Characterisation of porous solids using integrated nitrogen sorption and mercury porosimetry

The two different techniques of nitrogen sorption and mercury porosimetry, which are generally utilised completely separately, have been integrated into the same experiment to improve upon the information obtained from both methods. Nitrogen sorption isotherms have been run both before and after a mercury porosimetry experiment on the same sample. This experiment has revealed that for a particular type of sol-gel silica catalyst support the entrapped mercury is confined to only the very largest pores in the material. Light micrograph studies have shown that the spatial distribution of entrapped mercury is highly heterogeneous. These results suggest that mercury entrapment within the material is caused by a mechanism involving macroscopic () heterogeneities in the pore structure. These findings conflict with the usual assumptions generally made in simulations of porosimetry based on random pore bond network models. The new work has shown that, in conjunction with computer simulations involving the correct mercury retraction mechanism, mercury porosimetry and nitrogen sorption can be used to study the spatial distribution of all pore sizes within a mesoporous material. A percolation analysis of the nitrogen sorption data, obtained both before and after mercury entrapment, allowed broad features of the spatial disposition of variously sized pores to be determined. The results reported here also support the use of new, semi-empirical alternatives to the Washburn Equation to analyse raw mercury porosimetry data, rather than the traditional approach.     

Studies of the entrapment of non-wetting fluid within nanoporous media using a synergistic combination of MRI and micro-computed X-ray tomography

Three-dimensional magnetic resonance imaging (MRI) and micro-computed X-ray tomography (micro-CXT) have been combined to study the entrapment of mercury within nanoporous silica materials following porosimetry. MR images have been used to construct structural models of particular porous media within which several simulations of mercury intrusion and retraction have been performed with variations in the mechanism for the ‘snap-off’ of the mercury menisci. The simulations gave rise to different predictions for the pattern of the macroscopic spatial distribution of entrapped mercury, depending on ‘snap-off’ mechanism, which were then compared with corresponding experimental data obtained from micro-CXT images of real pellets containing entrapped mercury. The information obtained from the micro-CXT images, and also from the porosimetry curves themselves, was then used to constrain a model for the microscopic mercury retraction mechanism. Additional predictions of the retraction model were then subsequently confirmed using scanning loop experiments. The simulations showed that the overall level of entrapment of mercury was determined by the close interaction between the pellet macroscopic structure (particularly pore size spatial correlation), and the microscopic mercury retraction mechanism. Hence, it was subsequently possible to explain fully why high mercury entrapment occurred within one particular type of sol-gel silica material, while only low entrapment occurred in another batch of superficially similar material.     

APPLICATION OF A STOCHASTIC NETWORK PORE MODEL TO A CATALYST PELLET

A previously developed stochastic two-dimensional network pore structure model has been applied directly to a nickel/alumina commercial catalyst pellet. A technique has been devised to determine the pore diameter distribution function of cylindrical pore segments for any prescribed network dimension which will exactly replicate the experimentally observed mercury penetration curve for the pellet in the method of mercury porosimetry. This stochastic network representation for the catalyst pellet pore structure is superior to the classical parallel bundle model since it incorporates the element of pore interconnectivity. The model has been extended to investigate the phenomena occurring during the accumulation of a foulant deposit (e.g. coke in hydrocarbon catalysis) for the pore structure determined for a 10 × 10 set of network elements for the pellet under study. The analysis shows how the build-up of a deposit causes physical blocking of the smaller pores at quite low accumulations of foulant which results in inaccessibility of parts of the interior pore structure. This necessarily results in only partial filling of the pore structure with deposit, with a tendency for greater accumulation towards the pellet exterior. This kind of behaviour is not possible with the parallel bundle model. A detailed comparison of the two pore models in respect of accessible interior volume at various foulant accumulations is presented. The derived network model based upon the penetration curve gives an independent prediction of the mercury porosimeter retraction curve which is in reasonably close agreement with the experimental result, thus confirming the probable utility of the model in predicting and correlating other macroscopic properties of the catalyst pellet.     

APPLICATION OF A STOCHASTIC NETWORK PORE MODEL TO A CATALYST PELLET

A previously developed stochastic two-dimensional network pore structure model has been applied directly to a nickel/alumina commercial catalyst pellet. A technique has been devised to determine the pore diameter distribution function of cylindrical pore segments for any prescribed network dimension which will exactly replicate the experimentally observed mercury penetration curve for the pellet in the method of mercury porosimetry. This stochastic network representation for the catalyst pellet pore structure is superior to the classical parallel bundle model since it incorporates the element of pore interconnectivity. The model has been extended to investigate the phenomena occurring during the accumulation of a foulant deposit (e.g. coke in hydrocarbon catalysis) for the pore structure determined for a 10 × 10 set of network elements for the pellet under study. The analysis shows how the build-up of a deposit causes physical blocking of the smaller pores at quite low accumulations of foulant which results in inaccessibility of parts of the interior pore structure. This necessarily results in only partial filling of the pore structure with deposit, with a tendency for greater accumulation towards the pellet exterior. This kind of behaviour is not possible with the parallel bundle model. A detailed comparison of the two pore models in respect of accessible interior volume at various foulant accumulations is presented. The derived network model based upon the penetration curve gives an independent prediction of the mercury porosimeter retraction curve which is in reasonably close agreement with the experimental result, thus confirming the probable utility of the model in predicting and correlating other macroscopic properties of the catalyst pellet.     

Evaluation of mercury porosimeter experiments using a network pore structure model

A square network model has been developed to interpret mercury penetration and retraction behaviour in the widely employed mercury porosimetry technique for investigating pore structure and pore size distribution. A network of arbitrary size is constructed by assembling cylindrical pore segments of equal length and pseudo-random number generation is used to assign pore diameters according to any stipulated size distribution function. Application of the simple Washburn equation then predicts movement of mercury into the network under increasing pressure (penetration) and the corresponding withdrawal under reducing pressure (retraction) The network model is superior to the classical parallel bundle model, since it implicitly produces hysteresis between penetration and retraction, predicts that mercury entrapment on retraction is a result of interconnectedness of pore segments and provides a better estimate of the intrinsic distribution of segment sizes. Comparison with porosimeter experiments on a commercial hydrodesulphurisation catalyst show that the approach can be applied to practical measurements and the model may provide an improved basis for the study of diffusion, reaction and deactivation in catalyst pellets.     

Pore size distribution in Separon using mercury contact angles in pores and hysteresis in porosimetry

The porous co-polymer Separon HEMA 1000 for HPLC column packing was examined by using a special method of mercury porosimetry evaluation. The advancing and receding contact angles of mercury in pores were determined and the method used is described in detail. The pore distribution curves obtained from mercury porosimetry and from the nitrogen desorption isotherms are in good agreement. The dependence of the hysteresis of the porosimetry curves and mercury retention in the pores on the intrusion volume was investiaged to characterize the porous structure of the sample. The influence of the pore potential on the hysteresis was evaluated.     

A comparison of methods used to measure pore size in solids

The size of pores in a number of solid samples has been measured by nitrogen adsorption, oxygen adsorption, mercury porosimetry, scanning electron microscopy, and optical microscopy. All the pores in each of the solid samples investigated were straight, had a circular cross-section, and had similar dimensions. By assuming the existence of contact angle hysteresis, agreement between the microscopy pore radii and mercury porosinietry radii measured both from penetration and from retraction was obtained. Dimensional changes in the solid may have contributed to the pore radii determined by nitrogen adsorption and oxygen adsorption being larger than the radii determined by microscopy.     

Image-based characterization of cement pore structure using wood’s metal intrusion

Mercury intrusion porosimetry is a widely used technique for characterization of the pore size distribution of cement-based materials. However, the technique has several limitations, among which are the ink bottle effect and a cylindrical pore geometry assumption that lead to inaccurate pore size distribution curves. By substituting Wood’s metal for mercury as the intruding liquid, scanning electron microscopy and imaging techniques can be applied to the sample after intrusion. The molten Wood’s metal solidifies within the pore structure of the sample, which allows it to be sectioned and observed in the scanning electron microscopy. From here, the sample can be analyzed both qualitatively, by observing the changes in the appearance of the sample as the intrusion process progresses, and quantitatively, by applying image analysis techniques. This study provides insight for better interpretation of mercury intrusion porosimetry results and the possibility for quantitative characterization of the spatial geometry of pores in cement-based materials.     

Pore size distribution of portland cement slurries at very early stages of hydration (influence of curing temperature and pressure)

Pore size distribution of Portland cement pastes has been studied using helium picnometry and mercury porosimetry. Cement samples were hydrated under varying conditions of temperature and pressure and were investigated at very early stages of hydration : thickening, setting, and early hardening. The evolution of pore size distribution with time has been related to physical and chemical properties (compressive strength, shrinkage, and combined water). The interpretation has been based on the repartition between free pores of tubular shape and trapped pores of rounded shape, and a model is proposed for describing cement pore size distribution.     

TOMOGRAPHY OF MACRO-MESO-PORE STRUCTURE BASED ON MERCURY POROSIMETRY HYSTERESIS LOOP SCANNING Part II: MP Hysteresis Loop Scanning Along the Overall Retraction Line

The concept of macro-meso-pore structure tomography based on mercury porosimetry hysteresis loop scanning along the retraction curve (MP-SHL-R) is introduced. The random corrugaled pore structure (CPSM) model is used in the simulation of the present loop-scanning variant. The CPSM predicted, distribution (V_T) of trapped mercury, reported elsewhere, is employed in the definition of a retraction line‘free of entrapment’(V_r) and hence, a ‘nominal’ MP hysteresis loop scanning (MP-SHL-R(A’)) is constructed. The CPSM model have been used in MP-SHL-R(N)) scanning cycles applications to deduce the relevant intrinsic pore size distributions. These psds drawn on a 2-D and/or 3-D plots, that constitute the pore structure tomography, are compared graphically to those obtained by MP hysteresis loop scanning along the penetration line (Part I), Further the CPSM model, as applied in Part II, has been successfully used in regression trials of experimental MP hysteresis loop scanning data and generated the respective tomography spectra. It is concluded that given an MP overall penetration-retraction experimental data, the CPSM model can be best fitted over these data and hence achieve sensible predictions of pore structure tomography based on both MP scanning modes.     

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).     

Pore spectra from continuous scan mercury porosimetry

A method for obtaining pore spectra is described. Continuous pressure—volume data from mercury porosimetry were used to determine the volume distribution as a function of the intrusion and extrusion pressure or the pore radius for a number of porous samples.An explanation is offered for delayed intrusion of mercury into pores. Mercury vapor transfer has been postulated as a thermodynamically allowed mechanism in those few cases where pore size or constrictions prohibit liquid transfer.     

Mercury porosimetry of ceramics

Mercury porosimetry has been used in ceramics for the characterization of products and for studies of processing. Specifications including PSD (pore size distribution by mercury porosimetry) are now applied to magnesia refractories used in basic oxygen furnaces and to building brick which may be exposed to frost. Other products cited as examples are the silica fiber tile used on the space shuttle, plasma sprayed coatings, carbon composites and filters.In ceramic processing research, PSD has proved valuable for evaluating the firing of basic refractories, brick and sanitary ware. Pore growth during the early stages of sintering several materials was first identified by PSD. The character of clay agglomerates and the presence of alumina aggregates in compacts have been measured, the latter showing bimodal PSD. The progressive change in PSD while compacting glass spheres outlines the stages of compaction. The most frequent pore diameter in plaster slip casting molds correlates directly with plaster consistency.In dense or vitrified ceramics, errors may occur due to closed pores or pores with narrow openings. However, in ceramic compacts and highly porous ceramics, pores have several openings so PSD is a realistic measure of structure.     

Contact angle and damage during mercury intrusion into cement paste

The operant contact angle to be used for mercury intrusion porosimetry was measured directly by intrusion into specially prepared, cylindrical pores. It was found to vary for cement pastes of different ages, and for pastes containing flyash. It also changed when the paste was previously intruded and the mercury subsequently removed. Values of the contact angle ranged from 123° to 135°. The high pressures used during intrusion were found to reduce the pore volume of cement paste with the reduction being greater in the smaller pore (higher pressure) region. Distilling mercury from a paste was also found to alter the pore structure and this effect must be considered separately before alterations due only to intrusion are discussed.     

A generalized analysis for mercury porosimetry

A detailed analysis of mercury-intrusion data has been undertaken without specifying a particular pore shape. An equation, derived from a pore-size distribution function in generalized form, has been used to linearize the compression-corrected mercury-intrusion data of several samples on a log-log plot. Using log-log plots, volume changes due to sample compaction can be straightforwardly identified and then separated from volume changes due to mercury intrusion into pores.Equations have also been derived for calculating surface areas from the slope and intercept parameters of these log-log plots. These surface areas, which are compression-corrected and compaction-corrected, have agreed well with BET surface areas.Methods developed for mercury-intrusion porosimetry, to correct data for compression effects, linearize mercury-intrusion data, and calculate surface areas, have been effectively applied to water-intrusion porosimetry. As the hydrostatic pressure was increased on the water surrounding an untreated sample of macroporous polystyrene, water intruded the pores of this sample with a contact angle near 112°.     

A new approach for the characterization of the pore structure of dual porosity rocks

For the realistic representation of the pore space of dual porosity rocks, a new method of pore structure characterization is developed by combining experimental Hg intrusion/retraction curves with back-scattered scanning electron microscope (BSEM) images and inverse modeling algorithms. The pore space autocorrelation function measured by processing the digitized BSEM images is combined with the surface fractal dimension estimated from the high pressure Hg intrusion (MIP) data to derive a synthetic small-angle neutron scattering (SANS) intensity function, the inversion of which provides a volume-based pore body radius distribution (PBRD). The volume-based PBRD is fitted with a multimodal number-based PBRD consisting of two component distributions: one representing the macroporosity and another one representing the microporosity. Based on arguments of percolation theory, analytical mathematical models are developed to describe the Hg intrusion in and retraction from dual pore networks in terms of the complete PBRD, pore throat radius distribution (PTRD) of macroporosity, drainage accessibility functions (DAFs) of both porosities, and imbibition accessibility functions (IAFs) of both porosities. Inverse modeling of the Hg intrusion data set enables us to estimate the PTRD and DAFs. Inverse modeling of the Hg retraction datasets enables us to estimate a set of primary and secondary IAFs. The method is demonstrated by the pore structure characterization of four outcrop samples of carbonate and sandstone rocks. Analytic approximate equations developed from the critical path analysis (CPA) of percolation theory enable us to calculate explicitly the absolute permeability and the formation factor of the porous rocks using the estimated parameters (PBRD, PTRD, DAF) of the macroporosity. The measured permeability of cores is predicted satisfactorily and observed discrepancies may be attributed to large length-scale macro-heterogeneities which are not evident in BSEM images and Hg porosimetry data.