The fluctuation of chains and junctions in real vulcanizates with carbon blacks tended to be suppressed by the presence of three kinds of forces

namely network

trapped entanglement and carbon-polymer interaction forces. A new molecular theory of rubber elasticity

concerning the constraints of junctions

trapped entanglement and carbon-polymer interactions

was presented. It was then possible to relate the elastic equation of state to the molecular constitution through three important quantities (C100

C200 and C020). The severity of junction

trapped entanglement and carbon black-polymer interaction constraints could thus be characterized by four molecular para-meters(ΦΔc

ΦΔe

ΦΔcf and ΦΔef). A structural model of constituent chains and networks for vulcanizates with carbon blacks was proposed. The four constituent chains were taken as statistically elementary unit for network assembly. They were also considered as independent elementary unit taking part in the macroscopicdeformation. The ultimate networks were formed by the combination of three different kinds of networks

namely crosslinked

trapped entanglement and carbon black polymer chain networks. It was shown that the probability distribution functions of end-to-end vector for the four kinds of constituent chains mentioned above were different from the Gaussian function. Using the probability distribution functions and the proposed mechanism of large deformation

we have calculated the elastic free energy of deformation as the sum of two terms

one from the crosslink-entanglement networks and the other from the carbon black-polymer chain networks. The expression of the elastic free energy of deformation for vulcanizates with carbon black fillers was given in Equation(20). The relationship of stress and strain for four different types of deformation (uniaxial extension

equi-biaxial extension

unequi-biaxial extension and pure shear) were derived from the theory of elasticity for vulcanizates with carbon black fillers. These were given in Equation(21)

(22)

(23)and(24)

respectively.