Morphology-transport relationships for silica monoliths: From physical reconstruction to pore-scale simulations

Bridging scales in disordered porous media by mapping molecular dynamics onto intermittent Brownian motion

Owing to their complex morphology and surface, disordered nanoporous media possess a rich diffusion landscape leading to specific transport phenomena. The unique diffusion mechanisms in such solids stem from restricted pore relocation and ill-defined surface boundaries. While diffusion fundamentals in simple geometries are well-established, fluids in complex materials challenge existing frameworks. Here, we invoke the intermittent surface/pore diffusion formalism to map molecular dynamics onto random walk in disordered media. Our hierarchical strategy allows bridging microscopic/mesoscopic dynamics with parameters obtained from simple laws. The residence and relocation times - t_A, t_B - are shown to derive from pore size d and temperature-rescaled surface interaction ε/k_BT. t_A obeys a transition state theory with a barrier ~ε/k_BT and a prefactor ~10^-12 s corrected for pore diameter d. t_B scales with d which is rationalized through a cutoff in the relocation first passage distribution. This approach provides a formalism to predict any fluid diffusion in complex media using parameters available to simple experiments.

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.

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.

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.

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.

Response to "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 respond to the comments made by Hlushkou et al. (2013) [1] (JCA-13-207) to our earlier work [J. Chromatogr. A 1274 (2013) 65], wherein the authors have questioned the validity of our reconstruction of the bulk macropore space in a silica monolith and challenged the interpretations from subsequent computational fluid dynamic simulations. We provide an explanation as to why a monotonic trend in external porosity values cannot be expected with decreasing scanning resolutions. The observed deviations of the pore and skeleton size distributions from those in literature are explained based on the differences in methods used to calculate these distributions. The difference in the scaled axial velocity frequency distributions is explained based on the assumptions made and the distributions are redrawn to reflect the said assumptions. The normalized transient diffusion (peak parking) and dispersion simulations are repeated with a higher resolution of detection planes to measure the variance of spreading pulse, thereby providing an explanation for the anomalies pointed out in our earlier work. Finally, we explain our comparison of the computational expenses with previous work as a study of the trade-off in accuracy that results from the lower resolution scan and use of commercial CFD packages.

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.