Novel model for the sintering of ceramics with bimodal pore size distributions: Application to the sintering of lime

A mathematical model for the sintering of ceramics with bimodal pore size distributions at intermediate and final stages is developed. It considers the simultaneous effects of coarsening by surface diffusion, and densification by grain boundary diffusion and lattice diffusion. This model involves population balances for the pores in different zones determined by each porosimetry peak, and is able to predict the evolution of pore size distribution function, surface area, and porosity over time. The model is experimentally validated for the sintering of lime and it is reliable in predicting the so called “initial induction period” in sintering, which is due to a decrease in intra‐aggregate porosity offset by an increase inter‐aggregate porosity. In addition, a novel methodology for determination of mechanisms based on the analysis of the pore size distribution function is proposed, and with this, it was demonstrated that lattice diffusion is the controlling mechanism in the CaO sintering. © 2016 American Institute of Chemical Engineers AIChE J, 63: 893–902, 2017     

Depth-resolved impact of integration process on porosity and solvent diffusion in a SiOCH low-k material

The impact of plasma etching and chemical wet cleaning on solvent diffusion in porous network of a SiOCH low-k dielectric material is studied. Characterization of porosity and pore size distribution by means of ellipso-porosimetry and positron annihilation lifetime spectroscopy are presented. The results are compared with solvent diffusion kinetics, measured using probe molecules of different polarity, surface energies and molecular sizes. Infrared spectroscopy, Doppler broadening of annihilation radiation and time-of-flight secondary ion mass spectrometry measurements are also performed to investigate material modifications causing variations of diffusion kinetics.     

混凝土孔结构及其分形维数与氯离子扩散性能的关系

氯离子扩散系数是研究海洋环境下混凝土结构耐久性的重要参数之一。通过开展不同水胶比混凝土的压汞试验和盐雾扩散试验,研究了混凝土内部孔隙率、孔径分布及临界孔径对氯离子扩散系数的影响规律。结合Menger海绵体模型,建立孔体积分形维数与氯离子扩散系数的关系。结果表明:孔隙率和临界孔径与无量纲化氯离子扩散系数的相关性很高,可作为反映混凝土氯离子扩散性能的重要参数;通过数学分析计算得到的孔表面分形维数分布在2.56~3.86之间,孔体积分形维数分布在2.85~2.98之间;基于压汞法和分形理论计算得到的孔体积分形维数可以作为评价氯离子扩散系数的指标,在孔径小于10 nm、10～100 nm、100～1 000 nm以及大于1 000 nm四类区间,氯离子扩散系数随孔体积分形维数的增加而下降。     

Effective diffusivity and optimum apparent density of vanadia catalysts for sulfur dioxide oxidation

The effective diffusivities of air and SO₂ in four industrial vanadium pentoxide catalysts were measured at steady-state using helium as the counter diffusing gas. An improved catalyst mounting technique and diffusion cell were employed. The nonsurface component of diffusion was successfully correlated using Bruggeman's model for tortuosity. and ¯a based on pore size distribution data or calculated from specific pore volume and surface. However, it was necessary to use flow porosity in place of open porosity. Since the same pore model can be used for the catalytic oxidation So₂, non-reacting flow measurements can be employed to predict effective diffusivities under reaction conditions in this case.With models for the effective diffusivity and the kinetics of the catalytic oxidation of SO₂, an optimum apparent density of the catalyst may be determined which gives the maximum rate of reaction per unit volume of catalyst. Calculations are given for the SVD catalyst.     

Mathematical modelling of gas-solid reactions with solid product

Random pore structural models, that can be used with any type of pore size distribution, are developed for the study of gas-solid reactions with solid product under reaction conditions controlled by kinetics and diffusion in the product layer. An intraparticle diffusion and reaction model is also developed and used, along with the structural models, to study the transient behaviour of solid particles reacting under significant intraparticle diffusional limitations. Simulation results for the limestone-SO₂ system show that the transient behaviour of the reacting particles is strongly influenced by the type of the pore size distribution. Various pore structures characterized by the same values of internal surface area and porosity can lead to completely different reaction trajectories. The predictions of the mathematical models compare well with experimental data from the literature.     

Influence of mineralogy and firing temperature on the porosity of bricks

The changes in brick porosity upon firing (700 up to 1100 °C) and its relation to the mineralogical composition are examined. Two types of raw clay with a composition representative of that used in brick-making industry were selected to manufacture the bricks: one contains notable amounts of carbonates, with a grain size of under 1 mm, and the other is predominantly quartzitic and lacking in carbonates. We demonstrate that the presence or absence of carbonates strongly influences the porosity development and, therefore, the brick texture and physical-mechanical properties. The carbonates in the raw clay promote the formation of fissures and of pores under 1 μm in size when the bricks are fired between 800 and 1000 °C. The absence of carbonates results in a continuous reduction in porosity and a significant increase in the pore fraction with a radius (r)>1 μm as the firing temperature rises and smaller pores coalesce. Porosity and pore size distribution results obtained from the combined use of hydric tests (HT), mercury intrusion porosimetry (MIP) and digital image analysis (DIA) of scanning electron microscopy photomicrographs are compared. A clear correlation between the water absorption and drying behaviour of the bricks and the porosity plus pore size distribution is observed. DIA discloses the evolution of size, shape and connectivity of macropores (r> 1 μm) and evidences that MIP results underestimate the macropore content. Conversely, MIP gives a good estimate of the open porosity and of the distribution of pores with r<1 μm. It is concluded that the combined use of these complementary techniques helps to fully characterise the pore system of bricks. These results as well as the study of the evolution of the speed of ultrasound waves vs. time yield useful information to evaluate the bricks physical–mechanical behaviour and durability. The relevance of these findings in the conservation of historic buildings is discussed.     

Cryo-FIB–SEM and MIP study of porosity and pore size distribution of bentonite and kaolin at different moisture contents

Clays often constitute the main component of poultices used for salt extraction from porous materials in conservation intervention. Knowledge of the evolution in porosity and pore size of clay based poultices, due to shrinkage during drying, is of crucial importance for the selection of the most suitable poultice.We have studied the porosity and pore size distribution of kaolin and bentonite based poultices at different moisture contents. Both Mercury Intrusion Porosimetry (MIP) measurements on freeze-dried samples and cryo-FIB–SEM observations on wet samples are employed.The results show that these complementary techniques provide complete information on the porosity, pore size and pore structure of clay materials at different moisture contents. Both kaolin and bentonite poultices show a change of their total porosity and pore size distribution during drying: the changes are moderate in the case of kaolin, whereas the changes are very significant in the case of bentonite. These findings underline the necessity, when selecting a desalination poultice, of taking into account possible changes in its pore size distribution during drying, since these changes may affect the effectiveness of the salt extraction. Our results indicate that the good desalination efficiency of kaolin on substrate of pore size between 1 and 10 μm observed in practice is related to the presence in the poultice of pores that are very effective in capillary transport (0.2–2 μm) and to the relatively constant pore size distribution of the poultice during drying.     

Characterization of microporous activated carbons using molecular probe method

Accurate knowledge of an adsorbent’s porosity is fundamental for scientific and industrial applications of adsorption technology. Over the last decades many approaches have been established to assess porosity of adsorbent materials by analyzing their nitrogen uptake at 77 K with volumetric measurement devices. Despite using highly sophisticated physical models, all approaches make assumptions on pore shape as well as on the interactions between adsorbent and adsorptive molecules. Subsequently, significant differences in pore size distributions are observed depending on which modeling parameters were used. The molecular probe method presented in this paper therefore restrains to a minimum of approximations by measuring isotherms of chemically similar substances of increasing molecular size. Differences in pore volume can be reduced to sterical limitations in micropores below the size of adsorptive, leading to a high-resolution pore size distribution below 0.7 nm where only few comparable methods exist. The analytical procedure was customized to take account of the amorphous and heterogeneous pore structure of activated carbon. By measuring adsorption isotherms of N₂, n-hexane, iso-octane and cyclohexane on various activated carbons, it is shown that differences in pore accessibility of tested adsorptives are specific for each adsorbent. Using molecular probe molecules hence appears to be a promising method for a complementary porosity analysis of activated carbons.     

Optimal design of engineered gas adsorbents: Pore-scale level

This study presents an optimization methodology and results for the structure of gas adsorbents at a pore level by evaluating the effect of pore geometry, size and overall adsorbent porosity on ultimate working capacity of adsorbents used in pressure swing adsorption (PSA) processes. Three model pore network topologies are studied: parallel, grid-like and branched structures. These are “near” optimal structures for an adsorbent particle and their relative performance is compared in a two-step PSA cycle. The macropore network of such structured adsorbents is optimized through maximization of an objective function i.e. working capacity WC, defined as the number of moles adsorbed per unit volume of slab. Molecular and Knudsen diffusion are considered as the sole transport mechanisms in the macropore channels. An unexpected finding of this optimization technique is that the branched structure with a porosity of less than 50% represents an optimum structure with highest working capacity for the system considered. Furthermore, for faster cycles the advantage of branched structures is more obvious, reflecting the advantages of the pore network in facilitating diffusion more efficiently than other structures. A macropore channel density (defined as the density of macropores per metre of external surface) of below 10 is suggested for optimum performance for both “fast” and “slow” PSA cycles. The theoretical results of this study will be used as a priori results for the design of adsorbents at the macro-scale (bed) level.     

Isothermal Moisture Transport in Partially Saturated Porous Media

ABSTRACT

The prediction of a hydrodynamic model for the isothermal transport of liquid in partially saturated porous media is compared with experimentally obtained values of water transport in clay. The transport obeys the diffusion equation, The diffusion coefficient is described as a function of porosity, permeability and pore size distribution. The comparison indicates that the model needs some refinement.     

Microstructure of Gas Diffusion Layers for PEM Fuel Cells

The gas diffusion layer (GDL) is a critical component of a proton exchange membrane fuel cell, and can play a key role in fuel cell performance. In order to design reliable and durable fuel cells, knowledge of the GDL microstructure is necessary. Currently, characterization of GDLs is generally based on porosity measurements to obtain a pore size distribution. However, the pore size distribution in GDLs may not be the only factor that affects the fuel cell performance. Additional microstructural characterization of GDLs manufactured by three different vendors (Toray, SGL, and Freudenberg) has been investigated. In addition to the pore size distribution, other statistical information of GDL microstructure including size, shape, orientation, and distribution of pores have been characterized and compared. Among these GDLs, the Freudenberg sample was found to have the smallest pore size and orientation analysis indicated that the pores were randomly distributed. Pore roundness was the lowest and pore clustering was highest in Toray sample. The effect of threshold setting on pore size data was also studied and found to have negligible influence on the calculated distributions. The microstructures of the GDLs were reconstructed in three‐dimension using computer simulations and good agreement with the two‐dimensional image analysis data was observed. The present work opens new opportunities for experimentalists and modelers in the area of fuel cell research to take into account the statistical characteristics of GDL microstructure.     

Isothermal Moisture Transport in Partially Saturated Porous Media

The prediction of a hydrodynamic model for the isothermal transport of liquid in partially saturated porous media is compared with experimentally obtained values of water transport in clay. The transport obeys the diffusion equation, The diffusion coefficient is described as a function of porosity, permeability and pore size distribution. The comparison indicates that the model needs some refinement.     

烧结镍毛细芯的孔参数控制及其对抽吸性能的影响

本研究采用溶盐造孔法成功制备了孔隙率及孔径分布可控的高强度烧结镍毛细芯,分析了不同质量及粒度的溶盐对毛细性能的影响。实验结果表明：随溶盐添加量的增加,烧结镍芯孔隙率趋于线性增长,当添加量为40 wt%时,烧结镍芯孔隙率高达73 %,且有足够的强度。改变溶盐的粒度影响毛细芯孔径的分布,但对整体孔隙率影响不大。制备的试样的毛细抽吸特性研究表明,毛细芯的毛细抽吸性能不仅仅受孔隙率的影响,同样受孔径分布状态的影响,孔隙率相当的情况下,孔径较小且分布集中的毛细芯表现出更优异的毛细抽吸性能。     

Multiple linear equation of pore structure and coal–oxygen diffusion on low temperature oxidation process of lignite

This work aimed at studying the feasibility of calculating the coal–oxygen diffusion properties during the low temperature oxidation process of lignite so as to predict its spontaneous combustion process. Coal samples were oxidized in air ambient under different temperatures. Scanning Electron Microscope was used to indicate the surface morphology changes of oxidization. Then, based on fractal theory and flow characteristics, the fractal dimension of gas diffusion in the pore ways was calculated under different temperature. Considering pore size distribution, connectivity distribution and Fick diffusion mechanisms, the relationship between the gas diffusivity change with pore area fractal dimension and porosity was investigated, and multiple linear equation of the coal–oxygen diffusion coefficients and pore parameters was obtained. Comparison between the experimental data and model prediction verifies the validity of the model. The research provides a theoretical basis for the prediction model of coal–oxygen diffusion law.     

Impact of silica pore structure on the performance of metallocene catalysts in ethylene gas-phase polymerization

Several commercial silicas were used to support metallocene active centres, and the resulting precatalysts were used to study the impact of the pore size and pore size distribution of the support on the polymerization kinetics and resulting polymer properties. Pore volume distribution played a major role in the fragmentation of silica-supported catalysts, where mesoporous silicas with a narrow distribution in the region obtained higher activities and faster fragmentation than silicas with a broad pore volume distribution. Therefore, it is shown that care must be taken when using standard information on particle porosity, as this quantity can be misleading. It appears that the minimum pore size, particularly on the particle surface, can be a very important parameter even if it does not impact the estimate of the porosity.     

Use of X-ray tomography to study the porosity and morphology of granules

X-ray computed tomography (XRCT) is a technique that uses X-ray images to reconstruct the internal microstructure of objects. Known as a CAT scan in medicine, it has found wide application for whole-body and partial-body imaging of hard tissues (e.g., bone). A modern tabletop XRCT system with a resolution of about 4 μm was used to characterize some pharmaceutical granules. Total porosity, pore size distribution, and geometric structure of pores in granules produced using different conditions and materials were studied. The results were compared to data obtained from mercury porosimetry. It was found that while XRCT is less precise in the determination of total porosity in comparison to mercury porosimetry, it provides detailed morphological information such as pore shape, spatial distribution, and connectivity. The method is nondestructive and accurate down to the resolution of the instrument.Tomographic images show that the pore network of individual granules comprises relatively large cavities connected by narrow pore necks. The major structural difference between granules produced at different conditions of compaction and shear is a reduction in the pore neck diameter; the cavity size is relatively insensitive to these conditions. Comparison of pore size distributions determined from tomographic images and mercury porosimetry indicates that mercury intrusion measures the pore neck size distribution, while tomography measures the true size distribution of pores ca. 4 μm or larger (the instrument resolution).     

Hindered diffusion of asphaltenes through microporous membranes

The relationship between the diffusion coefficient of asphaltenes and pore size was studied experimentally using track-etched mica membranes. The asphaltenes were extracted from Kuwait atmospheric bottoms using criteria of n-pentane insolubility and tetrahydrofuran solubility at 25°C. Data were obtained for asphaltene fractions of narrow size range by using gel permeation chromatography to analyze the diffusion samples. The results show a very strong pore size effect on diffusion coefficient in the range 70–500 Å pore radius for asphaltenes whose GPC-equivalent polystyrene molecular weight is 3000 or greater. By properly accounting for the molecular size of the asphaltene fractions, we are able to obtain good agreement between the measured diffusion coefficients and those predicted from a hydrodynamic theory of hindered diffusion.     

Effects of nano-alumina content on the formation of interconnected pores in porous purging plug materials

The physical properties and microstructure of porous purging plug materials added with different nano-alumina contents and firing temperatures were investigated by means of X-ray diffraction, scanning electron microscopy, air permeability, pore size distribution, mean pore size, apparent porosity, bulk density, and cold crushing strength (CCS) tests. The results showed that the addition of nano-alumina had a great effect on the physical properties and microstructure of the porous purging plug materials. With increasing nano-alumina content in the composition, the main phase was α-Al₂O₃ in all compositions and the mean pore size, apparent porosity and air permeability all increased due to the increased number of pores and pore size of the specimens which facilitated the formation of interconnected pores. When the sintering temperature was changed from 1550 °C to 1650 °C, some of the smaller pores vanished due to solid phase sintering, which reduced the apparent porosity, and some open pores connected to form interconnected pores, which promoted increased air permeability. In addition, the strength and porosity were found to follow the relationship σ = σ₀ exp (-b P). When the apparent porosity increased, the CCS decreased, and vice versa.     

Cyclic cold isostatic pressing and improved particle packing of coarse grained oxide ceramics for refractory applications

This study investigated the cold isostatic pressing of coarse grained alumina refractories applying either a cyclic pressure increase or a cycling at maximum pressure. Additionally the effects of the maximum pressure and the particle size distribution on physical, mechanical and thermomechanical properties were analyzed. The cyclic pressure increase resulted in a slightly higher apparent density and lower apparent porosity. A cycling at maximum pressure decreased the median pore size to some extent. Remarkably, an optimized particle size distribution resulted in a lower apparent porosity, lower median pore size and in a higher Young's modulus before and after thermal shock together with a slightly lower relative decrease of the Young's modulus. A higher pressing pressure which decreased the apparent porosity did not affect the Young's modulus. Thus, apparently the optimized particle size distribution improved the particle packing which was associated with a smaller median pore size. This smaller pore size increased the number of pores relative to the total porosity, which then acted as points of crack initiation and crack deflection limiting the length of propagating cracks in case of thermal shock. Thus, tailoring the pore size distribution is a promising starting point to improve the thermomechanical properties of refractories.     

The Dependence of Pore Size Distribution on Porosity in Hot Isostatically Pressed Porous Alumina

Pore size distributions in porous alumina bodies produced by the capsule-free hot isostatic pressing technique have been determined experimentally. The distribution of pore diameter has been found to be dependent on the size of the pre-sintered powders and the amount of open porosity in the sintered body. An empirical model has been developed to predict the modal pore size as a function of median particle size and open porosity. The pore size distributions were found to widen with reduced porosity. They were also shown to be positively skewed. The skew reduced with decreasing porosity. The pore size variation with porosity for specimens produced with a sintering aid could not be described by the same mathematical functions developed for specimens produced by solid-state sintering.