Primitive Chain Network Simulations of Damping Functions for Shear, Uniaxial, Biaxial and Planar Deformations

Abstract

Damping functions of entangled polymers for shear, uniaxial, biaxial, and planar deformations, as well as normal stress ratios for shear deformations, were obtained from Brownian simulations making use of the primitive chain network model. To investigate the effect of the force balance over the entanglements and of the convective constraint release mechanism, comparisons with predictions of earlier theories and with experimental data in the literature were performed. It was found that the obtained damping functions are close to the three-chain theory [Marrucci, Greco, and Ianniruberto, Macromol Symp, 158, 57 (2000)] suggesting that the force balance is a dominant correction over the basic Doi-Edwards theory as compared with the effect of convective constraint release. Furthermore, the predicted normal stress ratio in shear, i.e., a quantity very sensitive to the different assumptions, is in good agreement with experiments, suggesting that the combination of force balance, convective constraint release, and other relaxation modes, as accounted for through the primitive chain network model, is quite acceptable.

Analytic solutions of the Rolie Poly model in time-dependent shear

“…Thus, it appears that improving the self-consistency of the tube model through CCR diminishes its predictive ability. However, primitive chain network simulations by Furuichi et al [34] have produced quantitative agreement with these damping function measurements. These simulations include all standard tube model relaxation processes, and also include a force balance around entanglements (FB), which is absent from the GLaMM and Rolie-Poly models.…”

“…The simulations of Furuichi et al [34] also suggest that errors due to omitting CCR and FB cancel to some extent in the Doi-Edwards model.…”

“…Simulation results [34] suggest that the force balance at entanglement points also needs to be considered to fully capture damping function measurements, but this may be alleviated by considering relaxation following a non-instantaneous deformation.…”

Primitive Chain Network Simulations of Conformational Relaxation for Individual Molecules in the Entangled State

“…[7][8][9][10][11][12] In this section, however, we briefly present the model used in this particular study to eliminate possible confusion among the various versions differing in minor aspects. In the model of the entangled polymer network, each entanglement node has four converging strands consistently with a binary assumption of chain interaction, and the node position {R} in space is determined by a force balance including the tensions of the conversing strands, the friction force against the medium, …”

Primitive chain network simulations for entangled DNA solutions

“…Force balance on entanglements is one aspect of the model that makes it different from other sliplink models, [26][27][28][29] and its effect on rheology has also been examined. 24,25 However, the model has not been frequently tested against other measures reflecting chain conformation, and, in some tests so far made on dielectric responses, 11,30 the primitive chain network simulation failed to quantitatively reproduce the experimental results. It is thus meaningful to test the model against other conformational measures to look for possibly missing ͑or wrongly accounted for͒ relaxation mechanisms.…”