the studies on filler-structure effects were carried out at high volume fractions of
fillers and thus the nonlinear viscoelastic behavior at low filler contents should be
explored.
In their work, Maier and Goritz proposed the dynamics of adsorption/desorption
of the polymer chains at the particle surface [33] and the Payne effect is due to the
stress-induced debonding of polymer chains from the filler surface. They derived
simple set of equations as well to account for the decrease of storage and loss
moduli with strain; however they failed to explain certain other rheological features
of the composites. Zhu and Sternstein suggested the polymer-filler interactions
including trapped topological entanglements are responsible for the reduction in
storage modulus with strain [34, 35]. The polymer filler interfacial interactions vary
according to the nature of the polymer-filler interface [36–39]. Maier and Goritz
considered the filler particles as multifunctional cross-links which can loosely or
strongly anchor to the rubber surface [33, 40]. Thus the amplitude of Payne effect
depends on the crosslink density as the loosely tied chains desorb with increase in
strain. The mechanism of Payne effect also involves the existence of cooperation
between the breakdown and reformation of the filler network and the molecular
disentanglement of the bound and free rubber [32, 40, 41].
The bonding and debonding between polymer chains and filler surfaces and its
effects on viscoelasticity have been studied and modeled [42, 43]. The studies on
the rheology of unfilled polymers could address adhesion and adhesive failure,
friction, and flow instabilities such as melt fracture, which can also be explored for
filled systems as well. Leger and co-workers [44] showed polymers slip on a flat
surface when sheared, regardless of the shear rate. There is a chance of a complex
disentanglement process between the tethered chains and the bulk polymer and this
develops with respect to shear rate. At sufficiently high strain rates, dynamic
decoupling occurs. According to Graham [45], the slip at polymer/filler interface
includes the effects of drag on polymer chains, disentanglement, and detachment
and reattachment of chains at the solid surface. In composites the entanglements are
more and this affect the particle diffusivity in a polymer matrix. The geometrical
confinements enhance entanglement interactions between polymer chains even in
the case of weak adsorption [46, 47]. In a general way we can say that the filled
(cross-linked) elastomers and filled (un-cross-linked) polymer melts show similar
nonlinear viscoelastic behavior with respect to both strain and filler characteristics.
In both cases, the entanglements are due to topological restraints (e.g. chemical
cross-links) or hydrogen bonding interactions. Thus both unfilled and filled elastomers have a common mechanism regarding the origin of the nonlinear
viscoelasticity.
Yatsuyanagi et al. [48] considered the existence of a percolation network
through a rigid amorphous layer formed around the particles and desorption and
adsorption of this layer happens during the Payne effect. It is also proposed that a
glass transition gradient exist near the surface of the filled polymer and that the
dynamics could be either enhanced or slowed down according to the interaction
of the chains with the surface [49, 50]. Montes et al. observed a maximum of
reinforcement when a continuous path is formed through the filler aggregates
Origin of Nonlinear Viscoelasticity in Filled Rubbers: Theory and Practice
9
fillers and thus the nonlinear viscoelastic behavior at low filler contents should be
explored.
In their work, Maier and Goritz proposed the dynamics of adsorption/desorption
of the polymer chains at the particle surface [33] and the Payne effect is due to the
stress-induced debonding of polymer chains from the filler surface. They derived
simple set of equations as well to account for the decrease of storage and loss
moduli with strain; however they failed to explain certain other rheological features
of the composites. Zhu and Sternstein suggested the polymer-filler interactions
including trapped topological entanglements are responsible for the reduction in
storage modulus with strain [34, 35]. The polymer filler interfacial interactions vary
according to the nature of the polymer-filler interface [36–39]. Maier and Goritz
considered the filler particles as multifunctional cross-links which can loosely or
strongly anchor to the rubber surface [33, 40]. Thus the amplitude of Payne effect
depends on the crosslink density as the loosely tied chains desorb with increase in
strain. The mechanism of Payne effect also involves the existence of cooperation
between the breakdown and reformation of the filler network and the molecular
disentanglement of the bound and free rubber [32, 40, 41].
The bonding and debonding between polymer chains and filler surfaces and its
effects on viscoelasticity have been studied and modeled [42, 43]. The studies on
the rheology of unfilled polymers could address adhesion and adhesive failure,
friction, and flow instabilities such as melt fracture, which can also be explored for
filled systems as well. Leger and co-workers [44] showed polymers slip on a flat
surface when sheared, regardless of the shear rate. There is a chance of a complex
disentanglement process between the tethered chains and the bulk polymer and this
develops with respect to shear rate. At sufficiently high strain rates, dynamic
decoupling occurs. According to Graham [45], the slip at polymer/filler interface
includes the effects of drag on polymer chains, disentanglement, and detachment
and reattachment of chains at the solid surface. In composites the entanglements are
more and this affect the particle diffusivity in a polymer matrix. The geometrical
confinements enhance entanglement interactions between polymer chains even in
the case of weak adsorption [46, 47]. In a general way we can say that the filled
(cross-linked) elastomers and filled (un-cross-linked) polymer melts show similar
nonlinear viscoelastic behavior with respect to both strain and filler characteristics.
In both cases, the entanglements are due to topological restraints (e.g. chemical
cross-links) or hydrogen bonding interactions. Thus both unfilled and filled elastomers have a common mechanism regarding the origin of the nonlinear
viscoelasticity.
Yatsuyanagi et al. [48] considered the existence of a percolation network
through a rigid amorphous layer formed around the particles and desorption and
adsorption of this layer happens during the Payne effect. It is also proposed that a
glass transition gradient exist near the surface of the filled polymer and that the
dynamics could be either enhanced or slowed down according to the interaction
of the chains with the surface [49, 50]. Montes et al. observed a maximum of
reinforcement when a continuous path is formed through the filler aggregates
Origin of Nonlinear Viscoelasticity in Filled Rubbers: Theory and Practice
9