Multi-chain slip-spring model for entangled polymer dynamics

Abstract

It has been established that entangled polymer dynamics can be reasonably described by single chain models such as tube and slip-link models. Although the entanglement effect is a result of hard-core interaction between chains, linkage between the single chain models and the real multi-chain system has not been established yet. In this study, we propose a multi-chain slip-spring model where bead-spring chains are dispersed in space and connected by slip-springs inspired by the single chain slip-spring model [A. E. Likhtman, Macromolecules 38, 6128 (2005)]. In this model the entanglement effect is replaced by the slip-springs, not by the hard-core interaction between beads so that this model is located in the niche between conventional multi-chain simulations and single chain models. The set of state variables are the position of beads and the connectivity (indices) of the slip-springs between beads. The dynamics of the system is described by the time evolution equation and stochastic transition dynamics for these variables. We propose a simple model which is based on the well-defined total free-energy and detailed balance condition. The free energy in our model contains a repulsive interaction between beads, which compensate the attractive interaction artificially generated by the slip-springs. The explicit expression of linear relaxation modulus is also derived by the linear response theory. We also propose a possible numerical scheme to perform simulations. Simulations reproduced expected bead number dependence in transitional regime between Rouse and entangled dynamics for the chain structure, the central bead diffusion, and the linear relaxation modulus.

Challenges in Multiscale Modeling of Polymer Dynamics

“…The longest relaxation time was found to scale with the number of entanglements, Z, as Z 3.5±0.1 , while the self-diffusion coefficient was found to scale as D cm ∼ Z −2.4±0.2 ; both agree well with experimental results [144]. Later on, the PCN model was extended to study the relationship between entanglement length and plateau modulus [145][146][147][148][149]. It was also extended to study star and branched polymers [150], nonlinear rheology [151][152][153], phase separation in polymer blends [154,155], block copolymers [156] and the dynamics of confined polymers [157].…”

Reptation and constraint release dynamics in bidisperse polymer melts

“…Our previous study estimates a gain in CPU time by two orders of magnitude compared to standard molecular dynamics with hard-core bead-bead interactions. 17 We also want to draw the reader's attention to the work of Chappa et al, 22 Uneyama and Masubuchi 23 as well as Ramírez-Hernández et al 24 who pursued similar approaches using multi-chain slip-spring models. In particular, Ramírez-Hernández et al 24 demonstrated good agreement of the loss and storage moduli for mono-and bidisperse polystyrene melts with experimental values.…”

Fluctuating Entanglements in Single-Chain Mean-Field Models

“…Very recently there have appeared newer multi-chain simulations [105,106] that fix many of the thermodynamic issues [107] associated with dynamics in the code by Masubuchi et al Therefore, these are a considerable improvement over the earlier PCN simulations. 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.…”

“…Third, if these springs do not contribute to the stress, then one expects violation of the principle of virtual work. Chappa et al [105] do not specify their stress tensor expression, whereas Uneyama and Masubuchi [106] consider both forms of stress, with and without the virtual springs.…”