Calculation Of Pore Size Distribution Research Articles

Pore structure of glasses derived from a leachable borosilicate precursor

The aim of the present study was the pore structure characterization of porous glass derived from a leachable precursor. Two independent techniques were applied on this purpose. The interpretation of the results obtained by these techniques, i.e. thermoporometry and nitrogen porosimetry was indicative for their supplementary character in what concerns the calculation of pore size distributions. The experimental work described in this study gives an example for the monitoring of the compositional evolution of phase separating compact-glass precursors of porous glasses.

Predictive modelling of nanofiltration: membrane specification and process optimisation

An important challenge for nanofiltration processes is the development of predictive models that convey a fundamental understanding and simple quantification of the governing phenomena in a way that has the potential for industrial application. The paper reviews one such approach, including: the formulation of a mathematically consistent description of rejection and flux at nanofiltration pores, the inclusion in calculations of pore size distributions with pore size dependent physical properties, the linearisation of these models to facilitate rapid calculations, and the use of such calculations to specify membranes for technically demanding separations. The present achievements and future challenges for predictive modelling of nanofiltration processes are assessed.

Characterization of porous microstructure by x‐ray microtomography

AbstractKnowledge of the porous structure of amorphous material is of fundamental importance in calculating geometric parameters such as total porosity, pore size distribution and physical parameters related to fluid flow inside void space. This work involved the measurement of microstructural parameters of petroleum reservoir rocks and porous ceramic filters. Microtomographic measurements of samples were performed by employing an x‐ray tube. Bremsstrahlung radiation was filtered in transmission mode with an Sn filter at 58.5 and 28.3 keV. The beam width was about 80 µm at the sample position center. Images were analyzed in two ways. In the first method, transepts of the images were analyzed in order to calculate the total porosity by means of the average particle and media linear attenuation coefficients. In the second method, images were studied using image analysis software, named Imago, allowing the calculation of total porosity and pore size distribution. The total measured porosity of the filter C90 was 73.8, 71.1, 74.4 and 71.5% using the Archimedes method, simple gamma‐ray transmission, transept and image analysis of the microtomography at 28.3 keV, respectively. Measured total porosity for one of the sandstones was 23.23, 24.70, 23.43, 29.68, 29.65 and 27.80% using Hg and gas porosimetry, the Archimedes method, simple gamma‐ray transmission and transept analysis of the microtomography at 58.5 and 28.2 keV, respectively. Copyright © 2002 John Wiley & Sons, Ltd.

Characterization of nanoporous materials from adsorption and desorption isotherms

We present a consistent method for calculation of pore size distributions in nanoporous materials from adsorption and desorption isotherms, which form the hysteresis loop H1 by the IUPAC classification. The method is based on the nonlocal density functional theory (NLDFT) of capillary condensation hysteresis in cylindrical pores. It is implemented for the nitrogen and argon sorption at their boiling temperatures. Using examples of MCM-41 type and SBA-15 siliceous materials, it is shown that the method gives the consonant pore size distributions calculated independently from the adsorption and desorption branches of the sorption isotherm. The pore size distributions, pore volumes and specific surface areas calculated from nitrogen and argon data are consistent. In the case of SBA-15 materials, the method evaluates also the amount of microporosity. The results of the NLDFT method are in agreement with independent estimates of pore sizes in regular nanoporous materials.

Effect of Carbon Deposits on the Structure of Hybrid C/TiO2/SiO2 Adsorbents

The structural characteristics of pyrocarbon/X (X = fumed silica, mesoporous silica gel, fumed titania/silica, CVD-TiO2/fumed silica, CVD-TiO2/silica gel) prepared using several precursors [CH2Cl2, cyclohexene and TiO(AcAc)2, where Ac = acetylacetonate] were studied using the nitrogen adsorption/desorption method and an improved technique to allow the calculation of pore size distributions applying regularization procedures. Various pore models were used for the carbon phase. The pyrocarbon structure and distribution on the TiO2/SiO2 supports depends primarily on the structural features of the titania phase which exhibits catalytic activity in the pyrolysis of organic materials. The formation of relatively large concentrations of pyrocarbon typically reduces the porosity and specific surface area of the hybrid adsorbents produced.

Capillary condensation in MMS and pore structure characterization

Phenomena of capillary condensation and desorption in siliceous mesoporous molecular sieves (MMS) with cylindrical channels are studied by means of the non-local density functional theory (NLDFT). The results are compared with macroscopic thermodynamic approaches based on Kelvin–Cohan (KC) and Derjaguin–Broekhoff–de Boer (DBdB) equations. We show that: The KC equations, which constitute the basis of the traditional BJH method for the pore size distribution analysis, are in error even in pores as large as 20 nm. The DBdB equations with consistently determined thickness of the adsorbed layer (disjoining pressure isotherm) can be justified for pores wider than ≈7 nm in diameter. As the pore size decreases, the macroscopic arguments become less accurate, and the NLDFT and DBdB results differ significantly in pores smaller than ≈4 nm. The adsorption–desorption isotherms predicted by NLDFT are found to be in quantitative agreement with the experimental nitrogen (77 K) and argon (87 K) isotherms on MCM-41 type materials with pores larger than 5 nm. Therewith, the experimental desorption branch corresponds to the equilibrium capillary condensation/evaporation transition. The experimental adsorption branch corresponds to the spontaneous spinodal condensation, which occurs at the limit of stability of adsorption films. The NLDFT method has been developed for the calculation of pore size distributions from both the adsorption and desorption isotherms.

Determination of pore size distribution in thin films by ellipsometric porosimetry

We show that ellipsometric porosimetry can be used for the measurement of the pore size distribution in thin porous films deposited on top of any smooth solid substrate. In this method, in situ ellipsometry is used to determine the amount of adsorptive, which is adsorbed/condensed in the film. Changes in refractive index and film thickness are used to calculate the quantity of adsorptive present in the film. Room temperature porosimetry based on adsorption of vapor of organic solvents has been developed. In this article, a method of calculation of pore size distribution and results of measurements on mesoporous and microporous xerogel films is discussed. Examination of the validity of the Gurvitsch rule for various organic adsorptives (toluene, heptane, and carbon tetrachloride) is carried out to assess the reliability of measurements of pore size distributions by ellipsometric porosimetry.

Sieving Coefficient of Polysulfone Membrane and Calculation of Pore Size Distribution.

Sieving Coefficient of Polysulfone Membrane and Calculation of Pore Size Distribution.

Nitrogen Adsorption Study of MCM-41 Molecular Sieves Synthesized Using Hydrothermal Restructuring

Nitrogen desorption scanning hysteresis loops (DSHLs) for large-pore MCM-41 silicas (pore diameter from 4.0 to 6.5 nm) are reported for the first time. DSHLs for MCM-41 were compared with those of conventional mesoporous silicas and no appreciable differences were found, although hysteresis loops and DSHLs for the latter were usually broader. Since desorption behavior of conventional porous silicas is appreciably influenced by pore connectivity, the observed similarity in hysteresis behavior suggests single-pore “blocking effects” for MCM-41 due to variation of pore diameter along its nonintersecting channels. It was also shown that the steepness of nitrogen desorption branches at relative pressures close to 0.4 often results from proximity of the lower pressure limit of adsorption-desorption irreversibility and consequently it is not justified to consider it as an indication of narrow pore size distribution. Thus, application of desorption data in calculations of pore size distributions may be grossly misleading.

Characterisation of Low-K Dielectric Films by Ellipsometric Porosimetry

AbstractEllipsometric porosimetry (EP) is a simple and effective method for the characterization of the porosity (volume of both open and close pores), average pore size, specific surface area and pore size distribution (PSD) in thin porous films deposited on top of any smooth solid substrat e. Because a laser probe is used, small surface area can be analyzed. Therefore, EP can be used on patterned wafers and it is compatible with microelectronic technology. This method is a new version of adsorption (BET) porosimetry. In situ ellipsometry is used to determine the amount of adsorptive which adsorbed/condensed in the film. Change in refractive index is used to calculate of the quantity of adsorptive present in the film. EP also allows the study of thermal stability, adsorption and swelling properties of low-K dielectric films. Room temperature EP based on the adsorption of vapor of some suitable organic solvents and method of calculation of porosity and PSD is discussed. Examination of the validity of Gurvitsch rule for various organic adsorptives (toluene, heptane, carbon tetrachloride and isopropyl alcohol) has been carried out to assess the reliability of measurements of pore size distribution by the ellipsometric porosimetry.

Calculation of Pore Size Distributions of Activated Carbons from Adsorption Isotherms

The ability to determine whether a pore size distribution can be fitted to a given set of experimental data is relevant to the development of pore network models of the internal structure of activated carbons and other amorphous adsorbents. A closely related problem that arises when pore size distributions can be fitted to a given set of data is to determine suitable methods to calculate reliable, stable, and representative pore size distributions. This paper addresses both of these issues by presenting a procedure to determine whether a pore size distribution based on a specified model pore geometry can be fitted to a set of experimental data and then using this procedure, in conjunction with regularization techniques that stabilize the calculations, to determine statistically significant pore size distributions. This approach has been demonstrated using the adsorption of methane at 308 K onto BPL-activated carbon as a case study.

Calculation of Pore Size Distribution in the Ellipsometric Porosimetry: Method and Reliability

AbstractEllipsometric porosimetry allows measurement of the pore size distribution in a thin porous film deposited on top of any solid substrate. The most important concept of this technique is the use of in-situ ellipsometry to determine the amount of adsorbate adsorbed/condensed in the film. Changes in refractive index and film thickness are used for calculation of the amount of adsorbate. A room temperature porosimetry based on adsorption of vapours of some organic solvents has been developed. In this paper, a method of calculation of the pore size distribution and reliability of the ELP results is discussed and the validity of the Gurvitsch rule for organic adsorbates (toluene, heptane, CCl4) is examined. Porous silica films on top of Si wafers were used for this analysis.

Pore Size Analysis of MCM-41 Type Adsorbents by Means of Nitrogen and Argon Adsorption

Methods of nonlocal density functional theory (NLDFT), proposed recently for predictions of adsorption equilibrium and calculations of pore size distributions in micro- and mesoporous materials, were tested on reference MCM-41 materials. Five newly synthesized MCM-41 adsorbents with presumably uniform pore channels varying from 32 to 45 Å were characterized by X-ray diffraction (XRD), nitrogen adsorption at 77 K, and argon adsorption at 77 and 87 K. New sets of intermolecular interaction parameters of the NLDFT model for N2and Ar adsorption on MCM-41 were determined. The parameters were specified to reproduce the bulk liquid–gas equilibrium densities and pressures, liquid–gas interfacial tensions, and standard adsorption isotherms on nonporous surfaces in the multilayer adsorption region. The pore size distributions calculated from the desorption branches of the experimental isotherms measured at three different temperatures were consistent with each other. Comparison of the NLDFT-calculated pore sizes with XRD data showed that the thickness of pore walls in the MCM-41 samples under consideration varied from ca. 6 to 12 Å. We found no correlation between the pore size and the pore wall thickness. The results obtained support the NLDFT model as a suitable tool for characterizing nanoporous materials and predicting adsorption equilibrium. The MCM-41 samples studied can be used as references for adsorption measurements.

Thickness and Stability of Adsorbed Film in Cylindrical Mesopores

The adsorbed film in small cylindrical mesopores is studied by using MCM-41 samples of uniform cylindrical channels as model systems. It is found that at a given relative pressure, the smaller the pore radius, the thicker the adsorbed film is, as postulated by Broekhoff and De Beer. Thermodynamics analysis established that the stability of the adsorbed film is determined by interface curvature and the potential of interaction between adsorbate and adsorbent. A semiempirical equation is proposed to describe the state of stable adsorbed films in cylindrical mesopores. It is also shown to be useful in calculations of pore size distributions of mesoporous solids.

FT30 membranes of characterized porosities in the reverse osmosis organics removal from aqueous solutions

Removal of some organic pollutants from aqueous solutions by reverse osmosis using commercial FT30 membranes of characterized porosities was investigated. The pore size distribution analysis and calculation of the effective number of pores have shown the presence of numerous narrow unimodally distributed pores in the upper selective membrane layer. The organic pollutant removal by reverse osmosis is governed mostly by mutual interactions between the membrane material, solute and water molecules.

Comparison of Nitrogen Adsorption and Mercury Penetration Results. Pore Size Distributions for a Series of Mo-A12O3 Catalysis with Increasing MoO3 Content

Scanning electron microscopic data, X-ray diffraction patterns and porosity measurements are consistent with a structure for an Mo-A12O3 catalyst series containing a single surface layer of Mo up to the point where the Mo loadings exceed the amount required for a monolayer. For greater Mo loadings than required for a monolayer, three dimensional orthorhombic MoO3 is also present. The cumulative pore volume, on an alumina basis, does not appear to be significantly altered by MoO3 loadings up to about 15 wt.%. The BET surface area, on an alumina basis, remains constant with Mo loading. However, the apparent surface area calculated from mercury penetration data decreases with Mo loading. For these materials with cylindrical pores, the Broekhoff-deBoer model for the calculation of pore size distributions produced closer agreement to the mercury penetration pore size distribution. This is in contrast to materials composed of nonporous spheres where the Broekhoff-deBoer model provided poorer agreement to mercury penetration results than either the Cohan or a packed sphere model. The results show that, within a factor of two the pore size distributions calculated from nitrogen adsorption and mercury penetration data are comparable.

Capacitance Measurements of Adsorption Isotherms and Capillary Condensation of 4He in Nuclepore: Calculation of Pore Size Distributions

Adsorption isotherms have been directly measured for 4He adsorbed in Nuclepore filters of four different pore sizes using a capacitive technique. Here we report the adsorption and desorption isotherms for the nominal 2000 Å pore diameter. The isotherms show hysteresis as a function of pressure, which is predicted by Saam and Cole. We use these isotherms and the theory of Saam and Cole to obtain a distribution in pore sizes for the Nuclepore.

Theoretical models for size-exclusion chromatography and calculation of pore size distribution from size-exclusion chromatography data

Size-exclusion chromatography (SEC) calibration curves are calculated using a range of models starting from those with simple, uniform pore geometry and culminating in a computer-assembled model, consisting of random-size touching spheres. This final model provides an excellent correlation between experimental data obtained with Hypersil and theoretical prediction with virtually no adjustable parameters. Very good correlation is also obtained using the uniform-size random-sphere model of Van Krefeld and Van den Hoed. It is shown that SEC calibration curves can also be predicted with remarkable accuracy from mercury porosimetry data on the assumption that the matrix consists of an assembly of cylindrical channels having the same pore-volume distribution as that provided by mercury porosimetry. A simple mathematical inversion of this procedure enables the pore size distribution to be precisely determined from any SEC calibration curve. A serious error in previous procedures is noted and corrected.

Method for the calculation of effective pore size distribution in molecular sieve carbon.

A method for the calculation of effective pore size distribution from adsorption isotherms in molecular-sieve carbon is described. This method is more exact theoretically as well as practically than previously described methods. An average potential function has been determined inside the slit-like pores. With the help of this function the doubtful use of the Kelvin equation can be avoided at the scale of molecular dimensions. The method gives poor values for the larger pores but can be combined with the well-known Dollimore-Heal method at a pore size of 1.34 nm. Calculation is possible over a wide range of pore sizes. The calculation is shown through two examples from N2 isotherms at 77.4K. The model can be extended to other pore shapes as well as to other adsorbent-adsorbate pairs.

Skin layer characterization of anisotropic membranes for ultrafiltration

A method for determining the separation curve based on molecular dimensions is described which allows calculation of the approximate pore size distribution of membranes and characterization of the skin layer of asymmetric membranes. The characteristics describing a membrane in the pressure-free state are discussed.