Following a brief review of some earlier theories of filler reinforcement that were based, at least partly, on thermodynamic treatments, a reinforcement equation is derived by a combination of thermodynamics and the elasticity theory of large strains. It consists of an elastic energy term and a surface energy term, and is given by:
In it, the “reinforcement energy,” R.E., is defined as the energy of the filler‐rubber mixture less that of the separate components. This is related to a fractional heat term (p) arising from the “expansion” of the rubber due to filler incorporation, the Young's modulus (E) of the rubber, the number of particles (n) of filler (considered as existing initially in an aggregate), the ultimate particle diameter (d), the volume of rubber (V1), the total energy of immersion per unit surface area (Γ) of the filler in the rubber, and the mean cohesion or aggregation energy per particle (δ) between the particles in the original aggregate.
The significance of R.E. in terms of actual reinforcement is discussed; R.E. is regarded as negative measure of reinforcement. Estimates are made of the magnitudes of the two energy terms and of the surface energies Γ and δ. These indicate that in mixtures containing very active fillers (such as carbon blacks in natural rubber), Γ is of the order of 100 ergs per sq. cm. and the surface energy term is dominant. A crude estimate indicates that δ is much less than Γπd2 for very active fillers, that these quantities may be of the same order of magnitude for less active fillers, and that δ may be larger than Γπd2 for inert fillers. In the last two cases, the surface energy term loses much or all of its dominant character.
Predictions from the reinforcement equation are examined in the light of available experimental results, and some apparent discrepancies are discussed. Expressions are given for corrections that need to be applied to the equation when particle dispersion is incomplete, or when the latter is a function of the filler concentration.