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.
Highlights
Multiscale modeling is a current trend in the field of molecular simulations, since combining information from different levels of description allows predicting material properties which depend on broad ranges of length and time scales at reasonable computational cost
Our principal aim is to check whether the unperturbed chain conformation of the initial configuration is retained during the Brownian dynamics/kinetic Monte Carlo simulations
A new methodology for mesoscopic simulations of crosslinked polymer networks and the corresponding C++ code have been presented in this article as an extension of our previous work concerning polymer melts
Summary
Multiscale modeling is a current trend in the field of molecular simulations, since combining information from different levels of description allows predicting material properties which depend on broad ranges of length and time scales at reasonable computational cost. Systematic coarse-graining methods, such as Iterative Boltzmann Inversion (IBI), have been utilized for the development of coarse-grained models of polymers [4,5,6,7,8,9]; in the case of IBI, a set of target structural and thermodynamic properties of an underlying atomistic model is reproduced at the new, less-detailed, level of description. Another promising approach is the integral equation coarse-graining method that employs the first-principles Ornstein–Zernike equation [10]
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