A tree-growing graphic model for asymmetrical phantom networks in polymeric gels undergoing dynamic mechanochemical coupling

Network structures of various polymers have significant effects on their mechanical properties;therefore,numerous studies have investigated the constitutive relationship between symmetrical network structures and their rubber elasticity in polymers.However,few studies have focused on asymmetrical network structures in polymers that undergo bond exchange reactions,selfassembly,or mechanochemical coupling—all of which are induced by transition probabilities of chemical bonding processes.In this study,an extended constraint junction and phantom network model is formulated using the tree-growing theory to establish a constitutive relationship between asymmetrical network structures and their rubber elasticity in polymers.A free-energy equation is further developed to explore working principles of configurational transitions on the dynamic rubber elasticity of symmetrical and asymmetrical network structures.The constitutive relationship between dynamic rubber elasticity and symmetrical and asymmetrical network structures has also been proposed for the gels undergoing mechanochemical and hydromechanical coupling.Finally,the effectiveness of this newly proposed tree-growing model has been verified by comparing with the classical affine network model,finite element analysis,and the experimental results of gels reported in literature.