Linear Viscoelasticity of Polymer Melts

The increasing use of plastics in high-tech applications calls for in-depth knowledge of the processes used to manufacture these objects, and a better match between materials and processing techniques. This approach to optimizing, or even selecting, a material in relation to a process invites us to consider ease of processing as a material property in its own right. In the case of polymers, processed from a malleable state obtained by raising the temperature (thermoplastic polymer) or from a liquid state prior to polymerization (thermosetting polymer), this property is characterized by rheological behavior in the molten or liquid state. While many problems can be solved by treating the molten polymer as a viscous fluid, a number of phenomena can only be understood in the field of viscoelasticity.

The term viscoelasticity will be defined as characterizing a particular mechanical behavior intermediate between the behavior of an ideal hooked solid and that of an ideal Newtonian liquid. As we shall see in this article, this means that the mechanical properties observed are generally dependent on time (or derived quantities) and temperature. This specificity leads us to observe a number of phenomena typical of the behavior of highly elastic materials under temperature conditions where the material is commonly described as molten.

The concepts and methods developed in this text deal more specifically with the linear viscoelastic behavior of polymer melts in shear, a fundamental characteristic of the particular rheological behavior of these materials. They are, in any case, limited to the case where the relationship between stress and strain is linear: a doubling of strain leads to a doubling of stress. This means that the moduli observed, i.e. the ratio of stress to strain, are not a function of strain amplitude. This condition is highly restrictive, as the formalism and concepts developed in linear viscoelasticity can only be applied in the case of small deformations of no more than a few percent. On the other hand, for fluids, well-controlled shear flows are easier to implement and the rheological functions described in this article are those obtained in simple shear kinematics, the notations being those classically used in this case.

Understanding the rheological phenomena and behaviours observed in processing tooling obviously falls within the domain of rheology in large deformation situations. However, while the principles of linear viscoelasticity are not directly applicable in terms of modeling processes involving large deformations, they do form the backbone for the development of concepts specific to nonlinear viscoelasticity, which will be the subject of another article, and the associated behavior laws, which are far more complex. The...