Statistical mechanics of fuzzy random polymer networks

A statistical mechanics framework of fuzzy random polymer networks is established based on the theories of fuzzy systems. The entanglement effect is manifested quantitatively by introducing an entanglement tensor and membership function and the amorphous structure is treated as the fuzzy random network made up of macromolecular coils entangled randomly. A random tetrahedral entangled-crosslinked cell is chosen as an average representative unit of the fuzzy random polymer network structure. By making use of the theory of fuzzy probability and statistical mechanics, the expression for the free energy of deformation is given, which fits well with the experimental data on rubber elasticity under various deformation modes. Both classical statistical theory and Mooney-Rivlin equation can be taken as its special cases.