of polymeric and silica monoliths with ion-exchange functionality, such as direct incorporation of ion-exchange functionality during monolith preparation and different postpolymerization alterations such as grafting and coating. The formulations and strategies presented are focused on materials intended for use in IC. We also discuss strategies for materials characterization, with emphasis on nondestructive techniques for the characterization of monolith surface functionality, especially those with applicability to in situ analysis. Finally, we describe selected IC applications of polymeric and silica monoliths published from 2008 to 2010.