Amorphous dense randomly packed structure

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. 

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]. 

A substantial amount of effort has been spent on finding model descriptions of the atomic scale structure of amorphous alloys. Such three-dimensional models have attempted to provide concrete though idealized pictures of the arrangements of the atoms that go beyond the information that can usually be obtained from experimental radial distribution functions. The most prominent among them are microcrystalline and cluster models, and models based on the dense random packing of hard spheres (DRPHS). 

Structures at all relevant length scales, as described in Sections 34.2.1-34.2.4, can be classified further into organized and random packing stmetures. For dense materials, structural organization is expressed in the presence (or absence) of a periodic crystal lattice. For microporous materials there is a clear distinction between crystalline zeohtes and amorphous sihea with a very short range order. Zeohte membranes may consist of a three-dimensional mosaic of crystaUites that may be either randomly orientated with respect to each other or possess a certain preferred orientation or texture (Lai et al., 2003). The polycrystaUine nature of and presence of texture in zeohte membranes can have important consequences for flux and separation behavior. 

Several cluster models have been tested to account for patterns of small clusters (p = 1 or 2 bar in Fig. 18). First, clathrate models have been examined. The most popular of these consists of a regular dodedecahedron with one H2O molecule at each of the 20 vertices and possibly one additional molecule at the center. In this model, HjO molecules form regular pentagons with a molecular angle HOH of 108°, which is intermediate between 104.5°, the value for the free molecule, and 109.5°, that for tetrahedral bonding in the diamond cubic structure. Such a clathrate model, stabilized by an additional proton, accounts well for mass spectrometry results, but is found to be far too symmetrical to account for the structure of neutral clusters. An amorphous model,derived from Polk s random dense packing, has been tested. This... 

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