Unveiling Nonlinear Extensional Flow Behaviors in Unentangled Polymer Liquids: A Mean-Field Anisotropic Diffusion Dumbbell Model Validated by Oligomers with Correlation Lengths

We develop a single-chain constitutive model that directly captures the nonlinear extensional rheological behaviors of unentangled polymer liquid (UPL) systems through dynamic evolution. This model is grounded in the theoretical consideration that the dynamic, polydisperse, and untraceable interchain anisotropic interactions among the stretching polymers can be shielded by chemically identical solvent oligomers with correlation lengths (CLs), and consequently characterized as a mean-field confinement, where only the individual evolution of a single chain needs to be examined. On this basis, chain-stretching-induced anisotropic diffusion characteristics of an unentangled polymer chain in the aligned direction are established and are believed to be consistently followed by concentrated UPL with segments of CL-scale reaching critical overlap, while effectively followed by concentrated UPL with weak CL overlap during dynamic evolution. The model directly predicts extensional rheological properties and material parameter variations of different components of concentrated UPL, exhibiting strong consistency with coarse-grained molecular dynamics (CG-MD) simulations and experiments. Specifically, the model successfully outputs the potential universality of polymer friction reduction in concentrated UPL under extensional flows. Our work provides new molecular-level insight into the nonlinear viscoelasticity of UPL systems.