Padé approximants for the acoustical properties of rigid frame porous media with pore size distributions

Expressions for the viscosity correction function, and hence bulk complex impedance, density, compressibility, and propagation constant, are obtained for a rigid frame porous medium whose pores are prismatic with fixed cross-sectional shape, but of variable pore size distribution. The lowand high-frequency behavior of the viscosity correction function is derived for the particular case of a log-normal pore size distribution, in terms of coefficients which can, in general, be computed numerically, and are given here explicitly for the particular cases of pores of equilateral triangular, circular, and slitlike cross-section. Simple approximate formulae, based on two-point Pade´ approximants for the viscosity correction function are obtained, which avoid a requirement for numerical integration or evaluation of special functions, and their accuracy is illustrated and investigated for the three pore shapes already mentioned

Pore size distributions derived from adsorption isotherms, immersion calorimetry, and isosteric heats: A comparative study

We compare the pore size distribution of a well-characterized activated carbon derived from model-dependent, adsorption integral equation (AIE) methods with those from model-independent, immersion calorimetry and isosteric heat analyses. The AIE approach applied to nitrogen gave a mean pore width of 0.57 nm; the CO2 distribution exhibited wider dispersion. Spherical model application to CO2 and diffusion limitations for nitrogen and argon were proposed as primary reasons for inconsistency. Immersion enthalpy revealed a sharp decrease in available area equivalent to a cut-off due to molecular exclusion when the accessible surface was assessed against probe kinetic diameter. Mean pore width was identified as 0.58 ± 0.02 nm, endorsing the underlying assumptions for the nitrogen-based AIE approach. A comparison of the zero-coverage isosteric heat of adsorption for various non-polar adsorptives by the porous test sample was compared with the same adsorptives in contact with a non-porous reference adsorbent, leading to an energy ratio or adsorption enhancement factor. A linear relationship between the energy ratio and probe kinetic diameter indicated a primary pore size at 0.59 nm. The advantage of this enthalpy, model-independent methods over AIE were due to no assumptions regarding probe molecular shape, and no assumptions for pore shape and/or connectivity.

Improvement of the Derjaguin-Broekhoff-de Boer theory for capillary condensation/evaporation of nitrogen in mesoporous systems and its implications for pore size analysis of MCM-41 silicas and related materials

In this work, we propose an improvement of the classical Derjaguin-Broekhoff-de Boer (DBdB) theory for capillary condensation/evaporation in mesoporous systems. The primary idea of this improvement is to employ the Gibbs-Tolman-Koenig-Buff equation to predict the surface tension changes in mesopores. In addition, the statistical film thickness (so-called t-curve) evaluated accurately on the basis of the adsorption isotherms measured for the MCM-41 materials is used instead of the originally proposed t-curve (to take into account the excess of the chemical potential due to the surface forces). It is shown that the aforementioned modifications of the original DBdB theory have significant implications for the pore size analysis of mesoporous solids. To verify our improvement of the DBdB pore size analysis method (IDBdB), a series of the calcined MCM-41 samples, which are well-defined materials with hexagonally ordered cylindrical mesopores, were used for the evaluation of the pore size distributions. The correlation of the IDBdB method with the empirically calibrated Kruk-Jaroniec-Sayari (KJS) relationship is very good in the range of small mesopores. So, a major advantage of the IDBdB method is its applicability for small mesopores as well as for the mesopore range beyond that established by the KJS calibration, i.e., for mesopore radii greater than similar to4.5 nm. The comparison of the IDBdB results with experimental data reported by Kruk and Jaroniec for capillary condensation/evaporation as well as with the results from nonlocal density functional theory developed by Neimark et al. clearly justifies our approach. Note that the proposed improvement of the classical DBdB method preserves its original simplicity and simultaneously ensures a significant improvement of the pore size analysis, which is confirmed by the independent estimation of the mean pore size by the powder X-ray diffraction method.

Pd/C catalysts based on synthetic carbons with bi- and tri-modal pore-size distribution:applications in flow chemistry

Two new types of phenolic resin-derived synthetic carbons with bi-modal and tri-modal pore-size distributions were used as supports for Pd catalysts. The catalysts were tested in chemoselective hydrogenation and hydrodehalogenation reactions in a compact multichannel flow reactor. Bi-modal and tri-modal micro-mesoporous structures of the synthetic carbons were characterised by N2 adsorption. HR-TEM, PXRD and XPS analyses were performed for characterising the synthesised catalysts. N2 adsorption revealed that tri-modal synthetic carbon possesses a well-developed hierarchical mesoporous structure (with 6.5 nm and 42 nm pores), contributing to a larger mesopore volume than the bi-modal carbon (1.57 cm3 g-1versus 1.23 cm3 g-1). It was found that the tri-modal carbon promotes a better size distribution of Pd nanoparticles than the bi-modal carbon due to presence of hierarchical mesopore limitting the growth of Pd nanoparticles. For all the model reactions investigated, the Pd catalyst based on tri-modal synthetic carbon (Pd/triC) show high activity as well as high stability and reproducibility. The trend in reactivities of different functional groups over the Pd/triC catalyst follows a general order alkyne ≫ nitro > bromo ≫ aldehyde.

Computer simulation of random parckings for self-similar particle size distributions in soil and granular materials: porosity and pore size distribution

A 2D computer simulation method of random packings is applied to sets of particles generated by a self-similar uniparametric model for particle size distributions (PSDs) in granular media. The parameter p which controls the model is the proportion of mass of particles corresponding to the left half of the normalized size interval [0,1]. First the influence on the total porosity of the parameter p is analyzed and interpreted. It is shown that such parameter, and the fractal exponent of the associated power scaling, are efficient packing parameters, but this last one is not in the way predicted in a former published work addressing an analogous research in artificial granular materials. The total porosity reaches the minimum value for p = 0.6. Limited information on the pore size distribution is obtained from the packing simulations and by means of morphological analysis methods. Results show that the range of pore sizes increases for decreasing values of p showing also different shape in the volume pore size distribution. Further research including simulations with a greater number of particles and image resolution are required to obtain finer results on the hierarchical structure of pore space.

Pore size characterization of mesoporous materials by a thermodynamic approach: A curvature-dependent solid-fluid potential

A thermodynamic analysis of nitrogen adsorption in cylindrical pores of MCM-41 and SBA-15 samples at 77 K is presented within the framework of the Broekhoff and de Boer (BdB) theory. We accounted for the effect of the solid surface curvature on the potential exerted by the pore walls. The developed model is in quantitative agreement with the non-local density functional theory (NLDFT) for pores larger than 2 tun. This modified BdB theory accounting for the Curvature Dependent Potential (CDP-BdB) was applied to determine the pore size distribution (PSD) of a number of MCM-41 and SBA-15 samples on the basis of matching the equilibrium theoretical isotherm against the adsorption branch of the experimental isotherm. In all cases investigated the PSDs determined with the new approach are very similar to those determined with the non-local density functional theory also using the same basis of matching of theoretical isotherm against the experimental adsorption branch. The developed continuum theory is very simple in its utilization, suggesting that CDP-BdB could be used as an alternative tool to obtain PSD for mesoporous solids from the analysis of adsorption branch of adsorption isotherms of any sub-critical fluids.

Characterization of expiration air jets and droplet size distributions immediately at the mouth opening

Size distributions of expiratory droplets expelled during coughing and speaking and the velocities of the expiration air jets of healthy volunteers were measured. Droplet size was measured using the Interferometric Mie imaging (IMI) technique while the Particle Image Velocimetry (PIV) technique was used for measuring air velocity. These techniques allowed measurements in close proximity to the mouth and avoided air sampling losses. The average expiration air velocity was 11.7 m/s for coughing and 3.9 m/s for speaking. Under the experimental setting, evaporation and condensation effects had negligible impact on the measured droplet size. The geometric mean diameter of droplets from coughing was 13.5m and it was 16.0m for speaking (counting 1 to 100). The estimated total number of droplets expelled ranged from 947 – 2085 per cough and 112 – 6720 for speaking. The estimated droplet concentrations for coughing ranged from 2.4 - 5.2cm-3 per cough and 0.004 – 0.223 cm-3 for speaking.

Accurate stratospheric particle size distributions from two separate flat-plate collection surfaces

Over the past two decades, flat-plate particle collections have revealed the presence of a remarkable variety of both terrestrial and extraterrestrial material in the stratosphere [1-6]. The ratio of terrestrial to extraterrestrial material and the nature of material collected may vary over observable time scales. Variations in particle number density can be important since the earth’s atmospheric radiation balance, and therefore the earth’s climate, can be influenced by articulate absorption and scattering of radiation from the sun and earth [7-9]. In order to assess the number density of solid particles in the stratosphere, we have examined a representative fraction of the so1id particles from two flat-plate collection surfaces, whose collection dates are separated in time by 5 years.

Grain size distributions of Magneli phases and metallic titanium in chondritic porous interplanetary dust particles

A mineralogical survey of chondritic interplanetary dust particles (IDPs)showed that these micrometeorites differ significantly in form and texture from components of carbonaceous chondrites and contain some mineral assemblages which do not occur in any meteorite class1. Models of chondritic IDP mineral evolution generally ignore the typical (ultra-) fine grain size of consituent minerals which range between 0.002-0.1µm in size2. The chondritic porous (CP) subset of chondritic IDPs is probably debris from short period comets although evidence for a cometary origin is still circumstantial3. If CP IDPs represent dust from regions of the Solar System in which comet accretion occurred, it can be argued that pervasive mineralogical evolution of IDP dust has been arrested due to cryogenic storage in comet nuclei. Thus, preservation in CP IDPs of "unusual meteorite minerals", such as oxides of tin, bismuth and titanium4, should not be dismissed casually. These minerals may contain specific information about processes that occurred in regions of the solar nebula, and early Solar System, which spawned the IDP parent bodies such as comets and C, P and D asteroids6. It is not fully appreciated that the apparent disparity between the mineralogy of CP IDPs and carbonaceous chondrite matrix may also be caused by the choice of electron-beam techniques with different analytical resolution. For example, Mg-Si-Fe distributions of Cl matrix obtained by "defocussed beam" microprobe analyses are displaced towards lower Fe-values when using analytical electron microscope (AEM)data which resolve individual mineral grains of various layer silicates and magnetite in the same matrix6,7. In general, "unusual meteorite minerals" in chondritic IDPs, such as metallic titanium, Tin01-n(Magneli phases) and anatase8 add to the mineral data base of fine-grained Solar System materials and provide constraints on processes that occurred in the early Solar System.

Accurate stratospheric particle-size distributions from a flat-plate collection surface

The first representative chemical, structural, and morphological analysis of the solid particles from a single collection surface has been performed. This collection surface sampled the stratosphere between 17 and 19km in altitude in the summer of 1981, and therefore before the 1982 eruptions of El Chichón. A particle collection surface was washed free of all particles with rinses of Freon and hexane, and the resulting wash was directed through a series of vertically stacked Nucleopore filters. The size cutoff for the solid particle collection process in the stratosphere is found to be considerably less than 1 μm. The total stratospheric number density of solid particles larger than 1μm in diameter at the collection time is calculated to be about 2.7×10−1 particles per cubic meter, of which approximately 95% are smaller than 5μm in diameter. Previous classification schemes are expanded to explicitly recognize low atomic number material. With the single exception of the calcium-aluminum-silicate (CAS) spheres all solid particle types show a logarithmic increase in number concentration with decreasing diameter. The aluminum-rich particles are unique in showing bimodal size distributions. In addition, spheres constitute only a minor fraction of the aluminum-rich material. About 2/3 of the particles examined were found to be shards of rhyolitic glass. This abundant volcanic material could not be correlated with any eruption plume known to have vented directly to the stratosphere. The micrometeorite number density calculated from this data set is 5×10−2 micrometeorites per cubic meter of air, an order of magnitude greater than the best previous estimate. At the collection altitude, the maximum collision frequency of solid particles >5μm in average diameter is calculated to be 6.91×10−16 collisions per second, which indicates negligible contamination of extraterrestrial particles in the stratosphere by solid anthropogenic particles.

Pore structure characterization of North American shale gas reservoirs using USANS/SANS, gas adsorption, and mercury intrusion

Small-angle and ultra-small-angle neutron scattering (SANS and USANS), low-pressure adsorption (N2 and CO2), and high-pressure mercury intrusion measurements were performed on a suite of North American shale reservoir samples providing the first ever comparison of all these techniques for characterizing the complex pore structure of shales. The techniques were used to gain insight into the nature of the pore structure including pore geometry, pore size distribution and accessible versus inaccessible porosity. Reservoir samples for analysis were taken from currently-active shale gas plays including the Barnett, Marcellus, Haynesville, Eagle Ford, Woodford, Muskwa, and Duvernay shales. Low-pressure adsorption revealed strong differences in BET surface area and pore volumes for the sample suite, consistent with variability in composition of the samples. The combination of CO2 and N2 adsorption data allowed pore size distributions to be created for micro–meso–macroporosity up to a limit of �1000 Å. Pore size distributions are either uni- or multi-modal. The adsorption-derived pore size distributions for some samples are inconsistent with mercury intrusion data, likely owing to a combination of grain compression during high-pressure intrusion, and the fact that mercury intrusion yields information about pore throat rather than pore body distributions. SANS/USANS scattering data indicate a fractal geometry (power-law scattering) for a wide range of pore sizes and provide evidence that nanometer-scale spatial ordering occurs in lower mesopore–micropore range for some samples, which may be associated with inter-layer spacing in clay minerals. SANS/USANS pore radius distributions were converted to pore volume distributions for direct comparison with adsorption data. For the overlap region between the two methods, the agreement is quite good. Accessible porosity in the pore size (radius) range 5 nm–10 lm was determined for a Barnett shale sample using the contrast matching method with pressurized deuterated methane fluid. The results demonstrate that accessible porosity is pore-size dependent.