Porosity of solids

The use of templates to control the porosity of solids is not limited to small organic molecules. Alternative templates include dendrimers [16, 17], polymers [18], hard templates such as nanoparticle colloidal suspensions [19] and latex spheres [20] or even biological materials like butterfly wings [21], DNA [22] or viruses [23]. 

The use of standard isotherms as a tool to characterize the porosity of solids (even for micropo-rous solids as it was shown) by means of one of the two methods described above may be appropriate. However, it is necessary to keep in mind that all of them are subject to the same limitation, that is, the difficulty of an appropriate choice of a nonporous reference material. The as-method chooses the standard isotherm according to the chemical nature of the sample to be studied, whereas the /-method chooses it independent of the nature of the nonporous adsorbent. 

The porosity of solid samples can be quantitatively studied by mercury poro-simetry. The total volume, specific surface area of the pores, bulk density, and particle size can be determined in 1.8 nm-300 pm pore size and 15 nm-3 mm particle size. The principle of the method is that there is a relationship between the pressure of mercury and the size of the pores filled with mercury. The pressure of mercury (p) required for its introduction into the pores of a given radius (r) can be expressed by Washburn s equation ... 

Reactants migrate between phases in order to react from gas phase to liquid, from fluid to solid, and between liquids when the reaction occurs in both phases. One of the liquids usually is aqueous. Resistance to mass transfer may have a strong effect on the overall rate of reaction. A principal factor is the interfacial area. Its magnitude is enhanced by agitation, spraying, sparging, use of trays or packing, and by size reduction or increase of the porosity of solids. These are the same operations that are used to effect physical mass transfer between... 

The total porosity of solids can be estimated by simple pycnometric methods using the differences in surface tension between gases and mercury. By definition, the porosity Pr(%) is given by ... 

In mercury porosimetry, the pores are filled with mercury under pressure (ISO 15901-1 2005, Pore Size Distribution and Porosity of Solid Materials—Evaluation by Mercury Porosimetry and Gas Adsorption—Part 1 Mercury Porosimetry). This method is suitable for many materials with pores in the diameter range of about 3 nm to 400 pm (especially within 0.1 to 100 pm). 

In gas adsorption for micro-, meso- and macropores, the pores are characterized by adsorbing gas, such as nitrogen at liquid-nitrogen temperature. This method is used for pores in the ranges of approximately <2 nm micropores), 2 to 50 nm (mesopores), and >50 nm macropores) (ISO/FDIS 15901-2, Pore Size Distribution and Porosity of Solid Materials—Evaluation by Mercury Porosimetry and Gas Adsorption, Part 2 Analysis of Meso-pores and Macro-pores by Gas Adsorption ISO/FDIS 15901-3, Part 3 Analysis of Micro-pores by Gas Adsorption). An isotherm is generated of the amount of gas adsorbed versus gas pressure, and the amount of gas required to form a monolayer is determined. 

As a conclusion, one can say that the thermogravimetric technique is a usefull method in the investigations of the porosity of solids. Our analysis, based on the Kelvin equation, of the thermogravimetric curves for silica gel wetted with liquid n-butanol and carbon tetrachloride leads to core/pore size distributions curves which are similar, but not identical in shape to the pore size distribution curves derived by standard procedure from low temperature nitrogen adsorption/desorption isotherms. The linear heating mode is... 

Some limited experimental results have been reported that fit this relationship. However, more detailed investigations are needed to nnderstand fully the evaporation phenomena. Only one case " has reported on the fate of the liquid film that remains after most of the liquid has evaporated. It was shown that we conld estimate the degree of porosity of solid surfaces from these data. Thus, we find a new method of determination of porosity of solids, withont the use of mercury porosim-eter. " The latter studies are much more accurate, as these were based on measurements of change of weight of drop vs. time under evaporation. At this stage in the literature, therefore, there is a need for more stndies on this dynamic system of liqnid drop-solid. 

In order to examine how impurities affect the resistance of both single-crystal and polycrystalline zirconia, samples were prepared and resistance was measured. Samples of polycrystalline zirconia and the zirconia single aystal with the same concentration of Y2O3 were used at temperatures of 400-800 C. The results of testing are shown in Figure 4.8. Based on the fact that the higher the sintering conditions of polycrystalline zirconia, the less the resistance and porosity of solid electrolyte... 

The curvature of the interface depends on the relative magnitudes of the adhesive forces between the liquid and the capillary wall and the internal cohesive forces in the liquid. When the adhesive forces exceed the cohesive forces, 9 lies in the range 0° < 9 < 90° when the cohesive forces exceed the adhesive forces, 90° < 9 < 180°. When 9 > 90°, the cos 9 term is negative, resulting in a convex meniscus towards the vapor phase and the liquid level in the capillary falling below the liquid level in the container (capillary depression). This occurs with liquid mercury in glass where 9 = 140° and also with water in capillary tubes coated internally with paraffin wax. Thus, liquid mercury is used in the evaluation of the porosity of solid adsorbents in the mercury injection porosimetry technique (see Section 8.5). 

Engelhardt reported 0.42 for the interstitial porosity of solid glass beads and 0.80-0.88 for the mobile-phase porosity of totally porous supports (57). 

Herino R, Bomchil G, Barla K, Bertrand C, Ginoux JL (1987) Porosity and pore size distributions of porous silicon layers. J Electrochem Soc 134(8) 1994-2000 International Organization for Standardization (2006a) Pore size distribution and porosity of solid materials by mercury porosimetry and gas adsorption - Part 2 analysis of mesopores and macropores by gas adsorption. ISO 15901-2 2006(E)... 

One of the alternative methods for assessment of the porosity of solids within the mesopore range was proposed at the beginning of 90s (see reference [449] and references therein). The method consists of the measurements of temperature programmed desorption of liquids wetting the porous solid perfectly. Experimentally obtained desorption curves representing the weight loss of the... 

Cordial thanks are also given to our colleague and friend Prof. h. c. Erich Robens, Friedrichsdorf and Mainz, for fruitful and interesting discussions over many years on the porosity of solids and also for valuable hints to experimental measurement procedures. 

This book is intended to present for the first time experimental methods to measure equilibria states of pure and mixed gases being adsorbed on the surface of solid materials. It has been written for engineers and scientists from industry and academia who are interested in adsorption based gas separation processes and/or in using gas adsorption for characterization of the porosity of solid materials. 

ISO 15901-1 2005. Pore size distribution and porosity of solid materials by mercury porosimetry and gas adsorption — Part 1 Mercury porosimetry. 

The samples for PALS experiments were prepared in the sandwich configuration (sample-positron source-sample). During the preparation it was formed into pastille (mechanically pressed to about 50 MPa) and placed in the argon pressure chamber. The other part of the same sample was mechanically compressed. The MCM-41 sample was put into a small tube, closed by two movable pistons sealed by 0-rings. The air from the container was evacuated to the pressure of about 0.5 Pa. Such a set was placed in the argon pressure chamber, so that mechanical pressure exerted by the pistons pushed by argon could be applied to the sample. The PALS spectra were collected in both cases in the pressure range 0.1-490 MPa. The positronium annihilation method for characterization of porosity of solids is based on the relation between ortho-positronium (o-Ps) lifetime and the size of free volume, in which o-Ps is trapped. The PALS spectra were processed as described in Ref. [9]. 

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