Classical Phenomenological Models of Polymer Viscoelasticity

Viscoelastic properties of entangled polymer fluids have been an important research area in polymer science and engineering. Unlike elastic solids or simple viscous liquids, entangled polymer fluids exhibit very complicated viscoelastic behavior in an external field, which indicates that the stress is a function of the whole deformation history rather than just of strain amplitude or of strain rate. In the recent half century, plenty of models and theories have been made to understand these viscoelastic properties. Some are based on the principles of continuum mechanics, such as the Maxwell model, the Voigt-Kelvin model, and the various constitutive models, all of which have parameters that are constant in space and time. An alternative model of polymer dynamics and rheology is modeled by a transient network where the entangled points are considered to act as temporary crosslinks and polymer chains are represented by beads and springs. The rheological behavior of the system depends on the kinetics of breakage and reformation of the network made of interacting polymer molecules. Others are microscopic theories for an entangled polymer fluids. One of the most famous and successful molecular theories is the tube theory. In this review article, we first introduce the basic concepts of the linear response of viscoelasticity and the Boltzmann's superposition principle. Then, we focused on the three classical phenomenological models, including the Maxwell model, the Voigt-Kelvin model, and the transient network model, which are still popularly employed in the field of entangled polymers and other viscoelastic materials. In particular, the detailed derivation and critical issues for these models are discussed. Microscopic theories of viscoelasticity will be detailedly and thoroughly introduced in other reviews.