Simulations Of Polymer Melts Research Articles

ML-GLE: A machine learning enhanced Generalized Langevin equation framework for transient anomalous diffusion in polymer dynamics

In this work we introduce ML-GLE, a machine learning framework to generate long-term single-polymer dynamics by exploiting short-term trajectories from molecular dynamics (MD) simulations of polymer melts. Even with current advances in machine learning for MD, these polymeric materials remain difficult to simulate and characterize due to prohibitive computational costs when long relaxation timescales are involved. Our method relies on a 3D neural auto-regressive model for single polymer lower dimensional collective variables, called normal modes. This enhances the Generalized Langevin Equation (GLE) capabilities in modelling diffusion phenomena. We exploit a particular GLE solution which is known to reproduce the mean square displacement curve relative to transient anomalous diffusion and connect it with the normal modes collective variables. ML-GLE is capable of emulating the single polymer statistical properties in the long-term, predicting the diffusion coefficient. As a consequence, this results in an enormous acceleration in terms of simulation time with respect to the full-size simulation. Moreover, this approach is also scalable with system size.

Thinning Approximation for Calculating Two-Dimensional Scattering Patterns in Dissipative Particle Dynamics Simulations under Shear Flow.

Modifications to improve thinning approximation (TA) were considered in order to calculate two-dimensional scattering patterns (2DSPs) for dissipative particle dynamics (DPD) simulations of polymer melts under a shear flow. We proposed multipoint TA and adaptive TA because the bond lengths in DPD chains vary widely when compared to those in Kremer–Grest (KG) chains, and the effectiveness of these two types of TA for the two major DPD parameter sets were investigated. In this paper, we report our findings on the original DPD model with soft bonds and that with rigid bonds. Based on the behavior of the 2DSPs and the distribution of orientations of the bond vectors, two spot patterns originating from the oriented chain correlations were observed when distinct distributions of the highly oriented bond vectors in the shear direction were obtained. For multipoint TA, we concluded that at least two additional midpoints ( are required to clearly observe the two spot patterns. For adaptive TA, a dividing distance of is sufficient for clear observation, which is consistent with the requirement of for multipoint TA.

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.

Estimating self-diffusion in polymer melts: how long is a long enough molecular simulation?

We performed molecular simulations of polymer melts of three different molecular weights, with 1000 polymers for simulation run time , where is the relaxation time, using the bond-fluctuation model. We computed the mean-squared displacement, and applied weighted least squares with statistical bootstrap to infer the self-diffusivity and the associated uncertainty from these long simulations. We investigated the effect of limited simulations by using only a subset of these long simulations. We found that using and was a safe choice that led to relatively stable estimates of the mean self-diffusivity. We considered simulations of much poorer quality, and , and found that the proposed method accurately reflected the uncertainty even in the shortest simulations. This is in contrast with the standard practice of using 2–3 independent simulation runs to characterise uncertainty, which not only underestimates the true uncertainty in poor data-sets, but is also computationally more demanding.

A fast numerical approach for the simulation of highly viscous non-isothermal non-Newtonian fluids

This paper deals with the efficient simulation of polymer melts, as an example of highly viscous non-isothermal non-Newtonian fluids. In flow fields of our interest, which are characterized by small Reynolds numbers and large Prandtl numbers, steep gradients occur in thin boundary layers of the temperature distribution, whereas the boundary layers associated with the velocity field possess a considerable different length scale. In order to benefit from these properties, we introduce a physically motivated multigrid approach by computing velocity and temperature fields on different meshes. This new development is achieved by the modification of a discrete projection method. Numerical experiments are presented which confirm that the method decreases the computational effort considerably, while preserving the numerical accuracy.

Implications of microscopic simulations of polymer melts for mean-field tube theories

Despite the success of the mean-field tube theory in predicting the stress relaxation of linear and branched polymers, several important issues remain unresolved. Recent simulation methods that address some of these issues are shedding light on the dynamics of entangled polymer molecules. In this survey, we consider a class of coarse-grained models for polymer melts called slip-link models, which have been used to study the phenomena of constraint release, branch-point diffusion, and the relationship between the plateau modulus and entanglement spacing. We also consider the bond-fluctuation lattice model, and the pearl-necklace molecular dynamics model in conjunction with recently developed algorithms to identify primitive paths. The ability of these latter models to identify the primitive path network enables molecular simulations to be used to test and improve mean-field tube models. The implications of these simulations for the mean-field tube potential in the absence of constraint release, and for the dilution exponent which controls the strength of constraint release, are examined.

Polymer diffusion in a lattice polymer model with an intrinsic reptation mechanism

Rubinstein's repton model, extended by van Heukelum and Barkema for the simulation of polymer melts, is studied. This model has two dynamical mechanisms, explicit reptation and sideways motion, each with a prescribed rate. We study how the polymer diffusion coefficient depends on the ratio γ of these rates, while the sum of these rates is kept constant. We find that the diffusion coefficient of the polymers as a function of γ is not simply a linear combination of the contributions of the individual mechanisms; there is a large amount of cooperativity between the two kinds of mechanisms. A better understanding of this cooperativity might benefit research in a wide range of topics.

Simulation of polymer melts. I. Coarse-graining procedure for polycarbonates

The paper introduces a systematic procedure to coarse grain atomistic polymer models into a mesoscopic model, which then allows an effective and fast simulation of melts. The method, which provides information on both static and dynamic properties, is tested for three different modifications of polycarbonate. The models successfully describe the variation in the Vogel -Fulcher temperature as well as the total chain extension. The effective speedup compared to the corresponding atomistic simulation is significantly above 10 3 .

Simulation of polymer melts. II. From coarse-grained models back to atomistic description

Starting out from a computer simulation of a rather simple bead spring model, where the parameters are determined from an atomistic model by a numerical renormalization procedure (preceeding paper), after long simulation runs the chemical details are reintroduced into the coarse-grained chains. The resulting microscopic structure is compared to neutron scattering results. The procedure is tested for two different polycarbonate modifications.

Simulation of polymer melts. II. From coarse-grained models back to atomistic description

Starting out from a computer simulation of a rather simple bead spring model, where the parameters are determined from an atomistic model by a numerical renormalization procedure (preceeding paper), after long simulation runs the chemical details are reintroduced into the coarse-grained chains. The resulting microscopic structure is compared to neutron scattering results. The procedure is tested for two different polycarbonate modifications.

Parallelization of a Monte Carlo algorithm for the simulation of polymer melts

The Continuum-configurational Bias Monte Carlo algorithm (CBMC) is a very efficient method for the simulation of polymer melts. This algorithm is well-suited to parallelization on shared-memory multiprocessors. The main effort for parallelization is often spent in the decomposition of the data structures and the design of the parallel program sections. We present some generally applicable methods to improve the optimization process on shared-memory multiprocessors using global address space and on distributed-memory multicomputers using message passing.