Abstract: 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.

摘要： 本文提出了炭黑填充硫化胶的网络结构是由交联网,缠结网和炭黑——高分子链网所形成的网络结构模型.基于该微观结构模型和弹性大形变机理用统计力学方法计算了三种网中各链组的末端距机率密度分布函数,三种网的形变自由能和炭黑填充硫化胶的总形变自由能,并根据弹性形变自由能同应力一应变间的关系得到了四种简单形变方式的应力一应变关系式.