Theory of Viscoelasticity in Temporarily Crosslinked Polymers (1) Treatment in Single Relaxation Time

A molecular theoretical investigation of the viscoelastic properties of amorphous polymeric substances within the rage of long relaxation time has been pursued using a temporarily crosslinked network structure model. The origin of the energy dissipation is ascribed to the slipping of chains and the change in number of chains induced by deformation. Since the slipping of chains exists, the inner deformation tensor of chains which is different from the observable deformation tensor of network structure can be introduced. Assuming that the inner deformation tensor is characterized by a single average deformation tensor, the relation between the observable and inner deformation tensors is obtained. The expression of the rate of change in number of chains is also obtained in the same formula with that of chemical reaction. The stress-deformation-time relation is proved to be the generalization of Maxwell model. This shows that the system considered is equivalent to the generalized three dimensional Maxwell model.