No abstract

A new implementation of constraint dynamics for the discrete slip-link model (DSM), which is statistically consistent with sliding dynamics of the chain, is proposed. The DSM agrees with linear viscoelastic (LVE) data for linear monodisperse entangled polymer melts at least as well as state-of-the-art tube models. The agreement with data can be obtained by fitting only two parameters, β and τ K that are independent of the molecular weight of the polymer. However, because the theory exists on a more-detailed level of description, it contains fewer assumptions than do existing tube models and assumptions of the latter may be examined. Several fundamental differences between DSM and tube models are revealed. For example, Rouse motion is an inappropriate realization of constraint dynamics in the slip-link picture. Moreover, the chain relaxation by sliding dynamics for the DSM is significantly different from the fraction of survived entanglements multiplied by the plateau modulus, whereas the tube model assumes that these are equivalent at long times. These two differences effectively cancel one another. Moreover, they could result in different bidisperse LVE predictions. On the other hand, several other assumptions made in tube theories are confirmed by the DSM results. Finally, model comparisons with experimental data exposed some limitations in the experiments.

A consistently unconstrained Brownian slip-link (CUBS) model with constant chain friction is used to predict the linear rheological behavior of linear, entangled polymeric liquids. As in the previously proposed slip-link model without constraint release (J. Rheol. 2003, 47, 213), this model contains segment connectivity, contour-length fluctuations, and chain stretching in a self-consistent and natural way. Constraint release is considered in a mean-field way, but including fluctuations, both as a binary interaction between chains, and as a multichain interaction. Unlike previous mean-field works, constraint release is included on the level of chain dynamics instead of assuming that the relaxation modulation is a product of two moduli found by independent processes. These dynamics require no additional parameters. The model may also be used to make nonlinear flow predictions without any additional parameters. We find that inclusion of the additional physics of constraint release improves the linear viscoelastic predictions of the model, both for monodisperse polymers and bidisperse polymer blends. The difference between binary and multichain interaction predictions is not sufficiently large to distinguish comparisons with data within uncertainty.

A method for incorporating reptation ideas in a temporary network model is used to predict the fluctuations of entanglement number and monomer density between entanglements in entangled polymeric liquids. The dynamic variables are chosen to be the number of Kuhn steps and the position of the entanglements. A chain of fixed number of Kuhn steps in a bath that fixes the chemical potential conjugate to the number of entanglements is considered. The static equilibrium statistics of such a model can be calculated analytically. Since the dynamics of the model may also be simulated, these analytic expressions may be used to check the algorithm. Also, the damping function is calculated analytically from these distributions, as well as normal stresses following a step shear.

A self-consistent reptation theory that accounts for chain-tube interactions, segment connectivity, chain-length breathing, segmental stretch, and constraint release is proposed. Simulation results are compared semiquantitatively to experimental observations in single-step strain flows. Since stochastic simulation techniques are used, no approximations, such as independent alignment or consistent averaging are needed to obtain results. The simulation results show excellent agreement with experimental trends in shear and normal stress relaxations, including the second normal stress difference, well into the nonlinear regime. For most of these experiments, the original Doi and Edwards theory, which incorporates independent alignment or consistent averaging, is not satisfactory. In the following companion paper, we show how the model is capable of describing double-step-strain flows for all stress components. Subsequent papers show excellent agreement for the inception of steady shear flow, and steady shear flow.