Random close packing model

If instead of carefully laying the layers one above the other, the spheres are simply packed into an odd shaped container, the process is known as random close packing or rep. The requirement of odd shape of the container is to prevent any deliberate introduction (nucleation) of 

Like in the ball and stick models of cm, in the rep model also the positional coordinates of spheres in the assembly are carefully determined. Space filling polyhedra can be built around each sphere in the assembly, in the manner of building Wigner-Seitz cell in a reciprocal lattice that is, by erecting perpendicular planes at the mid points of the lines connecting the 

The most popular of the potentials has been the Lennard-Jones (6-12) potential which is of the form, 

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Amorphous rare earth alloys exhibit the same variety of magnetic effects as is found for RI compounds. In addition their resistivity often manifests a behaviour which is typical of amorphous metals such as resistivity minima and negative temperature coefficients of resistivity. It is important to note that the unifying feature of all amorphous metals is the real space structure which can be described in terms o a random close packing model of hard spheres (Cargill, 1975). The magnetic feature thus depends on the type and concentration of the... 

Pouzot et al. (2004) reported applicability of the fractal model to )6-lactoglobulin gels prepared by heating at 80 C and pH 7 and O.IM NaCl. They suggested that the gels may be considered as collections of randomly close packed blobs with a self-similar structure characterized by a fractal dimension Z)f 2.0 0.1. 

Mellor, D.W. Random Close Packing (RCP) of Equal Spheres Structure and Implications for Use as a Model Porous Medium. Ph.D. thesis. Open University, 1989. 

To model the elastic properties of dispersions of soft particles, we consider a dispersion of N spheres in a periodic box, as shown in Fig. 6. The particles are either monodisperse with radius R or polydisperscd with a Gaussian distribution around a mean radius R. The concentration of particles is above the random close-packed volume fraction of 0c = 0.64 so that the particles are jammed together and form facets at contact. The contacts are assumed to be purely repulsive and frictionless and hence exert only a normal repulsive force at contact. The total elastic energy stored in the structure is the summation of the pairwise contact energies. Even at the highest volume fraction at near-equilibrium conditions, i.e., without flow, deformation of a particle is no more than 10% of its radius. Thus, the particle deformation is small compared to the size of the undeformed sphere and the contacts obey the Hertzian contact potential given by (1). 

A revised picture is needed to describe the structure of films composed of coadsorbed polar solute molecules and nonpolar solvent molecules. The close-packed model of Reis implies that the coadsorbed solvent should be relatively tightly bound. That this is apparently not the case is suggested by the ease with which the n-octadecane was removed from all the films. The data show that n-octadecane is more firmly attached to the surfaces on which stearic acid is adsorbed than to surfaces on which no acid is adsorbed. This means that the coadsorbed n-octadecane found is not present in the film as relatively large aggregates of randomly oriented solvent molecules on the surface. These aggregates, if they exist on the surface initially, should have been removed by the 5-second rinse. This is based on the fact that solvent was removed from the silver mirrors which had been immersed in pure n-octadecane containing no stearic acid. 

The atomic packing in disordered solids was investigated first by Bernal (1964), who considered the problem in the context of a model of a simple liquid that consisted of randomly close-packed hard spheres of uniform size and described the structure as a distribution of five different canonical polyhedra with well-defined volume fractions. 

The threshold volume fraction of percolation (( >,) is guided by the amphiphile shell length and the overall volume fraction of the dispersed phase. For zero shell length and no interparticle attractive interaction, according to the randomly close-packed hard sphere model, 4, = 0.65 systems with strong attractive interactions end up with (f), being lowered from 0.65 to 0.10. 

Thus, the analysis of the globular gel structure according to a particle packing model results in an overestimate of the particle diameter, whereas the cylindrical model results in an underestimate of the cylinder diameter. The appropriate geometry, therefore, appears to be a necked, random close-packed assemblage of particles whose relative density is 0.73. The necks are not large enough, however, to constitute smooth cylinders. 

In crystalline oxides and hydroxides of iron (III) octahedral coordination is much more common than tetrahedral 43). Only in y-FegOs is a substantial fraction of the iron (1/3) in tetrahedral sites. The polymer isolated from nitrate solution is the first example of a ferric oxyhydroxide in which apparently all of the irons are tetrahedrally coordinated. From the oxyhydroxide core of ferritin, Harrison et al. 44) have interpreted X-ray and electron diffraction results in terms of a crystalline model involving close packed oxygen layers with iron randomly distributed among the eight tetrahedral and four octahedral sites in the unit cell. In view of the close similarity in Mdssbauer parameters between ferritin and the synthetic poljmier it would appear unlikely that the local environment of the iron could be very different in the two materials, whatever the degree of crystallinity. Further study of this question is needed. 

In Figure 1, a is plotted vs. ax for a face-centered lattice (a close-packed lattice) and for a simple cubic lattice (a loose-packed lattice). We notice that (1) the dependence of a on ax can be regarded as being practically the same for both lattices and that, (2) tx undergoes a rapid change around x = xc, which is the point at which a = 0 (Fig. 1). However, p/a does not attain the value it would have for the case of the unrestricted random walk model at x = xc, since at this point, p/a > 1 (Fig. 2), while for unrestricted chain pja = 1. Moreover, the dependence of p/a on ax is not the same for the two lattices while a as a function of ax is practically independent of the lattice. 

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