Solids packing efficiency

Packing efficiency is defined as the percent of the total volume of a solid occupied by (spherical) atoms. The formula is... 

In general, the adsorption of ionic surfactants follows the Langmuir isotherm, as discussed in Section 4.1. The adsorption of the surfactants onto the solid surfaces is dependent on the orientation and the packing efficiency of the solid surfaces. The onset of the adsorption plateau may occur at the critical micelle concentration (c.m.c.) of the surfactant in water, as shown in Figure 4.28. If the adsorption isotherm... 

In this system, the continuous injection of the feed and the continuous collection of A and B from the extract and the raffinate is an ideal system which provides the maximum efficiency of the adsorbent. A and B are recovered diluted in the desorbent but can be obtained pure after distillation. From a practical point of view, the true moving bed concept would be extremely difficult to implement. Although recycling the liquid would be feasible, the circulation of a solid packing from the bottom to the top of the fixed column... 

The second portion of El-Hisnawi s study consisted of evaluating liquid-solid contacting efficiency and liquid holdup using impulse response tracer experiments. Experiments were performed using the same catalyst packing and solvents employed... 

The overall lattice energies of ionic solids, as treated by the Born-Lande or Kaputin-skii equations, thus depends on (i) the product of the net ion charges, (ii) ion-ion separation, and (iii) packing efficiency of the ions (reflected in the Madelung constant, M, in the Coulombic energy term). Thus, low-melting salts should be most... 

Previously known as cyclopolyphosphates, these rings may contain up to 12 tetrahedra, but those with three, four, and six units are most common (see Table 1). The cyclotri- and cyclotetraphosphate rings adopt puckered geometries typical of saturated six and eight atom rings. The predominance of even membered cyciophosphates reflects their ability to pack efficiently in the solid state, rather than any inherent stability over odd membered ones. This is often reflected by a high internal symmetry in the crystalline state an analysis of thirty reliably determined cyclohexaphosphate structures shows that 18 have inversion symmetry and a further seven have threefold (Dsd) internal symmetry. ... 

Traditional methods to estimate solid-phase density from molecular structure are primarily based on a simple summation of appropriate atomic or group volumes. The basic disadvantage of these group or volume additivity procedures is that they disregard crystal-packing efficiency and molecular conformation. Thus, conformational isomras, or even different compounds with the same functional group composition, wiU aU be calculated to have the same density. To solve this problem, Ammon and coworkers have developed a scheme to estimate molecular densities by predicting possible crystal... 

For unsaturated carboxyhc adds, the nature of the monolayer film will depend of the configuration of the double bond. For a trans double bond, the hydrocarbon chain will be more or less straight, so that lateral interactions and good packing efficiency may lead to the formation of a solid or an L2 film. The corresponding cis isomer has a forced bent structure, reducing its... 

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