A statistical mechanical approach to the Payne effect in filled rubbers

In this paper we apply and discuss some new aspects to the steric interaction of filler particles in reinforced elastomers under dynamic mechanical loading conditions. At certain concentration the filler particles (for example, carbon black, or silica) form loose clusters which themselves interact with each other and form a filler network with a significant contribution to the dynamic modulus of the rubber material. The filler concentration is relatively high, so that it is likely that the clusters undergo a 'jamming transition'. With increasing strain amplitude under periodic mechanical deformation the disruption of the filler network resp. of finite filler cluster configurations leads to dejamming observed as softening of the rubber. As a theoretical approach we map the problem on a simple one dimensional Ising model. We present here a static model of this jamming (dejamming) and discuss the consequences on the mechanical and deformation properties of the filled rubber.