Microscopic theory of linear, entangled polymer chains under rapid deformation including chain stretch and convective constraint release

Abstract

A refined version of the Doi and Edwards tube model for entangled polymer liquids is presented. The model is intended to cover linear chains in the full range of deformation rates from linear to strongly nonlinear flows. The effects of reptation, chain stretch, and convective constraint release are derived from a microscopic stochastic partial differential equation that describes the dynamics of the chain contour down to the length scale of the tube diameter. Contour length fluctuations are also included in an approximate manner. Predictions of mechanical stresses as well as the single chain structure factor under flow are shown. A comparison with experimental data is made in which all model parameters are fixed at universal values or are obtained from linear oscillatory shear measurements. With no parameter modification the model produces good agreement over a wide range of rheological data for entangled polymer solutions, including both nonlinear shear and extension.

Electrospun polymer nanofibers: Mechanical and thermodynamic perspectives

“…In such cases, a nonuniform tensile flow acts on the polymeric physical network, where topological links are formed as a result of chain entanglement (a polymeric physical network under very rapid deformation can be regarded as polymer gel). Although the behavior of polymer gels under rapid deformation has been discussed by many authors, [49][50][51][52][53] we are not aware of a solution for the specific problem occurring in the electrospinning process, namely local deformation of an elongated network of semidilute polymer solution.…”

Elongational Flow of Blends of Long and Short Polymers: Effective Stretch Relaxation Time

“…This constraint release process provides a second relaxation mechanism, commonly modeled as a local sideways hop of the tube at each constraint release event [3][4][5][6]. Accounting for constraint release has been essential in understanding the experimental lack of shear banding in strong flows of monodisperse melts [5,6]. It is also crucial in most industrial polymers, where polydispersity of chain length, and chain branching, result in a wide spectrum of constraint release rates.…”

“…Here, we have used the same definition of constraint release rate S as used by Graham et al [6], and retain the same prefactors as suggested by their equation for constraint release events of a tube. The second time scale is the constraint release Rouse time for the whole thin tube (comprising Z L thin tube segments), which is, similarly,…”

“…It might be that, before a test chain has escaped from its tube, one of the constraining chains moves out of the way, releasing the entanglement constraint. This constraint release process provides a second relaxation mechanism, commonly modeled as a local sideways hop of the tube at each constraint release event [3][4][5][6]. Accounting for constraint release has been essential in understanding the experimental lack of shear banding in strong flows of monodisperse melts [5,6].…”

“…Stretches in the thin and fat tubes are defined as t ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi hr r i=a 2 p and f ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi hR R i=a 2 f q , respectively [6,8], so taking the trace of Eq. (4) and averaging over fat tube segments gives…”