Morphology-transport relationships for SBA-15 and KIT-6 ordered mesoporous silicas.

Quantitative morphology-transport relationships are derived for ordered mesoporous silicas through direct numerical simulation of hindered diffusion in realistic geometrical models of the pore space obtained from physical reconstruction by electron tomography. We monitor accessible porosity and effective diffusion coefficients resulting from steric and hydrodynamic interactions between passive tracers and the pore space confinement as a function of λ = dtracer/dmeso (ratio of tracer diameter to mean mesopore diameter) in SBA-15 (dmeso = 9.1 nm) and KIT-6 (dmeso = 10.5 nm) silica samples. For λ = 0, the pointlike tracers reproduce the true diffusive tortuosities. For 0 ≤λ < 0.5, the derived hindrance factor quantifies the extent to which diffusion of finite-size tracers through the materials is hindered compared with free diffusion in the bulk liquid. The hindrance factor connects the transport properties of the ordered silicas to their mesopore space morphologies and enables quantitative comparison with random mesoporous silicas. Key feature of the ordered silicas is a narrow, symmetric mesopore size distribution (∼10% relative standard deviation), which engenders a sharper decline of the accessible-porosity window with increasing λ than observed for random silicas with their wide, asymmetric mesopore size distributions. As support structures, ordered mesoporous silicas should offer benefits for applications where spatial confinement effects and molecular size-selectivity are of prime importance. On the other hand, random mesoporous silicas enable higher diffusivities for λ > 0.3, because the larger pores carry most of the diffusive flux and keep pathways open when smaller pores have closed off.

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

We present relationships between the multiscale structure and the separation properties of size exclusion chromatography (SEC) columns. Physical bed reconstructions of wall and bulk regions from a 2.1 mm i.d. column packed with fully porous 1.7 µm bridged-ethyl hybrid (BEH) particles, obtained by focused ion-beam scanning electron microscopy, serve as geometrical models for the packing microstructure in wall and central regions of a typical narrow-bore SEC column. In addition, the intraparticle mesopore space morphology of the BEH particles is reconstructed using electron tomography, to ultimately construct a realistic multiscale model of the bed morphology from mesopore level via interparticle macropore space to transcolumn scale. Complemented by the results of eddy dispersion simulations in computer-generated bulk packings, relationships between packing microstructure and transchannel, short-range interchannel, as well as transcolumn eddy dispersion are used to analyze the fluid dynamics in the interparticle macropore space of the model. Further, we simulate hindered diffusion and accessible porosity for passive, finite-size tracers in the intraparticle mesopore space, to finally determine the effective particle and bed diffusion coefficients of these tracers in the hierarchical (macro-mesoporous) bed. Retention and transport properties of polystyrene standards with hydrodynamic diameters from 5 to 95 Å in tetrahydrofuran are subsequently predicted without introducing bias from arbitrary models. These properties include the elution volumes of the polystyrene standards, the global peak capacity (over the entire separation window), and the rate of peak capacity at any fixed elution volume. Optimal flow rates yielding maximal global peak capacity and a nearly uniform rate of peak capacity over the entire separation window are close to 0.04 and 0.20 mL/min, respectively. SEC column performance obtained for fully porous and superficially porous particles is compared by varying the core-to-particle diameter ratio ρ from 0 to 0.95. Because the separation window is narrowing more rapidly than the rate of peak capacity is growing with increasing ρ, core-shell particles always provide smaller global peak capacity; they still can be advantageous but only for simple sample mixtures. The presented morphology-performance approach holds great promise for method development in SEC.

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

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

Relationship between bed heterogeneity, chord length distribution, and longitudinal dispersion in particulate beds.

We analyse a relationship between the bulk microstructure of randomly packed beds, which we quantify through chord length distribution (CLD) analysis of the interparticle void space, and the associated flow heterogeneity, as expressed by the longitudinal dispersion coefficient at a Péclet number of Pe = 10. A random collection of physically reconstructed packings is complemented with a systematic set of computer-generated packings of monosized spheres, for which the packing-generation algorithm has been carefully adjusted to realize a monotonic variation of the bed porosity and microstructural heterogeneity. The most relevant difference in the morphology between these computer-generated and the physically reconstructed packings are structural defects present in the real packings, such as particle oligomers and larger voids as well as contaminations and particle debris. These defects influence the pore space morphology and introduce additional structural heterogeneity. Hydrodynamic dispersion coefficients for all packings are derived by implementing the lattice-Boltzmann method to simulate fluid flow and a random-walk particle tracking technique to record the transport of passive, point-like tracers in the flow fields. We propose a morphological descriptor, σ/µ, based on statistical parameters of a CLD (standard deviation σ and mean chord length µ) that can be used to predict the dispersion coefficient in packed beds, independent from the underlying particle size distribution, packing-generation protocol, bed porosity, and the occurrence of structural defects.

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.