Spherical particles, cubic array

The yield stress was estimated by assuming that the effective load-bearing cross section decreased as a result of interfacial debonding. For a cubic array of spherical PS particles that are partially detached from the LLDPE matrix (Figure 4), the effective load-bearing cross-sectional area (Aeff) is given by... 

Figure 4. Schematic of the cubic array of partially debonded, spherical particles. The effective cross-sectional area (A ) is defined.

Equation 3.11 can be used as a first estimate for the bulk resistivity of a packed cubic array of spherical particles. Equation 3.11 also indicates that the surface resistance of a particle is controlling over the conduction process for the condition that... 

The Dancoff Factor for Cubic Arrays of Spherical Fuel Particles, J. P. McNeece, T. J, Trapp (BNWL)... 

Ham [508] considered that the growth of a random array of precipitating particles could be approximated to a simple cubic lattice of spherical sinks of radius R to which more material diffused from the supersaturated solution. A model of the type is very similar to those models discussed by Reek and Prager [507] and Lebenhaft and Kapral [492], The analysis which Ham introduced highlights a similarity between the competitive effect and the Wigner—Seitz model of metals. 

The composition of the dense systems that have been simulated up to now is summarized in Table 1. The polymer chains are modeled as unbranched sequences of 100 isodieimetric units connected by links of length <7, while the filler particles are modeled as spherical entities with diameter a/. The simulated systems consist of three-dimensionally periodic arrays of cubic cells of edge 40 a containing Np polymer chains and Nf filler particles. The polymer units interact through a 12 — 6 Lennard-Jones potential Euu = — 2((r/ruu) ], where Tuu is the distance be-... 

The theoretical ID expression may be found using idealized unit cell lattice models. Wu [3,4] has suggested such an expression, based on a cubic lattice array for ID, as a function of volume fraction, and particle size for spherical, mono-sized particles ... 

In these simulations, a filled PDMS network was modeled as a composite of cross-linked polymer chains and spherical filler particles arranged in a regular array on a cubic lattice [14,40]. The arrangement is shown schematically in Figure 14.1. The filler particles were found to increase the iion-Gaussian behavior of the chains and to increase the moduli, as expected. It is interesting to note that composites with such structural regularity have actually been produced [60,61], and some of their mechanical properties have been reported [62,63]. 

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