Quantifying chain reptation in entangled polymer melts: Topological and dynamical mapping of atomistic simulation results onto the tube model

Filled Elastomers: Mechanistic and Physics-Driven Modeling and Applications as Smart Materials

Elastomers are made of chain-like molecules to form networks that can sustain large deformation. Rubbers are thermosetting elastomers that are obtained from irreversible curing reactions. Curing reactions create permanent bonds between the molecular chains. On the other hand, thermoplastic elastomers do not need curing reactions. Incorporation of appropriated filler particles, as has been practiced for decades, can significantly enhance mechanical properties of elastomers. However, there are fundamental questions about polymer matrix composites (PMCs) that still elude complete understanding. This is because the macroscopic properties of PMCs depend not only on the overall volume fraction (ϕ) of the filler particles, but also on their spatial distribution (i.e., primary, secondary, and tertiary structure). This work aims at reviewing how the mechanical properties of PMCs are related to the microstructure of filler particles and to the interaction between filler particles and polymer matrices. Overall, soft rubbery matrices dictate the elasticity/hyperelasticity of the PMCs while the reinforcement involves polymer-particle interactions that can significantly influence the mechanical properties of the polymer matrix interface. For ϕ values higher than a threshold, percolation of the filler particles can lead to significant reinforcement. While viscoelastic behavior may be attributed to the soft rubbery component, inelastic behaviors like the Mullins and Payne effects are highly correlated to the microstructures of the polymer matrix and the filler particles, as well as that of the polymer-particle interface. Additionally, the incorporation of specific filler particles within intelligently designed polymer systems has been shown to yield a variety of functional and responsive materials, commonly termed smart materials. We review three types of smart PMCs, i.e., magnetoelastic (M-), shape-memory (SM-), and self-healing (SH-) PMCs, and discuss the constitutive models for these smart materials.

Predicting High-Density Polyethylene Melt Rheology Using a Multimode Tube Model Derived Using Non-Equilibrium Thermodynamics

Based on the Generalized bracket, or Beris-Edwards, formalism of non-equilibrium thermodynamics, we recently proposed a new differential constitutive model for the rheological study of entangled polymer melts and solutions. It amended the shortcomings of a previous model that was too strict regarding the values of the convective constraint release parameter for the model not to violate the second law of thermodynamics, and it has been shown capable of predicting a transient stress undershoot (following the overshoot) at high shear rates. In this study, we wish to further examine this model's capability to predict the rheological response of industrial polymer systems by extending it to its multiple-mode version. The comparison with industrial rheological data (High-Density Polyethylene resins), which was based on comparison with experimental data available in (a) Small Amplitude Oscillatory shear, (b) start-up shear, and (c) start-up uniaxial elongation, was noted to be good.

Microstructural Dynamics of Polymer Melts during Stretching: Radial Size Distribution

The transient elongational viscosity ηe(t) of the polymer melt is known to exhibit strain hardening, which depends on the strain rate ε˙. This phenomenon was elucidated by the difference of chain stretching in the entanglement network between extension and shear. However, to date, the microscopic evolution of polymer melt has not been fully statistically analyzed. In this work, the radial size distributions P(Rg,t) of linear polymers are explored by dissipative particle dynamics during the stretching processes. In uniaxial extensional flow, it is observed that the mean radius of gyration R¯g(t) and standard deviation σ(t) remain unchanged until the onset of strain hardening, corresponding to linear viscoelasticity. Both R¯g and σ rise rapidly in the non-linear regime, and bimodal size distribution can emerge. Moreover, the onset of strain hardening is found to be insensitive to the Hencky strain (ε˙Ht) and chain length (N).

Experiments and Modeling of Flow-Enhanced Nucleation in LLDPE

A computational and experimental framework for quantifying flow-enhanced nucleation (FEN) in polymers is presented and demonstrated for an industrial-grade linear low-density polyethylene (LLDPE). Experimentally, kinetic measurements of isothermal crystallization were performed by using fast-scanning calorimetry (FSC) for melts that were presheared at various strain rates. The effect of shear on the average conformation tensor of the melt was modeled with the discrete slip-link model (DSM). The conformation tensor was then related to the acceleration in nucleation kinetics by using an expression previously validated with nonequilibrium molecular dynamics (NEMD). The expression is based on the nematic order tensor of Kuhn segments, which can be obtained from the conformation tensor of entanglement strands. The single adjustable parameter of the model was determined by fitting to the experimental FSC data. This expression accurately describes FEN for the LLDPE, representing a significant advancement toward the development of a fully integrated processing model for crystallizable polymers.

Mobility of Polymer Melts in a Regular Array of Carbon Nanotubes

In polymer nanocomposites, mechanical properties essentially depend on the alignment of nanoparticles and polymers. In this work, we investigate an entangled polymer melt in a confinement computationally, in order to get an insight into the mobility behavior of the polymer chains. The confinement consists of nanotubes, arranged in a hexagonal array. We use dissipative particle dynamics, a fast, soft-core simulation method, and reintroduce entanglement dynamics via slip-springs. We observe a distinct influence of the confinement as diffusion is increased in the direction parallel to the nanotubes. Furthermore, we observe that an orientation of the polymers parallel to the nanotubes and chains are compressed in the direction orthogonal to their primitive path. The diffusion parallel to the nanotubes increases further as we increase the nanotube volume fraction in our systems. Moreover, we investigate the slip-spring distribution in the proximity of the nanotube surfaces of our fast and simple slip-spring model, which we find to coincide with results reported for more sophisticated and expensive methods. Our DPD model shows potential applicability to a wide range of polymer nanocomposites while preserving reptation behavior, which is typically lost due to the use of soft-core models.

Thermodynamically consistent incorporation of entanglement spatial fluctuations in the slip-link model

We evaluate the thermodynamic consistency of the anisotropic mobile slip-link model for entangled flexible polymers. The level of description is that of a single chain, whose interactions with other chains are coarse grained to discrete entanglements. The dynamics of the model consist of the motion of entanglements through space and of the chain through the entanglements, as well as the creation and destruction of entanglements, which are implemented in a mean-field way. Entanglements are modeled as discrete slip links, whose spatial positions are confined by quadratic potentials. The confinement potentials move with the macroscopic velocity field, hence the entanglements fluctuate around purely affine motion. We allow for anisotropy of these fluctuations, described by a set of shape tensors. By casting the model in the form of the general equation for the nonequilibrium reversible-irreversible coupling from nonequilibrium thermodynamics, we show that (i) since the confinement potentials contribute to the chain free energy, they must also contribute to the stress tensor, (ii) these stress contributions are of two kinds: one related to the virtual springs connecting the slip links to the centers of the confinement potentials and the other related to the shape tensors, and (iii) these two kinds of stress contributions cancel each other if the confinement potentials become anisotropic in flow, according to a lower-convected evolution of the confinement strength or, equivalently, an upper-convected evolution of the shape tensors of the entanglement spatial fluctuations. In previous publications, we have shown that this cancellation is necessary for the model to obey the stress-optical rule and the Green-Kubo relation, and simultaneously to agree with plateau modulus predictions of multichain models and simulations.

Interaction of high-intensity focused ultrasound with polymers at the atomistic scale

Experiments show that high-intensity focused ultrasound (HIFU) is a promising stimulus with multiple superior and unique capabilities to induce localized heating and achieve temporal and spatial thermal effects in the polymers, noninvasively. When polymers are subjected to HIFU, they heat up differently compared to the case they are subjected to heat sources directly; however, the origins of this difference are still entirely unknown. We hypothesize that the difference in the macroscale response of polymers subjected to HIFU strongly depends on the polymer chains, composition, and structure, i.e. being crystalline or amorphous. In this work, this hypothesis is investigated by molecular dynamics studies at the atomistic level and verified by experiments at the macroscopic scale. The results show that the viscoelasticity, measured by stress-strain phase lag, the reptation motion of the chains, and the vibration-induced local mobility quantified by the root mean square fluctuation contribute to the observed difference in the HIFU-induced thermal effects. This unravels the unknown mechanisms behind stimulating the polymers by HIFU, and paves the way in front of using this method in future applications.

Insight into the Structure and Dynamics of Polymers by Neutron Scattering Combined with Atomistic Molecular Dynamics Simulations

Combining neutron scattering and fully atomistic molecular dynamics simulations allows unraveling structural and dynamical features of polymer melts at different length scales, mainly in the intermolecular and monomeric range. Here we present the methodology developed by us and the results of its application during the last years in a variety of polymers. This methodology is based on two pillars: (i) both techniques cover approximately the same length and time scales and (ii) the classical van Hove formalism allows easily calculating the magnitudes measured by neutron scattering from the simulated atomic trajectories. By direct comparison with experimental results, the simulated cell is validated. Thereafter, the information of the simulations can be exploited, calculating magnitudes that are experimentally inaccessible or extending the parameters range beyond the experimental capabilities. We show how detailed microscopic insight on structural features and dynamical processes of various kinds has been gained in polymeric systems with different degrees of complexity, and how intriguing questions as the collective behavior at intermediate length scales have been faced.

Simple, Accurate and User-Friendly Differential Constitutive Model for the Rheology of Entangled Polymer Melts and Solutions from Nonequilibrium Thermodynamics

In a recent reformulation of the Marrucci-Ianniruberto constitutive equation for the rheology of entangled polymer melts in the context of nonequilibrium thermodynamics, rather large values of the convective constraint release parameter β_ccr had to be used in order for the model not to violate the second law of thermodynamics. In this work, we present an appropriate modification of the model, which avoids the splitting of the evolution equation for the conformation tensor into an orientation and a stretching part. Then, thermodynamic admissibility simply dictates that β_ccr ≥ 0, thus allowing for more realistic values of β_ccr to be chosen. Moreover, and in view of recent experimental evidence for a transient stress undershoot (following the overshoot) at high shear rates, whose origin may be traced back to molecular tumbling, we have incorporated additional terms into the model accounting, at least in an approximate way, for non-affine deformation through a slip parameter ξ. Use of the new model to describe available experimental data for the transient and steady-state shear and elongational rheology of entangled polystyrene melts and concentrated solutions shows close agreement. Overall, the modified model proposed here combines simplicity with accuracy, which renders it an excellent choice for managing complex viscoelastic fluid flows in large-scale numerical calculations.

High-fidelity scaling relationships for determining dissipative particle dynamics parameters from atomistic molecular dynamics simulations of polymeric liquids

An optimized Dissipative Particle Dynamics (DPD) model with simple scaling rules was developed for simulating entangled linear polyethylene melts. The scaling method, which can be used for mapping dimensionless (reduced units) DPD simulation data to physical units, was based on scaling factors for three fundamental physical units; namely, length, time, and viscosity. The scaling factors were obtained as ratios of equilibrium Molecular Dynamics (MD) simulation data in physical units and equivalent DPD simulation data for relevant quantities. Specifically, the time scaling factor was determined as the ratio of longest relaxation times, the length scaling factor was obtained as the ratio of the equilibrium end-to-end distances, and the viscosity scaling factor was calculated as the ratio of zero-shear viscosities, each as obtained from the MD (in physical units) and DPD (reduced units) simulations. The scaling method was verified for three MD/DPD model liquid pairs under several different nonequilibrium conditions, including transient and steady-state simple shear and planar elongational flows. Comparison of the MD simulation results with those of the scaled DPD simulations revealed that the optimized DPD model, expressed in terms of the proposed scaling method, successfully reproduced the computationally expensive MD results using relatively cheaper DPD simulations.

Linear and Nonlinear Dynamic Behavior of Polymer Micellar Assemblies Connected by Metallo-Supramolecular Interactions

The linear and nonlinear rheology of associative colloidal polymer assemblies with metallo-supramolecular interactions is herein studied. Polystyrene-b-poly(tert-butylacrylate) with a terpyridine ligand at the end of the acrylate block is self-assembled into micelles in ethanol, a selective solvent for the latter block, and supramolecularly connected by complexation to divalent metal ions. The dependence of the system elasticity on polymer concentration can be semi-quantitatively understood by a geometrical packing model. For strongly associated (Ni2+, Fe2+) and sufficiently concentrated systems (15 w/v%), any given ligand end-group has a virtually 100% probability of being located in an overlapping hairy region between two micelles. By assuming a 50% probability of intermicellar crosslinks being formed, an excellent prediction of the plateau modulus was achieved and compared with the experimental results. For strongly associated but somewhat more dilute systems (12 w/v%) that still have significant overlap between hairy regions, the experimental modulus was lower than the predicted value, as the effective number of crosslinkers was further reduced along with possible density heterogeneities. The reversible destruction of the network by shear forces can be observed from the strain dependence of the storage and loss moduli. The storage moduli of the Ni2+ and Zn2+ systems at a lower concentration (12 w/v%) showed a rarely observed feature (i.e., a peak at the transition from linear to nonlinear regime). This peak disappeared at a higher concentration (15 w/v%). This behavior can be rationalized based on concentration-dependent network stretchability.

Determine Mesh Size through Monomer Mean-Square Displacement

A dynamic method to determine the main parameter of the tube theory through monomer mean-square displacement is discussed in this paper. The tube step length can be measured from the intersection of the slope-12 line and the slope-14 line in log-log plot, and the tube diameter can be obtained by recording the time at which g1 data start to leave the slope-12 regime. According to recent simulation data, the ratio of the tube step length to the tube diameter was found to be about 2 for different entangled polymer systems. Since measuring the tube diameter does not require g1 data to reach the slope-14 regime, this could be the best way to find the entanglement length from microscopic consideration.

Detection of molecular behavior that characterizes systems using a deep learning approach

Molecular dynamics (MD) simulation is a powerful computational method to observe molecular behavior. Although the detection of molecular behavior that characterizes systems is an important task in the study of MD, it is typically difficult and depends on human expert knowledge. Therefore, we propose a novel analysis scheme for MD data using deep neural networks. A key aspect of our scheme is the estimation of statistical distances between different ensembles that are probability distributions over the possible states of systems. This allows us to build low-dimensional embeddings of ensembles to visualize differences between systems in a compact metric space. Furthermore, the molecular behavior that contributes to the differences between systems can also be detected using the trained function of deep neural networks. The applicability of our scheme is demonstrated using three types of MD data. Our scheme could be a powerful tool to clarify the underlying physics in the molecular systems.

Topological Methods for Polymeric Materials: Characterizing the Relationship Between Polymer Entanglement and Viscoelasticity

We develop topological methods for characterizing the relationship between polymer chain entanglement and bulk viscoelastic responses. We introduce generalized Linking Number and Writhe characteristics that are applicable to open linear chains. We investigate the rheology of polymeric chains entangled into weaves with varying topologies and levels of chain density. To investigate viscoelastic responses, we perform non-equilibrium molecular simulations over a range of frequencies using sheared Lees⁻Edwards boundary conditions. We show how our topological characteristics can be used to capture key features of the polymer entanglements related to the viscoelastic responses. We find there is a linear relation over a significant range of frequencies between the mean absolute Writhe W r and the Loss Tangent tan ( δ ) . We also find an approximate inverse linear relationship between the mean absolute Periodic Linking Number L K P and the Loss Tangent tan ( δ ) . Our results show some of the ways topological methods can be used to characterize chain entanglements to better understand the origins of mechanical responses in polymeric materials.

Entangled polymer dynamics beyond reptation

Macroscopic properties of polymers arise from microscopic entanglement of polymer chains. Entangled polymer dynamics have been described theoretically by time- and space-averaged relaxation modes of single chains occurring at different time and length scales. However, theoretical and experimental studies along this framework provide oversimplified picture of spatiotemporally heterogeneous polymer dynamics. Characterization of entangled polymer dynamics beyond this paradigm requires a method that enables to capture motion and relaxation occurring in real space at different length and time scales. Here we develop new single-molecule characterization platform by combining super-resolution fluorescence imaging and recently developed single-molecule tracking method, cumulative-area tracking, which enables to quantify the chain motion in the length and time scale of nanometres to micrometres and milliseconds to minutes. Using linear and cyclic dsDNA molecules as model systems, our new method reveals chain-position-dependent motion of the entangled linear chains, which is beyond the scope of current theoretical framework.

Onset of static and dynamic universality among molecular models of polymers

A quantitatively accurate prediction of properties for entangled polymers is a long-standing challenge that must be addressed to enable efficient development of these materials. The complex nature of polymers is the fundamental origin of this challenge. Specifically, the chemistry, structure, and dynamics at the atomistic scale affect properties at the meso and macro scales. Therefore, quantitative predictions must start from atomistic molecular dynamics (AMD) simulations. Combined use of atomistic and coarse-grained (CG) models is a promising approach to estimate long-timescale behavior of entangled polymers. However, a systematic coarse-graining is still to be done for bridging the gap of length and time scales while retaining atomistic characteristics. Here we examine the gaps among models, using a generic mapping scheme based on power laws that are closely related to universality in polymer structure and dynamics. The scheme reveals the characteristic length and time for the onset of universality between the vastly different scales of an atomistic model of polyethylene and the bead-spring Kremer-Grest (KG) model. The mapping between CG model of polystyrene and the KG model demonstrates the fast onset of universality, and polymer dynamics up to the subsecond time scale are observed. Thus, quantitatively traceable timescales of polymer MD simulations can be significantly increased.

Molecular Dynamics Simulations for Resolving Scaling Laws of Polyethylene Melts

Long-timescale molecular dynamics simulations were performed to estimate the actual physical nature of a united-atom model of polyethylene (PE). Several scaling laws for representative polymer properties are compared to theoretical predictions. Internal structure results indicate a clear departure from theoretical predictions that assume ideal chain statics. Chain motion deviates from predictions that assume ideal motion of short chains. With regard to linear viscoelasticity, the presence or absence of entanglements strongly affects the duration of the theoretical behavior. Overall, the results indicate that Gaussian statics and dynamics are not necessarily established for real atomistic models of PE. Moreover, the actual physical nature should be carefully considered when using atomistic models for applications that expect typical polymer behaviors.

Modeling the relaxation of internal DNA segments during genome mapping in nanochannels

We have developed a multi-scale model describing the dynamics of internal segments of DNA in nanochannels used for genome mapping. In addition to the channel geometry, the model takes as its inputs the DNA properties in free solution (persistence length, effective width, molecular weight, and segmental hydrodynamic radius) and buffer properties (temperature and viscosity). Using pruned-enriched Rosenbluth simulations of a discrete wormlike chain model with circa 10 base pair resolution and a numerical solution for the hydrodynamic interactions in confinement, we convert these experimentally available inputs into the necessary parameters for a one-dimensional, Rouse-like model of the confined chain. The resulting coarse-grained model resolves the DNA at a length scale of approximately 6 kilobase pairs in the absence of any global hairpin folds, and is readily studied using a normal-mode analysis or Brownian dynamics simulations. The Rouse-like model successfully reproduces both the trends and order of magnitude of the relaxation time of the distance between labeled segments of DNA obtained in experiments. The model also provides insights that are not readily accessible from experiments, such as the role of the molecular weight of the DNA and location of the labeled segments that impact the statistical models used to construct genome maps from data acquired in nanochannels. The multi-scale approach used here, while focused towards a technologically relevant scenario, is readily adapted to other channel sizes and polymers.

Microscopic Dynamics and Topology of Polymer Rings Immersed in a Host Matrix of Longer Linear Polymers: Results from a Detailed Molecular Dynamics Simulation Study and Comparison with Experimental Data

We have performed molecular dynamics (MD) simulations of melt systems consisting of a small number of long ring poly(ethylene oxide) (PEO) probes immersed in a host matrix of linear PEO chains and have studied their microscopic dynamics and topology as a function of the molecular length of the host linear chains. Consistent with a recent neutron spin echo spectroscopy study (Goossen et al., Phys. Rev. Lett. 2015, 115, 148302), we have observed that the segmental dynamics of the probe ring molecules is controlled by the length of the host linear chains. In matrices of short, unentangled linear chains, the ring probes exhibit a Rouse-like dynamics, and the spectra of their dynamic structure factor resemble those in their own melt. In striking contrast, in matrices of long, entangled linear chains, their dynamics is drastically altered. The corresponding dynamic structure factor spectra exhibit a steep initial decay up to times on the order of the entanglement time τe of linear PEO at the same temperature but then they become practically time-independent approaching plateau values. The plateau values are different for different wavevectors; they also depend on the length of the host linear chains. Our results are supported by a geometric analysis of topological interactions, which reveals significant threading of all ring molecules by the linear chains. In most cases, each ring is simultaneously threaded by several linear chains. As a result, its dynamics at times longer than a few τe should be completely dictated by the release of the topological restrictions imposed by these threadings (interpenetrations). Our topological analysis did not indicate any effect of the few ring probes on the statistical properties of the network of primitive paths of the host linear chains.

A new insight into the conformation and melt dynamics of hydrogenated polybutadiene as revealed by computer simulations

Extensive molecular dynamics simulations of the macromolecular conformation and the melt dynamics for model polymers of different molecular weights have been carried out. The selected models are hydrogenated polybutadienes with a 2% content of ethyl branches and linear polyethylene. It will be shown that the density and chain stiffness are clearly affected by both the molecular weight and the presence of ethyl branches. Furthermore, the results obtained from the simulations on the molecular size and, more remarkably, chain dynamics, perfectly match the neutron scattering experiments performed by Zamponi et al. in hydrogenated polybutadienes. We observe a clear chain contraction and a slow dynamics for the hydrogenated polybutadiene with respect to the linear chain of the same molecular length. Using the Likhtman-McLeish definitions, the obtained values of the entanglement relaxation time (τe) and the tube diameter (a) are found to be in agreement with the available experimental data (by rheology and neutron spin echo) as well as with those obtained by the simulations. Finally, a very good agreement of diffusion coefficients as a function of the molecular weight between simulations and experiments is observed. Therefore, there exists a clear difference between the results obtained for branched and linear polyethylene, accounting for a definitive effect of the short chain branching on the conformational properties and the melt dynamics of polyolefins.

Nanoscale Study of Polymer Dynamics

The thermal motion of polymer chains in a crowded environment is anisotropic and highly confined. Whereas theoretical and experimental progress has been made, typically only indirect evidence of polymer dynamics is obtained either from scattering or mechanical response. Toward a complete understanding of the complicated polymer dynamics in crowded media such as biological cells, it is of great importance to unravel the role of heterogeneity and molecular individualism. In the present work, we investigate the dynamics of synthetic polymers and the tube-like motion of individual chains using time-resolved fluorescence microscopy. A single fluorescently labeled polymer molecule is observed in a sea of unlabeled polymers, giving access to not only the dynamics of the probe chain itself but also to that of the surrounding network. We demonstrate that it is possible to extract the characteristic time constants and length scales in one experiment, providing a detailed understanding of polymer dynamics at the single chain level. The quantitative agreement with bulk rheology measurements is promising for using local probes to study heterogeneity in complex, crowded systems.

Perspectives on the viscoelasticity and flow behavior of entangled linear and branched polymers

We briefly review the recent advances in the rheology of entangled polymers and identify emerging research trends and outstanding challenges, especially with respect to branched polymers. Emphasis is placed on the role of well-characterized model systems, as well as the synergy of synthesis-characterization, rheometry and modeling/simulations. The theoretical framework for understanding the observed linear and nonlinear rheological phenomena is the tube model, which is critically assessed in view of its successes and shortcomings, and alternative approaches are briefly discussed. Finally, intriguing experimental findings and controversial issues that merit consistent explanation, such as shear banding instabilities, multiple stress overshoots in transient simple shear and enhanced steady-state elongational viscosity in polymer solutions, are discussed, and future directions such as branch point dynamics and anisotropic monomeric friction are outlined.

Pulling-force-induced elongation and alignment effects on entanglement and knotting characteristics of linear polymers in a melt

We employ a primitive path (PP) algorithm and the Gauss linking integral to study the degree of entanglement and knotting characteristics of linear polymer model chains in a melt under the action of a constant pulling force applied to selected chain ends. Our results for the amount of entanglement, the linking number, the average crossing number, the writhe of the chains and their PPs and the writhe of the entanglement strands all suggest a different response at the length scale of entanglement strands than that of the chains themselves and of the corresponding PPs. Our findings indicate that the chains first stretch at the level of entanglement strands and next the PP (tube) gets oriented with the "flow." These two phases of the extension and alignment of the chains coincide with two phases related to the disentanglement of the chains. Soon after the onset of external force the PPs attain a more entangled conformation, and the number of nontrivially linked end-to-end closed chains increases. Next, the chains disentangle continuously to attain an almost unentangled conformation. Using the linking matrix of the chains in the melt, we furthermore show that these phases are accompanied by a different scaling of the homogeneity of the global entanglement in the system. The homogeneity of the end-to-end closed chains first increases to a maximum and then decreases slowly to a value characterizing a completely unlinked system.

Simulating the Flow of Entangled Polymers

To optimize automation for polymer processing, attempts have been made to simulate the flow of entangled polymers. In industry, fluid dynamics simulations with phenomenological constitutive equations have been practically established. However, to account for molecular characteristics, a method to obtain the constitutive relationship from the molecular structure is required. Molecular dynamics simulations with atomic description are not practical for this purpose; accordingly, coarse-grained models with reduced degrees of freedom have been developed. Although the modeling of entanglement is still a challenge, mesoscopic models with a priori settings to reproduce entangled polymer dynamics, such as tube models, have achieved remarkable success. To use the mesoscopic models as staging posts between atomistic and fluid dynamics simulations, studies have been undertaken to establish links from the coarse-grained model to the atomistic and macroscopic simulations. Consequently, integrated simulations from materials chemistry to predict the macroscopic flow in polymer processing are forthcoming.