Morphological Analysis of Disordered Macroporous–Mesoporous Solids Based on Physical Reconstruction by Nanoscale Tomography

Abstract

Solids with a hierarchically structured, disordered pore space, such as macroporous-mesoporous silica monoliths, are used as fixed beds in separation and catalysis. Targeted optimization of their functional properties requires a knowledge of the relation among their synthesis, morphology, and mass transport properties. However, an accurate and comprehensive morphological description has not been available for macroporous-mesoporous silica monoliths. Here we offer a solution to this problem based on the physical reconstruction of the hierarchically structured pore space by nanoscale tomography. Relying exclusively on image analysis, we deliver a concise, accurate, and model-free description of the void volume distribution and pore coordination inside the silica monolith. Structural features are connected to key transport properties (effective diffusion, hydrodynamic dispersion) of macropore and mesopore space. The presented approach is applicable to other fixed-bed formats of disordered macroporous-mesoporous solids, such as packings of mesoporous particles and organic-polymer monoliths.

Hindered Nanoparticle Diffusion and Void Accessibility in a Three-Dimensional Porous Medium

“…The confocal data revealed a disordered void network similar to that exposed in the SEM images, albeit at lower resolution ( Figure S1 of the Supporting Information). Using the two-dimensional confocal sections, we measured the void volume fraction φ = 0.50 ( 0.07 (i.e., porosity), the distribution of chord lengths (Figure 2b), 38 which characterize the size of the void spaces, and the distribution of minimum chord lengths (i.e., confinement lengths), which characterize the length scale of maximum confinement (Methods S1 and Figure S1 of the Supporting Information). An independent measure of porosity based on the change in sample mass upon saturating with fluid, φ = 0.52 ( 0.02, agreed well with the confocal value.…”

Sol‐Gel and Porous Glass‐Based Silica Monoliths with Hierarchical Pore Structure for Solid‐Liquid Catalysis

“…2 cannot be systematically exploited in practice until the disordered structures of macro-and mesopore space in these monoliths become known and their transport properties understood [58]. Recently, a direct route to the three-dimensional morphology of macroporous-mesoporous silica monoliths has been adapted [95], illustrated in Fig. 17, which relies on physical reconstruction of the hierarchical pore space using nanoscale tomography [96 -99]; focused ion beam-scanning electron microscopy (FIB-SEM) [100] is suited to reconstruct the interskeleton macropore space of (envisioned sol-gel and porous glass-based) silica monoliths with sub-micrometer macropore size and skeleton thickness, whereas scanning transmission electron microscopy (STEM) [101,102] is appropriate for the intraskeleton mesopore space.…”

Morphological Analysis of Physically Reconstructed Silica Monoliths with Submicrometer Macropores: Effect of Decreasing Domain Size on Structural Homogeneity

“…A mathematical description of the CLD is achieved by fitting the histogram with a k-gamma function, as shown previously. 12,17,25,33,34,38 The k-gamma function has been delineated as a descriptor of the void space distribution in disordered materials based on a statistical mechanics approach. 45 It is defined by the mean and the standard deviation of the CLD…”