Dynamics Of Polymer Melts Research Articles

Statistics and Dynamics of Polymer Melt in Neutral Diblock Copolymer Single-Crystal Platelets.

Polymer single-crystal (SC) platelets of poly(butylene oxide)-b-poly(lactic acid) (PBO-b-PLLA) of a well-defined shape, size, and grafting density have been fabricated and embedded into PBO melt for the study of the statistics and dynamics of the host polymers. The colloidal liquid-crystalline order of SCs above a threshold concentration of ∼2.2 vol % provides a confining environment for the molten PBO. Meanwhile, the peculiar type-A characteristics of PBO allow us to simultaneously probe the dielectric chain dimensions and the hierarchical dynamics of polymers under confinement. We observe negligible changes to the mean-square end-to-end distance of the polymer melt as well as the chain and segment dynamics, even the interlayer distance approaches the length scale comparable to the size of the host polymers. Our results provide direct evidence of the impacts of neutral walls on both the statistics and the dynamics of confined polymer melts, which can be also enlightening for the field of polymer nanocomposites.

Metabasin dynamics of supercooled polymer melt**Project supported by the National Natural Science Foundation of China (Grant No. 11804085) and the Doctoral Foundation of Heze University, China (Grant No. XY18BS13).

We employ molecular dynamic simulation to investigate metabasin dynamics for supercooled polymer melt. We find that, in a small system, the α-relaxation process is composed of a few crossing events that the monomers hops from one metabasin to another. Each crossing event is very rapid and involves a democratic movement of many particles, whereas such collective motion is not string-like. Evaluation on the contributions of metabasin exploration and democratic movement shows that the structural relaxation is mostly governed by the latter. Our calculated results show that the metabasin–metabasin transitions are not the main reason of spatially dynamical heterogeneity. It is different from the binary Lennard–Jones mixture model in which the metabasin–metabasin transitions are relevant for the spatially dynamical heterogeneity.

COOPERATIVE FREE VOLUME RATE MODEL APPLIED TO THE PRESSURE-DEPENDENT SEGMENTAL DYNAMICS OF NATURAL RUBBER AND POLYUREA

ABSTRACT We apply the cooperative free volume (CFV) rate model for pressure-dependent dynamics of glass-forming liquids and polymer melts, focusing on two new applications of the model, to natural rubber and to polyurea. In CFV, segmental relaxation times, τ, are analyzed as a function of temperature (T) and free volume (Vfree), where the latter provides an insightful route to expressing dynamics relative to using the system's overall total volume (V). Vfree is defined as the difference between the total volume and the volume at close packing and is predicted independently of the dynamics for any temperature and pressure using the locally correlated lattice equation-of-state analysis of characteristic thermodynamic data. The new results for natural rubber and polyurea are discussed in the context of results on a set of polymeric and small-molecule glass formers that had previously been modeled with CFV. We also discuss the results in the context of recent connections that we have made with the density-scaling approach.

The cooperative free volume rate model for segmental dynamics: Application to glass-forming liquids and connections with the density scaling approach⋆.

In this paper, we apply the cooperative free volume (CFV) rate model for pressure-dependent dynamics of glass-forming liquids and polymer melts. We analyze segmental relaxation times, [Formula: see text] , as a function of temperature (T and free volume ( [Formula: see text] , and make substantive comparisons with the density scaling approach. [Formula: see text] , the difference between the total volume (V and the volume at close-packing, is predicted independently of the dynamics for any temperature and pressure using the locally correlated lattice (LCL) equation-of-state (EOS) analysis of characteristic thermodynamic data. We discuss the underlying physical motivation in the CFV and density scaling models, and show that their key, respective, material parameters are connected, where the CFV b parameter and the density scaling [Formula: see text] parameter each characterize the relative sensitivity of dynamics to changes in T , vs. changes in V . We find [Formula: see text] , where [Formula: see text] is the value predicted by the LCL EOS at the ambient [Formula: see text] . In comparing the predictive power of the two models we highlight the CFV advantage in yielding a universal linear collapse of relaxation data using a minimal set of parameters, compared to the same parameter space yielding a changing functional form in the density scaling approach. Further, we demonstrate that in the low data limit, where there is not enough data to characterize the density scaling model, the CFV model may still be successfully applied, and we even use it to predict the correct [Formula: see text] parameter.

Influence of Branching on the Configurational and Dynamical Properties of Entangled Polymer Melts.

We probe the influence of branching on the configurational, packing, and density correlation function properties of polymer melts of linear and star polymers, with emphasis on molecular masses larger than the entanglement molecular mass of linear chains. In particular, we calculate the conformational properties of these polymers, such as the hydrodynamic radius , packing length p, pair correlation function , and polymer center of mass self-diffusion coefficient, D, with the use of coarse-grained molecular dynamics simulations. Our simulation results reproduce the phenomenology of simulated linear and branched polymers, and we attempt to understand our observations based on a combination of hydrodynamic and thermodynamic modeling. We introduce a model of “entanglement” phenomenon in high molecular mass polymers that assumes polymers can viewed in a coarse-grained sense as “soft” particles and, correspondingly, we model the emergence of heterogeneous dynamics in polymeric glass-forming liquids to occur in a fashion similar to glass-forming liquids in which the molecules have soft repulsive interactions. Based on this novel perspective of polymer melt dynamics, we propose a functional form for D that can describe our simulation results for both star and linear polymers, covering both the unentangled to entangled polymer melt regimes.

Influence of Branching on the Configurational and Dynamical Properties of Entangled Polymer Melts

We probe the influence of branching on the configurational, packing, and density correlation function properties of polymer melts of linear and star polymers, with emphasis on molecular masses larger than the entanglement molecular mass of linear chains. In particular, we calculate the conformational properties of these polymers, such as the hydrodynamic radius R h , packing length p, pair correlation function g ( r ) , and polymer center of mass self-diffusion coefficient, D, with the use of coarse-grained molecular dynamics simulations. Our simulation results reproduce the phenomenology of simulated linear and branched polymers, and we attempt to understand our observations based on a combination of hydrodynamic and thermodynamic modeling. We introduce a model of “entanglement” phenomenon in high molecular mass polymers that assumes polymers can viewed in a coarse-grained sense as “soft” particles and, correspondingly, we model the emergence of heterogeneous dynamics in polymeric glass-forming liquids to occur in a fashion similar to glass-forming liquids in which the molecules have soft repulsive interactions. Based on this novel perspective of polymer melt dynamics, we propose a functional form for D that can describe our simulation results for both star and linear polymers, covering both the unentangled to entangled polymer melt regimes.

Influence of knot complexity on glass-formation in low molecular mass ring polymer melts.

We perform molecular dynamics simulations on a coarse-grained polymer melt to study the dynamics of glass-formation in ring polymer melts of variable knot complexity. After generating melts of non-concatenated polymeric rings having a range of minimum crossing number values, mc, we compute the coherent intermediate scattering function, the segmental α-relaxation time, fragility, and the glass transition temperature as a function of mc. Variation of knot complexity is found to have a pronounced effect on the dynamics of polymer melts since both molecular rigidity and packing are altered, primary physical factors governing glass-formation in polymeric materials.

Application of proton field-cycling NMR relaxometry for studying translational diffusion in simple liquids and polymer melts.

With the availability of commercial field-cycling relaxometers together with progress of home-built instruments nuclear magnetic resonance relaxometry has gained new momentum as a method of investigating the dynamics in viscous liquids and polymer melts. The method provides the frequency dependence of the spin-lattice relaxation rate. In the case of protons, one distinguishes intramolecular and intermolecular relaxation pathways. Whereas the intramolecular contributionprevails at high frequencies and reflects rotational dynamics, the often ignored intermolecular relaxation contribution dominates at low-frequency and provides access to translational dynamics. A universal low-frequencies dispersion law holds which in pure systems allows determining the diffusion coefficient in a straightforward way. In addition, the rotational time constant is extracted from the high-frequency relaxation contribution. This is demonstrated for simple and ionic liquids and for polymer melts.

Role of Chain Length in the Formation of Frank-Kasper Phases in Diblock Copolymers.

The phase behavior of poly(styrene)-b-poly(1,4-butadiene) diblock copolymers with a polymer block invariant degree of polymerization N[over ¯]_{b}≈800 shows no evidence of Frank-Kasper phases, in contrast to low molar mass diblock copolymers (N[over ¯]_{b}<100) with the same conformational asymmetry. A universal self-concentration crossover parameter N[over ¯]_{x}≈400 is identified, directly related to the crossover to entanglement dynamics in polymer melts. Mean-field behavior is recovered when N[over ¯]_{b}>N[over ¯]_{x}, while complex low symmetry phase formation is attributed to fluctuations and space-filling constraints, which dominate when N[over ¯]_{b}<N[over ¯]_{x}.

Polymer Chain Mobility under Shear-A Rheo-NMR Investigation.

The local dynamics in polymer melts and the impact of external shear in a Couette geometry have been investigated using rheological nuclear magnetic resonance (NMR). The spin-spin relaxation time, T2, which is sensitive to chain-segment motion, has been measured as a function of shear rate for two samples of poly(dimethylsiloxane). For the low-molecular-weight sample, a mono-exponential decay is observed, which becomes slightly faster with shear, indicating restrictions of the polymer chain motion. For the high-weight sample, a much faster bi-exponential decay is observed, indicative of entanglements. Both components in this decay become longer with shear. This implies that the free polymer segments between entanglements become effectively longer as a result of shear.

Pressure-Dependent Dynamics of Polymer Melts from Arrhenius to Non-Arrhenius: The Cooperative Free Volume Rate Equation Tested against Simulation Data

We apply the cooperative free volume (CFV) model to analyze the segmental relaxation times, τ(T,V), of a model 20-mer polymer melt simulated via molecular dynamics over a broad pressure range. Thermodynamic characterization of the 20-mer allows determination of the constant contribution from the hard-core volume (Vhc), which then yields predictions for the free volume, Vfree = V – Vhc. The CFV rate model is based on an activation free energy that increases with the number of cooperating segments, n*, wherein the system’s free volume, Vfree, is what determines n*. The model predicts that on isotherms ln τ vs 1/Vfree is linear with T-dependent slopes. The 20-mer melt data follow this linear behavior at all temperatures. Assuming a fixed activation energy per cooperating segment leads to a very simple analytic form that describes all of the 20-mer melt’s high T behavior, including the Arrhenius to non-Arrhenius transition regime. This form reflects the importance of a gas kinetic contribution as well as both...

Capillary Rise: Validity of the Dynamic Contact Angle Models.

The classical Lucas-Washburn-Rideal (LWR) equation, using the equilibrium contact angle, predicts a faster capillary rise process than experiments in many cases. The major contributor to the faster prediction is believed to be the velocity dependent dynamic contact angle. In this work, we investigated the dynamic contact angle models for their ability to correct the dynamic contact angle effect in the capillary rise process. We conducted capillary rise experiments of various wetting liquids in borosilicate glass capillaries and compared the model predictions with our experimental data. The results show that the LWR equations modified by the molecular kinetic theory and hydrodynamic model provide good predictions on the capillary rise of all the testing liquids with fitting parameters, while the one modified by Joos' empirical equation works for specific liquids, such as silicone oils. The LWR equation modified by molecular self-layering model predicts well the capillary rise of carbon tetrachloride, octamethylcyclotetrasiloxane, and n-alkanes with the molecular diameter or measured solvation force data. The molecular self-layering model modified LWR equation also has good predictions on the capillary rise of silicone oils covering a wide range of bulk viscosities with the same key parameter W(0), which results from the molecular self-layering. The advantage of the molecular self-layering model over the other models reveals the importance of the layered molecularly thin wetting film ahead of the main meniscus in the energy dissipation associated with dynamic contact angle. The analysis of the capillary rise of silicone oils with a wide range of bulk viscosities provides new insights into the capillary dynamics of polymer melts.

Chain Dynamics in Polymer Melts at Flat Surfaces

We investigate, by extensive molecular dynamics simulations as well as a simplified single-chain model, the influence of steric hindrance on the dynamic properties of nonentangled chains in polymer melt due to confining surfaces. We extend the Rouse model to also include wall effects, using an additional potential that results from the assumption that chain conformations have reflected random-walk statistics, as first advocated by Silberberg. Results for end-to-end vector and Rouse mode correlation functions of chains end-tethered to the surface compare well with those obtained from molecular dynamics simulations of a multichain system using the Kremer–Grest bead–spring model (KG MD). Even though the additional single-chain potential is parameter-free, we show that the accuracy of the model for surface chains is comparable to that of the Rouse model for bulk chains. An analytic dumbbell model accurately describes the longest Rouse mode correlation function of surface-tethered “mushroom” chains immersed in...

Effects of counterion size and backbone rigidity on the dynamics of ionic polymer melts and glasses.

It is well-known that the nature and size of the counterions affect the ionic conductivity and glass transition temperature of ionic polymers in a significant manner. However, the microscopic origin of the underlying changes in the dynamics of chains and counterions is far from completely understood. Using coarse-grained molecular dynamics simulations of flexible and semi-flexible ionic polymers, we demonstrate that the glass transition temperature of ionic polymeric melts depends on the size of monovalent counterions in a non-monotonic manner. The glass transition temperature is found to be the highest for the smallest counterions and decreases with an increase in the counterion radii up to a point, after which the glass transition temperature increases with a further increase in the radii. This behavior is because the counterions have significant effects on the coupled dynamics of the charges on the chains and counterions. In particular, increase in the radii of the counterions leads to strongly coupled dynamics between the charges on the chains and the counterions. The static dielectric constant of the polymer melts also has a significant effect on the coupling and the glass transition temperature. The glass transition temperature is predicted to decrease with an increase in the dielectric constant. This, in turn, leads to an increase in the diffusion constant of the counterions at a given temperature. Backbone rigidity is shown to increase the glass transition temperature and decrease the coupling. Furthermore, faster counterion dynamics is predicted for the melts of semi-flexible chains in comparison with flexible chains at the same segmental relaxation time. As the semi-flexible chains tend to have a longer segmental relaxation time, semi-flexible polymers with high dielectric constants are predicted to have diffusion constants of counterions comparable with flexible polymers.

Stringlike Cooperative Motion Explains the Influence of Pressure on Relaxation in a Model Glass-Forming Polymer Melt.

Numerous experiments reveal that the dynamics of glass-forming polymer melts are profoundly influenced by the application of pressure, but a fundamental microscopic understanding of these observations remains incomplete. We explore the structural relaxation of a model glass-forming polymer melt over a wide range of pressures (P) by molecular dynamics simulation. In accord with experiments for nonassociating polymer melts and the generalized entropy theory, we find that the P dependence of the structural relaxation time (τα) can be described by a pressure analog of the Vogel-Fulcher-Tammann equation and that the characteristic temperatures of glass formation increase with P, while the fragility decreases with P. Further, we demonstrate that τα for various P can quantitatively be described by the string model of glass formation, where the enthalpy and entropy of activation are found to be proportional, an effect that is expected to apply to polymeric materials under various applied fields.

Effect of chain stiffness and temperature on the dynamics and microstructure of crystallizable bead-spring polymer melts.

We contrast the dynamics in model unentangled polymer melts of chains of three different stiffnesses: flexible, intermediate, and rodlike. Flexible and rodlike chains, which readily solidify into close-packed crystals (respectively, with randomly oriented and nematically aligned chains), display simple melt dynamics with Arrhenius temperature dependence and a discontinuous change upon solidification. Intermediate-stiffness chains, however, are fragile glass-formers displaying Vogel-Fulcher dynamical arrest, despite the fact that they also possess a nematic-close-packed crystalline ground state. To connect this difference in dynamics to the differing microstructure of the melts, we examine how various measures of structure, including cluster-level metrics recently introduced in studies of colloidal systems, vary with chain stiffness and temperature. No clear static-structural cause of the dynamical arrest is found. However, we find that the intermediate-stiffness chains display qualitatively different dynamical heterogeneity. Specifically, their stringlike motion (cooperative rearrangement) is correlated along chain backbones in a way not found for either flexible or rodlike chains. This activated "crawling" motion is clearly associated with the dynamical arrest observed in these systems, and illustrates one way in which factors controlling the crystallization versus glass formation competition in polymers can depend nonmonotonically on chain stiffness.

Capillary filling dynamics of polymer melts in nanopores: experiments and rheological modelling

The spontaneous capillarity-driven flow behaviors of PE melts through AAO nanopores suggest that the zero-shear-rate viscosity of the PE melts decreases, which can be predicted by a modified Lucas–Washburn law considering the polymer rheological model.

Consequences of Increasing Packing Length on the Dynamics of Polymer Melts

We revisit the nonuniversal aspect of polymer dynamics by considering both new and existing data on the zero-shear viscosity and linear viscoelastic response of various polymers, each with a wide range of molecular weights. Analysis of the zero-shear viscosity data in terms of the packing length p, whose role in entanglements has been discussed previously by Fetters and co-workers, reveals a behavior that is irreconcilable with our current understanding based on the tube model. Specifically, we find that the transition regime between Rouse and pure reptation dynamics, currently understood as the regime where contour length fluctuations are active, systematically shrinks as the packing length of the polymer increases. Further, we find that the slope of the loss moduli in the high-frequency wing of the terminal peak of well-entangled systems also decreases from the common −0.25 to −0.125 with increasing p. This is contrary to the single expected value of −0.25 from tube models which include contour length f...

Molecular Dynamic Study of the Structure and Dynamics of Polymer Melt at Solid Surfaces

We investigate the dynamic and static properties of a polymer melt near solid surfaces. The melt, composed of linear chains, is confined between two solid walls with one of the walls being repulsive; whereas the opposite, attractive wall, is characterized by different degrees of roughness, caused by an array of short perpendicular pillars with variable grafting density. We demonstrate the remarkable fact that the conformations of chains in the melt at the interfaces are mostly unaffected by the strength of substrate/polymer attraction. Moreover, they practically coincide with the conformations of a single end-grafted chain at the critical point of adsorption, in agreement with Silberberg’s hypothesis. This agreement is corroborated by the analysis of the size distributions of trains, loops, and tails of melt chains at the walls that are found to be perfectly described by analytical expressions pertaining to end-grafted single chains at critical adsorption. The adsorbed amount at the attractive bottom surface is found to scale with macromolecule length as regardless of adsorption strength. We also find that the pressure of the melt PN decreases as (where P∞ is the extrapolated pressure for N → ∞) with growing length N of the chains whereas the surface tension γ at both walls is found to decline as . Eventually, a study of the polymer dynamics at the rough interface reveals that surface roughness leads to dramatic drop of the coefficient for lateral diffusion whenever the separation between obstacles (neighboring pillars) becomes less than where Rg is the unperturbed radius of gyration of chains in the bulk.

Molecular Dynamics of Polymer Composites Using Rheology and Combined RheoNMR on the Example of TiO2-Filled Poly(n-Alkyl Methacrylates) and Trans-1,4-Polyisoprene

The determination of the interplay between polymeric matrices and filler particles in composites is of great interest to understand structure-property relationships and develop predictive theories. To study the molecular dynamics of polymers in composites, model systems based on poly(n-alkyl methacrylates), trans-1,4-polyisoprene (gutta percha), and titania (TiO2) were prepared and characterized using rheometry and a combined RheoNMR technique. Apparent entanglement molecular weights were obtained from small amplitude oscillatory shear (SAOS) experiments, which are related to the increasing physical cross-link density as a function of the filler content. Large amplitude oscillatory shear (LAOS) experiments were performed and analyzed within the FT-rheometry framework. The filler had a strong impact on the scaling behavior of the normalized third harmonic. A combined RheoNMR technique was used to simultaneously study the molecular dynamics via NMR and the corresponding mechanical response via rheometry. A strong correlation between the macroscopic mechanical properties and microscopic molecular dynamics was found, which might lead to a new understanding of polymer melt dynamics.