Free void space

The packing support consists of a floor grating material with bar openings spaced to give 57.5% free void area of cross-section. 

Loutfy and coworkers [29, 30] assumed a different mechanism of interaction between the molecular rotor molecule and the surrounding solvent. The basic assumption was a proportionality of the diffusion constant D of the rotor in a solvent and the rotational reorientation rate kOI. Deviations from the Debye-Stokes-Einstein hydrodynamic model were observed, and Loutfy and Arnold [29] found that the reorientation rate followed a behavior analogous to the Gierer-Wirtz model [31]. The Gierer-Wirtz model considers molecular free volume and leads to a power-law relationship between the reorientation rate and viscosity. The molecular free volume can be envisioned as the void space between the packed solvent molecules, and Doolittle found an empirical relationship between free volume and viscosity [32] (6),... 

To manufacture the brine, a vacuum salt is used to which the producer needs to add a small amount of anti-caking agent which forms a ferrohexacyanide complex in the brine. Because of the acidic process conditions, Fe ions tend to migrate into the electrolyser membranes until encountering a sufficiently high pH and then precipitate [1]. This is an undesirable effect as it can cause void spaces within the membrane and thereby increase the voltage needed for the electrolysis. For this reason the ferrohexacyanide is depleted into Fe(OH)3 under well-defined conditions of temperature, residence time, free chlorine and pH in a process step prior to filtration [2]. 

For a fast catalytic reaction, free access of gas, electrons, protons and water is needed. This leads to a best compromise of the volume fractions of protonconducting polymer, electron-conducting carbon, active sites and void space. 

It has been previously reported [21, 22] that metal colloids are formed by radiochemical reactions in water/alcohol solutions, in which the reduction of metal salts takes place by solvated electrons and free radicals produced under UV or y-ray irradiation. Ichikawa et al. have applied this photoreduction method to the surface-mediated reaction of metallic ions and succeeded in synthesizing metal/aUoy nanowires in the constrained cavities of mesoporous supports such as FSM-16 and MCM-41 [18-20, 23-25]. The adsorbed water and alcohol work not only as solvents in the nanoscale silica void space but also as a source of reducing species for metallic ions to metals under UV-vis and y-ray [11, 18, 19] irradiation. The results indicate the dense formation of Pt nanowires inside the charmels of mesoporous supports, such as FSM-16, which act as the templates. In fact, no any Pt wire is observed on the external surface of FSM-16 or amorphous silica surface. Short wires, 10 nm long, are also observed as a minor species in the samples in the initial stage of UV and y-ray irradiation. 

Figure 4.26 shows a cell model of the three phases. Gas in the upper region has a very low density and the molecules are free to fly around. When the vapor condenses into a liquid (shown lower right), the density is greatly increased so that there is very little free volume space the molecules have limited ability to move around, and they have random orientation that is, they can rotate and point in random directions. When the liquid freezes into a solid (shown lower left), the density is slightly increased to eliminate the void space, the molecules have assigned positions and are not free to move around, and there is now an orientation order that is, they cannot rotate freely and they all point at the same direction. 

Hydrate formation is physical rather than chemical in nature. Apparently, no strong chemical bonds are formed between the hydrocarbon and water molecules. Actually, the hydrocarbon molecules are free to rotate within the void spaces. 

The binuclear terbium centers and type I rotaxanes form a two-dimensional layer. Stacked layers are further interconnected via type II rotaxanes to form a three-dimensional polyrotaxane network, which has an inclined a-polonium topology with the binuclear terbium centers behaving as six-connected nodes (Fig. 20.4.10). The void space in the crystal packing is filled by a free rotaxane unit, NOJ and OH- counter ions, and water molecules. 

Next in importance for a proper understanding of size-distribution and particle-measurement is the manner in which fine material packs. It is well known that a column filled with sand may be shaken so that it will occupy less space. Similarly, certain soils may be pressed or tamped to become denser. Compaction is achieved at the expense of the void space, which may vary from a theoretical minimum of 26 percent to as high as 48 percent for spheres. Unfortunately there is no adequate method of describing a packing in terms of partide-orientation. We can only deal with it in terms of the free space present or the ease with which a liquid flows through it. Except in a statistical sense it is never possible to make two packings precisely identical unless we make a systematic arrangement of spheres. 

Finally, the catalyst should be available in a sufficiently high concentration in order to keep the construction volume of the reactor low. The decisive parameters here are the specific external catalyst surface ap (= square meters of catalyst surface per cubic meter reactor volume) for reactions controlled by external mass transfer, and the catalyst fraction 1-e, where e (= cubic meters of free gas space per cubic meter of reactor volume) is the void fraction of the fixed bed. 

The contact resistance should increase with a decrease in the ambient gas pressure when the pressure is decreased below the value where the mean free path of the molecules is large compared with a characteristic dimension of the void space, since the effective thermal conductance of the entrapped gas will be decreased for this condition. 

For molecular mean free paths much less than the mean free diameters of the intercrystalline void space in the zeolite bed, Din, is controlled by the same mechanism as in the gas phase, with a self-diffusion coefficient Dg. Due to the steric confinement, Dimer is reduced with respect to Dg by a tortuosity factor, Tb, with values typically of the order of 2-3. The mean free path can be estimated through the relation... 

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