Kraus model, filler networking

Starch nanocrystals were used to reinforce a non-vulcanised NR matrix. The NR was not vulcanised to enhance biodegradability of the total biocomposite. Non-linear dynamic mechanical experiments demonstrated a strong reinforcement by starch nanocrystals, with the presence of Mullins and Payne effects. The Payne effect was able to be predicted using a filler-filler model (Kraus model) and a matrix-filler model (Maier and Goritz model). The Maier and Goritz model showed that adsorption-desorption of NR onto the starch surface contributed the non-linear viscoelasticity. The Kraus model confirmed presence of a percolation network. ... 

Of the several mechanisms investigated, the most commonly adopted is based on the filler network breakage [48, 49]. Kraus [7, 50] proposed a phenomenological model of the Payne effect based on this interpretation. In this model, under dynamic deformation, filler-filler contacts are continuously broken and reformed. The Kraus model considers filler-filler interactions but the loss modulus and effect of temperature were not taken into account. In the model of Huber and Vilgis [9, 50, 51] the existence of dynamic processes of breakage and reformation of the filler network is explained. In this model, the Payne effect is related to the fractal nature of the filler surface. At sufficiently high volume fractions of filler, percolation occurs and a continuous filler network is formed, characterized by its fractal dimension and its... 

It must be noted that, apart the initial filler-filler network considerations of Payne and Kraus, fhe subsequenf models essentially recognized the fact—today widely accepted—that, except in very highly filled systems, direct filler-filler confacts are very unlikely. Explicitly stated by Aranguren et al., i in the case of silica-silicone sysfems however, it must be noted that successful BdR measurements imply that filler particles surface is completely wetted by the polymer. Therefore, contacts between filler aggregates can occur only Ihrough the polymer. The differences in the various models arise either from the description of the filled system or from the manner the local thermodynamics is treated. 

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