On the Geometry and Topology of 3D Stochastic Porous Media

The nature of geometric and topological information contained in statistical correlation functions was investigated systematically using simulated porous media, generated by the level-cut of Gaussian random fields. Pore space partitioning techniques based on multiorientation scanning were implemented to determine the pore and neck size distributions, coordination number distribution, and genus of a number of model porous media. These results were correlated with the statistical properties (porosity and correlation function) of the microstructure, revealing for the first time the extent of morphological diversity of a broad class of stochastically reconstructed porous media. It was found that the dominant factor explaining microstructural variability among the media studied is the dimensionless length of spatial correlation. Accordingly, the resolution at which the void space is discretized during simulation was shown to affect significantly the resulting pore and neck size distributions and specific genus. It was also found that the average coordination number of simulated porous media is independent of correlation length, but decreases slightly with decreasing porosity. Copyright 2000 Academic Press.     

Linking pore diffusivity with macropore structure of zeolite adsorbents. Part I: three dimensional structural representation combining scanning electron microscopy with stochastic reconstruction methods

In the present study we have employed advanced experimental and computational methods to characterize the structure of a binderless zeolite adsorbent with improved mass transfer characteristics. Hence, we have used standard and hybrid simulated annealing (SA) methods to stochastically reconstruct in three dimensions the adsorbent structure, by matching low order correlations, namely porosity and two point correlation function. These correlations are measured on two dimensional images obtained by Back-Scattered SEM micrographs taken on different samples of the adsorbent. In the standard SA method we have started from a purely random structure, while in the hybrid method we have started from a uniformly consolidated random sphere pack made by the Lubachevsky–Stillinger algorithm. It is found that the hybrid method preserves, besides low order correlations, pore and mass chord length distribution functions, which contain information on higher order correlations, while the standard SA method matches only low order correlations. This is because in the hybrid process we have initiated the SA algorithm starting from a structure that contains structural information of the sintered zeolite powder, in the form of a consolidated random sphere pack with the porosity of the final structure. Evidently, diffusion studies will enable us to further evaluate the structures developed by each method, as will be explored in a subsequent study.     

Pore Modification in Porous Ceramic Membranes With Sol-Gel Process and Determination of Gas Permeability and Selectivity

Summary: The aim of the study was to investigate the variation in total surface area, porosity, pore size, Knudsen and surface diffusion coefficients, gas permeability and selectivity before and after the application of sol-gel process to porous ceramic membrane in order to determine the effect of pore modification. In this study, three different sol-gel process were applied to the ceramic support separately; one was the silica sol-gel process which was applied to increase porosity, others were silica-sol dip coating and silica-sol processing methods which were applied to decrease pore size. As a result of this, total surface area, pore size and porosity of ceramic support and membranes were determined by using BET instrument. In addition to this, Knudsen and surface diffusion coefficients were also calculated. After then, ceramic support and membranes were exposed to gas permeation experiments by using the CO₂ gas with different flow rates. Gas permeability and selectivity of those membranes were measured according to the data obtained. Thus, pore surface area, porosity, pore size and Knudsen diffusion coefficient of membrane treated with silica sol-gel process increased while total surface area was decreasing. Therefore, permeability of ceramic support and membrane treated with silica sol-gel process increased, and selectivity decreased with increasing the gas flow rate. Also, surface area, porosity, pore size, permeability, selectivity, Knudsen and surface diffusion coefficients of membranes treated with silica-sol dip coating and silica-sol processing methods were determined. As a result of this, porosity, pore size, Knudsen and surface diffusion coefficients decreased, total surface area increased in both methods. However, viscous flow and Knudsen flow permeability were detected as a consequence of gas permeability test and Knudsen flow was found to be a dominant transport mechanism in addition to surface diffusive flow owing to the small pore diameter in both methods. It was observed that silica-sol processing method had lower pore diameter and higher surface diffusion coefficient than silica-sol dip coating method.     

Linking pore diffusivity with macropore structure of zeolite adsorbents. Part II: simulation of pore diffusion and mercury intrusion in stochastically reconstructed zeolite adsorbents

In the present study we complete the evaluation of three dimensional digitized reconstructions of a binderless zeolite adsorbent with improved mass transfer rates, by performing simulations of pore diffusion and Hg-intrusion porosimetry in these structures. It is seen that an excellent agreement with the experimental diffusivity is achieved (relative error of 1.2 %) for a pore structure that matches, besides low order correlations, chord length distribution functions that account for higher order correlations. Furthermore, simulations on a variety of reconstructed samples indicate that matching chord length distribution functions is a necessary (though probably not sufficient) condition for accurate structural representation. The average tortuosity factor is 2.68 and is nearly constant over a broad spectrum of pressures, when properly normalized. Hg-intrusion porosimetry simulations, performed with a pure morphology method, show a good agreement with the experimental curve for normalized cumulative intrusion volumes in the range of 50–88 %, but cannot make a distinction between structures with differences in higher order correlations. It is believed that SEM micrographs, properly obtained to represent realistic 2D sections of the material, contain sufficient structural information that can distinguish among pore structures with different mass transfer rates, when combined with stochastic reconstruction methods. Evidently, the direct link between these structural parameters and pore diffusivity will provide the necessary route to improve the mass transfer rate of porous adsorbents.     

Estimation of diffusion parameters in functionalized silicas with modulated porosity. Part II: pore network modeling

In this work, the pore structure of those five (5) silicas SiO2-X (see Part I) which have suffered gradual functionalization with functional groups X of increasing length (X = psi, [triple bond]Si-H, [triple bond]Si-CH2OH, [triple bond]Si-(CH2)3OH, [triple bond]Si-(CH2)11CH3), is modeled as a three-dimensional cubic network of cylindrical pores. Those hybrids organic-inorganic SiO2-X samples are characterized by different extent of pore blocking effects. The pores of samples are represented in a 9 x 9 x 9 lattice by the nodes as well the bonds that are interconnected in a so-called dual site-bond model, DSBM, network. The pore network is developed using a Monte Carlo statistical method where the cylindrical pores (nodes and bonds) are randomly assigned into the lattice, until matching of the theoretical results to the experimental data of N2 adsorption-desorption measurements. Thus, a visual picture of the porous solid is possible. This realistic network is used next in order to study the steady-state gas transport (Knudsen gas-phase and viscous diffusion) properties for the examined materials and how flow processes depend on the morphology of the pore structure. The pore diffusivity Dp and total permeability P of each porous medium is determined based on theoretical calculations and the structural statistical parameters, such as porosity epsilonp, tortuosity factor tau and connectivity c of pores is discussed with the corresponding experimental data described in Part I of this work. The results indicate clearly that the diffusion model made it possible to predict pore effective diffusivity in these porous media in very good agreement with the corresponding experimental results for all the examined solids (Part I). The pore diffusivity increases significantly as the value of the pore connectivity increases but the transport properties of the network are influenced strongly at lowest connectivity. Also the predicted tortuosity factor is related inversely to the extent of interconnection of pores in these solids, which indicates that the influence of pore branching to the tortuosity factor of the pore network decreases, as connectivity increases.     

Low Peclet mass transport in assemblages of spherical particles for two different adsorption mechanisms

The problem of flow and mass transport within an assemblage of spherical solid absorbers is investigated. We present and compare results from the numerical solution of the convection-diffusion equation in the sphere-in-cell geometry and in stochastically constructed 3-D spherical particle assemblages. In the first case, we make use of an analytical solution of the creeping flow field in the sphere-in-cell model while in the second we employ a full numerical solution of the flow field in the realistic geometry of sphere assemblages. Low to moderate Peclet numbers (Pe<10(2)) are considered where the validity of the sphere-in-cell model is uncertain. On the other hand, the selected porosities range from values close to unity, where the sphere-in-cell approximation is expected to hold, to intermediate values, where its applicability becomes again uncertain. In all cases, instantaneous and Langmuir adsorption is studied. It is found that the simplified sphere-in-cell approach performs adequately provided that proper account of the actual porous media properties (porosity and internal surface area) is taken. A simple match of porosity is not sufficient for a reliable estimation of adsorption efficiencies.     

Geometric and Topological Analysis of Three-Dimensional Porous Media: Pore Space Partitioning Based on Morphological Skeletonization

This article presents a versatile, rigorous, and efficient methodology for extracting various geometric and topological parameters of 3D discrete porous media. The new approach takes advantage of the morphological skeleton of the pore structure-a lower dimensional representation of the pore space akin to the topological "deformation retract". The skeleton is derived by a fully parallel thinning algorithm that fulfils two essential requirements: it generates a medial axis and preserves the connectivity of the pore space. Topological analysis is accomplished by classifying all skeleton points as node or link (branch) points according to the concept of lambda-adjacency in 3D discrete space. In this manner, node coordination number and link length distributions are directly obtained from the skeleton. Pore necks (throats) are identified through a search for minima in the hydraulic radius of individual pore space channels outlined by skeleton links. In addition to the determination of the size distribution of the constrictions (pore necks) that control nonwetting phase invasion, improved estimates of the distributions of effective hydraulic and electric conductivity of individual pore space channels are obtained. Furthermore, erection of planes at the location of pore necks results in partitioning of the pore space into its constituent pores. This enables the characterization of the pore space in terms of a pore volume distribution. The new methodology is illustrated by application to a regular cubic pore network and irregularly shaped 2D and 3D pore networks generated by stochastic simulation. In the latter case, important new results are obtained concerning the sensitivity of geometric and topological properties of the microstructure to the parameters of stochastic simulation, namely, the porosity and correlation function. It is found that model porous media reconstructed from the same porosity and correlation function can exhibit marked differences in geometry and connectivity, which correlate with differences in specific surface area. Copyright 2000 Academic Press.     

Correlation of structural and permeation properties in sol-gel-made nanoporous membranes

The aim of the present work was to establish a fundamental link between the basic structural properties of ceramic nanoporous membranes made by the sol-gel process and their respective transport properties, for a systematic evaluation of their performance in gas and liquid applications. For this purpose, supported and unsupported gamma-Al2O3 and TiO2 membranes were prepared from different colloidal dispersions (sols) by a sol-gel dipping process followed by drying and calcination, resulting in structures of crystallites of different shape and stacking arrangement. Accordingly, the pore structure of each membrane was simulated employing process-based reconstruction techniques and the permeation properties were predicted by solving the appropriate transport equations in the generated structures. Excellent agreement was achieved between the computed and experimental permeability values in the Knudsen and viscous flow regimes, validating the considerations made regarding the basic structural characteristics and the procedure for generation of the membrane structures. Moreover, it was shown that the shape and stacking arrangement of the primary particles (crystallites) of the sol have a major impact on the formation of pathways in the membrane pore structures and control the transport and therefore also the separation properties of these materials.     

Quantification of the pore size distribution (porosity profiles) in microfiltration membranes by SEM,TEM and computer image analysis

Transport properties of membranes are closely related to morphological properties like surface porosity and variation of their inner pore structure. Scanning electron microscopy (SEM) as well as transmission electron microscopy (TEM) are powerful tools to characterise the microscopical pore structure of membranes in a qualitative manner. In order to provide more quantitative data of surface and cross-sectional pores computer image analysis can be used. Parameters like ‘porous area fraction’ and ‘mean free path length’ have been selected to describe the pore distribution within porosity profiles in order to consider the effect that the pores within the cross-section are connected to each other.     

Preparation of stable MCM-48 tubular membranes

Stable mesoporous membranes with a cubic structure, based on the MCM-48 material, were successfully prepared on alumina supports by hydrothermal synthesis, starting from sols having both CTABr and TPAOH structure directing agents. The inclusion of a zeolite (MFI-type) precursor during membrane synthesis led to partial zeolite incorporation into the porous structure, giving rise to a hydrothermally stable membrane. The mean pore diameter of the membrane was 2.5 nm, and permeation experiments confirmed that transport across the membrane was governed by Knudsen diffusion and that there were no pinholes.     

医用多孔壳聚糖膜的制备及性能研究

以邻苯二甲酸二丁酯为致孔剂,制备了多孔壳聚糖膜,并用扫描电镜对其表面和断面形貌进行了分析,同时对膜的吸水性、水蒸气透过性、比表面积、力学性能及生物相容性等进行了考察。分析结果表明:以邻苯二甲酸二丁酯为致孔剂,制备的多孔壳聚糖膜孔径均匀,吸水性好,孔隙率高,比表面积大,膜的最大吸水率、孔隙率和比表面积分别为196%、71.5%和1.0472 m2.g-1;膜的力学性能好,最大抗拉强度为273.17MN/m2。     

Fabrication of Porous Polyimide Membrane with Through-Hole via Multiple Solvent Displacement Method

Porous polyimide (PI) membranes are widely used in separation processes because of their excellent thermal and mechanical properties. However, the applications of porous PI membranes are limited in the nanofiltration range. In this study, porous PI membranes with through-holes have been successfully fabricated by the novel multiple solvent displacement method. This new method requires only a porous polyamic acid (PAA) membrane, which was prepared by immersing PAA film in N-methylpyrrolidoneebk; (NMP) prior to immersing it in a mixed solvent consisting of NMP and a poor solvent, followed by immersion only in poor solvent. The pore size, morphology, porosity, and air permeability demonstrated that the fabricated PI membranes had a uniformly porous structure with through-holes over their surface. This new method enabled control of pore size (3–11 μm) by selecting a suitable poor solvent. This multiple solvent displacement method is highly versatile and promising for the fabrication of porous PI membranes.     

Nanoporous metals with controlled multimodal pore size distribution

A simple two-step dealloying strategy is described to make free-standing metal membranes with hierarchical porous architecture. This structure has a bimodal pore size distribution composed of large porosity channels and small porosity channel walls, where each pore size can be tailored independently of the others. A new gas-phase electroless plating technique was also developed here that could be used to uniformly fill porous structures with pore size as small as 10 nm.     

A mini-review of polymeric porous membranes with vertically penetrative pores

Membrane separation technology plays a pivotal role in modern industry and scientific research. The key to developing and improving membrane separation processes lies in designing and fabricating customized porous membranes with specific physical parameters, including pore diameter, porosity, pore size distribution, pore length (membrane thickness), pore geometry, and pore connectivity. Polymeric porous membranes with vertically-penetrative-pores (PPMVs) represent a distinct category among the available membranes due to their unique characteristics such as short transport path, small trans-membrane resistance, and simple pore geometry, as compared to other porous membranes with sponge-like channels. In practical applications, PPMVs offer several advantages, including achieving higher flux rates, facilitating easier unidirectional transport, and enabling harmless biological extraction. Moreover, PPMVs can serve as ideal model systems for theoretical investigations on the fundamental mechanisms of separation and transport in academic research. With substantial advancements in fabrication technologies and application fields of PPMVs in recent years, it warrants a comprehensive perspective. In this mini-review, we provide an overview of widely used fabrication methods for PPMVs, discuss their primary applications, and address the existing challenges and opportunities.     

Preparation of microporous membranes by paste method

Microporous membranes were prepared by the paste method. Certain properties of the resultant microporous membranes such as porosity, pore size, specific surface area, and N₂ gas permeability were estimated. Furthermore, the membrane structure was observed with the aid of scanning electron microscopy. It was elucidated that the membranes consist of aggregates of minute spherical particles, made up of poly(styrene-divinylbenzene) with micropores.     

Morphological analysis of physically reconstructed capillary hybrid silica monoliths and correlation with separation efficiency

We report an experimental study on the structural (especially radial) heterogeneity of eleven 100 μm i.d. capillary tetramethoxysilane-methyltrimethoxysilane hybrid silica monoliths with different pore and skeleton sizes, which were imaged by an optimized confocal laser scanning microscopy method. This method allows the optical sectioning of the monoliths, which is a prerequisite for quantitative morphological image analysis. Both radial porosity profiles and chord length distributions were calculated in the macropore domain for each column from at least 100 complete cross-sectional views along the column axis. The statistical approach visualized radial heterogeneities on different length scales in the monolithic structures. Chord length distributions followed a simplified k-gamma function, and a structural parameter obtained from this function is introduced to provide a scalar measure of column heterogeneity. It enables the comparison of monoliths with different pore sizes and helps to establish correlations between the microscopic properties of a column, eddy dispersion, and its separation efficiency.     

Concentration dependence of the distribution coefficient for macromolecules in porous media

Partitioning of macromolecules between pore and bulk solutions directly affects both equilibrium and transport processes such as exclusion chromatography and movement of solutes through porous media. Because of interactions between macromolecules and the pore wall, the variation of the macromolecule activity with concentration is different inside the pore than in bulk solution. This difference causes a concentration dependence of the distribution coefficient, as reported in experiments involving exclusion chromatography. In order to explain this effect, we develop a model for a concentration-dependent distribution which explicitly accounts for a coupling between pore–macromolecule and macromolecule–macromolecule interactions. Predictions using this model are reported for the case of rigid spherical macromolecules in both cylindrical and slit pores, including both steric (hard sphere–hard wall) and long-range (screened electrostatic) interactions. An important result is the existence of a general correlation between the first order concentration effect and measurable properties of the macromolecule and porous medium.     

气体分离用MOF基混合基质膜的界面构建策略

混合基质膜结合多孔填料优异的气体分离性能和聚合物材料良好的加工性能,被认为是最具有应用前景的一种气体分离膜材料。金属-有机框架材料(MOF)由于具有高比表面积和孔隙率、可调节的孔径以及可修饰的表面性能,成为制备混合基质膜的重要多孔材料。本文针对MOF基混合基质膜制备中所面临的主要挑战,聚焦于MOF和聚合物界面缺陷问题,分析了界面缺陷的产生原因及其对性能的影响,重点阐述了改善MOF填料和聚合物基质界面相容性的策略,以期为制备具有良好的界面形态和优异的气体分离性能的混合基质膜提供借鉴思路。     

The permeation of binary gas mixtures through support structures of composite membranes

The dusty gas model (DGM) is used to describe transport of binary gas mixtures through porous membrane supports to quantify the resistance towards permeation. The model equations account for three different transport mechanisms for the permeating components: conventional viscous pore flow, Knudsen diffusion, and binary diffusion. Experimental data obtained with the uncoated membrane supports are used to determine the morphological parameters needed in the DGM equations. Flat sheet and hollow fiber membrane supports are characterized by the permeation of a TCE/nitrogen vapor. The DGM shows an excellent fit to experimental data when the asymmetric structure of the membrane supports is taken into account, but the morphological parameters cannot necessarily be related to precise physical structure parameters such as pore size, porosity, and tortuosity. The DGM works well even when the membrane supports are modeled as a single homogenous structure. The membrane supports exhibit different resistances towards the various transport mechanisms that occur within the porous support and the resistances vary with process conditions so that support optimization is not straightforward. With the analysis presented in this paper and transport equations specific to the dense coating and module geometries, the influence of the support layer on gas or vapor separation can be quantified.