Structure effect, filling compound

Materials which such a complex structure cannot of course exhibit a simple rheological behavior, and relatively easy arguments may be produced to explain—so far qualitatively—how this complex structure affects most of the flow singularities of rubber compound. As illustrated in Figure 5.17, typical nonlinear effects observed with CB filled compounds appear as logical consequences of such a soft three-dimensional network of complex rubber-aggregate entities with connective filaments. 

Up to this point, the strain amplification factor can be viewed as a mere empirical approach to assign the modulus increase in CB filled compound to filler level. Equation 5.19 above essentially resulted from considerations on the hydrodynamic effects induced by the presence of solid particles ideally dispersed in a matrix with a considerably lower modulus. The empirical factor f in Equation 5.20 adds nothing in this respect and it is well known that both equations do not suit at all either highly loaded compounds, whatever is the grade of CB, or moderately loaded materials with high structure blacks. Over the last decades, several authors have developed theoretical considerations to model the likely effect of a so-called filler network structure and the associated energy dissipation process when filled compounds are submitted to increasing strain. 

For the transition metals it is often impossible to reach a noble gas structure except in covalent compounds (see effective atomic number rule) and it is found that relative stability is given by having the sub-shells (d or f) filled, half-filled or empty. 

At sufficiently low strain, most polymer materials exhibit a linear viscoelastic response and, once the appropriate strain amplitude has been determined through a preliminary strain sweep test, valid frequency sweep tests can be performed. Filled mbber compounds however hardly exhibit a linear viscoelastic response when submitted to harmonic strains and the current practice consists in testing such materials at the lowest permitted strain for satisfactory reproducibility an approach that obviously provides apparent material properties, at best. From a fundamental point of view, for instance in terms of material sciences, such measurements have a limited meaning because theoretical relationships that relate material structure to properties have so far been established only in the linear viscoelastic domain. Nevertheless, experience proves that apparent test results can be well reproducible and related to a number of other viscoelastic effects, including certain processing phenomena. 

An ordered distribution of spheres of different sizes always allows a better filling of space the atoms are closer together, and the attractive bonding forces become more effective. As for the structures of other types of compound, we observe the validity of the principle of the most efficient filling of space. A definite order of atoms requires a definite chemical composition. Therefore, metal atoms having different radii preferentially will combine in the solid state with a definite stoichiometric ratio they will form an inter-metallic compound. 

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