Abstract
The stiffening of elastomers by filler loading is both a surface and a volume effects. As expressed in a formula by Guth and Smallwood, volume effect means the increase of the strain energy, and is due to the stress disturbance in the matrix around filler particles. Therefore, a more general formula applicable also to reinforced hard polymers will be derived, provided that the volume dilation term is not omitted when the equation of equilibrium in terms of displacements is solved: The result of our analysis is presented in the text.
The analysis of surface effect has been developed by many investigators. Among them, Furukawa and A.M. Bueche modified the stress equation of rubber elasticity based on the kinetic theory by introducing the term accounting for additional network chains resulting from the adhesion of polymer molecules on filler surfaces. Recently, a more precise equation was derived by Sato which included, besides a surface and a volume effects, a cavity effect due to incomplete wetting.
There were many reports which suggested that the bond between rubber and active fillers, such as fine silica and carbon black, was so strong as to be considered chemical in nature. However, a variety of data suggesting the existence of weak bonds something thixotropic in nature were also presented.
F. Bueche proposed a molecular theory for the softening of filled rubber which was caused by prestretching. He indicated that short chains fastened their both ends to filler particles should be easily broken by a slight stretching owing to stress concentration, even when the adhesion was strong. He also showed that the recovery of hardness in prestretched, filled SBR was a rate process having an activation energy of about 22kcal/mole. Such a method of analysis is of promise for studying the rubber-filler interactions.
Some important reports on viscoelastic behaviour of filler-rubber systems are reviewed. Thomas et al. have accomplished their studies on the rupture of rubber in view of the energy balance theory, which was began about ten years ago. They found that the tearing energy was the order of 106 erg cm-2, considerably in excess of surface energy, and indicated that the irreversible dissipation of energy due to viscous or viscoelastic deformation around the tip of tearing front governed the rupture process. They also studied the dependence of rupture energy on rate, temperature, and filler loading, and observed a remarkable increase of the tearing energy over a range of rates and temperatures for SBR vulcanizate reinforced with F T black: Since this filler has a limited reinforcing ability, an enormous energy dissipation at the transition region will be ascribed to the increase of internal friction by filler.
