Porosity accessible

Figure 1.18 Electrochemical applications of ORMOSIL are due to the accessible porosity and the possibility to coat in thin films. (Reproduced from ref. 39, with permission.)...

Porosity of a separator is defined as the ratio of void volume to apparent geometric volume. It is usually calculated (eq 6) from the skeletal density, basis weight, and dimensions of the material and so may not reflect the accessible porosity of the material. 

The standard test method is described in ASTM D-2873. The actual or accessible porosity can also be determined by the weight of liquid (e.g., hexadecane) absorbed in the pores of the separator. In this method, the separator weight is measured before and after dipping in hexadecane solvent, and the porosity is calculated (eq 7) by assuming that volume occupied by hexadecane is equal to the porous volume of the separator. 

In this chapter, we present in some detail gas adsorption techniques, by reviewing the adsorption theory and the analysis methods, and present examples of assessment of PSDs with different methods. Some examples will show the limitations of this technique. Moreover, we also focus on the use of SAXS technique for the characterization of porous solids, including examples of SAXS and microbeam small-angle x-ray scattering (pSAXS) applications to the characterization of activated carbon fibers (ACFs). We remark the importance of combining different techniques to get a complete characterization, especially when not accessible porosity exists. 

The general approach for modelling catalyst deactivation is schematically organised in Figure 2. The central part are the mass balances of reactants, intermediates, and metal deposits. In these mass balances, coefficients are present to describe reaction kinetics (reaction rate constant), mass transfer (diffusion coefficient), and catalyst porous texture (accessible porosity and effective transport properties). The mass balances together with the initial and boundary conditions define the catalyst deactivation model. The boundary conditions are determined by the axial position in the reactor. Simulations result in metal deposition profiles in catalyst pellets and catalyst life-time predictions. 

In this section, two examples are presented for the application of a technique of low-melting-point alloy (LMPA) impregnation that provides for a visualization of the invasion of a nonwetting fluid into the pore spaces in a typical porous article. The visualization can be linked to the modeling of mercury porosimeter curves using 3-D stochastic pore networks. This makes the quantification of pore structure more direct. Quantified structures can be visually examined against sample particle sections. The visual comparison can be made more precise by image analysis of the accessible porosity made visible by metal penetration over a series of pressures. 

The chemical reaction between a solid and a reactive fluid is of interest in many areas of chemical engineering. The kinetics of the phenomenon is dependent on two factors, namely, the diffusion rate of the reactants toward the solid/fluid interface and the heterogenous reaction rate at the interface. Reactions can also take place within particles, which have accessible porosity. The behavior will depend on the relative importance of the reaction outside and inside the particle. Fractal analysis has been applied to several cases of dissolution and etching in such natural occurring caves, petroleum reservoirs, corrosion, and fractures. In these cases fractal theory has found usefulness for quantifying the shape (line or surface) with only a few parameters the fractal dimension and the cutoffs. There have been some attempts to use a fractal dimension for reactivity as a global parameter. Finally, fractal concepts have been used to aid in the interpretation of experimental results, if patterns quantitatively similar to DLA are obtained. 

To quantify this effect, two types of material porosity must be considered total porosity and accessible porosity. Total porosity, , is the volume fraction of pores in the material accessible porosity, is the volume fraction of pores which are members of clusters that extend to the surface of the material. In desorption of solute from a porous material, only solute which is initially present in accessible pores can be released. The fractional volume of accessible pores, e /e, is denoted . As the intuitive model of porous materials—developed in the previous paragraph—suggests, both accessible porosity and fractional accessible porosity increase as the total porosity increases. 

For Bethe lattices (see Chapter 4), the relationship of accessible porosity to total porosity can be analytically derived. For site percolation on a Bethe lattice with coordination number C, the accessible porosity is given by [45, 46] ... 

As noted previously, the critical probability for the Bethe lattice is (equivalent to Pc defined in Chapter 4) = /(( — 1). For lattices below this critical probability (e < Cc), the root of Equation 9-26 is e = e. The accessible porosity, from Equation 9-25, is zero, which indicates that a lattice spanning cluster is not present. For lattices above the critical probability (e > e ) Equation 9-26 can be solved to find e. Results for coordination numbers 3 and 4 are ... 

Solutions for other coordination numbers follow directly [45, 46]. Accessible porosity is found by substitution of the correct root of Equation 9-26 into Equation 9-25 the fraction of accessible porosity, [Pg.258]

In Figure 9.14b, the fraction accessible porosity is plotted versus the total porosity for Bethe lattices of coordination numbers 3 and 7. For all coordination numbers, a is zero for porosities less than the critical value. The critical porosity is indicated for each coordination number by the intercept of the curve with the x-axis. Above the critical porosity, rises sharply. In this transition region, the infinite, lattice-spanning cluster is growing and incorporating pores and smaller pore clusters that are isolated at lower porosities. At high porosities, 0a becomes equal to unity, indicating that all the pores are members of the infinite cluster. 

Figure 9.14 Fraction accessible porosity and mean cluster size for a Bethe lattice. Fraction accessible porosity and mean cluster size for Bethe lattices with f = 3 (solid lines) and 7 (dashed lines). The fraction of accessible porosity (b), or the fraction of porosity that is part of an infinite cluster, is plotted versus the total porosity. The mean cluster size (a) exhibits a singularity at the critical porosity.

Monolithic carbons are easier to handle than powdered materials. Direct shaping of monolithic mesoporous carbons during their preparation is highly desirable. Mesoporous carbon monoliths may be fabricated by using mesoporous silica monoliths as template. Carbon monoliths with well-developed and accessible porosity have been produced using silica monoliths with a hierarchical structure containing macropores and meso-pores as templates and furfuryl alcohol or sucrose as a carbon precur-... 

Multifunctional Zeolites Efficient, multifunctional zeolite-based catalysts allowing one-step complex reactions are of great interest in the field of fine chemicals and organic industrial synthesis [58]. Recendy, catalysts based on zeolites are relevant in emerging areas of interest such as the catalytic conversion of biomass to fuels and chemicals (see Section 8.2.1.3 for illustrative examples). This field needs to develop specific multifunctional catalysts having the correct polarity (adsorption properties) and reactant accessibility (porosity), which are efficient in water or biphasic operation with reactants and products of different polarities and sizes. Hence, great opportunities for zeolites and related materials are offered in this new field [59-61]. 

Rennie, A. J. R., and P. J. Hall. 2013. Nitrogen-enriched carbon electrodes in electrochemical capacitors Investigating accessible porosity using CM-SANS. Physical Chemistry Chemical Physics 15 16774-16778. 

The inner part of these channels is made of adamantane molecules which stack along the c-axis and point toward the center of the ctiaimels. The anhydrous character of this compound, which is probably due to the hydrophobic character of the adamantane, implies several original properties. In particular, as there is no water molecule, the crystal structure remains tmchanged up to 300 °C. A Langmuir surface area of 65 m g has been measured, in agreement with the presence of a small accessible porosity. The isostructural Y + compoimd doped with Eu " has been prepared and the characteristic blue luminescence of Eu + ions has been observed at room temperature. 

Comment. In many cases the density of the solid phase can well be approximated by using the respective literature values for the given chemical composition. For nonmacroporous samples with well-accessible porosity, the total pore volume and thus the backbone density can also be determined from the macroscopic density of the (degassed ) sample and the respective nitrogen sorption isotherm (see Chap. 21.6). 

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