Slip Spring-Based Mesoscopic Simulations of Polymer Networks: Methodology and the Corresponding Computational Code

Abstract

In previous work by the authors, a new methodology was developed for Brownian dynamics/kinetic Monte Carlo (BD/kMC) simulations of polymer melts. In this study, this methodology is extended for dynamical simulations of crosslinked polymer networks in a coarse-grained representation, wherein chains are modeled as sequences of beads, each bead encompassing a few Kuhn segments. In addition, the C++ code embodying these simulations, entitled Engine for Mesoscopic Simulations for Polymer Networks (EMSIPON) is described in detail. A crosslinked network of cis-1,4-polyisoprene is chosen as a test system. From the thermodynamic point of view, the system is fully described by a Helmholtz energy consisting of three explicit contributions: entropic springs, slip springs and non-bonded interactions. Entanglements between subchains in the network are represented by slip springs. The ends of the slip springs undergo thermally activated hops between adjacent beads along the chain backbones, which are tracked by kinetic Monte Carlo simulation. In addition, creation/destruction processes are included for the slip springs at dangling subchain ends. The Helmholtz energy of non-bonded interactions is derived from the Sanchez–Lacombe equation of state. The isothermal compressibility of the polymer network is predicted from equilibrium density fluctuations in very good agreement with the underlying equation of state and with experiment. Moreover, the methodology and the corresponding C++ code are applied to simulate elongational deformations of polymer rubbers. The shear stress relaxation modulus is predicted from equilibrium simulations of several microseconds of physical time in the undeformed state, as well as from stress-strain curves of the crosslinked polymer networks under deformation.

Modeling of Entangled Polymer Diffusion in Melts and Nanocomposites: A Review

“…An interesting approach in DPD method [191] is to incorporate the topological constraints and, thus uncrossability of polymer chains, by creating temporary cross-links, the so-called slip-spring (variation of the slip link model) following the philosophy of Likhtman [56]. According to this, the lateral motion of the polymer chain is restricted by links connected (by virtual springs) [192] to links on other polymer chains [56,193]. These slip-springs can be created and destroyed at chain ends [56].…”

“…Recently, a multiscale simulation strategy that linked detailed MD simulations to slip-springs based on Brownian dynamics/kinetic Monte Carlo (BD/kMC) simulations of long PE chains (N=260 to N=2080) melts was implemented by Sgouros et al [204] (Figure 14 and Figure 15) and Megariotis et al [193]. Such (BD/kMC) methodology was based on a Helmholtz energy function that incorporated bonded, slip-spring, and nonbonded interaction terms [205].…”

Developments in Polymer Theory and Simulation

“…Up to a critical level, the interaction between the filler and the matrix contributes to the reinforcement. Dynamical simulations of crosslinked polymer networks in a coarse-grained representation have been performed by Megariotis et al [5], where entanglements between subchains in the network are represented by slip springs. The ends of the slip springs undergo thermally activated hops between adjacent beads along the chain backbones, which are tracked by kinetic Monte Carlo simulation.…”

Viscoelastic Effects on Drop Deformation Using a Machine Learning-Enhanced, Finite Element method

“…A common approach to handling the polymer interaction with the flow at a macroscopic scale is to represent the polymer contribution to the stress tensor by means of a closed-form, "constitutive" equation; thus, e.g., the work of Yue et al [20][21][22] on drop deformation and complex two-phase flow using a diffuse-interface method and constitutive modeling; in [23], Pillapakkam employed an LS method to study rising bubbles in viscoelastic media, while Foteinopoulou and Laso [24] used a Phan-Thien--Tanner model together with an elliptic mesh-deformation algorithm to investigate bubble oscillation; Castillo et al proposed an LS method with a pressure-enriched FE space to study the two-fluid flow problem along with a Giesekus model for the polymeric liquid [25]; Fraggedakis et al [26] characterized the critical volume of a bubble rising in a viscoelastic fluid using an FEM-based method and the exponential Phan-Thien and Tanner model; using a coupled LS-VOF ("VOSET") method, Wang et al [27] studied drag reduction in cavity flow; Xie et al [28] focused on droplet oscillation under a Maxwell model using lattice Boltzmann techniques. In contrast to constitutive modeling, the "micro-macro" approach [29] tackles the polymer-flow interaction using stochastic and Brownian Dynamics (BD) simulations [30][31][32][33] to retrieve the polymer stress tensor from the internal configurations of the polymer particles advected by the flow. Taking the CONNFFESSITapproach of Laso and Öttinger [34], Cormenzana and co-workers [35] and later Grande et al [36] successfully handled free surface flows of polymer solutions, while Prieto [7,37] conducted multiphase simulations in viscoelastic fluids using a variance-reduced, stochastic implementation of a "micro-macro" method [38].…”

“…[ 28 ] focused on droplet oscillation under a Maxwell model using lattice Boltzmann techniques. In contrast to constitutive modeling, the “micro-macro” approach [ 29 ] tackles the polymer-flow interaction using stochastic and Brownian Dynamics (BD) simulations [ 30 , 31 , 32 , 33 ] to retrieve the polymer stress tensor from the internal configurations of the polymer particles advected by the flow. Taking the CONNFFESSITapproach of Laso and Öttinger [ 34 ], Cormenzana and co-workers [ 35 ] and later Grande et al.…”