A Multichain Slip-Spring Model with Fluctuating Number of Entanglements Based On Single-Chain Slip-Spring Model

Teng Ma, Hui-Feng Tan, Lin Yu
2017 Proceedings of the 3rd Annual International Conference on Mechanics and Mechanical Engineering (MME 2016)   unpublished
We present a multichain slip-spring model with fluctuating number of entanglements for dynamics of dense polymer melts, which is based on the single chain slip-spring model by Likhtman. By introducing the exclude volume interactions, a multichain version of slip-spring model can be presented with little modification. With this extension, inhomogeneous polymer system can be described properly. The renewal rules for the slip-spring satisfy the detailed balance condition and the number of
more » ... ngs is no longer constant but controlled through a chemical potential. This completion can predict the Possion distribution of Z under equilibrium states and the decrease in the number of entanglements when applied a steady shear flow. The results agree with theoretical predictions and experimental phenomenon. The model bridges the single chain slipspring model and multichain slip-spring model. Introduction Understanding of the dynamics of entangled polymer is very important for many industrial applications. However, for the wide range of spatial and temporal scales involved in the characterization of entangled polymer, theoretical modelling of such material is a difficult challenge. A most successful and advanced models was the tube model of Doi and Edwards[1-4], in which a probe Rouse chain is restricted in a tube formed by the topological constraints imposed by surrounding chains. The chain diffusion along the backbone more easily than lateral to the backbone, which is known as reptation. Based on this reptation idea, many important additional physical ideas, such as constraint release(CR)[5], contour-length fluctuations(CLF)[6], convective constraint release(CCR)[7], have been incorporated into tube model. These improvements have enriched the tube theory to account for many additional relaxation mechanisms. Tube model reveals the dominant relaxation mechanism and could describe numerous characteristic phenomena of entangled polymers successfully. However, it still failed in many respects, such as incorrect prediction for steady shear flow and it's difficult to be extended to various chain architectures. Tube model met these troubles mainly because it employ a single-chain motion to express multichain dynamics, thus introducing excessive assumptions and approximations. For the shortness of tube model, many researchers have transferred to slip-link model, which incorporate constraint release and fluctuations in the tube length in a more natural way. There are several excellent implementations of slip link models in the literature, such as the primitive chain network (PCN) model of 9] , the TIEPOS approach of Ramí rez-Herná ndez and co-workers [10, 11] , the DSM of Schieber and co-workers [12] [13] [14] . Likhtman [15] developed a dynamic one-chain slip-spring model of entangled polymers suitable for Brownian dynamics simulations. This model can describe the results from NSE, linear rheology and diffusion experiments properly. Many models extend Likhtman's model for its flexibility, extensibility and implementation simplicity. To simulate large scale or long time macroscopic phenomena, Uneyama slightly modified Likhtman's model to be suitable for simulations on a GPU [16] . The total number of slip-springs could fluctuates and controlled by a pseudo-chemical potential, which is originally introduced by Schieber [17] . However, the model still is single-chain model that it's hard to use it to 515
doi:10.2991/mme-16.2017.70 fatcat:d5d2bweqovbh3epyu4aqlcu6au