Self-Consistent Modeling of Constraint Release in a Single-Chain Mean-Field Slip-Link Model

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.

Monte Carlo simulations of densely-packed athermal polymers in the bulk and under confinement

“…For example the cumulative probability of the PP length as obtained from MC simulations of entangled athermal chains (Foteinopoulou et al, 2008) is in excellent agreement with the predictions of the thermodynamicalry-consistent slip-link model by Khaliullin and Schieber (2009). Same is true when we compare the distribution of the entanglement spacing against the exponential-type master curve proposed by Tzoumanekas and Theodorou (Kamio et al, 2007;Tzoumanekas and Theodorou, 2006).…”

“…The latter is frequently used to link the theory with experimentally observed rheological properties of polymeric melts through its connection to the plateau modulus (Everaers et al, 2004;Fetters et al, 1999;Foteinopoulou et al, 2009;Theodorou and Tzoumanekas, 2006;Tzoumanekas et al, 2009). Additionally, the derived entanglement statistics can be mapped (Anogiannakis et al, 2012;Foteinopoulou et al, 2008;Steenbakkers et al, 2014) into novel slip-link theories that describe the rheological behaviour of polymeric liquids (Khaliullin and Schieber, 2009;Likhtman, 2005;Marrucci and Ianniruberto, 2004;Masubuchi et al, 2003;Ramirez et al, 2007;Stephanou et al, 2011;Wang et al, 2012).…”

Fluctuating Entanglements in Single-Chain Mean-Field Models

“…With a small number of adjustable parameters it is now possible to describe many experiments simultaneously [6][7][8][9][10][11][12][13]. Other work has recently suggested that one of these parameters-the entanglement density-might be accessible from atomistic simulations [14][15][16][17][18][19][20][21][22][23][24][25][26].…”

“…The Doi-Edwards model contains very few fluctuations, yet the question of a factor of 4/5 in the plateau modulus persisted for many years, presumably related to monomer density fluctuations along a fixed, constant-length primitive path [7,35]. As one adds primitive-path-length fluctuations (usually called "contour-length fluctuations" or CLF), entanglement spacing fluctuations, etc., the prefactor changes more [10]. These fluctuations can be handled in a natural way using slip-link models and nonequilibrium thermodynamics.…”

Microscopic Description of Entanglements in Polyethylene Networks and Melts: Strong, Weak, Pairwise, and Collective Attributes

“…The tube model provides a basis for working out analytically the linear and nonlinear viscoelasticty of polymer melts 9,[16][17][18][19][20] and networks 10,15,[21][22][23][24] at a molecular level. Slip link models 19,20,24 also allow for analytical 8,[11][12][13]15,25,26 or stochastic simulation 14,[27][28][29][30][31][32][33][34][35][36][37] treatments with a molecular representation, at the single or many-chain level.…”