For optimal processing and design of entangled polymeric materials it is important to establish a rigorous link between the detailed molecular composition of the polymer and the viscoelastic properties of the macroscopic melt. We review current and past computer simulation techniques and critically assess their ability to provide such a link between chemistry and rheology. We distinguish between two classes of coarse-graining levels, which we term coarse-grained molecular dynamics (CGMD) and coarse-grained stochastic dynamics (CGSD). In CGMD the coarse-grained beads are still relatively hard, thus automatically preventing bond crossing. This also implies an upper limit on the number of atoms that can be lumped together and therefore on the longest chain lengths that can be studied. To reach a higher degree of coarse-graining, in CGSD many more atoms are lumped together, leading to relatively soft beads. In that case friction and stochastic forces dominate the interactions, and actions must be undertaken to prevent bond crossing. We also review alternative methods that make use of the tube model of polymer dynamics, by obtaining the entanglement characteristics through a primitive path analysis and by simulation of a primitive chain network. We finally review super-coarse-grained methods in which an entire polymer is represented by a single particle, and comment on ways to include memory effects and transient forces.
The behavior of a supercooled polymer melt composed of short chains with ten beads near an oscillating plate are simulated by using a hybrid simulation of molecular dynamics (MD) and computational fluid dynamics (CFD). In the method, the macroscopic dynamics are solved by using CFD, but, instead of using any constitutive equations, a local stress is calculated by using a non-equilibrium MD simulation associated at each lattice node in the CFD calculation. It is seen that the local rheology of the melt varies considerably in a thin viscous diffusion layer that arises near an oscillating plate. …
Molecular dynamics simulations are performed for a polymer melt composed of short chains in quiescent and sheared conditions. The stress relaxation function $G(t)$ exhibits a stretched exponential form in a relatively early stage and ultimately follows the Rouse function in quiescent supercooled state. Transient stress evolution after application of shear obeys the linear growth $\int_0^t dt'G(t')$ for strain less than 0.1 and then saturates into a non-Newtonian viscosity. In steady states, strong shear-thinning and elongation of chains into ellipsoidal shapes are found at extremely small shea…
Using molecular dynamics simulations, we study dynamics of a model polymer melt composed of short chains with bead number N=10 in supercooled states. In quiescent conditions, the stress relaxation function $G(t)$ is calculated, which exhibits a stretched exponential relaxation on the time scale of the $α$ relaxation time $τ_α$ and ultimately follows the Rouse dynamics characterized by the time $τ_{\rm R} \sim N^2 τ_α$. After application of shear $\gdot$, transient stress growth $σ_{xy}(t)/\gdot$ first obeys the linear growth $\int_0^t dt'G(t')$ for strain less than 0.1 but saturates into a non…
Ring polymers remain a major challenge to our current understanding of polymer dynamics. Experimental results are difficult to interpret because of the uncertainty in the purity and dispersity of the sample. Using both equilibrium and non-equilibrium molecular dynamics simulations we have systematically investigated the structure, dynamics and rheology of perfectly controlled ring/linear polymer blends with chains of such length and flexibility that the number of entanglements is up to about 14 per chain, which is comparable to experimental systems examined in the literature. The smallest conc…
We use non-equilibrium atomistic molecular dynamics simulations of unentangled melts of linear and star polymers ($\mathrm{C_{25}H_{52}}$) to study the steady-state viscoelastic response under confinement within nanoscale hematite $\left ( \mathrm{α-Fe_2O_3} \right )$ channels. We report (i) the negative (positive) first (second) normal stress difference and (ii) the presence of viscoelastic tension at low shear rates. We link these effects to bond alignment such that chains near the surface can carry the elastic force exerted on the walls, which decays as the chains become more aligned in the…
The integral equation coarse-graining (IECG) approach is a promising high-level coarse-graining (CG) method for polymer melts, with variable resolution from soft spheres to multi CG sites, which preserves the structural and thermodynamical consistencies with the related atomistic simulations. When compared to the atomistic description, the procedure of coarse-graining results in smoother free energy surfaces, longer-ranged potentials, a decrease in the number of interaction sites for a given polymer, and more. Because these changes have competing effects on the computational efficiency of the …
The dynamic rheology of a polymer melt composed of short chains with ten beads between rapidly oscillating plates is investigated for various oscillation frequencies by using the hybrid simulation of the molecular dynamics and computational fluid dynamics. In the rapidly oscillating plates, non-uniform boundary layer flows are generated over the plate due to inertia of the fluid, and the local rheological properties of the melt are spatially varied according to the local flow fields. Far from the plate, the local strain decreases as the oscillation frequency increases such that the dynamic rhe…
Orientational origin of nonlinear shear rheology in unentangled polymer melts
Department of Chemical Science and Engineering, Kyoto University（京都大学化学工程系）；Advanced Manufacturing Technology Institute, Kanazawa University（金泽大学先进制造技术研究所）
Several recently proposed semi--automatic and fully--automatic coarse--graining schemes for polymer simulations are discussed. All these techniques derive effective potentials for multi--atom units or super--atoms from atomistic simulations. These include techniques relying on single chain simulations in vacuum and self--consistent optimizations from the melt like the simplex method and the inverted Boltzmann method. The focus is on matching the polymer structure on different scales. Several ways to obtain a time-scale for dynamic mapping are discussed additionally. Finally, similarities to ot…
Medium or large amplitude oscillatory shear (M/LAOS) is sensitive to polymer chain structure, yet poses unsolved challenges for 'a priori' structural characterisation. In this letter, we present a MAOS protocol applied to near-monodisperse linear polymer melts, from which chain-stretch relaxation, a key structural feature, is clearly discernible. The third harmonics of MAOS frequency sweeps are decomposed into real and imaginary components and found to obey time-temperature superposition. The GLaMM molecular tube-based model of linear entangled melt rheology and structure, which has no free pa…
The COMOFLO dynamic Monte Carlo algorithm is extended to enable the simulation of steady-state extensional rheology of dense melts for the first time ever. This significant advancement provides the ability to accurately capture the extensional viscosity of entangled polymer melts from low deformation rates, throughout the strain hardening regime, and into the region of viscosity thinning To do so, the purely extensional flow field associated with a four roll mill experiment is implemented in three dimensions. Periodic boundary conditions exist in all directions to enable a uniform deformation …
Structural and thermodynamic consistency of coarse-graining models across multiple length scales is essential for the predictive role of multi-scale modeling and molecular dynamic simulations that use mesoscale descriptions. Our approach is a coarse-grained model based on integral equation theory, which can represent polymer chains at variable levels of chemical details. The model is analytical and depends on molecular and thermodynamic parameters of the system under study, as well as on the direct correlation function in the k --> 0 limit, c0. A numerical solution to the PRISM integral equati…
We present few ordering mechanisms in block copolymer melts in the coarse-graining approach. For chemically homogeneous or modulated confining surfaces, the surface ordering is investigated above and below the order-disorder temperature. In some cases the copolymer deformation near the surface is similar to the copolymer morphology in bulk grain boundaries. Block copolymers in contact with rough surfaces are considered as well, and the transition from lamellae parallel to perpendicular to the surface is investigated as a function of surface roughness. Finally, we describe how external electric…
A hierarchical (triple scale) simulation methodology is presented for the prediction of the dynamical and rheological properties of high molecular weight entangled polymer melts. The methodology consists of atomistic, moderately coarse-grained (mCG), and highly coarse-grained slip-spring (SLSP) simulations. At the mCG level, a few chemically bonded atoms are lumped into one coarse-grained bead. At this level, the chemical identity of the atomistic system, and the interchain topological constraints (entanglements) are preserved. The mCG potentials are derived by matching local structural distri…
We review some recent coarse-graining and multi-scale methods, but also put forward some new ideas for addressing such issues. We find that, if one is guided by nonequilibrium statistical mechanics and thermodynamics, it is possible to design well-founded multi-scale modeling tools that can link microscopic models with macroscopic constitutive equations. Such multi-scale modeling tools benefit from recently proposed approaches for static coarse graining which are mainly built on potentials of mean force. For dynamical properties, however, coarse-grained models need to account for dissipative e…
Extensive molecular simulations are applied to characterize the equilibrium dynamics, entanglement topology, and nonlinear extensional rheology of symmetric ring-linear polymer blends with systematically varied ring fraction $ϕ_R$. Chains with degree of entanglement $Z\approx14$ mixed to produce 10 well-entangled systems with $ϕ_R$ varying from neat linear to neat ring melts. Primitive path analysis are used to visualize and quantify the structure of the composite ring-linear entanglement network. We directly measure the quantity of ring-linear threading and linear-linear entanglement as a fun…
We introduce a mesoscale technique for simulating the structure and rheology of block copolymer melts and blends in hydrodynamic flows. The technique couples dynamic self consistent field theory (DSCFT) with continuum hydrodynamics and flow penalization to simulate polymeric fluid flows in channels of arbitrary geometry. We demonstrate the method by studying phase separation of an ABC triblock copolymer melt in a sub-micron channel with neutral wall wetting conditions. We find that surface wetting effects and shear effects compete, producing wall-perpendicular lamellae in the absence of flow, …
The classical rheological theories of entangled polymeric liquids are built upon two pillars: Gaussian statistics of entanglement strands and the assumption that the stress arises exclusively from the change of intramolecular configuration entropy. We show that these two hypotheses are not supported by molecular dynamics simulations of polymer melts. Specifically, the segment distribution functions at the entanglement length scale and below deviate considerably from the theoretical predictions, in both the equilibrium and deformed states. Further conformational analysis reveals that the intrac…
We numerically and analytically analyze the startup continuous shear rheology of heavily entangled rigid rod polymer fluids based on our self-consistent, force-level theory of anharmonic tube confinement. The approach is simplified by neglecting stress-assisted transverse barrier hopping, and irreversible relaxation proceeds solely via deformation-perturbed reptation. This process is self-consistently coupled to tube dilation and macroscopic rheological response. We predict that with increasing strain the tube strongly dilates, entanglements are lost, and reptation speeds up. As a consequence,…
Coupled length and time scales determine the dynamic behavior of polymers and underlie their unique viscoelastic properties. To resolve the long-time dynamics it is imperative to determine which time and length scales must be correctly modeled. Here we probe the degree of coarse graining required to simultaneously retain significant atomistic details and access large length and time scales. The degree of coarse graining in turn sets the minimum length scale instrumental in defining polymer properties and dynamics. Using linear polyethylene as a model system, we probe how coarse graining scale …
We study the nonlinear rheology of a glass-forming binary mixture under the reversal of shear flow using molecular dynamics simulations and a schematic model of the mode-coupling theory of the glass transition (MCT). Memory effects lead to a history-dependent response, as exemplified by the vanishing of a stress-overshoot phenomenon in the stress--strain curves of the sheared liquid, and a change in the apparent elastic coefficients around states with zero stress. We investigate the various retarded contributions to the stress response at a given time schematically within MCT. The connection o…
X-ray particle tracking velocimetry for steady-state rheological characterization: Case study of a complex polymer melt flow in material extrusion additive manufacturing
University of Stuttgart（斯图加特大学）；University of Milan（米兰大学）；CNR – Consiglio Nazionale delle Ricerche, Istituto di Chimica della Materia Condensata e di Tecnologie per l’Energia（意大利国家研究委员会凝聚态材料与能源技术研究所）
Numerically optimized reduced descriptions of macromolecular liquids often present thermodynamic inconsistency with atomistic level descriptions even if the total correlation function, i.e. the structure, appears to be in agreement. An analytical expression for the effective potential between a pair of coarse-grained units is derived starting from the first-principles Ornstein-Zernike equation, for a polymer liquid where each chain is represented as a collection of interpenetrating blobs, with a variable number of blobs, $n_b$, of size $N_b$. The potential is characterized by a long tail, slow…
We propose a dynamic coarse-graining (CG) scheme for mapping heterogeneous polymer fluids onto extremely CG models in a dynamically consistent manner. The idea is to use as target function for the mapping a wave-vector dependent mobility function derived from the single-chain dynamic structure factor, which is calculated in the microscopic reference system. In previous work, we have shown that dynamic density functional calculations based on this mobility function can accurately reproduce the order/disorder kinetics in polymer melts, thus it is a suitable starting point for dynamic mapping. To…
Although 3D printing has the potential to transform manufacturing processes, the strength of printed parts often does not rival that of traditionally-manufactured parts. The fused-filament fabrication method involves melting a thermoplastic, followed by layer-by-layer extrusion of the molten viscoelastic material to fabricate a three-dimensional object. The strength of the welds between layers is controlled by interdiffusion and entanglement of the melt across the interface. However, diffusion slows down as the printed layer cools towards the glass transition temperature. Diffusion is also aff…
We demonstrate that hierarchical backmapping strategies incorporating generic blob-based models can equilibrate melts of high-molecular-weight polymers, described with chemically specific, atomistic, models. The central idea behind these strategies, is first to represent polymers by chains of large soft blobs (spheres) and efficiently equilibrate the melt on mesoscopic scale. Then, the degrees of freedom of more detailed models are reinserted step by step. The procedure terminates when the atomistic description is reached. Reinsertions are feasible computationally because the fine-grained melt…
We present a novel thermodynamically guided, low-noise, time-scale bridging, and pertinently efficient strategy for the dynamic simulation of microscopic models for complex fluids. The systematic coarse-graining method is exemplified for low-molecular polymeric systems subjected to homogeneous flow fields. We use established concepts of nonequilibrium thermodynamics and an alternating Monte-Carlo--molecular dynamics iteration scheme in order to obtain the model equations for the slow variables. For chosen flow situations of interest, the established model predicts structural as well as materia…
We present a theoretical approach to scale the artificially fast dynamics of simulated coarse-grained polymer liquids down to its realistic value. As coarse-graining affects entropy and dissipation, two factors enter the rescaling: inclusion of intramolecular vibrational degrees of freedom, and rescaling of the friction coefficient. Because our approach is analytical, it is general and transferable. Translational and rotational diffusion of unentangled and entangled polyethylene melts, predicted from mesoscale simulations of coarse-grained polymer melts using our rescaling procedure, are in qu…
The theory to reconstruct the atomistic-level chain diffusion from the accelerated dynamics that is measured in mesoscale simulations of the coarse-grained system, is applied here to the dynamics of cis-1,4-Polybutadiene melts where each chain is described as a soft interacting colloidal particle. The rescaling formalism accounts for the corrections in the dynamics due to the change in entropy and the change in friction that are a consequence of the coarse-graining procedure. By including these two corrections the dynamics is rescaled to reproduce the realistic dynamics of the system described…
Rheological properties of a material often require to be probed under extensional deformation. Examples include fibrous materials such as spider-silk, high-molecular weight polymer melts, and the contractile response of living cells. Such materials have strong molecular-level anisotropies which are either inherent or are induced by an imposed extension. However, unlike shear rheology, which is well-established, techniques to perform extensional rheology are currently under development and setups are often custom-designed for the problem under study. In this article, we present a versatile devi…
Polydispersity is inevitable in industrially produced polymers. Established theories of polymer dynamics and rheology, however, were mostly built on monodisperse linear polymers. Dynamics of polydisperse polymers is yet to be fully explored -- especially how chains of different lengths affect the dynamics of one another in a mixture. This study explored the dynamics of bidisperse polymer melts using molecular dynamics and a bead-spring chain model. Binary mixtures between a moderately entangled long-chain species and an unentangled or marginally entangled short-chain species were investigated.…
The relationship between polymer topology and bulk rheology remains a key question in soft matter physics. Architecture-specific constraints (or threadings) are thought to control the dynamics of ring polymers in ring-linear blends, which thus affects the viscosity to range between that of the pure rings and a value larger, but still comparable to, that of the pure linear melt. Here we consider qualitatively different systems of linear and ring polymers, fused together in "chimeric" architectures. The simplest example of this family is a "tadpole"-shaped polymer - a single ring fused to the en…
We present a detailed derivation and testing of our approach to rescale the dynamics of mesoscale simulations of coarse-grained polymer melts (I. Y. Lyubimov et al. J. Chem. Phys. \textbf{132}, 11876, 2010). Starting from the first-principle Liouville equation and applying the Mori-Zwanzig projection operator technique, we derive the Generalized Langevin Equations (GLE) for the coarse-grained representations of the liquid. The chosen slow variables in the projection operators define the length scale of coarse graining. Each polymer is represented at two levels of coarse-graining: monomeric as …
A mesoscopic, mixed particle- and field-based Brownian dynamics methodology for the simulation of entangled polymer melts has been developed. Polymeric beads consist of several Kuhn segments, and their motion is dictated by the Helmholtz energy of the sample, which is a sum of the entropic elasticity of chain strands between beads, slip springs, and nonbonded interactions. The entanglement effect is introduced by the slip springs, which are springs connecting either nonsuccessive beads on the same chain or beads on different polymer chains. The terminal positions of slip springs are altered du…
A homogeneous thin polymer film with a stepped height profile levels due to the presence of Laplace pressure gradients. Here we report on studies of polymeric samples with precisely controlled, spatially inhomogeneous molecular weight distributions. The viscosity of a polymer melt strongly depends on the chain length distribution; thus, we learn about thin-film hydrodynamics with viscosity gradients. These gradients are achieved by stacking two films with different molecular weights atop one another. After a sufficient time these samples can be well described as having one dimensional viscosit…
Spatial confinement in nanoporous media affects the structure, thermodynamics and mobility of molecular soft matter often markedly. This article reviews thermodynamic equilibrium phenomena, such as physisorption, capillary condensation, crystallisation, self-diffusion, and structural phase transitions as well as selected aspects of the emerging field of spatially confined, non-equilibrium physics, i.e. the rheology of liquids, capillarity-driven flow phenomena, and imbibition front broadening in nanoporous materials. The observations in the nanoscale systems are related to the corresponding bu…
In this article we present and compare two different, coarse-grained approaches to model electrostatic interactions of disc-shaped aromatic molecules, specifically coronene. Our study builds on previous work [J. Chem. Phys. 141, 214110 (2014)] where we proposed, based on a systematic coarse-graining procedure starting from the atomistic level, an anisotropic effective (Gay-Berne-like) potential capable of describing van-der-Waals contributions to the interaction energy. To take into account electrostatics, we introduce, first, a linear quadrupole moment along the symmetry axis of the coronene …
