Random materials

G. H. Weiss, Aspects and Applications of the Random Walk Random Materials and Processes, series edited by H. E. Stanley and E. Guyon, North-Holland, Amsterdam, 1994. 

Schematic plot of g(r) as a function of r for a random material, a bcc crystal, and a glass with short-range crystal. 

Stanley, H. E. Fractal surfaces and termite model for two-component random materials. In book Fractals in Physics. Ed. Pietronero L., Tosatti E. Amsterdam, Oxford, New York, Tokyo, North-Holland, 1986,463 77. 

Z. Vardeny, E. Ehrenfreund Proceedings of the "Conference on Transport and Relaxation Processes in Random Materials", Gaithersburg 1985... 

The final structure of the particles after a long period of eomputing is shown in Fig. 5.16. It was evident that the stracture was dominated by fee shown as dark spheres, while most of the random material shown as light had disappeared. But there were still significant regions of bcc and hep. The fee was not all in the same orientation but had typically formed 3 crystallites in this size of packing. This suggests that 20 000 particles are required for each crystallite when nucleation is spontaneous and not dependent on any outside stimulation. Obviously, artificial... 

A typical picture showing these two effects is given in Fig. 5.18. Adhesion of less than 1 kT had little effect on the model, but adhesion of 2 kT slowed down the crystallization, leaving a lot of random material, which is shown as light colored spheres in Fig. 5.18. It was noticable too that the nuclei were more rounded in this case, as expected, because there was now an intafacial energy between random and structured phases, arising from the adhesion force. 

Torquato, S. (2009) Random Materials Microscopic and Macroscopic Properties,... 

H. Gisser (Frankford Arsenal) I would like to make a comment on the matter of side chains. in the case of teflon and hexafluoro-propylene, there is no question about the effect of trif 1uoromethyl group which increases the friction coefficient. When one studies polyalkyl methacrylate, one finds that the effect of side chain is different. Of course, the simplest one already contains a side chain, but when the length of side chain increases, for example, polyethyl methacrylate, polypropyl methacrylate, the friction coefficients decrease. It turns out that we are dealing with different materials. Polymethyl methacrylate is. an amorphous (random) material, but the higher methacrylates begin to show crystallinity. 

S. B. Savage, Disorder, Diffusion and Structure Formation in Granular Flows, in Disorder and Granular Media, Bideau, D. and and Hansen A. eds.. Random Materials and Processes Ser., 255-285, North Holland (1993). 

Note that for this case the HS upper bounds are identical to the Mori-Tanaka predictions for random materials of matrix-inclusion type with spherical inclusions [Mori Tanaka 1973, Weng 1984, Zimmerman 1994] and that Equation (91) corresponds to a relation known in geophysical context under the name Kuster-Toksbz relation [Kuster Toksoz 1974, Zimmerman 1991b]. It is shown below that in the alumina-zirconia system the Kuster-Toksoz relation. Equation (91), is an excellent approximation to the HS upper boimd for the tensile modulus (error <0.1 %) and for the shear modulus (error < 2.6 %) but not for the bulk modulus (error < 14.3 %). For the purpose of later reference we note that Equation (91) can be approximated by the following second-order polynomial ... 

Copolymerization of ADMET EP monomers with 1,9-decadiene, thereby forming linear EP copolymers with random branch distribution, has also been accomplished (Sworen et al., 2003). In this study it was again found that as the branch content increased, overall crystallinity as well as the melting temperatures and enthalpies decreased. In the cases of the highest amount of branch incorporation the random materials exhibited a broad, ill-defined melting behavior in contrast to the sharp melting endotherm observed for the precise models with similar branch content. This drastic difference in the behavior between precise and random models punctuates the effect of precise branch placement (Sworen et al., 2003 Smith et al, 2000). 

At the highest amount of acid incorporation studied, equivalent to that of COOH9, the random materials become amorphous as well, although with a significantly depressed Tg compared to the precision material displaying again the effect precise placement has on these materials. 

It is, of course, evident that no fluctuations exist in an ordered structure in which the nature of any atom in the system is known throughout, even if the system is of infinite extent. With fluctuations gone, the system behaves quite differently from a random material. It is for this reason that the use of a single, ordered configuration is disallowed, both physically and logically, as a representative of a disordered alloy at a given concentration. 

The first developments of the SEEM can be traced back at least to Cornell (1970), who studied soil settlement problems, and to Shinozuka (Astill et al. 1972), who combined FEM with Monte Carlo simulation for reliability analysis of stmctures with random excitation, random material properties, or random geometric properties. He introduced random fields and discretized them based on spectral representation theory... 

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