Guth-Gold equation has been estimated based on the theoretical and experimental consideration. The equation is only available to the filling of such particles of almost perfectly homogeneous dispersion as MT carbon blacks and glass beads. In most carbon blacks of higher reinforcement, however, the Guth-Gold equation consisting of the fIrst and second power of volume fraction of particle does not express the much higher modulus in the higher volume fraction.
In this report, the author introduces the third power of volume fraction to the Guth-Gold equation, which will be in good agreement with experimental results semiquantitatively. Furthermore, the coefficient of the third power is closely related to the formation of the super network connected by bound rubbers between carbon aggregates. It must be the fundamental structure to give the much higher modulus for the carbon black-filled rubber than the Guth-Gold equation.