  The study deals with the Payne effect (a substantial decrease in the storage
modulus of a particle-reinforced elastomer with an increase in the amplitude of
mechanical oscillations). The influence of temperature, concentration of filler
and amplitude and frequency of strains is analyzed on the mechanical response
of filled rubbery polymers. Constitutive equations are derived using the
concept of two interpenetrating networks: one comprises semiflexible polymeric
chains connected to temporary junctions, whereas the other is formed by
aggregated filler clusters. Adjustable parameters are found by fitting
experimental data for natural rubber, bromobutyl rubber and styrene-butadiene
rubber reinforced by carbon black and polymeric particles. The critical
concentration of particles is determined that characterizes transition from an
ensemble of disjoint clusters to the network of filler. The volume fraction of
filler corresponding to this transition is found to be close to theoretical
predictions based on the percolation theory, as well as to experimental data
for isolator-conductor transition.
