Reminder: Einstein–Smallwood

In the following sections we are going to study the reinforcement obtained by adding particles to the elastic matrix. The mechanisms of the effective enhancement of the elastic modulus cannot be explained by one simple theory, since several interactions and many different length scales are involved [179]. This is because there are different physical levels of reinforcement. The rubber matrix contributes through its rubber elasticity [7], whereas the filler particles contribute in different ways. The most well known of these are volume effects, also called hydrodynamics interactions (due to the analogy with the enhancement of the viscosity of liquids by the addition of particles).

In the context of carbon-black-filled elastomers, the contribution to reinforcement on small scales can be attributed to the complex structure of the branched filler aggregates as well as to a strong surface–polymer interaction, leading to the socalled bound rubber. Thus the filler particles are coated with polymer chains and the binding (physical or chemical) of elastomer chains to the surface of the filler particles changes the elastic properties of the macroscopic material significantly [2]. On larger scales the hydrodynamic aspect of the reinforcement dominates the physical picture. Hydrodynamic reinforcement of elastic systems plays a major role not only in carbon-black-filled elastomers, but also in composite systems with hard and soft inclusions. Finally, at macroscopic length scales filler networking at medium and high filler volume fractions plays a dominant role [179].

In this chapter we are going to concentrate – on a general basis – on the different mechanisms of elastomer reinforcement in the hydrodynamic regime. To do so, we present two different regimes of reinforcement mechanisms.