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

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.

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Coarse-Grained Kinetic Monte Carlo Simulation of Copper Electrodeposition with Additives

International Journal for Multiscale Computational Engineering ◽

10.1615/intjmultcompeng.v2.i2.90 ◽

2004 ◽

Vol 2 (2) ◽

pp. 313-327 ◽

Cited By ~ 32

Author(s):

Timothy O. Drews ◽

Richard D. Braatz ◽

Richard C. Alkire

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Kinetic Monte Carlo ◽

Coarse Grained ◽

Copper Electrodeposition ◽

Kinetic Monte Carlo Simulation

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Kinetic Monte Carlo Method

Computer Simulations of Dislocations ◽

10.1093/oso/9780198526148.003.0014 ◽

2006 ◽

Author(s):

Vasily Bulatov ◽

Wei Cai

Keyword(s):

Monte Carlo ◽

Kinetic Monte Carlo ◽

Dislocation Core ◽

Dislocation Motion ◽

Coarse Grained ◽

Solid Thin Films ◽

Finite Set ◽

And Migration ◽

Dynamics Simulations ◽

Straight Segments

The PN model discussed in the preceding chapter is a continuum approach that requires some atomistic input to account for non-linear interactions in the dislocation core. In this chapter, we introduce yet another continuum model that uses atomistic input for a different purpose. The kinetic Monte Carlo (kMC) model does not consider any details of the core structure but instead focuses on dislocation motion on length and time scales far greater than those of the atomistic simulations. The model is especially effective for diamond-cubic semiconductors and other materials in which dislocation motion is too slow to be observed on the time scale of molecular dynamics simulations. The key idea of the kMC approach is to treat dislocation motion as a stochastic sequence of discrete rare events whose mechanisms and rates are computed within the framework of the transition state theory. Built around its unit mechanisms, the kMC model simulates dislocation motion and predicts dislocation velocity as a function of stress and temperature. This data then can be used to construct accurate mobility functions for dislocation dynamics simulations on still larger scales (Chapter 10). In this sense, kMC serves as a link between atomistic models and coarse-grained continuum models of dislocations. The kMC approach is most useful in situations where the system evolves through a stochastic sequence of events with only a few possible event types. The method has been used in a wide variety of applications other than dislocations. For example, the growth of solid thin films from vapor or in solution is known to proceed through attachment and diffusion of adatoms deposited on the surface. Based on a finite set of unit mechanisms of the motion of adatoms, kMC models accurately describe the kinetics of growth and the resulting morphology evolution of the epitaxial films [95, 96, 97]. Similar kMC models have been applied to dislocation motion in crystals with high lattice resistance, such as silicon. In these materials, dislocations consist of long straight segments interspersed with atomic-sized kinks, depicted schematically in Fig. 9.1(a) as short vertical segments. As was explained in Section 1.3, dislocation motion proceeds through nucleation and migration of kink pairs and can be described well by a kMC model.

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Growth and arrest of topological cycles in small physical networks

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.2006305117 ◽

2020 ◽

Vol 117 (27) ◽

pp. 15394-15396

Author(s):

Timothy W. Sirk

Keyword(s):

Monte Carlo ◽

Random Graphs ◽

Kinetic Monte Carlo ◽

Polymer Networks ◽

Finite Size ◽

Characteristic Size ◽

Network Size ◽

Embedded Networks ◽

Metropolis Monte Carlo ◽

Chordless Cycle

The chordless cycle sizes of spatially embedded networks are demonstrated to follow an exponential growth law similar to random graphs if the number of nodesNxis below a critical valueN*. For covalent polymer networks, increasing the network size, as measured by the number of cross-link nodes, beyondN*results in a crossover to a new regime in which the characteristic size of the chordless cyclesh*no longer increases. From this result, the onset and intensity of finite-size effects can be predicted from measurement ofh*in large networks. Although such information is largely inaccessible with experiments, the agreement of simulation results from molecular dynamics, Metropolis Monte Carlo, and kinetic Monte Carlo suggests the crossover is a fundamental physical feature which is insensitive to the details of the network generation. These results show random graphs as a promising model to capture structural differences in confined physical networks.

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