In a recent reformulation of the Marrucci-Ianniruberto constitutive equation for the rheology of entangled polymer melts in the context of nonequilibrium thermodynamics, rather large values of the convective constraint release parameter βccr had to be used in order for the model not to violate the second law of thermodynamics. In this work, we present an appropriate modification of the model, which avoids the splitting of the evolution equation for the conformation tensor into an orientation and a stretching part. Then, thermodynamic admissibility simply dictates that βccr ≥ 0, thus allowing for more realistic values of βccr to be chosen. Moreover, and in view of recent experimental evidence for a transient stress undershoot (following the overshoot) at high shear rates, whose origin may be traced back to molecular tumbling, we have incorporated additional terms into the model accounting, at least in an approximate way, for non-affine deformation through a slip parameter ξ. Use of the new model to describe available experimental data for the transient and steady-state shear and elongational rheology of entangled polystyrene melts and concentrated solutions shows close agreement. Overall, the modified model proposed here combines simplicity with accuracy, which renders it an excellent choice for managing complex viscoelastic fluid flows in large-scale numerical calculations.

We provide a description of the Marrucci–Ianniruberto constitutive equation [Philos. Trans. R. Soc. London, A2003361677688] for the rheology of entangled polymer melts in the context of nonequilibrium thermodynamics and we properly extend it to account for a second normal stress difference by introducing a second order term in the relaxation tensor in terms of the conformation tensor. The modified model incorporates one additional parameter, the anisotropic mobility parameter α, which allows for nonvanishing predictions of the second normal stress coefficient. Application of the second law of thermodynamics and the requirement that the evolution equation must preserve the positive-definite nature of the conformation tensor between successive entanglement points along the chain for all times and all flow fields constrain the convective constraint release (CCR) parameter β ccr to values strictly greater than one (β ccr > 1) and the new parameter α to values in the interval 0 ≤ α ≤ 1 − β ccr –1. The modified model provides a satisfactory description of available experimental data for the transient and steady-state shear rheology of entangled polystyrene melts [ Schweizer Schweizer J. Rheol.20044813451363] and for the elongational steady-state stress of an entangled polystyrene solution [ Ye Ye J. Rheol.200347443468] over the entire range of shear and elongation rates covered in the rheological measurements.

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Bifunctional vinyl-terminated poly(dimethylsiloxane) chains are endlinked by tetrafunctional tetrakis(dimethylsiloxy)silane cross-linkers to produce irregular polymer networks with controlled stoichiometric imbalance and extent of reaction. The results are used as input to create comparative, nominally the same, three-dimensional Monte Carlo computer microstructures. Stress relaxation laboratory measurements and bead-spring molecular dynamics (MD) simulations are performed to estimate the relaxation shear modulus. It is found that the MD estimates reproduce quite well the measured equilibrium shear modulus G, despite the strikingly different time scales of measured and MD relaxation moduli. However, it is also seen that for near-stoichiometric networks the classical affine network model (ANM) gives equally good predictions of G. Additional MD simulations with phantom strands and regular networks are carried out. It is demonstrated that the ANM success is accidental since it is based on the fortuitous cancellation of two unrelated inaccurate assumptions of regular defect-free polymer networks and phantom strands that can freely pass through each other and themselves. Several contemporary theories of the elasticity of ideal Gaussian polymer networks are considered, and it is demonstrated that none of them is particularly suitable for predicting the shear modulus of the studied end-linked polydimethylsiloxane (PDMS) networks. It is shown that by taking into account the effects of trapped entanglements, reasonable qualitative and, at times, even semiquantitative predictions can be achieved. However, because of the ambiguity problems in the empirical fitting of the effective concentration of trapped entanglements, the resulting theoretical predictions are overall notably less accurate and less reliable than those obtained with the coarse-grained MD simulations that automatically account for the uncrossability of network strands. This emphasizes the incompleteness of the current theoretical descriptions of the effects of entanglements on the elastic behavior of irregular end-linked polymer networks with various values of the extent of reaction and stoichiometric imbalance and also suggests using our validated Monte Carlo microstructures to further study these effects.