Single-Chain Slip-Link Model of Entangled Polymers:  Simultaneous Description of Neutron Spin−Echo, Rheology, and Diffusion

Abstract

The model presented in this paper describes simultaneously three different experimental techniques applied to different monodisperse polymer melts: neutron spin-echo (NSE), linear rheology, and diffusion. First, it shows that the standard tube model cannot be applied to NSE because the statistics of a one-dimensional (1D) chain in a three-dimensional (3D) random-walk tube become wrong on the length scale of the tube diameter, whereas all available NSE data are for scattering vectors in this range. Then a new single-chain dynamic slip-link model on the basis of a recent network model by Rubinstein and Panyukov is introduced. Instead of solving the model analytically, which would require uncontrolled approximations, the model is formulated in terms of stochastic differential equations, suitable for Brownian dynamics simulations. I perform these simple simulations, demonstrate that the model describes individual experiments well, and then compare the results with experiments on monodisperse polyethylene, polyethylene-propylene, polyisoprene, polybutadiene, and polystyrene. For all polymers, model parameters from one experiment are obtained, and the others are predicted without fitting. The results show some systematic discrepancies, suggesting possible inadequacy of the Gaussian chain model for some of the polymers, and possible inadequacy of time-temperature superposition.

Challenges in Multiscale Modeling of Polymer Dynamics

“…The strain-hardening behavior of polymer blends has been observed with 5% highly entangled chains [140]. Likhtman [141] introduced a new single-chain dynamic slip-link model to describe the experimental results for neutron spin echo, linear rheology and diffusion of monodisperse polymer melts. All the parameters in this model were obtained from one experiment and were applied to predict other experimental results.…”

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

“…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).…”

“…This unique behaviour is intimately related to the uncrossability of chains which effectively leads to topological constraints between chains in the form of entanglements (deGennes, 1980;Doi and Edwards, 1988). The original reptation theory, based on the tube model, and more recent theoretical concepts have captured qualitatively and quantitatively the effect of entanglements on polymer dynamics and rheology (deGennes, 1980;Doi and Edwards, 1988;Kroger, 2004;Likhtman, 2005;Likhtman and McLeish, 2002;Marrucci, 1996;Marrucci and Ianniruberto, 2004;McLeish and Larson, 1998;Ramirez et al, 2007;Stephanou et al, 2011;Wang et al, 2012). Additionally, density is one of the key factors which affect profoundly the static, dynamic and rheological properties of entangled polymers (Daoud et al, 1975;Doi and Edwards, 1988;Edwards, 1966;Fleer et al, 1993).…”

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.…”