Fluctuations in entanglements of polymer liquids

Abstract

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.

Quantitative comparison of primitive chain network simulations with literature data of linear viscoelasticity for polymer melts

“…They report that the mean step length of the obtained primitive chain scales consistently with the packing length proposed by Fetters et al [2]. Tzoumanekas and Theodorou [3], as well as Foteinopoulou et al [4] use well equilibrated atomistic configurations of polyolefin chains, and identify the primitive paths by minimizing the total path length (instead of the energy), also showing that statistics for strand length in the primitive chain network is consistent with that predicted by Schieber with a sliplink model [5]. Shanbhag and Larson [6] also report consistent results obtained with the bond-fluctuation model.…”

Fluctuating Entanglements in Single-Chain Mean-Field Models

“…Entanglements are imposed by a chemical potential bath that allows the number of entanglements on the chain to fluctuate. Together with the free energy of the chain, this formulation allows analytic expressions for equilibrium chain conformations [21,103].…”

“…Both groups use the idea of Schieber [103] to treat the number of entanglements as a stochastic variable, which is controlled by a chemical potential bath as in a grand-canonical ensemble. However, they have also added springs between the chains, which raises issues about three of the criteria above.…”

Single Chain Slip-Spring Model for Fast Rheology Simulations of Entangled Polymers on GPU

“…As mentioned, the total number of slip-springs, Z, is not constant but fluctuates in time since slip-springs are dynamically constructed or destructed. To handle such a variable, it is convenient to use grand canonical type ensemble for slip-springs, which is originally introduced by Schieber 37) for the slip-link model.…”