Filler geometry

Filler architecture Filler geometry to some extent is influenced by the way in which the fillers are extracted and processed. The aspect ratio (the ratio of filler length to diameter) is an important characteristic for any material to be used as filler. Thus fillers with high aspect ratio are long and thin, while those with low aspect ratio are shorter in length and broader in the transverse direction [1]. 

Once the nanotubes have been characterised and polymer/ nanotubes elaborated, their microstructures have to be precisely determined to understand the relations between the process and the nanocomposites macroscopic properties. It is expected that the microstructural parameters that will play major roles (in addition to the filler geometry) are the nanotube dispersion and orientation... 

E and E correspond to the elastic moduli of composite and matrix, respectively represents the shape factor, which is dependent on filler geometry and loading direction q)f is the inorganic volume fraction 11 is given by the expression... 

Fig. 1 Surface/volume S/V) ratios for varying filler geometries, r is the radius, / is the length, and t is the thickness of fillet Taken from [37], Copyright 2006 by SAGE Publications. Reprinted by Permission of SAGE Publications, reproduced from [36], Copyright 2004, with permission from Elsevier...

Abstract This chapter deals with the non-linear viscoelastic behaviour of rubber-rubber blend composites and nanocomposites with fillers of different particle size. The dynamic viscoelastic behaviour of the composites has been discussed with reference to the filler geometry, distribution, size and loading. The filler characteristics such as particle size, geometry, specific surface area and the surface structural features are found to be the key parameters influencing the Payne effect. Non-Unear decrease of storage modulus with increasing strain has been observed for the unfilled vulcanizates. The addition of spherical or near-spherical filler particles always increase the level of both the linear and the non-linear viscoelastic properties. However, the addition of high-aspect-ratio, fiber-like fillers increase the elasticity as well as the viscosity. 

Influence of Filler Geometry and Size in Different Length Scales... 

As reported by Ashton et al. (1969), Halpin and Tsai introduced approximate equations for square fiber reinforcement by reducing Hermans (1967) solution using numerical solutions of elasticity theory. Equations for slender rigid inclusions at low concentrations were developed by Russel and Acrivos (1973). As for effective thermal expansion coefficient of filled polymers, the effects of filler geometry and constituent material properties have been studied by Kerner (1956). 

The excluded volume theory is the most commonly used continuum analytical model of percolation. The excluded volume of an object is defined as the volume around the object into which another identical object cannot enter without contacting the first object as illustrated in Figure 2. ° The principal concept in the excluded volume model is that the percolation threshold of a system is determined by the excluded volume of filler particles, rather than their true volume. This is particularly applicable to asymmetrical, unaligned objects for which the excluded volume can differ significantly from their true volume. Therefore, this model has been applied to describe critical percolation phenomena for a wide variety of filler geometries. In addition, excluded volume arguments provide useful theoretical approximations in many computational stu-dies. Excluded volume solutions were first formulated for soft-core (interpenetrable) fillers, and later extended to core-shell (impenetrable hard-core surrounded by a penetrable shell) fillers. ... 

Filler geometry affords one system of classification based purely on the mechanics of reinforcement ... 

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