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Claude Tricot

Extracting Dispersion from Roughness

Laboratoire de Mathematiques Pures, Universite Blaise Pascal 63177 Aubiere, France

ABSTRACT A mathematical analysis of surfaces may help to understand how the carbon black is dispersed into polymer. Rubber samples are broken out, and the rupture interface is scanned with a pro lometer. The roughness is detected at the micron scale. Roughness functions are de ned, measuring the average oscillations of the surface. The roughness behaviour is "fractal" for small scales until around 10 microns, then become linear. A roughness ratio is de ned, depending both on the scale and on the mixing time. There is evidence to suggest that the roughness ratio does not depend on the polymer, but only on the dispersion of the ller. A dispersion factor is derived, and results are shown on three dierent compounds.

AGGREGATION AND DYNAMIC Carbon black is composed of particles of 10 to 100 nanometers (see e.g. [1]) which are solidly fused together to form aggregates (also called primary agregates [2]) which may vary in size from 50 to several hundreds nanometers. During mixing with Elastomer and during normal usage of the nal product, the aggregates can be considered as unbreakable. During mixing, aggregates coalesce to form larger agglomerates (or secondary aggregates), bound by weak Van der Waals forces, forming what is commonly called the Carbon Black Network. This network aect the response of the rubber compound to strain energy input into a non-linear behavior. Agglomerates are breakable when conventional mechanical mixing energy is used to disperse the llers. The dependancy of energy dissipation due to strain energy input may be explained at the particle scale through a simple mechanical model [3]. It is more dicult to understand the global process of energy dissipation, through an observation of the structure of the Carbon Black Network. It seems certain that the geometry of the network is one of the major factors in the thermodynamic response of rubber compounds to strain. In order to further understand the impact of geometry, one has to nd parameters which (i) describe this geometry, and (ii) are possible to calculate from direct measurements. One problem is that the 3D-structure of the Carbon Black Network cannot be sized directly after mixing. Data are usually obtained using microscopic techniques ranging from the Transmission Electron Microscope to the most commonly used Optical Microscope. These evaluations allow to analyse 2D projections of a given volume of compound but not to obtain pure 3D data, nor to distinguish between aggregates and agglomerates. Until now, it has been impossible to establish direct relationships between the network structure and the dynamic response of the compound. KK3.8.1

STRUCTURE We consider a rubber compound having a ller loading below the percolation treshold. Dierent structures may aect the compound in dierent ways. For example, let us imagine that the black pellets are perfectly broken in their individual aggregates so that the