Brownian simulations of a network of reptating primitive chains

Abstract

A new model for Brownian dynamics simulations of entangled polymeric liquids is proposed here. Chains are coarse grained at the level of segments between consecutive entanglements; hence, the system is in fact a network of primitive chains. The model incorporates not only the “individual” mechanisms of reptation and tube length fluctuation, but also collective contributions arising from the 3D network structure of the entangled system, such as constraint release. Chain coupling is achieved by fulfilling force balance on the entanglement nodes. The Langevin equation for the nodes contains both the tension in the chain segments emanating from the node and an osmotic force arising from density fluctuations. Entanglements are modeled as slip links, each connecting two chain strands. The motion of monomers through slip links, which ultimately generates reptation as well as tube length fluctuations, is also described by a suitable Langevin equation. Creation and release of entanglements is controlled by the number of monomers at the chain ends. In a creation event, the partner chain segment is chosen randomly among those spatially close to the advancing chain end. To validate the model, equilibrium dynamics simulations were run for monodisperse linear chains containing up to Z=40 entanglements. The results show, in agreement with experiments, (i) a Z3.5±0.1 dependence of the longest relaxation time, (ii) a Z−2.4±0.2 dependence of the self-diffusion coefficient, and (iii) a relaxation modulus proportional to the square of the end-to-end vector correlation function, consistently with the dynamic tube dilation concept.

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.…”

Inter-Chain Cross-Correlation in Multi-Chain Slip-Link Simulations without Force Balance at Entanglements

“…The model developed in this study is based on the earlier one so-called primitive chain network model [14][15][16] To compensate the absence of the Langevin dynamics of {R}, a weak tension that withdraw the chain from the tube is applied at both ends of the chain. Such a tension is not necessary for the original model in which the Brownian dynamics of chain ends plays the role.…”

Test of the Stretch/Orientation-Induced Reduction of Friction for Biaxial Elongational Flow via Primitive Chain Network Simulation

“…In the PCN model 14) , the polymer melt is represented by a set of primitive chains in 3 , contour length fluctuation 17) and thermal [18][19][20] and convective 21) constraint release. The model has been extended to involve the finite chain extensibility in the subchain tension.…”