Dense-random-packed

Reference porosity for a dense random packing of monodisperse spheres s = 0.36-0.40... 

Figure 9.22 The major reasons for change of porosity value comparing to a porosity of a dense random packing of monodispherse. Upward arrows correspond to increase, and downward to decrease of porosity (see text for more comments).

Table 9.8 Distribution of D-Polyhedrons in a Dense Random Packing of Monospheres...

Local structural features have been postulated for amorphous polymer systems, based on the asymmetry of chain-like molecules. Flory (56) has shown that molecular asymmetry in itself is no barrier to a dense random packing of the chains are sufficiently flexible. Robertson (57) suggests, however, that some degree of local alignment is required simply to accomodate linearly connected sequences in the rather limited space available. Unfortunately, Calculations of local cooperative effects are extremely difficult and sensitive to specific assumptions about available packing arrangements. 

The denslflcation process of 2D discotic fluids has also been addressed by geometrical methods, for instance by Sutherland and Mason ). The latter carried out a computer simulation from which 2D radial density distributions could be derived. With increasing density the peaks became sharper and more manifold. Sutherland estimated the onset of dense random packing to be at a packing density of 0.82-0.83. 

We consider first the simulation of the atomic structure of vitreous silica because the majority of the simulations of amorphous oxides were done for this material. Some of these have simulated the formation of the vitreous silica surface in a very detailed fashion. Furthermore, the methods developed for the simulation of vitreous silica and its surface may be used with some modifications for other amorphous oxides. Subsequently, we consider less detailed methods of simulation of amorphous oxide surfaces which are not limited to Si02 but can be applied to various oxides. Finally the least detailed but the most general model - the Bernal surface (BS) - represents the atomic arrangement at the surface of any amorphous oxide (most important for physical adsorption) by the dense random packing of hard spheres. 

An even more general and correspondingly less detailed atomic model of amorphous oxide surfaces has been called the Bernal surface (BS)[3, 21]. It is based upon the fact that many oxides and halides can be regarded as close-packed arrays of large anions with much smaller cations occupying interstitial (usually tetrahedral or octahedral) positions (see., e.g. Ref. [4]). In line with this point of view, the BS is a surface of a collection of dense randomly packed hard spheres, a sphere representing an oxide anion. The cations in interstitial positions between hard spheres are excluded from the simulation since they do not attract adsorbed molecules due to their small polarizability. Thus only the atomic structure of the oxide ions is considered. This is called the Bernal structure and has been used for modelling simple liquids and amorphous metals [15]. 

IV. Structural Properties of Dense Random Packings of Hard Disks... 

Our polygon description of the structure of 2D dense random packings of hard disks parallels Bernal s description of three-dimensional (3D) dense random packings of hard spheres as space-filling arrays of elementary polyhedral units ( Bernal holes, or canonical polyhedra ) [2-5]. Bernal s approach to 3D liquid structure is discussed in more detail in Section IV.A. 

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