Specific bulk volume

Bulkiness, or specific bulk volume, is defined as the reciprocal of the bulk density [5,62]. It is often measured for the packaging of powders and, as expected, is affected by particle size. Bulkiness will increase with a decrease in overall particle size. A sample exhibiting a wide particle size distribution, however, will result in a lower bulkiness because the small particles will occupy the void spaces formed by the larger particles. 

Bulkiness The specific bulk volume, the reciprocal of bulk density, is often called bulkiness or bulk. It is an important consideration in the packaging and filling of powders for tablet production. The bulk density of calcium carbonate can vary from 0.1 to 1.3, and the lightest or bulkiest type would require a container about 13 times larger than the heaviest type. Bulkiness increases with a decrease in particle size. In a mixture of materials of different sizes, however, the smaller particles sift between the larger ones and tend to reduce the bulkiness. 

Many of the applications for composite materials involve their (relative) lightweight, resistance to weathering and chemicals, and their ability to be easily fabricated and machined. Bulk applications employ composites that are relatively inexpensive. Combinations of rigorous specifications, low volume, specific machining and fabrication specifications, and comparative price to alternative materials and solutions allow more expensive specialized composites to be developed and utilized. 

The pore volume j)er unit mass, Vg, (a measure of the catalyst pellet porosity) is also a parameter which is important and is implicitly contained in eqn. (14). Since the product of the particle density, Pp, and specific pore volume, V, represents the porosity, then Pp is inversely proportional to Fg. Therefore, when the rate is controlled by bulk diffusion, it is proportional not simply to the square root of the specific surface area, but to the product of Sg and Vg. If Knudsen diffusion controls the reaction rate, then the overall rate is directly proportional to Vg, since the effective Knudsen diffusivity is proportional to the ratio of the porosity and the particle density. 

According to this definition, the failure to qualify as macroscopic can be traced to one or more properties that lack intensive or extensive character. This failure can usually be attributed to surface effects, i.e., to properties that still depend on the shape or size of the system in a nonextensive manner. We know that, for sufficiently large systems, the surface effects (which scale as r2) eventually become negligible compared with the bulk volume effects (which scale as r3). (Although the preceding remarks are specific to ordinary 3-dimensional systems, similar remarks apply to edge effects in 2-dimensional systems or end effects in 1-dimensional systems.) Empirically, we know that macroscopic character, once established, persists for all larger sizes. Hence, the operational definition above allows us to determine the smallest sample of S that still qualifies as macroscopic in a particular experimental framework. 

Specifically, this volume focuses on the synthesis, processing, and structural tailoring of nanocrystalline and nanoporous materials. Nanocrystalline materials possess unique hybrid properties characteristic of neither the molecular nor the bulk solid-state limits and may be confined in nanometersized domains in one, two, or three dimensions for unusual size-dependent behavior. Nanoporous materials, characterized by well-defined pores or cavities in the nanometer size regime and controlled pore diameter and structure, give rise to unique molecular sieving capabilities and ultrahigh internal surface areas. Nanoporous structures also act as hosts and templates for the fabrication of quantum dots and quantum wires. 

The total pore volume, Vp, sometimes called specific pore volume when referred to unit mass, is the total internal volume per unit mass of catalysts. Some of this pore volume may be completely enclosed and thus inaccessible to molecules participating in a catalytic reaction. The total accessible pore volume is often derived from the amount of vapour adsorbed at a relative pressure close to unity, by assuming that the pores are then filled with liquid adsorptive. The accessible pore volume may be different for molecules of different sizes. It may be useful to determine the dead space by means of a nonsorbable gas (normally helium) in conjuction with the determination of the bulk volume of the catalyst by means of a non-wetting liquid (mercury). 

Vj, is the specific pore volume of the material typical values are 200-400 cm /kg for zeolites and up to 1000 cm /kg for activated carbon, n is the actual number of molecules contained in the micropores the excess adsorption subtracts from n the number of molecules which would have been present in the micropores at the bulk density in the absence of adsorption. The (oversimplified) case when absolute adsorption is described by the Langmuir equation and the gas obeys the perfect gas law p - PjRT) has been worked out in detail for the isotherms and thermodynmnic functions (enthalpy, entropy, etc.) [2j. 

In all cases, 5% of 1, the cross-linking agent, and (sometimes) additional monomer were copolymerised radically in the inert solvent mixture acetonitrile/benzene 1 1 (1 g of monomer mixture/1 mL of solvent mixture). Swellability ratio of the specific gel bed volume to the bulk volume. Splitting percentage percentage of templates that could be split olf. 

The bulk density of a powder is obtained by dividing its mass by the bulk volume it occupies. The volume includes the spaces between particles as well as the envelope volumes of the particles themselves. The true density of a material (i.e., the density of the actual solid material) can be obtained with a gas pycnometer. The bulk density of a powder is not a definite number like true density or specific gravity but an indirect measurement of a number of factors, including particle size and size distribution, particle shape, true density, and especially the method of measurement. Although there is no direct linear relationship between the flowability of a powder and its bulk density, the latter is extremely important in determining the capacity of mixers and hoppers and providing an easily obtained valuable characterization of powders. 

These reactions would be expected to cause a permanent volume expansion inasmuch as nephelite has a lower true specific gravity than the weighted mixture of the original corundum, silica, and mullite. The bulk volume increase of about 14% was associated with the change in mineralogy. This fact, coupled with the increase in thermal expansion of the outer layer, which contained alkalies, results in slabbing or shelling of the surface. 

The pore volume and pore surface-area as a function of pore radius for an active mass formed from 3BS paste on lead-antimony grids are presented in Fig. 3.29(a) and (b), respectively. The pore volume begins to rise at a pore radius of 1 pm and the surface area at a pore radius of 0.1 pm. Pores with 0.1 pm radius have a specific pore volume of 0.065 cm g , which is about 62% of the total pore volume. The surface area of the pores of this same size is only 6% of the total surface-area of the PAM. These results demonstrate that the macrostructure of the PAM is basically built up of pores with radii larger than 0.1 pm (macro-pores), and these pores serve as the main transport system for the flows of ions and H2O between the bulk of the solution... 

Fig. 2.4 a Volume fraction of the double-gyroid network phase as function of the parameter t fitted with (/) = 101.5 — 68.1 -1. b Specific surface area to bulk volume ratio of the double-gyroid plotted versus the network phase volume fraction in units of the cubic unit cell dimension L... 

Due to the particular thin film design of lithium battery electrodes, it might be misleading to select the optimal type and amount of conductive carbon exclusively based on its percolation threshold. It is important to note that the PT only applies for electrical resistivity relationships of the bulk volume. Thus for an optimal electrical electrode performance, specific thin film parameters such as the electrode thickness must be taken into consideration. Nevertheless, electrical resistivity measuranents of blends of conductive carbons and the active electrode material provide useful comparative information about the electronic properties of different carbons. In general, conductive carbons provide the conductive matrix in which the... 

As discussed above, every laser exposure of a sample leads to the removal of a bulk volume - that is, many monolayers of matrix molecules of the sample. The term desorption is, therefore, somewhat ill-chosen for this process, and was so even for the field desorption for which it was originally coined. Ablation (removal of bulk material from surfaces) is the more specific term, and is used interchangeably with desorption throughout this chapter. The processes of material ablahon and the ionizahon of a minor fraction of the matrix and analyte molecules are, no doubt, intimately intertwined, and both take place on a micrometer geometric and a nanosecond time scale. It is experimentally very difficult - if not impossible - to sort out the complex contributions of the physical processes induced by the laser irradiation in all detail. Despite this complexity, it is of considerable merit to treat the ablation and ionization mechanisms separately. From such a discussion, some basic understanding can be derived, particularly, because the vast majority of the ablated material comes off neutral. 

Total or absolute porosity is a measure of the total void volume and is the excess of bulk volume over grain volume per unit of bulk volume. It is usually determined as the excess of grain density (i.e. specific gravity) over dry density per unit of grain density and can be obtained from the following expression ... 

Specific surface n. Of porous solids, massed fibers, and particulate materials, the total surface area per unit of bulk volume or per unit mass. Specific surface is usually measured by gas adsorption or estimated from mercury-porosimetry measurements. 

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