Porous materials, particle density

The skeletal density, p, also called the true density, is defined as the density of a single particle excluding the pores. That is, it is the density of the skeleton of the particle if the particle is porous. For nonporous materials, skeletal and particle densities are equivalent. For porous particles, skeletal densities are higher than the particle density. 

Table 6.2 summarizes the low pressure intercept of observed shock-velocity versus particle-velocity relations for a number of powder samples as a function of initial relative density. The characteristic response of an unusually low wavespeed is universally observed, and is in agreement with considerations of Herrmann s P-a model [69H02] for compression of porous solids. Fits to data of porous iron are shown in Fig. 6.4. The first order features of wave-speed are controlled by density, not material. This material-independent, density-dependent behavior is an extremely important feature of highly porous materials. 

Surface-initiated ATRP was applied not only on planer substrates but also on various kinds of flne particles. The latter systems will be reviewed separately in Sect. 5.1. Porous materials are also fascinating targets for chromatographic application making use of the unique structure and properties of high-density polymer brushes. Wirth et al. were the first to report the grafting of poly(acrylamide) (PAAm) on a porous silica gel [109,110]. 

A porous particle contains many interior voids known as open or closed pores. A pore is characterized as open when it is connected to the exterior surface of the particle, whereas a pore is closed (or blind) when it is inaccessible from the surface. So, a fluid flowing around a particle can see an open pore, but not a closed one. There are several densities used in the literature and therefore one has to know which density is being referred to (Table 3.15). True density may be defined as the mass of a powder or particle divided by its volume excluding all pores and voids. True density is also referred to as absolute density or crystalline density in the case of pure compounds. However, this density is very difficult to be determined and can be calculated only through X-ray or neutron diffraction analysis of single-crystal samples. Particle density is defined as the mass of a particle divided by its hydrodynamic volume. The hydrodynamic volume includes the volume of all the open and closed pores. Practically, the hydrodynamic volume is identified with the volume included by the outer surface of the particle. The particle density is also called apparent or envelope density. The term skeletal density is also used. The skeletal density of a porous particle is higher than the particle one, since it is the mass of the particle divided by the volume of solid material making up the particle. In this volume, the closed pores volume is included. The interrelationship between these two types of density is as follows (ASTM, 1994 BSI, 1991) ... 

For porous materials pp < Pabs and cannot be measured with such methods. A mercury porosimeter can be used to measure the density of coarse porous solids but is not reliable for fine materials, since the mercury cannot penetrate the voids between small particles. In this case, helium is used to obtain a more accurate value of the particle density. Methods to measure the particle density of porous solids can be found in Refs. 2 and 5. 

The static liquid holdup is often correlated by the Eotvos number, Eo (= pi.0dp/ffL> where dp is the nominal particle diameter and g the gravitational acceleration). Such a correlation103 is illustrated in Fig. 6-5. The correlation indicates that smaller particle diameter and fluid density and larger surface tension give larger static liquid holdup. The correlation also indicates that a porous material gives a larger static liquid holdup than a nonporous material. 

Quoted density values in standard reference works are of the materials true density. If density is determined using a gas pyknometer, the volume measured would include closed pores but exclude open pores i.e. the measured density would be the apparent density. If the suspending liquid penetrates all the cracks and fissures on the particle surface, the measured volume would be the same as that determined by gas pyknometry but the total mass would be greater due to the included liquid that will remain with the particle as it falls in the liquid, hence its sedimentation density will be intermediate between the apparent density and the true density and greater than the effective density. These differences are usually not highly significant for coarse particles unless they are highly porous. 

Cracking catalysts are highly porous materials with large internal surface areas. Thus, for example, a fresh synthetic silica-alumina catalyst typically has a pore volume of about 0.5 cc./g. and a specific surface of the order of 500 m.Vg., equivalent to about 56 acres (almost 0.1 square mile) per pound. Compared with the internal pore surface, the external surface of the discrete particles of catalyst used in commercial plants is insignificant. This is illustrated by the following tabulation, which shows the external surface areas of spherical particles of the diameters employed commercially. A particle density of 1.0 g./cc. was assumed, about equal to the observed particle density for fresh synthetic silica-alumina. 

The use of gas diffusion electrodes is another way to achieve high current densities. Such electrodes are used in the fuel-cell field and are typically made with porous materials. The electrocatalyst particles are highly dispersed inside the porous carbon electrode, and the reaction takes place at the gas/liquid/solid three-phase boundary. COj reduction proceeds on the catalyst particles and the gas produced returns to the gas compartment. We have used activated carbon fibers (ACF) as supports for metal catalysts, as they possess high porosity and additionally provide extremely narrow (several nm) slit-shaped pores, in which nano-space" effects can occur. In the present work, encouraging results have been obtained with these types of electrodes. Based on the nanospace effects, electroreduction under high pressure-like conditions is expected. In the present work, we have used two types of gas diffusion electrodes. In one case, we have used metal oxide-supported Cu electrocatalysts, while in the other case, we have used activated carbon (ACF)-supported Fe and Ni electrocatalysts. In both cases, high current densities were obtained. 

In Eq. [3-22], concentration is expressed as mass of chemical per volume of porous media. The volume of porous media, also termed aquifer volume, is defined to include both particle grains and pore water. Equation [3-22] can be rewritten in terms of the aqueous chemical concentration (Caq), the sorbed chemical concentration (Cs), the water-filled porosity, n, the distribution coefficient Kd, and the bulk density of the porous material pb. Bulk density is defined as the weight of dry solids divided by the volume of aquifer from which they were taken. 

Model templated structures can be assembled from Monte Carlo simulations of binary mixtures of matrix and template particles [55-57]. Upon removal of the template from the quenched equihbrated structure, a porous matrix is recovered with an enhanced accessible void volume for adsorption. GCMC simulation studies have established that the largest enhancement of adsorption uptake occurs when the template particles used to fashion the porous matrix are the same size as the adsorbate molecules for which the adsorbent is intended [55]. The enhanced adsorption capacity of the templated material relative to a nontemplated matrix is noticeable even for modest template particle densities [55]. 

Practically, this method works well for spherical or near-spherical particles however, it produces erroneous results for nonspherical particles. Moreover, this method is not suitable for porous material because the effective particle density is not known and the volume measured is the envelope volume. Special care is required to avoid crowding of the orifice otherwise, special treatment is needed to analyze the instrument counts. 

The macropores are not straight cylinders but bounded with changing widths and sometimes narrow slits or dead-end pores. Therefore, a tortuosity factor is introduced in the balance equations. Principally speaking, the tortuosity factor should be dependent only on the inner geometry of the adsorbent pellet but not on operation parameter of fluid properties such as the pressure, the temperature, the density, the viscosity, or the molar fluxes of the components. However, this is not true for some publications because of the difficulty to clearly separate the contributions from the particle porosity Sp and the Knudsen diffusion. Therefore, the tortuosity factors published in the literature are often greater than 3 up to 6 which can be expected due to the inner structure of the porous material. 

Given the size of clay particles (10-1,000 nm), they are found in solution as colloidal dispersions or gels. At low water content, they can be obtained as dry powders, and can form solid porous materials upon compaction. In all these regimes, their properties crucially depend on the charge density and on the nature of the counterions. Most counterions are mono- or divalent, usually alkaline (most commonly sodium Na" or potassium or alkaline earth cations (most commonly calcium Ca " ). They are not incorporated in the clay layers. Rather, they are located near the surface, either between different layers, in the so-called interlayer porosity, or on the external surfaces of clay stacks (typically 10 layers). Such stacks are called particles, and their assembly to form a porous material then leaves voids called interparticle porosity, with sizes between a few nanometers to tens of nanometers, which are usually saturated by an electrolyte solution. 

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