Pore Size Distribution Function Research Articles

World of nanostructures - nanotechnology, surface properties of chosen nanomaterials

The paper presents the basic information on nanotechnology and the recent results of studies of physicochemical properties of chosen nanomaterial surfaces (montmorillonites, carbon nanotubes, smart surfaces) by means of complex measuring methods. Physicochemical properties of nanomaterial surfaces by means of the special thermogravimetry Q-TG, sorptometry, porosimetry, atomic force microscopy (AFM) and scanning electron micrograph (SEM) methods were investigated. A numerical and analytical procedure for the evaluation of total heterogeneous properties (desorption energy distribution and pore-size distribution functions) on the basis of liquid thermodesorption from the sample surfaces under the quasi-equilibrium conditions and sorptometry techniques are presented. The evaluation of the fractal dimensions of nanotubes using the sorptometry, porosimetry, thermogravimetry Q-TG and AFM data are presented. The comparison of fractal coefficients calculated based on them with the results from Q-TG, sorptometry, porosimetry and AFM gave good agreement.

Behavior of Acetonitrile Confined to Mesoporous Silica Gels As Studied by 129Xe NMR: A Novel Method for Determining the Pore Sizes

129Xe NMR spectra of xenon dissolved in acetonitrile confined into three mesoporous silica gels with nominal pore diameters of 40, 60, and 100 A have been measured over the temperature range 170-245 K. The spectra consist of a number of lines, which contain detailed information on the system. The most interesting result is that the chemical shift of a particular signal observed below the melting point of confined acetonitrile is highly sensitive to the pore size, and hence its shape is sensitive to the pore size distribution function. This signal originates from the xenon atoms sited in very small cavities built up inside the pores during the freezing transition. It can be used to determine the size or even the size distribution function of the pores. In addition, the emergence of this signal reveals the phase transition temperature of acetonitrile inside the pores, which can also be used to determine the size of the pores. The difference in the chemical shifts of two other signals, which arise from xenon dissolved in bulk and confined acetonitrile, provides still another novel method for determining the size of the pores.

A method for predicting heat and moisture transfer through multilayered walls based on temperature and moisture content gradients

A mathematical formulation applied to a numerically robust solver is presented, showing that moisture content gradients can be used as driving forces for heat and moisture transport calculation through the interface between porous materials with different pore size distribution functions. For comparison purposes, several boundary conditions are tested—in order to gradually increase the discontinuity effects—and a detailed analysis is undertaken for the temperature and moisture content distributions and sensible and latent heat fluxes, when the discontinuity on the moisture content profile is taken or not into account.

Interaction of surfactants with ion-exchange membranes

In the present paper, we have compared the measuring results of the water content and electrotransport properties of the heterogeneous and perfluorinated homogeneous ion-exchange membranes with the variable saturation degree by surface-active counter-ions. Pore-size distribution functions for the heterogeneous membranes are investigated and the specific internal surface area is calculated. The key role of the surfactant-adsorption on the internal and external boundaries of the ion-exchange membranes is revealed. The correlation between percolation phenomena in the perfluorinated membrane with tetrabutylammonium ions and effects of the system transition to overlimiting state is found.

Characterization of physicochemical properties of high-temperature superconductor surfaces using nitrogen adsorption

Nitrogen adsorption measured at 77K was used to characterize the energetic and geometrical heterogeneity of high-temperature superconductor surfaces. The porosity of the solids (specific surface area, radii and volume of the pores, as well as the pore-size distribution function) was determined from adsorption data for a series of oxide superconductors ((RE)1.85Ce0.15CuO4−δ, RE=Pr, Nd, Sm; (RE)Ba2Cu3O7−δ, RE=Y, Er; HgBa2Ca2Cu3O8+δ). It is shown that the adsorption isotherms of all samples are S-shaped and belong to group II according to the Brunauer–Emmett–Teller (BET) classification. On the basis of the isotherms of nitrogen adsorption, fractal dimensions were determined.

Toward Solving the Unstable Linear Fredholm Equation of the First Kind: A New Procedure Called the Adsorption Stochastic Algorithm (ASA) and Its Properties

The paper consists of three main parts. In the first, a new “adsorption stochastic algorithm” (called ASA) for solving the unstable linear Fredholm integral equation of the first kind is proposed. In this program, some procedures of estimating the relative minimum in one dimension are tested. The newly developed algorithm is applied in the second part for reconstructing some pore size distribution functions (monomodal and multimodal). Moreover, the influence of a random noise on the stability of the solution of the inverse problem is studied. In the third part, the experimental verification of the above-mentioned method is presented. The results calculated by ASA are compared with those obtained by applying advanced regularization CONTIN and INTEG algorithms. It is shown that the developed ASA method always provides stable and very similar results to Tikhonov's regularization method. Moreover, the ASA computations obtained for the Nguyen and Do local isotherms as the kernel are very similar to the results calculated by the most sophisticated regularization density functional theory software. Summing up, the method can be very useful for evaluating the pore size distribution from experimental data.

Nanostructure and properties of ZnO films produced by the pyrosol process

Indium doped ZnO films were deposited by the pyrosol process on glass substrates at different temperatures from solutions containing In/Zn molar ratios up to 10%. The nanostructure of the films was investigated using grazing-incidence small-angle X-ray scattering (GISAXS). The mass density was determined by X-ray reflectivity and the composition by X-ray photoelectron spectroscopy. The GISAXS measurements revealed an anisotropic pattern for films deposited at 573 and 623 K and a isotropic one for those deposited at higher temperatures. The anisotropic patterns indicate the presence of elongated nanopores with their long axes perpendicular to the film surface. In contrast, the isotropic nature of GISAXS patterns of films grown at high temperatures (673 and 723 K) suggests the presence of spherical voids. The pore size distribution function determined from the isotropic patterns indicates a multimodal size distribution. On the other hand, the measured mass density of the doped films with isotropic nanotexture is higher than that of the anisotropic films while the electric resistivity is significantly lower. This is in agreement with the detected strong reduction of the void density and specific surface area at approximately constant pore size.

Estimation of the pore-size distribution function from the nitrogen adsorption isotherm. Comparison of density functional theory and the method of Do and co-workers

A comparative analysis of the results for the estimation of the pore-size distribution based on the methods of Do and co-workers (ND) and density functional theory (DFT) is given. A new algorithm (ASA, Adsorption Stochastic Algorithm) is adopted and it is shown that this algorithm can be successfully applied for the determination of the PSD curve from the ND method. The obtained results show that, generally, the ND and DFT methods lead to almost the same PSD curves and this similarity is observed for carbons of different origin and possessing different pore structures. However, if the contribution of micropores to the PSD increases, the differences in the fit of ND and DFT to the experimental data are more pronounced.

Combination of SANS and 3D stochastic reconstruction techniques for the study of nanostructured materials

Ceramic nanostructured materials have recently received scientific and industrial interest due to their unique properties. A series of such nanoporous structures were characterised by SANS techniques. The resulting scattering curves were analysed to obtain basic structural information regarding the pore size distribution and autocorrelation function of each material. Furthermore, stochastic reconstruction models were employed to generate 3D images with the same basic structural characteristics obtained from SANS. Finally, simulation results of permeation on the reconstructed images provide very good agreement with experimental data.

Parallel tempering method for reconstructing isotropic and anisotropic porous media

A parallel tempering method was developed for the reconstruction of porous media using information extracted from 2D digitized microscopy images. The method affords significant improvement over simulated annealing, can be easily parallelized, and works generally for isotropic and anisotropic structures. Inclusion of the pore size distribution function in the reconstruction method was decisive for best results. The validity of the results has been checked by comparing cluster size distribution functions, percolation, and transport properties between original and reconstructed images.

The Application of a CONTIN Package for the Evaluation of Micropore Size Distribution Functions

This paper consists of three main parts. In the first part, the new model isotherm equations for adsorption on heterogeneous microporous solids are presented, using different (and never before utilized) pore-size distribution functions. In the second part, freshly developed adsorption isotherms are applied to check the power of the CONTIN algorithm. Finally, in the third part, the micropore-size distributions (MPSD) of two strictly microporous activated carbons (of synthetic origin) are calculated on the basis of different adsorption models and numerical methods of solving the global adsorption isotherm equation. The following methods are put to use: the recently developed gamma-type adsorption isotherm (GTAI) equation, applied for the first time in adsorption studies, the modified Galerkin method, CONTIN, and, finally, the density functional theory. The usefulness of CONTIN and the similarities between the results of the applied methods are discussed. The influence of the heterogeneity parameter (n) of the Dubinin−Astakhov equation as well as the relation between characteristic adsorption energy and pore diameter on the shape and position of the MPSD is considered. Some remarks on the optimization process of fitting GTAI to experimental data are also given.

Modeling of Chemical Vapor Infiltration Rate Considering a Pore Size Distribution

To analyze chemical vapor infiltration (CVI) rates, a simulation model (PC model) was proposed, which is capable of considering difficulties of densification in the internal regions of porous bodies and the pore closure phenomena. In the model, a fictitious tapered pore is constructed based on the pore size distribution of the preform body, and variation of the pore shape during the process is calculated. For simulation study, fictitious tapered pores were constructed using different pore size distribution functions of Gaussian, δ‐function, and flat distribution, and their shapes and characteristics were compared. In the case of the Gaussian flat distribution (large dispersion), the fraction of fine pores was large and these pores became closed near their mouths. Reconversion of temporal fictitious pore shape into the pore distribution function was attempted and the PC model was successfully applied to monitor variations in the pore size distributions during the CVI process.

Pore size distribution model derived from a modified DR equation and simulated pore filling for nitrogen adsorption at 77 K

The Dubinin–Radushkevich (DR) equation has been used extensively to characterize microporous materials. However, it assumes a continuous pore filling mechanism and does not reduce to Henry’s law at low adsorptive pressures. In this study, we modify the DR equation by introducing adsorption density and the correlation between pore filling pressure and critical pore size for N 2 adsorption at 77 K. This modified DR equation is used as the local isotherm in the generalized adsorption isotherm (GAI) to interpret N 2 adsorption isotherm at 77 K. To solve the GAI, a modified normal distribution is developed and used as a distribution function of pore size on the domain [0, ∞). Pore size distribution (PSD) analyses of several adsorbent samples are carried out using this model. The results are found comparable with other popular PSD methods (e.g. MP, JC, HK and DFT).

Improved Pore-Size Analysis of Carbonaceous Adsorbents

An improvement was proposed for the pore-size analysis of active carbons based on low-temperature (77 K) nitrogen adsorption isotherms measured over a wide range of relative pressures (5 × 10−7–0.995). It was shown that the applicability of the Barrett, Joyner and Halenda (BJH) computational method based on the Kelvin equation could be extended significantly towards small mesopores and large micropores when a proper t-curve was used to represent the film thickness of nitrogen adsorbed on the carbon surface. It was proposed that the aforementioned t-curve be obtained from the nitrogen adsorption isotherm at 77 K on a macroporous carbon black by fitting its multilayer part to the calibrated t-curve for nitrogen adsorbed at 77 K on a macroporous silica. To date, the Harkins–Jura or Halsey t-curves have been used to describe the pressure-dependence of the film thickness. This appears to be inaccurate, especially in the range of low relative pressures. It was shown that this inaccuracy makes the pore-size analysis questionable. However, the t-curve proposed in this work gave the pore-size distribution functions for the carbons studied thereby reproducing the total pore volume and showing realistic behaviour in the range at the borderline between micropores and mesopores.

Effect of particle-size and pore-size distributions in cross-flow filtration

This paper presents the results of a finite-element model of cross-flow filtration that examines both radial and axial variations in velocity and concentration for different particle-size and pore-size distributions modeled using a lognormal distribution function. Also examined was the roll of particle diffusion. Assuming that the properties of the fluid were independent of the particle concentration allowed the Navier–Stokes equations to be solved independently from the mass transport problem. Flow at an inlet Reynolds number of 2000 was examined at constant inlet pressure and pressure outside the membrane. Once the velocity profiles had been determined, concentration profiles and permeate concentration were calculated for monodisperse particles as a function of pore-size distribution. The permeate concentrations were then numerically integrated to determine the permeate concentration of polydisperse particles. These results demonstrate that a six-order-of-magnitude reduction in the particulate concentration in the permeate can only be achieved when both the pore-size and particle-size distributions are narrow. Furthermore, they provide guidance for the average pore size necessary to achieve a specified level of purity in the permeate depending on the particle-size distribution and operating conditions of the filtration unit.

Investigations into provenance and properties of ancient building sandstones of the Zittau/Görlitz region (Upper Lusatia, Eastern Saxony, Germany)

AbstractMineralogical and technical properties were investigated of building sandstones from ancient monuments of the Zittau/Görlitz region (Germany) as well as material from potential source quarries. The complex study included macroscopic rock description and detailed investigations by polarizing microscopy (phase composition, texture, grain size distribution), cathodoluminescence (quartz types, feldspar and kaolinite content), scanning electron microscopy (accessories, pore cement, diagenetic grain surface features) as well as the analysis of open macroporosity (total water uptake) and the pore size distribution function (Hg porosimetry). For the first time, mineralogical and technical data were obtained for building sandstones of the Zittau region. The results not only confirmed earlier conjectures concerning different source areas for the ancient building sandstones of the Zittau and Görlitz area but also allowed the unequivocal assignment of historically used material to specific sandstone occurrences. The data obtained provide a comprehensive basis for the interpretation of weathering damage suffered by the historical monuments and give useful hints for their successful conservation and reconstruction.

An adsorption equilibrium model for Type 5 isotherms

Vapor adsorption on porous materials for non-wetting adsorbent–adsorbate pairs, characterized by a Type 5 isotherm, results in low loading at low relative pressure and increased loading due to capillary condensation behavior at higher relative pressure. The relationship between capillary condensation and the Kelvin equation suggests that a simple expression can be developed in which the adsorption equilibrium is obtained from an integrated pore size distribution function. This new expression is shown to describe the Type 5 isotherms of water adsorption on activated carbon. In addition, this expression has useful properties including: (1) finite saturation limit, (2) readily calculated Henry’s constant, and (3) readily calculated heat of adsorption, (4) can be written explicitly in terms of partial pressure or adsorbed phase loading and (5) parameter values attributable to the distribution function.

Porosity of silicon carbide ceramics

A set of ceramic samples based on silicon carbide with substantially varying integral porosity (from 1 to 10 %) was studied. The pore size distribution was examined by optical microscopy (for pores ranging from 10 mm to hundreds of microns in size), scanning electron microscopy (0.5 - 10 mm), and small-angle X-ray scattering (0.04 - 0.20 mm). The obtained pore size distribution function was used to estimate the integral porosity of ceramics, which was compared with the estimates of porosity obtained by the dilatometric technique. Relative contributions of large, small, and fine pores into the integral porosity of ceramics were found. The average pore sizes and average distances between them were estimated for each range of pore sizes.

Sieve mechanism of microfiltration separation

Abstract A theoretical model of dead-end microfiltration purification (MFP) of dilute suspensions is suggested. The model is based on a sieve mechanism of MFP and takes into account the probability of membrane pore blocking during MFP of dilute colloidal suspensions. An integro-differential equation (IDE) that includes both the membrane pore size and particle size distribution functions is deduced. According to the suggested model a similarity property is deduced, which allows one to predict the flux through the membrane as a function of time for any pressure and dilute concentration based on one experiment at a single pressure and concentration. For a narrow pore size distribution in which one pore diameter predominates (track-etched membranes), the IDE is solved analytically and the derived equation is in a good agreement with the measurements on four different track-etched membranes. A simple approximate solution of the IDE is deduced and that approximate solution as well as the similarity property of MFP process is in a good agreement with the measurements on a commercial Teflon microfiltration membranes.

Textural Analysis of Sulphated ZrO2–SiO2 Sol–Gel Catalytic Supports by N2 Sorption and X-Ray Diffraction

The textural properties of sulphated ZrO2-SiO2 catalytic supports of different compositions were investigated through N2 sorption and X-ray diffraction (conventional and SAXS) methods. The materials were synthesised by the sol-gel procedure from a mixture of zirconium(IV) tert-butoxide and tetraethyl orthosilicate. The final products were obtained after drying at 125oC followed by calcination at 400oC. The porous structures of the substrates were found to depend on their composition: at low zirconia contents these were formed by slit cavities while at high ZrO2 concentrations the void structure became open; both cavities and necks were of similar size. In the first case, the pore size distribution function could be obtained from an analysis of the ascending boundary curve of the N2 isotherm since adsorption occurred on a flat surface. In the second case, a unique pore-size distribution was obtained either from the ascending or descending boundary curves of the N2 isotherm. A tubular geometry seemed approp...