A mean-field anisotropic diffusion model for unentangled polymeric liquids and semi-dilute solutions: Model development and comparison with experimental and simulation data

A coarse-grained mesoscopic model was developed based on the ansatz that a specific polymer molecule diffuses through the nearby neighboring chains more easily in the direction parallel to its molecular axis than perpendicular to it. This idea is modeled using a mean-field approach in terms of an anisotropic diffusion matrix, which represents enhanced diffusion along the chain background once a significant degree of molecular extension and orientation has developed in response to an applied flow field. The rheological and microstructural characteristics of this model are examined and compared with atomistic nonequilibrium molecular dynamics (NEMD) simulation data of short-chain polyethylene liquids and experiments of semi-dilute DNA solutions under shear flow. Rheological and microstructural properties examined include the viscosity, normal stress coefficients, conformation tensor, etc., to gauge the usefulness of the model. In addition, this model was further coarse-grained to the continuum level through pre-averaging, and was also compared with the simulation and experimental data to examine the relationships between different levels of description on the rheological and structural properties of unentangled polymeric materials under shear flow. At the mesoscopic level, the polymer molecules are modeled as bead-spring chains using the finitely extensible nonlinear elastic (FENE) force law. Brownian dynamics (BD) simulations of this coarse-grained model displayed remarkable quantitative agreement with NEMD simulations of dense liquids and experiments of semi-dilute DNA solutions for system properties with a single adjustable parameter representing the relative magnitude of diffusive enhancement along the chain backbone. Furthermore, the BD simulations revealed the dependence of system response on the chain stretching at low values of Weissenberg number ( Wi) and on the rotational motion of individual chains induced by shear flow at high values of Wi, similarly to the NEMD simulation data. The continuum model matched the mesoscopic model at low shear rates, but greatly diverged at high values of Wi where the tumbling dynamics of the individual chains dominated the system response. This provides direct evidence that the onset of rotational motion under shear in these liquids is responsible for the well-known breakdown in pre-averaged constitutive equations at the continuum level of description. Furthermore, a possible explanation of the shear stress plateau