On polydispersity, molecular weight distribution and rheology

One of Scott Milner's many key contributions to polymer physics lies in relating polymer structure and dispersity to polymer dynamics and rheology. For monodisperse linear polymers the key mechanisms are well established: reptation, contour length fluctuations and constraint release [Milner and McLeish, Physical Review Letters 81, 725 (1998)]. Of course, practical industrial materials are always polydisperse, giving rise to a multiplicity of constraint release timescales, which in turn affects all other relaxation mechanisms. Classically this is handled by the "double reptation" ansatz, which often works for well-entangled polymers [e.g. Milner, Journal of Rheology 40, 303-315 (1996)] but is known to fail when pushed. In the first half I will describe how we develop from the simple model for monodisperse chains towards a description for full polydispersity, as encoded in recently released software (https://github.com/chinmaydaslds/LP2R, Das and Read, Journal of Rheology 67, 693-721 (2023)). The proper description for relaxation in an arbitrary blend of linear polymers requires consideration of multiple embedded tubes affecting the different relaxation pathways; we propose a novel but minimal description involving five embedded tubes. Building on prior work for binary blends, we derive scaling level descriptions of the relaxation pathways. We use a large number of existing experimental results on the stress and dielectric relaxations to validate our model. In the second half, I will discuss more recent progress on inference of molecular weight distribution from linear rheology, making use of our improved forward prediction model rather than the approximate double reptation methodology.