Amorphous packing density

There is great interest in the development of methods that allow the identification of a reasonably good structure with which to start the simulation of dense atomistically detailed polymer systems. The problem of generating dense polymer systems is formidable due to the high density and the connectivity of polymer systems. For crystal structures this can be systematically achieved [33,34] for amorphous structures, however, there is no generally satisfactory method available. Two recent developments in methods for generating amorphous packing (Santos, Suter) are reviewed in Section 3. 

Packing Density of Silanol Groups on the Surface of Crystalline and Amorphous Silica... 

Parallel investigations of amorphous silica and quartz were executed by Stober (173, 218, 219, 225) with many reactions. No essential difference in reaction behavior and in the packing density of the surface groups was observed. Of course, quantitative measurements were not as accurate with quartz powder as with high surface area Aerosil. 

It can be shown that the ratio v3lvg is equal to the ratio of polymer packing densities coefficients in the amorphous and crystalline states, KJKC at Tg, because, by definition, Ka = NA V /va and Kc - NA Vi/yC)where vj is the Van der Waals volume of the chain repeat unit. The calculated values of (ATc)g correlate with the characteristic chain parameter a/o, the relationship between them being expressed by a linear equation... 

Generally speaking, these properties are almost independent of the crosslink density in the same way as they are almost independent of the chain length in linear polymers. Thus, there are no fundamental differences between thermosets and amorphous thermoplastics in the glassy state, although certain second-order effects linked to crosslinking can be observed, sometimes, on packing density and local mobility. 

The structural perfectness of amorphous solids is usually characterized by the packing density K 39) which is determined by... 

Under defined conditions, the toughness is also driven by the content and spatial distribution of the -nucleating agent. The increase in fracture resistance is more pronounced in PP homopolymers than in random or rubber-modified copolymers. In the case of sequential copolymers, the molecular architecture inhibits a maximization of the amount of the /1-phase in heterophasic systems, the rubber phase mainly controls the fracture behavior. The performance of -nucleated grades has been explained in terms of smaller spherulitic size, lower packing density and favorable lamellar arrangement of the /3-modification (towards the cross-hatched structure of the non-nucleated resin) which induce a higher mobility of both crystalline and amorphous phases. 

The microstructure of various amorphous silicas was first discussed in a comprehensive manner by Iler in his early book The Colloid Chemistry of Silica and Silicates (I). Iler drew attention inter alia to the importance of the dense silica particle size and particle packing density in controlling the surface and colloidal properties of sols, gels, and precipitates. In particular, he showed how a change in coordination number of these globular... 

Ooh = 1) is obtained after preliminary treatment of the samples in vacuo at 180-200 °C, when for each Si atom there is approximately one OH group. The average value of the silanol number for such a state, aon = 4.6 OH groups per square nanometer, is a physicochemical constant (it is independent of the type of the amorphous silica used, the method of preparing it, and the structural characteristics, that is, the specific surface area, the type of pores, the distribution of the pores according to their diameter, the packing density of the particles, and the skeleton structure of Si02). 

Fig. IS. Comparison of radial distribution functions for an MD-generated amorphous hard-sphere soUd at a density (po 1.2) very slightly less than the amorphous close-packed density (circles), and a random closed-packed assembly of macroscopic spheres at po —1.22 (histogram). From Refs. 10 and 78.

Both Fade approximant " and the more powerful Tova approximant" predictions of the tails of the virial series are consistent with the location of the first-order pole at the crystal close-packed density, as required by the closure for the virial series. In fact, Baram and Luban" give this as a conclusion of their work. The known virial coefficients in the soft-sphere, inverse twelfth power models also imply that the virial series contains information on the crystalline phase at very high pressure, but is unrelated to the freezing transition, the glass transition, or the amorphous solid equation of state. °... 

The metal-modified amorphous sUica powders have a packed bulk density of at least 0.2g/cm. Packed density is measmed by placing a weighed quantity of sample in a graduated cylinder, and tapping the cylinder until the volume is essentially constant. 

The packing density of the constituent atoms in the interior regions of protein molecules is, on average, equivalent to that of most organic compounds in the crystalline state. As such, it is possible to consider that membrane proteins may exhibit some of the solid-state electronic properties which have been extensively studied in elemental amorphous materials and organic polymers. Such properties include electronic conduction via localized and delocalized electronic states. When localized states are... 

In the literature several models have been described in which amorphous alloys are, considered to be relatively stable if certain requirements are fulfilled. In many of the alloys Aj that can be obtained in the amorphous state there is a substantial difference in size between the metallic radii of the components (r > rg). In addition, the composition of many amorphous alloys made by means of liquid quenching is close to X = 0.2. This led Polk (1970) to propose a stability criterion for amorphous alloys in which the size difference in atomic radii and the asymmetry in composition is of prime importance. This stability criterion is based on the possibility of obtaining a higher packing density when the holes available in the dense random packing of the larger A atoms are filled by the smaller B atoms. In recent years it has... 

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