Calculation Of Pore Size Distribution Research Articles

Comparison of heterogeneous pore models QSDFT and 2D-NLDFT and computer programs ASiQwin and SAIEUS for calculation of pore size distribution

The pore size distributions (PSD) of selected carbons were calculated from their nitrogen adsorption isotherms using both the QSDFT model implemented in ASiQwin version 3.0 software (Quantachrome Instruments) and 2D-NLDFT model implemented in SAIEUS software (Micromeritics). The results showed that both the QSDFT and the 2D-NLDFT methods give similar PSDs despite the different methods for accounting for the heterogeneity of the carbon adsorbent. The characteristic features of the methods and software were discussed and possible improvements were proposed.

Dual gas analysis of microporous carbons using 2D-NLDFT heterogeneous surface model and combined adsorption data of N2 and CO2

Knowledge of the pore structure of carbon materials including micropores is crucial for applications such as double layer supercapacitors, gas separation, and other applications requiring high specific surface area materials. High surface area is always associated with fine micropores. The pore size distribution (PSD) of microporous carbons is usually evaluated from nitrogen adsorption isotherms measured at 77K in the relative pressure range from 10−7 to 1. Due to the very slow gas diffusion into fine pores at cryogenic temperatures and low pressures, the adsorption measurements may be extremely time consuming and sometimes inaccurate when the adsorption equilibrium is difficult to achieve during the measurement. In this work, we discuss an approach in which the carbon PSD is calculated from the combined N2 and CO2 data measured in the pressure range from 1 to 760Torr. Under such conditions, the diffusion into micropores is usually fast and equilibration times are short for both measurements. In the PSD calculations we use 2D-NLDFT models for carbons with heterogeneous surfaces (J. Jagiello and J.P. Olivier, Adsorption19, 2013, 777–783). We show that both isotherms can be fitted simultaneously with their corresponding models and as a result the unified PSD can be obtained.

Uncertainty in pore size distribution derived from adsorption isotherms: I. Classical methods

Procedures for propagation of uncertainty in pore size distribution calculation based on classical methods for both micro and mesoporous materials are described. Uncertainty in experimental adsorption isotherm data and uncertainty in temperature are introduced as the main sources for uncertainty in height and position of peaks of PSD determined via classical mesopore size distribution determination method. Uncertainty in PSD derived from classical micropore size distribution methods mainly arises from uncertainty in experimental isotherm data. Calculation step size is shown to have some effects on magnitude of uncertainty in micropore calculation. Micropore size distribution calculations are also highly sensitive to the adsorptive molecular diameter.

Improved analytic methods for coal surface area and pore size distribution determination using 77 K nitrogen adsorption experiment

77K nitrogen adsorption was the most widely used technique for determining surface area and pore size distribution of coal. Brunauer–Emmett–Teller (BET) and Barrett–Joyner–Halenda (BJH) model are commonly used analytic methods for adsorption/desorption isotherm. A Chinese anthracite coal is tested in this study using an improved experimental method and adsorption isotherm analyzed by three adsorption mechanisms at different relative pressure stages. The result shows that the micropore filling adsorption predominates at the relative pressure stage from 6.8E−7 to 9E−3. Theoretically, BET and BJH model are not appropriate for analyzing coal samples which contain micropores. Two new analytic procedures for coal surface area and pore size distribution calculation are developed in this work. The results show that BET model underestimates surface area, and micropores smaller than 1.751nm account for 35.5% of the total pore volume and 74.2% of the total surface area. The investigation of surface area and pore size distribution by incorporating the influence of micropore is significant for understanding adsorption mechanism of methane and carbon dioxide in coal.

Composite materials: Textural characteristics

Calculation of pore size distribution of complex materials needs special approaches. • Self-consistent regularization is effective tool to analyze data for complex materials. • Model with slit/cylindrical pores and voids between nanoparticles is appropriate for composites. • The SCV/SCR method gives better results than NLDFT or QSDFT for composites. A self-consistent regularization (SCR) procedure applied to integral adsorption equations based on a complex model with slit-shaped and cylindrical pores and voids between spherical nonporous particles packed in random aggregates (SCV model) for two or three types of components (activated carbon, carbon black, silica gel, fumed silica) in composites gives more clear pictures of pore size distributions (PSD) than nonlocal density functional theory (NLDFT) or quenched solid DFT (QSDFT) methods. Results of this approach for individual adsorbents are comparable with the results of NLDFT or QSDFT methods using complex pore models (slit/cylindrical or slit/cylindrical/spherical pores). The SCV/SCR method is useful to study the textural features of hybrid materials, the PSD of which is difficult to be calculated using standard approaches. The PSD of complex materials can also be estimated using (1) high-resolution microscopic methods ( e.g. HRTEM) with software (Fiji/ImageJ) used for quantitative treatment of images; (2) cryoporometry based on low-temperature 1 H NMR spectroscopy; and (3) small angle X-ray scattering (SAXS). Results of these methods can effectively amplify results of the standard adsorption methods.

Characterization of Porous Materials by Magnetic Relaxometry in the Earth’s Field

In this paper, it is shown how free induction decay signals recorded in the Earth’s magnetic field from water protons confined in porous media can be used to derive transversal relaxation times (T 2) and their distributions. After T 2 determination of six sintered glass samples with various pore sizes, the common theoretical model can be fitted to the data set. The T 2 distribution of water protons in a bimodal porous system is analyzed and compared to mercury porosimetry results. The implications for the calculation of pore sizes and pore size distributions of porous media by this method are discussed.

Pore size distribution calculation from 1H NMR signal and N2 adsorption–desorption techniques

The pore size distribution (PSD) of nano-material MCM-41 is determined using two different approaches: N2 adsorption–desorption and 1H NMR signal of water confined in silica nano-pores of MCM-41. The first approach is based on the recently modified Kelvin equation [J.V. Rocha, D. Barrera, K. Sapag, Top. Catal. 54(2011) 121–134] which deals with the known underestimation in pore size distribution for the mesoporous materials such as MCM-41 by introducing a correction factor to the classical Kelvin equation. The second method employs the Gibbs–Thompson equation, using NMR, for melting point depression of liquid in confined geometries. The result shows that both approaches give similar pore size distribution to some extent, and also the NMR technique can be considered as an alternative direct method to obtain quantitative results especially for mesoporous materials. The pore diameter estimated for the nano-material used in this study was about 35 and 38 Å for the modified Kelvin and NMR methods respectively. A comparison between these methods and the classical Kelvin equation is also presented.

Quenched solid density functional theory method for characterization of mesoporous carbons by nitrogen adsorption

Quenched solid density functional theory (QSDFT) model for characterization of mesoporous carbons using nitrogen adsorption is extended to cylindrical and spherical pore geometries. The kernels of theoretical isotherms in the range from 0.4 to 50 nm are constructed accounting for different possible variations of the pore shapes in micropore and mesopore regions. The results of QSDFT method are illustrated with experimental data on adsorption on novel CMK-3 and 3DOm carbons. The proposed method is recommended for pore size distribution calculations for micro–mesoporous carbons obtained through various templating mechanisms.

On the application of focused ion beam nanotomography in characterizing the 3D pore space geometry of Opalinus clay

The evaluation and optimization of radioactive disposal systems requires a comprehensive understanding of mass transport processes. Among others, mass transport in porous geomaterials depends crucially on the topology and geometry of the pore space. Thus, understanding the mechanism of mass transport processes ultimately requires a 3D characterization of the pore structure. Here, we demonstrate the potential of focused ion beam nanotomography (FIB-nT) in characterizing the 3D geometry of pore space in clay rocks, i.e. Opalinus clay. In order to preserve the microstructure and to reduce sample preparation artefacts we used high pressure freezing and subsequent freeze drying to prepare the samples. Resolution limitations placed the lower limit in pore radii that can be analyzed by FIB-nT to about 10–15 nm. Image analysis and the calculation of pore size distribution revealed that pores with radii larger than 15 nm are related to a porosity of about 3 vol.%. To validate the method, we compared the pores size distribution obtained by FIB-nT with the one obtained by N 2 adsorption analysis. The latter yielded a porosity of about 13 vol.%. This means that FIB-nT can describe around 20–30% of the total pore space. For pore radii larger than 15 nm the pore size distribution obtained by FIB-nT and N 2 adsorption analysis were in good agreement. This suggests that FIB-nT can provide representative data on the spatial distribution of pores for pore sizes in the range of about 10–100 nm. Based on the spatial analysis of 3D data we extracted information on the spatial distribution of pore space geometrical properties.

Dependence of pore size on catalyst concentration used in synthesis carbon nanotubes

Single-walled carbon nanotubes using chemical vapor deposition with two different concentrations of catalyst were synthesized. Characterization of samples with electron microscopy and Raman spectra has shown that there are a large number of single-walled carbon nanotubes distributed evenly in samples with the range of distribution diameters ranging between 1.10 and 1.45 nm. Nitrogen adsorption at 77 K and pressure up to 1 bar were measured in both samples. Results shows that the surface area depends on the concentration of iron catalyst used for making the nanotube. Calculation of pore size distribution in micropore and mesopore range of samples shows that the shape of isotherm and also size of pores in the samples depend on the catalyst concentration. Sample with more catalyst has a wider pore

Moisture sorption properties of chitosan

The moisture equilibrium isotherms of chitosan were determined at 20, 30, 40, 50 and 60 °C, using the gravimetric static method. Experimental data were analyzed by the GAB, Oswin, Halsey and Smith equations. Isosteric heat and differential entropy of sorption were determined from the GAB model using the Clausius-Clapeyron and Gibbs-Helmholtz equations, and pore size distribution was calculated by the Kelvin and Halsey equations. The GAB and Oswin equations showed best fit to the experimental data with R 2 ≈ 99% and low mean relative deviation values ( E% < 10%). Monolayer moisture content values (from 0.12 to 0.20 kg kg −1) and water surface area values (from 450 to 700 m 2 g −1) decrease with increasing temperature. Isosteric heat and differential entropy of sorption were estimated as a function of moisture content. The Kelvin and Halsey equations were adequate for calculation of pore size distribution, which varied from 0.5 to 30 nm.

Quenched solid density functional theory and pore size analysis of micro-mesoporous carbons

We present a new model of adsorption on micro-mesoporous carbons based on the quenched solid density functional theory (QSDFT). QSDFT quantitatively accounts for the surface geometrical inhomogeneity in terms of the roughness parameter. We developed the QSDFT models for pore size distribution calculations in the range of pore widths from 0.4 to 35 nm from nitrogen at 77.4 K and argon at 87.3 K adsorption isotherms. The QSDFT model improves significantly the method of adsorption porosimetry: the pore size distribution (PSD) functions do not possess gaps in the regions of ∼1 nm and ∼2 nm, which are typical artifacts of the standard non-local density functional theory (NLDFT) model that treats the pore walls as homogeneous graphite-like plane surfaces. The advantages of the QSDFT method are demonstrated on various carbons, including activated carbons fibers, coal based granular carbon, water purification adsorbents, and mirco-mesoporous carbon CMK-1 templated on MCM-48 silica. The results of PSD calculations from nitrogen and argon are consistent, however, argon adsorption provides a better resolution of micropore sizes at low vapor pressures than nitrogen adsorption.

Resistivity measured by direct and alternating current: why are they different?

Abstract. Mathematical modeling of a little known model of IP referred to as "induced polarization caused by constrictivity of pores" was developed. Polarization occurs in all types of rocks if surface areas and transfer numbers are different for connected pores. The duration of the polarization process depends on two parameters: pore radii of connected capillaries and transfer numbers. During the polarization process all contacts between pores of different transfer numbers will be blocked and the electrical current will flow through the remaining canals. Two phenomena control the amplitude of potential difference at time-on: 1. Successive blockage of pores increases the resistivity of sediments and results in increased measured potential difference. 2. Excess concentration of electrolyte at the boundaries between pores with different radii provides an additional potential. The amplitude of the potential difference (voltage) of such rocks not only depends on solutions filling pore spaces, porosity and tourtuosity of pores channels, but also on ion mobility, diffusion coefficient, and difference of transfer numbers. During time-on a voltage is occurred due to flowing current Ucurr (t) and excess concentration Uexcess (t) at the contacts. However during the time-off only the excess of concentration Uexcess (t) is involved in the diffusion process which tends to level the ion concentration along the pores. It was found that the measured chargeability is proportional to the porosity. Blockage of pores and excess/loss ions at the contacted pores control this physical parameter. However the relationship between resistivity and porosity is very complicated. Mathematical modeling and laboratory measurements both confirmed the membrane IP effect diminishing with increasing salinity of fluid filled pores of rocks. Membrane polarization does not exist on high frequency of electrical current. As a result the resistivity measured by direct and alternating current is different. The new algorithm was tested on laboratory measurements data showing its good agreement with theory. The calculation of pore size distribution using IP laboratory data has been presented. The definition of the membrane IP effect is: "Membrane IP is the successive blockage of inter-pore connections due to the excess distribution of ions during current flow".

The cluster model: A hierarchically-ordered assemblage of random-packing spheres for modelling microstructure of porous materials

A new structural model based on the premises widely used for describing the structure of random materials, and especially aerogels, is introduced. Aerogels are described as an assemblage of randomly-packed spheres in several hierarchically-ordered levels. A new algorithm has been developed for constructing structural models from these premises using computer simulation. Subsequently, several techniques based both on the Monte Carlo technique and on geometrical considerations for characterizing real systems have been simulated, and textural parameters of the models have been obtained, including specific surface area, specific porous volume and the apparent density of the systems. This characterization process yields a set of parameters used for testing the capacity of the models to reproduce the structure of several real systems, like aerogels. Special attention has been paid to the pore size distribution calculations: the Monte Carlo integration and the triangulation algorithms have been compared.

How realistic is the pore size distribution calculated from adsorption isotherms if activated carbon is composed of fullerene-like fragments?

A plausible model for the structure of non-graphitizing carbon is one which consists of curved, fullerene-like fragments grouped together in a random arrangement. Although this model was proposed several years ago, there have been no attempts to calculate the properties of such a structure. Here, we determine the density, pore size distribution and adsorption properties of a model porous carbon constructed from fullerene-like elements. Using the method proposed recently by Bhattacharya and Gubbins (BG), which was tested in this study for ideal and defective carbon slits, the pore size distributions (PSDs) of the initial model and two related carbon models are calculated. The obtained PSD curves show that two structures are micro-mesoporous (with different ratio of micro/mesopores) and the third is strictly microporous. Using the grand canonical Monte Carlo (GCMC) method, adsorption isotherms of Ar (87 K) are simulated for all the structures. Finally PSD curves are calculated using the Horvath-Kawazoe, non-local density functional theory (NLDFT), Nguyen and Do, and Barrett-Joyner-Halenda (BJH) approaches, and compared with those predicted by the BG method. This is the first study in which different methods of calculation of PSDs for carbons from adsorption data can be really verified, since absolute (i.e. true) PSDs are obtained using the BG method. This is also the first study reporting the results of computer simulations of adsorption on fullerene-like carbon models.

Characterisation of porous media by the virtual capillary condensation method

A computational methodology for the calculation of pore size distribution from three-dimensional digitally represented porous media of any pore morphology is described in this work. The methodology consists of two steps: simulation of capillary condensation for a given porous medium by the Volume of Fluid (VOF) method, and then evaluating the equivalent pore size distribution from the calculated dependence of the fraction of filled pore volume on the liquid–vapour interface curvature radius. The methodology is first demonstrated on the example of capillary condensation in a single ink-bottle pore and then used for the evaluation of pore size distribution in three classes of porous media with qualitatively different microstructure: model Vycor glass represented by Gaussian porous media; model nanoparticle assemblies; and model open-cell solid foams created by colloidal templating. The relationship between the shape of the pore-size distribution and the morphological features of the porous medium is discussed, and the mean pore radius evaluated by the virtual capillary condensation method is compared with the equivalent hydraulic radius in each case. The two radii are shown to be correlated, but the correlation coefficient is different, and therefore characteristic, for each class of porous media.

Testing the feasibility of using the density functional theory route for pore size distribution calculations of ordered microporous carbons

The pore size distribution (PSD) characterization of microporous carbon materials is traditionally obtained from the analysis of N2 adsorption isotherms at 77 K. In this work, we aim at testing the feasibility of using the density functional theory (DFT) route for PSD calculations of interconnected carbon pore structures. The first step of this study was to generate using an atomistic simulation approach, an ordered porous carbon material with well-defined porosity using NaY zeolite as a templating matrix. For this purpose, we used the grand canonical Monte-Carlo (GCMC) technique in which the carbon–carbon interactions were described within the frame of a newly developed tight binding approach and the carbon–zeolite interactions assumed to be characteristic of physisorption. We calculated the PSD of such a carbon porous material. At a second stage, we calculated nitrogen adsorption isotherms at different temperatures. These data were subsequently used as inputs for DFT calculation to obtain the PSD. Comparisons between DFT–PSD and MC–PSD are made. In particular, we show that with an appropriate wall thickness of two graphene layers, the PSD obtained from DFT calculation agrees well with that from direct analysis of the simulated structure.

Adsorption Hysteresis of Nitrogen and Argon in Pore Networks and Characterization of Novel Micro- and Mesoporous Silicas

We report results of nitrogen and argon adsorption experiments performed at 77.4 and 87.3 K on novel micro/mesoporous silica materials with morphologically different networks of mesopores embedded into microporous matrixes: SE3030 silica with worm-like cylindrical channels of mode diameter of approximately 95 angstroms, KLE silica with cage-like spheroidal pores of ca. 140 angstroms, KLE/IL silica with spheroidal pores of approximately 140 angstroms connected by cylindrical channels of approximately 26 angstroms, and, also for a comparison, on Vycor glass with a disordered network of pores of mode diameter of approximately 70 angstroms. We show that the type of hysteresis loop formed by adsorption/desorption isotherms is determined by different mechanisms of condensation and evaporation and depends upon the shape and size of pores. We demonstrate that adsorption experiments performed with different adsorptives allow for detecting and separating the effects of pore blocking/percolation and cavitation in the course of evaporation. The results confirm that cavitation-controlled evaporation occurs in ink-bottle pores with the neck size smaller than a certain critical value. In this case, the pressure of evaporation does not depend upon the neck size. In pores with larger necks, percolation-controlled evaporation occurs, as observed for nitrogen (at 77.4 K) and argon (at 87.3 K) on porous Vycor glass. We elaborate a novel hybrid nonlocal density functional theory (NLDFT) method for calculations of pore size distributions from adsorption isotherms in the entire range of micro- and mesopores. The NLDFT method, applied to the adsorption branch of the isotherm, takes into account the effect of delayed capillary condensation in pores of different geometries. The pore size data obtained by the NLDFT method for SE3030, KLE, and KLE/IL silicas agree with the data of SANS/SAXS techniques.

Characterization of Micro-Mesoporous Materials from Nitrogen and Toluene Adsorption: Experiment and Modeling

Universal mechanisms of adsorption and capillary condensation of toluene and nitrogen on ordered MCM-41 and PHTS materials are studied by means of high-resolution experiments and Monte Carlo molecular simulations. A molecular simulation model of toluene adsorption in silica nanopores, which accounts for surface heterogeneity, and a hybrid molecular-macsroscopic method for pore size distribution (PSD) calculations have been developed. For a range of reference materials, the PSD results obtained from toluene isotherms are consistent with the results of nitrogen adsorption using the nonlocal density functional theory method.

Evaluation of slitlike porosity of carbon adsorbents

Deviations of a pore shape from a slitlike one were analyzed for a variety of carbon adsorbents on the basis of calculations of pore size distributions (PSDs) with respect to the pore volume ( f V( x)) used for estimation of the PSDs related to the specific surface area ( f S( x)) applying several models of pores: individual slitlike pores and mixtures of slitlike and cylindrical pores and gaps between spherical particles. The use of complex pore models allows us to diminish the difference between S BET and the specific surface area ( S sum) calculated from f S( x).