Nonlinear modification of the Rouse model constraining volume conservation of deforming chains

Recent experimental observation in fast extensional flow of polymer melts and solutions displayed as presence and absence of viscosity thinning, respectively, has necessitated and also initiated nonlinear modification of the Rouse model, the fundamental molecular model for unentangled polymeric liquids. On that account, concept of reduction of bead friction is introduced in the form of variable friction coefficient \(\zeta (t)\) sometimes with corresponding variation of the Brownian force. This work presents mathematical constraint based on reasonable assumptions for volume conservation of deforming chains and accordingly formulates the rheological constitutive equation. The equation of constraint for volume conservation possibly relieves in part the complication introduced by the friction reduction and intrinsic flow-induced anisotropy in nonlinear modification of the Rouse model. The suggested constitutive equation expresses description in simple rheometric flows quite similar to that of the previous model with B-variation given by Sato et al. (2021) when both are formulated with effects of finite extensibility (FENE) and friction reduction. In addition, the molecular dynamics simulation demonstrates possible validity of the current hypothesis, the constraint of chain volume conservation.

Graphical abstract