Blend rules for homogenous and heterogenous systems

Blend rules for (a) homogeneous and (b) heterogeneous systems are proposed in a form of P = (ϕ m 1 P 1 + ϕ m 2 P 2 )/(ϕ m 1 + ϕ m 2 ), where P is the property, and ϕ, the volume fraction of component 1 or 2. For (a) m >1 and for P 2 > P 1 , an S‐shaped relation occurs between P or ϕ 1 . On the contrary, for (b) m <1, an anti‐S‐shaped relation occurs. When the hard component forms particles in continuous soft media, P is larger than the arithmetic mean P̄ . When the interface slips, a mean of harmonic function holds so that 1/ P = ϕ 1 / P 1 + ϕ 2 / P 2 and P < P̄ . For special cases, i.e., the filler in the rubber and the rubber particles in the resin, the strength at break attains a maximum at 20 and 13% of particles, respectively. For rubber blended with a small amount of polypropylene by dynamic vulcanization, the latter forms a continuous phase, reinforcing rubber domains by the plastic force when the size of rubber particles becomes very small. © 1994 John Wiley & Sons, Inc.